The Scientific Harrovian - Issue 6, June 2021 by Harrow International School Hong Kong

Issue VI

Scientific Har r ovian Future Of Fa r m i n g M at e r i a l Sustainability C a n t o r ’s Paradise Infinity on Ear th

Science and Society Har r ow Inter national School Hong Kong

2 Uncited images from Unsplash

About the Scientific Harrovian

The Scientific Harrovian is the Science Department magazine, which provides a platform for students to showcase their research and writing talents, and for more experienced pupils to guide authors and to develop skills to help them prepare for life in higher education and beyond.

Copyright © 2020 by The Scientific Harrovian. All rights reserved. No part of this book or any portions thereof may be reproduced or used in any matter whatsoever without express written permission of the p u b l i s h e r, e x c e p t f o r t h e u s e o f b r i e f q u o t a t i o n s i n a b o o k r e v i e w.

MESSAGES

It has been a joy to witness the creation of such a wonderful Sixth Edition of the Scientific Harrovian. This really is a publication for pupils by pupils and so my congratulations and thanks go to all writers, editors and illustrators for their scientific passion and hard work. They have all created something to be proud of and cherish. Extra special thanks have to go to the Scientific H a r r o v i a n ’s E d i t o r - i n - C h i e f A n n i e Kim and Head Designer Isabel Chau. Despite juggling the demands of a busy first term they have never let the Scientific Harrovian team lose t h e i r w a y. I have been inspired by the plethora of articles on the theme of ‘Science in Society’. This theme couldn’t be better suited to a time where society and Science could not be more i n t e r l i n k e d . Wr i t t e n a n d i l l u s t r a t e d f r o m Ye a r 7 t o Ye a r 1 3 p u p i l s , t h e y are all united by their desire to e ff e c t i v e l y c o m m u n i c a t e S c i e n c e t o t h e p u p i l b o d y. W h e t h e r y o u would like to find the answer to big questions in the article “Science, cosmology and the existence of God” or would like to determine whether p s y c h e d e l i c s a r e m o r e ‘ Vo o d o o o r Science’, there is something for everyone in this edition. I hope that whichever articles you read or illustrations you admire that you feel as inspired as I have.

Siobhan McCrohan Te a c h e r o f B i o l o g y

MESSAGES We l c o m e ! The theme of Edition VI of the Sc ienti f ic Harrov ian is Sc ienc e a n d S o c i e t y, a n e x t r e m e l y r e l e v a n t topic in this challenging time when scientific knowledge is more i m p o r t a n t t h a n e v e r. As well as the usual ar ticles by the ver y talented writers of our team, this issue includes some featured a r t i c l e s f r o m t h e Wo r l d M a t h e m a t i c s Championships and an inter view from the Hong Kong Dolphin C o n s e r v a t i o n S o c i e t y. I would like to thank Stephenie for trusting me with the role of Editor-in-Chief, and the Scientific Harrov ian executive team for helping to make this issue possible. I would also like to thank all our contributors for their hard work and organisation despite being online f o r a s i g n i f i c a n t p a r t o f t h e y e a r, juggling internal assessments and managing universit y applications. L a s t l y, t h e c o n t r i b u t i o n s o f o u r Y 1 3 leavers have been invaluable, and we wish you the very best for university and beyond. Congratulations to the following pupils for receiving HM sendups for their excellent per formance on the f ir st Sc ienti f ic Harrov ian Qui z Ex travaganza. Individual: Sen Yi Mok Te a m : S e n Y i M o k , A n d r e w H u n g , Jeffrey Ling, Daniel K an We h o p e w e c a n c o n t i n u e t o m a k e t h e Sc ienti f ic Harrov ian more engaging for all pupils in the school.

Dear readers, We a r e n o w a t t h e e n d o f t h e a c a d e m i c y e a r, a n d I ’ v e w i t n e s s e d the Scientific Harrov ian Issue VI come together bit by bit : the planning and research by the writers and the meticulous per fecting by the editors. Of course, I cannot forget to mention our dear illustrators that I’ ve been spamming over email. Their beautiful illustrations have added ex tra flavour and colour to the ar ticles and inspired the design of this issue. Special thank s go to S e Ly n , T i n a a n d E t h a n f o r t h e i r numerous contributions throughout t h e y e a r. In this issue, we present to you seventeen ar ticles from different fields of science, all with a united t h e m e : “ S c i e n c e a n d S o c i e t y ”. T h e seven new additions to our issue VI-i add even more variet y than before, and I can assure you that they will fascinate you.

I hope you enjoy reading this as much as we enjoyed creating it!

It has been a pleasure to be a par t of this issue’s creation. I can’ t wait for you to turn the page!

Yo u r s f a i t h f u l l y,

H o l d o n a n d e n j o y,

Annie Kim

Isabel Chau

Editor-in-Chief

Head Designer

CONTRIBUTORS THE TEAM

Editor-in-Chief Annie Kim Year 12, Wu Former Editor-in-Chief Stephenie Chen Year 13, Gellhorn Head Designer Isabel Chau Year 12, Gellhorn Biology Head Editor Hoi Kiu Wong Year 13, Wu Chemistry Head Editor Jasmine Chan Year 13, Wu Physics Head Editor Callum Sanders Year 10, Shaftesbury Technology Head Editor Edward Wei Year 11, Peel Marketing Director Jenny Kim Year 11, Anderson

CONTRIBUTORS

WRITERS Jasmine Chan Year 13, Wu

Parry Chan Katrina Cheng Year 12, Shaftesbury Year 13, Gellhorn

Daniel Kan Year 9, Shaftesbury

Christine Li Year 11, Gellhorn

Edward Wei Year 11, Peel

Hanson Wen Year 9, Peel

Alyssa Wong Year 11, Anderson

Hoi Kiu Wong Year 13, Wu

Josiah Wu Year 13, Churchill

Joshua Yen Warren Zhu Year 12, Shaftesbury Year 12, Churchill

ILLUSTRATORS Isabel Chau Year 12, Gellhorn

Joy Chen Year 10, Gellhorn

Susanna Fung Year 6, Fry

Ethan Lan Year 7, Shackleton

Se Lyn Lim Year 12, Wu

Reika Oh Year 11, Gellhorn

Kayan Tam Year 13, Wu

Emily Tse Year 11, Keller

Callum Sanders Tina Wu Year 10, Shaftesbury Year 11, Gellhorn

CONTRIBUTORS

EDITORS Haley Chan Year 13, Wu

Joy Chen Year 10, Gellhorn

Iris Cheung Year 12, Gellhorn

Joanna Fung Year 8, Fry

Diya Handa Year 13, Anderson

Catrina Kean Year 12, Gellhorn

Alison Kerr Year 11, Wu

Jenny Kim Year 11, Anderson

Jonathan Lee Year 12, Peel

Kirsty McCallum Year 12, Wu

Helen Ng Year 10, Gellhorn

Kee Meng Tan Year 12, Churchill

Tobey Poon Year 11, Churchill

Emily Tse Year 11, Keller

Michelle Yeung Year 13, Keller

FEATURED WRITERS Daniel Kan Year 9, Shaftesbury

Benjamin Law Year 9, Peel

Chloe Levieux Year 11, Gellhorn

Kevin Liew Year 11, Peel

Helen Ng Year 10, Gellhorn

Andrew Wang Year 11, Peel

Alan Li Year 13, Peel

INDEX P h y s i c s a n d Te c h n o l o g y

Science, Cosmology And The Existence Of God J o s h u a Ye n

Will Building A Dyson Sphere Solve The Ear th’s Energy Problems? A l y s s a Wo n g

33 52

Antimatter And The Ozma Pr oblem Ho i K i u Wo n g

Mat er ial Sus t ainabilit y : H o w To P r o v i d e T h e Same Wit h Les s ? Katrina Cheng

Biology and Chemistr y

120

Graphene: Super Carbon?

138

Pink Dolphins : The W h i t e Ta b o o

Parr y Chan

Alan Li

Mat hematics and Logic

142

Real Life Application Of Co mp l e x Nu mb e r s

150

Cantor ’ s Paradis e Infinity on Earth

166

Introduction to Graph Theory

186

Agent -bas ed modelling and its application in Cov i d -1 9 p r e d i c t i o ns

J o s i a h Wu

J o s h u a Ye n

J o s i a h Wu

Ps y c h e d e l i c s : Vo o d o o Or Science?

Application Of The Hu ma n Mi c r o b i o me

F e a t u r e d a r t i c l e s f r o m t h e Wo r l d Mat hematics Champions hips

Ha n s o n We n

198

89 105

Daniel Kan

Wa r r e n Z h u

Future Of Farming E d wa r d We i

Sunscreens Jasmine Chan

Game Theor y And Ho w I t A i d s Ou r Wo r l d To d a y Helen Ng, Daniel K an, Benjamin Law

206

J o s h Nas h A nd Hi s C o n t r i b u t i o n To S D G K e v i n L i e w, Ch l o e L e v i e u x , A n d r e w Wa n g

Physics and Te c h n o l o g y

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Science, Cosmology and the Existence of God J o s h u a Ye n The existence of god has been one of the most controversial discussions in society, philosophy and science. Whether there is a god or not has significant ramifications on society and would significantly change the way we live. This is why I would like to weigh in on the scientific side of this debate and demonstrate why there is most likely a creator of the universe (a god) given our understanding of cosmology and causation.

PHYSICS AND TECHNOLOGY A simple formulation argument:

the

If you have had any past experience with the philosophy of religion, you probably know that what I am referring to in my abstract is what philosophers call a cosmological argument. This is an argument from our understanding of the universe to the existence of a god. While there are multiple formulations of this argument, for the sake of simplicity, I will be using the Kalam cosmological argument 1 , an argument from the finitude of the past 2 . The argument goes as follows: Premise 1 (P1): If the universe began to exist, then the universe must have had a cause Premise 2 (P2): The universe began to exist Therefore, Conclusion 1 (C1):

The universe has a cause [1]

Premise 3 (P3): If the universe has a cause, the cause is a god Premise 4 (P4): The universe has a cause (C1) Therefore, Conclusion 2 (C2): The cause is a god. Since this argument is laid out in a deductive syllogism 3 (that of modus ponens), we can see that if the premises are true the conclusion logically follows. In other words, one cannot accept our premises and disagree with our conclusion. Therefore, in this article, I will be defending each of these premises to demonstrate the truth of this argument.

1 “Kalam” is an Islamic school of thought which formulated this form of cosmological arguments (those from the finitude of the past) 2 The finitude of the past is a concept where the universe is past finite and has a beginning; this is in stark contrast to an infinite past. 3 A deductive syllogism is a way of laying out an argument which makes it such that if the premises are true, the conclusion must be accepted. In the case of this article, while the premises aren’t necessarily defended via a priori methods and should be seen as a fundamentally inductive argument, the use of this syllogism entails that one should argue against the premises, not the conclusions.

PHYSICS AND TECHNOLOGY Premise 1: If the universe began to exist, then the universe has a cause

T he first premise of the argument is relatively

controversial in the fields of science and philosophy as it is based on the principle of temporal causation. This is the idea that all finite and temporal beings require a cause for their existence 4 . This law undergirds all logical thinking and is a necessary belief for all our pursuits, especially those within science. A good example of this law would be boiling water. The heat of the fire is the cause or the reason behind the fact that the bonds between water molecules break down and evaporate. It would be scientifically incorrect to claim that the water molecules just evaporated without a cause. This line of reasoning undoubtedly conforms with all our experiences and is the strongest intuition that we have. We know that things must have a cause and there cannot be uncaused phenomena. A further reason which supports the principle of temporal causation is the idea that something cannot come from nothing. This comes in the form of the Latin old saying “ex nihilo, nihil fit”- roughly translating to “nothing comes out of nothing.”

If this saying stands, all things which are contingent or subject to time must require a cause. The change of a state of absolute nothingness to a state with something is impossible without an external cause. This concept can be rearranged into a simple deductive syllogism: P1: If something cannot come from nothing, all things that come into existence must come from something P2: Something cannot come from nothing C1: Therefore all things must come from something P1 of this argument appears to be self-evident and does not require much explanation. There exists either something, or there exists nothing. Hence, if something cannot come out of nothing, then it follows that something must require an antecedent cause.

4 This is to be contrasted with causation simpliciter, the idea that every single being which exists must have a cause. 5 Now it is clear to note that the theist does not believe in ex nihilo creation simpliciter. Instead, he is just claiming that there are no physical entities. The reason for this is simple, a god is not physical and is a transcendent being. Hence, when a theist uses ex nihilo, he is referring to the idea that there was no physical entities prior to the creation.

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Hence, the crux of this argument depends on the strength of P2, which is undeniable. Throughout the history of mankind, no one has ever experienced an ex nihilo (out of nothing 5 ) creation (in the strict sense of the term). For if anyone were to point to anything in the world and suggest that it was self-caused, one would rightfully dismiss him as insane. For example, if an explosion occurred in the school’s Science department, surely we would be looking for a cause of such a tragedy instead of suggesting that the explosion just appeared ex nihilo. Despite this apparent strength, a physicist named Lawrence Krauss has suggested that due to developments in quantum physics, we have observed particles that

come into being without an apparent cause and appear to support the hypothesis of an ex nihilo creation [2]. While this approach has been growing in popularity, especially when some scientists start realising the philosophical implications of a finite universe, such a rebuttal, fails to gain traction within academia since Krauss’ hypothesis egregiously overlooks the sea of quantum energy that these particles are fluctuating out of. In reality, this is no ex nihilo causation, instead it is just particles fluctuating from a state of quantum energy. With this in mind, it appears that the first premise of our argument is well defended and supported, allowing us to move onto the more controversial premise - whether or not the universe has a beginning.

PHYSICS AND TECHNOLOGY Premise 2: The Universe Began to Exist Historically, the second premise of the argument has been defended predominantly by philosophical arguments. In this case, I will be approaching this premise from the perspective of science, more specifically the Big Bang hypothesis and the Second Law of Thermodynamics. Under the Big Bang hypothesis, space, time and matter came into existence a finite time ago. In this model, the universe is currently growing in size and expanding into nothingness. This hypothesis is supported by two pieces of evidence, Cosmic Microwave Background Radiation (CMBR) and redshift. CMBR is a form of radiation which is present in low amounts throughout the entire universe. This suggests that in the past, the universe was dense and “hot”, pointing towards an explosion of energy from a singularity. Over time, this energy “spread out” through the universe leading to this current state of low energy. Red-shift also provides good evidence for the expanding model of the universe. Red-shift is the concept that as celestial bodies move away from each other or towards each other, the wave frequencies of their light are changed. This leads to either red or blue shifts respectively. Due to universal red-shift that we observe in celestial bodies, we can infer that stars and galaxies are moving away from each other. This suggests that the universe is expanding from an initial singularity in the finite past. These observations have contributed heavily to the development of the Friedmann-Lemaitre-RobertsonWalker spacetime model which shows that given the current understanding of universal expansion, we can trace the boundary of spacetime back to a finite point in the past. Physicist P.C.W. Davis comments on such a model as follows, “If we extrapolate this prediction to its extreme, we reach a point when all distances in the universe have shrunk to zero. An initial cosmological singularity therefore forms a past temporal extremity to the universe. We cannot continue physical reasoning, or even the concept of spacetime, through such an extremity. For this reason

PHYSICS AND TECHNOLOGY

most cosmologists think of the initial singularity as the beginning of the universe. On this view the big bang represents the creation event; the creation not only of all the matter and energy in the universe, but also of spacetime itself [3].” Apart from this relatively empirical approach to the beginning of the universe, a finite universe is also defended mathematically by theoretical physicists Arvind Borde, Alan Guth, and Alexander Vilenkin in their paper “Inflationary spacetimes are not past-complete [4]”. In this paper, they demonstrate that “a cosmological model which is inflating or just expanding sufficiently fast must be incomplete in null and timelike past directions [5]”. This essentially means that in any expanding universe, it is inevitable that one reaches a singularity in the past. The universe cannot, mathematically, contract for infinity, hence there must have been a beginning. Since our universe is expanding, it follows that there must have been a beginning. Now, let us turn to the Second Law of Thermodynamics. The Second Law of Thermodynamics also states that the entropy of a closed system increases irreversibly. When the entropy 6 of a system reaches its maximum, we arrive at what scientists like to call “the heat death” of the system. In such a state, there is no longer any usable energy and the universe would, quite literally, die, as nothing can be done or changed. Now the problem arises for the proponent of an infinite past. If the universe has been around for past infinity, why are we not currently at heat death? How are we still alive and experiencing the movement of energy and other phenomena that would be impossible in a system with maximum entropy? Since we have established from the Big Bang and the Second Law of Thermodynamics that the universe must have a beginning, it follows that the universe is past finite. This is the idea that one cannot trace the causal/ temporal chain of the universe back for infinity, since there would be a point where the chain stops.

6 Entropy is a complex idea but is best explained as the unusable thermal energy within a system. If a system reaches maximum entropy, the system becomes “heat dead” and nothing can be carried out in such a system

Conclusion 1: The universe has a cause Since this argument is deductively valid and the premises are true (as I have shown above), it logically follows that the universe must have a cause for its existence.

PHYSICS AND TECHNOLOGY Premise 3: If the universe has a cause, the cause is a god However, our Conclusion 1 raises an instant question: what is the nature of this cause, and what are its attributes? 7

In order to elucidate these characteristics, I will split them into primary natures and secondary natures. Primary natures are aspects that are directly deduced from the argument, and secondary natures are aspects that can’t be directly deduced from the argument yet can be reasonably inferred. The three primary natures are timelessness, transcendence and a personal connection with the creation. I will spend some time here to elucidate each point. Timelessness: What does it mean to be timeless? This is a complex question and has been a matter of intense philosophical debate, but for the sake of simplicity, I would define timelessness as a property which shows that a being is not restricted by the passing of time or time does not act on such a being. With this in mind, how do we know that our cause of the universe is timeless? Since there were no physical states of affairs or change before the existence of the universe, it was a period of physical nothingness, we can state that this period is timeless. Yet since this cause existed prior to the universe in this state of physical

nothingness, it follows that it must exist timelessly. For there was no change in the state of affairs in regards to this cause. Of course, this changed when the cause caused the universe into existence. At this point, one can say that this cause is now in a temporal relationship with the universe and is no longer timeless. Yet, for all intents and purposes, we can safely conclude that this cause was timeless sans creation [6]. Transcendence: Why must this cause be transcendent? This is quite self-explanatory. Since the cause existed prior to the universe, it must transcend the universe. Personal: Finally, we know that the cause must be personal. Due to the nature of causation, the cause is always related to the effect (either directly or indirectly). Since we have no evidence to suggest that anything physical existed prior to the universe, it is safe to assume that there was nothing prior to the universe. When we return to our understanding of direct and indirect causation, we can know that indirect causes only happen when the causal antecedent is causing

7 At this point, it is important to note that these are not scientific observations or empirical demonstrations of this cause. Instead, these are philosophical conclusions given the situation that we are exposed to.

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another being or entity and the indirect cause comes as a side effect. Since there are no beings sans the universe, we can see that this cause cannot be indirect and has to be a direct personal cause of the universe.

more probable that the creator of the universe is immensely powerful. Great knowledge follows on from immense power. If something created the entire universe, it implies that it knows quite a lot.

The secondary attributes include free will, immense power and immense knowledge. Free will comes from the question of why there is something rather than nothing. Since there are no physical laws (that we know of) before the universe’s creation, there appears to be nothing “determining” the cause. There is no reason why the cause had to cause the universe; it could have done otherwise. Why this universe instead of another? Why did this specific universe come into existence instead of another one with vastly different laws of nature? Surely there is nothing necessary about the conditions in the world that we live in. Hence, it appears that this cause does have free will. The attribute of immense power originates from the fact that it created everything in existence, while it is possible for some “butterfly effect” 8 cause, it is

So let us summarise these attributes and see what it can tell us about the nature of this cause. As we have established, the primary attributes are timelessness, transcendence, and a personal and direct relation with the cause. The secondary attributes are free will, immense power and immense knowledge. Of course, if one were to claim that this directly proves the existence of the God of classical theism or the Christian God, he would be insane. But when we look at these attributes, it is undeniable that they point towards a theistic explanation of the universe instead of an atheistic one. For it would be an extreme form of atheism, perhaps one not worthy of the name of “atheism”, to suggest that there exists a personal, transcendent, powerful, timeless cause of the universe.

Conclusion 2: The cause is a god Since we know that the universe does have a cause (Conclusion 1), it follows from Premise 3 that the universe’s cause is a god. I would like to make it clear that this is not an argument for the Christian God, nor is it an argument for monotheism. However, it does point to a cause which has theistic properties. 8 This is the idea that a small cause can lead to a large effect (latter on in the causal chain)

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Two objections:

Any argument about the existence of a god is expected to raise controversy and discussion. Especially when the argument is so simple, yet so powerful. Hence, I feel that I would be doing the Kalam a disservice if I fail to discuss two of the most common objections.

1) What caused a god?

Although the objection “what caused a god?” is a rather unfounded argument with little to no reason backing it, it is Dawkins’ self-proclaimed “knockdown argument” of cosmological arguments and therefore requires a quick shout out before it can be dismissed with a quick exclamation of “You’ve gotta be kidding me!” The reason why we can dismiss this rebuttal easily is due to the fact that the objector does not understand the Kalam cosmological argument. If we were saying that all things that exist require a cause, then this objection would be valid. Yet this is not what I have been defending. If you look at the fine-print of any cosmological argument, it is clear that this is not what we are referring to when we raise a causal principle like the principle of temporal causation When we raise cosmological arguments, we have a very specific goal in mind. Instead of defending the need for causation simpliciter, one only argues that things which have temporal relationships require causation. It does not apply to timeless or past infinite beings. Therefore, it can only be concluded that such a rebuttal is aimed at a strawman which no theist has ever tried to defend in the past.

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2) Does the nondeterministic 9 nature of quantum mechanics undermine classical ideas about causality?

Due to recent developments in quantum mechanics, some people have suggested that traditional ideas about deterministic causes do not apply. They would suggest that the Kalam is incompatible with non-deterministic causation and would fail. There are a few responses that a Kalam defendant can turn to. Firstly, it appears that causes do not need to be deterministic to be causes. Even in a non-deterministic universe, causation is still very much real. Since a “cause” is defined as something which leads to another event or causes a change, it appears that even if something is completely non-deterministic, it can still be regarded as a cause.

9 relating to the philosophical doctrine that all events, including human action, are a determined by causes regarded as external to the will.: “a deterministic theory”

PHYSICS AND TECHNOLOGY One can take a random number generator and say that it is the cause of the picked number even though it is random. Furthermore, under the assumption that we have free will, we are technically not “determined”. Despite this freedom, we can act as causes of certain effects. Us swinging a racket would lead the tennis ball to fly back to the other side of the court. Hence, objects do not need to be deterministic to be a cause. Secondly, it appears that even quantum physics abides by certain causal rules. Although some physicists would present the idea that the quantum realm is completely random and is a mess of particles and energy fluctuating in and out of existence, Robert Koons explains that causal relations exist in his book Realism Regained: An Exact Theory of Causation,

According to the Copenhagen version of quantum mechanics, every transition of a system has causal antecedents; the preceding quantum wave state, in the case of Schrodinger evolution, or the preceding quantum wave state plus the observation, in the case of wave packet collapse. Teleology and the Mind [7]: Therefore, it would appear that causation is very much existent in quantum mechanics even if they are not strictly deterministic. With these rebuttals to objections that arise from quantum physics, we can reach the conclusion that the principle of temporal causation appears to remain intact and there is no knockdown or significant argument which can be raised from the quantum physics side of things.

PHYSICS AND TECHNOLOGY Bibliography

Final Thoughts: Since both of these arguments against the Kalam have been shown to be vacuous, it appears that one can rationally support the premises of our argument. Turning back to our formulation, since this is a deductive argument with sound premises, we can see that the conclusion logically follows; that there is an immensely powerful, transcendent, personal cause for the universe — a god.

[1] Craig, William Lane. The Kalam Cosmological Argument. Wipf and Stock, 2007. [2] Krauss, Lawrence Maxwell. A Universe f ro m N o t h i n g. S i m o n & S c h u s t e r, 2 0 1 2 . [ 3 ] P. C . W . D a v i e s , “Spacetime Singularities i n C o s m o l o g y, ” i n T h e Study of Time III, ed. J . T. F r a s e r ( B e r l i n : S p r i n g e r Ve r l a g , 1 9 7 8 ) , pp. 78-9. [4] Borde, A. et al. “Inflationary spacetimes are not past-complete.” Physical Review Letters ( 2 0 0 1 ) : n . Pa g. [5] Ibid. [6] Craig, William Lane. Time and Eternity: Exploring God’s Relationship to Time. C r o s s w a y, 2 0 0 1 [7] Koons, Robert C. Realism Regained: An Exact Theory of C a u s a t i o n , Te l e o l o g y, and the Mind. Oxford University Press, 2000.

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Will Building a Dyson Sphere Solve Earth’s Energy Problem? Alyssa Wong

PHYSICS AND TECHNOLOGY Earth has an energy problem. But for most of human history, energy consumption was modest [1]. People relied on caloric energy from the food they consumed or on animal power to perform daily tasks. Burning biomass such as wood was the biggest source of energy. Then came the Industrial Revolution in the 1800s and the rise of the new Holy Trinity of energy: coal, natural gas, and petroleum, all of which are non-renewable fossil fuels. Our current annual global energy consumption is estimated to be 580 million terajoules –– roughly equivalent to the energy we would use if all 7.5 billion of us boiled 70 kettles of water per hour every day for a year [2, 3]. 80% of this energy comes from fossil fuels, a leading source of global warming pollution, damaging the planet at almost every stage [4]. The extraction of fossil fuels, done mostly through mining or drilling, damages land, threatens the health and safety of miners and causes water and air pollution. The refining and purifying of fuels into a usable state leaves excess waste material disposed of in ways detrimental to the health of the environment and the community. The transportation of fossil fuels over long distances also generates its own pollution and may result in disastrous accidents such as oil spills and gas leaks. And the burning of fossil fuels releases soot, the health consequences of which include chronic bronchitis and aggravated asthma, as well as sulfur dioxide and nitrogen oxide, leading to acid rain. Most significantly, it releases carbon dioxide, a greenhouse gas that traps heat in the atmosphere and causes global warming. The hotter, drier climate has driven both the Australian bushfires and California wildfires –– we are literally setting the planet on fire.

PHYSICS AND TECHNOLOGY But the solution to Earth’s energy problem might not come from the Earth itself. At any moment, the sun emits about 3.86 x 10 26 watts of energy - 7 x 10 17 times more energy than we need [5]. We’re just not harnessing it. Yet. In 1960, British-American theoretical physicist Freeman Dyson first speculated about Dyson spheres, hypothetical megastructures that encircle a star to capture a large percentage of its power output [6]. A Dyson sphere would not be a literal solid sphere enclosing the sun, as the immense tensile strength needed is physically impossible to achieve with our current technologies. A structure like that would also be liable to drift and crash into the sun [7]. Instead, if we were to build a Dyson sphere, we would most likely use a Dyson swarm model, which is a collection of solar panels situated in orbit around the sun (See Fig. 1) [7, 8].

These solar panels would be very large lightweight mirrors, concentrating solar radiation down on focal points (heat engines combined with solar cells) where it would be transformed into useful work and beamed across space for use elsewhere [8]. They would need to operate without repairs for long periods of time and be cheap to produce, most likely made of polished metal foil bound to some supports (See Fig. 2) [9].

Fig 1. Dyson swarm 3D model

Fig. 2 Solar panel 3 D model

PHYSICS AND TECHNOLOGY The sun is massive, so in order to surround it with solar panels, we would need to disassemble an entire planet. The easiest victim would be Mercury –– it’s the closest to the sun, has no atmosphere, only has about a third of the surface gravity of Earth, and is composed of 30% silicate and 70% metal, mainly iron or iron oxides, materials that will be used for the swarm [8, 9]. The initial energy generating source will be a 1 km 2 array of solar panels, constructed on Mercury itself and then launched into space [8]. These will provide the energy to run miners which strip mine the planet’s surface and refiners, extracting valuable elements and fabricating them into swarm panels [9]. This forms a feedback loop, where the material removed will be made into solar captors that generate energy, allowing more material to be removed. 1/10ths of all the energy will be used to propel material into space. We can take advantage of Mercury’s low gravity to use mass-drivers such as railguns to launch the panels at high speeds into space –– much more efficient than using rockets. The entire process would be carried out by an army of automated robots overseen by a small group of human controllers [8, 9]. Assuming the overall efficiency of the solar captors is 1/3, that it takes five years to process the material into solar captors and place them in the correct orbit, and that half of the planet’s material will be suitable to construct solar captors, Mercury itself will be completely disassembled in 31 years and 85 days, thanks to exponential growth. The power available increases initially in five-year cycles, which gradually smooth out to become linear on the log scale (See Fig. 3) [8].

Fig 3. Power available during the disassembly of Mercur y

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Illustration by Callum Sanders

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Harnessing even a tiny fraction of the sun’s energy using the Dyson sphere would give us the energy for projects such as terraforming planets, forming space colonies, or building other megastructures such a stellar engine to move our star, and thus the solar system, through the galaxy. So if building a Dyson sphere can solve our energy problem and offer almost unlimited energy from our current energy consumption standpoint, why haven’t we done it yet? Well, because it’s impossible. For now, at least. The Dyson sphere was originally conceptualised as a way for an intelligent alien civilisation to satisfy their energy needs after having gained the ability to use and store all of the energy available on its planet, meaning the aliens are already a Type 1 civilisation on the Kardashev scale. The Kardashev scale is a method of measuring technological advancement based on the amount of energy a civilisation can use [10]. A Dyson sphere is an indicator of a transition to a Type 2 civilisation, which can use and control energy at the scale of its planetary system, and an eventual evolution to a Type 3 civilisation, which can control energy at the scale of its entire host galaxy [10]. We haven’t even reached the threshold to become a Type 1 civilisation yet, so trying to build a megastructure around the sun is probably not a good idea.

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Building a Dyson sphere would be the largest, most ambitious project undertaken by humanity and would require global cooperation on a level we just haven’t reached yet. We also don’t yet have the technology to achieve some of the more ambitious steps necessary.

The plan involves mining Mercury until the planet is entirely disassembled. The deepest mine on Earth, the Mponeng Gold Mine, has a depth of 4 km below the surface [11]. The radius of Mercury is 2,439.7 km [12]. Additionally, Mercury is supposed to be mined mostly by robots, which we don’t even have in mines on Earth yet [11]. There’s also the issue of Mercury’s unusable mass, which becomes debris [11]. Transmitting power back to Earth poses another problem. Wireless transmission of electricity is possible, but not exactly easy. Microwaves can transmit electricity, though the furthest distance scientists have been able to do so is 148 km, with most of the energy being lost [11]. Lasers are another possibility yet similarly have

limited distance. Unfortunately, we currently are not able to transmit any of all that glorious solar energy across the 102.1 million km between Mercury and Earth [13]. We have far from exhausted the solutions to our energy problem right here on Earth. In 2019, only around 11% of global primary energy came from renewable technologies, 7% being hydropower, one of our oldest and largest sources of lowcarbon energy [14]. The World Wildlife Federation’s 2011 Energy Report states ‘it is technically possible to achieve almost 100% renewable energy sources within the next four decades’, with the major sources being wind, solar, biomass and hydropower. It estimated that a million onshore and 100,000

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offshore wind turbines could meet a quarter of the world’s energy demand by 2050 [15]. When energy consumption is narrowed down to just electricity, which is easier to decarbonize as it is less reliant on oil and gas, around a quarter of energy comes from renewables [14]. These numbers can still be increased. Although there is concern that the deployment of renewables will result in higher electricity prices, research has shown this doesn’t have to be the case. Energy storage is swiftly evolving and growing cheaper, meaning an energy grid run entirely on renewable energy up to 95% of the time is an increasingly realistic idea [16]. If renewables alone cannot save

the planet, we can look to nuclear energy, which still poses a risk of radioactive contamination and dangerous nuclear waste, but has a small land footprint and low CO 2 emissions, allowing it to eventually replace fossil fuels at a low cost [17]. While uranium, the fuel most widely used for nuclear fission, is not technically renewable, existing uranium from U-mine sites and existing spent fuel in fast reactors provide sufficient uranium fuel to produce 10 trillion kWh/year for thousands of years, making it a sustainable energy source [18]. Uranium extracted from seawater is replenished continuously, so if seawater extraction production costs fall and the source of uranium changes from mined ore to seawater, nuclear energy would also become a renewable energy source [18].

PHYSICS AND TECHNOLOGY Will building a Dyson sphere solve Earth’s energy problem? No. But innovation in order to improve renewable energy technology, a push to increase sustainable energy consumption, and a transition to a green economy will. Once we’ve done all that, building a Dyson sphere may no longer be an impossible concept, but rather the logical next step to open up limitless possibilities.

PHYSICS AND TECHNOLOGY Bibliography

18, 2020,https://en.m.wikipedia.org/wiki/ Kardashev_scale

[1] “Earliest Energy.” Earliest Energy | EME 803: Applied Energy Policy, Penn State College of Earth and Mineral Sciences, https://www.e-education.psu.edu/eme803/ node/502#:~:text=Prior%20to%20that%2C%20 early%20people,an%20important%20 source%20of%20heat.

[11] “A Few More Notes On The Impracticality Of Building A Dyson Sphere.” Forbes, Forbes Media, LLC, April 18, 2012, https://www. forbes.com/sites/alexknapp/2012/04/04/a-fewmore-notes-on-the-impracticality-of-building-adyson-sphere/#5b1be47f31ae

[2] “Terajoules of Energy Used.” The World Counts, https://www.theworldcounts.com/ challenges/climate-change/energy/globalenergy-consumption/story [3] Gray, Richard. “The biggest energy challenges facing humanity.” BBC Future, BBC, 13th March 2017, https://www.bbc.com/ future/article/20170313-the-biggest-energychallenges-facing-humanity [4] “The Hidden Costs of Fossil Fuels.” Union of Concerned Scientists, Jul 15, 2008, https://www.ucsusa.org/resources/hiddencosts-fossil-fuels#:~:text=Burning%20 fossil%20fuels%20emits%20a,the%20 environment%20and%20public%20 health.&text=Acid%20rain%20is%20formed%20when,precipitation%20that%20is%20 mildly%20acidic [5] “The Sun’s Energy.” The University of Tennessee Institute of Agriculture, https:// ag.tennessee.edu/solar/Pages/What%20Is%20 Solar%20Energy/Sun%27s%20Energy.aspx [6] Mann, Adam. “What Is a Dyson Sphere?” Space.com, August 01, 2019,https://www. space.com/dyson-sphere.html [7] Dvorsky, George. “How to build a Dyson sphere in five (relatively) easy steps.” Sentient Developments, March 20, 2012, http://www. sentientdevelopments.com/2012/03/how-tobuild-dyson-sphere-in-five.html [8] Sandberg, Anders and Armstrong, Stuart. “Eternity in six hours: intergalactic spreading of intelligent life and sharpening the Fermi paradox” Future of Humanity Institute, Oxford University Philosophy Department, 2012, http://aleph.se/papers/Spamming%20the%20 universe.pdf [9] Kurzgesagt - In A Nutshell. “How to Build a Dyson Sphere - The Ultimate Megastructure.” YouTube, 20 Dec 2018, https://www.youtube. com/watch?v=pP44EPBMb8A&t=472s [10] Knapp, Adam. “Kardashev scale.” Wikipedia, Wikimedia Foundation, October

[12] Williams, David R. “Mercury Fact Sheet.” NASA, 27 September 2018, https://nssdc.gsfc. nasa.gov/planetary/factsheet/mercuryfact.html [13] “How far is Mercury from Earth? Accurate distance data.” The Sky Live, https:// theskylive.com/how-far-is-mercury [14] Ritchie, Hannah and Roser, Max. “Renewable Energy.” Our World in Data, 2017, https://ourworldindata.org/renewable-energy [15] “Is It Possible for the World to Run on Renewable Energy?” Knowledge@ Wharton, Wharton School of the University of Pennsylvania, Apr 23, 2015, https:// knowledge.wharton.upenn.edu/article/can-theworld-run-on-renewable-energy/ [16] “GE’s North American Studies Show No Hard Limit to Renewables on a Grid System.” GE News, May 23, 2016, https://www.ge.com/ news/press-releases/ges-north-americanstudies-show-no-hard-limit-renewables-gridsystem [17] “3 Reasons Why Nuclear is Clean and Sustainable.” Office of Nuclear Energy, United States Department of Energy, April 30, 2020, https://www.energy.gov/ne/articles/3-reasonswhy-nuclear-clean-and-sustainable [18] Conca, James. “Is Nuclear Power A Renewable Or A Sustainable Energy Source?” Forbes, Forbes Media, LLC, Mar 24, 2016, https://www.forbes.com/sites/ jamesconca/2016/03/24/is-nuclear-powera-renewable-or-a-sustainable-energysource/#1d8e1814656e Fig 1. by Aicrovision (TurboSquid), https:// www.turbosquid.com/3d-models/dyson-swarm3d-model-1369830

Fig 2. by Aicrovision (TurboSquid), https:// www.turbosquid.com/3d-models/dyson-swarm3d-model-1369830 Fig 3. by Stuart Armstrong and Anders Sandberg, http://aleph.se/papers/ Spamming%20the%20universe.pdf

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Antimatter and The Ozma Problem Hoi Kiu Wong

Introduction The Ozma Problem was something that lingered in the back of my mind ever since I was first introduced to it. I remember sitting in the classroom near the end of the school year when Dr Daniel, my Year 9 Physics Teacher, decided to go beyond the specification in the Section of Astrophysics and led the class into a whole new world of Quantum Physics. Back then, I remember being confused about the entire idea; however, I have come to realise that it is important for us to find out more about Particle Physics and the Quantum world, as the knowledge we can acquire from it can help us understand more about the nature of the Universe that we live in, as well as the beginning of it. In understanding Particle Physics, we can turn towards understanding the Ozma Problem and how it was solved, which I will delve into in this article.

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Illustration by Se Lyn Lim

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The atom Whether you have or have yet to enter the world of Quantum Physics, you may have learnt that the Atom is defined as the ‘smallest unit of matter’. In fact, the word ‘atom’ means ‘indivisible’ in Greek, as it was previously known that atoms cannot be divided into anything tinier [1]. However, we now know that we can go smaller than the atoms, to the subatomic particles - protons, neutrons and electrons [2] - which are made up of even smaller particles known as quarks and leptons [3]. Protons and neutrons are made of two types of quarks: ‘up’ quark and the ‘down’ quark. These quarks have electrical charges that are fractions of the proton’s charge (an ‘up’ quark has ⅔ positive charge and a ‘down’ quark has ⅓ negative charge). A proton is made up of two ‘up’ quarks and one ‘down’ quarks (⅔ + ⅔ -⅓ = 1) so overall the charge adds up to +1, whereas a neutron is made up of two ‘down’ quarks and one ‘up’ quark (⅔ -⅓ -⅓ = 0) which gives the neutron a neutral charge (See Fig. 1) [4]. The electron (a lepton), the up quark, and the down quark (quarks), which are all fermions, are probably the most well known out of the elementary particles. It is through decades of scientific research and, in particular, the research at CERN with the Large Electron Positron (LEP) collider allowed scientists to discover and learn more about these elementary particles [4].

Fig 1. The sets of up quarks and down quarks in a proton (left) and in a neutron (right)

PHYSICS AND TECHNOLOGY In the LEP, positrons and electrons were accelerated around the 27-kilometre circumference of the collider and collided with one another when they reached the same point at the same time. This caused an annihilation to occur (as matter is colliding with antimatter). This annihilation was the key moment for scientists, as the goal was to observe in detail what was released in the aftermath of the collision. To do this, the Collider was equipped with four detectors, built around the four collision points within underground halls. They were capable of registering the particles by their energy, momentum and charge, thus allowing physicists to tell what particle reaction happened and what elementary particles were involved [17]. Many of these emergent elementary particles from the annihilation were unknown before the LEP was built; for instance, the two heavier versions of the electron (the ‘muon’ and the ‘tau’), the two heavier versions of the up quark (the ‘charm’ and ‘top’), as well as the two heavier versions of the down quark (the ‘strange’ and the ‘bottom’) [4]. These newly discovered particles were also revealed to have anti-versions of themselves.

Fig 2. The Standard Model of Elementary Particles.

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The LEP was dismantled in 2001 and was replaced by the Large Hadron Collider (LHC), which is the world’s largest and highest-energy particle collider and the largest machine in the world. The name might sound familiar to you because recently in 2012, it became well known for discovering the Higgs Boson [18]. The discovery of the Higgs Boson is particularly fascinating because, in the 1970s, scientists found out that electricity, magnetism, light and certain types of radioactivity are all manifestations of a force called the electroweak force. The equations detailing the electroweak force correctly describes its force-carrying particles: the photon, the W bosons and Z bosons. All of these emerge with no mass, which is correct for the photon, but not for the W and Z bosons, whose masses are approximately 100 times that of a proton. It is later when theorists Robert Brout, François Englert and Peter Higgs solved the problem. They proposed that W and Z bosons interact with an invisible field, which is now called the ‘Higgs field’. After the Big Bang, the Higgs field was zero, but as the universe cooled and expanded, the field grew, which meant that any particle interacting with it would acquire mass (The Higgs Effect). The more the particle interacts with this field, the heavier it becomes. Photons, as they don’t have a mass, don’t interact with it. The Higgs boson in turn became the associated particle of the Higgs field [19].

Fig 3. Collision at the LHC that produced a Higgs Boson and a Z Boson. The two grey projections represent the particles that decayed from a bottom and an antibottom quark, which was likely to have decayed from the Higgs Boson. The green lines represent electrons and positrons, which likely decayed from a Z boson. [20]

Therefore, discovering antimatter and using it in theories and experiments are fundamental in discovering how the universe began, and the nature of it at a quantum scale.

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Nature of the universe

Einstein’s theory of relativity reveals the interconnection between energy and matter, perfectly shown in his famous equation E=mc 2 . It shows how energy can congeal itself into matter, and in reverse, how matter can turn into energy. The nature of the universe can be further explained when Einstein’s theory is combined with Newton’s Laws of Motion. Take a box for example. To move the box, you have to exert a force onto it, and this resultant force will cause it to accelerate in the direction of the force. This acceleration, as it depends on the force, also depends, in proportion, on the mass of the box. According to Newton’s Laws of motion, if a body is stationary and you apply a force on it for a second, then the speed will increase by some amount. If you apply the same force on the same body again, then the body will increase in speed by the same amount. However, in Einstein’s theory of relativity, this change in speed alters - the next push will increase its speed less than what it did on the first push. If the body is travelling near to the speed of light, pushing it would increase the speed by a negligible amount [4]. Therefore, Newton’s

Laws of motion are only accurate for day to day motion, not in the situation where particles are moving in an accelerator at high relativistic speeds. In contrast to Newton’s Laws of Motion, Einstein’s theory states that the mass of a body increases the faster it travels. Near to the speed of light, its mass becomes infinite. Hence, it is impossible to accelerate the object to the speed of light [4]; light is the only thing that can reach the speed of 299,792,458 metres per second [5]. Take a moving particle. It has energy congealed in its matter, and energy in its motion, which is known as its kinetic energy. The total energy, E, of the moving particle is not the sum of these two forms of energy, but the square root of the sum of the square of the energy of motion, pc (product of momentum and speed of light) and the square of the energy in its mass ,mc 2 . This may seem familiar to you, as this applies Pythagoras’ theorem. The length of the hypotenuse is proportional to the energy of the moving particle (See Fig. 4) [4].

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Fig 4. Conflation of Einstein’s theory of Relativity with Pythagoras’ theorem. The amount of energy of a body is the square root of the sum of the square of the energy of the body when stationary, mc 2 , and the square of the energy of its motion, pc. [4]

This means that a photon travelling at the speed of light, with no mass, has energy due to its motion. As the law of the conservation of energy states, energy cannot be created nor destroyed but can be transferred from one form to another. This shows how the energy of a photon can be transformed into energy trapped in matter. But how is it possible for an electron with a negative electrical charge to come from the energy of photons, which has no electric charge? Under the principle of charge conservation, the only way is that a positron, the anti-version of the electron, is also made. Scientists believe that this was what happened right after the Big Bang, the birth of the universe - light consisting of massive amounts of energy congealed into pieces of matter and antimatter, and when matter and antimatter meet, they annihilate one another, which in turn releases energy. Hence, Einstein’s theory of relativity provided us with the key into the world we live in as well as the one into the antiworld; now, we just need to find the lock [4].

We know that light is made up of photons (quanta of electromagnetic radiation) and the energy of each photon is the product of Planck’s constant and the frequency, E=hf. In an atom of an element, there are discrete and unique energy levels due to the number of quantum waves that can fit into a ‘loop’. Therefore, when electrons move from a high energy level to a lower energy level, the discrete energy difference between the two levels is released in the form of photons, which give out a specific wavelength, and in turn, a specific colour. The colour emitted is unique for each element. This atomic spectrum can be observed by adding the element into a flame and looking at the light through prisms or diffraction grating. In 1896, Peter Zeeman, the Dutch spectroscopist, noticed that when powerful magnets were placed near his samples, the yellow lines emitted by the sodium changed slightly. The yellow lines changed from being sharp and defined into broad. It was later discovered that the broadening lines were actually due to a separation of one line into multiple lines. Why did this happen?

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The electron spin This is because the electron has its own magnetism; in other words, the magnetic field interacts with the magnetic dipole moment that is associated with its orbital angular momentum [13]. This in turn affects the energy of the sodium samples (each of the levels split into substates of equal energy [14]), which results in an alteration of the atomic spectra. It has effectively been shown that an electron can act as a small bar magnet with a north and south pole and that it has an intrinsic rotary motion known as ‘spin’, which can orientate itself clockwise or anticlockwise in a magnetic field. It’s important to note that spin is an ‘intrinsic rotary motion’ because an electron, in reality, is not a ball but an infinitely small point that cannot spin. Spin is an odd physical phenomenon that is still challenging among physicists to explain. It is like the spin of a planet in that it gives a particle angular momentum and a small magnetic field known as a magnetic moment; however, due to the size of subatomic particles like the electron, its surface would have to be moving faster than the speed of light to produce the measured magnetic moments (which is impossible). Moreover, spin is quantised, so only certain discrete spins are allowed. This can be demonstrated using the SternGerlach experiment [15] (See Fig. 3).

In the Stern-Gerlach experiment, a beam of silver atoms is ejected into an inhomogeneous magnetic field. According to classical physics, it is expected that the magnetic moments of the silver atoms are randomly orientated, so they should be deflected by different amounts depending on their orientations. However, they found that half of the silver atoms were deflected upwards and half of them were deflected downwards by the same amount (two discrete points of accumulation in the machine). These two states are known as ‘spin up’ and ‘spin down’, showing the quantised nature of the spin. If you look at the silver atom, there are in total 47 electrons. In 46 of these electrons, each spin-up is paired with one spin down. The spins neutralise each other, so what is left is one unpaired electron - the 5s electron. This electron can be either spin up, spin down or any superposition of these two states - which means that its spin can point in any direction. As all the silver atoms have spins pointing in different directions, they are effectively unpolarised. The inhomogeneous magnetic field, therefore, acts as a filter and forces the spin of a silver atom to take a random orientation in either the same or the opposite direction of the magnetic field. If the spin state of a silver atom is closer to up, it is very unlikely to change its direction to down [16].

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Dirac

Fig 5. Dirac’s equation

Dirac’s equation (See Fig. 5) was derived in 1928 and it combined quantum mechanics with Einstein’s theory of relativity (the behaviour of fast-moving bodies) [4]. His equation was revolutionary because it revealed the existence of the antiworld - the equation works not only for an electron but also for a positron (the antiparticle of the electron) [12]. Quantum mechanics deals with the motion of tiny particles; their small size brings about uncertainty in the accuracy of their position in time and space. In 1926, Erwin Schrodinger derived the equation of quantum mechanics for slow-moving particles (‘slow-moving’ relative to the speed of light) known as The Schrodinger’s Equation. It explained how electrons behave in atoms, and that an electron in a hydrogen atom is moving with a speed of about two thousand kilometres per second. It also explained why the orbital motion of electrons in atoms caused spectral lines to multiply in magnetic fields (but doesn’t explain electrons’ ‘spin’) [4]. Oscar Klein tried to generalise Schrodinger’s theory by using E 2 and Einstein’s hypotenuse relation. The square root of 25 can be either +5 or -5 (positive or negative). Since you can’t have negative length, the negative answer was rejected (taken as false); however, it left people feeling unsure. Dirac wanted to write an expression for the energy of an electron using E instead of E 2 (using a

way other than square rooting the whole Einstein Hypotenuse equation). He aimed to find an equation showing how a sum of some amount of mc 2 and pc would give E (in this case, the energy of an electron) [4]. Imagine a right-angled triangle with the side lengths of 3, 4 and 5 (5 being the length of the hypotenuse), and as I have mentioned above, we are taking some amount of ‘3’ and ‘4’ and they should add up to 5. This can be written as 4a + 3b = 5 Then, square the equation to get 16a 2 + 12ab + 12ba + 9b 2 = 25 This equation should be the same as the hypotenuse form, where 16 + 9 = 25, which means that a 2 = 1, b 2 = 1, and ab + ab = 0. However, there are no numbers when squared would give 1 but whose product ab would be zero [4]. This is not only for 3, 4 and 5; but for any combination. Effectively, we are trying to match the two equations E 2 = b 2 (mc 2) 2 + a 2(pc) 2 + a × b[(pc) × (mc 2)] + b × a[(mc 2) × (pc)] and E 2 = (mc 2) 2 + (pc) 2 This cannot be solved using numbers but it can with matrices. The two matrices that can solve Dirac’s problem are

a 2 and b 2 each equal to 1 and if you multiply ab and ba, you get and

So ab + ba = 0, which solves Dirac’s problem [4].

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Antimatter and CP symmetry Antimatter, as the name suggests, is the opposite of matter. For instance, in the antiworld, positrons (anti-version of the electron) and antiprotons (anti-version of the proton) would exist. However, if these particles and their respective antiparticles are the same but different at the same time, what does that mean? It means that the anti-version of a particle (made of matter) would have the opposite charge and would be mirrored, in other words, it would show parity. This is known as CP Symmetry - C for Charge and P for Parity [4]. The thing that stays the same between the particle and its anti-version is its mass. To help with the understanding of CP Symmetry, I have included a diagram (See Fig. 6) that illustrates this.

Fig. 6 ‘Day and Night’ - A painting made by Maurits Cornelis Escher in 1938. The painting is mirrored (parity) and its charge is swapped over (represented by the colour change between black and white). As you can see, after changing its ‘charge’ and parity, the painting afterwards (on the right bottom corner) is identical to the original one (on the left top corner).

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Mirror symmetry and parity A right-handed coordinate system is useful in finding out what a mirror image shows. The coordinate system shows the x-axis (represented by your index finger), the y-axis (represented by your middle finger) and the z-axis (represented by the thumb) (See Fig. 7) [7].

Fig. 7 The Right Hand Coordinate System and the Left Hand Coordinate System (which are mirror images of each other). For the right-hand coordinate system, the direction at which the thumb is pointing at is along the z-axis, the index finger is pointing in the direction along the x-axis and the middle finger is pointing the direction along the y-axis (for the left-hand coordinate system, it is along the -y-axis).

If you place your right hand next to the mirror, then the mirror image should show the x-axis and the z-axis going in the same direction as that of your right hand; however, the y-axis becomes -y. Hence, the mirror image is a left-handed coordinate system (See Fig. 7) [7]. This demonstrates how mirror reflections show a change in handedness. Imagine a screw. If you turn it clockwise next to a mirror, the mirror image should show the screw turning anticlockwise. In mechanics terminology, the screw we are turning clockwise is a right-handed screw and the mirror image shows a left-handed screw. In Mirror Symmetry (also known as parity conservation), there should be no change in handedness; therefore, the laws of nature should show no preference for righthandedness or left-handedness [7].

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Parity can be described as a transformation - a mirror reflection and a rotation of 180° about the new y-axis [7]. (x, y, z) (x, -y, -z)

(x, -y, -z) (-x, -y, -z)

This transformation can be seen with electromagnetism. If you place a solenoid next to a mirror, then using the right hand grip rule, your thumb should show the direction of the magnetic field when you fingers are curled up in the direction of conventional current. If you apply the same rule for the mirror image of the solenoid, you will find that the direction of the magnetic field will be opposite to that of the solenoid itself [7].

Fig. 8 A positively charged particle in a magnetic field, and its mirror image.

If you look at a positively charged particle moving in a magnetic field at a certain direction (as seen in Fig.8), then using Fleming’s Left-Hand rule, we can determine the direction of the force on the charged particle. The mirror image would have the positively charged particle moving in the same direction (parallel to that of the original one) but its magnetic field and force would be going in the opposite directions. You can see the parity transformation of the mirror image from the original. What is more astonishing is that this parity transformation obeys the laws of electromagnetism - like charges repel [7]!

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The Ozma Problem

The Ozma Problem poses the scenario where you are a scientist on Earth who just received a mission to communicate with aliens, and your first task is to tell them which direction left is. How can we do this?

PHYSICS AND TECHNOLOGY This is a challenging task because everything that is controlled by gravity and the strong nuclear force shows mirror symmetry. Which means that up and down, left-hand side and right-hand side, are all relative to one another [6]. For example, if you set up two cameras in a laboratory and record a video of an experiment taking place, then take this original video of the experiment and mirror it, and subsequently send both videos (nonmirrored and mirrored) to another laboratory, the scientists at the other laboratory wouldn’t be able to distinguish between the two - whether one of the videos was real or the mirrored version. This reinforces the fact that the laws of nature are ‘mirror symmetric’ [7]. If there are no shared reference objects between us and the aliens that can help us solve this problem, then how are we supposed to tell them what left is? Most would think that up to this point, this task is virtually impossible. However, In 1956, the Chinese-American physicist Chien Shiung Wu conducted a nuclear physics experiment, and the aim was to see whether or not P-conservation (conservation of parity) also applies to weak nuclear force, just as it does with electromagnetism and strong nuclear force [8]. The results of the experiment have established that the conservation of parity was violated by the weak nuclear force, which meant that it would be possible to distinguish between a mirrored version of the world and the mirror image of the current world, as they would behave differently [8]. Wu’s experiment monitored the decay of Cobalt-60 atoms that were aligned by a uniform magnetic field (the weak interactions are responsible for decay) [8]. The alignment of the atoms is important as it minimises the random fluctuations that occur at higher temperatures. When the temperature gets closer to absolute zero, the cobalt nuclei can behave like tiny bar magnets, each of them having a north and south pole. This gives them their ‘spin’ which allows them to line up with the direction of the magnetic field lines [7]. Cobalt-60 is an unstable isotope so it will undergo decay to the stable isotope of Nickel-60. Electrons and gamma rays are emitted in this process as well [8].

Fig. 9 The Beta Decay of Cobalt-60.

The emission of gamma rays is essential in determining whether the weak nuclear force obeys or violates the conservation of parity. Gamma rays are photons and they go through an electromagnetic (EM) process when released from the Cobalt-60 nuclei. The emission of gamma rays is essential in determining whether the weak nuclear force obeys or violates the conservation of parity. Gamma rays are photons and they go through an electromagnetic (EM) process when released from the Cobalt-60 nuclei.

PHYSICS AND TECHNOLOGY Electromagnetic (EM) radiation obeys the conservation of parity, hence they would be emitted almost symmetrically in all directions (isotropically). Thus, the distribution of the gamma rays acts as a control for the distribution of the emitted electrons. The experiment used this principle, counting the rate of emission for gamma rays and electrons in two distinct directions and making comparisons. If the counting rates for the electrons were similar to those of the gamma rays, then parity would be conserved by the weak interaction. However, if the counting rates were very different, then the weak interaction violates the conservation of parity [8]. Asymmetry is shown as the electrons appear to be emitted predominantly in one direction than the other, which is in the direction opposite to the direction of the magnetic field [7], which in turn is opposite to the nuclear spin (See Fig. 10) [9] [10].

Since the direction of the magnetic field in the mirror-reversed arrangement is upwards, it should be in the same direction as the emission of electrons (predicted direction of beta emission if parity were conserved). This is contrary to observation because the experiment has shown that the emission of electrons (beta emission) is going downwards. The mirror-reversed arrangement is not realised in nature so mirror symmetry is violated. In turn, the conservation of parity is violated in the weak nuclear force [7]. So we can tell the aliens that they should do the same experiment as Wu did, and the end that emits the most electrons is the end that we call ‘south’. Then, label the ends of the magnetic axis of the field used for lining up the nuclei, and this in turn can be used for labelling the ends of a magnetic needle. Take a long piece of wire and arrange it to carry electric current away from you and place the magnetic needle above the wire. The north pole of the needle will point in the direction we call ‘left’ [11].

However, we encounter another obstacle. What if the aliens are made out of antimatter and they all live in an antiworld? Could there be a way of determining this? And how would we be able to explain what ‘left’ is to them now? [6] Fig 10. The β decay of Cobalt-60 and its mirror image - notice how the original arrangement shows the rotational axes as left-handed and the mirror-reversed arrangement shows it as right-handed. For your information, the direction of the magnetic field in the original arrangement is going downwards whereas in the mirror-reversed arrangement, the direction of the magnetic field is going upwards (See Mirror Symmetry And Parity).

PHYSICS AND TECHNOLOGY

In order to determine whether or not the aliens are made out of antimatter and live in an anti-world, we can look into the electrically neutral variety of K mesons. When they decay, a pion that is either positively or negatively charged is produced, which is accompanied by an electron or a positron respectively. Asymmetry can be seen in these decays because if matter and antimatter were perfectly opposite to one another, the chance of each decay occurring would be the same. However, in reality, they are a bit different [4]. The Neutral K and the anti-K each have 2 versions: short and long-lived. The long-lived versions (of both the original one and the anti-version one) show a bigger effect in the difference - hence it is used. Whether the K is mirrored or not, the decay of the long-lived K into a positron (along with a negatively charged pion) is always more likely to happen than the decay of the long-lived K into an electron (along with a positively charged pion). Out of 2000 decays, approximately 1003 of them will result in a positron (with negatively charged pion) and 997 of them will result in an electron (with a positively charged pion) [4]. Notify the aliens so that they can identify K, and since we can’t use the name since aliens would call it something else, tell them that it is the thing that weighs slightly more than half the mass of a proton or antiproton. Since they would also call the proton something else, tell them what we mean by the proton - the massive particle in the ‘nucleus’ at the centre of the alien’s simplest atom. Once the aliens have identified K, tell them that we are talking about the electrically neutral one (since there is K + and K - ). We need to tell them that the property that holds the atom together is what we call ‘charge’ and that we are talking about the K with no charge. The alien now knows that we are talking about the long-lived K 0 [4]. Then, ask the alien:

‘Is the lightweight particle that is produced most often in the decays of the long-lived K 0 (or anti-K 0 ) the same as you find in your atoms, or is it the opposite?’.

I f the alien answers that it is the same, then there are positrons orbiting the

atoms in the alien world, which means that the alien is made of antimatter.

I f the alien answers that it is the opposite, then the alien is made of matter

because electrons are orbiting their atoms, just like what we find in our world.

the aliens are made of antimatter, we can tell them what ‘left’ is by saying that the thing that they decay into less frequently (the electron) is made of matter and is moving in a ‘left-handed’ way [6].

I f the aliens are made of matter, then they can conduct the method I have mentioned above that applies the Wu Experiment [4].

PHYSICS AND TECHNOLOGY

Science fiction or reality For several decades, people have been fascinated by antimatter and its annihilation when it meets with matter where both matter and antimatter are destroyed (a self-destruction). This meeting is almost instantaneous and releases a large amount of energy. An annihilation of just one kilogram of antimatter will release about ten billion times the amount of energy given out when a kilogram of TNT explodes [4]. Hence, there is no question as to why people ponder about whether antimatter weapons should be the ‘next big thing’; however, in reality, it is not feasible to make these weapons.

This is because even before making a kilogram of antimatter, making a single gram of it (which would equate with the Hiroshima bomb with a yield of 20 kilotons of TNT) would take a long time. For example, in order to make a gram of antiprotons, you will need 6 × 10 23 (Avogadro’s constant) of them. The quickest source is at the Fermilab, USA. In the month of June 2007, they produced 10 14 antiprotons. If they were able to do this for a year, they could get approximately 10 15 , which is equivalent to 1.5 billionths of a gram. Annihilating this amount of antimatter releases 270 Joules only, which is the same amount of energy required to illuminate a single electric light bulb for five seconds [4]. This shows how inefficient the process of making these antiparticles is. We can only make a few of them over a long period of time, and due to the law of the conservation of energy (some energy is wasted in the process of making the

antiparticles), the energy released from the annihilation would be less than the total energy we would have to put into the whole project! Another reason why making weapons of antimatter is unrealistic is the way in which we have to store them. This means that we have to ensure that the antimatter doesn’t get in contact with matter. You would need a high vacuum and a container with strong electric and magnetic fields. This is possible as scientists have successfully stored antiparticles in Penning traps for many weeks, but there is a limit to how many you can keep in one bottle. When lots of charged particles are in a small volume, they will repel one another. Hence, it becomes more difficult to keep them inside the magnetic bottle. Approximately a million antiprotons is the largest number successfully stored however that is actually many billions of times smaller than the number of antiprotons required for a gram [4].

PHYSICS AND TECHNOLOGY

Fig 11. An artist’s rendition of an antimatter propulsion system

One suggestion is storing antiprotons and positrons together. As antiprotons are negatively charged and positrons are positively charged, this takes away the problem of electric repulsion. However, this poses another problem due to the fact that if the antiprotons and positrons paired up, the overall net charge would be 0 (neutral). Which means that the electric and magnetic fields cannot keep the antiparticles inside anymore as they can only affect charged particles, so they will move out and annihilate. There are also other potential ways in storing antiparticles like antihydrogen atoms; however, these ways also place a limit to how many can be stored per bottle [4]. Regardless of these limitations, research into fuelling spacecrafts with antimatter continues. In the

Cassini-Huygens probe to Saturn, more than half of its weight was in its fuel and oxidiser tanks, and the launch vehicle weighed more than 180 times the probe itself. If antimatter fuel could be used, then a mass equivalent to a grain of rice could power a spaceship to Mars instead of using three tonnes of chemical propellant. Antimatter fuel for space travel at the moment is still not possible because in order to store even one millionth of the amount needed for the Mars trip, a lot of electric force is needed to push on the walls of the fuel tank (due to the electrical repulsion between the antiparticles of the fuel). This means that the equipment in producing this strong electric and magnetic field in the antimatter fuel tank would weigh a lot, which counteracts the primary advantage of antimatter fuel [4].

In the media, Science Fiction has made false statements about antimatter weapons. In Dan Brown’s Angels and Demons, it mentions how antimatter annihilation results in ‘No byproducts. No radiation. No pollution.’, which is false since a large amount of energy is released in the form of gamma rays [4].

PHYSICS AND TECHNOLOGY

Conclusion If you have read up to this point, I hope that this article has offered you a good insight into concepts ranging from the existence of antimatter to the realms of the universe. Indeed, the world of quantum physics is a complicated one, and there is so much more about it that I didn’t include in this article. During my research, I was utterly astounded by how physicists could derive equations that link space, energy and momentum together in such an impeccable way. I am confident that more discoveries in quantum physics will soon come to fruition, and they will help us understand things that we have yet to find out. There is just so much out there that we still do not know.

‘Those who are not shocked when they first come across quantum theory cannot possibly have u n d e r s t o o d i t .’ - Neil Bohr

PHYSICS AND TECHNOLOGY BIBLIOGRAPHY [1] Sharp, Tim. “What Is an Atom?” LiveScience, Purch, 11 Sept. 2019, www.livescience. com/37206-atom-definition.html. [2] “Origins: CERN: Ideas: The Building Blocks Of Matter.” Exploratorium, www. exploratorium.edu/origins/cern/ideas/standard. html#:~:text=Scientists%20once%20thought%20 the%20most,particles%20called%20protons%20 and%20neutrons. [3] “Tara Shears - Antimatter: Why the AntiWorld Matters.” Performance by Tara Shears, YouTube, The Royal Institution, 18 Oct. 2013, www.youtube.com/watch?v=0Fy6oiIRwJc

Encyclopædia Britannica, Inc., 20 June 2011, www.britannica.com/science/Zeeman-effect. [15] “What Exactly Is the ‘Spin’ of Subatomic Particles Such as Electrons and Protons? Does It Have Any Physical Significance, Analogous to the Spin of a Planet?” Scientific American, Scientific American, 21 Oct. 1999, www. scientificamerican.com/article/what-exactly-isthe-spin/. [16] The institute for physics education research, Münster university, creator. SternGerlach Experiment (U2 07 03). YouTube, Stefan Heusler, 25 June 2019, www.youtube. com/watch?v=PH1FbkLVJU4.

[4] Close, Frank E. Antimatter. Oxford University Press, 2018.

[17] “Large Electron–Positron Collider.” Wikipedia, Wikimedia Foundation, 8 July 2020, en.wikipedia.org/wiki/Large_ Electron%E2%80%93Positron_Collider.

[5] The Editors of Encyclopaedia Britannica. “Speed of Light.” Encyclopædia Britannica, Encyclopædia Britannica, Inc., 17 May 2019, www.britannica.com/science/speed-of-light.

[18] “Large Hadron Collider.” Wikipedia, Wikimedia Foundation, 3 July 2020, en.wikipedia.org/wiki/Large_Hadron_Collider.

[6] Reich, Henry, director. How to Tell Matter From Antimatter | CP Violation & The Ozma Problem. YouTube, Minutephysics, 26 Feb. 2020, www.youtube.com/watch?v=Elt0Gt9Cb6Q [7] Daniel, Michael. “The Ozma Problem .” Physics Review, May 1998, pp. 19–22. [8] “Wu Experiment.” Wikipedia, Wikimedia Foundation, 29 June 2020, en.wikipedia.org/ wiki/Wu_experiment.

[19] “CERN Accelerating Science.” CERN, home.cern/science/physics/higgs-boson. [20] Wolchover, Natalie, and substantive Quanta Magazine moderates comments to facilitate an informed. “The Physics Still Hiding in the Higgs Boson.” Quanta Magazine, 2019, www. quantamagazine.org/the-physics-still-hiding-inthe-higgs-boson-20190304/. Fig 1 Wikimedia Commons

[9] “Madame Wu and the Backward Universe.” Galileo’s Pendulum, 8 Mar. 2014, galileospendulum.org/2014/03/08/madame-wuand-the-backward-universe/.

Fig 2 Wikipedia

[10] Nave, Carl Rod. Parity, hyperphysics.phyastr.gsu.edu/hbase/quantum/parity.html.

Fig 4 Wikimedia Commons

Fig 5 BBC (©StellarioCama)

[11] Gardner, Martin. The New Ambidextrous Universe: Symmetry and Asymmetry from Mirror Reflections to Superstrings. Dover Publications, 2005.

Fig 6 Talk by Tara Shears - Antimatter: Why the anti-world matters (The Royal Institution) [3]

[12] Highfield, Roger. “How Dirac Predicted Antimatter.” New Scientist, 12 May 2009, www. newscientist.com/article/dn17111-how-diracpredicted-antimatter/.

Fig 8 Reproduced from Figure 3 of Daniel, Michael. “The Ozma Problem .” Physics Review, May 1998, p.21 [7]

Fig 7 Scratchapixel

[13] Nave, Carl Rod. “Zeeman Effect in Hydrogen.” Zeeman Effect, hyperphysics.phyastr.gsu.edu/hbase/quantum/zeeman.html.

Fig 9 Wikipedia [8]

[14] The Editors of Encyclopaedia Britannica. “Zeeman Effect.” Encyclopædia Britannica,

Fig 11 Wikimedia Commons

Fig 10 Wikimedia Commons

PHYSICS AND TECHNOLOGY

Material Sustainability: How to pr ovide the same with less? Katrina Cheng

Illustration by Isabel Chau

PHYSICS AND TECHNOLOGY

“Plastic accounts for about 1% of t h e U K ’s c a r b o n d i ox i d e e m i s s i o n s, and plastic bags make up 1% of p l a s t i c u s e. ” Ju l i a n M A l lwo o d , Professor of Engineering at the U n i ve r s i t y o f C a m b r i d ge, o n c e s a i d . In fact, “even if all plastic bags were scrapped and their substitutes we r e c a r b o n n e u t r a l … we wo u l d o n ly b e a d d r e s s i n g 0 . 0 1 % o f t h e U K ’s carbon footprint”. To t r u l y r e d u c e c a r b o n emissions and find the solution, we need to start focusing on scale and identif ying areas that can actually make a significant difference. Out of the total global carbon emission, 64% are energyrelated, of which 35% are f r o m t h e i n d us t r y, 31 % are from buildings, and 27% are from transport. Climate scientists tell us that we have to cut our gas emissions to zero by 2050 and that we are not even close to this goal. Environmental impacts of material production and processing are becoming increasingly impossible to ignore and one of our biggest opportunities for change comes from material efficiency e s s e nt i a l l y, providing the same with less.

Steel is 100% recyclable once it is produced as it has a theoretically endless life cycle. Here is the cycle simplified: iron ore is mined, melted then manufactured, the consumer orders the required steel for its required purpose (transport , buildings, appliances) and the steel enters its ‘use’ phase. Once the steel is exhausted, it is recycled through melting or used as steel scrap where the whole cycle repeats. To address material sustainability regarding the whole cycle, we can target the two areas with the most significant gain and which save as much as 75% of energy: material design and material reuse.

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one. M AT E R I A L D E S I G N

“At least 25% of liquid steel and 40% of liquid aluminium ne ver g e t m a d e i n t o p r o d u c t s ,” A l l w o o d s t a t e s . F o r s i m p l i c i t y , m a t e r i a l s in the industry are manufactured into regular shapes and sizes, which are then cut into smaller pieces according to the appliance n e e d e d . Un f o r t u na t e l y, b y d o i n g s o , t h e r e a r e m e t a l s i n p e r f e c t condition that are left unused when cutting and processing. In r e a l i t y, t h e m e t a l s c ra p f o r m e d i s m o r e o f a ha b i t ra t h e r t ha n a n e c e s s i t y. I f m a n u f a c t u r e r s s t a r t e d u s i n g a l l m e t a l s m a n u f a c t u r e d t o ma x i mu m e f f i c i e n c y, w e c o u l d c u t c a r b o n e m i s s i o n s b y 7 % i n t h e a l u m i n i u m i n d u s t r y a n d a f u r t h e r 1 6 % i n t h e s t e e l i n d u s t r y. I n t his s e c t i o n o f t he pa p e r, we w i l l e x pl o r e d i ff e r e nt way s o f s av i ng materials through different designs; we will also explore reasons why good-quality steel and aluminium remain unused and start i n t r o d u c i n g p o t e n t i a l s o l u t i o n s t o a c h i e v e m a x i m u m e f f i c i e n c y.

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1. YIELD LOSSES

Imagine this scenario: you are making cookies for your afternoon tea p a r t y . Yo u r o l l o u t t h e cookie dough into a rectangular block and bring out your circular s h a p e d c o o k i e c u t t e r . Yo u fit as many circles onto the dough until there is no more extra space. Then you would usually take the leftover dough, roll it out, and repeat this process until you use up all the dough. With your freshly baked cookies and drinks prepared, your tea party begins. In the construction i n d us t r y, we call the process used by the cookie-cutter a s ‘ b l a n k i n g ’. S a d l y , i n the material i n d us t r y,

we cannot very easily roll the leftover dough out again and repeat procedures. Instead, the leftover dough, known as m e t a l ‘ s c r a p ’, w i l l s i m p l y not be part of the final component and will need to be recycled under an energy-intensive melting process, further contributing to the greenhouse gas effect. In a later section titled ‘ M a t e r i a l R e u s e ’, w e w i l l explore how such scrap in good condition and without surface corrosion can be trimmed and processed to be part of a new application - a process that sounds very ideal, yet is only done on a very small scale.

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Reasons for yield loss

Despite very few customers actually wanting the shape they purchase, the reason that the steel and aluminium industry continues to manufacture fixed sizes is due to economic reasons a n d m a n u f a c t u r i n g s i m p l i c i t y. F o r instance, because aircraft wings are thinner at the tip than the centre, a perfectly uniformed plate will need to be wedged into the shape of the airfoil. Also, can makers, similar to cookie-making, want circular disks of aluminium sheets to make t he c a ns . Howe v e r, t he y r e c e i v e perfectly rectangular sheets from which they blank circles and send the leftover scrap for remelting. Poor tessellation will cause us to scrap 26% of all liquid steel and 41% of all liquid aluminium; this is recycled and melted in an energyintensive process, once again contributing to the total global carbon footprint. Imagine pieces of scrap that might never end up in any components or applications but are forever part of a permanent energy-demanding cycle! Liquids solidif y from the outer surface into the inner surface, and for liquid metals with complex compositions, the whole

composition of the remaining liquid changes. As a result, the head and tail of each aluminium cast are removed by scalping. After casting, most steel and aluminium are rolled out, which has a significant throughput in the middle of each coil or place, forcing the head and tail of any rolled material to be cut off. At the same time, the cracked edges formed during rolling are also trimmed. This will already contribute to around 25% of all yield losses in steel and a further 40% of all yield losses in aluminium. A d d i t i o na l l y, a l t h o u g h m o s t s h e e t s are supplied flat, their final product is not flat in use. This requires the c o m m o n p r o c e s s o f ‘ d e e p d r a w i n g ’, which is forming and moulding the flat sheet into shape. If a sheet is formed without gripping its edges, a cup, for instance, will be very s h a l l o w a n d t e a r. S i m i l a r l y, i f e d g e s are not restrained, the edges will wrinkle. Deep drawing allows the gripping of the edges to prevent wrinkling and tearing. A ver y clever and efficient process at that; howe v e r, i t r e q ui r e s a b o u t 25mm t o be trimmed from each finished part - leading to a further yield loss of about 15%.

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Potential solutions to reduce yield losses Designers of metal components are largely unaware of the implications of their geometric choices, but they could employ potential designs with tessellating or nearly tessellating shapes. Let ’s take a look at the clothing and textiles i n d u s t r y. T h e y f a c e a s i m i l a r c h a l l e n g e f o r f a b r i c , and have now developed sophisticated computer algorithms to maximise clothing yield from rolls of fabric. In fact , many cut out the fabric with fast laser cutters to further optimise blanking patterns. Sp e a k i n g t e c h n i c a l l y, i f w e ha d a l a r g e v a r i e t y of shapes, the chance of finding small pieces to f i t i n b e t we e n la rg e r o ne s is hi g he r, i nc r e as i ng t h e y i e l d . Ye t a t p r e s e n t , t h e b l a n k i n g p r o c e s s e s used in cutting parts from metal are designed to cut one piece from the coil then move forward to cut the same shape again along the coil, giving very little opportunity for tessellation. Similar t o t h e t e x t i l e i n d us t r y, l a s e r c u t t i n g f o r m e t a l is o c curr i ng ; howe v e r, t he pr o c e s s is r e lat i v e l y s l o w, ma k i n g i t v e r y d i ff i c u l t t o c o m p l e t e l y translate fabric cutting into metal sheets.

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Many exciting manufacturing technologies are under development , and the whole field of 3D printing has attracted a lot of attention. The 3D printing machine can essentially make shapes and objects programmed into it. For example, the aerospace industry is looking at making complex parts of titanium using this new t e c h n o l o g y. 3 D p r i n t i n g f o l l o w s a p r o c e s s k n o w n a s ‘selective laser melting’ where the powder of the material is placed under a scanning laser that then draws the pattern of the product , melting and bonding t h e p o w d e r. T h i s p r o c e s s r e p e a t s u n t i l a l l l a y e r s a r e formed. 3D printing has its drawbacks, however : only powdered metals are usable, which is formed by energy-intensive processes of spraying and freezing, lasers are energy-demanding, printing rate is slow a n d s u r f a c e s a n d s m a l l c o r n e r s c a n b e o f b a d q u a l i t y.

Over-specification The cost of steel is lower compared to the cost of labour in developed countries, so it is generally cheaper to save the cost of labour than to save materials. During construction, designers do not ever want a lack of materials to be a concern or a problem since when everything is in excess, the risk of a m a t e r i a l p r o b l e m i s l o w e r. I n g e n e r a l , t h e m a i n d r i v e r of over-specification is conser vatism. Designers often over-specif y the amount of steel in a building by 3040% even though they rarely have been required to use this surplus; they are concerned that clients will change the specification of their buildings at a late stage, so they factor and build in extra capacity ‘just in case’ any plans change. In a case where clients ask for lightweight, efficient buildings, designers know exactly what to do and can lead to a saving of 50% of the material used. This suggests that over-specif ying is not a technical challenge and may even reduce the overall cost , but will only occur through conscientious clients requesting it. After the analysis of 23 buildings in London, a report found that on average only 50% of the steel in their beams was utilised in meeting the standards, suggesting that if we met Eurocode requirements rather than exceeding it , we can cut emissions from commercial buildings by 80%.

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Illustration by Tina Wu

PHYSICS AND TECHNOLOGY

2. ADAPTED DESIGNS Structural optimisation is a discipline dealing with the optimal design of load-carrying mechanical structures to minimise the total weight of the structure subject. Apart from aerospace applications where every extra mass makes a big difference, optimisation is rare and is usually only limited to small moving parts.

Beams Figure 1 shows a simple point load supported by an arm some distance from a wall. It can r e p r e s e n t a c r a n e o r a b a l c o n y . To make sure the arm won’ t break , we need to ensure it is strong enough by designing for stiffness rather than strength. The arm from Figure 1 has a uniform load spread, so it is most likely to break at the wall. For a stronger arm that won’ t break at the wall, we want it deeper near the wall and shallower near the tip. This brings us to Figure 2, a more optimised design in which the depth of the arm varies, giving the arm a high stiffness at the t i p . A l r e a d y, F i g u r e 2 i s l i g ht e r than Figure 1 by 16% and has r e d u c e d me t a l us e . Howe v e r, b o t h the first and second beam would fail when a load is applied. The Figure 2 beam’s failure will star t at the upper and lower surfaces. L o g i c a l l y, i t ma k e s s e n s e t o have more material on the upper

and lower surfaces and make t h e m i d d l e t h i n n e r. T h i s t h e o r y brings us to Figure 3, in which the cross-section of the beam l o o k s l i k e a c a p i t a l “ I ”. T h i s i s t h e standard form in which structural steel is used. I-beams are made by rolling with specially shaped rollers with the same crosssection along their length due to manufacturing convenience. If we compare Figure 1’s design with a standard I-beam with constant cross-section, 54% of the mass is saved; if we then compare Figure 1’s design with Figure 3’s variable I-beam, there is another 85% reduction in mass. As loading increases, the required deflection must decrease, and to do so, the cross-sectional area m u s t i n c r e a s e . We s h o u l d a i m t o reduce the required loads and increase allowed deflections - an application already being used in t h e i n d u s t r y.

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1. 2. 3.

Standard universal I-beams are the key components of steel-framed buildings. They are designed for bending stiffness and used as horizontal beams to support floors and roofs; they are manufactured in a standardised set of geometries and listed by steel producers. Within the list, their geometry is constant; a constant cross-section is chosen for ease of manufacture, so it is not p e r f e c t l y e ff i c i e nt . Howe v e r, o nc e a ga i n, clients will often over-specif y ‘just i n c a s e ’, w h i c h m a y b e q u i t e w a s t e f u l knowing that the office is already strong enough to hold a swimming pool on e a c h f l o o r. O v e r - s p e c i f i c a t i o n o c c u r s i n construction because of a process called rationalisation. A young civil engineer would choose to design a building according to standard codes and choose t he o pt i mum b e a ms ; howe v e r, whe n a n older and more experienced engineer reviews the design, he or she will reduce the number of different beam sections required. This decision simplifies the job for building contractors because of the lower cost of steel compared to the cost of labour in developed countries.

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Steel reinforcing concrete In an exploration of beams in construction, there are obvious and significant opportunities to reduce metal use, but they are not currently taken because of the h i g h e r r e l a t i v e c o s t s o f l a b o u r. T h e example used here would be steelreinforcing bars, commonly known as rebars. They are extensively used to provide structural reinforcement for concrete. Concrete is made of ceramic and other aggregates, making them strong in compression but weak in tension. On the other hand, steel rebars have properties opposite to those of concrete strong in tension, but weak in compression - and, thus, are added to provide tensile strength to concrete. Since rebar designs are often constrained by strength rather than stiffness, the selection of a stronger steel type to make the rebar would mean less material is needed to provide the same tensile strength. So if stronger steel were selected to make the r e b a r, mas s r e q ui r e d c o ul d a l r e a d y be reused. There is a degree of rationalisation in the selection and in the layout of reinforcing steel since bars of the same diameter and same spacing are used across large areas to simplif y detailing, identification, laying and checking. This adds 15-30% more reinforcing steel than is strictly required to me e t c o d e s . Mo r e o v e r, t he r e is a different issue with the overspecification of loads with rebars. Un f o r t u na t e l y, e v e n i f t h e b u i l d i n g as a whole is designed without over-specification, designers and

contractors would still make choices m a k i n g e x c e s s r e b a r. T h i s i s b e c a u s e the simplicity and speed in laying out rebar in simple geometries at a single spacing and with as little different bar diameters as possible reduce the risk of mistakes and make inspections e a s i e r. On a more positive note, modern computer control systems such as Qube can design meshes with var ying lengths, spacing and diameters. They minimise overspecification with an advanced finite element approach for designing and detailing reinforcement using the Bamtec prefabricated rolled reinforcement carpet system. These carpets typically comprise of smaller diameter bars which are placed at a reduced spacing to achieve the same reinforcement area required by design. These rolled carpets are robotically manufactured and read from detailed drawings. These complex bar sequences significantly reduce the degree of rationalisation without any loss of stiffness. Each bar is spot welded to thin gauge steel straps during manufacture and can quickly and easily roll out when transported to the construction site. Although it is not necessarily what is happening in practice, Qube’s approach is an attractive example of intelligent innovations that can lead to material savings. It is estimated that if size and placement optimisation is carried out to its maximum, we could reduce 15% of global rebar production.

PHYSICS AND TECHNOLOGY

To p o l o g y To p o l o g y o p t i m i s a t i o n t a k e s a 3 D d e s i g n a n d l i t e r a l l y removes material from it to achieve the most efficient design. There is no concern about aesthetics, traditional approaches, and any other usual design c o n s t r a i n t s . We s t a r t w i t h a v e r y regular finite element analysis, FEM, of mesh occupying design space where the initial analysis will show the stress distribution and efficiency throughout this design space. The optimiser will remove the elements not under so much stress a n d w i t h l i t t l e s t r a i n e n e r g y. A s the areas are removed, the overall structure is analysed and checked to observe any changes. The topology optimisation of structures has proven to be a valuable tool for the identification of best concepts in the early phases of the design process. To p o l o g y o p t i m i s a t i o n w o n d e r f u l l y embodies the definition of material sustainability and is entirely a d a p t e d i n t o m o d e r n t e c h n o l o g y. It is widely used in the lightweight design of structures in the a u t o m o t i v e a n d a e r o s p a c e i n d us t r y, as well as civil, material, and bioengineering with the aim of further expansion into other industries. In the beginning, the design variables are selected, and limitations of these variables and system performance factors such as stress and buckling are defined. By changing variable values, we can test to see how different changes can give the best combination among the design space. Design variables, size, and properties of materials are selected t o b e o p t i m a l . To p o l o g y o p t i m i s a t i o n h e l p s t o a c h i e v e efficient designs within a small time inter val. With the help of FEM software, we can check designs for range, different loads and conditions and design and manufacturing constraints. Nowadays, we can use drawing software in forming different topologies and alter old designs to produce new alternative ones in virtual environments.

PHYSICS AND TECHNOLOGY

Conclusion By using less metal in designs for all steel and aluminium, we could potentially use 30% less metal than we do at present , with no change in the level of material service provided, simply by optimising product designs and controlling loads they experience. In fact, it can lead to a 30% reduction in all emissions associated with steel and aluminium production. The consequence of this saving would actually lead to a greater reduction in emissions than estimated due to three co-benefits demonstrated with moving articles:

In any moving application, lighter vehicles use less fuel. If we stopped compensating for weight saving by introducing new luxury features, we would have reduced emissions even more than our estimate.

Lighter weight products have improved performance. Lighter cars accelerate, brake and turn better and lighter shipping containers can be lifted more r a p i d l y.

One lighter component leads to another lighter component. The weight of the structure of oil rigs below its surface depends on the weight of the topsides, and the decreased weight o f t r a i n s l e a d t o r e d u c e d r a i l w e a r.

In general, there are different motivations for and against metal conservation in different industries. It is not only the size that benefits or the weight saving that motivates change but also other factors of costs and the preferences of customers.

PHYSICS AND TECHNOLOGY

two. M AT E R I A L R E U S E

PHYSICS AND TECHNOLOGY

1 . M A N U FA C T U R I N G S C R A P C u r r e n t l y, 35% o f t h e w o r l d ’ s s t e e l i s m a d e from scrap, and the rest is from newly mined ore. Metal scrap is essentially the leftover product of manufacturing and consumption, such as parts of vehicles, building supplies and surplus materials, which are then put to use and returned to the c ycle again. Using m e t a l s c r a p c a n s a v e e n e r g y. Ma k i n g liquid steel from steel scrap requires one-third of the energy needed to make the same steel from ore, emitting less than one-quarter of the carbon dioxide e mis s i o ns . Howe v e r, s c ra p r e c y c l i ng involves melting with a temperature of around 1500 degrees Celsius, adding to the energy required. Overall, steelmaking accounts for 9% of global carbon dioxide emissions, of which 1% is directly from steel scrap melting. Now looking at aluminium, one-third of the world’s aluminium is made from scrap. Since producing liquid aluminium from scrap needs around 20 times less energy than from ore, recycling aluminium is much more attractive and in demand. Recycling both steel and aluminium may seem like a very energy-efficient process compared to the energy needed from making new metal from ore, thus increasing recycling rates in the metal i n d u s t r y. H o w e v e r, c o n s i d e r i n g t h a t global metal demand will almost double over the next 40 years, the total energy required and the carbon footprint from scrap recycling will be very significant. Is there an alternative? Albeit on a small scale, metal reuse without melting is already possible. By making the right design choices, looking into emerging technologies, and adopting more collaboration between different sectors, limitations of metal reuse can be surpassed and metal reuse can be deployed on a large scale.

PHYSICS AND TECHNOLOGY

Right design choices Without standardisation, disassembly is expensive, unless products are designed with disassembly in mind. For instance, to reuse components, we want to find components that can easily separate from parent products, without an overall effect on others, with just superficial change o r s i mpl e t r i mmi ng. Mo r e o v e r, structures are built upon the premise of certified elements and well-executed fabrication and erection, along with marked standard specifications. Engineers, without the pressure of time, look favourably upon reusing steel and will most definitely enjoy an interesting challenge. Most of them would have no problem using r e us e d s t e e l ; howe v e r, t he s t e e l would have to be certified with the required properties and pass a controlled supply chain process. This will not only reassure the engineers but also gain a client ’s confidence. Hence, reuse of construction materials would only be adopted by engineers and clients if the material properties are known. A way of doing so is at regular intervals; we can mark and regulate different steel sections with information to determine steel s i z e , g ra d e a n d q u a l i t y, r e m o v i n g the need to test and certif y the steel at the end of its life. The 1990s saw a shift from manual labour to mechanised demolition methods, further driven by governmental pressure to reduce

health and safety risks and by commercial pressure for timesaving. Demolition machines badly deform steel, which is not a problem for metals that are recycled through melting, but it is a major barrier to reuse w i t h o u t m e l t i n g . Ye t s i t e o w n e r s have a strong preference towards demolition in deconstruction due to its speed and ease. The consequence of this preference is that even when a building can be deconstructed, contractors will still opt for deconstruction, giving t he i r r e as o n as t i me . Howe v e r, when we look at the timeline, many derelict buildings are left for quite some time after planning decisions are made and before any action starts. By changing the sequence of decisions and effectively using this time for deconstruction instead of demolition, deconstruction can easily become the next norm. Mo r e o v e r, whe t he r i t is d e mo l i t i o n or deconstruction, contractors rarely own large stockyards that can hold large amounts of secondary steel, so they need to find a buyer or storage site before they start their job for the materials to be claimed immediately afterwards. Nonetheless, the economic value of scrap is fairly l o w, c r e at i n g a l o w-p r o f i t ma r g i n and discouraging any incentive to find ways to reclaim steel for reuse - a cycle that will repeat itself if we don’ t add other factors.

PHYSICS AND TECHNOLOGY Un f o r t u na t e l y, o u r w o r l d ha s o t h e r i n c e nt i v e s n o t t o b e e c o - f r i e n d l y. M o s t m a n u f a c t u r e r s d o n o t s e e s c r a p as part of their core business resulting in production lines designed without considering the value of scrap. Larger blanking skeletons are chopped into small pieces for ease of handling and to prevent disruption to overall construction, instead of considering factors such as where to cut to minimise scrap produced. For instance, the aerospace industry places a high priority on the weight of materials, meaning 90% of high-quality aluminium is turned into chips. They will sell swarf with alloys mixed for a price of around 1% of what they pa i d f o r, y e t s wa r f c a n b e up to 90% of their output. Looking on the bright side, Abbey Steel, a family run business, buys steel obtained from a diverse range of UK manufacturing industries and resells the processed sustainable s t e e l b a c k i n t o t h e i n d u s t r y. Industries consume large amounts of steel, leading to the production of waste material, a byproduct of this process. These waste materials cannot be used in any of the processes and are destined to be recycled through smelting. Abbey Steel steps in and reclaims the steel to be trimmed and put back into the supply chain - “reused n o t r e c y c l e d ”. B y d o i n g s o , the only energy required is for transportation and reprocessing of the steel, already reducing carbon dioxide emissions to 2.3 tonnes of CO2 per tonne of metal. Abbey Steel - the world’s first green brand of sustainably sourced steel - has been created to showcase a prime steel byproduct sourced from multi-industr y applications. This environmentallyfriendly inspiration would be able to grow its business further if people were more willing to segregate more cut-outs for sale, especially to have car manufacturers hand over scrap.

PHYSICS AND TECHNOLOGY

Emerging innovative technologies New creations such as solid bonding can bond aluminium chips into solid material without any melting, potentially replacing recycling by melting. Solid bonding is welding without addition of a brazing filler at a temperature below a metal’s m e l t i n g p o i n t . To b e g i n w i t h , clean chips of a single alloy are compressed under high pressure and at a temperature of 450-500 degrees celsius. The high pressure and extension cause surface oxide layers to crack , revealing reactive aluminium metal which can be welded into a solid product. The oxide remains on the interface, but as an applied strain stretches the material, clean metal becomes exposed. Entrapped air oxidises some of the exposed metal and, provided the strains are great enough, clean metal will be extruded through cracks in the oxide. Solid

bonded chips require 100 times less energy than the manufacture of primary aluminium, reducing carbon dioxide emissions by 96%. Although the solid bonded material shows a reduction of around 10% in ultimate tensile strength and 15% i n d u c t i l i t y, f u r t h e r d e v e l o p m e nt can potentially reduce these differences. Overall, the surface quality and bonding of the bar pieces were ver y good. At the same time, many applications, including aluminium window frames, do not actually demand the full strength and full ductility of aluminium, meaning sustainable solid bonded material can be used here instead. If more trials succeed, the technology of solid bonding could soon be seen in the market - reusing 100kt of aluminium scrap would avoid up to 750kt of carbon dioxide emissions.

PHYSICS AND TECHNOLOGY

Adopting collaboration between different sectors

The lack of trust between sectors about the quality of steel can be a central problem and deter them from s t e e l r e u s e . Ve r y f e w w i l l c o n s i d e r reused steel if it costs more or takes mo r e t i me . Howe v e r, s o me d e lay s can be tolerated if the costs are lowered, or on the other hand, one may decide to pay more to speed up t h e p r o g ra m. Aft e r s u r v e y i n g ma n y, there is a common perception that reusing steel is difficult, and there is an overall scepticism over steel reuse across the supply chain. The considerable difference between the perception of barriers and the experienced barriers indicates the lack of communication across the s u p p l y c h a i n . To l i s t , f a b r i c a t o r s are prevented from steel reuse due to the lack of the certification of the steel and the fact that the practice is uncommon; stockists have business models that will not allow long-term steel storage and there is no large cheap storage land, making it not economically viable. Demolition contractors also face the lack of a reliable market for reused steel, and structural engineers are p r e s s e d f o r t i m e . On t h e c o nt ra r y, architects, main contractors and structural engineers are protected by this costly structure as they would simply charge higher costs to clients. Nonetheless, green projects do happen if there is a motivation to preserve a valued heritage or if reused elements serve a decorative purpose. Successful steel reuse projects are the result of a willing client and a tightly integrated team that perhaps is responsible for both design and rebuilding. For example, when the owner of the new building also owned the previous building (or has a strong relationship with the previous owner) or when the main contractor

is t he d e s i g ne r, a ny l e ga l unc e r t a i nt y is eliminated. When there is an opportunity for reuse, there are few obstacles to forming a practical plan. Still, there are limitations: structural design usually assumes elements will be fabricated as required, and this might not be the case with reused elements as desired sizes or lengths may not be available, and there would need to be substantial c ha ng e s t o pla n. Mo r e o v e r, t he r e is an old and new perception to reused steel where clients feel that reused steel is inferior and thus refuse to accept reused steel. People can be very stubborn at times and refuse to accept new practices - once again where development of trust and communication is needed. Let us be reminded that if just one sector in the supply chain is unwilling to adopt reused steel, the project cannot and will not go ahead. Building trust can take time, and if the different s e c t o r s hav e no t wo r k e d t o g e t he r, they will rely on common practice and industry norms, meaning s t e e l r e u s e b e c o m e s u n l i k e l y . To overcome this, fabricators can be involved in projects from the start and will have more time to prepare for any uncommon operations. Indeed, as suggested by Allwood and Cullen, steel reuse can play an important part of a global strategy for the efficient use of materials as the carbon and energy embodied in structural frames can represent up to 20–30% of the as sumed 50-year lifetime carbon footprint of a building. “ Steel reuse can play an important part of a global strategy for the efficient use of materials as the carbon and energy embodied in structural frames can represent up to 20–30% of the as sumed 50-year li f e t i m e c a r b o n f o o t p r i n t o f a b u i l d i n g .” “Steel reuse is a potentially excellent strategy and general guidance about the reuse process is available. Nonetheless, widespread r e u s e d o e s n o t s e e m t o o c c u r .”

PHYSICS AND TECHNOLOGY

2. LONGER LIFE PRODUCTS Most demand for products in developed economies isn’ t to expand the overall stock but to replace existing items. For instance, we destroy 33% more fridges ever y year than we make cars. This suggests the need to modif y products and develop adaptable designs.

Reasons for replacing goods:

Degraded failure - the product can no longer be used. For example when clothes are worn out or when metal surfaces are damaged.

Inferior failure - the user has changed, meaning the original product is no longer valuable to existing customers. For example, clothing no longer fits or a two-seater car cannot f i t a n e w b o r n b a b y.

Unwanted failure - the product still functions but is not valued by its current o wn e r. For example, the latest fashion or styling has changed or new legislations are introduced.

For degraded components, we can intervene through design changes, possible restoration to original speciation, or condition monitoring and maintenance for better prediction of when a component needs replacement or restoration. In fact , all of these practices are already i n u s e ; h o w e v e r, i t s h o u l d b e a p p l i e d a t a l a r g e r s c a l e a n d m o r e w i d e l y. Construction quality measures how a particular work meets the demanded requirements of that project. Durability is a quantifiable indicator informing us of the extent to which a material maintains its o r i g i na l r e q u i r e m e nt s . E v i d e nt l y, t h e g r e a t e r t h e ma t e r i a l d u ra b i l i t y, the lower the time and resources required to maintain it becomes.

PHYSICS AND TECHNOLOGY In the case of some assets, it is assumed that through their service life they shall r e c e i v e pr o p e r ma i nt e na nc e . Howe v e r, i n t he c o n s t r u c t i o n i n d us t r y, t h i s i s n o t t h e c a s e a n d buildings are not catered for maintenance. With some exceptions, for example, an oil rig placed in the Nor th Sea has a guaranteed ser vice life. Buildings are rarely demolished due to a performance failure but instead, their value to owners or tenants has declined, classif ying them as unsuitable or unwanted. Same goes with cars; the second-hand car industr y is big and growing, not because the car cannot function anymore, but because the first owner wants it replaced due to p e r s o na l a nd s o c ia l r e as o ns . Mo r e o v e r, e l e c t r i c cables could technically last for years, but due to population growth and those who are hungry for t h e l a t e s t t e c h n o l o g y, o l d e r c a b l e s mus t t ra n s m i t power beyond the original design load, making it u n s u i t a b l e . We u s u a l l y d i s c a r d o u r f r i d g e b e c a u s e it is a few millimetres short of lubricants in s ma l l b e a r i ngs i n f r i d g e c o mpr e s s o r s . Howe v e r, replacing compressors can be labour-intensive as they are designed to be sealed and not replaced. As we are aiming to reduce metal demand, we must start identif ying the areas likely to fail and start designing the products so that there is a simple a n d c o m m o n m e a n s t o r e p l a c e t h e f a i l e d p a r t s o n l y. Due to the imminent danger related to environmental issues and growing public awareness, governments around the world have been forced to implement stricter environmental policies that have s u c c e s s f u l l y d r i v e n s o m e c ha n g e s . Un d o u b t e d l y, these force organisations to play a greater role in recycling activities, regardless of costs. R e ga r d i n g m e t a l s us t a i na b i l i t y, i n d e v e l o p i n g and underde veloped countries , 1-2% of the population makes a living by picking recyclable waste to sell - an area not often looked at with much significance. In fact , the efficiency of waste collection is so high that hardly any metal will go to the landfill. Although much of today ’s wastepicking activities remain unregulated or nonformalised, international organisations have been working to formalise and organise these wastepickers. The importance of a comprehensive policy framework to address the issue of recycling a c t i v i t i e s a nd me t a l r e c y c l i ng , i n pa r t i cula r, c a n not only enhance employment opportunities but also promote a cleaner environment.

PHYSICS AND TECHNOLOGY

CONCLUSION In this article, we have explored ways of addressing material sustainability divided into two sections: material design and material reuse. Under ‘ Material D e s i g n ’, w e d i s c o v e r e d t h e r e a s o n f o r materials not being used to their full potential: manufacturing simplicity and over-specification. Regarding the reasons explored, we consider potential solutions to maximise material usage, including adapted engineering designs and newly invented technologies. Then moving onto the second method of a c h i e v i n g ma t e r i a l e f f i c i e n c y, t i t l e d ‘ M a t e r i a l R e u s e ’, w e l e a r n t a b o u t t h e metal recycling processes and what limits the lack of material recycling i n t h e c o n s t r u c t i o n i n d u s t r y. We a l s o investigated how just by extending the p r o d u c t ’s l i f e e x p e c t a n c y, w e c a n a c h i e v e a large decrease in carbon emissions. To c o n c l u d e , t h e r e a r e m a n y i n g e n i o u s and innovative ways to reduce material usage, but whether or not they are adopted depends heavily on many other factors. In the future, material demand, especially metals, will only e v e r i n c r e a s e . We n o t o n l y n e e d t o s t a r t researching ways to meet these demands but also need conscientious people to carry out the plans and think for the b e t t e r m e n t o f s o c i e t y. R e g a r d i n g t h e reduction of global carbon footprints, material sustainability has much potential. As scientists, engineers, and conservationists, we need to find ways to overcome the many limitations material sustainability has brought and will bring to us and, on top of that , pave new paths for the generations to come.

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Bibliography A b b e y, To n y. “ W h a t I s To p o l o g y Optimization and Why Is It Useful?” P T C , P T C , 2 7 Ju l y 2 0 2 0 , w w w. p t c . com/en/blogs/cad/what-is-topologyoptimization. “A b s o l u t e Z e r o . ” U K F I R E S , u k f i r e s . org/absolute-zero/. Admin, Abbeysteel. Abbeysteel™ and Shearing Co Ltd - Steel Stockholder a n d S u p p l i e r o f C u t S t e e l B l a n k s , w w w. abbey-steel.co.uk/welcome/. A l l w o o d , Ju l i a n M . , e t a l . S u s t a i n a b l e Materials: with Both Eyes Open. UIT Cambridge, 2012. “ B e a m a n d Tr u s s B r i d g e s . ” B r i g h t H u b E n g i n e e r i n g , 8 M a r. 2 0 1 0 , w w w. b r i g h t h u b e n g i n e e r i n g. c o m / s t r u c t u r a l engineering/65884-construction-ofbeam-and-truss-bridges/. Buildsum. (2014, May 03). Why use r e i n f o r c e m e n t i n C o n c r e t e . Re t r i e v e d D e c e m b e r 0 3 , 2 0 2 0 , f r o m h t t p s : / / w w w. youtube.com/watch?v=vuZcPTp51Zk B u r j K h a l i f a : Ta l l e s t B u i l d i n g i n t h e Wo r l d - M e g a S t r u c t u r e s N a t i o n a l Geographic. (2016, August 04). Re t r i e v e d D e c e m b e r 0 3 , 2 0 2 0 , f r o m h t t p s : / / w w w. y o u t u b e . c o m / watch?v=xsVUsk82Qtw C o l l i n s , D. , S a y s , A . , & A z a m . ( 2 0 1 9 , November 29). Stiffness and def lection: Mechanical properties of materials. Re t r i e v e d D e c e m b e r 0 3 , 2 0 2 0 , f r o m h t t p s : / / w w w. l i n e a r m o t i o n t i p s . c o m / mechanical-properties-of-materialsstiffness-and-deflection/ C o o p e r, D a n i e l R . , a n d Ju l i a n

M. Allwood. “The Influence of Defor mation Conditions in Solid-State A l u m i n i u m We l d i n g P r o c e s s e s o n t h e Re s u l t i n g We l d S t r e n g t h . ” Jo u r n a l o f M a t e r i a l s P r o c e s s i n g Te c h n o l o g y, v o l . 2 1 4 , n o. 1 1 , 2 0 1 4 , p p. 2 5 7 6 – 2 5 9 2 . , doi:10.1016/j.jmatprotec.2014.04.018. D u n a n t , C y r i l l e F. , e t a l . “ O p t i o n s t o M a k e S t e e l Re u s e P r o f i t a b l e : A n Analysis of Cost and Risk Distribution a c r o s s t h e U K C o n s t r u c t i o n Va l u e C h a i n . ” Jo u r n a l o f C l e a n e r P r o d u c t i o n , E l s e v i e r, 1 5 Fe b . 2 0 1 8 , w w w. sciencedirect.com/science/article/pii/ S0959652618304542. Gaille, Louise. “13 Beam Bridge Pros a n d C o n s . ” V i t t a n a . o r g , 1 9 M a r. 2 0 1 8 , vittana.org/13-beam-bridge-pros-andcons. M i l l e r, B r a n d o n . “ 1 4 Tr u s s B r i d g e s Advantages and Disadvantages.” Green G a r a g e , 2 7 M a r. 2 0 1 9 , g r e e n g a r a g e b l o g. org/14-truss-bridges-advantages-anddisadvantages. Wo r l d E c o n o m i c Fo r u m . ( 2 0 1 6 , Fe b r u a r y 19). Self-healing concrete for lowcarbon infrastructure | Abir AlTa b b a a . Re t r i e v e d D e c e m b e r 0 3 , 2 0 2 0 , f r o m h t t p s : / / w w w. y o u t u b e . c o m / watch?v=8QXVwU82wrw S e r g e n t , Fr a n . “ M a t e r i a l D e m a n d Re d u c t i o n i n B u i l d i n g s . ” T h e U s e L e s s G r o u p , 8 A p r. 2 0 1 9 , w w w. u s e l e s s g r o u p . org/research/buildings. Ye l l i s h e t t y, M o h a n , e t a l . “Environmental Life-Cycle Comparisons o f S t e e l P r o d u c t i o n a n d Re c y c l i n g : Sustainability Issues, Problems and Prospects.” Environmental Science & Po l i c y, v o l . 1 4 , n o . 6 , 2 0 1 1 , p p . 6 5 0 – 663., doi:10.1016/j.envsci.2011.04.008.

Biology and Chemistr y

Illustration by Reika Oh

BIOLOGY AND CHEMISTRY

Psychedelics: Voodoo or Science?

Warren Zhu

What images pop out when you hear LSD, DMT and Magic Mushrooms? Hippies running around naked with flowers around their neck? Or freshmen parties streaming with vomit and chants? Ye s , y e s , y e s . T h e r e c k l e s s u s e o f psychedelic drugs is almost invariably tied to the Hippie movement star ting from the 60s, and most have been criminalised since then. Most would silently walk away from the hippies chanting love and peace and sex ; it all seems pretty voodoo and nonsensical. But what if I tell you that psychedelics have been shown to do the following:

1 . Rc ae nl iceevre pdaet ai et hn t as n(x8i 0e %t y of rf ocma n c e r

patients demonstrated clinically significant reductions in anxiety)

2 . Suppress depression 3 . Aa dl ldeivci tai toen a(l8c0o%h oal /f tt eo rb a6 cmc oo n t h s , 67% after 1 year for tobacco)

4 . Improve OCD symptoms 5 . Increase the personality

trait of Openness to Experience, which correlates with creativity and empathy

Why do these drugs under the ‘Psychedelics’ umbrella have such a huge effect ? Is it just bad science or is there really something behind these infamous Hippie drugs?

BIOLOGY AND CHEMISTRY First , let ’s look at the chemical structure of psychedelics.

T he Chem ic al Structure

The organic compound tryptamine is common in all psychedelics (See Fig. 1). Tr y p t a m i n e i s o n e of the signalling F i g . 1 Tr y p t a m i n e ( C 1 0 H 1 2 N 2 ) molecules used between cells in plants, fungi, and animals. Perhaps the most famous of the tr yptamines is the neurotransmitter serotonin. An elevated level of serotonin correlates to a decreased l e v e l o f a n x i e t y, a n e l e v a t i o n i n m o o d , a n d r e l i e f of distress. The tryptamine in the psychedelic compounds has a complementary shape with a serotonin receptor called 5-HT2A , meaning t hat i t c a n b i nd t o a nd a c t i vat e t he r e c e pt o r, mimicking the effects of high levels of serotonin. What is more incredible is that LSD’s affinit y to the serotonin receptor 5-HT2A is even better than serotonin itself! It is better than serotonin at fitting into a receptor designed for serotonin!

Illustration by Isabel Chau

BIOLOGY AND CHEMISTRY Effects on the Brain

Our brain is normally pretty rigid. There are a few neural pathways that we us e o ft e n, a nd t ho us a nds t hat a r e b a r e l y a c t i vat e d. Howe v e r, und e r the influence of psychedelics, one approaches a semi-dreamlike state, with thousands of novel brain pathways lighting up and uncommon connections forming. In technical jargon, there is an increase of ‘entropy ’ in the brain, making it more disorderly and chaotic. This can yield a plethora of benefits, as it provides a whole host of new thoughts and ideas that normally would not be conjured by oneself. This can be a source of creativity and a way to increase one’s empathy towards others. The leading hypothesis is that these novel connections are being made because of the decreased activity of an area of the brain called the ‘default m o d e n e t w o r k ’. T h i s i n c l u d e s t h e m e d i a l p r e f r o n t a l c o r t e x , t h e p o s t e r i o r cingulate cortex , the hippocampus, the inferior parietal lobe, and the temporal lobe. The ‘default mode network ’ is the part of the brain that causes you to think about all the preps that you haven’ t done and all the lessons that you’re having but don’ t want to have in the middle of an intensely boring lesson; it generates the constant chattering of the mind and is also turned off when skilled meditators are meditating. In this sense, the mind of a person on a psychedelic trip bears resemblance to a person in deep meditation. As the activity of the ‘default mode network ’ decreases, the sense of the self as a separate entity from the w o r l d d i m i n i s h e s t o o . A t t h i s s t a g e , t h e r e i s a s o r t o f ‘ e g o d e a t h ’, i n w h i c h one feels completely merged with the world. (Bear with me, I know this sounds pretty voodoo.) This may be the reason for the miraculous effect of p s y c h e d e l i c s o n r e l i e v i n g d e a t h a n x i e t y, a s d e a t h i s t h e d i s s o l u t i o n o f t h e d i s t i n c t b o u n d a r i e s b e t w e e n ‘ t h e m ’ a n d ‘ m e ’, i n w h i c h o n e i s r e t u r n e d t o t h e wo r l d as a p i l e o f o rga ni c matt e r, wa i t i ng t o b e d e c o mp o s e d a nd r e us e d. I will elaborate further in the conclusion of the ‘entropic brain hypothesis’ which will help us to conceptualize why psychedelics have these effects.

BIOLOGY AND CHEMISTRY

Illustration by Joy Chen

BIOLOGY AND CHEMISTRY Voodoo or Science? It is clear that the use of psychedelics, especially under professional guidance and advice, can dramatically alter one’s perspective on life and improve one’s q ua l i t y o f l i v i ng. Howe v e r, mo r e research is needed to determine how much of the observed effect comes from psychedelic rather than the placebo effect, and how much is really due to the compound itself. This is evident in how much a psychedelic experience relies on the purposeful creation of an environment that is conducive to its use, and how drastic a difference there is between recreational use of the drug and clinical use of the drug. The effects of psychedelics may partly be attributed to a ‘self-fulfilling prophecy ’ in which one’s expectation for the drug’s effectiveness ultimately makes the drug effective. Some researchers have postulated that psychedelics a r e n o m o r e t h a n a n ‘ a c t i v e p l a c e b o ’, meaning that psychedelics merely assist one in actualising one’s expectation of their effects instead of having any real effects themselves. This is further complicated by the fact that a double-blind controlled experiment is almost impossible to conduct with psychedelics simply because of the unique effects of t he d r ug. Mo r e o v e r, i t has a lway s been known that the placebo effect is the strongest in the newest drug due to the mysterious aura surrounding its existence.

Considering the mystery surrounding psychedelics and the cultural taboo around psychedelic drugs, the placebo effect may be exaggerated f u r t h e r. As you can see, it is all a big hot me s s . Howe v e r, t he r e is s t i l l g r e at hope about the effectiveness of psychedelics. For example, one of the leading hypotheses is the ‘entropic brain hypothesis’ which states that because psychedelics increase the entropy (disorder) inside the brain, the brain’s normal way of functioning is disordered and one can jump out of the previous rigid way of thinking. Depression, under this hypothesis, is a mode of operation in which one has trapped oneself within a solely pessimistic view of the world, and addiction, too, is the brain craving for order and returning to its default way of operating.

Perhaps it is fair to say that psychedelics are voodoo and science - where the immeasurable spiritual and materialistic sciences coincide and synthesise. And, at the end of the day, why should we even care, so long as they help and save lives?

BIOLOGY AND CHEMISTRY

Photo by Isabel Chau

BIOLOGY AND CHEMISTRY Bibliography Barrett, Frederick S., Hollis Robbins, David Smooke, Jenine L. Brown, and Roland R. Griffiths. “Qualitative and Quantitative Features of Music Reported to Support Peak Mystical Experiences During Psychedelic Therapy Sessions.” Frontiers in Physiology 8 (July 2017): 1–12. doi:10.3389/fpsyg.2017.01238. B o g e n s c h u t z , M i c h a e l P. , A l y s s a A . F o r c e h i m e s , J e s s i c a A . P o m m y, C l a i r e E . W i l c o x , P. C . R . B a r b o s a , a n d R i c k J. Strassman. “Psilocybin-Assisted Tr e a t m e n t f o r A l c o h o l D e p e n d e n c e : A P r o o f - o f - C o n c e p t S t u d y. ” J o u r n a l o f Psychopharmacology 29, no. 3 (2015): 2 8 9 – 9 9 . d o i : 1 0 . 11 7 7 / 0 2 6 9 8 8 111 4 5 6 5 1 4 4 . B r e w e r, J u d s o n . T h e C r a v i n g M i n d : F r o m Cigarettes to Smartphones to Love—Why We Get Hooked and How We Can Break B a d H a b i t s . N e w H a v e n , C o n n . : Ya l e University Press, 2017. B u c k n e r, R a n d y L . , J e s s i c a R . A n d r e w s H a n n a , a n d D a n i e l L . S c h a c t e r. “ T h e B r a i n ’ s D e f a u l t N e t w o r k : A n a t o m y, Function, and Relevance to Disease.” A n n a l s o f t h e N e w Yo r k A c a d e m y o f S c i e n c e s 11 2 4 , n o . 1 ( 2 0 0 8 ) : 1 – 3 8 . d o i : 1 0 . 11 9 6 / a n n a l s . 1 4 4 0 . 0 11 . Carbonaro, Theresa M., Matthew P. B r a d s t r e e t , F r e d e r i c k S . B a r r e t t , Katherine A. MacLean, Robert Jesse, M a t t h e w W. J o h n s o n , a n d R o l a n d R . Griffiths. “Survey Study of Challenging Experiences After Ingesting Psilocybin Mushrooms: Acute and Enduring Positive and Negative Consequences.” Journal of Psychopharmacology 30, no. 12 (2016): 1268–78. Carhart-Harris, Robin L., et al. “Neural Correlates of the Psychedelic State as Determined by fMRI Studies with Psilocybin.” Proceedings of the National Academy of Sciences of the United States of America 109, no. 6 (2012): 2138–43. d o i : 1 0 . 1 0 7 3 / p n a s . 111 9 5 9 8 1 0 9 . “Psilocybin with Psychological Support f o r Tr e a t m e n t - R e s i s t a n t D e p r e s s i o n : A n O p e n - L a b e l F e a s i b i l i t y S t u d y. ” L a n c e t Psychiatry 3, no. 7 (2016): 619–27. doi:10.1016/S2215- 0366(16)30065-7. Carhart-Harris, Robin L., Mendel Kaelen, and David J. Nutt. “How Do Hallucinogens Work on the Brain?” Psychologist 27, no. 9 ( 2 0 1 4 ) : 6 6 2 – 6 5 . Carhart-Harris, Robin L., Robert Leech,

P e t e r J . H e l l y e r, M u r r a y S h a n a h a n , A m a n d a F e i l d i n g , E n z o Ta g l i a z u c c h i , Dante R. Chialvo, and David Nutt. “The Entropic Brain: A Theory of Conscious States Informed by Neuroimaging Research with Psychedelic Drugs.” Frontiers in Human Neuroscience 8 (Feb. 2014): 20. doi:10.3389/fnhum.2014.00020. Fadiman, James. The Psychedelic Explorer ’s Guide: Safe, Therapeutic and S a c r e d J o u r n e y s . R o c h e s t e r, V t . : P a r k S t r e e t P r e s s , 2 0 11 . G r o b , C h a r l e s S . , A n t h o n y P. B o s s i s , a n d Roland R. Griffiths. “Use of the Classic H a l l u c i n o g e n P s i l o c y b i n f o r Tr e a t m e n t of Existential Distress Associated with C a n c e r. ” I n P s y c h o l o g i c a l A s p e c t s of Cancer: A Guide to Emotional and P s y c h o l o g i c a l C o n s e q u e n c e s o f C a n c e r, Their Causes and Their Management, Grob, Charles S., Alicia L. Danforth, G u r p r e e t S . C h o p r a , M a r y c i e H a g e r t y, C h a r l e s R . M c K a y, A d a m L . H a l b e r s t a d t , a n d G e o r g e R . G r e e r. “ P i l o t S t u d y o f P s i l o c y b i n Tr e a t m e n t f o r A n x i e t y i n P a t i e n t s w i t h A d v a n c e d - S t a g e C a n c e r. ” Archives of General Psychiatry 68, n o . 1 ( 2 0 11 ) : 7 1 – 8 . d o i : 1 0 . 1 0 0 1 / a r c h g e n p s y c h i a t r y. 2 0 1 0 . 11 6 . K i l l i n g s w o r t h , M a t t h e w A . , a n d D a n i e l T. G i l b e r t . “ A Wa n d e r i n g M i n d I s a n U n h a p p y Mind.” Science 330, no. 6006 (2010): 932. d o i : 1 0 . 11 2 6 / s c i e n c e . 11 9 2 4 3 9 . Moreno, Francisco A., Christopher B. W i e g a n d , E . K e o l a n i Ta i t a n o , a n d P e d r o L . D e l g a d o . “ S a f e t y, To l e r a b i l i t y, a n d Efficacy of Psilocybin in 9 Patients with O b s e s s i v e - C o m p u l s i v e D i s o r d e r. ” J o u r n a l o f C l i n i c a l P s y c h i a t r y 6 7 , n o . 11 ( 2 0 0 6 ) : 1 7 3 5 – 4 0 . d o i : 1 0 . 4 0 8 8 / J C P. v 6 7 n 111 0 . N o u r, M a t t h e w M . , L i s a E v a n s , a n d Robin L. Carhar-Harris. “Psychedelics, Personality and Political Perspectives.” Journal of Psychoactive Drugs (2017): 1–10. P a h n k e , Wa l t e r, “ T h e P s y c h e d e l i c Mystical Experience in the Human Encounter with Death. Harvard Theological Review 62, no. 1 (1969): 1–22. POLLAN, M. (2019). HOW TO CHANGE YOUR MIND: The new science of psychedelics. I m a g e source: https://weandthecolor. com/commissioned-illustrations-by-robbieporter/22382

BIOLOGY AND CHEMISTRY

Applications of the Human Microbiome Hanson Wen I n 2 0 0 7, T h e U n i t e d S t a t e s National Institutes of Health research started a project called the Human Microbiome Project [1], which means from then on, the science community had accepted the human microbiome as an important subject. The human microbiome has been chosen as one of the ten science breakthroughs of the year in 2011 by the Science magazine [2]. Other famous science magazines have also started including the Microbiome section from then on. But what is it? The definition of it in simple terms is all of the microorganisms in a human in a specific area such as skin, lungs, mammary glands, placenta and so on.

The microbiome can take up to 4% of your weight and can do many things. For example, scientists have discovered that humans cannot digest seaweed because no enzymes coded by the human genome can break down the carbohydrates that are tangled with sulfur molecules which are within the plant. But what happens when we eat seaweed? There is a type of marine bacteria (Zobellia galactanivorans) that can digest seaweed, and the same kind of enzyme that these bacteria produce has been found in the human-gut bacteria of Japanese individuals [3]. The microbiome can give us power where we are lacking.

BIOLOGY AND CHEMISTRY

Illustration by Se Lyn Lim

BIOLOGY AND CHEMISTRY The microbiome also aids us in other ways. One of them is that it helps your immune system defend y o u r b o d y. B a c i l l u s s u b t i l i s i s a bacterium that has been found to contribute to the activation of the production of antibodies and other useful molecules to help white b l o o d c e l ls f i g ht i nf e c t i o n [4]. Another ability of microbiomes is that it can affect your emotions, and even affect your brain. A study [5] shows that bacteria in your gut produce 95% of the feel-good h o r m o n e , s e r o t o n i n , i n y o u r b o d y. If you extract the gut microbiome of a person in depression and place it in mice, the mice will have symptoms of depression too.

Ho w c a n the m ic ro b io m e affect our emotions? There are three routes to our brain. Fir st is the endocrine s y stem [6]. The hormones that the bacteria produce can diffuse straight into the blood from the brain. The second route is the vagus nerve [7]. The vagus nerve system can not only go from the brain to t h e b o d y, b u t i t c a n a l s o b e b i directional and go from the body to the brain. Last is the lymphatic system [8]. The microbiome can influence the brain through this system, but this system is also bi-directional. A study shows that gut microbiome inflammation can affect depression and anxiety [9]. These systems, combined, can largely influence the host ’s everyday life, even for things such as choosing what you eat.

As you can see, the microbiome can affect the human body quite a lot, but how can we manipulate the microbiome to help us?

A pplications in Medicine There is an infection called Clostridioides Difficile Infection (CDI). It is caused by a spore-forming bacteria called Clostridioides difficile. It produces spores in the g u t o f t h e h o s t ’ s b o d y. O n e w a y o f treating it is to perform a Fecal M i c r o b i o t a Tr a n s p l a n t a t i o n ( F M T ) , which is transplanting the gut microbiome of a healthy person to the gut of a person with CDI. FMT is an effective treatment for C D I [ 1 0 ] . Tr a d i t i o n a l l y , C D I w a s treated using antibiotics such as va nc o my c i n. Howe v e r, w i t h t his method, we have to face the risk of superbugs and also disrupting the balance of the microbiota in the gut. In contrast , FMT restores the beneficial bacterias in the guts, restoring the microbiome, and it also has a high cure rate and low recurrence rate.

A pplications in Sk incare Skincare can be a large market for h u ma n m i c r o b i o m e t e c h n o l o g y, a s microorganisms can significantly affect the skin. [11] “ Physiological effect of a probiotic on skin” shows that S. epidermidis could inhibit acne caused by P. a c n e s b y f e r m e n t i n g glycerol. [12] Many companies are working on microbiota skincare [13]; for ex ample , this [14] “ face vinegar ” (See Fig. 1) uses the same principle as the research I have mentioned above. It contains glycerol which can inhibit the growth of P. Acnes.

Fig 1. A picture of “face vinegar” [15]

BIOLOGY AND CHEMISTRY

Wild Imagination

For now, these are only the cultivated applications of the human microbiome, but as this technology develops, it will change how we live. This is a wild imagination of the future as this technology develops.

BIOLOGY AND CHEMISTRY Yo u o p e n y o u r g r o g g y e y e s , lug yourself off the bed and drag your body to the kitchen. The coffee maker screeches so you pick it up and add coffee p o w d e r . Yo u t h e n a d d a s m a l l packet of gooey stuff into it. It dissolves into your hot coffee a n d a s y o u d r i n k i t . Yo u c a n f e e l the smooth lubricating feeling of the coffee going down your throat. The microorganisms in the packet stick to your throat, keeping your throat moisturised for 2 hours. As it finally touches down on the stomach, the rest of the living organism reaches your gut. It slowly spreads, causing a nice warm feeling in your body that makes you h a p p y f o r t h e r e s t o f t h e d a y. Yo u a r e o n y o u r w a y t o w o r k and touch the sticky handle of the metro. There are harmful bacteria that cause flu if it gets in your body fluid. The microhand sanitizer you applied this morning is coming into effect. The microbiome is attacking the harmful germs, and your hands turn blue because the signalling bacteria is notif ying you when t h e r e i s a b a t t l e g o i n g o n . Yo u realize it and quickly spray disinfectant alcohol on your h a n d s . Un f o r t u n a t e l y, s o m e o f t h e bacteria survived the alcohol. It managed to get into your mouth because you were going to be late and ended up eating your breakfast in your working space. The immune system is actively

killing the germs, while the bacteria in your mouth signals the immune system to produce more antibodies. After 5 hours of work , the bacteria is finally killed, and your microbiome and immune system prevent you from catching the flu. However during the fight , you arrived at the office, and while you were picking up the stack of paper on your desk , you accidentally got a paper cut. Yo u g o t o t h e f i r s t a i d b o x a n d t a k e o u t a f l a t p l a s t i c c y l i n d e r. It contains microorganisms that can heal your wound in a matter of hours. As you place this cylinder on your wound, the fungus gets into action. It builds a bridge across the wound, t h e n p u l l s i t t o g e t h e r. T h e n t h e fungi form a solid structure. T h e y t h e n s e l f - d e s t r u c t . Yo u take the plastic cylinder off and wait for your wound to heal. To n i g h t , a s y o u s h o w e r , t h e shampoo you use contains the microbiome which inhibits oil a n d k e e p s y o u r h a i r h e a l t h y. T h e shower gel contains anti-odour organisms and the toothpaste inhibits odour and kills germs in your mouth. That is a normal day of a person living in a highly m i c r o b i o m e d e v e l o p e d s o c i e t y. It is not certain if this will ever happen to us, but there is lots of potential in the applications of the Human Microbiome.

That is a normal day of a person living in a highly microbiome developed society. It won’t be certain if this will ever happen to us, but there is lots of potential in the applications of the Human Microbiome.

BIOLOGY AND CHEMISTRY

Bibliography [1] “Human Microbiome Project.” Wikipedia, Wikimedia Foundation, 10 Apr. 2020, en.wikipedia. org/wiki/Human_Microbiome_Project. [2] Cohen, J., et al. “Breakthrough of the Year, 2011.” Science/AAAS | Special Issue: Breakthrough of the Year, 2011, 2011, www.sciencemag.org/site/ special/btoy2011/. [3] Keim, Brandon. “Gut Bacteria Give Super Seaweed-Digestion Power to Japanese.” Wired, Conde Nast, 4 June 2017, www.wired.com/2010/04/ sushi-guts/. [4] “B Subtilis Probiotic – Why Is It Useful?” Bacillus Subtilis Probiotic Benefits - Probiotics. org, probiotics.org/bacillus-subtilis/. [5] FeaturedNeurosciencePsychology·June 6, 2020, et al. “How Gut Bacteria Negatively Influences Serotonin and Blood Sugar Levels.” Neuroscience News, 17 Sept. 2019, neurosciencenews.com/gut-bacteria-serotoninblood-sugar-14930/#:~:text=Summary%3A%20 A%20new%20study%20shows,serotonin%20 levels%20causes%20metabolic%20problems. [6] C;, Rastelli M;Cani PD;Knauf. “The Gut Microbiome Influences Host Endocrine Functions.” Endocrine Reviews, U.S. National Library of Medicine, pubmed.ncbi.nlm.nih.gov/31081896/.

of Neuroinflammatory Diseases, Including Multiple Sclerosis, Neuromyelitis Optica and Alzheimer’s Disease.” Clinical & Experimental Neuroimmunology, U.S. National Library of Medicine, Aug. 2017, www.ncbi.nlm.nih.gov/pmc/ articles/PMC5703598/. [9] Peirce, Jason M., and Karina Alviña. “The Role of Inflammation and the Gut Microbiome in Depression and Anxiety.” Wiley Online Library, John Wiley & Sons, Ltd, 29 May 2019, onlinelibrary. wiley.com/doi/10.1002/jnr.24476. [10] Nood, Els van, et al. “Duodenal Infusion of Donor Feces for Recurrent Clostridium Difficile: NEJM.” New England Journal of Medicine, 31 Jan. 2013, www.nejm.org/doi/10.1056/ NEJMoa1205037. [11] Muizzuddin N;Maher W;Sullivan M;Schnittger S;Mammone T; “Physiological Effect of a Probiotic on Skin.” Journal of Cosmetic Science, U.S. National Library of Medicine, pubmed.ncbi.nlm. nih.gov/23286870/. [12] D. Blank-Porat, T. Gruss-Fischer, et al. “Staphylococcus Epidermidis in the Human Skin Microbiome Mediates Fermentation to Inhibit the Growth of Propionibacterium Acnes : Implications of Probiotics in Acne Vulgaris.” Applied Microbiology and Biotechnology, Springer Berlin Heidelberg, 1 Jan. 1970, link.springer.com/article/10.1007/ s00253-013-5394-8.

[7] Bonaz, Bruno, et al. “The Vagus Nerve at the Interface of the Microbiota-Gut-Brain Axis.” Frontiers in Neuroscience, Frontiers Media S.A., 7 Feb. 2018, www.ncbi.nlm.nih.gov/ pmc/articles/PMC5808284/#:~:text=The%20 microbiota%2C%20the%20gut%2C%20 and,afferent%20and%2020%25%20efferent%20 fibers.

[13] “35 Microbiome Skincare Products.” TrendHunter.com, TREND HUNTER Inc., 19 Feb. 2019, www.trendhunter.com/slideshow/ microbiome-skincare.

[8] Tsunoda, Ikuo. “Lymphatic System and Gut Microbiota Affect Immunopathology

[15] “Face Vinegar 200ml.” Know To Glow, knowtoglow.com/products/face-vinegar-200ml.

[14] “Hibiscus Vinegar Toners.” TrendHunter. com, TREND HUNTER Inc., 29 Jan. 2019, www. trendhunter.com/trends/face-vinegar.

BIOLOGY AND CHEMISTRY

FUTURE OF FARMING Edward Wei

The Food Crisis

The current population of t h e w o r l d i s 7. 7 b i l l i o n , and this is due to rise to 9.3 billion in 2050; the urban population from 4 .1 t o 6 . 3 b i l l i o n ; t h e world will require 70% more food than it did in 2 0 0 9. S i m i l a r l y, a s g l o b a l demand for food increases, our world’s food production a l s o c o nt i n u e s t o f a c e a t h r e a t o f l i m i t e d wa t e r s u p p l y, scarce land and climate change. A limitation on these resources means that 90% of crop production is e x p e c t e d t o b e f r o m h i g h e r y i e l d s a n d c r o p i nt e n s i t y, and only 10% from the expansion of culturable land ( P l a n t F a c t o r y , 2 0 2 0 ) . Tr a d i t i o n a l o p e n f i e l d f a r m i n g methods are no longer efficient enough to provide for the world’s demands. This article discusses why we need a new method of farming and an outline of the method.

Illustration by K a y a n Ta m

BIOLOGY AND CHEMISTRY

Why Not Conventional Farming?

Conventional farming is becoming increasingly more arduous and unsuitable to carr y out due to several trends: climate change, the lack of agrochemicals, a ballooning carbon footprint and a labour shortage crisis.

BIOLOGY AND CHEMISTRY

Climate Change

Growing crops on an open field always comes with risks - the yield and quality depend on weather conditions and seasons, so there is no reliable nor stable supply of plant-grown food. This is especially significant when considering the effects of climate change: rising temperatures and more frequent extreme weather cases can lead to lower yield or even making the environment inhospitable for certain crops. When the latter scenario is reached, farmers will have a difficult time adapting to alternative crops to grow as they lack the experience and knowledge to grow such c r o p s e f f e c t i v e l y. E x t r e m e w e a t h e r conditions like flooding or droughts can harm crops and reduce yield. US farmers already spend 11 billion dollars annually fighting weeds that compete with crops for light , water and nutrient s [3]. This is due to increase as warmer temperatures, wetter climates, and an increase in CO2 levels stimulate the growth of pests, weeds and fungi. A greater population of pests requires an increase in the use of pesticides to combat them, which is detrimental to human health. Desertification and to a lesser extent urbanisation - is taking arable land away from farmers. The UN suggests that 12 million hectares of cultivable

land are lost annually due to droughts and deser tification [5]. Switching to farming in greenhouses can protect the crops from the effects of climate change, but several disadvantages affect e f f i c i e n c y. F i r s t l y, i t i s n o t v e r y e n e r g y e f f i c i e nt ; as greenhouses depend on natural sunlight, the incident light is not regulated. Apart from not being a b l e t o c o nt r o l l i g ht q u a l i t y, t h i s also means that solar light intensity is often too dim at dawn, sunset and night, and on days where it is c l o u d y, ra i n y o r c o l d , a n d t o o h i g h around noon on sunny days. It is also difficult to regulate temperature and humidity as it is considerably d e p e n d e n t o n s o l a r l i g h t i n t e n s i t y. To m a i n t a i n a n d r e g u l a t e o p t i m a l temperature, greenhouses are often ventilated, but this allows insects and diseases in, obligating the use of pesticides. CO2 levels also cannot be maintained at a high level if ventilated. It is predicted that by 2050, we would lose about 2% of the world’s fertile land due to rising sea levels and desertification, while freshwater demand will balloon by 55%. If everyone switched to greenhouses to grow crops, the land saved would only just be able to offset the predicted land loss while halving the percentage increase in freshwater demand to 28% [14].

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2. Agrochemicals Spillage and the overuse of agrochemicals can also harm the environment. The term ‘agrochemical’ refers to all the different types of chemicals used to aid farming, such as pesticides, herbicides, fungicide, nematicide, synthetic fertilisers, growth hormones and more. Excessive use of fertilisers leads to the contamination of nitrates in groundwater which can leach into nearby lakes, causing eutrophication, the rapid growth of algae, and the decay of many aquatic lifeforms. Pesticides sprayed onto entire f ields using equipment mounted on vehicles like planes and tractors often drift away - some older variants like DDT can remain active for a very long time, c o nt a mi nat i ng w i l d l i f e , wat e r, f o o d a nd humans [2]. Humans are also running out of an essential mineral to plant growth - phosphates. Phosphates are the only form of phosphorus that plants can absorb, and they are critical to seed production, root growth, hastening p l a nt ma t u r i t y, s t a l k s t r e n g t h , r o o t r o t resistance and resistance to winter kill (NRCS). This is because phosphorus f o r m s p a r t o f a n e s s e n t i a l c h e m i c a l - AT P (adenosine triphosphate) - responsible for the storage and transfer of energy throughout the plant. While phosphate minerals are not “used up” like fossil fuels, our method of applying it to crops causes it to disperse throughout the environment making them difficult to retrieve and reuse. Thus, several reports have warned that global reser ves will be depleted within the next 50 years or so.

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3. Carbon Emissions Conventional farming has quite a large carbon footprint. For most cities, the demand for food dramatically exceeds what is and can be cultivated in the surrounding region; thus, they import their food from large global supply chains with massive carbon footprints. The higher proportion of the population gaining access to electricity means more usage of refrigerators, supporting the trend of buying imported food. One study found that the transportation of ordinary and small commercial trucks a r e 0 . 8 k g a n d 1 . 9 k g - C O 2/ t o n o f f o o d / k m o n a v e r a g e , w i t h c a r b o n emissions from cargo ships being lowest and aeroplanes having the highest. Additional CO2 is emitted when food is cooled (which it often needs to be). Food in a supermarket in the USA travels on average 2000 km between production and consumption sites [9]. Despite all of this, the most significant contributor to the agriculture sector ’s carbon footprint is not the transportation of food, but rather deforestation to provide land for the crops. A study showed that tropical deforestation for agriculture and tree plantations releases 2 .6 Gt of CO2 per year [9].

BIOLOGY AND CHEMISTRY

Labour Shortage Crisis There is a labour shortage crisis occurring i n t h e a g r i c u l t u r a l s e c t o r. A n i n c r e a s i n g proportion of the population living in urban areas means fewer people are working on farms. This is driven by the growing role of supermarkets and TNCs in supplying food driven by urbanisation. These organisations favour large agricultural producers, leading to a shift in employment in the food sector: fewer people are working in agriculture and more in retailing, food vending, wholesaling, transport and food processing [8 ]. A d d i t i o na l l y, c o u nt e r -u r b a n i s a t i o n , t h e migration of people from urban areas to rural areas, effectively leads to the urbanisation of the rural regions - services and facilities are built so people working on farms can switch jobs to work in those new places o f e m p l o y m e n t w h i c h g i v e h i g h e r p a y. T h i s is all spurred on by the lack of interest in farming amongst the younger generation in the US, only 9% of farmers are below the age of 35 [1]. This leads to reduced crop yields, crop intensity and changes in traditional cropping patterns. The latter could mean a loss in crop diversity; this can be seen in Bangladesh which has lost more than 7000 types of landraces over time. Many of these crops were pest resistant , tolerant to salinity and able to be grown in many different environments, as well as having medical properties, great taste and high nu tritional value s [6].

BIOLOGY AND CHEMISTRY

Farming in the 21st centur y

To f u l f i l t h e f o o d r e q u i r e m e n t s o f t h e f u t u r e , t h e new agricultural cultivation technique has to achieve much higher yields, while simultaneously protecting the environment, improving health and driving economic developments. This new farming t e c h n i q u e c a l l e d “ V e r t i c a l F a r m i n g ”, f o u n d e d i n 1 9 9 9 by Dick s on Despommier and his students , could be a possible amelioration to the world’s food crisis. Ve r t i c a l f a r m i n g i s t h e c o n c e p t o f g r o w i n g f r u i t s a n d v e g e t a b l e s i n m u l t i p l e l a y e r s . Ve r t i c a l f a r m i n g has four main types: skyscraper farms, wall and roof farms, vertical greenhouses and plant factories.

BIOLOGY AND CHEMISTRY

Skyscraper Farms

Fig. 1. Picture of a Skyscraper Farm

Wall and Rooftop Farms

Fig. 1 is likely the first picture to come to mind when you hear the term “ vertical farming” - massive skyscrapers containing pastures full of vegetables, fruits, trees and even animals. While images such as above are aesthetically pleasing, i n r e a l i t y, s k y s c ra p e r s f a r ms a r e likely the least viable of the four types. Skyscrapers are expensive real estate; thus, it is usually reser ved for high-value economic activities. Cultivation of crops or humane rearing of animals has lowvalue density - profitable when the context is the countryside where the land is bountiful and cheap, but not when using premium real estate, even if you grow highvalue crops. A d d i t i o na l l y, the cost of growing scales with the height of the building - pumping water and vertically moving phytomass takes considerable energy and increases the cost.

In contrast with skyscraper farms, wall and rooftop farms do not take up valuable real estate, but rather a i m t o u t i l i s e u n u s e d s p a c e s t o g r o w f o o d . Wa l l a n d rooftop farms add visual appeal to urban areas and can also be useful in combating the urban heat island effect. An urban heat island is a metropolitan area that is significantly warmer than its surrounding rural areas due to human activities. Moderating this effect can i m p r o v e a i r a n d wa t e r q u a l i t y, a s t h e e f f e c t h e a t s t h e water that drains into sewers and is released into lakes and rivers, reduces deaths due to extreme heat and s a v e s e l e c t r i c i t y. T h i s i n v e s t i g a t i o n f o u n d t h a t w a l l a n d rooftop farms can be 30 to 40 degrees Fahrenheit lower than conventional rooftops and minimise energy use by 0. 7 % [11 ]. Howe v e r, t he o v e ra l l i mpa c t ga i ne d f r o m wa l l and rooftop farms is negligible. Despommier and his students went on to calculate that rooftop farms would o n l y b e a b l e t o s u p p l y 2 % o f N e w Yo r k ’ s p o p u l a t i o n i n 2015 even when fully utilising every one of its rooftops.

BIOLOGY AND CHEMISTRY

Vertical Greenhouses

Ve r t i c a l g r e e n h o u s e s a r e l a r g e t r a n s p a r e n t boxes that grow crops in multiple levels. This creates an immediate problem with lighting, as the glass or polymer structure already absorbs a fraction of the light spectrum and the stacked layers create shadows. The solution is to rotate levels vertically to ensure even sunlight exposure as well as installing artificial lighting. Ve r t i c a l g r e e n h o u s e s t r a d e g r e a t e r c r o p d e n s i t y with higher capital costs and electricity costs, making it more fitting for urban environments where land is premium. The vertical greenhouse could play an essential role in solving global challenges as they require 10 to 15 times less land a nd wat e r t ha n c o nv e nt i o na l f a rmi ng. Howe v e r, they are subjected to the same problems as traditional greenhouses mentioned above.

Plant Factories Plant factories are the most technologically advanced of vertical farms. They are airtight, highly climate controlled, sterile, windowless buildings with stacked layers of plants, growing in hydroponics or aeroponics, relying on 100% artificial lighting. This is the version which this essay will focus mostly on as they have the most significant potential to combat the world food crisis.

Fig. 2. Indoor Plant factory

BIOLOGY AND CHEMISTRY The world is desperately in need of a methodology to effectively produce high-qualit y foods, improve social welfare and enhance the quality of life with minimum consumption of resources and emission of environmental pollutants . Plant factories have the potential to fulfil this requirement.

Why Plant Factories?

BIOLOGY AND CHEMISTRY How Plant Factories Help Social Welfare

Plant factories enable complete control of the environment. Thus, production is year-round, unaffected by seasons and climate, providing a reliable source of food which prevents prices from fluctuating. This also means that the cultivation of wide varieties of regional crops is possible by adjusting the environment (though this is not possible yet as will be explained later). A d d i t i o na l l y, b e i n g c l o s e d o f f t o t h e o u t s i d e w o r l d trivialises the pesticide usage as the crops are protected from harmful organisms; fruits and vegetables grown in plant factories are not only healthier but also have increased shelf lives as bacterial loads can be 1/100 to 1/1000th of field-grown variants [9]. The use of aeroponics and hydroponics means that only the necessary minerals are present and absorbed by the crops and that heavy metals or pathogens found naturally in the s o i l a r e n o t p r e s e n t , m a k i n g t h e c r o p s m u c h h e a l t h i e r. Fur thermore, plant factories could potentially solve the problem of food deserts. Food deserts are areas that have limited access to cheap and nutritious food. This phenomenon is caused by urbanisation which leads to changes in the demands of food. People in urban areas consume more in general and desire greater food varieties: dairies, meat, fish, processed food, organic vegetables and fast-food [12]. Among these food types, the most concerning is processed foods. Processed foods consist of foods that have additional salt , sugar or fats added into it ; ultra-processed foods take a step beyond, adding artificial colouring, flavours and preservatives, and are often pre-prepared frozen food or microwave food. In par t due to longer working hours and lower prices as well as the growing influence of supermarkets in supplying processed food, the preference for this category of food is very high. One study found that ultra-processed foods comprise about 60% of the total caloric intake in the USA [10]. A d d i t i o na l l y, t ra n s p o r t a t i o n , s t o ra g e a n d r e t a i l s h e l f conditions can have severe repercussions on the quality of food. A study found that in just three days, lettuce stored on retail shelves experienced a 64.6% weight loss overall as well as a 48% loss in ascorbic acid (vitamin C) [7]. The consequences are severe: many urbanites face malnutrition from overconsumption of calorie-dense foods, leading to o b e s i t y, n u t r i e nt d e f i c i e n c i e s a n d i l l n e s s e s . Pl a nt f a c t o r i e s are possible solutions as they can be built near or in urban areas, thus supplying cheaper fresh produce and reducing nutrient loss due to transportation and storage. T h i s i s , h o w e v e r, s t i l l j us t a p o s s i b i l i t y, a s p l a nt f a c t o r i e s are still relatively immature as an industry and most companies are focusing on planting premium crops like kale with higher profit margins to pay back investments.

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BIOLOGY AND CHEMISTRY How Plant Factories Help the Environment

A d d i t i o na l l y, t h e us e o f a e r o p o n i c s a n d h y d r o p o n i c s in vertical farms reduces water consumption per unit of crop grown. The best plant factories produce 1 kg o f l e ttu c e o n j us t 1. 2 L o f wat e r, whi c h is ne a r l y 2 0 0 times less than traditional farming methods (around 237 L). This has vast prospects in heightening water s e c u r i t y, i m p r o v i n g wa t e r q u a l i t y (a s t h e r e i s n o leaching of nutrients) and halting marsh destruction. As mentioned above, plant factories can be built near urban areas, thus reducing greenhouse gas emissions f r o m t ra ns p o r t at i o n. Howe v e r, t he mo s t s i g ni f i c a nt impact on reducing carbon footprint stems from how high the crop yields of plant factories are - 286 km/ m 2/ y e a r c o m p a r e d t o 3 . 9 k m / m 2/ y e a r i n c o n v e n t i o n a l farms [14]. This means that the capacit y in returning land to forests and shrublands is massive.

Current Issues and Potential Improvements The drawbacks There are several main problems with plant factories, and that can all be attributed to one root cause: the c o s t o f e l e c t r i c i t y. T h e h i g h e n e r g y costs mean that current vertical farms are restricted to only specific types - leaf y greens. They are composed of about 95% water and have a high edible mass percentage, meaning that less energy is needed to produce lots of edible mass. This hinders the positive impact that plant factories have on the environment as they are unable to cultivate staple crops like rice. Rice consists of 19% of the world’s c a l o r i e s , b u t , u n f o r t u na t e l y, o n l y contain 15% water and have a much lower edible mass percentage than leaf y greens, requiring 30 times more

energy than lettuce [9], and making them economically unfeasible - any rice grown must have a price tag far above the market price just to break even, so despite their health benefits, a limited number of consumers are willing to buy them. Suppose plant factories can improve to a point where it becomes economically viable to grow staple f o o d s l i k e r i c e a n d g r a i n . We c a n e x p e c t t o r e c l a i m 1 7. 6 % o f l a n d and reduce global freshwater consumption by up to 91% [13]. There are two main ways to achieve this goal - by improving the efficiency of the technology used in plant factories and through data collection.

BIOLOGY AND CHEMISTRY

Role of Data Analysis Sensors and data analyses are widely used in plant factories to measure multitudes of variables and their effects on plant growth. Fine-tuning v a r i a b l e s l i k e t e m p e ra t u r e , h u m i d i t y, air composition, air current speed, i o n c o n c e nt ra t i o n s , l i g ht i nt e n s i t y, and light spectrum to maximise the efficiency of growth is a substantial part of the journey in bringing staple foods into plant factories. Let ’s take the example of controlling light. Each plant can absorb different spectrums of light more than others. Thus LED grow lights are being used to emit specific spectrums of light (light recipes) tailored to e a c h p l a n t t o e n h a n c e e f f i c i e n c y. A d d i t i o na l l y, in sunlight to a n d f l o w e r. light recipes

most crops use changes determine when to grow By emitting different at opportune moments,

we can lengthen flowering periods to increase the size of the plant, decrease the root growth phase to increase the edible mass percentage (due to usage of aeroponics and hydroponics, crops don’ t need large and complex root systems to absorb enough nutrients) and e v e n a l t e r t he t as t e , s ha p e , c o l o ur, and texture of a plant. The extent of change is considerable: fieldgrown plants tend to have an edible mass percentage of 40% while crops grown in plant factories can achieve 92% [13]. Fur thermore , by omitting certain unnecessary growth phases, one can also reduce growth time by a sizable amount - about 10-20 times per year [9]. This not only increases yield but also increases data collection, as many more experiments can be done in the same period.

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BIOLOGY AND CHEMITRY Role of Genetics Apart from the use of computer science, we can also improve efficiency by using genetic engineering to make higher yield crops and select different variants of staple crops that are more suitable to plant factory environments, such as those with a higher edible mass percentage and s h o r t e r h e i g h t s . We c a n a l s o b r e e d o r g e n e t i c a l l y modif y existing crops for faster harvest cycles.

R o le o f Te c hno lo g ic a l Advancements Te c h n o l o g i c a l a d v a n c e m e n t s s u c h a s c h e a p e r g e n e editing techniques, automation, accurate sensors, and better LED lights can all significantly increase yield. For example, more efficient LED lights emit less waste heat , which saves electricity and allows the lights to be placed closer to the plant without risking heat damage, i m p r o v i n g c r o p d e n s i t y. T h i s a l s o m e a n s t h a t m o r e l i g h t emitted is being absorbed by the plants, decreasing t h e a m o u n t o f e n e r g y w a s t e d . Ye a r b y y e a r , m o r e advanced LED lights can emit a broader range of the light spectrum, giving more flexibility in manipulating growth cycles and increasing yield. They are also g e tt i ng c he a p e r a nd hav i ng l o ng e r l i f e s pa ns . Mo r e o v e r, with decreasing costs per watt of various forms of renewable energies, we can increase profitability while reducing the environmental impact of plant factories. The technology-rich environment is also attracting t h e y o u n g e r g e n e r a t i o n i n t o t h e f a r m i n g i n d u s t r y.

BIOLOGY AND CHEMISTRY

Conclusion With all the benefits of plant factories, it is easy to predict that in the upcoming decades, traditional farming will gradually be replaced by plant factories. As technology continues to advance, plant factories will be a b l e to sustain the future population while also protecting the environment , improving health conditions and driving economic development.

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BIOLOGY AND CHEMISTRY Bibliog raphy [1] “(Infographic) The U.S. Farm Labor Shortage.” AgAmerica, 11 Mar. 2020, agamerica.com/the-impact-of-the-farm-laborshortage/. [2] “Agrochemical.” Agrochemical - an Overview | ScienceDirect Topics, www.sciencedirect. com/topics/earth-and-planetary-sciences/ agrochemical. [3] “Climate Impacts on Agriculture and Food Supply.” EPA, Environmental Protection Agency, 6 Oct. 2016, 19january2017snapshot. epa.gov/climate-impacts/climate-impactsagriculture-and-food-supply_.html. [4] Djurfeldt, Agnes Andersson. “Urbanization and Linkages to Smallholder Farming in SubSaharan Africa: Implications for Food Security.” Global Food Security, vol. 4, 2015, pp. 1–7., doi:10.1016/j.gfs.2014.08.002. [5] “The High Price of Desertification: 23 Hectares of Land a Minute - World.” ReliefWeb, reliefweb.int/report/world/high-pricedesertification-23-hectares-land-minute. [6] “Impact of Changing Cropping Pattern on Farm Land. Is It Time to Go Back to Traditional Crops?” Grainmart News, 21 July 2020, w w w. g r a i n m a r t . i n / n e w s / i m p a c t - o f - c h a n g i n g cropping-pattern-on-farm-land-is-it-time-to-goback-to-traditional-crops/. [7] Managa, Millicent G., et al. “Impact of Transportation, Storage, and Retail Shelf Conditions on Lettuce Quality and Phytonutrients Losses in the Supply Chain.” Wiley Online Library, John Wiley &amp; Sons, Ltd, 4 July 2018, onlinelibrary.wiley.com/doi/full/10.1002/ fsn3.685. [8] Pendrill, Florence, et al. “Agricultural and Forestry Trade Drives Large Share of Tropical Deforestation Emissions.” Global Environmental Change, Pergamon, 20 Mar. 2019, www.sciencedirect.com/science/article/ pii/S0959378018314365#:~:text=Tropical deforestation for agriculture and tree plantations releases 2.6 GtCO2 yr.&text=29–39% of emissions are, mainly in beef and oilseeds.&text=Imported deforestation emissions rival domestic agricultural emissions in many countries. [9] “Plant Factory.” Google ¹Ï®Ñ, Google, books.google.com.hk/books?hl=zhTW&lr=&id=z-C7DwAAQBAJ&oi=fnd&pg=PP1 &dq=vertical+farming&ots=zDkfyJgkev&sig= Q G G Ta l E w i N 0 w r F z s O T m q N W D 7 u m U & r e d i r _ esc=y#v=onepage&q&f=false.

[10] “Processed Foods and Health.” The Nutrition Source, 24 June 2019, www.hsph.harvard.edu/ nutritionsource/processed-foods/. [11] “Using Green Roofs to Reduce Heat Islands.” EPA, Environmental Protection Agency, 11 June 2019, www.epa.gov/heatislands/using-greenroofs-reduce-heat-islands. [12] Weiss, Author Tamar. “Industrial Age Farming: How Urbanization Is Changing the Industry - Start-Up Nation Central Blog.” Start, 16 Jan. 2017, blog. startupnationcentral.org/agritech/industrialage-farming-how-urbanization-is-changing-theindustry/. [13] “How Much Can Vertical Farming Improve?”, Exa Cognition, 10 Jan 2019, https://www. youtube.com/watch?v=qGyAeqdkkbw&t=6s. [14] “Does Vertical Farming Work?”, Exa Cognition, 26 Oct 2018, https://www.youtube. com/watch?v=dnCQuwCtqJg&t=223s Fig 1 Source: “This Is Why We Should Be Farming in Skyscrapers.” City Monitor, 26 May 2015, citymonitor.ai/environment/why-weshould-be-farming-skyscrapers-1029. Fig 2 https://futuretodayinstitute.com/trend/ aeroponics-vertical-cultivation-and-indoorplant-factories/indoor-plant-factories/

BIOLOGY AND CHEMISTRY

Sunscreens By Jasmine Chan

Fig.1 Examples of Sunscreens

Sunscreens are a very common household item, probably something you are familiar with - an item to bring to a sunny area such as a tropical island, or the beach. Not only does it prevent painful burns, but it also reduces the risk of damage to the body by the sun’s rays. In this article, I will explore the science behind sunscreens.

1. INTRODUCTION TO SUNSCREENS Sunscreen, commonly known as sunblock , is a substance that can absorb or reflect ultraviolet (UV) radiation from the sun on the skin which is exposed to sunlight. It can be in the form of a lotion, spray or gel which helps to protect the skin against sunburn. [1] They work by absorbing UV radiation into heat , [2] helping t o r e d u c e t he r is k o f s k i n c a nc e r, sk in ageing, and sunburns . [3]

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1.1 T HE HIS TOR Y SUNSCREENS

The use of sunscreen arose in the 1920s when salicylate - a salt or ester of salicylic acid - was found with the ability to reduce sunburning effects after prolonged exposure to t he sun. [4, 5] Dur i ng t he 1 9 30 s , Fra nz Gr e i t e r, a Sw is s c he mis t r y student, suffered from sunburn after climbing Mount Piz Buin (See Fig. 3) located on the Swis sAu s t r i a n b o r d e r. T h i s e x p e r i e n c e inspired him to develop and invent a substance that prevents sunburns. [6] In 194 6, Greater succe s s f ull y created the first sunscreen, known as the ‘Piz Buin Glacier Cream’ (See Fig.4). [ 7 ] This sunscreen only had an SPF of 2 (the meaning of SPF is introduced in Section 1.2), which meant that it was relatively ineffective. [8] Meanwhile, in 1944, Benjamin Green, an airman and pharmacist from Miami, Florida, used a mixture of cocoa butter and red veterinary petroleum to protect himself and the other soldiers from the sun during the battlegrounds of WWI I. [6, 7 ] A f e w y e a r s lat e r, Gr e e n formulated ‘Coppertone Suntan Oil’ (See Fig.5) by adding more cocoa butter and coconut oil to t h e r e d v e t e r i n a r y p e t r o l e u m . [ 7, 9 ]

Fig.2 Examples of the Effect of Sunscreen under UV Camera Lens

Fig.3 Photograph of Mount Piz Buin

Fig.4 Photograph of the First Piz Buin Glacier Cream

Fig.5 Photograph of the First Coppertone Suntan Oil

BIOLOGY AND CHEMISTRY

1.2 THE STANDARDIS ATION R ATING OF SUNSCREENS Over time, sunscreens became widely p o pula r, a nd a s t a nda r d is at i o n rat i ng s c a l e f o r suns c r e e n was d e v e l o p e d b y Gr e i t e r, known as the sun protection factor (more commonly known as SPF). [8, 10] SPF is a quantity used to measure the protectiveness of sunscreens against UVB (more information about the types of UV radiation will be introduced in Section 2). The SPF number is based on how long it takes for the skin to redden with and without the sunscreen (See Fig.6). This means that as the number increases, the level of protection increases. For example, if it takes 10 minutes for the skin to become red, if an SPF 50 sunscreen is applied, then it would take 50 times longer (equivalent to around 500 minutes/8 hours) for the skin to become burnt. [10]

Fig.6 Visual Example of the SPF Rating

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2. INTRODUCTION T O U LT R A V I O L E T R ADIATION To u n d e r s t a n d h o w s u n s c r e e n works, the basics of UV radiation need to be understood first. As ultraviolet radiation has shorter wavelengths than visible light , it carries more energy than visible light; hence, it can cause photochemical damage to skin cells by damaging the cellular DNA . [3, 11, 12] Photochemical damage can lead to photocarcinogenesis - the sequence of biochemical events t h a t l e a d s t o s k i n c a n c e r. [ 1 3, 1 4]

2.1 T YPE S OF U LT R A V I O L E T R ADIATION Ultraviolet radiation covers a broad spectrum, from 40400nm. There are four types of ultraviolet light listed in order of shortest to longest i n w a v e l e n g t h : V a c u u m U V, U V C , U V B a n d U VA ( S e e F i g . 7 ) . U VA a n d U V B a r e t h e h a r m f u l wavelengths whereas the other UV radiation does not cause any damage to the skin. This is because it is completely absorbed by the ozone in the atmosphere before it reaches the sur face of Ear th. [3]

BIOLOGY AND CHEMISTRY

Fig.7 Visual Diagram of the Electromagnetic Spectrum with Close-Up to the Ultraviolet Light and Visible Light Spectrum

2 .1.1 U LT R A V I O L E T -A ( U V A ) U VA h a s a w a v e l e n g t h o f a p p r o x i m a t e l y 3 2 0 400nm which makes up 95% of the UV light from the sun that reaches the Ear th’s surface. U VA c a n p e n e t r a t e d e e p l y t h r o u g h t h e s k i n and into the connective tissues. This promotes photoaging, causing pre-maturing, ageing a n d w r i n k l i n g o f t h e s k i n [ 3 , 1 5 ] b e c a u s e U VA destroys the structure of collagen, a protein in the skin, by regulating the formation of MMPs (matrix metalloproteinase), an enzyme that can degrade the matrix of collagen and elastin in proteins. [14] As the shape o f c o l l a g e n i s a l t e r e d d u e t o U VA , w r i n k l e s a r i s e s i n c e t h e s k i n l o s e s e l a s t i c i t y. [ 1 6 ] A d d i t i o n a l l y, U VA c a n i n c r e a s e t h e s e v e r i t y of cutaneous lupus erythematosus (See Fig.8) - an autoimmune disease (lupus) where the immune system attacks healthy skin, as well as solar urticaria (See Fig.9) - a rare allergy to sunlight that causes hives to form on the skin. [14, 16, 17] Some studies h a v e s h o w n t h a t U VA c a n f o r m f r e e r a d i c a l o x y g e n s p e c i e s ( ˙ O H , O 2-˙ ) i n t h e e p i d e r m a l cells that indirectly impairs the activity of antigen-presenting cells - cells that initiate the humoral (immune) response. [14, 18, 19, 20] This causes a person to develop a weak immune system and therefore increases the r i s k o f s k i n c a n c e r. [3, 1 4]

Fig.8 Example of Cutaneous Lupus Erythematosus

Fig.9 Example of Solar Urticaria

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BIOLOGY AND CHEMISTRY 2 .1. 2 U LT R A V I O L E T -B ( U V B ) UVB, which has a wavelength of around 290-320nm, is only responsible for 5% of the UV light reaching the Ear th’s surface as 95% of it is absorbed in the atmosphere before r e a c h i n g t h e E a r t h ’ s s u r f a c e . I n c o m p a r i s o n t o U VA , U V B does not penetrate as deeply into the skin, meaning that it is relatively less harmful to the skin (See F i g .1 0 ) . U V B c a u s e s t h e s k i n t o p r o d u c e m o r e melanin which causes a person’s skin to appear d a r k e r. Ho w e v e r, t h i s d i r e c t l y d a m a g e s t h e D N A , i n c r e a s i n g t h e r i s k o f s k i n c a n c e r. [3] UVB also exacerbates solar ur ticaria. [14]

Fig.10 Visual Diagram of UVA and UVB

2.1.3 UVA A ND UV B The human skin contains molecules that are structured to absorb the energy of U VA a n d U V B w a v e l e n g t h s . T h i s m a k e s t h e electrons in the molecule jump to a higher energy level as they become excited. When these electrons go back to the ground state, energy in the form of heat is released, which causes molecules to undergo a chemical reaction. [21] This released energy turns on the skin’s natural antioxidant network , which deactivates free radicals and highly destructive reactive oxygen species (ROS), s u c h a s h y d r o g e n p e r o x i d e ( H 2O 2) a n d s i n g l e t o x y g e n ( 1O 2) . [ 2 0 , 2 1 ] T h i s d e a c t i v a t i o n process increases the cellular damage in the skin due to a process known as oxidative stress, which causes an imbalance between the production of free radicals and the body ’s ability to neutralise the free radicals. The ROS and free radicals formed can react with DNA, causing mutations to occur and h e n c e l e a d i n g t o s k i n c a n c e r. [ 2 1 ] H o w e v e r, s m a l l a m o u n t s o f U VA a n d U V B are essential as they are needed for the synthesis of vitamin D. Vitamin D regulates the concentration of calcium and phosphate i n t h e b o d y, w h i c h i n t u r n k e e p s b o n e s a n d t e e t h h e a l t h y. [ 1 2 , 2 2 ] A d e f i c i e n c y o f v i t a m i n D c a n l e a d t o r i c k e t s ( S e e F i g .1 1 ) , a t y p e o f deformation in children, and osteomalacia ( S e e F i g .1 2 ) , a t y p e o f b o n e p a i n i n a d u l t s . [ 2 3 ]

Fig.11 Example of Rickets

Fig.12 Comparison of the Bones of a Normal Person and a Person Suffering from Osteomalacia

BIOLOGY AND CHEMISTRY

3. T YPES OF SUNSCREEN There are two types of sunscreen: physical sunscreen or chemical sunscreens (See F i g .1 3) . P h y s i c a l s u n s c r e e n s can reflect or refract UV light whereas chemical sunscreens absorb UV light. [1] In most modern sunscreens, both organic and inorganic compounds are present . [3]

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BIOLOGY AND CHEMISTRY 3.1 CHEMICA L SUNSCREENS Chemical sunscreens are usually organic, aromatic substances such as avobenzone, oxybenzone and octinoxate. They can block the m a j o r i t y o f U VA a n d U V B r a d i a t i o n [10, 19, 21] and are structurally conjugated with a carbonyl (C=O) group. [1] Chemical sunscreens work by absorbing into the skin and subsequently absorbing UV rays. These UV rays are then converted into heat and released from the b o d y. [ 2 4] A s t h e U V r a y s a b s o r b e d hav e h i g h e n e r g y, t h i s c a us e s t h e electrons in the molecules within the aromatic substances to be in an excited state, causing them to jump to a higher energy level. When the electrons return to their ground state, they release longer wavelengths of UV radiation which have lower e n e r g y. [ 1 9 ] S o m e o r g a n i c c h e m i c a l s are photostable, whereas some are not, meaning that they would break down over time as the exposure to UV light increases. Hence, sunscreen should be reapplied multiple times t h r o u g h o u t t h e d a y. [3]

Fig.13 Visual Diagram of How Chemical and Physical Sunscreens Work

Fig.14 Examples of Compounds in Chemical Sunscreens

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Illustration by Se Lyn

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BIOLOGY AND CHEMISTRY 3.2 PHYSICAL SUNSCREENS Physical sunscreens are commonly inorganic substances that sit on top of the skin after application and can reflect or scatter UV light. This includes chemicals such as zinc oxide Fig.15 Visual Diagram of What is a Semiconductor and How (ZnO) and titanium dioxide it Differs from Metals and Insulators ( T i O 2) . These chemicals in sunscreen are 1/20th smaller than conventional pigments, known as microfine pigments. They are then dispersed and spread evenly into a base. Combinations of these chemicals with other substances can potentially reduce UV transmission, which means that it provides good protection for the s k i n a g a i n s t U VA a n d s o m e Fig.16 Visual Diagram of How a Photocatalyst Works wavelengths of UVB. Both titanium dioxide and zinc oxide can reflect and scatter UV and visible light and absorb can jump up into from the valence UV l i g ht . [4] The s e c he mi c a ls a r e when excited) of the photocatalyst. semiconductors (substances that [ 2 7, 2 8 , 2 9 ] T h e e x c i t a b i l i t y o f t h e conduct electricity under specific chemical depends on its crystalline conditions) that can absorb light and structure and the band gap - the generate reactive species, meaning difference in energy between the that they are photocatalysts. highest occupied energy state of [25, 26] They can promote the the valence band and the lowest transformation of organic molecules unoccupied state of the conduction when absorbing UV radiation. b a n d ( S e e F i g .1 5 ) . [4 , 2 8 ] T h i s [26] When the photocatalyst creates pairs of negative electrons absorbs UV radiation, it produces ( e -) a n d p o s i t i v e h o l e s ( h +) . A r e d o x pairs of electrons and holes. r e a c t i o n t h e n o c c u r s ( S e e F i g .1 6 ) . The positive holes break water The electron of the valence band molecules, which forms hydrogen (the band of electron orbitals that g a s ( H 2) a n d h y d r o x y l r a d i c a l s ( ˙ O H ) electrons can jump out of ) of the - this is the oxidation reaction. The photocatalyst becomes excited negative electrons react with the when is illuminated with light, oxygen molecule to form superoxide which promotes the electron to a n i o n s ( O 2-˙ ) - t h i s i s t h e r e d u c t i o n the conduction band (the band reaction. This photocatalyst cycle of electron orbital that electrons repeats once light is available. [27]

BIOLOGY AND CHEMISTRY 3.2 COMPARISON BET WEEN CHEMICAL AND PHYSICAL SUNSCREENS Chemical sunscreens are easier to use than physical sunscreens, as physical sunscreens tend to leave a white cast or residue on the face (the reasons behind this will b e a d d r e s s e d i n S e c t i o n 4. 2) . Howe v e r, phy s i c a l suns c r e e ns are hypoallergenic, which means that they are more suitable for sensitive skin as they reduce the irritation to the skin. [10] Physical sunscreens are also more moisturising for the skin as they are denser than chemical sunscreen. [21] A d d i t i o na l l y, c h e m i c a l s u n s c r e e n r e q u i r e s a r o u n d 1 5 -30 minutes for the sunscreen to be effective whereas physical sunscreen is immediately effective. [30]

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4. PROPERTIES OF SUB STANCES IN PHYSICAL SUNSCREENS The ability of a substance to block light in physical sunscreens are determined by several physical properties: the substance’s opacity and pa r t i c l e s i z e . [4]

4.1 OPA CIT Y The opacity of a physical sunscreen is calculated by Snell’s Law of R e f r a c t i o n ( S e e F i g .1 7 ) : N p s i n i / Nm sin r where Np is the refractive index of the pigment in the physical sunscreen, Nm is the refractive index of the adjacent medium which is air in this case, i is the angle of incidence (the angle between the incident light ray and the normal), and r is the angle of refraction (the angle between the emergent light ray and the normal). [31, 32] Refraction occurs when light meets a boundary between two media, and because there is a change in the refractive index (usually entering a medium with a

Fig.17 Visual Diagram of Snell’s Law of Refraction

BIOLOGY AND CHEMISTRY higher refractive index), the velocity of light travelling in this ne w me d i um w i l l b e d i ff e r e nt ( i f t he r e f ra c t i v e i nd e x is hi g he r, then velocity will decrease). Molecules with a high refractive i nd e x c a n i nc r e as e t he r e f l e c t i v e ne s s o f t he suns c r e e n. [4] As the refractive index of the pigment increases, opacity increases since more light is scattered. [33] A s the sunscreen is more opaque, the sunscreen has a white tint when applied t o t h e f a c e . T h i s i s k n o w n a s w h i t e c a s t i n g ( S e e F i g .1 9 ) .

Fig.19 Examples of White Casting on Different Skin Tones

Nowadays, cosmetic chemists have incorporated more brown p i g m e n t s i n s u n s c r e e n s u c h a s i r o n o x i d e ( F e 2O 3) , w h i c h reduces the white-casting effect , making the sunscreen seem more natural on the face. This type of sunscreen is known as tinted sunscreens. The additional use of apigments can also enhance the scattering effect of the physical sunscreens, making the sunscreen more effective overall as different p i g me nt s hav e d i ff e r e nt r e lat i v e o pa c i t i e s ( S e e Fi g. 2 0) . [4]

Fig.20 Comparison of the Relative Opacities of Different Microfine Pigments

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BIOLOGY AND CHEMISTRY 4.2 PARTICLE SIZE The particle size of a pigment is the average size of the particles in the pigment . [34] The best pigments used in physical sunscreen is when the diameter of the particle is half of the wavelength of visible light. [4] A s me nt i o ne d i n S e c t i o n 3, o ne of the most common pigments used in physical sunscreen is titanium dioxide. As the size of titanium dioxide is relatively small (200500nm in size), they generally have a greater ability to reflect light. [34] Despite par ticles being small w h i c h c a n l e a d t o t ra n s p a r e n c y, t h e ability of the particle to reflect and scatter UV radiation is retained. As the particle size varies, the type of scattering changes. In titanium dioxide, two types of scattering c a n o c cur, Mi e s c att e r i ng a nd Rayleigh scattering (See Fig.21). [4] Fo r pa r t i c l e s i z e s la rg e r t ha n a wavelength of light , Mie scattering occurs, which is a type of scattering that produces a pattern similar to an antenna lobe. For larger particles, the antenna lobe like shape would have a sharper and more intense forward lobe. [35] For par ticle sizes around a tenth of the wavelength of light , Rayleigh scattering occurs where the patterns for forward and backward scattering are symmetrical. [36]

Fig.21 Visual Diagram of Mie and Rayleigh Scattering

CONCLUSION I hope you have learnt more about the science behind sunscreens as well as ultraviolet radiation. I am in awe of the complexity of such a basic household item, something that we do not usually think twice about. As science advances, I believe that chemists will be able to develop new chemical sunscreens that eliminate the white-casting effect and are just as effective as physical sunscreens!

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BIOLOGY AND CHEMISTRY BIBLIOGRAPHY [1] HariKishan, M. C. Sai, et al. “Sunscreen & Sunscreen Agents : A Review.” PharmaTutor, www. pharmatutor.org/articles/suncreen-agents-review. [2] “The Difference between Physical and Chemical Sunscreen.” Piedmont Healthcare, www.piedmont. org/living-better/the-difference-between-physicaland-chemical-sunscreen. [3] “The Science of Sunscreen & How It Protects Your Skin.” Compound Interest, 5 June 2014, www.compoundchem.com/2014/06/05/ sunscreenchemicals. [4] Murphy, G. M. “Sunblocks: Mechanisms of Action.” Photodermatology Photoimmunology & Photomedicine, 15 Sept. 1998, onlinelibrary.wiley. com/doi/pdf/10.1111/j.1600-0781.1999.tb00051.x. [5] “List of Salicylates.” Drugs.com, www.drugs.com/ drug-class/salicylates.html. [6] “Sunscreen: A History.” The New York Times, 23 June 2010, www.nytimes.com/2010/06/24/ fashion/24skinside.html. [7] “The History of Sunscreen.” Panama Jack, panamajack.com/blogs/from-panama-jack/thehistory-of-sunscreen. [8] “The History of Sunscreen.” Weldricks Pharmacy, www.weldricks.co.uk/news/the-history-of-sunscreen. [9] Bellis, Mary. “So Who Invented Sunscreen?” ThoughtCo, 23 Nov. 2019, www.thoughtco.com/ suncreen-history-1992440. [10] Waxman, Eliana. “Feel the Burn? Explaining the Science of Sunscreen.” UChicago Medicine, UChicago Medicine, 18 July 2018, www.uchicagomedicine.org/ forefront/health-and-wellness-articles/explaining-thescience-of-sunscreen.

[16] Eastham, A. Brooke, and Ruth Ann Vleugels. “Cutaneous Lupus Erythematosus.” JAMA Dermatology, Mar. 2014, jamanetwork.com/journals/ jamadermatology/fullarticle/1843885. [17] Hecht, Marjorie. “Solar Urticaria: Symptoms, Treatment, and More.” Healthline, 11 Mar. 2020, www. healthline.com/health/skin-disorders/solar-urticaria. [18] “Antigen-Presenting Cells.” Nature Research, www.nature.com/subjects/antigen-presenting-cells. [19] Gabros, Sarah. “Sunscreens And Photoprotection.” StatPearls, U.S. National Library of Medicine, 29 Sept. 2020, www.ncbi.nlm.nih.gov/books/NBK537164. [20] Serpone, Nick, et al. Inorganic and Organic UV Filters: Their Role and Efficacy in Sunscreens and Suncare Products. 2005. [21] Wong, Michelle. “Chemical vs Physical Sunscreens: The Science (with Video).” Lab Muffin Beauty Science, 31 Mar. 2018, http://labmuffin.com/ chemical-vs-physical-sunscreens-the-science-withvideo. [22] “Sun Protection.” Soulage Wellness & Aesthetic Center, www.soulagemedspa.com/contents/ourproducts/sun-protection. [23] “Vitamin D.” NHS, 3 Aug. 2020, www.nhs.uk/ conditions/vitamins-and-minerals/vitamin-d. [24] Hanson, Kerry. “Column: How the Chemistry of Sunscreen Is Protecting Your Skin This Memorial Day.” PBS, Public Broadcasting Service, 29 May 2017, www.pbs.org/newshour/science/column-chemistrysunscreen-protecting-skin-memorial-day. [25] Hanania, Jordan, et al. “Semiconductor.” Energy Education, 31 Jan. 2020, energyeducation.ca/ encyclopedia/Semiconductor.

[11] “Ultraviolet (UV) Radiation.” American Cancer Society, www.cancer.org/cancer/cancer-causes/ radiation-exposure/uv-radiation.html.

Fig 1 stylecaster.com

[12] Donev, Jason. “Ultraviolet Radiation.” Energy Education, 4 Jan. 2019, energyeducation.ca/ encyclopedia/Ultraviolet_radiation.

Fig 3 wikipedia.com

[13] Black, H. S., et al. “Photocarcinogenesis: an Overview.” Journal of Photochemistry and Photobiology. B, Biology, U.S. National Library of Medicine, Aug. 1997, pubmed.ncbi.nlm.nih. gov/9301042.

Fig 5 coppertone.com

Fig 15 energyeducation.ca

Fig 6 nytimes.com

Fig 16 nature.com

Fig 7 klaran.com

[14] Latha, M. S., et al. “Sunscreening Agents: a Review.” The Journal of Clinical and Aesthetic Dermatology, U.S. National Library of Medicine, Jan. 2013, www.ncbi.nlm.nih.gov/pmc/articles/ PMC3543289.

Fig 17 buphy.bu.edu

Fig 8 dermnetnz.org

Fig 19 [21] and naturallycurly.com

[15] “Photoaging.” Canadian Dermatology Association, 14 Mar. 2018, dermatology.ca/public-patients/skin/ photoaging.

Fig 2 dailymail.com

Fig 4 pizbuin.com

Fig 9 sciencealert.com Fig 10 suntribesunscreen.com Fig 11 corpus.nz

Fig 12 yashodahospitals.com Fig 13 mw-fp.com Fig 14 [21]

Fig 20 [4] Fig 21 [35]

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Graphene: Super Carbon? Parry Chan

Introduction What do you think of when someone mentions the word “ Carbon” ? Whether it is fuel oil, charcoal or dead plants, in this article, I will describe the physical and chemical properties of graphene and how these properties enabled graphene to be named the “super c a r b o n ”. T h i s “ f a n t a s y m a t e r i a l ” can potentially have an enormous impact on human development in the future. In 2010, scientists Andre Geim and Kostya Novoselov were awarded the Nobel Prize in Chemistry for their astonishing experiments with this material.

Structure Graphene is a single layer of graphite, the material pencil tips are made from. It has a multi-layer structure with carbon atoms bonded to another three carbon atoms with a delocalised electron.

Graphene has an extremely high thermal conductivity at 2500 W/ mK due to two major reasons. First , graphene is the thinnest material ever known to mankind. At one atom thick , the material has a ver y high sur face-area-to-volume ratio which enables heat to pass t h r o u g h e a s i l y. S e c o n d l y, t h e f r e e to-move delocalised pi electrons can move around due to the delocalised electrons of carbons. Graphene’s ability to transfer heat increases exponentially as electrons move faster and faster in high temperature. Graphene also has a higher electrical conductivity than all other substances. Its electrical conductivity is 35% higher than c o pp e r, a v e r y c o mmo n mat e r ia l f o r wiring and computer components. The delocalised electrons have an absence in charge localisation a s t h e y c a n m o v e a r o u n d f r e e l y. To g e t h e r w i t h t h e h a l f - i n t e g e r quantum Hall effect and ultra-high mobility of the charge carriers which travel 100 times faster than silicon, graphene scores top of t h e l e a d e r b o a r d f o r c o n d u c t i v i t y. Due to graphene’s strong covalent bonds, it has the highest tensile strength amongst all the other materials with an intrinsic strength of 130 GPa (100 times the strength o f s t e e l ) . I nt e r e s t i n g l y, i t c a n s t i l l be stretched at a maximum of 125% of its size, which makes it ideal for use as an electronic component. Another property of graphene is its t r a n s p a r e n c y. T h e m a t e r i a l i s o n l y a single layer of graphite, a oneatom-thick layer of carbon atoms. Due to its ex treme thinness, only 2% of light is blocked by the material.

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Illustration by Se Lyn

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BIOLOGY AND CHEMISTRY 1. Phone Screens Applications

A damaged or broken phone screen is something everyone has experienced at least once. Graphene can prevent this from happening in the future due t o i t s t ra n s p a r e n c y, h i g h h e a t c o n d u c t i v i t y a n d s t r e n g t h . I n 2 0 1 7, physicist s from the Universit y of Sussex solved the problem by combining silver nanowires with this one-atom-thick material that is 200 times stronger than steel, which is more conductive than copper and as flexible as r u b b e r. Ho w e v e r, w i t h t h e c u r r e n t t e c h n o l o g y, g ra p h e n e i s m o r e expensive to produce than indium tin oxide (current phone screen material) and it is still under development so phone companies are not considering it at the moment.

2. Water Filtration Systems The UN predicts that 14% of the world population will experience wa t e r s c a r c i t y b y 2 0 25 . E v e r y d a y, 900 children across the world die due to diarrhoeal diseases caused b y c o n t a m i n a t e d wa t e r. Su r p r i s i n g l y, graphene might be a solution for the lack of clean water in underdeveloped countries and provide millions of people with a clean water source. When graphene oxides pile up w i t h e a c h o t he r, a g ra phe ne oxide membrane is formed. The membrane has narrow pores that are semipermeable to ions and molecules, acting as a filter for harmful substances and providing p e o p l e w i t h c l e a n d r i n k i n g wa t e r. Mo r e o v e r, graphene is also hydrophilic, attracting water to move towards it , which allows water to continuously flow through it.

BIOLOGY AND CHEMISTRY 3. Surface Coatings G l o b a l l y, c o r r o s i o n c o s t s p e o p l e 1. 5 trillion pounds a year; graphene is possibly a great solution for such an issue. It is proven that although graphene is naturally hydrophilic, it turns hydrophobic (water-repelling) when e x p o s e d t o a m b i e n t a i r. T h i s g i v e s i t a wa t e r p r o o f i n g p r o p e r t y, s o p e o p l e can use it on surfaces such as shoes, windshield and windows for safety and convenience because graphene is also extremely transparent and thin. Fur thermore, graphene is also ver y successful in being chemical-proof. An experiment at the Massachusetts Institute of Te c h n o l o g y exposed graphene and conventional polymers in water vapour at 100 degrees Celsius to experiment with both materials’ resistance to chemicals. It was concluded that graphene had no sign of degradation on its surface for 2 weeks whereas traditional coatings started degrading after 3 hours and failed after 12 hours. The property of being chemical-resistant makes the material applicable on buildings, cars, boats, etc for weathering prevention.

4. Ex traction of Graphene One factor slowing down graphene’s development is our inadequate ability to extract it from graphite. A common way of obtaining the material is the Ta p e M e t h o d , w h i c h i n v o l v e s t e a r i n g off layers of graphene from graphite multiple times until the layers of graphene are one-atom-thick . There are other extraction methods such as the Blender a n d h e p t a n e - w a t e r interface film formation methods. Howe v e r, they are inefficient because t h e y r e q u i r e h i g h s k i l l and equipment whilst producing smaller amounts of graphene.

Conclusion Despite the jaw-dropping features of graphene, we still have a long way to go to commonise this “ fantasy m a t e r i a l ”. A f t e r r e a d i n g t h i s passage, I hope you now know more about graphene and how much of an impact it can have on our lives.

References American Coatings Association. (n.d.). Graphene Coatings: Exciting Properties and Wide-Ranging Potential. Paint.org. Retrieved May 19, 2021, from https:// www.paint.org/coatingstech-magazine/ articles/graphene-coatings-excitingproperties-and-wide-ranging-potential/ Berger, M. (n.d.). What is Graphene? Graphene properties and applications. Nanowerk. https://www.nanowerk.com/ what_is_graphene.php Li, D., & Kaner, R. (2008). GrapheneBased Materials. Science, 320(5880), 1170-1171. Retrieved May 19, 2021, from http://www.jstor.org/ stable/20054827 The Graphene Experts. (2017). Graphene-Info. Graphene-Info.com. h t t p s : / / w w w. g r a p h e n e - i n f o . c o m / graphene-structure-and-shape The University of Manchester. (n.d.). Energy - Graphene - The University of Manchester. Www.graphene. manchester.ac.uk. https://www. g r a p h e n e . m a n c h e s t e r. a c . u k / l e a r n / applications/energy/ Westervelt, R. (2008). Graphene Nanoelectronics. Science, 320(5874), 324-325. Retrieved May 19, 2021, from http://www.jstor.org/stable/20055022

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Why Sleep? Christine Li

SLEEP CYCLES

INTRODUCTION Yo u m a y h a v e h e a r d o f t h i s o l d m a x i m : “ Live your life, chase your dreams, you can sleep when you’re dead!” Bu t f ra n k l y, t h i s i s t h e m o s t m o r t a l l y unwise advice. Sleep deprivation is directly linked to depression, amnesia and even death. The ‘ life lesson’ above, which has many advocates and is viewed as an indicator of hard work , is robbing precious time from our lives

Sleep is scientifically defined as a state of reduced consciousness, activity and response. During the night, humans experience sleep cycles that typically last for around 90 minutes and can be categorised into two main phases: REM (Rapid Eye Movement) and NREM (Non-Rapid Eye Movement) Sleep. They alternate within one sleep cycle, and if we delve deeper into the NREM phase of sleep, there are three different stages that feature the NREM sleep: NREM-1, NREM-2 and NREM-3.

Falling Asleep The sense of drowsiness is coordinated by a person’s circadian rhy thm, which, although endogenous, can be adjusted to the local environment by external cues called zeitgebers, which include light and temperature. The primary circadian clock in mammals is located in the suprachiasmatic n u c l e u s ( S C N ) 1, w h i c h r e c e i v e s i m p u l s e s d u e t o l i g h t d e t e c t i o n f r o m t h e eyes. The retina contains specialised photosensitive ganglion cells and subsequently transmits electrical signals to the SCN via the optic nerve. In response, the SCN prompts the pineal gland to secrete melatonin - a hormone that signals biological night and creates the onset of sleepiness. 1. Suprachiasmatic nucleus (SCN): a pair of distinct groups of cells located in the hypothalamus.

BIOLOGY AND CHEMISTRY N R E M -1

Fig. 1: Electroencephalography for different stages of sleep

The NREM-1 stage constitutes 5-10% of the total sleep duration, and it is a transitional phase where a person might start floating in and out of consciousness. During this process, one might experience hypnic myoclonia, where one’s muscles jerk , followed by a falling sensation that jolts one back into wakefulness. On the electroencephalogram (EEG), the predominant brain waves slow to four to seven cycles per second, a pattern called theta waves (see Fig. 1). Body temperature begins to drop, muscles relax , and eyes often move slowly from side to side. People in stage N1 sleep lose awareness of their surroundings, but they a r e e as i l y ja rr e d awa k e . Howe v e r, people who have woken from this phase often report that they do not remember drifting off at all.

NR EM-2 After winding down in NREM-1 sleep, their sleep cycle progresses into stage two, which makes up 50% of their total sleep and lasts for 10 to 25 minutes. Their eyes are still, and their heart rate and breathing are slower than when awake. Their b ra i n’s e l e c t r i c a l a c t i v i t y is i rr e g u la r, featuring both K-complexes and sleep spindles on an EEG. The sleep spindles occur because the brain starts to disconnect from outside sensory input and begins the process of memory consolidation. They are believed to be useful in preventingone from waking up (which speeds up the sleep process). The pattern called K-complex (see Fig. 1) is believed to be representative of a built-in vigilance system that keeps one poised to awaken if n e c e s s a r y. T h e y c a n b e p r o v o k e d by certain sounds or other external or internal stimuli. Sleep talking and bruxism happen at this stage

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NREM-3

REM Sleep

E v e nt u a l l y, l a r g e , s l o w b ra i n wav e s called delta waves become a major feature of the EEG, and they enter deep sleep. Breathing becomes mo r e r e g ula r, b l o o d pr e s sur e f a l ls , and the pulse slows to about 20% to 30% below the waking rate. The brain becomes less responsive to external stimuli, making it difficult to wake the sleeper ; people being woken from this stage of sleep often appear disoriented and feel g r o g g y f o r mi nu t e s . Sl e e p t e rr o r, sleepwalking and bedwetting might occur for children below 12 years old. As they reach adolescence, these disorders usually diminish.

Now the person enters the four th stage of sleep, which, as the name suggests, is characterised by rapid eye movements (their eyeballs oscillate rapidly in different directions). This was first discovered by Eugene Aserinsky in 1953 when he taped electrodes to his son’s brain whilst he was sleeping and connected them to an electroencephalogram machine ( E E G ) t o m o n i t o r h i s b r a i n a c t i v i t y. That night, to his surprise, the pen that registered brain activity swang back and forth, resembling brain waves during the period of wakefulness and showing that his son was in a state of alertness. The fact that his son’s eyeballs were darting in random directions led to correlated with dreaming. Because his conclusion that eye movements, a s w e l l a s b ra i n a c t i v i t y, i s o f their discoveries, Asrinsky and Kleitman are now considered the founders of modern sleep research.

Above all, the body recuperates at this stage: increased blood flow to muscles provides restorative oxygen and nutrients to organs; hormones pertaining to growth and appetite control are secreted which rejuvenates the body even more; cytokines, which are produced during sleep, alleviate stress and help produce infection-fighting antibodies. Deep sleep plays a large part in restoring alertness, as researchers have shown that when one sleeps after a period of sleep deprivation, they spend a greater proportion of sleep time here.a

Although the extraocular muscles are active in manipulating movements of their eyeballs, other parts of the body are in a temporal paralysed state. Sleep paralysis suggests that even if a person is woken up from this stage of sleep,

BIOLOGY AND CHEMISTRY

they would find it difficult to manoeuver their bodies and move around. This loss of motor tone of muscles throughout the body (except in the extraocular m u s c l e s 2) d i r e c t l y c o n t r a s t s w i t h the high level of brain activity that is featured by low-voltage, highfrequency and desynchronised beta waves; hence REM sleep is also given the romantic name of ‘ t h e P a r a d o x i c a l S l e e p ’. Mo r e o v e r, i t is b e l i e v e d t hat t he motion of the eyes correlates with their actions in their dreams - if they

a r e c l i mb i ng a la d d e r, t he i r e y e s will move upwards and downwards; s i m i l a r l y, i f t h e i r e y e s m o v e f r o m left to right , it may suggest that they are dreaming about watching a movie. REM sleep duration increases progaressively over the course of the night, and the final period of REM sleep may last half an h o u r. T h e r o l e o f t h i s s t a g e o f sleep in consolidating memory is significant, and this will be discussed in more detail in the next section.

2. Extraocular muscles: They control the movements of the eyeball and the superior eyelid.

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MEMORY CONSOLIDATION

Fig. 2: Position of the Hippocampus in the Brain

There are many types of memories, each supported by distinct neural systems throughout the brain. Declarative memory is the remembrance of knowledge of fact-based information, for example, the capital of France or what you had for breakfast. The hippocampus (see Fig. 2), situated in the medial temporal lobes of the cerebrum, is largely responsible for converting shor t-term memor y into longterm m e m o r y. During this process, sensory data is initially transcribed and temporarily recorded in the neurones as s h o r t -t e r m m e m o r y. T h e d a t a then travels to the hippocampus, where neurones in the cortical area are strengthened and enhanced. Due to the p h e n o m e n o n o f n e u r o p l a s t i c i t y, new synaptic buds are formed, which allows new connections between neurones and strengthens the neural network where the information will be r e t u r n e d a s l o n g -t e r m m e m o r y.

The secret in improving the effectiveness in retaining those me mo r i e s , howe v e r, l i e s i n t he process of sleep. Scientists have hypothesised that REM sleep plays an essential role in the acquisition of learned material. This was confirmed by the research in which where an increase in REM sleep was observed in individuals who had engaged in an intensive language course. Slow-wave sleep (SWS), experienced by people during stage three of their sleep also plays a significant role in consolidating declarative memory as it helps to encode shor t-term memor y into the temporary store in the anterior part of the hippocampus. EEG monitoring people’s brain activities during these stages of sleep have shown electrical impulses moving between the brainstem, hippocampus, thalamus, and cortex , which serve as relay stations of memory formation. Through a continuing dialogue between the cortex and hippocampus, the memory is then repeatedly reactivated, driving its gradual redistribution to long-term storage in the cor tex . This suggests that instead of pul l i ng a n a l l-ni g ht e r, i t is w is e r to get enough sleep after the memorisation of facts before a big test comes up the next day! Another type of m e m o r y, p r o c e d u ra l m e m o r y, r e f e r s t o t h e remembering of how to do certain activities - for instance, riding a bicycle or playing the piano. The consolidation of such memories relies mostly on REM sleep.

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Illustration by Tina Wu

WHAT ’S THE PURPOSE OF DREAMING? Although humans spend approximately one-third of our lives sleeping, scientists have always failed to find the purpose of dreams. This section of the article aims to explain the various theories regarding dreaming and how they collapse under scepticism, then point out what scientists must consider in their research and studies to find the true meaning behind dreams.

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Fig. 3: Freud’s Three Levels of Mind

In Freud’s theor y, dreams are meaningful. They represent our unconscious wishes, urges and feelings, which help us understand and resolve hidden conflicts. He breaks down dreams into two key components: manifesting content and latent content; the former one is directly shown in dreams, and the latter represents the hidden meaning behind the dreams. For instance, in a dream of being chased by a monster - the manifest content would be the imagery of this event , but the latent content could be interpreted as a sign that one would be potentially chased out of

their job, which reveals their feelings of anxiety and insecurity at work . Dreams can also be a disguised fulfilment of a repressed wish. Freud believes that dreams allow a gratification of certain drives through visual fantasy or the manifesta content. Howe v e r, Fr e u d ’s t h e o r i e s have been debunked by many researchers over the years as his research was biased - Freud solely paid attention to information that supported his already expressed views, and not those who would have contradicted his theories.

BIOLOGY AND CHEMISTRY Activation-Synthesis Theory On the other hand, the activationsynthesis theor y suggested by psychiatrists J. Allan Hobson a n d R o b e r t M c C a r l e y i n 1 9 7 7, strongly proposes that dreams are meaningless. Activation refers to the random and continual electrical impulses fired by the brainstem to the frontal part of the brain during REM sleep, and synthesis is the attempt of the cerebral cortex to try and make sense of the electrical stimuli through creating dreams. In this hypothesis, the main function of dreams is essentially a thinking process wherein the brain attempts to make sense of neural activity that takes place during sleep. Howe v e r, evidence has accumulated over the last 30

y e a r s t o d i s p r o v e t h i s t h e o r y. The first piece of evidence that disproved it emerged one PET3 scanning of the brain was developed. According to the o r i g i na l t h e o r y, t h e b a r ra g e of random stimulation coming up from the brainstem was synthesised by the prefrontal c o r t e x i nt o d r e a ms . Howe v e r, scans of the brain in the REM state showed that the cortex was selectively activated. The emotional brain (the limbic system) and the visual brain were highly activated, yet the prefrontal cortex was excluded from this stimulation. Over the last few years, Hobson has been so drastically redrafting the theory that it is now just a pale shadow of its original presentation.

Fig. 4: Structure of the Brain

3. PET: An imaging test of the brain through the use of a radioactive substance called a tracer to look for disease or injury in the brain. It can also show how the brain and its tissues are working.

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“ W e s l e e p i n o r d e r t o f o r g e t .”

This theor y was proposed by Graeme Mitechison and Francis Crick in 1983, in which they stated that dreams are essentially the product of the process of memory consolidation. Mitechison and Crick believed that there are two main categories of m e m o r y. A d a p t i v e m e m o r i e s a r e the ones that are useful to retain, including new skills or knowledge. There are also parasitic memories, characterised by useless and random information that disrupts the efficient organisation of m e m o r y. S i n c e o u r b r a i n c a n n o t handle the vast amount of i n f o r ma t i o n i s p e r c e i v e d i n a d a y, during the REM phase of sleep, we ‘save more space’ for more useful memories by forgetting those that we do not need. The essentiality of this mechanism is shown through the observation of two species of mammals who cannot REM sleep - the dolphin and the spiny anteater (or echidna). Both have an abnormally large cortex , presumably because they cannot ‘unlearn’ through the reverse-learning process and must store everything they have ever seen and heard. The removal of certain unwanted memories requires the elimination of certain undesirable modes of interaction in networks of cells in the cerebral cortex . The ‘clearing’ process begins by the brain sifting through information gathered throughout the day and then forgetting or eliminating parasitic thoughts by removing certain

undesirable modes of interaction in neural networks within the cerebral cortex (where memories are stored) during a process called reverselearning. Random but powerful stimuli are sent up from the brainstem to the cortex to weaken unwanted neural connections in the brain and thus, cutting off memories from one a n o t h e r. T h e r e f o r e , t h e f a c t t h a t the stimuli from our brainstem are entirely random might be the cause for bizarre and illogical dreams that occur during REM sleep! Never theless, this theor y fails to explain various phenomena because, after all, if what it suggests is correct, people who lack REM sleep should suffer from memory impairment. Howe v e r, patients who take antidepressants that block REM sleep also have functioning memory just as people who do not take the medicine do. The theory is unable to explain how the brain decides which memories to keep and which to unlearn. More i m p o r t a nt l y, t h e a t t e m p t o f i t i n trying to explain the existence of dreams might just as well fail. If the stimuli from the brainstem are truly random, then why do so many of our dreams seem to have a storyline and a narrative instead of being composed of random images and figures? The most undermining doubt is perhaps that not a shred of evidence has arisen to show that the human brain makes parasitical connections - those are something known only to occur with computer networks.

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A New Theory is Needed As you can see, many theories have failed to offer a thorough explanation of the existence, process and purpose of dreaming; more research is still needed to unveil the true nature of dreaming. Considering the characteristics of theories that attempt to explain this phenomenon and the fact that many of the dreams can be somewhat be controlled by individuals subjectively rather than being a random display of images, it is possible that a future theory that tries to elucidate the purpose of dreaming might interpret it as a combination of : 1. The manifestation of our desires and wishes that cannot be achieved in reality 2. A product of natural biological processes

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BIOLOGY AND CHEMISTRY SLEEP DEPRIVATION Nowadays, sleep deprivation has become a normalised condition f o r ma n y, e s p e c i a l l y o u r c u r r e nt generation. The negative impacts it has on our health should not b e i g n o r e d o r t a k e n l i g h t l y. Just one week of insufficient sleep can alter the activity of our genes, which may a f f e c t o u r r e s p o n s e t o s t r e s s , i m mu n i t y, inflammation and overall health. Sleeping two to three hours a night will result in impaired cognition as excessive sleepiness reduces our ability to think and process information. This is also shown by a loss in concentration and mental agility; for instance, sufferers of sleep deprivation would experience difficulty in mental addition and spelling words. In addition, our interpretation of events may be affected as we lose the ability to make sound decisions; we can no longer accurately a s s e s s t h e s i t u a t i o n , p l a n a c c o r d i n g l y, and choose the correct b e h av i o u r. The human memory will suffer too, as overworked neurons no longer function to coordinate information p r o p e r l y, which leads to the loss of the ability to access previously learned information. Sleeping between five to six hours a night increases the risk of high blood pressure. Since our blood pressure drops during sleep, not experiencing this nightly drop in pressure becomes a risk factor for heart disease. Severe sleep deprivation can result in delirium - the first stage of psychosis when people cannot interpret reality and their urge for sleep b e c o m e s u n b e a r a b l e . T h i s w a s e x p e r i e n c e d b y P e t e r Tr i p p , w h o s t a y e d awake for a record-breaking 201 hours in 1959. For much of the stunt , he sat in a glass booth in Times Square. After a few days, he began to hallucinate and self-talk , and for the last 66 hours, the obser ving scientists and doctors gave him drugs to help him stay awake. Afterwards, he suffered psychologically and began to think he was an imposter of himself - a thought which he kept for some time. Never theless, recover y of sleep deprivation psychosis is possible by getting enough sleep.

BIOLOGY AND CHEMISTRY Factors that Affect Sleep Many drugs affect our qualit y of sleep. They can be categorised into three groups: stimulants, prescriptions and soporifics. Stimulants make people more alert and keep them awake, but they also reduce the quality of sleep. Caffeine is an example of a stimulant, and the fact that it has a half-life of over five hours means that it is better to d r i n k i t e a r l y. O t h e r w i s e , i t w i l l make it harder to fall asleep. S i m i l a r l y, p r e s c r i p t i o n s s u c h as antihistamines have side effects on sleep as they inhibit histamines, a chemical produced by the central ner vous system that is responsible for wakefulness. Therefore, routinely using them to treat insomnia is not recommended. Soporifics, on t h e c o nt ra r y, ma k e s i t m o r e likely to fall asleep. Alcohol is a typical example of this kind o f d r ug ; howe v e r, d r i nk i ng i t isnot a solution for insomnia as people are likely to become tolerant to alcohol, reducing t h e e f f e c t s i t h a s o n t h e b o d y. Zeitgebers are environmental triggers that affect our circadian rhythms, and they mainly come in the form of electronic lights. The more light that we are exposed to, the more we will be awake as it suppresses the sleep hormone, melatonin. Noise and anxiety must also be taken into account when dealing with insomnia. Although most people prefer silence to fall asleep to, once in stage 3 or 4 of NREM, noise is no longer a factor because the brain is completely ‘switched off ’ from the external environment.

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IMPROVING SLEEP QUALIT Y 1. Regularity Tr y t o s l e e p a n d w a k e a t c o n s i s t e n t t i m e s n o m a t t e r whether it ’s the weekday or the weekend. Our circadian rhythm functions on a set loop, aligning itself with sunrise and sunset. Being consistent with sleep and waking time can improve both the quantity and the quality of sleep. Irregular sleep patterns, on the other hand, alters one’s levels of melatonin, thus affecting one’s circadian rhy thm. 2 . Te m p e r a t u r e Keep the temperature cool when sleeping. During sleep, the core body temperature drops by approximately one degree Celsius to initiate sleep and subsequently to stay asleep. It is best to aim for a bedroom temperature of about 18 degrees Celsius as it matches the progress of sleep, leading it to the correct destination. 3. Darkness Darkness in the evening is required to trigger the release of melatonin, which helps regulate the healthy timing of our sleep. In the last hour before bed, try to stay away from computer screens or smartphones, and dim down half the lights in the house. This will make one feel sleepier and in turn, make it easier to fall asleep. 4. Reduce Irregular Or Long Day time Naps While short 10 to 20-minute power naps are beneficial, long or irregular napping during the day can confuse one’s internal clock , causing one to struggle to sleep at night. One study found that participants who t o ok day t i me nap s e nde d up f e e l i ng s l e e p i e r.

S h o u l d Yo u U s e t h e S n o o z e B u t t o n ? The shor t answer is, you should not. When obser ving the cardiovascular response to an alarm, scientists found a spike in heart rate and an increase in levels of stress hormones, thus forming an assault on the cardiovascular system.

BIOLOGY AND CHEMISTRY

A LAST NOTE “ Sleep is not a luxur y; it is a biological necessit y. '' - - M a t t h e w Wa l k e r Sleep plays an irreplaceable role in our lives and its value should not be underappreciated. It helps us in consolidating memory and learning, and depriving one of sleep can p u t o n e i n r e a l d a n g e r. S o next time, when you’ve got a big exam coming up, try to sleep more; the idiom “sleep on it ” has a real scientific basis!

Bibliography [1] Learning, Lumen. “Introduction to Psychology – Lindh.” Sleep and Sleep Stages | Introduction to Psychology – Lindh, courses. lumenlearning.com/suny-fmcc-intropsych/ chapter/outcome-sleep-and-dreams. [2] “K-Complex.” Wikipedia, Wikimedia Foundation, 1 Jan. 2021, en.wikipedia.org/wiki/K-complex. [3] DrawItKnowIt. “Neuroscience - Sleep Cycle EEG.” YouTube, YouTube, 17 July 2016, www.youtube.com/ watch?v=NO-iUU8PIcE. [4] “Peter Tripp.” Wikipedia, Wikimedia Foundation, 7 Sept. 2020, en.wikipedia.org/wiki/Peter_Tripp. [5] “Circadian Rhythm.” Wikipedia, Wikimedia Foundation, 3 Mar. 2021, en.wikipedia.org/wiki/Circadian_rhythm [6] “The Science of Sleep.” The Science of Sleep HelpGuide.org, www.helpguide.org/harvard/ biology-of-sleep-circadian-rhythms-sleep-stages.htm

[7] “Sleep, Learning, and Memory.” Sleep, Learning, and Memory | Healthy Sleep, healthysleep.med.harvard.edu/healthy/ matters/benefits-of-sleep/learning-memory [8] “Crick-Mitchison Theory.” Crick-Mitchison Theory Definition | Psychology Glossary, w w w. a l l e y d o g . c o m / g l o s s a r y / d e f i n i t i o n . php?term=Crick-Mitchison+Theory+ . [9] khanacademymedicine. “Dream Theories Freud, Activation Synthesis Hypothesis | MCAT | Khan Academy.” YouTube, YouTube, 20 Jan. 2015, www.youtube.com/watch?v=UAXapQvZe2w. [10] Gogh, Jake Van. “Were Freud's Theories Scientific?” Medium, Medium, 19 Dec. 2018, jakevangogh.medium.com/were-freuds-theoriesscientific-71ec91ca9acf. [11] Mawer, Rudy. “17 Proven Tips to Sleep Better at Night.” Healthline, Healthline Media, 28 Feb. 2020, www.healthline.com/nutrition/17-tips-to-sleepbetter#5.-Try-to-sleep-and-wake-at-consistent-times.

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Pink Dolphins: The White Taboo Alan Li

Pink dolphins, also known as IndoPacif ic Humpback Dolphins , or Chinese White Dolphins, are a vulnerable species. They were first recorded in 1637 but had been known by Hong Kong’s fishermen for centuries. Pink dolphins were traditionally seen as the “ White Ta b o o ” b y l o c a l f i s h e r m e n a n d w e r e l e f t alone, but in modern times, more people seek out dolphin-watching tours for memorable moments with this beautiful s p e c i e s . Un f o r t u na t e l y, i n j us t 1 4 y e a r s , the population of pink dolphins has plummeted by 78% to a mere 32 in 2018. To l e a r n m o r e a b o u t p i n k d o l p h i n s a n d their current situation, we interviewed Viena Mak from the Hong Kong Dolphin Conservation Society (HKDCS). Viena is a dolphin researcher who started her career as an intern. She worked with Dr Samuel Ho, who didn’ t want his team to have sedentar y research; he wanted to show the public how to conserve the dolphins. They founded HKDCS in 2003 for dolphin research and education.

BIOLOGY AND CHEMISTRY What do you do? We c o l l a b o r a t e w i t h s c h o o l s a f e w times a year to bring students to observe the habitats of marine animals i n Ho n g K o n g . We d o l a n d -b a s e d sur veys and underwater noise acoustic surveys. We teach the students about marine life and how research can be a way of conser vation. It is a memorable way of learning about t h e s e a n i m a l s a n d t h e i r h a b i t a t s . We also go to the sea with colleagues and volunteers to record dolphin sightings and behaviours for our research. Yo u c a n f i n d t h e m o n o u r w e b s i t e . Besides these, we also host talks, workshops, and movie screening activities to reach wider audiences, so that more people know why and how the dolphins are suffering and why we have to protect the ocean b e f o r e i t i s t o o l a t e . We a l s o wr i t e letters to the government to express our concerns about their reclamation projects that have a huge impact on the dolphin population. For example, j us t o u t s i d e o f Ha r r o w, t h e r e i s a reclamation project which is part of t h e L a n t a u To m o r r o w V i s i o n . P e o p l e may not be aware of this small part of reclamation which the government is planning just outside the waters of Tu e n M u n . S o , w e t e l l t h e g o v e r n m e n t why these waters are important to the pink dolphins as they are still in a recover y stage —we cannot just take the waters away from the dolphins.

How are land reclamation programmes affecting the pink dolphins? The Hong Kong-Zhuhai-Macau bridge is an example of a completed reclamation project. The whole bridge takes about one hundred sixty-five hectares of reclamation work in northeast Lantau. This caused a total and irreversible habitat loss for the dolphins. These

waters were an important habitat where the dolphins would feed, socialise, and nurse their young, making them crucial for the next generation of d o l p h i n s t o s u r v i v e . S e c o n d l y, t h e noise pollution caused by construction can be very disturbing for the soundsensitive pink dolphins. Dolphins rely on echolocation to feed and communicate, so loud noise will mask their ability to hunt and communicate. When we obser ved the dolphins after the bridge was built , we learned that although the dolphins could travel through the bridge, they rarely go through the bridge because they see i t a s a p h y s i c a l b a r r i e r. T h e y w o u l d turn around and go back , so the bridge separates the dolphins from the north and south of the bridge. Fur thermore, the toxins from construction accumulate in the dolphins’ bodies and get released through breastfeeding, which means the toxins are passed on to their young. That 's why people are finding more dolphin calves dying on the beach— the pollutants affect the dolphins’ reproductive and immune systems.

What can we do to help conserve the pink dolphins? I think public engagement is critical, but it is also important to start with the small things, such as using ocean-safe sunscreens or avoiding the application of sunscreens when you go to the beach. People should live an ocean-friendly lifestyle by recycling their plastics and reducing their seafood consumption. If you want to participate in dolphin watching, I recommend that you avoid riding on Wa l l a - w a l l a b o a t s o p e r a t e d b y l o c a l fishermen who don’ t follow the code of conduct on dolphin-watching. Instead, book a trip on our website or at Hong K o n g D o l p h i n Wa t c h . I n 2 0 1 5 , w e f o u n d one dolphin named WL212 outside of Ta i O p i e r . W L 2 1 2 h a d c u t s f r o m t h e blades of a boat turbine that were so deep that its tail almost fell off.

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What will happen to the pink dolphins? It is difficult and not quite appropriate to use the current situation as a baseline for environmental strategies in the future because all the mitigation measures for the reclamation work have not yet started. The government promised that there would be a large, protected marine area in Nor th Lantau, but this is not scheduled to start until 2023 after all the construction works are completed. We a r e e x p e c t i n g t h a t t h e d o l p h i n s ’ h a b i t a t s w i l l gradually improve due to the establishment of t h e m a r i n e p a r k a f t e r 2 0 2 3 . A marine protected area is an area where future construction works are prohibited and boat speeds are limited to a certain range, so there will be less fishing inside the area. But all these waters, including those taken by reclamation projects, belonged to the dolphins in the p a s t . We a r e n o t b u i l d i n g e x t r a h a b i t a t s f o r them; we are simply attempting to limit human d i s t u r b a n c e s i n s o m e a r e a s . We a r e i n d o u b t that this measure will drastically increase the dolphin population. But because it is something that the government has promised, we think that this will be very important for the dolphins.

Learn more about the East Lantau Reclamation project

Learn more about pink dolphins

Image source: https://www.greenqueen.com.hk/help-hong-kong-dolphin-tours-days-awayfrom-closing-down-due-to-low-tourism/

BIOLOGY AND CHEMISTRY

Mathematics featuring ar ticles fr om the Wor ld Maths Competition I n O c t o b e r, s e v e r a l H a r r o w s t u d e n t s competed in the World Mathematics Championships. The following articles were written as part of the Inspiration round where we were instructed to write an essay about how one particular mathematician contributed to 3 of the Sustainable Development Goals (SDGs). The SDGs are 17 interlinked goals intended to be a “blueprint to achieve a better and more sustainable future for all”.

Photo by Isabel Chau

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Re al L i f e Applications of Complex Numbers Josiah

Let’s start with the basics. At a young age, we were taught how to count with positive numbers, such as one, two or three. Later in primary school, we were also introduced to negative numbers: for example, -19 is a negative number. I’m also going to assume that you are familiar with square roots (if not, you should revise). It is commonly taught to students that one cannot take the square root of negative numbers. But what if we could? You may be wondering, “How is it possible to take the square root of a negative number?” In fact, mathematicians before the 16th century would’ve thought so as well. This was until Italian mathematician Gerolamo Cardano broke the convention by inventing imaginary numbers, in a desperate attempt to solve cubic equations. Throughout history, mathematicians have always loved to break their own rules: apart from taking the square root of a negative number, Ramanujan once proved that 1 + 2 + 3 + 4… all the way up to infinity is equal to -1/12. Another mathematician, Georg Cantor, proved that there are as many even numbers as positive integers. Therefore, what Cardano did was not uncommon (at least in historical records).

MATHEMATICS So what is an imaginary number? An imaginary number is a multiple of i = √-1. For example, √-25 is an imaginary number because it can be rewritten as √-25 = √25 × -√1 =5i. Furthermore, one can add a real number to an imaginary number to form a complex number. To demonstrate this, one can add 3, a real number, to 3i, an imaginary number, to form the complex number 3+3i.

Illustration by Ethan Lan A common visualisation of complex numbers is the use of Argand Diagrams. To construct this, picture a Cartesian grid with the x-axis being real numbers and the y-axis being imaginary numbers. An important property of complex numbers is the Euler’s formula: it states that every complex number, can be rewritten in the form of re =r(cos + i sin ), where e=2.71828... is the Euler’s constant, r is the ‘distance’ of the complex number from the origin and is the angle of the complex number from the positive real axis (anticlockwise, in radians). On the left is an illustration of this. Euler’s formula is described to be the most beautiful mathematical result in history by many mathematicians. Its aesthetic beauty lies in the fact that it implies a magical relationship between real numbers and imaginary numbers. Although I would like to demonstrate the elegant proof for this formula, it is unfortunately outside the scope of this article.

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Applications

Illustration by Ethan Lan

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Signal Processing Suppose a pianist is recording in a music studio. He invites you to a game - to guess what musical notes he plays without looking at the piano. As someone who doesn’t have perfect pitch (the ability to tell what musical note it is just by hearing), how would you win this game? It turns out, there is a way to always deduce what notes he is playing without cheating. Firstly, record his playing in an audio-editing software. The software will store the recording in a waveform.

One can then apply Fourier Transform to the waveform signal to figure out which frequencies are the most prevalent within the recording. This can be shown by deducing the ‘peaks’ in the resulting frequency distribution after Fourier Transform has been applied.

As there are evident peaks at 256 Hz and 391 Hz (which correspond to C4 and G4, respectively), we can therefore deduce that the pianist must have played C and G on the piano.

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MATHEMATICS Knowing the locations of peaks is incredibly important to audioeditors and music producers. They can not only derive the source of any background noise but also use its frequency as a reference to eliminate them through the means of Equalisation (EQ). The idea behind the Fourier Transform is rather genius; it proposes that any complicated wave can be decomposed into multiple sinusoidal waves with varying frequencies. What Fourier Transform does is that it predicts which frequency is likely to be equivalent to one of such sinusoidal waves. It does this by ‘wrapping’ the wave around the origin in the complex plane and computing the sum of complex coordinates of all possible points on the wrapped wave.

AC Circuit Analysis Complex numbers are also utilised in calculations of current, voltage or resistance in AC circuits (AC stands for Alternating Current, which is a current that changes magnitude and direction over time). A common application of complex numbers (more specifically, Euler’s formula) is to compute the potential difference across two AC power supplies with respect to time. On the right is an example of such a calculation.

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MATHEMATICS To find the combined potential difference, simply adding VA and VB together will not work. However, we can express both voltages as the Real Part (x-coordinate on the Argand Diagram) of a complex number.

*It is conventional to use j instead of i to represent imaginary numbers in circuit analysis, to avoid confusion with current (which its symbol is i or I). We can then add the numbers and factorise:

complex

Furthermore, complex numbers are also used to express the magnitude and phase of impedance in an AC circuit. Impedance is very similar to resistance - it slows down the electrons in the circuit. The distinction is that impedance causes a phase shift on the electrical current, while resistance does not. Impedance takes place in common electrical components such as inductors and capacitors, and so having a complex number representation is crucial.

In general, complex numbers serve as a representation of phase, which is essential to analysing AC circuits.

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Quantum Mechanics Quantum Mechanics is a field of Physics that deals with the motions and interactions between subatomic particles mainly Bosons (e.g. a photon) and Fermions (e.g. a neutron). It provides a mathematical description of their behaviour in terms of probabilities. In fact, complex numbers form the fundamental basis of Quantum Mechanics.

One main area of concern in Quantum Mechanics is to find the wave function of a subatomic particle. A wave function, simply put, is a complex probability distribution indicating the possible positions of the particle on a specific time. A fundamental formula in Quantum Mechanics, in which the role of the wave function is significant, is the Schrödinger Equation:

The importance of the Schrödinger Equation to Quantum Mechanics is analogous to that of Newton’s Second Law to Classical Physics; they both provide a sensible mathematical prediction of a particle’s position and momentum. The system of complex numbers is essential to the field because it is a convenient language for expressing wave functions without breaking the rules.

Theory using the Schrödinger Equation mentioned above. By using the formula, they proved that the two atoms in a hydrogen molecule are, in fact, ‘sharing’ electrons to form what we know as a covalent bond. Immediately after this, several other chemists continued developing their theory of bonding, such as Linus Pauling’s discovery of resonance and orbital hybridisation. In summary, without the development of Quantum Mechanics, scientists wouldn’t be able to discover the electronic structure of atoms, nor be able to come up with the concept of bonding between atoms.

Furthermore, a direct application of Quantum Mechanics is that it accelerated the expansion of Chemistry. In 1927, Walter Heitler (not Hitler!) and Fritz London formulated the Valence Bond

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Conclusion Although we cannot physically visualise complex numbers, it is difficult to deny its importance to the scientific community. Complex numbers perfectly demonstrate the role of mathematics in science - it acts both as a powerful language to describe complicated phenomenons, and a comprehensive toolkit to solve difficult problems.

Bibliog raphy Signal Processing (Fourier Transform) Star, Zach. “The Mathematics Of Signal Processing | The Z-Transform, Discrete Signals, And More”. www.youtube. com, 2019, https://www.youtube.com/ watch?v=hewTwm5P0Gg&t=1350s&ab_ channel=ZachStar. “Fourier Analysis”. En.Wikipedia.Org, 2020, https://en.wikipedia.org/wiki/Fourier_analysis. Accessed 9 Nov 2020. Chan, Justin. “Application Of Fourier Transform : Signal Processing”. www.youtube.com, 2017, https://www.youtube.com/watch?v=9uv3m8jkVg&ab_channel=JustinChan. Accessed 9 Nov 2020. AC Circuit Analysis Chan, Justin. “Application Of Fourier Transform : Signal Processing”. Www.Youtube.Com, 2017, https://www.youtube.com/watch?v=9uv3m8jkVg&ab_channel=JustinChan. Star, Zach. “The Real World Uses Of Imaginary Numbers”. Www.Youtube.Com, 2018, https://www.youtube.com/watch?v=_ h49ilnTmW4&t=630s&ab_channel=ZachStar.

“Complex Numbers And Phasors”. Https://Www. Electronics-Tutorials.Ws/, 2020, https://www. electronics-tutorials.ws/accircuits/complexnumbers.html. Johnson, Robert. “Using Complex Numbers In Circuit Analysis And Review Of The Algebra Of Complex Numbers”. 2020, http://www.its.caltech. edu/~jpelab/phys1cp/AC%20Circuits%20and%20 Complex%20Impedances.pdf Quantum Mechanics DeCross, Matt et al. “Schrödinger Equation | Brilliant Math & Science Wiki”. Brilliant.Org, 2020, https://brilliant.org/wiki/schrodingerequation/ Accessed 9 Nov 2020. Karam, Ricardo, ed. by. Why Are Complex Numbers Needed In Quantum Mechanics? Some Answers For The Introductory Level. University Of Copenhagen, 2020, https://www.ind.ku.dk/english/research/didacticsof-physics/Karam_AJP_Complex_numbers_in_ QM.pdf. Trejo, Miguel. “The Math Behind Schrödinger Equation: The Wave-Particle Duality And The Heat Equation.”. Medium, 2020, https:// towardsdatascience.com/the-math-behindschr%C3%B6dinger-equation-the-wave-particleduality-and-the-heat-equation-d5837bf4b13f.

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Cantor ’s Paradise:

Joshua Yen

Aus dem Paradies, das Cantor uns geschaffen, soll uns niemand vertreiben können. (No one shall expel us from the paradise that Cantor has created for us.) -David Hilbert 2

Abstract: In this article, I attempt to argue for spatio-temporal finitism from a wide range of paradoxes and conceptual arguments. If successful, my arguments would demonstrate that an actually infinite past and an actually infinite large universe is impossible. As seen in my previous entry “Science, Cosmology and the Existence of God”, such conclusions will have significant metaphysical and philosophical implications, though I would not delve into these here. Rather, I will stay with the cosmological conclusions, which is spatio-temporal finitism. 3

1 Notes behind the third edition of Cantor’s Paradise: Infinity on Earth. The additions made to this version remain relatively unchanged. The only differences and editions are those on the Quilted Universe theory and the possibility of a multiverse. 2 Hilbert, David (1926), “Über das Unendliche”, Mathematische Annalen, 95 (1): 161–190, doi:10.1007/ BF01206605, JFM 51.0044.02 3 That space and time are both finite and are not infinite

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Infinity on Earth1 Arguments against the Actuality of the Actual Infinite from Paradoxes: While Cantor’s set theory was developed in the 19th century, discussions of the nature of the potential and actual infinite date back to the ancient Greeks. It is in the works of Aristotle, more specifically his Physics, where we first find a significant discussion of the impossibility of an actual infinite series in reality. These critiques are commonly referred to as Zeno’s paradoxes attributed to Zeno of Elea who predominantly used these paradoxes to demonstrate that motion is an illusion. Though this is not the goal of our article, his “dichotomy” paradox is integral to our current discussion. Dichotomy Paradox:

The Dichotomy Paradox is twofold. Not only does it suggest that, given an actually infinite length, one cannot finish traversing the length, but it also suggests that if there were an actually infinite length, one cannot even start traversing the length. Now, this does not seem, prima facie, a fundamental problem for the proponent of infinite sets. 4 Yet if we apply such reasoning to reality, counterintuitive results arise. To demonstrate, Zeno asks us to imagine a man at the start of the race; “a moving object [does not move] because it has to reach the halfway point before it reaches the end”. 5 Viz ., before the man moves one meter, he must move half a meter, and before he can move half a meter he must move a quarter of a meter… resulting in a series represented as follows: {... ⅛, ¼, ½,1}. From now on, this type of series will be labelled the Z-series.

Figure 1 - A demonstrative diagram of the Dichotomy Paradox

4 Nor am I raising it as a problem for a proponent of the actual infinity, it is only a problem for those who believe in an actual infinity in reality which these problems arise for, and this goes for every paradox I raise in this section 5 Arist. Phys. VI.9, 239b9-14, trans. Waterfield.

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From this reasoning, it appears that the man cannot finish the race because before he reaches the end of the series, he must have crossed the preceding half, and before that, the preceding half, ad infinitum. The inverse is also true. Before one can start the race, they must cross a half, then the preceding half, then the preceding half of that half, suggesting that the man cannot even start the race. Now, this result is absurd. In reality, we see people completing races and distances all the time. While it may be tempting for one to believe that the actual infinity is impossible, based on my preliminary remarks, in reality, the argument laid out by the dichotomy paradox is far from sufficient. 6 Let us return to our distinction between the actual infinite and the potential infinite, the paradox can only challenge the actual infinite if, and only if, the Z-series can be seen as an actually infinite series.

Now a response to this would be the idea that the divisions on the line are only a potential infinite. Such is the response of Aristotle who writes, “I have argued that no actual magnitude can be infinite, but it can still be infinitely divisible, and so we are left with things being infinite potentially”. 7 Will this defence suffice for the proponent of the actual infinite in reality? I believe not. What this defence shows, I believe, is not that Zeno’s dichotomy paradox is rendered futile in regards to the actual infinite, but that it cannot be used as an argument against a potentially infinite series. As we can see, far from defeating the paradox, it seems like this response fails to address the problem and is no defence of the actual infinite at all. One could happily accept the existence of the potential infinity, yet wholeheartedly reject the reality of the actual infinity. "8

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However, the question still remains: can the Z-series be seen as an actual infinite? I believe so. Since the cardinalities 9 of two sets are equivalent if their elements can be ordered in a 1-1 correspondence with each other 10 , then it does appear Since cardinal numbers are abstractions of an aggregates’ order, we can write the set {... ⅛,¼,½,1}as {1,½,¼,⅛... }. Then, we can place the two series in 1-1 correspondence: {(1,1),(2,½),(3,¼) n-1 ,(4,⅛),...,(n,½ ),...}

Since the cardinality of the set of positive integers is , it follows 0 that the cardinality of the Z-series is also . This conclusion is echoed in 0 Benardete’s 1964 work Infinity, “Zeno confronts us with a series that is actually infinite. It is in no way reducible to the potential infinite. Infinity figures in the paradox as something very much more substantial than a mere facon de parler 11”. Hence, it seems evident that Zeno’s dichotomy paradox and his Z-series poses a significant problem for the proponent of actual infinities in reality.

6 It is dependent on further ideas and implications like the discrete or continuous nature of time and space.

way. What seems more likely to be true is that the number of divisions on the line are actually infinite or the idea that both the length and its components are both defined and finite.

7 Arist. Phys. III.6, 206a14-21, trans. Waterfield. 8 I would like to further question Aristotle’s methodology here. For it seems absurd to suggest that the number of points on a definite and finite line is of a potential infinite with a “non-existent” limit. Even without my further discussion of bijection with the natural numbers, it seems absurd to suggest that the points on a defined line are only potentially infinite, for if there can be a measurable cardinality for a line, the units too can be measurable in a similar

9 Cardinality: the number of elements within the set 10 Jourdain, Philip E.B. “First Article.” Contributions to the Founding of the Theory of Transfinite Numbers, by Georg Cantor, Dover Publications, 1915, p.87. 11 “Infinity.” Infinity: An Essay in Metaphysics, by Jose A. Benardete, Oxford University Press, 1964, p.13.

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MATHEMATICS To revive their case, a critic of our paradox can suggest that the argument is wrong via modus tollens. Since divisions are actual infinities, it follows that actual infinities must exist in reality, for magnitudes and lines do exist (upon which infinite divisions can be applied).

Let us turn to the chemical structure of the world. In physics, we can see that all objects are made up of molecules which are further made up of atoms which are then made up of smaller quantum particles. As you get smaller down the hierarchy, you soon reach these unique and indivisible particles. 12

While it is true that if these divisions are actual, there would now be an infinite number of points on any given line, there is no reason to believe that this is the case. What appears to be more reasonable is to view divisions as conceptual impositions on actual phenomena, not as actual phenomena themselves.

With this in mind, even though it is true that we can conceptually divide finite lines ad infinitum, we have no reason to believe that a similar division occurs in the physical world. From this fundamentally finite nature of the building blocks of the universe, it follows that the universe itself is finite. 13 That said, one can suggest that this idea of a fundamental indivisible quantity is inapplicable to time. While such features can be found in physical reality, can the same features be applied to the passage of time? 12 Note that there is a significant difference between the conceptual and the physical. All discussions here are focused towards the physical infinite instead of the conceptual infinite. 13 For one cannot create an actual infinite out of only finite aggregates.

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It would appear prima facie, that one cannot apply the same argument from fundamental divisions to demonstrate the finite nature of time, a fortiori, it can be argued that one can carry out a Z-series division on the nature of time. Hence, demonstrating the existence of the actual infinity in concreto. In response to this, one can propose that time is the changing states of affairs. 14 Ex hypothesi, we can soon see that states of affairs will play the same role as our fundamental physical elements in our previous arguments. From this, we can also conclude that time itself must be finite, as like in the previous argument, time is constructed from finite aggregates.

14 Evidently, one can quickly object to this view by claiming that it is controversial, and I would not deny this charge. However, I do believe that when compared to its alternatives, it is by far the most parsimonious view to hold and is indeed the one which is least fraught with difficulty. As seen in our current discussion on Zeno’s paradoxes, any view which suggests that time is a mental imposition on the changing of events are plagued with physical problems of movement and change (the Z-divisions would apply and time itself should not be able to move). As a result, it appears that time must be

Hence, we can see that the very problems raised by the dichotomy paradox forcing the philosopher to adopt worldviews that entail spatio-temporal finitism. Viz ., by accepting that all matter and time are composed of fundamentally finite divisions or particles, we can see that the entirety of space and time are indeed finite. 15 This conclusion from the dichotomy may not be as originally expected. This is not an argument directly from the dichotomy to the impossibility of the actual infinity, rather an argument from the results of the dichotomy which forces anyone who believes in motion and the passage of time to commit themselves to spatio-temporal finitism. 16 a real phenomena in the physical world, not an external imposition. 15 As seen in footnote 31 and 52, this is not an instance of an argument from composition, rather a result from a mathematical concept. 16 Note that this is not finitism simpliciter. In the first two formulations of this document, I had a variety of other neo-Zeno paradoxes, these can be found in the appendices at the end.

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The Grim Reaper Paradox While the dichotomy paradox does appear to be sufficient to defeat the notion of an actual infinite in reality, another paradox, one of the more recent paradoxes against the existence of an actually infinite series of causes, has been developed by Benardete. Benardete’s formulation can be summarised as follows:

Imagine that there exists a man Fred and an infinite number of Grim Reaper mechanisms.

The Grim Reaper machines have two functions, first to check whether Fred is alive, secondly, if Fred is alive, to kill Fred.

The last Grim Reaper performs this task at exactly one minute afternoon.

The next to last Reaper carries out this task half a minute afternoon, then the Reaper before the penultimate one would carry out this task a quarter minute afternoon and so on.

(As in the Dichotomy paradox) If there exists an actually infinite number of divisions in time, there cannot be any first Reaper, for each Reaper, there are an infinitely many Reapers existent before said Reaper

Fred cannot survive the ordeal, for there would always be a Grim Reaper to have killed him

Fred cannot have been killed by any specific Reaper, because before each Reaper, there was a previous Reaper that killed him, and a previous one before that.

Hence, it seems impossible for Fred to die with certainty from a definite cause, all the while having to be dead at the same time. 17

MATHEMATICS Now, these arguments are powerful, but what are Benardete’s solutions? In his book Infinity, he concludes “although [the man] did not die of any single bullet wound, his death was caused by the infinite fusillade of shots”. 18 What does Benardete mean with such brief and oracular comments? While I am loath to misrepresent his views and end up attacking a strawman, it implies that Benardete is suggesting, though not a single bullet killed the man, it was the totality of bullets that led to the man’s death, the aggregate of all the attempts which killed the man. 19 Yet is this concept of the “totality” or “fusion” of bullets killing the man satisfactory to solve the paradox? I believe not. Despite the intricate development by Hawthorne, it seems problematic to suggest that a fusion of bullets could kill a man, even if no specific bullet actually hit the man. For if no definite bullet hit the man, how can one even develop such a situation to suggest that the totality of bullets killed him? For imagine a man at D-Day storming the beaches of Normandy.

As the first man on the beaches, the machine guns of the German army are all focused on him. Despite the attempts and hundreds of bullets flying at him, none of them hit him. With this in mind, since he is unscathed by any bullet, it would be absurd to suggest that he died, let alone to suggest the totality of bullets flying at him, though not hitting him, did cause his death. So it does appear that Benardete and Hawthorne’s solutions are unsatisfactory when held under scrutiny and the Grim Reaper’s paradox truly has had its revenge. So what does the Grim Reaper’s paradox tell us? I believe that it is more restrained and more precise than the Dichotomy. As seen, the Grim Reaper tells us nothing about infinite space or infinite cardinality; rather, it is directly focused on an actually infinite series of causes, and as an extension of that, time. Hence, what we learn from the Grim Reaper paradox is the idea that both time and series of causes have to be finite, proposing an absolute beginning to any physical or temporal entity before which it either did not exist or was not a physical or temporal entity.

17 Benardete, J. A. Infinity: An Essay in Metaphysics. Oxford University Press, 1964. For Koons’ development see Koons, Robert C. “A New Kalam Argument: Revenge of the Grim Reaper.” Noûs, vol. 48, no. 2, 2014, p. 256. www.jstor.org/stable/43828872. Accessed 2 Dec. 2020. 18 “Minims and the Continuum.” Infinity: An Essay in Metaphysics, by J. A. Benardete, Oxford University Press, 1964, p. 260. 19 This idea of the “fusion” of the events is further developed by Hawthorne in his paper BeforeEffect and Zeno Causality (Hawthorne, John. “Before-Effect and Zeno Causality.” Noûs, vol. 34, no. 4, 2000, pp. 622–633. JSTOR, www.jstor.org/stable/2671884. Accessed 2 Dec. 2020.)

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The paradox of the Man with Infinite Knowledge:

While there are many more paradoxes against the realisation of the actual infinite, the final paradox against such a phenomenon is a personal creation. Now, I would like to make clear that there may exist flaws in my paradox which I have not thought of yet, but if the paradox is sound, it should demonstrate that an actually infinite set cannot be realised in reality, nor could someone obtain a complete and thorough understanding of an actually infinite number of objects or knowledge given certain restrictions. In this paradox, let us imagine a man, Z, who only has a thorough and complete understanding of a transfinite set (for the sake of the demonstration I will use ). This 0 can be written as: (1) Let x be the total cardinal aggregate of the knowledge of man Z (2) Let man Z only have a thorough and complete understanding of a transfinite set, viz., Z knows nothing other than the transfinite cardinal. Now, a thorough and complete understanding of the cardinality of a set implies that the man knows the number of elements within the set for the number of elements inside

a set determines the magnitude of the set, which is the cardinality of the set. For example, we know that the cardinality of the set {1,2,3,4,5} is 5 from our knowledge that there are five elements within the set. With this in mind, it follows that a thorough and complete knowledge of the cardinality of the transfinite set 0 would give the man an actually infinite magnitude of knowledge whose cardinality is 0, such that: 20 = (3) {x= } 0 We can further note that the cardinality of all individual knowledge is 1; the cardinality of an aggregate M “arises from the aggregate M when we make abstraction of the nature of its various elements m and of the order in which they are given in” 21 . From which it follows that if a man’s knowledge increases by one individual knowledge, the cardinality of his newfound aggregate knowledge would be n+1. This can be notated as: (4) Let n be the total cardinal aggregate of the knowledge of man Z (5) Z learnt a new knowledge -> his total cardinal aggregate of his knowledge would be n+1

MATHEMATICS Now let us return to man Z with the understanding of the cardinality of an actually infinite set. Despite having actually infinite knowledge (3), it can be easily demonstrated that there is knowledge that he doesn’t know—since infinite set theory is not the only knowledge that exists, there must be something that Z doesn’t know (2). Let q be such knowledge: (6) {(

q)(q

x)}

Let the cardinality of q be 1: = (7) q=1 Since q is not part of Z’s understanding, it is possible for Z to learn that he does not know q and increase his knowledge. From (4) and (5), the intuitive result would be: (8) Prior to the obtainment of q, = from (3);{x= } 0 (9) After the obtainment of q, whose cardinality is 1, x would increase by one so that {x+1= +1} 0 Prima facie, this appears to be logical as, given any additional knowledge, it is clear that the cardinality of

one’s total knowledge would be greater than the knowledge prior to learning something new. For it is apparent that: 22 (10) x<x+1, x+1>x However, like Hilbert’s hotel paradox, we know that the intuitive results of (9) are incorrect under the rules of transfinite arithmetic. According to Cantor, it is wrong to carry out transfinite addition as one would with finite addition so that instead of (9), the cardinality of the aggregate x after learning new knowledge should still be { 0 } = (11) From (3) ( x)(x= 0 , 0 +1= 0 → = = x+1=x} Yet this is clearly an absurd result given our paradox! How could a person possibly learn new knowledge and not have their total aggregate of knowledge increase? Surely one can learn more even if they have grasped the cardinality of the actual infinite, or perhaps, in other words, there cannot be a limiting factor of knowledge such that when one conceptualises the cardinality of the transfinite numbers they can learn no more or extend their aggregate knowledge any further!

20 Furthermore, one can note that we wouldn’t call someone who didn’t know all the elements within a set to be someone who has a thorough and complete understanding of said set. 21 Ibid. p.86.; it is also good to note that Frege also believed that “it was possible to count anything that was an object of thought” (“The Foundations and Philosophy of Cantorian Set Theory” Georg Cantor His Mathematics and Philosophy of the Infinite, by Joseph W. Dauben, Princeton University Press, 1990, p. 220.) This further suggests that this distinction of the numerical cardinality of thoughts is a possible distinction and not just one of hypothesis. 22 Further developments for this can be seen and explained in the section of conceptual arguments.

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Illustration by Ethan Lan

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MATHEMATICS Hence, I believe that the paradox of the man of infinite knowledge is a powerful demonstration against the possibility of the actual infinite in reality and a powerful argument against the idea that one can possibly obtain a complete understanding of a transfinite set. To develop this idea further, let us imagine the implications of knowing an actually infinite set. Based on our aforementioned demonstration that one increases their knowledge once their aggregate knowledge reaches the size of an actually infinite cardinal, let us conceive of two more people A and B. Let it be the case that A only knows how to play basketball before he obtains a complete and thorough understanding of the actually infinite set and let B only know both how to play basketball and how to play football before obtaining a complete and thorough understanding of the actually infinite set, such that: (12) Prior to obtaining the knowledge of an actually infinite set, A only knows how to play basketball such that, if r is the cardinal aggregate of A prior to learning the actually = infinite set, r=1 (13) Prior to obtaining the knowledge of an actually infinite set, B only knows how to play basketball and football such that, if f is the cardinal aggregate of B prior to learning the = actually infinite set, f=2 Now when after the obtainment of the complete and thorough understanding of the actually

infinite set, we see that both A and B now both have the same aggregate knowledge, despite the fact that the knowledge they had previously was exactly the same, such that: (14) After learning the knowledge of the actually infinite set, both r and f have a cardinal aggregate of aleph = null. {f= ,= r= } 0

If this result isn’t confusing enough, now imagine that B learns a new piece of knowledge, how to build a house, for example, we also see that his total aggregate of knowledge = does not change such that {f= 0 } = (15) {f+1=

}

So what can we see from this further development of the paradox? Not only is the paradox a problem for the physical world, but it also has significant conceptual implications. Once someone’s knowledge reaches that which can be put into bijection (1-1 correspondence) with any transfinite number, their knowledge cannot be increased any further. This is regardless of how much knowledge they had before obtaining the understanding of the transfinite, be it one or one million, once someone has a complete and thorough understanding, they can no longer increase their total aggregate knowledge, though they can learn new things. As a result, I feel that this paradox is a more complete paradox than the Hilbert’s Hotel formulation and is a useful tool in exploring the consequences and implications of an actually infinite state of affairs both physically and conceptually.

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MATHEMATICS Arguments against the Actuality of the Actual Infinite from Conception: The conceptual discussion against the formation of an actual infinite in reality is more subtle than our previous discussion. While it is undeniable that the usage of paradoxes demonstrates the absurdities of the infinite, are there any further reasons to explain why the infinity encounters these problems when we try to apply them to reality? To answer this question, I would turn to the argument from magnitude which stems from six premises to the impossibility of a transfinite in reality: 1. Magnitude in the universe is objective 2. Magnitude in the universe is diverse 23 3. Magnitude of objects can be arranged via their sizes in the following relationships, x<y, x>y, x=y (where x and y represent variables) 4. Magnitude increase simply by addition

can

denoted

5. Magnitude decrease simply by subtraction 24

can

denoted

6. (from 4 and 5) x+y>x, x-y<x (where x represent variables and y positive magnitudes) If these six observations are true, it follows that the actualisation of transfinite arithmetic is impossible in reality, for propositions like +y= , would violate 0 0 observation 6 despite being mathematically possible.

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With this in mind, let us turn to our six observations and see whether they are true and applicable to our current physical world. I have already defended (1) and (2) above so I would discuss (3)-(6). To me, these four observations are non-controversial. Observation (3) follows from the diversity of magnitudes; on the assumption that there are different magnitudes, it follows that there would be magnitudes which have the same size, “=”, and magnitudes which have different sizes, “<” and “>”. Observation (4) and (5) appear to be self-evident. If there is a change of a magnitude, given the use of a proper unit, one can accurately use addition and subtraction to denote the change. From which observation (6) logically follows, an increased magnitude is analytically greater than the original magnitude and the same applies to the decreased magnitude, mutatis mutandis. Hence, it appears that in any world where these six observations hold (our world being one of them), the truth of these six observations implies the impossibility of the actualisation of

the transfinite system. From this, it also follows that in any world which supports the transfinite system, one cannot accept the actualisation of finite arithmetic as it would lead to contradiction (from which anything follows). Now a common response would be that I am once again begging the question against the nature of the actual infinity. By presupposing that transfinite arithmetic cannot be true in premise (6), I have presupposed what I am trying to prove. However, let us not be so hasty in this supposition. While it would be question-begging if I were to accept these premises a priori, I am actually arguing for them a posteriori. These premises are individual propositions which are always verified and never falsified in our understanding and observation of the world around us. Hence, I would not be begging the question against the actual infinity in reality, rather I am using the features of our present universe to demonstrate that the actual infinity cannot be realised.

23 There exists a variety of magnitudes. 24 Addition and subtraction can be developed to more complex procedures like multiplication and exponentiation, however these can be seen as developments of addition and are not of significant importance here.

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Apropos Physics: Now we have established spatio-temporal finitism, two propositions come immediately to mind. First, we can be assured that the size of the universe 25 is finite. Secondly, we can be assured that the temporal nature of the universe is also finite and there cannot be any infinite regress or infinite past/ future scenarios. 26 Now the first proposition is not too controversial, all paradoxes and arguments can be applied to any view on the nature of space. However, if one were to turn to the second proposition, the discussion becomes more complicated. Here, one must take into consideration both A and B theories of time. While I would not go into depth here, a brief understanding of both these theories is integral to our current discussion. The A-theory of time is essentially a dynamic and “common-sense” theory of time. This is the idea that the usage of tensed language accurately represents the passage of time. States of affairs that happened prior to the current state of affairs can be seen as occurring in the past whereas states of affairs that have not happened yet are, for this moment, non-existent, and will come into being in the future. The B-theory of time is the opposite of the dynamic theory of time, unlike the aforementioned “tensed” theory of time, the B theory is closer to a static theory of time which states that time is a preexisting construct and we are only

traversing an already formed construct. In this view, time does not pass, but we find ourselves at different points on this “block” of time. It is undeniable that the arguments against a transfinite series are more potent against an A theory of time, whereas when it comes to the B theory of time, a lot of our arguments become irrelevant. Since time is not growing, arguments from successive addition, including the argument from magnitude and the man of infinite knowledge paradox, do not apply. As a result, it appears that the only arguments which do apply to a B-theory of time would be our Grim Reapers paradox, our dichotomy and our argument from axioms and function graphs. Hence, while a B theorist would still have difficulties with an infinitely existing time, these problems are less significant than those posed to the A theorist who would bear the full force of my arguments. 27

25 Referring to the totality of existent matter, if there is a multiverse, then the usage of the word “universe” here would include these other universes as well. 26 One ought to note that “infinite” here means actually infinite not potentially infinite.

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To c o n c l u d e : From the various paradoxes and conceptual arguments raised, we have established that we cannot actualise an actually infinite magnitude in reality. As a result, we should believe in spatio-temporal finitism and that there are finite boundaries to both space and time. Keeping that in mind, one must remember that the mathematical nature of the infinite is still useful and helpful and that it would be an error to affirm finitism simpliciter.

Bibliography: Hilbert, David (1926), “Über das Unendliche”, Mathematische Annalen, 95 (1): 161–190, doi:10.1007/BF01206605, JFM 51.0044.02 Arist. Met. XI.6 Arist. Phys. trans. Waterfield Hilbert, David. “On the Infinite.” Philosophy of Mathematics: Selected Readings, edited by Paul Benacerraf and Hilary Putnam, 2nd ed., Cambridge University Press, Cambridge, 1984, pp. 183–201. Cantor, Georg. Contributions to the Founding of the Theory of Transfinite Numbers. Translated by Philip E. B. Jourdain, Dover Publications, 1915. Cantor to Hermite, November 30, 1895: Cantor (III), 48 (as cited in Dauben 1990) Cantor’s letter to Franzelin in Cantor (1887), 399-400. (as cited in Dauben 1990) Bolzano, Bernard. Paradoxes of the Infinite. Translated by Fr, Prihonsky, Routledge & Kegan Paul Ltd, 2015. Koons, Robert C. “A New Kalam Argument: Revenge of the Grim Reaper.” Noûs, vol. 48, no. 2, 2014, pp. 256–267., www.jstor.org/ stable/43828872. Accessed 2 Dec. 2020. Benardete, J. A. Infinity: An Essay in Metaphysics. Oxford University Press, 1964.

Hawthorne, John. “Before-Effect and Zeno Causality.” Noûs, vol. 34, no. 4, 2000, pp. 622– 633. JSTOR, www.jstor.org/stable/2671884. Accessed 2 Dec. 2020. Dauben, Joseph W. Georg Cantor His Mathematics and Philosophy of the Infinite. Princeton University Press, 1990. Cantor, Georg. Letter to Gustav Enestrom. 1886 (as cited in Dauben 1990) Fraenkel, Abraham A., et al. Foundations of Set Theory. Kindle ed., Elsevier, 2001. Herbrand 1932, p.3, footnote 3. (As cited in Fraenkel 2001) Craig, William Lane. Time and Eternity: Exploring God’s Relationship to Time. Crossway Books, 2001. Feser, Edward. Five Proofs for the Existence of God. Ignatius Press, 2017. Craig, William Lane. The Kalam Cosmological Argument. Wipf and Stock, 2007. Plantinga, Alvin. The Nature of Necessity. Clarendon Press, 1974.

Image Source https://www.space.com/30203-observatory-tospot-colliding-black-holes-in-space.html

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Introduction to By Josiah Wu

Graph Theory is a branch of mathematics that has numerous applications across the different sciences, especially in Computer Science. Without Graph Theory, navigation apps such as Google Maps would not be able to find the shortest route from your house to school efficiently, and search engines wouldn’t be able to show the websites you wanted on the first page. As a disclaimer, this article will not discuss this:

Figure 0.1 - a Cartesian x-y graph

Instead, the whole article will be dedicated to introducing structures like these: Note: Do not ask me why mathematicians would want to confuse themselves by naming two different objects by the same name. Figure 0.2 - examples of graphs

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Graph Theory 1. The Basics Below is an example of a graph.

Figure 1.1 - Map of the London Underground

This is also an example of a graph:

Figure 1.2 - A Relationship Map

A graph is a mathematical structure consisting of vertices and edges. In the example of the tube map (Figure 1.1), the stations are the vertices, while the subway lines in between neighbouring stations are the edges. This is an example of an undirected graph because no edges have designated directions.a In the example of a relationship map (Figure 1.2), the individuals themselves are the vertices and the arrows are the edges. Because the edges of the graph have directions, it is a directed graph.

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MATHEMATICS For simplicity, mathematicians use circles to represent vertices and straight lines to represent edges. Mathematicians also represent graphs in formal notation; they denote a graph G as a set of vertices V and a set of edges E, i.e. G = (V, E). Below is an example of a graph written in formal notation.

Figure 1.3 Graph G

You may wish to picture a graph as a subway map, in which the vertices are the stations and the edges are the train lines. For example, if a ‘passenger’ wants to ‘travel’ from v 6 to v 5 , he or she must take the e 7 ‘train’. This metaphor will allow you to understand the terminologies used in Graph Theory more easily. Mathematicians refer to a journey from one vertex to another as a walk. For instance, below are a few possible walks from v 6 to v 4 .

Figure 1.4a - Walk A

Figure 1.4b - Walk B

Figure 1.4c - Walk C

WA = <v6, e7, v5, e6, v4>

WB = <v6, e7, v5, e5, v3, e 3, v 2, e 4, v 4>

WB = <v6, e7, v 5, e5, v 3, e3, v 2, e 1, v 1, e 2, v 4>

MATHEMATICS In particular, Graph theorists are generally interested in the following type of walks: • Paths - a walk with no repeated vertices. • Trails - a walk with no repeated edges. • Cycle - a walk whose start vertex and end vertex are the same. And the following types of graphs: • Connected Graph - a graph in which a walk exists between any pair of vertices. • Subgraph - a graph whose vertices and edges appear in another graph. • Tree - a graph with no cycles. Moreover, notice that v 5 is connected by three edges; hence the degree of v 5 is 3. If we add up the degrees of each vertex in graph G, we obtain the sum of 14, which is twice the number of edges (7). This demonstrates the fundamental theorem of Graph Theory for undirected graphs:

Theorem 1.1 For all undirected graphs, the sum of degrees of vertices is always twice the number of edges. Proof Consider any undirected graph G (we will use the above example). Now remove all the edges of G, leaving only its vertices, as shown below. Figure 1.5 - Graph G - E(G)

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MATHEMATICS Now each edge is added one at a time.

Notice that when an edge is added, the degree of each end vertex increases by one. Consequently, we can observe that each edge contributes two to the degree sum, and so the degree sum must have twice the number of edges. Q.E.D. As a result of this theorem, one can prove the following observation:

Corollary 1.1 For all undirected graphs, the number of vertices having an odd number of degrees is always even. Proof Notice, for every undirected graph, vertices either contain an odd number or an even number of degrees. Now

Figure 1.6 - Adding edges to graph G

consider the sum of those which are odd (which we will denote as P) and the sum of those which are even (which we will denote as Q). By Theorem 1.1, P + Q must be even since it must be a multiple of 2. Clearly, Q is even, and so it must follow that P is even. Therefore, the number of odd degrees is even, as desired. Q.E.D.

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2. The Seven Bridges of Königsberg Graph Theory was founded upon a solution to a famous problem in Mathematics - The Seven Bridges of Königsberg. In the city of Königsberg, Prussia (now known as Kaliningrad, Russia), there are seven bridges across the rivers in the city centre, as shown:

Figure 2.1 - The Seven Bridges

Some locals then wondered, is there a way to design an on-foot tour such that it traverses each bridge exactly once and starts and ends at the same place? It certainly looks possible, but how would we know? This riddle baffled the citizens for a while, as they couldn’t prove nor disprove whether such a tour is possible. Fortunately, Leonhard Euler, a famous mathematician, discovered a solution to this seemingly trivial problem. He later published his results to the Academy of Sciences of St. Petersburg in 1735, which became the first paper in the history of Graph Theory.

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So how did Euler solve the problem? In his paper, Euler first simplified the problem by reconstructing the diagram, leaving only landmasses. He then observed that in such a tour, no vertex can have an odd degree. This is because whenever one enters a vertex by an edge, it must also be able to leave the vertex by another edge. Or else, there is no way to exit the vertex after entering it!

Now we return to the graph in question; by counting the number of edges connected to each vertex, we can see that all the vertices are of odd degree. As a result, a tour around all bridges that starts and ends at the same location does not exist.

But what if all the vertices of a graph have even degrees? How can we guarantee that a tour always exists in that graph? The actual answer to this is rather complicated, so I will simply leave the proof below for those who are interested.

Figure 2.2 - Even degree vertex vs Odd degree vertex

Figure 2.3 - Graph of Königsberg Bridges

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Theorem 2.1 A closed trail that traverses every edge of an undirected graph G is called the eulerian tour of G. An eulerian tour of G only exists if the degree of every vertex is even. Proof Since G is connected and every vertex has an even degree, G cannot be a tree and so it must contain a cycle, say C 1 . As C 1 is a cycle, every vertex of C 1 must be of even degree. Now consider G 1 = G - E(C 1 ). If G 1 has no edges, then C 1 is the eulerian tour that completes the proof. Otherwise, pick another cycle from G 1 , say C 2 . This is always possible because all vertices of G1 must be of even degree. Now consider G 2 = G 1 - E(C 2 ) and repeat the procedure until all the edges are exhausted. Hence, G = C 1 U C 2 U C 3 … U C n for some positive integer n. Note that each edge of G belongs to exactly one of C 1 , C 2 , … C n .

Figure 2.4 - Removing cycles from graph G

We then prove, via contradiction, that the eulerian tour of G must contain all these cycles. If it doesn’t, then there is a cycle, say C, that is not part of T. But since G is connected, C and T must share at least one vertex, say ‘v’. However, a new eulerian tour can be created by starting at v, then travelling around C back to v, followed by traversing around T. This contradicts the notion that T is an eulerian trail (because T must cover all edges of the graph). Therefore, T must contain the cycles C 1 , C 2 … C n , and so an eulerian tour is created by joining these cycles. Q.E.D.

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3. What’s the shortest route? We have all used navigation software at some point in our lives. More than a billion users around the world use Google Maps every month. Humans in the 21st century rely on navigation software to provide the quickest route to their desired destination. But how does the computer achieve that? Specifically, the problem is that there are infinitely many ways to travel from point A to point B, and we wish to find the one which is the quickest. In Computer Science, this is referred to as the Shortest Path Problem. Although there is no optimal solution to this problem, computer scientists

have come up with algorithms that effectively tackle the problem. The solution to the problem requir quires breaking down a map ap into a weighted graph. A wei weighted graph is a graph whose edges are assigned a numerical value. In this context, the values represent the time taken to travel from one location to another. To demonstrate how all this works, we will use the London Underground map as an example. Firstly, we convert the map into a graph, then assign each edge with its respective weights (travel time in minutes), as follows:

MATHEMATICS Suppose we want to find the shortest journey from Green Park to King’s Cross St. Pancras. We can then apply Dijkstra’s Algorithm to generate a spanning tree, in which we can obtain the shortest path. The specific definitions of the terms are irrelevant to this discussion.

Dijkstra’s Algorithm (Simplified version)

1. Assign the start vertex, s, with the number 0.

Input: a weighted and connected graph G and a vertex of G, s.

2. Of all unassigned vertices in G, find the one vertex v such that it has the lowest dist(v). If there are no labelled edges, label the edge connecting s and v. Else, label an edge connecting v and a vertex incident to another labelled edge.

Output: a spanning tree T of G, rooted at vertex s, whose path from s to each vertex v is the shortest path from s to v in G. Functions: dist(v) = the weight of the shortest walk from s to v.

3. Assign v with dist(v). 4. Repeat steps 2 and 3 until all vertices are assigned. Return graph T that contains all labelled edges and assigned vertices.

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Figure 3.2 - Applying Dijkstra’s Algorithm to the weighted graph

MATHEMATICS Using the spanning tree, we can deduce the shortest route from Green Park to King’s Cross St. Pancras. Notice that there is only one unique walk from the two stations within the spanning tree this is the shortest route.

Other algorithms can also solve the problem (e.g. A* search algorithm, FloydWarshall algorithm, etc.). In reality, computer scientists often choose the most timeefficient algorithm; the measure of the efficiency of an algorithm is called the Time Complexity, denoted by the big O notation. For example, Dijkstra’s algorithm has a time complexity of O(V 2 ).

Figure 3.3 - Minimum Spanning Tree & the Shortest Route

4. Graph Colouring Consider the following riddle: how many colours are required to fill in the map below such that no two neighbouring regions share the same colour?

Figure 4.1 - Map of Europe

Figure 4.2 - Map of the United States

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If you guessed more than four colours, then you are incorrect. The Four Colour Theorem states that for any map, no more than four colours are required to colour the regions so that no two adjacent regions share identical colours. The Four Colour Theorem is the first theorem in mathematical history that has been proven with the aid of computational technology. It involves brute-forcing all scenarios i.e. all possible types of maps, then proving that at most four colours are sufficient.

Another result due to the research on graph colouring is Chavtal’s Art Gallery theorem. This theorem states that for any polygonshaped art gallery with n vertices, it takes at most [n/3] guards to monitor the whole gallery. ([n/3] means the largest integer less than n/3). To understand this theorem fully, we first have to define what ‘monitor’ actually means. In this context, a point in the polygon is observable if there exists a straight line segment inside the polygon that connects the point with a guard.

Figure 4.3 - Observable and non-observable locations in the Art Gallery Problem

The theorem, therefore, states that [n/3] guards are always sufficient to observe all points within the polygon with n vertices.

MATHEMATICS

So how exactly are these two theorems related to g raphs? The answer is that both involve transforming the diagram into a triangulated graph, which is then used to arrive at the final result (i.e. the theorems themselves). The first steps to prove the Four Colour Theorem were provided by Alfred Kempe in 1879. For every region that has more than three sides, add necessary edges to split the region into smaller triangles. Add vertices to all intersections of region borders to form a graph.

It can be proven that the graph is 3-colourable. This means three colours are sufficient to colour the vertices such that no two adjacent vertices share the same colour. Since there are n vertices, at least one set of vertices of the same colour must have at most [n/3] vertices and this is where the guards will be placed. Consequently, the theorem is proven.

Figure 4.4 - Triangulation of a map Kempe then argues that, if the regions of this triangulated graph are colourable by four colours, then the original graph must also be as well. In the proof of the Art Gallery Theorem, a similar trick is used as n - 3 noncrossing diagonals are drawn between the corners of the walls until the interior is triangulated. Each corner is also labelled as a vertex.

Figure 4.5 - Triangulation of an art gallery

Figure 4.6 - Location of the guards as a result of Chavtal’s Art Gallery Theorem

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5. Introduction to Spectral Graph Theory ( Wa r n i n g : r e q u i r e s A - L e v e l F u r t h e r Mathematics knowledge) Spectral Graph Theory is a sub-field of Graph Theory that studies the properties of graphs through the use of matrices. If you are not familiar with matrices, do not expect yourself to fully comprehend this chapter; feel free to skip ahead. A common tool in spectral graph theory is the adjacency matrix. It essentially indicates which pairs of vertices are connected with an edge. For vertices v i and v j in a simple graph, A i,j = 1 if v i and v j are connected by an edge; else, A i,j = 0. Below is an example of an adjacency matrix.

Figure 5.1 - Graph G and its adjacency matrix

One important property of adjacency matrices is that you can raise the power, r, of the matrix, and hence derive the number of walks of length r between vi and vj, as follows.

Figure 5.2 - Square of an adjacency matrix and its implications

MATHEMATICS This means that we can find the number of ways travelling from one vertex to another using r edges, where r can be any positive integer. The adjacency matrix, therefore, is useful for this very purpose. Adjacency Matrices can also be used to determine whether a graph is bipartite. A bipartite graph is a graph whose vertices can be separated into two sets such that no edges are connecting two vertices within their respective sets.

Figure 5.3 - An example of a bipartite graph

In particular, if a simple graph is bipartite, then the mean of eigenvalues of its adjacency matrix must sum to zero. Firstly, for any matrix M, the eigenvalue tttis a specific number (not necessarily real) that satisfies the following equation Mv=

where v is an arbitrary vector. To find the eigenvalues , we need to evaluate the equation below: det(MProof: Mv= (M-

I)=0

v → Mv-

I)v=0 → det(M-

Iv=0 → I)=0

After the eigenvalues of the adjacency matrix are obtained, if the eigenvalues sum to zero, then the graph must be bipartite. Below is an example of such a calculation:

Figure 5.4 - Finding eigenvalues of A

The proof for this observation is beyond the scope of this article as it requires an advanced understanding of Linear Algebra.

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6. PageRank Algorithm and Markov Chain When you search for something on the World Wide Web, the website you wanted most likely appears on the first page. But, given there are millions of possible websites linked to your query, how do search engines manage to find the one you want and sort it to the top of the list? The answer to this question is the PageRank algorithm. The PageRank algorithm was created by Google in the early 2000s, and ultimately led to its prominence and popularity as a search engine. The algorithm outputs a score between 0 and 1, which estimates the credibility of a website by counting the number and the quality of links to that website, then sorts the list in ascending order of scores. The algorithm begins by drawing a directed graph, where the vertices are the websites themselves. If a certain website A cites another website B, then an edge is drawn from vertex A to vertex B (notice that order matters!). In this example, we will assume that a web search generates only five websites, V, W, X, Y, Z, for simplicity.

Given this complicated network of citations, how can the search engine distinguish which one is more credible than the other? This is where the algorithm kicks in. The algorithm begins by assuming there are 10000 users on each website. At each turn, each user goes to another website that is referenced by its current website. For example, a user at site Y may go to either site Z or site X in his/ her next turn. We will assume that the probability of a user clicking on any one of the referenced websites is equal. For example, the probability of a user at W going to V = the probability of a user at W going to Y = 0.5.

Figure 6.2 - Flow of users from website W at turn 0 Here is the initial state of the directed graph, but with the probabilities labelled.

Below is the resulting directed graph between V, W, X, Y, Z.

Figure 6.1 - Citations of websites, represented by a directed graph

Figure 6.3 - Flow of users from all websites at turn 0, with designated probabilities

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MATHEMATICS After each turn, the number of users can be calculated using probabilities. For example, at turn 1, the number of users at Z = the number of users from X + the number of users from Y + number of users from V =⅓×10000+⅓×10 000+½×10000=11666.666... users. In this model, we round any non-integer number of users for simplicity. We can leave the calculations to the computer and simulate what happens at every turn:

Figure 6.4 - Number of users on each website at turns 0,1,2

The algorithm then finds, by calculation, the number of users after a lot of turns (by a lot, we mean millions; as close to infinity as possible). Finally, that number is divided by the number of users in all websites (in other words, 50000) to output a score between 0 and 1, which is then compared and ranked in descending order. The procedure is finished and the algorithm outputs the sorted list of websites. According to the rankings, W is the most credible website out of the five websites.

Figure 6.5 - Number of users on each website at turn 1000000

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MATHEMATICS Mathematicians refer to this sort of simulation as a Markov Chain. A Markov Chain is a statistical model which simulates a sequence of events according to certain probability constraints. Markov Chains have numerous applications across different fields (not just pure sciences), including equilibrium reactions in Chemistry, population models in Biology, inputoutput models in Economics, etc. In general, Markov Chains is the go-to tool for creating statistical models and simulations in scientific research.

7. Conclusion There are many more elegant theorems and applications that I have yet to introduce about Graph Theory. However, I feel that the chapters above should suffice for general readers to understand a thing or two about this beautiful field of Mathematics. Graph Theory has been my favourite branch of Mathematics since I discovered it two years ago. It is different from other topics in Mathematics, such as Calculus, in the sense that it can be easily picked up by children. In general, I hope that I convinced you that Mathematics can be more fun than simply memorising formulas, as the beauty of the subject lies beneath them (applications, derivations, etc.).

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Bibliog raphy 1. The Basics - Gross, Jonathan & Yellen, Jay. Graph Theory and its Applications, 2nd edition, CRC Press, 2006. pp. 2,7. - Graph Theory, Wikipedia. Author and Date unknown. https://en.wikipedia.org/wiki/Graph_theory 2. The Seven Bridges of Königsberg - Paoletti, Teo. “Leonhard Euler’s Solution to the Königsberg Bridge Problem”, Convergence, May 2011.https://www.maa.org/press/periodicals/ convergence/leonard-eulers-solution-to-thekonigsberg-bridge-problem - Gross, Jonathan & Yellen, Jay. Graph Theory and its Applications, 2nd edition, CRC Press, 2006. pp. 156-157. - “Activity: The Seven Bridges of Königsberg”, mathisfun.com. Author and Date unknown. h t t p s : / / w w w. m a t h s i s f u n . c o m / a c t i v i t y / s e v e n bridges-konigsberg.html 3. What’s the shortest route? - Shortest Path Problem, Wikipedia. Author and Date unknown. https://en.wikipedia.org/wiki/ Shortest_path_problem

- Adjacency Matrix, Wikipedia. Author and Date unknown. https://en.wikipedia.org/wiki/ Adjacency_matrix - Star, Zach. “The Applications of Matrices | What I wish my teachers told me way earlier”, YouTube. Oct 2019. https://www.youtube.com/ watch?v=rowWM-MijXU 6. PageRank Algorithm and Markov Chain - How Google Search Works, Google, 2011. Author unknown. https://web.archive.org/ web/20111104131332/https://www.google.com/ competition/howgooglesearchworks.html - PageRank, Wikipedia. Author and Date unknown. https://en.wikipedia.org/wiki/ PageRank#cite_note-1 - Markov Chains, Brilliant.org. Author and Date unknown https://brilliant.org/wiki/markov-chains/ - Brin, Sergey & Page, Lawrence. The Anatomy of a Large-Scale Hypertextual Web Search Engine, the Computer Science Department of Stanford University. Date unknown. http://ilpubs.stanford. edu:8090/361/1/1998-8.pdf - Star, Zach. “The algorithm that started Google”, YouTube. Sep 2019. https://www.youtube.com/ watch?v=qxEkY8OScYY

- Gross, Jonathan & Yellen, Jay. Graph Theory and its Applications, 2nd edition, CRC Press, 2006. pp. 147-149.

Image source

- Smith, Harry. “3.4 Using Dijkstra’s Algorithm to find the shortest path”, Edexcel AS and A Level Further Mathematics Decision Mathematics 1, Pearson Education Limited, 2017, pp. 66-72.

0.2 https://imada.sdu.dk/~btoft/GT2009

0.1 https://www.mathexpression.com/solvesystem-of-linear-equations-graphically.html 1.1 https://content.tfl.gov.uk/standard-tube-map.pdf

4. Graph Colouring

1.2 https://citoolkit.com/articles/relationship-mapping

- Four Colour Theorem, Brilliant.org. Author and Date unknown. https://brilliant.org/wiki/four-colortheorem/

1.3, 4a, 4b, 4c, 1.5, 1.6 Josiah Wu

- Gross, Jonathan & Yellen, Jay. Graph Theory and its Applications, 2nd edition, CRC Press, 2006. pp. 340-344. - Ainger, Martin & Ziegler, Günter. “Chapter 39, Five-Coloring plane graphs” & “Chapter 40, How to guard a museum”, Proofs from THE BOOK, 6th edition, Springer-Verlag GmbH Germany, 2018. pp. 277-284 - Star, Zach. “A visibility problem, how many guards are enough?”. YouTube. Sep 2019. https:// www.youtube.com/watch?v=UIne3HdEBn4 5. Introduction to Spectral Graph Theory - Weisstein, Eric W. Adjacency Matrix, From MathWorld - A Wolfram Web Resource. Date unknown.https://mathworld.wolfram.com/ AdjacencyMatrix.html

2.1 https://en.wikipedia.org/wiki/Seven_Bridges_ of_K%C3%B6nigsberg 2.2, 2.3, 2.4, 3.1, 3.2, 3.3 Josiah Wu 4.1 https://4.bp.blogspot.com/-kmwsRHp-sz4/ TWDcs6KeBkI/AAAAAAAAAGA/mpU26WQAohE/ s1600/blank_europe_map.gif 4.2 https://pwerth.faculty.unlv.edu//BlankmapUS-1860.jpg 4.3, 4.4, 4.5, 4.6, 5.1, 5.2 Josiah Wu 5.3 https://duckduckgo. com/?q=bipartite+graphs&atb=v264-4&ia x=images&ia=images&iai=https%3A%2 F%2Fi1.wp.com%2Ftechieme.in%2Fwpcontent%2Fuploads%2FBIPARTITE.png 5.4, 6.1, 6.2, 6.3, 6,4, 6.5 Josiah Wu

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Agent-based modelling and its application in Covid-19 predictions By Daniel K an

1. Introduction: On 11th March 2020, the World Health Organization officially declared Covid-19 as a pandemic. By then, over 118,000 cases had already been reported. On 28th March 2021, the global cases had surpassed 125 million cases, with over 2.7 million deaths [1]. Apart from the patients directly affected, Covid-19 has also affected the lives of almost everyone on earth. To face this unprecedented challenge, policymakers and scientists around the world have turned to mathematical modelling for help. Broadly speaking, models for predicting Covid-19 transmission can be split into two main categories: compartmental models, and agentbased models. Compartmental models are usually simpler and less computationally expensive. On the other hand, agent-based models are usually more complex and focus more on details, and therefore are more computationally expensive. In this article, I will be focusing on agent-based modelling.

Figure 1: An example of a simulation,

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2. About Agent-based modelling Before we define an agent-based model, we should first define a simulation.

2.1. W hat are simulations? A simulation is defined as “a situation in which a particular set of conditions is created artificially to study or experience something that could exist in reality” [2]. In other words, a computer simulation is an abstract version of reality, artificially programmed using a computer to study, experience, and extract data from. An example of a simulation could be a simulation of a plane flight, a rocket landing, an economy, an ecosystem, or a pandemic.

2.2. Why are simulations useful? Simulations are useful because they can model real-life behaviour without needing actual resources. This can save time and resources and perform experiments that may otherwise be impossible. Furthermore, using a computer simulation for a pandemic means you are not risking any people or animals in the process of the simulation, because everything is run on the computer.

2.3. Agent-based models (ABM) Agent-based modelling is a type of simulation modelling b a s e d o n s i m u l a t i n g t h e a c t i o n s a n d i n t e r a c t i o n s between entities called agents. An agent-based model is usually composed of the following [3]:

2.3.1. Agents Agents are autonomous individuals, who individually make their own decisions under a behaviour defined by a set of rules. Agents can represent different things, such as humans, animals, organisations, particles, atoms, etc.

2.3.2. Decision- making rules A set of rules which decide the behaviour of the agents. These describe the actions and interactions of the agent.

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2.3.3. Environment The environment is the space where the agents exist. It can be based on data such as geographical terrain, or it can simply be a blank space where the agents move.

2.3.4. Time A model iterates through time, and in each iteration, the agents can perform certain actions. Each iteration can represent different units of time (hour, day, year, etc.). Altogether, the agent-based model models the behaviour of the agents and environment, and the consequences of different behaviour changes in agents. In Covid-19 models, agents usually represent individual people who follow a certain set of decisionmaking rules (e.g. whether or not to socially distance themselves from others). The environment is usually represented by homes, workplaces, and streets. Each iteration of time can represent an hour or a day.

Figure 2: An example of an agent-based model

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3. Imperial College London simulation To better understand the use of agent-based modelling in Covid-19 predictions, let us look at one of the most famous cases where the UK government has relied on an agent-based model to guide its policy decision in the early days of Covid-19. The content of this following chapter is all based on data and theories from [6].

3.1. Introduction On the 16th of March, the Imperial College Covid-19 Response Team led by Professor Neil M. Ferguson published a research paper about the impact of nonpharmaceutical interventions to reduce COVID-19 mortality and health care demand [6]. I n t h e r e p o r t , a n agent-based simulation model was used to model the spread of the virus.

3.2. The model The model is an agent-based model which simulates the spread of the virus. Each country is split into cells, and the population is allocated into cells based on population density data. People are assigned ‘Places’, which represent workplaces, schools, etc., and they interact with other people in cells in these places. The simulation uses spatial mixing and probability distributions: the probability that people in one cell will infect people in another cell in another region. Covid-19 spreads across the model by a function called ‘Infect sweep’, where the force of infection is calculated. The Force of Infection (FOI) is defined by the per capita rate at which a susceptible individual contracts infection [7]. Transmission of the virus is divided into three mechanisms: • Household infections (between family members) • Place infections (at work, school, etc.) • Spatial infections (when travelling around)

Figure 3: Professor Neil Ferguson

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3.3. Strategies The report outlined two intervention strategies: 1. Mitigation 2. Suppression. Strategy #1 Suppression Here, the aim is to reduce the reproduction number (the number of new cases each case is expected to generate [8]), R, to below 1. This would reduce or even eliminate the transmission of the virus. However, intervention policies would need to be maintained until the virus is no longer in the population. Strategy #2 Mitigation Here the aim is to reduce the health impact of the epidemic by flattening the curve 1 whilst not reducing R to below 1. This would slow down the virus and its impact but not eliminate the spread. Non-pharmaceutical interventions (NPIs) are methods that reduce the spread of an epidemic without using pharmaceutical drugs [9]. The report considered five NPIs: 1. Case isolation in the home 2. Voluntary quarantine 3. Social distancing of those over 70 years of age 4. Social distancing population

the

entire

5. Closure of schools and universities A mixture of these NPIs could be (and were) used to further slow the spread. In mitigation strategies, these policies were assumed to be enforced for three months, and suppression strategies were assumed to be enforced for five months.

1. Slowing the spread of the epidemic so that the peak number of people requiring care is reduced to prevent the health care system from exceeding its capacity. https://en.wikipedia.org/wiki/Flattening_the_curve

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3.4. Application of the model Using the model, the research team was able to produce predicted data for mitigation and suppression. For example, the graph below outlined the effects of different combinations of NPIs in mitigation.

Figure 4: From Report 9: Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand [6].

This graph shows that mitigation has slowed down the spread compared to doing nothing, and that, once interventions were relaxed, the number of occupied critical care beds seemed to drop. However, the report suggested that if interventions were introduced too early, too little of the population would become immune, which would lead to the possibility of a second wave. Data was also produced for suppression.

Figure 5: From Report 9: Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand [6]

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This graph predicted that once interventions are relaxed, infections will begin to rise, resulting in a later peak (Nov 2020 – Dec 2020). From this, we can tell that the intervention policies may have to be maintained for longer. Other strategies could also be explored, such as only applying policies when cases exceed a certain number. These could be tested using the model, and the data produced could be analysed to see if it is a viable strategy. As concluded at the end of the report, a mitigation strategy is unlikely to be feasible without the health care system and hospitals in the UK being overwhelmed many times over. They, therefore, conclude that suppression is the only viable strategy to tackle the virus. Overall, using the simulation allowed the researchers to compare different combinations of strategies and consult whether or not they will be effective.

3 . 5 . I m p a c t o f t h e Re s e a r c h Originally, on 3rd March 2020, the UK government announced their strategy towards tackling the pandemic [10]. The paper describes a plan using a mitigation strategy to reduce the spread by gradually introducing measures and restrictions. The ultimate goal was to achieve “herd immunity”. Herd immunity [11] is when most of a population is immune to an infectious disease, enabling “herd immunity” for those who are not immune to the disease. To achieve this, about 60% to 70% [12] would have to be infected, and since most people are immune, the virus would be unable to spread, and the population will be immune as a result. However, as concluded above, according to the team at Imperial College, suppression is the only viable strategy for containing the pandemic, whilst mitigation exceeded hospital bed limits many times over. After the Imperial research team published their paper on the 16th March 2020, the UK government abandoned their herd immunity strategy, and new measures began to be implemented. By March 23rd, one week after the paper was published, the lockdown was announced [13].

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Illustration by Susanna Fung

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4. Problems with using simulations Whilst agent-based models have been used extensively in Covid-19 predictions, it is not without controversies.

4 . 1 . Va l i d i t y o f d a t a Validity is concerned accuracy of the data.

with

the

When making a computer simulation, many assumptions are made. For example, human behaviour is unpredictable, and sometimes even irrational. However, most models will assume that if under the law, most people will obey social distancing. Many assumptions such as these mean that the data produced will be different from real-life. This is why when making a model predicting Covid-19, a clear list of assumptions should be considered and communicated to policymakers [15]. Another way accuracy is questioned are bugs in the code. Errors in code can lead to accuracy errors since they lead to the model producing

undesirable behaviour and hence undesirable output. If a model is incorrectly programmed, the simulated scenario will be wrong. However, if the code is open-sourced (code made freely available), then the public will be able to validate the code, hence reducing the likelihood of a significant bug.

4.2. Reliability of data Reliability is concerned consistency of the data.

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Some models are stochastic, meaning that they contain a random variable and so the outputted data will vary each time. This behaviour is usually intentional, and this enables the model to simulate the randomness of real life. However, when the model is too stochastic, it can lead to great variation in the outputted data. Therefore, some people criticise that these models are unreliable. This is why stochastic models are often run multiple times and an average is taken. However, this variation in data produces uncertainty for decision-makers and can make them question the reliability of the data produced by the model.

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5. Covasim At the time of writing, we are still under the presence of Covid-19. Currently, we are still indecisive about what approach to modelling is the best to predict Covid-19. Fortunately, many different models are uploaded online and free for the public to run. One such model is Covasim.

5.1. Overview

5.2. Application

Covasim is a stochastic agent-based model of COVID-19 dynamics and interventions made by Kerr Cliffe et al.. The paper regarding this model can be found here [14].

I ran the model, and I was able to produce results for my scenarios.

In Covasim, each individual falls into different categories: susceptible, exposed, infectious, recovered, and dead. The original model can be downloaded from their GitHub. Running a simplified version of the model on the app can be found here. 3 In the app, there are 4 different interventions: Physical distancing, Schools/university closures, Testing and Contact tracing.

I used a population size of 10,000, with an initial 10 infections. The model was set to run for 90 days, and all other model parameters were left as default. I also introduced some interventions. I enforced 20% (mild) social distancing, did not close down any schools/universities, tested 10% of the population every day, and traced 80% of all diagnosed cases. All interventions were introduced on day 20 and lasted until the end of the model.

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After running the model, I produced these results.

Figure 6: The data that was produced by running the parameters listed above from https://covasim.idmod.org/

These results show that by the end of the 90 days, around 1350 people contract the virus, 9 of which end up dying. This means that in 90 days, the model predicts that 13.5% of the total population contract the virus, and around 0.1% of the population will die. The model also shows other statistics such as total diagnoses. From this we can see that out of all of the infections, only about half are known and diagnosed, which suggests that more effective testing and tracing is needed.

Since this is a stochastic model, an average should be taken for more reliable results. Also, if we ran the model under different scenarios and compared the data, we would be able to see which interventions will produce the most desirable outcome. If you want to try this out on your own, you can go to https://covasim. idmod.org/.

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6. Conclusion: In conclusion, since the rise of Covid-19 infections, policymakers and scientists turned to agent-based modelling, a type of simulation, to make predictions and decisions with many examples of models that all in some way predict different aspects of Covid-19. Being able to produce data without using reallife resources is always useful.

For example, the simulation produced by Imperial College London has had a profound impact on the UK government’s decision to lockdown. Even though agent-based modelling is not perfect and has many flaws concerning validity and reliability, I think that the positive outweighs the negatives. The output data will not be identical to a real-life scenario, but the patterns observed are generally correct if the model is written properly.

Bibliog raphy

Nature 460, 687 (2009). https://doi. org/10.1038/460687a

[1] “WHO Coronavirus (COVID-19) Dashboard.” World Health Organization, World Health Organization, 2021, covid19.who.int/.

[6] Neil M Ferguson, Daniel Laydon, Gemma Nedjati-Gilani et al. Impact of nonpharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand. Imperial College London (16-03-2020), doi: https://doi.org/10.25561/77482. , https://spiral. imperial.ac.uk:8443/handle/10044/1/77482 , https://spiral.imperial.ac.uk:8443/ bitstream/10044/1/77482/14/2020-03-16COVID19-Report-9.pdf

[2] “simulation.” Oxford Learner's Dictionaries, Oxford University Press, 2021, https://www. oxfordlearnersdictionaries.com/definition/ english/simulation?q=simulation, Accessed 28 March 2021. [3] Wikipedia contributors. "Agent-based model." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 13 Mar. 2021. Web. 23 Mar. 2021. https://en.wikipedia.org/wiki/Agentbased_model [4] Christine S.M. Currie , John W. Fowler , Kathy Kotiadis , Thomas Monks , Bhakti Stephan Onggo , Duncan A. Robertson & Antuela A. Tako (2020) How simulation modelling can help reduce the impact of COVID-19, Journal of Simulation, 14:2, 83-97, https://doi.org/10.1080/ 17477778.2020.1751570 [5] Epstein, J. Modelling to contain pandemics.

[7] Wikipedia contributors. "Force of infection." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 31 Dec. 2020. Web. 27 Mar. 2021.

Image source Fig.1. Gomez, Faustino & Miikkulainen, Risto. (2003). Active Guidance for a Finless Rocket Using Neuroevolution. Lecture Notes in Computer Science. 2724. 10.1007/3-540-45110-2_105.

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Game theory and how it aids our Helen Ng, Daniel Kan, world today Benjamin Law 1. INTRODUCTION John Nash (1928-2015) was a mathematician who made significant contributions to the fields of mathematics and economics and won a Nobel in Economics in 1994 and Abel Prize in Mathematics [1]. Nash has solved not only pure mathematics work like nonlinear partial differential equations but he has also introduced game theory which is extremely prominent in today’s business world. This essay will discuss how game theory can be applied to other aspects of society to aid sustainable development goals set by the UN. Specific examples include: 1) reducing income inequality and 2) improving the efficiency of travel networks. They reflect Sustainable Development Goals 10: reducing inequalities and 9: innovations, industry and infrastructure respectively [2]. Game theory is a process of analysing the strategic interaction between two or more players in a game, and it dictates how a player can best play a game. A game is defined as a set of circumstances that has a result dependent on the actions of the players - this can be nearly any situation involving two or more people. There are two types of game theories: competitive game theory and cooperative game theory. Competitive game theory is based on the assumption that the players would like to maximise their payoff, whether that be the most points, money or any other valuable rewards. On the other hand, cooperative game theory dictates that groups of players called coalitions will work together to reach a common goal.

Illustration by Tina Wu

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2.REDUCING PAY GAPS As of 2020, for every dollar a man makes, a woman makes an average of $0.81. Even the controlled pay gap, that is, when employing characteristic factors are “controlled”, dictates that for every dollar a man makes, a woman only makes $0.98. This puts a woman at an accumulated loss of $80,000 over her lifetime [3]. Therefore, in an ideal world of meritocracy, a person should be paid for the amount of work that they contribute to a team, such as a company, without taking into account factors like race, ethnicity, gender or sexuality. This falls in line with SDG Target 10.2 - “to empower and promote the social, economic and political inclusion of all, irrespective of age, sex, disability, race, ethnicity, origin, religion or economic or other status” and ultimately reducing inequalities. Putting this into the words of game theory, a player should receive their fair payoff of a value true to only the amount of contribution they give.

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2.1 Scenario Let a set of three workers N = {A, B, C} gain a net asset of 500 thousand dollars after completing a 50-page long business proposal, and the asset is to be divided up amongst the players. If each player works at a different rate, how should the money be distributed? If the players were to be working in different coalitions of all possible sizes (which means all subsets except for the empty set), let the table below be the mapping of a characteristic function v that links the powerset (2 N = number of subsets for “N” given number of players; the proof uses binomial theorem) to the amount that they would write (could be any positive real number R + ). Therefore, v := 2 N → R + .

As stated in the table above, the total amount of pages (work) done by the three workers individually is not enough to pull together the proposal: the teamwork has brought extra magic to the coalition. Therefore, how should the asset be divided?

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2.2 Shapley value using marginal contribution In a cooperative game, to determine what’s fair, a Shapley value is given to every player according to the contribution they bring to the team. The Shapley value is determined by taking the average of each player’s marginal contribution to other players in different permutations as represented by the table below.

The last row of Table 2.2 is the Shapley value ( i ) of each player; in other words, the contribution that they bring to the 50-page proposal. To find out the amount of money the workers should each receive, simply put into the equation:

Which yields 153 thousand for worker 1; 163 thousand for worker 2 and lastly 183 thousand for worker 3. In the process, only the amount of work done by each worker has been taken into consideration, thus ensuring equality for individuals no matter their personal backgrounds.

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3 . T R A F F I C N E T WO R K S Transportation is a crucial part of our societies: it covers everything that has to travel from one place to another, whether that be a person or valuable goods. However, more often than not, these trips are time-sensitive and increasing travel time would mean that less profit can be made, ultimately impacting the economy. SDG Target 9.1 also states “developing quality, reliable, sustainable and resilient infrastructure, including regional and transborder infrastructure” is needed “to support economic development and human well-being”. Therefore, a smooth traffic network is essential to ensure the proper functioning of all industries and to underpin the development of a country. A traffic network is a structure which involves players driving along routes. This could simply be a highway, power lines, air routes, or even an online network sending packets of data from one point to another. Within the network, each player aims to strategically choose their route to minimise travel time and avoid congestion.

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Let there be two points, A and B, and each player aims to go from A to B within the least amount of time - which means taking the route with the least congestion. Assume that cars come out of A at a constant rate, and also leave immediately once they reach B. The “speed” of the car is defined as the number of patches it moves across in one tick, in other words, the distance it travels over 1 unit of time. The two routes AC and DB are more sensitive to congestion because the speed of a car travelling across it is the number of total cars divided by the number of cars going that route then divided by 10. For example, if there were 100 cars in total and 20 cars went through AC, the speed will be 0.5. The speed of a car going through CB or AD would be the same: both are one patch per tick. The simulation below models the situation when 500 cars all decide to travel from A to B via C. It would take 8324 ticks for all the cars to complete their journey.

The table above shows that if exactly half the cars take the upper route and lower route respectively, all the cars can travel from A to B within the shortest time. This is the Nash Equilibrium. This is because if the drivers were split evenly between the two routes, none of them would have the incentive to switch from one route to the other, as that would increase the time taken. Therefore, if we test the simulation again with 225 taking route AC and 275 taking route AD, the result would be 7758 ticks. The cars will take longer to finish compared to the Nash equilibrium.

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3 . 2 B r a e s s ’s Pa r a d o x In the previous example, the equilibrium was found very easily. However, if we introduce an extra route CD, counterintuitively, it will increase the time it takes for all the cars even if the time it takes to cross this new highway is defined as zero because the new Nash equilibrium dictates that all the cars would go from A to C to D then to B. This is the only equilibrium because only then, no driver would benefit by switching lanes. If we run the simulation, this remains true. The extra lane does not improve the traffic; instead, the congestion is now worsened.

Therefore we can conclude that adding extra lanes doesn’t necessarily benefit traffic, but can often even make it worse. In this model, cars can directly “teleport” from C to D, but in real life it would take much longer, meaning if it did take time to go from C to D, the congestion would well be even worse. This implies that building new roads should always be considered with care since they do not necessarily improve traffic.

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4. CONCLUSION Above were just two examples of how game theory can be applied to better our society. The applications of game theory extend long beyond the gender pay gap and traffic network models above; however, within the time allowed, these were the two models chosen by us to best represent the diversity of game theory applications. Furthermore, the two models have been greatly simplified compared to a real-life situation. For example, Section 2 mentions giving salary according to work done, but in a running company, if a worker is on sick leave or maternity/paternity leave, there should be compensations for the worker even if she/he is unable to work. Section 3 discusses a traffic network that takes cars from one point to another; however, a highway in real life would have more entries and exits, posing significantly greater complications. Further research and modelling could be conducted to best simulate a realistic scenario that takes into account factors including but not limited to the ones suggested above.

Bibliog raphy [1] Goode, Erica. “John F. Nash Jr., Math Genius Defined by a ‘Beautiful Mind,’ Dies at 86.” The New York Times, The New York Times, 24 May 2015, www.nytimes.com/2015/05/25/science/john-nash-abeautiful-mind-subject-and-nobel-winner-dies-at-86.html [2] United Nations. “THE 17 GOALS | Department of Economic and Social Affairs.” United Nations, United Nations, 2015, sdgs.un.org/goals. [3] Payscale. “Gender Pay Gap Statistics for 2020.” PayScale, 2020, www.payscale.com/data/genderpay-gap.

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Jo h n N a s h a n d h i s Introduction Josh Nash was a quirky professor at Princeton University whose students described him as a ‘world-class troll’. He was an adamant classical music lover who could whistle an entire music piece in elementary school. However, most importantly, he was one of the most beautiful mathematical minds of all time. This man was none other than John Forbes Nash Jr., an American mathematician whose work had significant impacts on various fields including economics, geometry, and social sciences. He is most known for his Nash Equilibrium, our primary focus in this essay. It was a game-changer for game theorists, and gave insight into the complex process of decision making that applies to almost every academic field and helps explain common phenomena in our daily lives.

An interview with John Nash. Source: pbs.org

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contributions to SDGs Kevin Liew, Chloe Levieux and Andrew Wang In the 1950s, an American non-profit global policy think tank, RAND Corporation, led investigations into game theory for its potential usage in global nuclear strategies. During this time, the organisation published papers written by John Nash in which he outlined the Nash equilibrium. A Nash equilibrium is the stable state of a system where, for a certain amount of people, no one can change their strategy to gain a more desirable outcome as long as the other n-participants’ plans do not change. The theory provided a way of predicting the possible outcome of a game with n-players in which each acted to maximise self-interest. To fully understand the extent of this theory’s significance, we must establish the definitions of critical key terms. A strategy takes into consideration all combinations for every possible situation of a game, allowing one participant to make a move that can maximise the benefits they receive from it. Nash established that pure strategy dictates the actions a player will make in any given situation, whilst mixed methods (of which there is an infinite amount) assign as n-probability to each pure strategy to allow n-players to pick them randomly. A non-zero sum game refers to a situation where one person’s gain or loss may not necessarily affect another person’s failure or success. In other words, n-players’ interests are not directly opposed, so the wins and losses in a game do not necessarily balance each other out to zero, and there is a possibility of mutual gain in a win-win situation. So, Nash proved that for a finite n number of players in a non-zero-sum non-cooperative game, there exists a Nash equilibrium in mixed strategies. Assuming your superior intellect allows you to understand the term ‘non-cooperative’, we will move on to explore the infamous example of the Prisoner’s Dilemma to further cement this concept.

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P r i s o n e r ’s D i l e m m a First, let us explain the Prisoner’s Dilemma. This problem was initially proposed back in 1950 by Merrill Flood and Melvin Dresher, two American mathematicians working at RAND Corporation. The Prisoner’s Dilemma analysed, as part of RAND’s research into game theory, why two entirely rational individuals might choose not to cooperate, even if they could gain a better outcome for themselves by working together. There are many interpretations and variants of the Prisoner’s Dilemma. However, for the sake of consistency, we will be using the following scenario: two members of a crime syndicate have been caught by the police and taken in for questioning. The two criminals have no means to communicate with each other once arrested. The District Attorney lacks enough evidence to associate them on the principal charge, but they have enough to convict both prisoners on a lesser crime. The District Attorney gives the two prisoners the same offer separately; they can either confess that the other prisoner committed the crime, or they can remain silent and cooperate with the other prisoner. This proposal can lead to 1 of 4 outcomes. If prisoner A confesses and prisoner B does not, prisoner A’s sentence will be lowered down to 1 year, whereas prisoner B will serve 10 years. If prisoner B confesses and prisoner A does not, the reverse happens. Both prisoners staying silent leads to both serving 2 years. Both prisoners admitting their guilt results in them serving 3 years. Just for simplicity, we will ignore the limitations of this Nash equilibrium – these outcomes do not

affect either prisoner’s reputation within the crime syndicate, and they will not get retribution or payback on each other. No external factors influence their decision. From the perspective of prisoner A, if prisoner B were to confess, his best option would be to do the same and only receive 3 years of imprisonment instead of 10. Alternatively, if prisoner B did not disclose information, it would also be in prisoner A’s best interest to confess to only serve 1 year in prison instead of 3. This is because if prisoner A also decided to stay silent, he would run the risk of getting 10 years in jail if prisoner B changed his mind and decided to confess. Both prisoners are likely to have this thought process, and so this would most likely lead to the result where both receive 3 years in jail. This outcome is the only one with a Nash equilibrium as no prisoner can change their strategies to gain a lighter sentence if the other prisoner’s choice to confess remains constant. As such, we can conclude that the most optimal outcome for both prisoners collectively would be to stay silent. However, this is not feasible as the possibility of the other individual betraying the prisoner for their gain is more than likely enough to sway their opinion into confessing. This example relates to the real world where due to several participants or parties only seeking to benefit themselves, the situation does not result in the optimal outcome for all parties and thus ends in a Nash equilibrium where everyone suffers more.

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1. Regulations of CO2 emissions

As we have covered the basics of the Nash Equilibrium, we will move on to one of the most paramount applications of the Nash Equilibrium – the regulation of CO 2 emissions. Climate change and global warming are substantial global concerns, but as each country individually has an economic interest in emitting CO 2 for their industrial production, global inaction occurs. This refusal to make personal sacrifices for the collective greater good is a Nash equilibrium. All countries produce CO 2 to create cheap energy. Hence, there is less impetus to deviate from their original energy plans. Countries may also be tempted by freeriding off of other nations’ climate action, which can offer the prospects of benefits of policy action without the costs of abatement, creating a second Nash equilibrium. The Nash Equilibrium can also explain how every individual following their optimal course of action does not yield the best outcome for the group. Therefore, we need intervention if we wish to reach the desired outcome for everybody, namely via the use of treaties or legally binding documents, such as the Paris Agreement, to enforce and impose guidelines. However, Nash’s theory does not account for the consequences of irrational behaviour; history has shown that humans are not rational beings. On June 1, 2019, US President Donald Trump announced that the U.S. would withdraw from the 2015 Paris Agreement on climate change mitigation, stating that it ‘will undermine [the U.S.] economy’ and ‘puts [the U.S.] at a permanent disadvantage’. President Donald Trump chose to free-ride off of the climate action of other nations and avoid the burden of carbon abatement costs, ignoring the Nash equilibrium.

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FEATURED ARTICLES Providing an insight into climate change scenarios, the Nash Equilibrium helps to target the UN’s social development goals, one being climate action. Target 13.2 involves integrating climate change measures into national policies. John Nash’s work also directly targets Partnership, the 17th SDG, by helping countries cooperate and abide by a particular set of guidelines to achieve sustainability. For example, the Nash Equilibrium could convince governments to work together towards Life Below Water, the 14th SDG, by lessening the effect of global warming to keep sea temperatures from rising. They could also implement specific policies to protect the incomparable biodiversity of the aquatic world. Hear it from Nash himself: “The best for the group comes when everyone in the group does what’s best for himself and the group.”

Paris agreement signature ceremony. Source: Flickr

2. Applications in sports

In sports scenarios, the use of illegal performanceenhancing drugs can cause a significant disadvantage towards rule-abiding players. The Nash Equilibrium, just like in the CO 2 emissions example, provides an insight into the case by emphasising the importance of intervention, like mandatory blood content checks and a penalty for violation of fair play. The Nash Equilibrium can be applied to almost every competitive event like this and dramatically helps sustainable development goal 16 – Peace, Justice, and Strong Institutions – by promoting an international institution of fair play (16.6) and a law regulating sports events. (16.3)

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N a s h ’s p e rs o n a l e x p e r i e n c e s and mental illness Nash suffered and then recovered from schizophrenia, a severe mental disorder in which people interpret reality abnormally. The Swedish Academy of Sciences almost denied him his Nobel prize for his work in economics as members felt that esteeming a ‘madman’ would damage the Nobel brand’s image and ruin the prize ceremony. However, the prize committee recognised that mental illnesses were, after all, valid medical conditions, just like other conditions such as heart disease. Nash’s recognition as a mathematician secured his prize, regardless of his schizophrenic condition. Winning the Nobel prize, one of the highest honours that a mathematician can get, broke the negative stigma regarding the mentally ill. SDG 3.4 aims to ‘promote mental health and well-being’, and SDG 16.6 seeks to ‘promote and enforce non-discriminatory laws and policies for sustainable development’. With his success, Nash created awareness for both goals, revealing how the ignorant discriminatory behaviour towards people suffering from mental health issues prevented the acknowledgement of their impactful achievements. Policies must be put in place to create a more inclusive, accepting, and sustainable society where everyone excels and thrives. Shattering the public’s prejudice, Nash’s accomplishments send a powerful message that mental illnesses should not deprive one’s standing in a sustainable society, and that we should recognise people for who they are, and not whether they conform to any ideal.

John Nash at the Nobel prize ceremony. Source: American Experience, PBS

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Conclusion There you have it – John Forbes Nash Junior. Generations will remember one of the most brilliant mathematical masterminds, whose Nash Equilibrium provides an acute insight into the consequential governmental decisions that dictate the sustainability of our future, as well as the complex mechanisms that operate in our daily lives. So, the next time you and your friend find yourself participating in a failed bank heist, or signing on the most recent global climate change agreement, think back to John Nash and his explorations on the consequences of selfishness. In the long run, a collectivist approach is a much better approach than self-centred desires: as Josh Nash said, “Perhaps it is good to have a beautiful mind, but an even greater gift is to discover a beautiful heart!”

Bibliog raphy Cazals, Charles. “How Game Theory Affects Your Everyday Life”. http://www. thelondonglobalist.Org/, 2020, http://www. thelondonglobalist.org/how-game-theory-affectsyour-everyday-life/. Yurcaba, Jo. “As A Professor, John Nash Was Tough, Quirky, And Hilarious, According To His Former Students”. Bustle, 2020, https://www. bustle.com/articles/85520-as-a-professor-johnnash-was-tough-quirky-and-hilarious-accordingto-his-former-students. Khan, Sal. “More On Nash Equilibrium (Video) | Khan Academy”. Khan Academy, 2020, https://www.khanacademy.org/economicsfinance-domain/ap-microeconomics/imperfectcompetition/oligopoly-and-game-theory/v/moreon-nash-equilibrium.

“Game Theory”. En.Wikipedia.Org, 2020, https:// en.wikipedia.org/wiki/Game_theory. Accessed 16 Nov 2020. “Strategy (Game Theory)”. En.Wikipedia.Org, 2020, https://en.wikipedia.org/wiki/Strategy_ (game_theory). Accessed 16 Nov 2020. “A ‘Beautiful Mind’ and his Nobel Prize”. Christie’s, 2020, https://www.christies.com/ features/A-Beautiful-Mind-John -Nash-and-the-Nobel-Prize-10124-7.aspx. Accessed 16 Nov 2020. Goode, Erica. “John F. Nash Jr., Math Genius Defined by a ‘Beautiful Mind,’ Dies at 86”. The New York Times, 2020, https://www.nytimes.com/2015/05/25/science/ john-nash-a-beautiful-mind-subject-and-nobelwinner-dies-at-86.html.

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