Summer Junior Project Prize

Prize2020 ∏

∑

Δ

Contents

Introduction

RDW 3

Foreword

The Warden 4

Roman Foundation Myth

Fergus MacInnes, Remove 5

The Battle of Teutoberg Forest

Tom Payne, Shell 11

A Piece Under Quarantine

Kim Chin, Shell 10

Murder Mystery

Freddie Finlan, Remove

Do Computers have a positive impact on Chess?

Inha Choi, Remove 24

Fly Fishing on The Nadder

Ned Tucker, Shell 29

A Poem Under Lockdown

Freddie Finlan, Remove

The DariĂŠn Gap - A looking-glass into Colombia

Bernardo Mercado, Shell 36

14

30

Do Derivatives Belong in a Retail Investor’s Portfolio? Russell Kwok, Remove 40 An Introduction to the Problem of Evil

Toby Rooth, Shell 50

My Arcade Cabinet

Rohan Haripaul, Remove 57

Understanding the depths of quantum computing

Hyunjo Kim and Yikai Zhou, Shell 64

Metal Work Projects

George Beattie, Remove

2

82

INTRODUCTION

During Summer Term 2020 the Shell and Remove year groups were set the challenge of completing a short project on a subject of their choice. The task was voluntary and the mode of submission was up to them. The purpose of the exercise was to celebrate students’ individual interests and endeavour. It was expected that work should be scholarly and ideally of interest and use to others.

The Academic Prefects were asked to mentor the Junior entrants and then to judge their submissions. The best projects were sent up to the Warden for consideration for a prize.

40 boys entered and the following publication is a selection of the best – those that won prizes or were commended. Where possible, the original formatting has been preserved.

RDW

3

FOREWORD, by the Warden

It was a great pleasure to be presented with such a variety of outstanding individual work. The breadth of entries is astonishing and the quality of research, analysis and innovative creation was a real highlight of the Summer Term.

This document showcases the best submissions and includes such diverse topics as Quantum Computing, Murder Mystery and Sculpture. As well as being culturally and academically exceptional, this selection represents individual passions and, in all cases, a tremendous amount of hard work.

I offer my heartiest commendation to all Shells and Removes who participated in the Junior Project Prize and my particular praise to the winners selected for this publication.

My thanks to Mr. Woodling, Mr. Barlass and to the Academic Prefects for helping to create a bright spot this summer.

4

Roman Foundation Myth

Fergus MacInnes, Remove

According to legend, Rome was created by the struggle between twin brothers Romulus and Remus, with the former winning the rivalry and naming Rome for himself. How and why did the ancient Romans use the myth of Romulus and Remus to validate their power and justify their ideals?

Quotations of Livy are taken from Rev. Canon Roberts’ translation of Livy’s history of Rome: Book 1. Quotations of Plutarch are taken from ‘The Parallel Lives by Plutarch, published in Vol.1 of the Loeb Classical Library Edition, 1914’.

Introduction

While the myth of Romulus and Remus was not set down until 500 years after the founding of Rome, it had a significant impact on the thought of the Roman people for the duration of the republic and empire. The three most significant attributes of Roman society that were justified using the myth were the authority of the republic and the later Roman emperors, Rome’s unforgiving attitude towards conquering its neighbours, and how Rome defined the role of women.

Both Livy and Plutarch provide useful insight into what was accepted by the Roman people to be the myth of Romulus and Remus, and how it portrayed the just values of Roman society.

The authority of Rome’s leaders

The god-like attributes of Romulus were key to justifying the autocratic rule of the Augustinian government. Being written around the 3rd Century BC, the myth would have been used by the late republic and the Roman emperors, beginning with Augustus. Augustus liked to assert his descendency from the founders of Rome to assure the people that he had inherited the authority of a divine ruler like Romulus. In a state in which handling of power was key to military and political success, it was of paramount importance that the Roman people felt like they were under the control of a legitimate ruler to prevent rebellion which could hinder progress as an empire. The idea that divine right had been inherited from the founders of Rome was key to the justification and stability of Augustus’ reign.

5

In Titus Livius’ History of Rome, Livy, when referring to Romulus, writes ‘we find nothing incompatible with the belief in his divine origin and his admission to divine immortality after death’. It is stated almost as fact by Livy that Romulus was characteristically divine from the beginning to the end of his life. Plutarch also discusses Romulus’ acquaintance with divinity, writing ‘when Romulus was busily engaged in some sacrifice, being fond of sacrifices and of divination, the herdsmen of Numitor fell in with Remus’. This crude comparison between Romulus’ interest with the gods and Remus’ business with causing fights highlights the importance of priorities in Roman leadership. It was seen that since Romulus had made sacrifices to the gods, so they were on his side. It was also believed that for this reason Romulus successfully killed Remus. If Romulus’ acquaintance with the divine was believed by the Roman people, it could have been manipulated in such a way as to justify the rule of later leaders too, such as Emperor Augustus.

Augustus, wishing to soothe the political turmoil at the end of the republic, attempted to connect the imperial family to the origins of Rome and the myth of Romulus and Remus. Neighbouring panels of his Ara Pacis (Altar of Peace) depict the myth of Romulus and Remus, placing him sideby-side with the divine origin of the twins. This brought attention to his association with divinity, which he used to justify the strict Autocratic rule of the imperial family.

Rome’s unforgiving will to conquer its neighbours

There are many ways in which the myth of Romulus and Remus justified Rome’s attitude towards conquering territories near and far. It is undisputed that the Roman Empire’s most famous attribute commonly known to us is its military capability. At its largest, the Roman Empire encompassed an area of five million square kilometres. Justification for this expansion of the empire was key to its success and continuation of conquering new territories. The myth of Romulus and Remus provided two simple solutions to this problem: that Rome was a self-sufficient and independent state on account of the self-sufficiency of its founders, and that it had the divine right to wage war against its enemies on account of the superiority of its founder Romulus over his brother Remus.

The early self-sufficiency of the twins is evident, particularly in Livy’s account of the myth. Livy writes ‘a thirsty she-wolf from the surrounding hills… …came to them, [and] gave them her teats

6

to suck’. Notice that the she-wolf actively cared for them, rather than the children being passively cared for. This distinction between being passive and active underlines how Livy attempts to portray the twins as being less dependent on carers. In addition, the idea that the she-wolf ‘gave them her teats to suck’ implies that the children neither needed her milk nor necessarily accepted her offering. By choosing to express the bringing up of the twins in this way, Livy avoids the idea that the twins were in need of care and attention, but rather implies that the resources were at their disposal, and not necessary. This would be a useful source to draw upon for those who were trying to justify the expansion of the Roman Empire by suggesting that nearby resources and territories were at their disposal in the same way that the she-wolf was at the disposal of the twins.

Plutarch also supports the idea that the twins were self-sufficient by writing a very minimal amount about the care of Faustulus for the twins, despite the period making up the majority of their upbringing. All we hear of Faustulus’ efforts is that the twins were’ taken up and reared by Faustulus’. This simplistic description attempts to minimise the attention drawn to how they were passively brought up. Plutarch swiftly goes on to distract the audience from this by discussing the reason why the twins were called Romulus and Remus. In this way, Plutarch manages to mention how they were brought up without leading the reader to think too strongly that the twins were helpless and in need of care. Thus, the twins are portrayed to be less dependent on others. This would help to justify the expansion into other territories, by suggesting that the Romans should be less dependent on trade with neighbours but should rather expand into those territories and name them as part of the Roman Empire, to continue in the same vain that the twins did in being selfsufficient.

Livy naturally portrays Romulus as the superior twin, comparing them by writing ‘Romulus successfully defended himself, but Remus was taken prisoner’. The clarity of this comparison is of great significance. Livy is deliberately encouraging the reader to take up confidence in the character of Romulus. The word ‘himself’ further emphasises his self-sufficiency, by suggesting that he needed no help from others. This would be particularly useful to justify their conquering spirit, by implying that it was better to conquer your allies rather than to conquer with allies. It may be helpful to substitute some of the terms for other terms, relevant to the roman empire. For example, this could be written as ‘Rome successfully defended itself, but its neighbours were taken

7

prisoner’. It would not be implausible to suggest that this is what Livy is attempting to imply, since Romulus may be seen as the figurehead for Rome, and Remus may be seen as the personification of Rome’s neighbours. Therefore, Rome’s confidence in the expansion of the empire is justified by Livy by its natural and inherited superiority over any other state or tribe.

Plutarch, on the other hand, emphasises the power of Romulus through describing the strength of Remus on his own and using this to propel the position of Romulus by the final killing of Remus

by Romulus. When Remus is taken prisoner by Numitor, Numitor ‘was amazed at the young man’s complete superiority in stature and strength of body’. Plutarch is meaning that Remus was superior above other men in general, rather than above Romulus, since Romulus was not present at that time. By showing the strength of Remus, the reader is compelled to believe that Romulus must be even stronger because Remus ‘was smitten’ by Romulus. By implying then that Romulus is superior to even those considered to be superior above other men, Plutarch encourages the belief that Rome, by inheriting this superiority from its founder, was superior above even those provinces which were considered to be superior to all other states, and thus has the right to invade and conquer those territories.

The implication from Livy that nearby resources are at the disposal of the twins and thus their descendants, and the idea that Romulus, and thus his descendants, had superiority over others are key to the portrayal of the twins, and thus the roman empire, as having a given duty to rule over their neighbours. Therefore, both Livy and Plutarch make the self-sufficiency of both twins, and the superiority of Romulus of upmost concern and significance, to highlight the importance of these attributes in justifying the expansion of the Roman empire.

The role of women in Rome During the late republic, many men took the belief that women were “out of control”, on account of the high adultery rates during times of Civil Warfare in Rome. Among them, Augustus, the first Emperor, tried implementing his Julian Laws. One such part of these laws, Lex Iulia de Adulteris Coercendis, punished adultery with banishment. This involved ‘Dummodo in diversas insulas relegentur’ (both parties are sent to different islands). Indeed, Augustus drew on the ancient myth of Romulus and Remus to try to surmount the challenge of enforcing these laws and encouraging

8

the people to follow them. Publicly declaiming the need for restoration of the “good ideals of our ancestors”, Augustus wanted to persuade the people to follow these laws by citing the treatment of women in the myth of Rome’s founding.

Livy expresses the importance for women in society by saying that ‘through the absence of women there was no hope of offspring’. In this way, Livy makes clear Rome’s dependence on women in its early foundation. Having described how the Sabine women were abducted, he also said that the women ‘would live in honourable wedlock, and share all their property and civil rights’. Augustus called upon this idea when attempting to encourage adherence to his new laws. He justified the treatment of women with the familiar argument that if it was done in the past, it is right to be done in the present. In addition, by associating himself with the customs of early Rome, he was associating himself with the same superior wisdom of the divine Romulus. In this way, he made his laws seem more just and well established through Roman history.

Women, while being citizens, could not vote or have any formal political influence. This was justified by Augustus through the myth of the abduction of the Sabine women, by referring to the role of the Sabine women in their abduction and lives with Roman husbands. Plutarch describes how ‘when the signal was given, [Romulus’ followers] drew their swords, rushed in with shouts, and ravished away the daughters of the Sabines’. In this account, the Sabine women are dramatically at the expense of the Romulus’ followers. Furthermore, their actions are fully endorsed by Romulus, who was of divine origin and superior stature. This all aided the case of Augustus in justifying the treatment and delegation of rights of women in Roman society, further using history to justify the present.

Therefore, through the repetitious association of Augustus’ laws with the customs of early Rome, Augustus made what we might call today a rather precarious justification for the domestic treatment of women in society as inferior to and at the expense of their husbands. However, Augustus also understood the importance of women as the means through which Rome continued its population past the first generation. The ancient myth of Romulus and Remus provided a sure and stable vindication of his Julian laws which were so crucial to the continued functioning of the Roman state.

9

Conclusions The myth of Romulus and Remus served as a key tool to be used in the hands of Augustus and the late Republic in justifying all areas of Roman ideals. Through the repeated motif of rooting himself and his method of governing in the myth, Augustus grew his support and allowed his reign to precede itself with its peace and prosperity. The maintenance of power and control in the roman empire was key to its long-term success as one of the world’s most prosperous empires to have existed. Thus, the political policies and laws of its leaders defined the rule of many of the greatest and worst Roman Emperors. Amongst them, it was Augustus who pioneered the association of the imperial family with the divine origin of Romulus and Remus. The authority of the autocratic rule of the emperor, the ruthlessness of the Roman empire, and the place of women in society were all in desperate need of stable justification when the Roman republic fell apart and the new age of imperial Rome began. It may have been that without the steady rooting in the myth of Romulus and Remus, Augustus’ rule might not have been so peaceful as it was, left with the remains of a Rome broken by civil war.

10

The Battle of teutoberg forest

Tom Payne, Shell

https://www.youtube.com/watch?v=xKzKnz8AA2U

11

A Piece under quarantine Kim Chin, Shell

12

Kim Chin, Shell

13

murder mystery

Freddie Finlan, Remove

The clock ticked to half-past eight. I squeezed the last bag into the car and slammed the boot door with a resounding bang. A flock of crows flew from a tree to my left, cawing indignantly in anger at my rude shock. A flock? No, a murder. That’s the word: a murder of crows. The children were already in the car, they had been for the last fifteen minutes, growing restless from the anticipation of the journey. Emma was still in the house – presumably performing her fifth makeover of the day. It was starting to get dark and a slight chill was beginning to settle on the nape of my neck as the wind blew softly against it.

“Emma, please hurry up!” I called somewhat angrily. “It’s bloody freezing and I want to get on the road before it gets darker.” No reply, meaning she was about halfway done. I sighed, looking around the overgrown garden. The silence was eerie, causing shivers to go up and down my body. The common feeling when alone was creeping over me, the feeling of being watched.

Finally, the porch light flickered on and Emma walked out. Tall, blonde with hazel eyes she stared at me patronizingly. Laughing, she walked past me and opened the car door. Shaking my head in a disapproving way I followed. As I stepped into the car; the boys in the back groaned profusely. “Can you put in the destination, honey?” I asked as I started the engine. We were going to a rustic boutique hotel, only about an hour away. The hotel seemed to be your typical Tudor home: steep gable roof, elaborate masonry chimneys, embellished doorways and a wooden framework. By the look on the website, it seemed to be run by a very respectable Russian businessman and seemed like the perfect place for us to have a weekend away from work and school. I drove down the road in a triumphant manner – a satisfying conclusion to my hard work. It had been five years since I started working at the law firm and we finally had the money to get away, even as far as suburban London. Emma switched on the radio and we were met with the nine o’clock news.

“The local police of Hackney have apologized today for being ‘unable’ to find answers for the disappearances that have been occurring for the last couple of weeks. A spokesman commented that ‘It has been the sole mission for the police, 14

and they are using all the resources they can to identify the culprits. Last night, two schoolgirls, both fifteen, were taken and were last seen leaving the school together.

This incident has increased the already high pressure on the local authorities and council to find a solution. The local MP commented ‘The council are taking steps in ensuring safety for the people of London, while our local authorities are working together to find answers to this situation.’ In other news, the Labor MP Clive Lewis has had to formally apologize …’.

I turned the radio off and looked at Emma. She gave a perfunctory shake of her head, clearly worried about the situation. It had been hot gossip for the people of our group of friends and the most recent disappearances were beginning to worry the area, me included. It started about six weeks ago, in the middle of June. A young boy was taken just down the road from where we lived – something that has never escaped my mind. He was never found, vanished into thin air. The response of the local council was rapid: curfews were set for nine o’clock, children had to be accompanied by an adult, all doors must be locked, and the list goes on. Clearly however, this had little effect as another seven people have disappeared, all around our neighborhood, leaving chaos, confusion and fear.

We pulled in at a petrol station. I stepped out the car and took a deep breath, the fumes in the air drifting into my nose. After hearing the news on the radio, I was satisfied with the knowledge that several other cars were lined up beside me.

Furthermore, a policeman stood at the door of the Tesco Express opposite me – a gun prepared to fire sat in his holster. I walked past him, giving him a slight nod of my head, into the shop. I made straight for the counter, grabbing a bottle of water and some chewing gum on the way, so we could get straight back on the road. On the television behind the scrawny teenager at the till, I faintly heard the news story that I didn’t want to hear. ...

Gravel rolled beneath the wheels as we made our way up the drive to the house towering over the forest of green. The smoothness of the road was a sense of comfort to me, following the events of the last weeks. Its white and black stone were barely visible through the dark, but the presence it had was clear to see.

Trees blocked us from the darkness of the night and applauded us with their frantic 15

rustling. Falling leaves fell from the interlocking branches above, branches that grew so thickly no moonlight could break through. It seemed that nothing could find us here. I pulled the car over directly next to the main entrance and was met by a dark shadow. He immediately opened the car boot and took the luggage without so much as a word and walked back inside. Taken aback, I watched him put our bags in the main lobby and walk back towards us with a slight grimace on his face.

“Hello!” he called out with a thick Russian accent. “I am Alek, welcome.” He raised his hand. I grasped it firmly and replied with a jovial greeting. He had a strong grip; I could feel scars snaking down the palm of his hand and he was clearly sweating.

Alek was around six foot two, a gangling youth – considerably younger than me or Emma. “I trust you had a pleasant journey; I feared that the wind would hinder your arrival.”

“We got here in good time actually, we -” But I stopped abruptly when Alek turned and stepped back through the door. More than anything I was growing concerned with what Alek’s idea of manners was. Tentatively, we stepped across the gravel and through the door. My eyes were blinded by a royal chandelier, a bright red floor and early 20th century contemporary art was scattered around the wall – a great contrast to the Tudor black and white on the exterior. From a twisting staircase in the corner footsteps were heard, and sure enough an old stout man appeared. He gave a quaint smile, showing brilliant white teeth, and opened his arms wide in welcome.

Behind him Alek scampered, looking sheepish.

“I see that you have met Alek,” he said, giving a sideward glance at him, “I hope he welcomed you warmly.” He brought out a set of keys from his pocket and beckoned us to follow.

“I didn’t catch a name.”

“Forgive me, I am Igor and owner of Cedar Hotel.” It was clear he didn’t want to chat as he strode down the corridor in a determined manner, not once glancing back as he spoke. Suddenly, he stopped at a door protruding his keys. He turned the disheveled golden lock and opened the door. “Breakfast is served from eight to ten tomorrow, and we wish you a pleasant visit,” he announced before walking away into the abyss.

16

It was certainly a mysterious welcome. ...

Light lazily drifted in through a window opposite the bed. I groaned turning over, so my face was pressed against the pillow. With the window slightly ajar, a light breeze floated in. A coffee stood at the side of the bed, which I quickly grabbed. Emma was not in the room, probably already at breakfast. I took a sip of the coffee, very powerful coffee, and received a sharp jolt in the head. I got changed into a maroon jumper and a new pair of corduroy trousers and went down to breakfast. A clock at the opposite end of the corridor told me it was nearly eleven, meaning I had missed breakfast. I wondered why Emma hadn’t woken me up: she knew I had had a hard week and needed rest, but not eleven hours sleep. I walked back into the main room, where the chandelier shone brightly. From a room to my right I could hear soft footsteps and voices. As quickly as I heard them, they vanished and were replaced by the sound of crunching gravel. Through the door the children ran in laughing, followed by a bemused Emma. The eldest was called Kenedy, the youngest Martin.

“Why didn’t you get me up?” I asked curiously.

“We did.” she responded. “You were at breakfast with us and then went back to the room.” She looked confused and shocked. “Do you not remember?” I thought back, bewildered. Before I had a chance to think anymore Alek walked in holding a small canister and a set of keys. He hastily shoved the canister into a bag around his waist and walked towards me.

“These silver keys will get you into the gardens and pool, the gold to the tennis courts and red to the bar area.” He handed me the set of keys and briskly walked up the stairs. Again, I was slightly concerned with the way he was acting, and I was also curious as to what was in the canister. I put the keys into my jacket pocket and beckoned to the children to follow.

“I’m just going to freshen up back at the room.” Emma called as we walked out the door. A fog covered the courtyard with a heaviness you could almost cut with a knife. In the distance I could make out dark wooden signs and so I stepped onto the gravel, which let out a resounding groan. We followed the signs to the garden and 17

pool talking about football and putting the world to right. As we walked in between the thick rose hedges something caught my eye. I didn’t stop to look, but it was cylindrical and metal - as soon as I glimpsed it, it was gone.

“Dad, did you hear that?” Kenedy said loudly, “Dad?” “Sorry, what did you say?”

“Martin said Sharp is out for the season.” We were back to our football debates, but the metal object was still in my mind. We arrived at a huge row of rhododendrons, which guarded the entrance to the pool. I fumbled with the keys before managing to produce the silver and unlock the door. There were a row of sunbeds surrounding a brilliantly blue pool, which was rippling softly with the wind. As Kenedy and Martin hurled themselves into the pool I sat and looked over the landscape. In the distance I could see the faint of glow of London, which gave me a gentle reminder of our isolation from the rest of the world - I sighed peacefully. It felt nice being away from endless traffic, litter covering the streets and drunks keeping me up at night. Instead it was peace, calm and remoteness. There was a distinct silence, a silence you could not get in the city. The trees whispered silently to each other, the water twinkled at me mischievously and the sun smiled down at me – I felt like nothing could go wrong. The unmistakable sound of crunching gravel came from behind the rows of flowers, Emma had finally come down. The door opened, but Igor walked through smiling. He looked weary, with sunken eyes and slightly hunched shoulders. He wore a blue sweater with black jeans and a crammed brown satchel was sitting around his waist. He nodded politely at me and waved kindly at the children. He went through another door at the other end of the pool and vanished. Another couple of hours passed, the wind still whistling and the leaves still talking – but Emma had still not arrived.

I felt my pockets before remembering I left my phone in the room. It was approaching one o’clock, so I told the boys to get ready for lunch. As we walked back to the dining room my eyes searched for the metal object I had seen earlier.

I inspected every patch of ground, every bush, every possible place it could have been. It was nowhere to be seen. I wondered whether it was a trick of the light, a shiny rock, a continuum of my state this morning. Or, had someone moved, had 18

someone left it there and released their mistake. My sense of anxiousness had once again replaced my sense of tranquility.

Ten minutes later we were all sitting around the table. Emma had returned looking very dazed and not contributing to the conversation. I decided not to ask her what she had been doing, merely because she looked like she could pass out any second.

Her skin was pale with a green tint, her hair was messy and knotted and her eyes were well embedded into her face. After eating a huge plate of chicken wings, I told Emma to go up to bed and get some rest. She did without answering.

After an afternoon of tennis, swimming and walking the boys and I returned to the lobby. It was approaching five and the sun was still blazing down on the hotel. We sat on some deck chairs in the gardens at the back of the hotel playing cards. As we played the sky was transforming from a pale blue to a dull grey and the soft wind had picked up. The sun that had dominated the sky an hour earlier had lost its battle and was imprisoned behind the thick clouds. The leering clouds pushed us inside where were met with the smell of fine food.

“Shall we get mum?” Martin asked, “Dinner starts in ten minutes.”

“No, leave her to rest, I think. Yes, leave her to rest.” I’d never seen her look so ill as I had at lunch and so I thought I made the right decision. I thought about my experience this morning and her state at lunch and wondered again if something was wrong. I had been suspicious of everything since the first night, but what was happening only served to emphasize those suspicions. We sat down at a little table by the window, watching the wind batter the trees and leaves falling limply down.

From a door to the right Alek appeared with some bread and olive oil and asked for our drinks. I ordered a small batch bourbon; it was a drink I needed at that moment.

Despite the tranquility the place had I was feeling worried. I was generally not an apprehensive person, the opposite in fact, but it was all I could feel at that moment.

Alek returned with our drinks and a selection of starters: meats, cheeses and bites.

I took my drink quickly, but before I was able to take a sip, I saw something through the window. Igor was hastily running through the howling wind. I watched him run past the sign, which read “To the pool and gardens”. I took a sip. Then another. And then I knew where he was going – he was going to the whatever was behind the door at the far end of the pool.

19

“I think I left they keys at the pool.” I said quickly. I finished my drink with one last gulp and got up. “I won’t be long.” I marched to the front door and once outside began a brisk jog. Rain gently spat into my face, while the wind continued to howl.

I could hear his footsteps pound the gravel further down the path. Then nothing.

The turn of a key. The door squeaked open. I stopped jogging as I stepped onto the gravel - I didn’t want to be heard. Once I had heard the second door open, I began to move swiftly down the path. I slipped through the first door and moved cautiously past the pool. Suddenly, a howl of wind erupted in the sky causing rain to fire down and making me stumble. I approached the second door. A sign reading “Staff Only” was rattling violently from a nail and the door itself was swinging open and closed. I peered through, looking for Igor. All I saw was a path leading into the woods that surrounded the hotel – Igor had vanished. I slunk past the door and went down the path.

The trees towered above me, as if they were guarding Igor’s secret. As I got to the first tree, I hid behind it and peeked at what was in front. I could make out in the distance a dim light, glowing tantalizing. I went from tree to tree methodically.

Something appeared at the corner of my eye. I squinted through the rain and could make out a large brick well. I looked back at the house then my eyes fixed to the well.

Sticks and twigs were snapping underneath my feet, the noise echoing in the wind and the ground was becoming more uneven as I made my way to the well. My clothes were drenched, my mind was numb, my confusion twofold. I got to the well and gasped for air. The wind was at full throttle and the rain was now something from a monsoon – it did not feel like July.

As I caught my breath, I investigated the well and took a step back. I couldn’t believe what was inside. It had been filled with the same metal cannisters which I had seen Alek with earlier. Immediately, I realized something. The metal object I had seen earlier was a canister and it wasn’t there on my return because Igor had taken it with him in his satchel. I fell to the floor. I had to find out what he was doing with them and I knew the house was the answer. Despite solving the first confusion, even more new ones had surfaced. What was happening at Cedar hotel? What were the cannisters for? I moved towards the house. The lights were on and I could hear 20

a slight hissing noise. The house was made from thick concrete and I could see oil lamps inside. There were two doors one on the front and back and windows were scattered around the outside.

I peered through the closest window. The room was empty: no chairs, no tables, no Igor, but there was a staircase leading both up and down. The hissing continued as I made my way around to the backdoor. The wind was making the windows rattle evilly and trees continued to block me from any light. The door was locked. I didn’t try to force it open; I didn’t want to be noticed, so I went to the other door – it was locked. My adventure was over, I thought, the children are probably worried, and Emma needs me right now. I began to walk away from the house. We will leave first thing tomorrow, I said to myself. Another howl of wind and then a bang. I turned in the direction of the bang and my heart leapt. A light was coming from the floor about ten meters behind the house. I ran back, marking the spot where I saw it.

The light was flickering on and off and as I got closer, I could see that it was a trap door with a tunnel leading towards the house. The wind must have pulled it open, I thought, as I slipped down into the dim tunnel. I pulled the hatch above me down and looked forward. The flickering light created an eerie effect on the tunnel as I walked through. The concrete floor had canisters, shoes and socks scattered over it and the air was pungent. I could still hear the hissing noise; it was reverberating around the tunnel. I approached the door at the end of the tunnel. Everything was silent, except the persistent hiss. I slowly opened the door.

I saw nothing. The room was pitch black. But I could hear. I could hear amid the hissing. I could hear nails slowly scrape the floor and walls, moans and grunts echoed around the room and rasping breaths. I felt the wall for a light switch.

A very weak light flickered on. I had to cover my mouth to stifle a scream. Eight people were sprawled across the floor. Their hair had all been cut, their skin was purple, and their eyes were bleak and dead. Their ghostly stare resided themselves in me, I could feel their emptiness and hopelessness. I had seen them before, or some of them anyway. I had seen them walk past my house, go to my children’s school – a shiver was sent down my body. I was getting light-headed, my head was spinning, my eyes were blinded by the horror. I fell against the wall. I heard a bang from above, quick footsteps, and a loud shout. He was coming, I thought. I tried 21

to get up, but my legs weren’t working, my brain was fuzzy, my sight was blurred, the footsteps were getting closer, I pushed, I began to panic, I couldn’t move, the footsteps were getting louder, I had lost all sensation, I gave up. The door banged open.

Through the haze of my eyes I could make out a pair of polished black shoes.

Suddenly, the hissing noise stopped, and I could hear heavy breathing.

“Alek, he’s here, bring them down.” I heard Igor say with anger in his voice. I heard a muffled response from a phone, and then a beep. Igor bent down to face me; his face twisted in rage. “You’re a stupid man, a very stupid man. I suppose you know what’s happening here.” I shook my head. I squinted around, looking at the people that were scattered across the floor. My eyes settled on a young boy, blonde hair in tuffs. I was hit by a sudden realization and my mind spun around. This was the boy who disappeared on my road. These were the people that were kidnapped, these were the people who had been all over the news. “Are you feeling light-headed yet?” He said to me. He was pacing up and down the room anxiously, his phone still in his hand. I didn’t answer but just stared into the distance, terrified. My hands started to vibrate even more, I tried to crawl to the door, but it was pointless. My muscles weren’t working, my vision was still blurred, and my head was spinning even more. “That hissing noise you hear; it is releasing a certain gas which will sedate you – lucky for you I’ve switched it off. We knew you thought something wasn’t right, the cannisters, your wife -” “What’s wrong with her?” I interrupted with a rasping breath. “What’s going on here?”

“It seems she inhaled too much of the gas, rather like you now.” He coughed and looked around. “Anyway, as I was saying, these are the people that have been disappearing. They will be moved back to Russia in the near future, but there has been lots of interfering.” He glanced back at me. “We set up this hotel so we could stay in the UK for as long as was necessary; it’s surprising no one noticed that when we arrived the disappearances started. We’d like to keep our profile low, with no attention. Unfortunately for you, with what you know, I’ve told Alek to bring your wife and children down – we need to take care of the situation, you understand.

It’s our business.” As he said this the trap door could be heard creaking open, along 22

with the sound of grunting and muffled screams. The door flew open and the two children were shoved to the floor, their arms tied, and their mouths covered. Behind them Alek walked in, holding a gun to Emma’s head. “Your time is up, I’m afraid.”

Igor produced a gun from his jacket pocket and directed it in between Martin’s eyes.

“Alek, get them lined up; I want to enjoy this one.” Alek shoved me and Emma in line with the children. “I haven’t shot a person in years.” He murmured to himself, as he pressed the gun against Martin’s head.

The noise echoed deafeningly from the confines of the room. I turned to see my son flop over like a dead salmon. A gaping hole was left, filling with blood and brain which gushed out like water from a hydrant. Before I had a chance to acknowledge what happened the air was filled with another crack, followed by the sound of a body keeling over. The room was filled with the smell of raw meat, hurting my nostrils. Through the blur I could see him getting closer, I could hear the next break in the air as Emma flopped over into my lap. I then felt the gun, hot and evil, pushed against my scalp. I closed my eyes and took my last breath.

“Authorities were called to the new Cedar Hotel, a new establishment on the Eastern side of London today as four guests have vanished without a trace. The owner of the hotel Igor Grigorovich has told local investigators that “The family went outside to have drinks after their dinner and never returned. We searched the grounds and buildings, but to no avail. It is most regrettable for this to happen at my establishment and I would like to send my condolences to friends and family of the four.” This is the first disappearance involving an entire family and it has increased the pressure on local authorities to find the source. Reporting live from Cedar Hotel, Nick Bryant. Back to you Corrie.”

Freddie Finlan, Remove

23

do computers have a positive impact on chess

Inha Choi, Remove NB: It is recommended that one understands the chess annotation symbols and chess algebraic notation prior to reading the article. An easy explanation can be found in https://en.wikipedia.org/wiki/ Algebraic_notation_(chess) Chess is an ancient game, played from 6th century AD (Wikipedia, n.d.), which is now played prominently around the world1. Due the recent developments of computers and, more specifically, chess engines, in Chess, now, computers play an irreplaceable role. All chess books inevitably are verified with engines before being published, and there is not a single grandmaster who does not verify his opening preparation with a chess engine. Despite these positive effects that the development of computers had brought upon chess, it can be argued that chess engines are negatively impacting chess for a few reasons.

This can include factors such as cheating, or excessive opening preparation, which clearly is harmful to the game. Considering a variety of effects the computer has had on the game, and evaluating its significance, we will conclude whether computers are beneficial to the game.

Perhaps the most significant role that computers play in modern day chess is its role in opening preparation. Opening preparation is the process anticipating the opening moves of the opposing player in advance of the game, through a chess database2, and preparing for it in advance. This usually allows the players to play the best moves in the beginning of the game, drawing the opponent into a position in which the player with more opening preparation is more comfortable and most likely better objectively, leading to a practical, and theoretical advantage.

This, in itself, is not inherently harmful. Opening preparation for the games is natural given the intrinsic competitive spirit of the game. However, due to the excessive usage of computers in preparation, some games finish without a single original move being played, especially in theoretical and doubleedged openings such as the ‘Sicilian Defence’ or the ‘Benko Gambit’, in which the calculative prowess of computers becomes most apparent. The game below is an example of this happening: 3In this game, the two players played until move 20 solely with opening preparation, from a very double-edged variation of the Sicilian Najdorf, a variation of the Sicilian Defence. In this position, after 21. Nxc8+, Black played 21..Kf6??, which was the first original move of the game. Following this mistake, the white player, who clearly had been better prepared, exploited the mistake and the game concluded in 4 more moves (all of which were part of White’s preparation). In games like such, chess becomes a battle of computers and memory, rather than a game of original ideas and calculation. It can be argued that, when considering games such as this, opening preparation is devaluing the qualities we value the game for.

Figure 1 Position after 21. Nxc8+

25-30 million people according to recent polls (Winter, 2009) This is easily accessible by everyone and thus done by all strong players (e.g. https://www.chessgames.com/index.html a free chess database) 1 2

3

Paris 1999 I. Timmermans – P.Chomet (1-0)

24

This argument, however, cannot be applied for the whole of chess and opening preparation in general. This is because, when one player actively plays to neutralise the effect of opening preparation through playing stable and safe variations, where the importance of understanding the position trumps the significance of raw calculation, which although may not produce an objective advantage, it can always ensure a practical advantage given through more experience and understanding. Computers too, on this front, are not invincible. In fact, in terms of understanding positions, as a computer evaluates the position through extensive, short term calculations of concrete variations, unlike humans, who have a general strategic goal (e.g. control of the white squares4), the computer is close to incompetent in areas as such5. This is clearly demonstrated in this example: 6In this position, while computers indicate that this is an easy win for white, due to the material imbalance, it is clear to humans that it is in fact a draw, as if white plays the move 1. Ba4+!., 1..Kxa4 must be played as black has no choice but to capture eventually as Kc4 leads to a repetition of moves with Bb3+ followed by Ba4+, leading to a draw through repetition. Following this move, all moves are then forced: 2.b3+ Kb5 3. c4+ Kc6 4.d5+ Kd7 5.e6+ Kxd8 (or Ke8 – it does not matter) 6.f5 is a clear draw as black does not have a way to infiltrate. However, computers, due to the lack of strategic understanding, still evaluate it as a win.

Using this blind spot of computers, strong players such as Magnus Carlsen sidestep opening preparation through the theoretically unchallenging, but strategically sound London System, which leads Figure 2 An Endgame Study by W.E Rudolph to positions in which engines are no better than humans. As he (Mukhuty, 2019) intends to outplay players through raw skill rather than memorisation or intensive preparation7, he, and many others like him8, plays in this way, adding originality to the game.

We can see this as being a clear benefit that chess engines have brought for humans. Because of this, even before the prominence of chess computers, as opening preparation was still extensive, as more openings were studied into larger depth by humans, continually, the number of original moves played in a game decreased. With the engines having demonstrated to us the consequences of excessive opening preparation, evidently, it is not dissuading us from playing original moves, but rather encouraging it.

Through this we can see that, although engines can cause harm in the opening phase if both play intending to do so, it has encouraged very strong players to play more originally than they would have before engines.

Therefore, we can see that, assuming we act appropriately in response to the use of engines in the opening phase, engines cause the games to be played in a more original manner.

After having looked at the opening, naturally, looking at the effects of computers in the middle game is most logical. Before discussing the more complex and controversial effects of the computers in the middle game, we must first consider the obvious, unhealthy impact of computers on chess – cheating. ⁴A very common theme in the English openings (Cummings, 2016) ⁵Previous Chess World Champion Botvinnik remarked that engines were ‘Tireless giants’ on account of their raw calculation ⁶There are different versions of the same puzzle ⁷Notable game: M. Carlsen – E. Tomashevsky, Tata steel masters 2016 ⁸Anatoly Karpov frequently used the 6.Be2 variation in the Sicilian defence for similar reasons

25

It is long since the match between IBM’s Deep Blue and Garry Kasparov was fair. In other words, engines are now much stronger than humans. In fact, differently to the supercomputer IBM needed to beat Kasparov, now, an engine with the computational power of a phone can crush even the strongest humans with ease9. Using this, there have been incidents where certain players attempted to cheat, both for money and fame. The most famous incident is perhaps the cheating scandal in the 39th Chess Olympiad (Wikipedia, 39th Chess Olympiad, n.d.). Three French players used engines in order to win prize money and beat other genuine players. Furthermore, as a separate matter from genuinely cheating, some players are falsely accused10- it can definitely be argued that, in this way, engines are destroying the spirit of the game.

Although it may seem that this issue is inevitably damaging, due to the efficiency of FIDE (the international chess federation) and the development of technology to stop such actions (e.g. metal detectors). FIDE have successfully mitigated the damages done by cheating, through slapping sanctions at the responsible parties (FIDE, 2019) and preventing such matters from happening initially through training arbiters (FIDE, FIDE Arbiter’s handbook, 2018). With this having been considered, it still cannot be said that the effect of cheating is completely neutralised as it is impossible to stop all incidents and not all damage can be mitigated. However, we can see that the damages done by cheating is not as large as it might be expected. Also, even if this were the case, it is the players, not the engine that does the damage. Although engines may produce a better way to cheat, to argue that engines are causing cheating would be to say that guns are causing murders. Even before engines, there were players who bribed other players for a win or a draw.

Should cheating be the only effect computers had on the middle game, it would be clear that computers are negatively affecting the game. This is not the case, as computers have been constantly teaching us and improving our understanding of the game, as will become apparent in the next paragraphs.

Until recently, many experts and chess masters opined that chess was studied to such an extent that, when played perfectly, it would be a draw without much action throughout the game11. Recently, with the emergence of a chess engine called ‘AlphaZero’, pioneering a new swashbuckling and attacking, yet sound style of play. In a 100-game match played against Stockfish, an open source engine that was previously the strongest, AlphaZero comfortably obliterated it with a score of 28 wins and 72 draws (Wikipedia, AlphaZero, n.d.). His attacking prowess is shown in this game against Stockfish.

Figure 3 Position after the 50th move

12 In the following diagram, AlphaZero had given up 2 pawns and a

rook for a bishop in order to generate an attack. It is to note that in this position, although only in terms of material, that white is losing.

However, the material was not lost – AlphaZero had given it up in order to gain a positional advantage. Here, we can see the aggressive playing style of AlphaZero: although white has less material, its attack is fierce – in fact, none of black’s pieces are performing a better job than the white bishop as they are passive, defending the f7 pawn. In this position, AlphaZero demonstrates the power of his position with 51.g4!!.

⁹Magnus Carlsen had a peak rating of 2882 while the elo rating of Stockifish is 3438. The difference of the rating is as big as the difference between a club player and a grandmaster.

10 Vladimir Kramnik was falsely accused of cheating by Topalov in the 2006 World Championship Match – referred to as the ‘toiletgate scandal’ (Barden, 2006) 11 This is due to the fact that Stockfish, who was thought to play perfectly, played in a stodgy and defensive style 12 (Chessgames.com, 2017)

26

With this move, which apparently threatens nothing, AlphaZero delivers the coup de grâce. Despite its innocuous looks, this leaves Stockfish in zugzwang (i.e. it is in a position in which any move it makes worsens the position). Stockfish had to inevitably give up a pawn with 51.d5, and AlphaZero went on to win the game.

Games such as these help us understand that, as of yet, the game has not been concluded to be an objective draw and that an attacking style still holds significance.

Some people and strong players, such as GM Robert Hess, states that, although this informs us that chess cannot be concluded as being a draw yet due to the new information provided by AlphaZero, but it does not assist humans in playing the game as its playing ability of engines is based on its massive calculating capacity – a trait that humans do not possess.

This, however, could not be further from the truth. This may apply for older engines such as Stockfish or Fritz, which were taught by humans to play chess. AlphaZero, on the other hand, taught itself, through playing millions of games with itself, noting the strategies which led to victory. Through this, while Stockfish was confined to the human understanding of chess, AlphaZero pioneered new ideas in the game of chess, which were previously rejected or even unknown by humans. With this, AlphaZero informs humans on previously unknown themes and strategy, clearly benefitting the game.

A typical example is when AlphaZero plays both h4 and a4, in order to gain space in both flanks.

This idea was previously rejected due to the weakness on g5 it created and, Karpov, a previous world champion, remarked that this was ‘no way to play chess’. However, through successes by AlphaZero against Stockfish through playing h413, this affected the human practice of chess on the highest levels.

At move seven, inspired by AlphaZero, Maxime Vachier Lagrave (MVL) played 7.h4, and even 8.h5. This move, which would have been considered an inaccuracy 10 years ago, gave MVL an opening advantage, which eventually led to a win.

With all factors having been taken into account14, it is evident that computers have constantly been increasing our knowledge of the game.

Although factors such as cheating and excessive opening preparation can be used to argue otherwise, it is clear that these are caused by the individual players, rather than the engines, and can be avoided in some cases (e.g. Magnus Carlsen’s London System). As the engines are constantly teaching us and supporting us in our improvement in our understanding of chess, we can safely conclude that it is beneficial to the game.

Figure 4 Position after 7.h4

Good example in the third game of its ‘top 20 games’ (Deepmind, 2018) The endgame is not discussed, as computers have not made a significant impact on the endgame

13 14

27

Bibliography Barden, L. (2006). Kramnik’s carry on over his own convenience. The Guardian.

Chessgames.com. (2017, Dec 4). AlphaZero (Computer) vs Stockfish (Computer). Retrieved from Chessgames.com: https://www.chessgames.com/perl/chessgame?gid=1899416 Cummings, D. (2016). Opening Repertoire - the English. New in Chess.

Deepmind, G. (2018). Deepmind.com. Retrieved from AlphaZero Resources: https://deepmind.com/research/open-source/alphazero-resources FIDE. (2018). FIDE Arbiter’s handbook. Retrieved from arbiters.fide.com: http://arbiters.fide.com/images/ stories/downloads/2018/Arbiters-Manual-2018-v1.pdf FIDE. (2019, 12 5). FIDE Ethics Commission announces the sanctions against Igor Rausis. Retrieved from FIDE.com: https://www.fide.com/news/246 Mukhuty, S. (2019, 5 30). The Problemist Diary Part 4: Theatrical Positional Draw. Retrieved from Chessbase: https://chessbase.in/news/Problemist-diary-part-4-The-Theatrical-Positional-Draw Roeder, O. (2018, 1 3). Chess’s New Best Player Is A Fearless, Swashbuckling Algorithm. Retrieved from fivethirtyeight.com: https://fivethirtyeight.com/features/chesss-new-best-player-is-a-fearless-swashbuckling-algorithm/#:~:text=Two%20broad%20themes%20emerged%3A%20 First,not%20stodgy%2C%20defensive%20and%20careful.

Wikipedia. (n.d.). 39th Chess Olympiad. Retrieved from Wikipedia: https://en.wikipedia.org/wiki/39th_ Chess_Olympiad#Controversies Wikipedia. (n.d.). History of Chess. Retrieved from Wikipedia: https://en.wikipedia.org/wiki/History_of_ chess#:~:text=The%20history%20of%20chess%20can,the%20game%20spread%20to%20Persia.

Winter, E. (2009, March 29). How many people play chess? Retrieved from chesshistory.com: https://www. chesshistory.com/winter/extra/chessplayers.html#:~:text=’Today%2C%20according%20to%20recent%20polls,’

28

fly fishing on the nadder

29

Ned Tucker, Shell

a poem under lockdown Freddie Finlan, Remove

30

31

32

33

34

35

The DariÉn Gap A looking-glass into colombia

Bernardo Mercado, Shell The first settlement in the Darién Gap (Tapón de Darién), and on the mainland Americas was started by the Spanish in 1510, only to have it later torched after 14 years. Similarly, the Scottish attempted to set up a colony here, sending 1200 settlers in 1698. Few returned, and the ill fate of the colony survives in the history of the Kuna Indians, as well as the financial ruining and eventual incorporation of the country into the United Kingdom, which they had resisted for so long.

The topography and physical landscape vary between the two countries: in Colombia (one of the most biodiverse countries in the world), the area is dominated by the flat marshland, due to the river delta of the Atrato. There is also a mountain range extending from Colombia’s Pacific coast into Panama, covered mostly by rainforest. To enter from Panama, you must register with the border police (Servicio Nacional de Fronteras, or Senafront) who guard the dangerous area, who can turn you back at any point.

Drawing back through Colombian History

Though the region has been one never fully under Colombian (or any) control, we can use it as a marker of some aspects of past Colombia, as well as mention its geopolitical context, as this is an area surprisingly relevant to Colombian and Panamanian history as well as some issues of the region. Not withstanding the lack of control governments have had on the area, it is the location where criminal activities and rebel groups are natural drawn to – not a revelation, but the huge relevance and part of Colombian history the lines drawn over it and the substances which flow in and out play is surprising and can be twisted quite well into a tale of the history of Colombia, from its conception as Gran Colombia, to where it is now.

Its being divided between two countries has some significance, both as a symbol of Panamanian independence and foreign influence. It was the US that aided Panama and rebels in gaining independence from Bogotá, with which it had no land route. The departing of Panama was in large part due to the effects of the Thousand Days’ War, which had had sever repercussions, and caused continued instability in government. The Isthmus Department declared independence and, with US bigger-navy diplomacy, seceded, though the news was delayed by a couple of days and reached Bogotá on November 6, 1903.

The US had aided Panama largely because of the potential of the Panama canal, and after Colombia had proved a more difficult negotiator, backed Panamanian rebels, and instead took the land in a treaty (the Hay-Bunau-Varilla Treaty) signed by no Panamanians, establishing the Panama Canal Zone as US territory. This was one of the multiple countries that seceded from what was originally Gran Colombia, which had become Venezuela, Ecuador and Colombia (then New Granada), the latter of which Panama eventually too seceded from, finalising the failure of Bolívar’s vision.

Another large aspect of the Darién Gap are the guerrilla groups, which to this day, still operate in the area, carrying out drug trafficking and killing and torturing many making their journey through

36

here. The history of these groups, most notably the FARC, stems from ‘La Violencia,’ a civil war between the two major parties in Colombia (the Liberals and Conservatives), which came despite the Colombian commitment to democratic institutions. The war killed between 200,000 and 300,000 and came after the assassination of popular Liberal candidate, Jorge Eliécer Gaitán.

The war ended with General Gustavo Rojas Pinilla installing a dictatorship (the third and final) in the country and was overthrown with support from the newly formed National Front. This coalition meant that there would be every four years, a change in ruling party, and parity in other offices, with mixed results – it became seen as repression and led to guerrillas M-19 and the FARC being created as communist insurgency groups, and some of the military also separated into rightwing paramilitary group, though eventually they became involved in the drug trade.

This is one of the primary activities that happens now with the groups in the Darién, and cocaine in 1982 surpassed coffee as Colombia’s primary export, thanks largely to cartel operations. The Medellín cartel was once in charge of 80% of the world’s cocaine market and operated from as far south as Bolivia, up to Canada, and in almost every country betwixt them.

Pablo Escobar, the notorious leader, was elected to the city council, just showing how much control he exerted over the city, which still struggles with his legacy as either a modern Robin Hood or a ruthless criminal – however, there has been a tremendous success in bringing the city under control, by creating a metro, a modern plaza, and installing public transport in the form of cable cars from the mountainsides down to the Central Business District. On a lighter, though less relevant, note, Pablo Escobar also introduced hippos to Colombia (an invasive species) and in Comuna 13, escalators have been used to connect the distant community, and are a form of public transport and have been incorporated into the local community and culture, being painted over as communal spaces – most of the Medellín’s revival comes down to a series of urban revival projects, meant to bring it up to the present and showcase Colombian innovation.

However, since Pablo Escobar’s death in 1993, the violence stemming from cartels has mostly abated, though it still remains in smaller similar groups. The FARC has continued, though after Juan Manuel Santos was elected, he began peace talks with the guerrilla group, to many people’s surprise.

However, the 2016 referendum to ratify the agreement was unsuccessful, despite the polls indicating that it would be otherwise. The ‘No’ side was mainly backed by ex-president Uribe, who had been an independent candidate, and argued that the deal was too forgiving of the FARC’s illegal activities and horrifying methods, whilst the ‘Yes’ side argued that the people should put it behind them, though (according to Colombian accounts) there were many other issues and much more behind the referendum.

One of the more interesting thing that the vote revealed was that the regions most affected by the actions of the FARC, and of the groups similar to the ones which still lie in the Darién, voted largely

37

for the agreement, including the department of Chocó (which includes the isthmus), Nariño and Putumayo. The cities and more heavily populated regions (minus Bogotá), and those less affected, voted against the deal. A later deal was approved by Congress, FARC ceased (mostly) to be a military group, and Santos was awarded the Nobel Peace Prize.

However, the region, despite efforts from both governments to push inside, has not yet fallen under the control of either, and insurgents and FARC dissidents remain in there, along with native tribes and the local flora and fauna – drugs also flow in and out, not having stopped despite the fragile peace achieved by Santos and the dramatic downsizing of cartels. Atrocities are still committed there and many adventurers who try to cross don’t make it out.

The Darién Gap has also seen attempts on both sides to try to create a route through the gap, consensus collapsed in the 70s, partially due to indigenous peoples and environmental damage, drug trafficking and violence, and preventing foot-and-mouth disease from moving into North America. The primary reason cited, however, is the economic cost building a road through the isthmus would incur.

As a result, it cuts South from North America, effectively a ‘sea’ of jungle slicing the Pan-American highway, and the continents, in two. It covers both coasts, and ends in Turbo, Colombia and Yaviza, Panama. The only safe and more feasible crossing is by the Atlantic, though there are routes inland via canoe or by foot.

More recently, there was the crisis in Venezuela, with hyperinflation and mass exodus, and in response, many neighbours and Latin American countries closed their borders and raised restrictions on the Venezuelan migrants. Colombia, despite the ideological differences with the Maduro government, has offered humanitarian aid, and opened its arms to Venezuelans escaping the regime – this was not only on the part of the government, however, and the people of Colombia welcomed Venezuelans into their homes, in a way in return for the same warmth they received from Venezuela when Colombians fled from the FARC and the wars.

This also raises another interesting part of the Darién Gap’s modern story: it is often traversed by migrants seeking the US – groups travel often on foot through the dense forest, whether from Bangladesh and South Asia, or from Africa and the many other parts of the world which are entangled in war and violence, who first fly into Ecuador due to its more lax visa policy, and traverse both Colombia and the Darién Gap, and then continue onto the American border, to hopefully make it through.

As well as the dangers of simply getting lost in the isolated region, or the difficulty posed by the geography, the nature in the area is obscure, relatively unknown, and may very well poison / kill you on your journey through the Americas, only adding on to the potential ways to die in the Darién Gap.

38

For the people living inside, if they are not in the drug trade, there is little they can earn a living from, and so the few people seeking to travel across inland by canoe or foot provide a source of income, by selling items from the area. Thus, it is very difficult to live in the area, and poverty / basic living is common, in this case facilitating manipulation and detachment from government.

However, for the people crossing and those living there, the situation stays the same. In many ways, it remains as wild as it was in the days of the first European settlers. For now though, unless we were to change course, it seems like the Panamanian and Colombian governments will leave the region mostly to its own devices, for fear of destroying the biodiversity that exists in its own microcosm, freed from government and the modernising world, and splitting the Americas in twain.

Bernardo Mercado, Shell

39

Do derivatives belong in a retail investor’s portfolio ?

Russell Kwok, Remove Disclaimer: The author of this essay is not a qualified financial advisor and thus, all content is for informational purposes only and not to be treated as investment advice. Any loss is in no manner the responsibility of the author. It is very important to do your own analysis before making an investment. Derivatives are leveraged and complex securities and may incur substantial losses. To invest in such instruments, please follow all regulations and follow professional advice.

The recent volatility the financial markets, with fastest bear market on record in 19 days (LPL Research, 2020), have brought to mind the 2008 recession, which had led to financial catastrophe for millions of people around the world, in addition to the collapse of many renowned institutions such as Lehman Brothers. The current consensus of economists is that it was catalysed by investors gaining subprime credit exposure through derivatives. (Coghlan, et al., 2018) Thus, they are often derided as risky and complex. That view, however, is overgeneralising and may potentially exclude many opportunities that permit an intelligent investor to increase their returns, while derisking. (Asness, 2010) Truly, what harms investors is a lack of understanding. (Marolia, 2015) In view of these misconceptions, this essay will explore the types and structures of derivatives, the risk-reward ratio compared to other asset classes and examples where such securities are not only profitable, but beneficial for individual investors.

Derivatives are defined as “financial securities with a value that is reliant upon or derived from, an underlying asset or group of assets”. (Chen, 2020) This is done through a contract in which a writer promises to deliver some value, or the underlying goods to the purchaser of this agreement. The earliest example of derivatives in use comes from Aristotle’s Politics.

He recounts the activities of a fellow philosopher, Thales of Miletus: “he raised a small sum of money and paid round deposits for the whole of the olive-presses… and when the season arrived, there was a sudden demand for a number of presses at the same time… by letting them out on what terms he liked, he realized a large sum of money” (Aristotle, 1981) Thus, many who claim they are recent exploitative inventions of Wall Street are mistaken. In the latter example, derivatives were utilised for speculation, which is often mistakenly portrayed as their primary use in the financial markets.

This belief is fallacious because there are actually multiple uses for such instruments; in fact, their invention was due to a need to facilitate hedging, which is still the most common use.

(CFTC, n.d.) It means trying protects oneself against volatile asset prices by using derivatives to offset losses and gains on other securities they own; this is known academically as reducing variance. (Gilson & Black, 1993) Such ‘insurance’ is crucial for farmers and all sorts of businesses around the world who need to lock in prices to ensure costs stability and guaranteed payments.

Another use is to adjust your asset allocation without transacting any underlying assets, so as to minimise frictional costs. For intelligent investors, in addition to hedging, one can write (i.e. sell) contracts to generate cash, often without buying or selling equities, and decrease cost basis

40

Δ which will increase returns. There are many other uses, such as arbitrage (taking advantage of minor market errors), but they are accessible mostly for institutional investors and hence, do not provide any practical value to the retail investor.

Derivatives, as described, are an umbrella term for many different types of securities, such as swaps, futures, options and other more esoteric iterations such as weather derivatives that permit hedging of adverse meteorological conditions that could affect crops. For individual investors though, futures and particularly options, are the main structure for gaining exposure to this asset class. This is because they require relatively little collateral (cash used to backstop investors in case one cannot satisfy the contract) and are simple to understand. Let us first elaborate on their structures, in order to illustrate that their reputation of complexity and opacity is a fallacy, obstructing a path that could lead to not only better, but safer returns.

In essence, futures are “standardized agreements to buy and sell fixed amount of a certain commodity at a specified location at a future time for a predetermined price”. (Rogers, 2007) Given the exceedingly particular verbiage, it would wise to break it down into four sections: the agreement; the location; the time; and the price. The first section is self-explanatory, as derivatives are contracts between two or more counterparties. The second part describes the delivery or settling in cash of the goods one has ordered through the agreement; this can be problematic for retail investors as one needs a warehouse but 95% of commodities with such a mechanism do not take delivery. (Hecht, 2020) This is because, one can ‘roll-over’ one’s contract- in other words, extend the delivery date through a new contract. This is not difficult if one has a competent broker. The time is simply the month in which the contract expires, and delivery occurs, while the price is the agreed value at which to buy or sell the particular goods.

One makes a profit in futures by utilising the spread between ‘spot prices’, or current prices, and ‘future prices’, which are prices in the chosen month. If one believes future prices will be higher than the contract price for let’s say, December, one can buy that future and sell it when it converges to your target price.

But why even invest in commodities? Studies have shown that commodity futures returns are negatively correlated with equity and bond returns and are positively correlated with inflation, unexpected inflation, and changes in expected inflation.’ (Rouwenhorst & Gorton, 2004) This means that one could potentially profit during periods of market volatility and tumult, providing better risk-adjusted returns. Even for non-physical futures, such as E-mini S&P 500s, there is no management fees, better liquidity and cheaper margin, reducing overhead expenses, resulting in higher profits.

41

Δ Options and futures are very similar instruments, but with a slight difference- the former are contracts giving one the right (i.e. an option), rather than the obligation, to purchase or to sell the underlying asset. Thus, this can apply for individual stocks, which makes them, perhaps, more relevant for the individual intelligent investor. As they are rights to buy assets at a certain price, many variations exist, but once again, a proper retail investor should only put money in their circles of competence.

The two main types of ‘plain vanilla’ options, Wall Street jargon for the basic or standard version, which are European and American. The former is less common and is used for indices or currencies rather than individual equities, as they can only be exercised on the expiration date. The latter is an option that can be exercised at any time one desires within the contract period (Hanson, 2008). When one desires to buy or write (i.e. sell) an option, there are some vital specifications to consider. Firstly, one has to determine if it is a right to buy- a call option as if ‘calling in the asset’- or to sell – a put option, as if ‘putting it on the market’-. Then the quantity of a particular asset is agreed on, along with the expiration date, and the strike price. (OCC, 1994) The latter is like the price of the future; that is to say the value at which the transaction is to occur. As it is a right, rolling over is not necessary, as one can leave the option unexercised (albeit losing the premium, which is price of the option). If one does indeed exercise it, either cash or the asset is delivered or for the latter, sold.

Alternatively, options can be compared to a loan. Using this analogy, one can borrow the entire purchase price with only a moderate interest rate (premiums in this case) upfront with minimal collateral; if the investment did not succeed, principal would not have to be returned.

(Greenblatt, 1999) Such generous terms cannot be found in any bank in the world, even if one had the highest credit score.

Given the strike price and premium, one can deduce three different situations in which an option holder can be in: in-the-money (ITM); at-the-money (ATM) and out-of-the-money (OTM). ITM options mean that the underlying asset price is under (for a put) or above (for a call) the strike price, so exercising the right would result in profit. ATM option have a current price at strike price, so no loss or profit is incurred if exercised forthwith. OTM is the exact opposite of ITM and results in an immediate loss if exercised; one would purchase them because they are cheaper, and so allow the investor to make greater gains when the stock price exceeds the strike for the option to become ITM. Generally, due to their chance of potential profit being discounted in the price of the option if exercised, so ITM and ATM options are extremely expensive. Thus, in reality, it would be more difficult profit using them.

42

Δ In every intelligent investment, we have to ensure it is “one which, upon thorough analysis, promises safety of principal and a satisfactory return. Operations not meeting these requirements are speculative.” (Graham & Dodd, 1940) Hence, one needs to examine the risks involved in derivatives before gaining exposure to them. Market risk is probably on the top of one’s mind, as it is most direct and most common, as it is defined as ‘the risk of loss from adverse price movements in the market’. (Krawiec, 1997) This is most dangerous if one enters unhedged transactions, also known as ‘naked’ trades, as one might be forced in a margin call to liquidate other holdings in order to satisfy the contract, realising all losses and eliminating your capital.

This brings to mind the critical concept of margin in this asset class, as it is partly the reason for its popularity. Margin is merely collateral held by one’s broker to ensure one is able to satisfy the contract. (Fortune, 2003) In this way, one can build up a substantial quantity of derivatives with little money; in other words, one can gain leverage. Therefore, intelligent retail investors can boost returns without incurring too large a risk, if one is judicious about the gearing involved.

The most severe risks though are often neglected; they are counterparty risk and credit risk, in which the other side of the contract fails to deliver on their promises. Margin aims to mitigate (Cherubini, 2005), as it ensures the other side is faithful to the contract. In actuality, one could view the Great Recession partially as a counterparty risk crisis. (Thakor, 2015) However, this is not a grave concern if individual investors dissociate themselves from large contracts on illiquid markets, which are often fraudulent and exploitative.

Through the examination above, it is demonstrated that many risks associated with derivatives are in fact affecting mainly investors who are institutional, highly leveraged, or engage in less established mechanisms such as illiquid contracts.

Regardless of the veracity of the academic discourse on the merits of derivatives above, what critics of such instruments say are very true if one deals speculatively in them. Consequently, would be prudent to examine some scenarios in which derivatives truly aid the intelligent investor in making safer and better investments. Buying futures is a simple strategy, as it is the only way to gain exposure to commodities, so we will focus on three main strategies to do with options. For simplicity’s sake, they will all be for long positions.

1.) Writing or selling options.

This means one will be on the other side of the trade and will receive a premium for it (i.e. the cost to buy an option). The Chicago Board Options Exchange (CBOE) has

43

Δ noted that only about 5% of options are actually exercised (Shwager, 1990), implying that most options expire without being exercised, enabling their writers to collect the full premium. Moreover, time decay, a “measure of the rate of decline in the value of an options contract due to the passage of time” (Chen, 2020), is always working against the buyer, so as a seller, you benefit. To reduce the probability that the options writer faces adverse losses during volatile times via forced selling or buying of the stocks on the open market, the writer should always hold underlying stock concerning the options contract.

However, this risk can be exploited safely and lucratively if an investor desires to sell or buy some shares of a business; this is because one can effectively be paid to do so.

Let us assume one has analysed ADT Inc. (ADT) and recognised that it provides an attractive price at $4, given that it is worth the target price of $7.5. You could sell OTM put options- effectively, allowing someone to sell to you- with exercise price $4, which will allow you to be paid to purchase it. If one’s convictions are correct, the price will revert towards the $7.5 in the fullness of time. When you desire to close one’s position, you can sell an OTM call option- allow someone to buy from you-. It is particularly advantageous as one can pick the strike price as close as possible above the market price to maximise premiums. (Elias, 2001) By doing, it is possible to reduce cost basis towards zero, greatly expanding one’s margin of safety.

Normally, a company’s market value will only gradually reach intrinsic value, with frequent fluctuations. In these scenarios, one can even write call options around 10%20% above current price to generate premiums. That said, one should always buy back the calls when it is 25% of the premium obtained (Elias, 2001), or else, the price could exceed the strike price and generate a loss.

44

Δ 2.) Long straddle.

There are many complex ways to construct options in a manner that permits maximum profit for a certain viewpoint; these structures are short-term and constitute as speculation, something an intelligent retail investor should avoid. Nevertheless, there is one, known as a long straddle, which is statistically a profitable and safe method to exploit significant price movements in any direction.(Surur & Isynuwardhana, 2018) This methodology is most appropriate for major news or earnings releases in comparatively volatile businesses, like drug companies.

This strategy consists of purchasing a put and a call on the same underlying security with the same expiration date. (CME Institute, n.d.) The only downside, though, is that the total premiums paid is quite large, so only large moves are profitable. One can add the total premium to either side of the current price to discover the range at which the price needs to exceed; when it is so, one can exercise the options and realise the profits. The chart above shows Biogen Inc. (BIIB), a large biomedical corporation releasing news that a landmark drug for Alzheimer’s disease was delayed, resulting in a 12% decline.

(Griffin & Lipschultz, 2020) One might notice the start of a recovery at the end; hence, such trades are short-term and need to be closed in 2-3 days once profit is made.

3.) Long-Term Equity Anticipation Securities (LEAPS) or Warrants These instruments may sound rather byzantine, but they are basically long-term options.

LEAPS last for almost 2½ years while warrants are issued by the underlying company and can last for any long period of time, even for perpetuity. (Kumar, 2019) These are traded securities and can be found for most large companies, so they are not illiquid.

45

Δ One can actually replicate one’s portfolio with these securities, but with extra safety, as it involves less initial capital and limited losses. Even for staid blue chips like Johnson & Johnson (pictured below), such derivatives can boost otherwise unspectacular returns with safe amounts of leverage.

Some might wonder why using LEAPS are more advantageous than utilising margin loans, even when LEAPS have a maximum 100% loss and are time-constrained securities.

The key difference is that they are provide non-recourse leverage. (Mishuris, 2017) This means that they do not affect the rest of the portfolio in a worst-case scenario. For example, if one utilises margin loans, a margin call could occur, forcing one to change asset allocation and perhaps increase risk. Using long-term options, the only capital at risk of permanent loss is the premium; this can be equivalent to an equity position many times of the price of the option.

The time-constraint aspect of long-term options can be somewhat problematic for the intelligent investor, but like futures, one can roll-over the option, potentially making it last for more than 5 years. (Seagler, n.d.) This is not a difficult procedure if one has a competent broker. However, in behavioural investing, a stock owner is vulnerable to many biases that inhibit returns. One is known as the endowment effect. It leads one to value their holdings more than if they did not own it. (Kahneman, et al., 1991) The second most damaging bias would be anchoring. It is when one’s initial exposure is promoted during analysis, which impedes the inclusion of new evidence. (Boo & Furnham, 2011) Another is loss aversion, in which the investor does not sell suboptimal investments, as doing so would realise a loss and cause discomfort. By holding it, one is in an illusion in which one believes it is a temporary setback. (Kahneman & Tversky, 1979) With an option that has a fixed expiration date, which

46

Δ is effectively a forced liquidation date, these biases are less likely to impact the investor, since they will force the investor to make a decision of whether it is worth re-establishing the position from a perspective of not owning it and thus be able to take a completely fresh view of the investment.

A successful use of LEAPS would be Wells Fargo (WFC) in 1992, when it was in the midst of a real-estate downturn. (Greenblatt, 1999) One could purchase 2-year LEAPS costing $14, strike price at $80 with current market price of $77. Assuming one has done sufficient research of the business, and estimated intrinsic value at, for example, $160, which is not unreasonable if market conditions normalise and earnings continue to grow. On an investment of $14, if the price does reach the target price, it would imply a profit of $66. This is a risk/reward ratio of 1:5 compared to a 1:2 ratio if one purchased equity only, which is most exceptional.

The approaches detailed above are only three out of tens of options strategies that exist (Cohen, 2005), but the ones illustrated provide lower risk exposure and deserves consideration in the portfolio of the informed investor. Some may wonder why these methods are still profitable if they are already known, given the widespread agreement regarding the assumptions outlined in the Efficient Market Hypothesis; this is because of the dissemination of inaccurate information and negative attitudes towards financial derivatives within society, making this asset class inefficient. (Ackert & Tian, 2001) Furthermore, individual investors have the advantage of being small and agile, with the ability to evade many risks that ensnare larger investors. Opportunities are plentiful, but as always, only proceeding with diligence and caution can profits emerge, allowing for long-term wealth generation.

Bibliography

Ackert, L. F. & Tian, Y. S., 2001. Efficiency in Index Options Markets and Trading in Stock Baskets.

Journal of Banking and Finance, 25(9), pp. 1607-1634.

Aristotle, 1981. The Politics. 2nd Edition ed. s.l.:Penguin Classics.

Asness, C., 2010. Institutional Investor. [Online] Available at: https://www.institutionalinvestor.com/article/b150qd3fhy4cwb/using-derivatives-and-leverage-to-improve-portfolio-performance?Keywords=Asness&OrderType=1&PeriodType=4&StartDay=0&StartMonth=1&StartYear=2010&EndDay=0&EndMonth=12&EndYear=2010&ScopeIndex=0 [Accessed 15 June 2020].

Boo, H. C. & Furnham, A., 2011. A Literature Review of The Anchoring Effect. Journal of Behavioral and Experimental Economics, 40(1), pp. 35-42.

CFTC, n.d. Commodity Futures Trading Commission. [Online]

47

Δ Available at: https://www.cftc.gov/LearnAndProtect/EducationCenter/FuturesMarketBasics/index.htm [Accessed 27 May 2020].

Chen, J., 2020. Investopedia. [Online] Available at: https://www.investopedia.com/terms/d/derivative.asp [Accessed 19 May 2020].

Chen, J., 2020. Investopedia. [Online] Available at: https://www.investopedia.com/terms/t/timedecay.asp [Accessed 28 May 2020].

Cherubini, U., 2005. Counterparty Risk in Derivatives and Collateral Policies: The Replicating Portfolio Approach, Bologna: University of Bologna.

CME Institute, n.d. CME Group. [Online] Available at: https://www.cmegroup.com/education/courses/option-strategies/straddles.html [Accessed 28 May 2020].

Coghlan, E., McCorkell, L. & Hinkley, S., 2018. Institute for Research on Labor and Employment.

[Online] Available at: https://irle.berkeley.edu/what-really-caused-the-great-recession/ [Accessed 18 May 2020].

Cohen, G., 2005. The Bible of Options Strategies: The Definitive Guide for Practical Trading Strategies. 1st Edition ed. s.l.:FT Press.

Elias, S., 2001. Generate Thousands in Cash On Your Stocks Before Buying Or Selling Them. 3rd Revised Edition ed. Leawood, KS: Leathers Publishing.

Fortune, P., 2003. Margin Requirements Across Equity-Related Instruments: How Level Is the Playing Field?. New England Economic Review, 27 November.

Gilson, R. J. & Black, B. S., 1993. The Essentials of Finance and Investment. 1 ed. s.l.:Foundation Press.

Graham, B. & Dodd, D. L., 1940. Security Analysis. 2nd Edition ed. New York: McGraw Hill Education.

Greenblatt, J., 1999. You Can Be a Stock Market Genius: Uncover the Secret Hiding Places of Stock Market Profits. 1st Edition ed. New York: Touchstone.

Griffin, R. & Lipschultz, B., 2020. Bloomberg.com. [Online] Available at: https://www.bloomberg.com/news/articles/2020-04-22/biogen-alzheimer-s-drughits-delays-caused-by-data-covid-19 [Accessed 28 May 2020].

Hanson, W., 2008. InvestorPlace. [Online] Available at: https://investorplace.com/2008/11/option-styles-american-vs-european/ [Accessed 27 May 2020].

Hecht, A., 2020. The Balance. [Online] Available at: https://www.thebalance.com/taking-delivery-of-commodities-via-the-futuresmarket-4118366

48

Δ [Accessed 27 May 2020].

Kahneman, D., Knetsch, J. L. & Thaler, R. H., 1991. Anomalies: The Endowment Effect, Loss Aversion, and Status Quo Bias. The Journal of Economic Perspectives, 5(1), pp. 193-206.

Kahneman, D. & Tversky, A., 1979. Prospect Theory: An Analysis of Decision under Risk.

Econometrica, 47(2), pp. 263-291.

King, L. W., 2008. Yale Law School: Avalon Project. [Online] Available at: https://avalon.law.yale.edu/ancient/hamframe.asp [Accessed 20 May 2020].

Krawiec, K. K., 1997. More Than Just “New Financial Bingo”: A Risk-Based Approach to Understanding Derivatives. The Journal of Corporate Law, 23(1), pp. 2-63.

Kumar, S., 2019. Value Stock Guide. [Online] Available at: https://valuestockguide.com/all/stock-warrants/ [Accessed 28 May 2020].

LPL Research, 2020. LPL Research. [Online] Available at: https://lplresearch.com/2020/03/12/the-fastest-bear-market-ever/ [Accessed 18 May 2020].

Marolia, V., 2015. Derivatives Don’t Kill People... People Kill People, Orlando, FL: Regal Point Capital Management, LLC. Mishuris, G., 2017. Supplement to Q1 2017 Quarterly Letter, s.l.: Silver Ring Value Partners.

OCC, 1994. Characteristics and Risks of Standardized Options. 1st Edition ed. Chicago: Options Clearing Corporation.

Rogers, J., 2007. Hot Commodities: How Anyone Can Invest Profitably in the World’s Best Market.

Reprint Edition ed. New York: Random House Trade Paperbacks.

Rouwenhorst, K. G. & Gorton, G., 2004. Facts and Fantasies about Commodity Futures, Cambridge, MA: National Bureau of Economic Research.

Seagler, S., n.d. Snider Advisors. [Online] Available at: https://www.snideradvisors.com/blog/when-should-you-roll-over-a-covered-call/ [Accessed 8 Jun 2020].

Shwager, J. D., 1990. Market Wizards. Reissue Edition ed. s.l.:HarperBus. Surur, G. N. I. & Isynuwardhana, D., 2018. Return Analysis on Contract Option Using Long Straddle Strategy and Short Straddle Strategy with Black Scholes. International Journal of Academic Research in Accounting, Finance and Management Sciences, 8(4), pp. 16-20.

Thakor, A. V., 2015. The Financial Crisis of 2007–2009: Why Did It Happen and What Did We Learn?. The Review of Corporate Finance Studies, 4(2), p. 155–205.

49

An introduction to the problem of evil.

Toby Rooth, Shell The Problem of Evil: Christianity has been scrutinised since it first emerged from Judea. Over the centuries there has been much debate over the key ideas and basis for the religion. Ecclesiastical critics such as philosopher J.L. Mackie and Epicurus make feasible arguments against the church and the concept of God’s omnipotence, omnibenevolence and the existence of evil. Epicurus argued1 that God’s omnibenevolence, His omnipotence, and the existence of evil could not all be compatible. The problem of evil has been presented consistently by philosophers and theologians throughout time. However, arguably the most succinct explanation is written by the eighteenth-century philosopher, David Hume: “Is He willing to prevent evil, but not able? then He is impotent. Is He able, but not willing? then He is malevolent. Is He both able and willing? whence then is evil?”2 Hume considered evil to be decisive evidence against the existence of God as do many atheists. Consequently, the problem of evil remains the backbone of many atheist arguments.

This put Christian theologians in a position where they either had to admit that God is not both omnipotent and omnibenevolent (being ignorant of the scriptures) or explain the existence of evil. However, the Bible confirms both God’s omnipotence (As well as being referenced in the bible “For His invisible attributes, namely, his eternal power and divine nature, have been clearly perceived”3, the Fathers of the early Church considered the fact that God created everything as decisive proof of His omnipotence) and omnibenevolence (referenced in the Bible, “But you, Lord, are a compassionate and gracious God, slow to anger, abounding in love and faithfulness”4) to be true, and as the Bible is divine (“All Scripture is breathed out by God”5,) or at least θεόπνευστος (inspired) by God , evil became the subject of many theodicies.6 The question is clear, ‘Si deus est, unde malum?’ (‘If God exists, why is there evil?’)”7.

Moral Evil and Natural Evil: When approaching evil in this way, it is common practice to divide it into two parts: moral evil and natural evil. Moral evil is generally considered to be the acts of mankind which inflict pain and suffering upon ourselves or others. Many Christians believe that this evil was the result of ‘the Fall’ when man fell from grace, as well as some believing it to be bestowed upon oneself from birth or as a result of free will and human agency. “The intent of man’s heart is evil from his youth”8.

Natural evil is that which happens without human

There are no existing texts by Epicurus containing this argument, however, the author Lactantius attributes the Epicurean paradox (a version of the problem of evil) to Epicurus in his work De Ira Dei, 13, 20-21.

2 David Hume, Dialogues Concerning Natural Religion (originally published in 1779), Norman Kemp Smith, ed. (New York: Bobbs-Merrill Co., Inc., 1947), 198.

3 Romans 1.20 4 Psalm 86.15 5 2 Timothy 3.16 6 An attempt to explain the problem of evil 7 Barry L. Whitney, What are they saying about God and evil? Published by Paulist Press (1989), p. 3.

8 Genesis 8.21 1

50

involvement, such as earthquakes and tsunamis. The consensus is that natural evil occurs as a punishment from God, as a result of the moral evil that humans create. However, this varies depending on the theodicy in question.

The Faith Solution: Throughout time, many a biblical scholar, theologian, and philosopher have pondered the problem of evil. Most of these intellectuals take a rational approach to explaining the problem of evil. However, some theologians prefer to take a much more teleological stance towards the problem, arguing that we should trust in God, as (in the words of Rahner) we must accept the “incomprehensibility of suffering”9, understanding that experiencing evil is part of God’s plan, and we should have faith in his providence. In the Bible, Job is tested by God10 and comes to accept that his suffering is beyond his understanding11. “For as the heavens are higher than the earth, so are my [God’s] ways higher than your ways, and my thoughts than your thoughts.”12 Job maintains faith in God, even when all seems lost, and God rewards him for his faith. This way of explaining evil is perhaps so appealing due to its simplicity, meaning that it’s easily understood and applicable almost every type of evil. Unlike other theodicies, the faith solution grants an instant justification and consolation for one’s suffering, whereas in the case of other theodicies such as Augustine’s, coming to the answer that one’s suffering is just a ‘privation of good’, is not quite as comforting as knowing that their suffering happens for a good purpose. This teaches the Christian to maintain faith in God, just as Job did, to obtain this greater good.

Whilst the faith solution has many benefits, it possesses many downfalls and loopholes too.

The nature of the solution dictates that it is broadly applicable to all kinds of evil. Paul Schilling makes the point that with this justification of evil, one can claim any action to be justified by God for reasons only He can know by claiming faith in His providence.13 This same concept applies to natural evil and has a similar effect. Amid a natural disaster, say an earthquake, an operation is coordinated to provide aid to those in need. The faith solution here would remove one’s responsibility and duty to help those people, as their suffering is justified in the eyes of God. However, we are still obliged to help those people, as demonstrates through the teachings of Christ.

The answer that the faith solution presents can be frustrating, as it arguably avoids tackling the problem of evil directly. That being said, the faith solution presents a feasible argument as to why we shouldn’t question this problem, however this can feel rather evasive at times and doesn’t give a satisfactory answer to how God can be both omnibenevolent, omnipotent, and allow evil to exist.

Karl Rahner, “Why does God allow us to suffer?” p. 208.

Job 1.8–12 11 Job 42.1–6 12 Isaiah 55.9 13 Paul Schilling, God and Human Anguish, p. 66-67.

9

10

51

In short, the faith solution can be consoling as it grants instant comfort for one’s suffering, but it also has the potential to make human accountability/responsibility for evil idle, as all evils are justified by God. Moreover, the faith solution can be regarded insubstantial when finding an answer to evil, and keeping faith can be hard, especially when expected to do so blindly.

The Augustinian Theodicy: The Augustinian theodicy is one of the most important concepts when it comes to explaining the problem of evil. Augustine’s work is regarded as arguably the most influential after Saint Paul, “shaping biblical exegesis”15 and creating a lasting theological methodology. The Augustinian theodicy (developed in his books City of God and Confessions) has been adapted and elaborated on by many theologians and philosophers alike (labelled as Augustinian by John Hick). Perhaps the most famous interpretations of Augustine’s theodicy are to be found in the writings of Thomas Aquinas and John Calvin, who further developed the idea. Augustine writings here were heavily influenced by the first chapters of Genesis.

The Augustinian theodicy can be outlined in four parts. The first is that Augustine defines evil as ‘privatio boni’, a privation (or corruption) of good. God intended for us to choose good (“For I know the thoughts that I think toward you, saith the Lord, thoughts of peace, and not of evil”)16, but as He gave us free will, one has the option to choose evil (“And God said, Let us make man in our image, after our likeness: and let them have dominion over the fish of the sea, and over the fowl of the air, and over the cattle, and over all the earth”)17 and in doing so corrupts our use of it. Augustine wrote that “evil has no positive nature; but the loss of good has received the name ‘evil’”18. Paul Tillich and Martin Heidegger have expressed that evil should be regarded as ‘nonbeing’.19 God created the world ‘ex nihilo’ (out of nothing), and as God is ideally perfect, one must conclude that He made a perfect world (“God saw everything that he had made, and, behold, it was very good”20). In Genesis, Moses appears to claim that God originally created the world without moral or natural evil. Instead, moral evil enters the world as the result of the original sin, a by-product of his creations.21 Augustine believed evil to be a distinct lack of good, and evil enters the world in the sense that mankind turns away from good, losing their innocence, and becoming preoccupied with catering for their own desires and needs. It is when this state of total goodness is corrupted that ‘evil’ (or a lack of good) enters the world. It is now when the atheist asks, ‘what does Augustine have to say in response to natural evil?’ Well, Augustine believed that natural evil is the corruption of good in the wills of those who have the ability James O’Donnel, St Augustine, Encyclopaedia Britannica (Feb 19, 2020).

Jeremiah 29.11 16 Genesis 1.26 17 Augustine of Hippo, The City of God, Book XI, Chapter 9.

18 See John Hick, Evil and the God of Love, 182ff.

19 Genesis 1.31 20 Stephen Menn, Descartes and Augustine. Cambridge University Press (2002), p. 168.

14 15

52

to affect natural phenomenon, e.g. Satan and his cohorts (fallen angels), who try with all their might to dissuade the Christian from keeping faith in God. At no point is Augustine prepared to suggest that God is responsible for evil in any way. This leads to the third part. Augustine’s theodicy dictates that mankind is solely responsible for the existence of moral evil, and that God is not responsible for evil – it wasn’t created by Him and was “certainly not desired by God” 21 The doctrine of the original sin informs us that all humans are guilty of disobedience through the original sin, expressed by the Apostle Paul “Wherefore, as by one man sin entered into the world, and death by sin; and so death passed upon all men, for that all have sinned”22.Augustine’s theodicy explains that God’s omnibenevolence maintains perfection, without responsibility for suffering.

As with any theodicy, Augustine’s has its criticism in abundance. John Hick argued that if God made a perfect world, it would have been impossible for it to go wrong (for humans to become immoral). Hick also disputed Augustine’s point that God remains without responsibility for evil.

Hick writes that if God knew the choices that humans would make (regarding Augustine’s views on predestination) he must be somehow responsible for them. Furthermore, there has been much criticism of Augustine’s theodicy from a scientific point of view. Hick described the theodicy as “implausible” considering Charles Darwin’s theory of evolution, as it would render the fall from grace inaccurate.23Augustine proposes that all men were seminally present in Adam, however if Adam didn’t exist as such, mankind could not be seminally present in him, flawing Augustine’s theodicy. Arvind Sharma has pointed out that natural evil cannot be so in the way that Augustine proposed, as scientific consensus suggests that natural disasters have occurred before the existence of humans, therefore making it impossible for natural evil to occur as a result of sin.24 Lastly, Augustine believed that God was also omniscient, meaning he reliably knows what people will do. If this is so, as argued by David Ray Griffin, people would not truly be free. With this concept, he proposed that the original sin must itself be indirectly caused by God, rendering any punishment unjust.25 These are just three of the most basic contradicting arguments among many others.

The Irenaean Theodicy: The work of Saint Irenaeus of Lyons has influenced the theological sphere greatly, as well as being a heated topic of debate. Irenaeus proposed a theodicy which became a major part of considering the problem of evil. His theodicy (like Augustine’s) has been developed and elaborated on over the centuries by countless philosophers, theologians and Christian thinkers, perhaps most notably Barry L. Whitney, What are they saying about God and evil? Paulist Press (1989), p. 29.

Romans 5.12 23 Stephen Davis, Encountering evil: live options in theodicy. Westminster John Knox Press. Davis, 2001, p. 54.

24 Sharma, A primal perspective on the philosophy of religion. Springer, 2006, pp. 85-8.

25 David Ray Griffin, God, Power and Evil: A Process Theodicy, (1976).

21 22

53

by Origen, Schleiermacher and Hick (again Hick took the liberty of labelling adaptations of the theodicy as ‘Irenaean’).

The Irenaean theodicy can be outlined in three parts. The first part of his theodicy sets the important distinction between humans being in the image of God and humans being in the likeness of God. In the Bible it says “God created man in his own image, in the image of God he created him”26, and how this is interpreted is fundamental to the Irenaean theodicy. Irenaeus makes the distinction that we were created in God’s image (in so far as we possess a free will and intellect), but not his likeness. He believed that we are first created in his image, then we develop and into the likeness of God (inheriting his infallibly good characteristics), eventually reaching a point where we live like him.

It’s a two-stage creation process and Irenaeus is proposing that the creation is incomplete as of now. One can think of mankind as a new-born baby. The baby is created in the image of its mother and then grows into her likeness. Mankind is the same. John Hick wrote that to be created in the image God means to have the potential to have knowledge and be in a relationship with God (which we currently have, like a baby being able to develop into the likeness of its mother) however, this is fulfilled when the creation is complete and we come to be in the likeness of God. The second part of the Irenaean theodicy dictates that one experiences suffering for the moral development of mankind. Friedrich Schleiermacher argued that as “God would create flawlessly” it would be illogical for a perfect world to go wrong. Irenaeus saw the world in a very teleological sense, where humans would learn more about good by experiencing evil. This became known as ‘soul-making’. Irenaeus argued that a world without evil and suffering would be less suited to the development of humans, especially without meaningless suffering. He proposed that this was the purpose of natural evil, seemingly meaningless suffering has the divine purpose to develop feelings such as compassion and sympathy. Hick elaborated on this by arguing that suffering is necessary for the development of humans and in response to meaningless suffering, claimed that if all suffering and evil had purpose mankind would be unable to develop feelings of compassion and sympathy. Irenaeus writes “A world without problems, difficulties, perils, and hardships would be morally static. For moral and spiritual growth comes through response to challenges; and in a paradise there would be no challenges.”27 In the Bible it reads “And God saw everything that he had made, and, behold, it was very good.”28 Irenaeus (contrary to Augustine) interpreted this as the world being fit for purpose (for the development of humans), rather than without evil.

He referenced the Book of Jonah to illustrate how suffering would result in atonement and bring oneself closer to God. Unlike Augustine, Irenaeus believed that God is in part responsible for suffering, as he permits it for soul-making. He believes that for humans to truly learn, we must be Genesis 1.27 Irenaeus, Church Fathers: Against Heresies, 28 Genesis 1.31 26 27

54

given free will with the choice to actually do evil. We must learn from real consequences if you will. Lastly, Irenaeus lays out his beliefs of when mankind will become in likeness with God. Influential works have much criticism, and the Irenaean theodicy is no exception. Dewi Phillips presents the argument that, concerning the Holocaust, any theodicy which explains evil to be instrumental or teleological should be treated as inadequate, as the scale on which people suffered is too great to be justified by any means, regardless of what benefits it might bring.29 However, one can argue that while God permits evil per se, event such as the Holocaust are caused by humans, and not God. C. Robert Mesle also argued that although suffering is sometimes indirectly beneficial, often it does more harm than good.30 Another Process theologian David Ray Griffin challenged the idea of ‘soul-making’ by proposing that God inflicts pain for his own ends, which he viewed as corrupt.

Summary The problem of evil is a nuanced and complex topic with many details and difficulties. Whilst there is no definitive answer, there are premises with which a conclusion can be drawn.

The faith solution provides a consoling answer to the problem of evil as it grants one with the peace of mind that there is a reason for one’s suffering that only God can know. In addition to being easily understood, the faith solution also proposes that we should not question God, (“But let him ask in faith, nothing wavering. For he that wavereth is like a wave of the sea driven with the wind and tossed”)31 and accept that it is foolish to try to understand His ways. However, although this way of thinking is credible, it’s inherently unsatisfactory when trying to find an answer to evil, regardless of how valid its points may be. Paul Schilling points out that the faith solution grants one the power to do evil without bearing responsibility, as God willed them the do so for a reason they cannot question. The faith solution is thus ill-founded, consequently providing no satisfactory solution to the problem of evil.

The Augustinian theodicy presents an argument that has stood for many centuries; a testament to the strong case it exhibits. Augustine writes about his theodicy in great depth, justifying, deliberating, and explaining each principle that led him to his conclusion. However, perhaps being ignorant to the extent which he wrote, I dislike his theodicy (favouring Irenaeus’). The premise for my disliking of his theodicy lies in Augustine avoiding admitting that God has any responsibility for evil, or that evil exists as such. If God did create the world ‘ex nihilo’ then he must have some level of responsibility for his creations, even if their suffering is justified. To further this, if God 29 Hugh Campbell and Michael Wilkinson, Philosophy of Religion: An introduction. Continuum International Publishing Group (2010).

30 C. Robert Mesle, Process theology: a basic introduction, Chalice Press (1993).

31 James 1.6

55

does have responsibility for his creations, and is truly omniscient, he must, in turn, be indirectly responsible for the original sin, rendering any punishment unjust. The Irenaean theodicy presents a better argument regarding God’s responsibility for evil.

The Irenaean theodicy presents a much more logical answer to the problem of evil. Instead of redefining evil to support God, Irenaeus admits that God is responsible for some suffering, but it’s justified due to it being a ‘soul-making’ necessity. Moreover, the Irenaean theodicy dictates that we are yet to develop into the likeness of God, which is a much more reasonable and satisfying conclusion that is perfectly feasible. The idea that we need to develop and endure difficulties to reach a true state of perfection (or become in the likeness of God) is more true to day to day life as we know it and is a more rational and logical solution. This is why the Irenaean theodicy is the most convincing argument.

Toby Rooth, Shell

56

My Arcade Cabinet Rohan Haripaul, Remove

57

58

59

60

61

62

63

understanding the depths of quantum computing...

Hyunjo Kim and Yikai Zhou, Shell

Definitions: Information - An interpretation of the particular system’s state - fixed set of distinguishable values Computation - A physical process where there is a fixed set of states and finite in time Introduction Quantum computing can be seen as the ‘gold rush’ of the 21st Century. In 2017 and 2018 alone, there has been an investment of $450 million just from private investments and the US government has authorised $1.2 billion to be invested into quantum information science over the next five years. So, what is causing this boom? In order to find out what this quantum computing frenzy is all about, we need to understand the differences from classical computing. This study will embody the basic studies and ideas of Quantum Physics and Computing, Qubits and Quantum Gates, Deutsch's problem and basic algorithms, Shor’s algorithm.

Classical Computing Classical computing stores and processes information through a binary unit, or bits. (e.g. 11001 can refer to a classical state of 25) We can refer to Figure 1, to understand how classical computing stores information. Specifically, Shannon’s entropy focuses on how many bits are required to store a certain variable. Basically what Shannon’s Entropy actually means is that the summation for each symbol of the probability of that symbol times the logarithm b of one over the probability of that symbol. 1/P can be expressed as P-1 and by using logarithmic identities, we put a negative sign in front of the Σ. To understand this, I will give an example: There is Machine 1 where A, B, C, or D is given as an output. The chance that the next letter will be A is 25%, B is 25%, C is 25%, D is 25%. Machine 2 → A is 50%, B is 12.5%, C is 12.5%, D is 25%. What is the minimum number of questions you need to ask you would expect to ask to find out what the next number is? Here is the answer: 1.

Is it A or B? → Through this we can eliminate half of the possibilities → If yes, we will end up with two symbols, A and B (both equally likely).

2.

Is it A? → Then, we will know what symbol it is. * Of course, the same will apply if we got C or D Two Questions are needed for Machine 1 as: 0.25 * 2 + 0.25 * 2 + 0.25 * 2 + 0.25 * 2 = 2

64

▷ For Machine 2: 1.

Is it A? → If it is A, it is complete, but if it is not, we still have B, C, D. 2.

Is it D? → If it is D, it is complete, but if it is not, we still have B, C. 3.

Is it C? → Then, you will definitely know which symbol it is.

Be careful! The minimum is not three questions… In fact it is 1.75 (on average) questions as: 0.5 * 1 + 0.125 * 3 + 0.125 * 3 + 0.25 * 2 = 1.75 What can we understand from this analogy? Machine 2 is producing less information as there is less uncertainty (smaller amount of questions that needs to be asked). Shannon calls the unit of this entropy as bits and we see in computers that they are in binary. Computers store information using bits because 0s and 1s are like making choices as we can see in the Machine Analogy…

To make things simpler, I will just quickly simplify Shannon’s entropy where all states are equiprobable as that is how classical computing works.

From this simplification, we can now understand how information is stored. For example, if a state has 64 states, there will be 6 bits.

65

≼ Now, we will look at the computation of classical computing. In order for classical computing to work and compute a function, we need to see if there is an algorithm in place. It should be able to process a number of states, the final state, and understand the parameters which control the behaviour of abstract to controlled models. Although we will not go in detail about the computation of classical computing, we will show you how decisions are made in computers through logic gates. Figure 2; shows an easy representation of logic gates using logic.ly.

Logic gates are the fundamental constituents of digital integrated circuits. They are devices which implement the Boolean functions to accrue one output from two inputs.

Boolean algebra is the mathematics we use to peruse digital gates. We implement Boolean laws to diminish and simplify a complex Boolean expression to reduce the number of logic gates required. The various logic gates consist of AND, OR, NOT, NAND, NOR, AOI*, OAI*, E/XOR and E/XNOR gates. Logic gates may be adhered or cascaded together to conceive a logic gate function with any desired number of inputs, or to form combinational and sequential type circuits, or to produce various logic gate compounds from accustomed gates.

The usage of the term 'gate' is eminently suitable as logic gates can be simply appreciated by examining the basic function of a gate: to control a flow. In a computer, a gate controls the flow of electric current through a circuit. The gate consists of transistors. The transistors used in the construction of logic gates are classified into two basic categories, PMOS and NMOS transistors that are found in the ubiquitous CMOS (complementary metal-oxide semiconductor) technology. Logic gates are analogous to taps, permitting and restricting current flow. The current that flows through a gate establishes a voltage at a point in the circuit. This voltage represents a single 'bit' of information. The voltage may either be high (representing the value '1') or low (representing the value '0').

Logic gates within a microchip are conceived of an arrangement of transistors.

Regarding modern microchips, the transistors are of the kind called Metal-Oxide-Semiconductor FieldEffect Transistor (MOSFET), and the material used to conceive the semiconductor is silicon. A MOSFET has three components; the three regions are arranged horizontally adjacent to one another. By conjoining MOSFETs, we obtain a microchip. The microchips are further aligned to make up a storage unit in the CPU. Quantum Computing We know that as classical computers go to atomic, molecular level, pair injunction does not work and the ideas and the laws that govern classical computing do not work any more as there are now quantum effects. Also, classical computing cannot emulate/simulate quantum phenomena. If classical computing encounters intractable problems, the complexity of the solution will exponentially increase. One of these hard, intractable problems is simulating a quantum realm. Richard Feynman discussed that these quantum-based computers will be able to simulate the quantum realm, and effectively simulate

66

≥ themselves. To give an insight, quantum computers can solve problems 100 million times faster than classical computers.

Now, I will talk about what kind of quantum effects we are talking about: superposition, and entanglement.

Superposition is the counterintuitive ability of a quantum object to exist in a multitude of states. Let me give you an example - the double-slit experiment. There are two very narrow slits and photon emitters. Let’s say we put the photon detectors behind the gaps on the metal sheet. The upper detector will be state (1) and the other will be state (0). What will actually happen is that both detectors will detect the photon. This is because of the Heisenberg Uncertainty Principle; Heisenberg told us that we cannot both know the coordinate and the momentum of the particle. As we know the wavelength of the photon, we are unsure about its coordinate. Thus, what is happening now is that we have a probabilistic measurement where one half goes through the upper slit, whilst another half goes to the bottom slit.

Similar to what I just talked about, a similar phenomenon happens in quantum computing. In a bit, the spin of an electron (spin up/spin down) determines if it is a 0 or a 1. In quantum computing, a qubit takes both the value of 0 and 1, these quantum objects will be in two states until it is measured. However, before it is measured, the electron (inside the computer) will exist in something called a ‘quantum superposition’.

The fact that the probability varies can be manipulated by quantum operations, but before we go into how quantum operations work, I will talk about entanglement.

Quantum entanglement is when two quantum objects interact. First, I will talk about spin. All fundamental particles have this thing called spin. Although the particles are not actually spinning, they have an angular momentum and an orientation in space. Entangled particles are dependent on each other meaning that the measurement on one partner will affect the other partner immediately. The way it works in quantum computers is that the quantum computer leverages entanglement between qubits and the probabilities according to superposition to execute a series of operations using quantum algorithms that will be demonstrated in the latter sections of our study.

Information Quantum computers are the pinnacle of human technology at present. By availing the unique phenomena of quantum mechanics, we are capable of making prominent ameliorations in computing speeds. These phenomena incorporate complex probability amplitudes, quantum interference, quantum parallelism, quantum entanglement, decoherence and the unitarity of quantum evolution. We employ these phenomena to permit the secure transmission of classical information (quantum cryptography), the use of controlled quantum evolution for efficient computation (quantum computation, the possibility of preserving quantum coherence in the presence of irreversible noise processes (quantum error correction) and the use of quantum entanglement to permit reliable transmission of quantum states (teleportation).

The common theme of all these insights is the use of quantum entanglement as a computational resource.

In quantum computation, a quantum algorithm is an algorithm which runs on a realistic model of quantum

67

∏ computation. There’re several quantum algorithms which are in application in quantum computing. Shor’s algorithm, Deutsch algorithm, Simon’s algorithm, Grover’s algorithm, Fourier fishing and many others.

Quantum computers can solve strenuous computational problems such as integer factorisation of astronomical numbers. These computational tasks can execute exponentially faster on a quantum computer than on a classical computer. The aspiration of conceiving a quantum computer was first proposed in 1981 by Nobel laureate Richard Feynman. Feynman envisioned a machine which computes efficiently by simulating quantum mechanical systems. The computational power from quantum computers would have eminent effects on a vast variety of topics, applications to a multitude of problems outside quantum mechanics. Computation has diversified away from its narrow beginnings of facilitating simulations of Newtonian mechanics. The studies of quantum algorithms have diverged greatly from simply simulating quantum physical systems to impact a vast majority of fields, including cryptography, information theory, language theory, and mathematics. There are various models of quantum computing, they incorporate the quantum circuit model, adiabatic quantum computer, quantum Turing machine, one-way quantum computer, and various quantum cellular automata. The mainstream models implement the quantum circuit. Quantum circuits are paved based on quantum bits, also known as qubits. They are analogous to the bit in classical computation. A bit, in its presence, can be of value of 1, or 0. Quantum bits acquire both the characteristics of a mainstream bit, and they can be in a superposition of the 1 and 0 states. However, when qubits are measured the result of the measurement is always either a 0 or a 1; the probabilities of these two outcomes depend on the quantum state that the qubits were in immediately prior to the measurement. Computation is performed by manipulating qubits with quantum logic gates.

About Qubits and Quantum gates Qubits A qubit is the minimal amount of information of quantum information. For example, we could look at the polarisation of a single photon in which the two states will be determined by if it is in a horizontal or vertical polarisation, but because of superposition.

Let’s look at some of the mathematical models: A qubit can be represented as a linear superposition of basis vectors. The vectors are expressed as seen in Figure 3 in the bra--ket notation, formulated by 20th Century Physicist Dirac. These two computational basis states are said to exist within the Hilbert Space (Hilbert Spaces are tools when modelling quantum mechanics mathematically). Figure 4 shows how qubit basis states can be combined to create product basis states. The rule is that if there are n qubits, they have a superposition state vector in 2n dimensional Hilbert space.

68

∏ What is a pure qubit state? It is where there is a coherent superposition of the basis states. We can derive from this the fact that a single qubit can be represented linearly with “ket 0” and “ket 1”. Look at Figure 5 for the mathematical expression.

I will deconstruct Figure 5 which reads: “ket phi” = alpha “ket 0” plus beta “ket 1”. Both ɑ and are the probability amplitudes which can be complex numbers (a + bi). A probability amplitude describes the relationship between the wave function and the measurement of the system. The probability to find the particle at x at some time t is equal to the modulus squared of the probability amplitude. By referencing to the Born Rule, the probability of outcome “ket 0” with value 0 is modulus ɑ2 and the probability of outcome “ket 1” with value 1 is modulus 2 , because these two equate to probabilities, the equation must equal to 1, so we can come up with this equation: |ɑ|2 + | |2 = 1 From this we can understand how qubits work. From the equation above, you can see that there is no certain value for 1 and 0. The qubit only contains the probability of one another.

Therefore, there is no way to know due to the superposition state if the qubit state is “1” or “0”. The diagram right next here shows the equation of a superposition. It can be written as a superposition of the basis vectors “ket 0” and “ket 1”, where the coefficient are complex numbers. The theta is the coaltitude in respect to the z axis and the phi is the longitude in respect to the x axis. The cosine half angle and the sine half angle can represent the amplitudes, where e^iphi can be expressed in the polar form of a+bi. Until it is measured, the probability of the superposition remains to be equal.

Quantum Gates A quantum gate is basically a quantum circuit that runs on a small number of qubits. Unlike many classical computers, quantum gates can be reversed.

Logic reversibility is where you are able to reconstruct the input from the output of a computation. Quantum logic gates are represented by unitary matrices which is a form of a complex square matrix in which its conjugate transpose is also its inverse. To easily express this, the matrix is flipped over on its diagonal row and the conjugate of the inverse is calculated (Look at deepai.org for more info). In this section about Quantum Gates, we will look at the Hadamard (H) Gate, Pauli-X Gate, Pauli-Y Gate, Pauli-Z Gate, the Phase Shift gate, and the Square root of the SWAP Gate.

69

≠ The Hadamard Gate as shown in Figure 6 shows the calculations.

As we are dealing with quantum gates, there is no definite value of 0 and 1. Therefore, we will assign them as equal probabilities, which then makes the probability amplitude 1/root 2. The H Gate is a combination of “ket 0” and “ket 1”, if we would look at a Bloch Sphere (geometrical representation of a pure state space of a qubit), it would be shown as the combination of two rotations.

The effect of a Hadamard Gates is that they expand the range of states it’s possible for the quantum computer to be in. Because of this very expansion, what occurs is that it actually creates the possibilities of short cuts, which may help some computations to become quicker. (Understand that by the term ‘quicker’ we are not referring to the internet or simply typing in a google search engine, but for example you could find the next prime number more quickly) Let me use an analogy… If we are playing chess and we create a new rule that is only in our favour, so the rook can now travel diagonally, we could possibly checkmate our opponent more quickly.

The Pauli-X gate is the quantum equivalent of a NOT gate. A NOT gate in classical computing is where it inverts the value of the input. In Boolean Algebra, the NOT Function follows the Complementation Law of inversion as seen in Figure 7. In the bloch sphere representation, it is a rotation in the x axis by π radians (180 degrees), it can be represented like in Figure 8.

The Pauli-Y Gate rotates around the y axis. It switches the amplitudes and multiplies them by ±i (imaginary number).

The Pauli-Z, it rotates a single qubit by π around the z axis. These Pauli Gates are the fundamental operations and the easiest of all quantum gates. When we actually use these gates for a programme Pauli Gates prove to be so important. Look at Figure 10 for the representation of the Pauli-Z gate mathematically.

70

≠ The last quantum gate we will talk about is the Phase Shift Gates. This is a group of single-qubit gates that leave “ket 0” unchanged but changes “ket 1” to e^iphi “ket 1”. This modifies the phase of the quantum state, but does not alter the probabilities of “ket 0” and “ket 1”. To elaborate, waves are characterised by amplitude and phase and in the Bloch sphere, this phase shift gate is equivalent to tracing a horizontal circle by phi radians. These phase shifts helps to unlock different values. The amplitudes and phases will influence the resulting quantum state, and correspond to the same physical state, but they are not interchangeable. From this idea, we can conclude that global phase factors are unphysical, thus undetectable. We can say “ket phi” is equal to “ket e^jphi” which leads us to the equation as seen in Figure 11 where 0<=p<=1 is the probability of the bit being in state 0, whereas 0<=phi<=2π. As aforementioned, the phase shift gate facilitates the process of reaching all values of p and phi.

Lastly, we will look at the implementation of the square root of the SWAP Gate. The SWAP Gate swaps two qubits, with the basis states of “ket 00”, “ket 11”, “ket 10”, “ket 01”.

It is represented by a matrix that looks like Figure 13. However, the Square Root of the SWAP Gate performs half-way of the qubit swap. Any many-qubit gate can be constructed using a single qubit gate and this very gate. With more than one application required, it is transformed to a Bell state, where the specific quantum states of two qubits can represent the simplest examples of quantum entanglement. Thus, we can understand the matrix representation from Figure 14. We will look at quantum operations now using quantum algorithms.

Quantum Algorithms Shor’s algorithm Shor's algorithm is a polynomial-time algorithm utilised in quantum computing or integer factorization, contrived by the renowned mathematician Peter Shor. The mathematical expression for this algorithm is to factor a number N in O [(log N)3] time and O (log N) space (detailed mathematical explanation of the algorithm is provided in the extra information document). No other classical algorithm innovated can factor O [(log N) k] for any value of k in a conceivable amount of time. Au contraire to classical algorithms, Shor’s algorithm can evaluate the factors in polynomial time. It is eminently more efficient as normal computers, which use classical algorithms, which enumerates prime factors of astronomical integers by guessing, inputting a number and to scrutinise if the number is a prime factor of the original integer or not. On the other hand, Quantum computers, with the application of Shor’s algorithm, still inputs a prediction of a factor however can fabricate a better guess for the following predictions.

71

∞ Deutsch algorithm The Deutsch–Jozsa algorithm is a deterministic quantum algorithm advocated by the renowned physicist, David Deutsch. When a deterministic algorithm derives an input, the output would always be identical.

Simon’s algorithm is the first quantum algorithm to show an exponential increase in speed in comparison to the best classical algorithm in solving a specific problem. This quantum algorithm is based on quantum Fourier transform. In the Deutsch–Jozsa algorithm we use an oracle to determine if a binary function f(x) : {0,1}^n {0,1}f(x): {0,1} n→{0,1} is constant or balanced. The motivation is to show a black box problem that can be solved efficiently by a quantum computer with no error, whereas a deterministic classical computer would need many queries to the black box to solve the problem. More formally, it yields an oracle relative to which EQP, the class of problems that can be solved exactly in polynomial time on a quantum computer, and P are different Simon’s algorithm Simon’s algorithm is the first quantum algorithm to show an exponential increase in speed in comparison to the best classical algorithm in solving a specific problem. This quantum algorithm is based on quantum Fourier transform. Simon’s algorithm is eminently similar to Shor’s algorithm. We are given an unknown black box function which is determined to be either one-to-one or two-to-one, which have the following properties:

Mathematical Explanation Shor’s algorithm

72

â&#x2C6;&#x17E;

Furthermore, we need to set up quantum parallelism, which we achieve so by conceiving an entangled state; we need apply a 2-dimensional Hadamard gate (as we have seen in the Quantum Gates section) to output being:

Now we look at the quantum oracle, which is a "black box" operation that is used as input to another algorithm. Often, such operations are defined using a classical function. I will walk you through the input of the quantum oracle.

73

∑ Initially, we apply linearity to the superposition going into the oracle’s register. Then we set “r” as the period of the function and D as the domain. I assumed that “r” is a divisor of D, as if it isn’t it requires a much more complicated explanation which is not suitable for this part. Utilising the function is periodic injective along with one unknown variable. We can gather from injective periodicity that the domain can be split into many disjoint cosets of size a, each as a sub-domain to the function. With the aid of a bit of group theory we can simplify down the r ≡ [0, a-1] = [0,1,2,...,a-1]. Then we deconstruct our simplified answer.

Moreover, we proceed to finalise the output of the oracle.

Finally, we move onto the QFT. We apply the QFT at the output of the oracle then proceed to work out the QFT of the entire superposition.

74

∑ Order Finding Problem The input: A positive function where xʳ ≡ (mod N) N≥2.

The output: The order “r” for the input function.

The order finding problem is used to find the period of a function. We can use Phase Estimation (explained in the section below) to solve the problem, which can be understood as: accumulating an eigenvalue e²^π^i^rho for a unitary operator U and an eigenvector |u ..

We apply the unitary operator into the circuit above and we acclaim the fact that U is unitary and the eigenvector of |u .

75

∂

** The phase estimation was used for the algorithm to compute the period of the function by securing the eigenvector with its eigenvalues of the Unitary operator.

Phase Estimation We presume a unitary operator of “U” has an eigenvector of alongside an eigenvalue of e^2^π^rho where the known value is the “rho”. Our aspiration is to obtain an estimation for . The input is the eigenvector and controlled U²ʲ operator where “j” is a non-negative integer.

76

â&#x2C6;&#x201A; Quantum circuit:

We assume that there is an oracle which is applicable for U²ʲ where the control state is semiclassical quantum Fourier transform (t-bit). We then proceed to the algorithm

and j is a

We conceive superposition from the initial state the apply a black-box algorithm to the state. Then we proceed to measure the output. Phase estimation is used to solve the order-finding problem.

77

∫

Deutsch-Jozsa Algorithm Let f: [0,1]ⁿ---> [0,1] be a function where f is a constant if f(x) does not alter for all options of x€[0,1]ⁿ.

F is considered balanced when f(x)=0 for half of the outputs and the other half resulting in f(x)=1. This algorithm is used to determine if f is balanced or constant.

The o with a cross denotes tensor product. For more information about tensor products, visit: https://en.wikipedia.org/wiki/Tensor_product Simon’s Algorithm Simon’s algorithm is the first quantum algorithm to show an exponential increase in speed in comparison to the best classical algorithm in solving a specific problem. This quantum algorithm is based on quantum Fourier transform. Simon’s algorithm is eminently similar to Shor’s algorithm. We have an input of [0,1]ⁿ---> [0,1]ⁿ and already know that s € [0,1]ⁿ such that [f(x)=f(g)]--->[x o g €[0ⁿ,s]]. Our intention is to find s.

78

∫

Our initial register is deterministic, and we proceed to utilise the orthogonality of |f(x)>for each value of “y”. Since our output has two situations, we have two various expressions as shown above. We are required to apply two Hadamard transformations and also use a black box algorithm to find the output.

Fourier Transformation

79

≈

The Fourier transform can be defined as an improper Riemann integral, making it an integral transform.

After we obtain the Fourier coefficient, we can substitute it in from the Fourier series into Fourier transform. It can both be expressed as a domain of a period’s function.

Conclusion Joey and I worked really hard to find the essence of quantum computing whilst working on this project.

When we said that we will, ‘Understand the depths of quantum computing…’, we really tried to see the proofs, the mathematical explanations although it was an arduous task for us. But, from our mathematical explanations and the concepts of quantum computation, we can derive that the benefits of quantum computation surely surpass the benefits of classical computation. We challenge more and more people to look at the next technological breakthrough - quantum computation. The prototype built by IBM can be accessed anywhere in the world via the Cloud and everyone can try to engineer quantum softwares.

Our goal for this project was not simply to see why quantum computation actually works but to show how efficient quantum computing would be. The future of quantum computation is bright, but it is essential for it to become accessible and we hope that our project helped people to understand the domain of quantum computation.

80

â&#x2030;&#x2C6; Bibliography: 1.

https://en.wikipedia.org/wiki/Information_theory

2.

https://towardsdatascience.com/the-intuition-behind-shannons-entropy-e74820fe980 0

3.

https://www.quantiki.org/wiki/shors-factoring-algorithm

4.

https://algassert.com/post/1718

5.

https://en.wikipedia.org/wiki/Shor%27s_algorithm

6.

https://en.wikipedia.org/wiki/Quantum_computing#:~:text=Quantum%20computing% 20is%20 the%20use,are%20known%20as%20quantum%20computers.

7.

https://uwaterloo.ca/institute-for-quantum-computing/quantum-computing-101

8.

https://www.nature.com/articles/npjqi201523

9.

https://qiskit.org/textbook/ch-algorithms/simon.html

10.

https://en.wikipedia.org/wiki/Deutsch%E2%80%93Jozsa_algorithm

11.

https://en.wikipedia.org/wiki/Quantum_algorithm#:~:text=In%20quantum%20computi ng%2C%20 a%20quantum,quantum%20circuit%20model%20of%20computation.

12.

https://www.quantum-inspire.com/kbase/deutsch-jozsa-algorithm/

13.

https://qiskit.org/documentation/tutorials/circuits/3_summary_of_quantum_operations .html

14.

https://en.wikipedia.org/wiki/Quantum_logic_gate

15.

https://dash.harvard.edu/bitstream/handle/1/11084801/Yung_IntroductionQuantum. pdf?sequence%3D1

16.

https://www.springer.com/gp/book/9783540785316

17.

https://www.quantiki.org/wiki/quantum-gates

18.

https://www.nature.com/articles/s41598-019-49657-1

**All mathematical work in this project has been done by either Joey or Hyunjo

81

Metal Work Projects George Beattie, Remove

82

83

84

85

86

87

88

89

90

91