Lions & Unicorns Symposium 2023 by nhehspublications

Contents Introduction

Rishi Sunak's ‘Unicorn Kingdom’?

Aidan S., Aditya S., Poppy E., Sophie C., with Mr Fernando Gilgamesh's Enkidu as a proto-unicorn, and other contenders for this title

Roxana Q., Tessa W., Daniel Z., Jin H., with Mrs Tollit English lions, Scottish unicorns, and their combination in the history of Britain

Stella W., Yara Alamad F., John C., Zorawar B., with Miss Finch Li-ion batteries: storing the world’s renewable energy, or is a unicorn like hydrogen needed?

Annabelle T., Aditi R., Joaquin S., William S., with Dr Cooper Emblem poetry: the 17th-century poet Hester Pulter

Ife A., Isabel H., Hattie C., Auberon D., Timi A., with Dr Klimt Orwell’s ‘The Lion and the Unicorn’. Britain and Britishness in the 1940s, and today

Eleanor C-S., Zerui L., Aidan A., Katarina G., with Dr Keshavarz The so-called ‘Lion and Christian’ problem

Meher G., Adeline G., Kevin Z. and Eugene S., with Ms Bowness The Paradox of Enrichment: why increasing productivity results in increased top predator biomass, but not lower down the chain

Michael L., Harry B., Gaia N., Daisy S., with Dr Hayes-Smith Student Feedback

Audience Feedback

A final thought

Front cover: “Royal coat of arms, Lemon Street, Truro” by Tim Green, licensed under CC BY 2.0. Rear cover: Image adapted from “Royal coat of the arms of the United Kingdom” by Reynolds Stone, licensed under CC BY 4.0.

Introduction “A unicorn is nothing more than a big horse that comes to a point” - Terry Pratchet Now in its fourth year, the annual collaboration between Notting Hill & Ealing High School and Harrow School has developed its own tropes. Every year we worry that the students won’t get on, that the questions will be duds, that the presenters will forget their lines. And yet, once again, the Year 10s (or Removes in Harrow jargon) prove our worries completely unfounded and produce a remarkable display of scholarship, engagement and flair. This year’s theme, Lions and Unicorns, was an unusual beast that mixed reality and myth, the natural and the contrived. The students’ response upon hearing it, the focus of their efforts for the coming term, was what you might expect: utterly nonplussed. But they, like we did when formulating their groups and questions, realised the richness that lay under the surface. As the students demonstrated, the imagery of both creatures is ubiquitous and their meaning is powerful; where else can you find something that links ancient epics, mediaeval heraldry and billion-dollar startups! After a tentative start in the Speech Room at Harrow, the groups dispersed to begin their research in the library. Despite the esoteric nature of their topics, the real challenge was not academic but logistical - organising meetings around Duke of Edinburgh, hockey games and drama rehearsals almost proved too much! Fortunately, all was well in the end and the eight articles presented here were submitted on time. We hope that you, as the students did, will find that anything and everything is interesting if you give it the chance to be. The symposium evening came round surprisingly quickly and the students found themselves with only an hour’s preparation before they needed to speak with authority on their topic - and they did just that. Each group did a remarkable job of relaying the depth of their research to the audience and excellently responded to questions. In the end, it was obvious that the students were the real Lions and Unicorns - sometimes wilful, occasionally capricious, but all times unapologetically bold and unique. Finally, a huge thank you must be given to the following: Notting Hill & Ealing High School Ms Bowness, Mr Fernando, Mrs Tollit, Miss Finch, Dr Klimt, Ms Copin Harrow School Dr Keshavarz, Dr Hayes-Smith, Miss Fox All the catering staff who provided excellent nourishment. All the students who were truly superb.

Dr Joe Cooper, Master in Charge of the Scholars, Harrow School

Rishi Sunak's ‘Unicorn Kingdom’? Aidan S., Aditya S., Poppy E., Sophie C., with Mr Fernando Recently in Business Connect, the Prime Minister addressed his campaign for the UK to emerge as a ‘Unicorn Kingdom’ (Great Campaign, 2022). There are several definitions for a unicorn, but in this case, it’s a startup company with a value of over $1 billion. This term was coined by Aileen Lee in 2013 (Iberdrola, 2023), who used it to represent the rarity of these companies. Sunak wants to expand the ecosystem of AI and tech unicorns in the UK with the help of expertise from companies in the Silicon Valley. We will talk about how this vision will boost the economy, the benefits of AI, the issue of too much growth, achievability and a productivity increase. Which will highlight why his vision is just. The development of unicorns and high-tech startups can lead to enormous growth of the UK’s economy and GDP. Investment from foreign sources can cultivate a country's economy, causing capital inflow and investment activity. Revolut, a UK unicorn providing banking services, raised a huge $1.72B from investors, making it valued at $33B (Bloomberg, 2021) and the largest privately held financial technology start-up in Europe. Unicorns can stimulate economic growth, leading to positive effects on the broader economy, like job creation and increased consumer spending. The unemployment rate in the UK declined in 2010, when unicorns became popular, from 8% to 3.5% in 2022 (Marcotrends, 2010), highlighting the impact of unicorns in providing jobs for people and boosting the economy.

The growth of AI unicorns has the potential to improve the quality of life and advance safety teams for its citizens. A student went missing in Hong Kong for eight days in November 2023, but was eventually found alive despite being exposed to a strong typhoon while on a muddy mountain. Drones and AI photo analysis tools helped narrow down the search area in the difficult terrain and situation, highlighting the potential of AI technology to assist traditional

search methods. If more unicorns were to emerge in the UK more revolutionary technology could surface and potentially save and elongate lives (SCMP, 2023). Furthermore, global dominance achieved through AI gives the UK potential to become a global superpower. Right now, the UK is a very powerful country, within the world’s top five; however since the dissolution of the USSR (1991), the US has been the world’s sole superpower. This is largely due to their presence in the AI industry and its profits. Startups boost the economy with new jobs, and new political alliances from sharing technology. New AI can strengthen the statistical side of the army and also enable the rapid exchange of cultural practices (Wiki, 2023). Some core traits of a superpower are economic, military, political and cultural power, so becoming a unicorn kingdom would boost all of these and create the opportunity for a bipolar world (Forbes, 2020). Furthermore, ever since the 2008 financial crisis, along with other developed countries Britain experienced a productivity slowdown. Although, according to the LSE, “the UK’s slowdown has been more dramatic with the UK ranking 31st out of 35 OECD countries in growth of output per hour from 2008 to 2017’” LSE Blogs). The UK relies on innovation to close the productivity gap and a Unicorn Kingdom will foster innovation hence increasing productivity. This will help grow the economy as more will be produced in less time while also costing less for businesses for labour and the UK productivity puzzle will be solved. However, critics argue that AI has the potential to take away jobs and leave humans feeling redundant. Elon Musk painted a grim picture of things, if let loose: “We are seeing the most destructive force in history here. You can have a job if you want one for personal satisfaction but AI will do everything” (Personnel Today, 2023). Many people find a purpose in life through their work so it poses a question of our meaning in this world, as AI will be able to do all jobs for us. AI advancement has been rapid, causing many to feel uneasy about what the future may hold if they continue to develop and be funded. On the contrary, the creation of a Unicorn Kingdom could cause too much growth, resulting in a crippling effect on the UK’s economy. The UK is already in the midst of an inflation crisis (Commons Library, 2023) and a Unicorn Kingdom could worsen this; this is shown through the idea of the Phillips Curve (Investopedia, 2023). The creation of startups would create lots of job opportunities and lower the rate of unemployment, this means lots of people have money to spend; people would then spend it. This in turn causes companies to raise the price of their products, causing overall inflation. Inflation can then increase poverty rates and devastate the economy, causing the UK to only lower their GDP as a unicorn kingdom. Finally, we are posed with the question of is this ‘Unicorn Kingdom even achievable? Sunak wants the UK to become like Silicon Valley, which is home to 136 unicorns (SG nalytics, 2022), yet in comparison, a Unicorn Kingdom seems impossible. Silicon Valley was driven by the race to the moon (Power & Beyond, 2023), causing the US government to start funding many companies that were there, triggering a significant boost in their advancement. Without incentives like this, the Unicorn Kingdom could take years and still not be as successful. Furthermore, Silicon Valley was created when technology was groundbreaking, and people were more interested in risking the industry. Technology isn’t new anymore and there are easier jobs with better pay so this would also lessen the drive.

To conclude, Rishi Sunak’s proposition for a Unicorn Kingdom is on the whole just and would benefit the UK. Although questions could be raised on how this affects the people’s mental health and its achievability, it’s safe to say that its potential benefits outweigh the barriers of the project. The UK could become a global superpower with AI as its tool, hence attracting more tourists, while boosting its economy, recreating the UK’s dominance that it experienced in the past. Furthermore, referring to the overall topic of Lions and Unicorns, the UK (the lion) with the help of a Unicorn Kingdom would achieve economic prosperity and global dominance in AI, the tool viewed as the key to the future. Bibliography and references Amadeo, K. (2022), ‘An annual review of the U.S. economy since 1929’, The Balance. Available at: thebalancemoney.com/us-gdp-by-year-3305543 (accessed: 26 October 2023). Anderson, S. (2023), ‘The phillips curve economic theory explained’, Investopedia. Available at: investopedia.com/terms/p/phillipscurve.asp Clawson, T. (2021), ‘A change of mindset: U.K. Unicorns and why they matter’, Forbes. Available at: forbes.com/sites/trevorclawson/2021/10/30/a-change-of-mindsetuk-unicorns-and-why-they-matter/ (accessed: 24 October 2023). Commons Library (2023), ‘Rising cost of living in the UK’. Available at: commonslibrary.parliament.uk/research-briefings/cbp-9428/ ‘Cyber security that learns you’ Darktrace. Available at: darktrace.com/ (accessed: 31 October 2023). Faragher, J. (2023), ‘‘No more jobs’ thanks to AI, says Elon Musk’. Available at: personneltoday.com/hr/elon-musk-ai/ Great Campaign (2022), available at: greatcampaign.com/unicorn-kingdom/ Hayes, A. (2023), ‘Venture capital: What is VC and how does it work?’, Investopedia. Available at: investopedia.com/terms/v/venturecapital.asp (accessed: 02 November 2023). Iberdrola (2023), Available at: iberdrola.com/innovation/unicorn-companies-technology-startups. Lo, C. and Heung, S. (2023), ‘Hong Kong teen missing for week ‘ate leaves and drank stream water’ to survive’, South China Morning Post. Available at: scmp.com/news/hong-kong/society/article/3237522/search-missing-hong-kong-teen-17-enters-seventh-day-parents-joinrescue-teams-scouring-country-park (accessed: 31 October 2023). LSE Blogs (2020), accessible at: blogs.lse.ac.uk/businessreview/2020/03/07/if-the-uk-is-high-tech-why-is-productivity-growth-slow-economists-weigh-in/ Metcalf, T. and Spezzati, S. (2021), ‘Revolut draws Softbank investment to hit $33 billion value’, Bloomberg.com. Available at: bloomberg.com/news/articles/2021-07-15/revolut-draws-softbank-investment-to-hit-33-billion-valuation?leadSource=uverify+wall (Accessed: 26 October 2023). Morrison, S. (2023), ‘The story of Silicon Valley – how it began, how it boomed, and where it’s headed’, Power & Beyond. Available at: power-and-beyond.com/the-story-of-silicon-valley-how-it-began-how-it-boomed-and-where-its-headed-a-9836fd8f0adf6d3535810e709d99fec3/ (accessed: 25 October 2023). Saito-Chung, D. (2012), ‘Georges Doriot helped Spark Venture Capital Industry’, Investor’s Business Daily, available at: investors.com/news/management/leaders-and-success/georges-doriot-founded-insead-and-pioneered-the-us-venture-capital-industry/ (accessed: 29 October 2023). SG Analytics (2022), ‘Is Silicon Valley Still Dominating Global Innovation?’ Available at: sganalytics.com/blog/is-silicon-valley-still-dominating-global-innovation-/ Tamplin, T. (2023), ‘Unicorn: Meaning, characteristics, financial aspects, criticisms’, Finance Strategists available at: financestrategists.com/financial-advisor/startup-funding-strategies/unicorn/ (accessed: 20 October 2023). The Venture Capital & Private Equity Country Attractiveness Index (2020), available at: blog.iese.edu/vcpeindex/unitedkingdom/ (accessed: 28 October 2023). MacroTrends (2010), U.K. Unemployment Rate 1991-2023, available at: macrotrends.net/countries/GBR/united-kingdom/unemployment-rate (accessed: 07 November 2023). Walch, K. (2023), ‘Why the race for AI dominance is more global than you think’, Forbes, available at: forbes.com/sites/cognitiveworld/2020/02/09/why-the-race-for-ai-dominance-is-more-global-than-you-think/?sh=1eaa72b1121f (accessed: 07 November 2023). World domination (2023) Wikipedia. Available at: en.wikipedia.org/wiki/World_domination (Accessed: 30 October 2023).

Gilgamesh's Enkidu as the first proto-unicorn, and rival contenders for this title Roxana Q., Tessa W., Daniel Z., Jin H., with Mrs Tollit The symbol of a unicorn is almost everywhere we look: on advertisements, on television, even on our old pyjamas. This mythical beast has been significant throughout history, captivating our imagination globally and serving as a symbol of strength, power and mystery. The unicorn figure has developed across time and by many different stories and cultures. This essay will explore the origins of this magical creature: what was the ‘proto-unicorn’ and could it be found in the figure of Enkidu from the ancient epic poem of Gilgamesh? Gilgamesh is the oldest extant literary work in the world. It was written in ancient Mesopotamia, possibly around 2100 BCE. It details the exploits of the giant, half-god, Gilgamesh, king of Uruk, accompanied by his companion and friend, Enkidu. Gilgamesh is first shown to be a cruel and unjust king, who abuses his subjects and his power. The people of Uruk ask the goddess Anu to create an equal in strength and character to Gilgamesh in the hope that he might be challenged. Enkidu is thus made from clay, almost in human form, but with his body covered in hair, hooves and two horns protruding from his head. At first, he is a wild man, separate from society and living with the herd as an animal himself; finally his great strength is noticed. A prostitute, Shamhat, from the temple of Uruk, is then sent to Enkidu to trap him so that he may be brought to the city and rival Gilgamesh. After they spend seven days and seven nights together, he is humanised. He follows Shamhat into society and eventually meets Gilgamesh. Enkidu fights Gilgamesh, who eventually defeats him, but subsequently gains respect for him and his strength and they befriend one another. While on their travels together, Gilgamesh and Enkidu commit acts of hubris, one of which tragically leads to Enkidu’s death. Gilgamesh is devastated and goes on a quest to find the secret to eternal life. While his search is eventually futile, he comes to terms with the inevitable ending of his life, and is able to return to Uruk content with the fact that his legacy and his people will continue to live on even after he is gone. Thanks to both the life and death of Enkidu, Gilgamesh is shaped into a better man and ruler, with more compassion and an acceptance of his own mortality.

Throughout the epic, Enkidu is presented as a wild beast, tamed by a woman, who becomes the figure that changes Gilgamesh for the better. While he lacks a ‘single horn’, he is described as covered in hair, reminiscent of an animal's coat, and possesses incredible strength. Enkidu’s connection to the natural world is emphasised as he lives among the wild animals, eating grass and drinking from watering holes; he stands apart from human society, living a solitary life. Unicorns are also often depicted as unique and solitary creatures, like Enkidu, renowned for their strength and power; guardians of nature possessing a deep connection to the natural world. Enkidu’s life in the wilderness, alongside animals and consuming a natural diet, reflects a similar affinity for nature. Unicorns are known for their elusiveness, often appearing only to the pure of heart; Enkidu’s remoteness from human society adds this element of mystery to his character. But, without the single horn which we now so closely associate now with the unicorn, to what extent is Enkidu really a ‘proto-unicorn’': are there any better contenders? One particularly fascinating aspect of the unicorn’s history is the obsession that Elizabeth I had with the wild creature. In the 1500s, she acquired a collection of magnificent spiral narwhal horns thought to be worth around £10,000 (approximately £2 million in today’s currency). She also had a cup made from a ‘unicorn’s’ horn to drink from, believing that if poison touched it, it would explode. This suggests an incredibly strong belief in the powers that they could hold; purity, according to the self-styled virgin queen, possessed great power. This is an early insight into characteristics that we still associate with unicorns in the present day: as protective and strong creatures, even defending the monarch from danger. Before Elizabeth, in medieval times, there was the well-known story of the Virgin and the Unicorn, also known as the ‘Seduced Unicorn’. In this story the unicorn is Figure 1: Fragment of a baked clay tablet inscribed described as a ferocious animal that is so fast with a Babylonian account of how the Gods that it is impossible to catch. The unicorn, determined to send a flood to destroy the earth in The however, becomes docile when a virgin, Epic of Gilgamesh. symbolic to the mother of Christ, the Virgin Mary, is presented in front of it. In many representations, a virgin is used to lure the unicorn. She heads to the forest until a unicorn sees her and jumps into her lap. Some representations of this moment involve the unicorn sucking on the virgin’s breast until it falls asleep, and it is caught by hunters and ultimately taken to the king. Like Enkidu, its feral nature is tamed. There are other, earlier figures from history that may look more like our current version of a unicorn. In 2697 BCE, i.e. earlier than Gilgamesh, an animal called a ‘Qilin’ is said to have appeared in the garden of the Chinese emperor. This creature is said to have a single horn on its forehead, a yellow belly and a multicoloured back, strangely similar to our unconscious idea that a unicorn is ‘rainbow’ coloured. It is described as gentle, never eating grass or living vegetation, differing greatly to the wild beast, Enkidu. The Qilin is also said to have predicted the future 6

greatness of Confucius’s unborn child. These traits of the animal are interestingly similar to the ideas surrounding unicorns that we unconsciously have: as somewhat magical and very gentle animals.

Figure 2: An experiment conducted with ‘unicorn’ horns in poison.

Figure 3: 4th Century Qilin tomb guardian. Placed in tombs, it provided a means to get to heaven.

Another contender for the title of ‘proto-unicorn’' is Rishyasringa, mentioned in Buddhist and Hindu scriptures, which date back to the first millennium BCE. According to Hindu epics, he was born a boy with the horns of a deer. As his story progresses, we learn that he was lured by royal courtesans, which led to the untimely death of King Dasharatha. Although this physical description is in stark contrast to our modern idea of a modern unicorn, it is actually quite similar to the description of Enkidu, once he has been tamed. The fact that Rishyasringa was lured links many stories over time: from Gilgamesh to the notes of Isidore of Seville in the 7th Century. Most of these stories have the idea of the ‘Seduced Unicorn’, transforming from a wild and mad beast, to a creature with human-like obedience and respect through being tamed by a woman. Another alternative candidate which, interestingly, spans Russian as well as Indian mythology of around 1500 BCE was the ‘Indrik’ or ‘Indra's Unicorn.’ This mythical being shares similarities with unicorns, such as being a solitary, powerful creature associated with nature. However, the Indrik is more explicitly linked to Hindu religious mythology, whereas Enkidu’s portrayal transcends religious contexts. In conclusion, it is our opinion that Enkidu presents a compelling case as a proto-unicorn. His unique characteristics: his strength, connection to nature, and elusiveness align with the traits commonly associated with unicorns in various mythologies. While there are other contenders, such as the Indrik, Qilin and Rishyasringa, Enkidu’s status as one of the earliest literary characters in human history gives him a strong claim to the title of the proto-unicorn; yet that is not to say that he was the finished, modern-day product. As with all myths the image of the unicorn evolves and will continue to do so; the unicorn of our imagination today will not be entirely the same as the unicorn of our imagination tomorrow. “I believe in everything until it's disproved. So I believe in fairies, the myths, dragons. It all exists, even if it's in your mind. Who's to say that dreams and nightmares aren't as real as the here and now?” 7

Bibliography and references Primary sources/Translations · Ancienttexts.org (2019) Epic of Gilgamesh: Tablet I. [online] Available at: http://ancienttexts.org/library/mesopotamian/gilgamesh/tab1.htm. Verma, C.D. (2010), The Myth of Rishyashringa: An Indian Source of the ‘Waste Land’ (‘The Waste Land’ Rrappraised in relation to the Mahabharata). Indian Literature, 54(2 (256)), pp.151–161. Available at: jstor.org/stable/23342057?seq=3 Secondary sources/Research papers Spark Notes, Enkidu Character Analysis in The Epic of Gilgamesh. Available at: sparknotes.com/lit/gilgamesh/character/enkidu/. Encyclopedia Britannica (2016), ‘Enkidu’, Encyclopædia Britannica. Available at: britannica.com/topic/Enkidu. Encyclopedia Britannica (2018), ‘Unicorn’. Available at: britannica.com/topic/unicorn. Malevus (2023), ‘Indrik: A Unicorn-esque Mythical Creature in Slavic Legends - Malevus’, Available at: malevus.com/indrik/ ‌ Wikipedia (2019), ‘Vedas’, Wikipedia. Available at: en.wikipedia.org/wiki/Vedas. Mythology.net (2017), ‘Qilin - Mythical Creature from China’, Available at: mythology.net/mythical-creatures/qilin/.

Image references · Figure 1: The British Museum, K.3375, The British Museum. Available at: britishmuseum.org/collection/object/W_K-3375. Accessed 06.11.2023. Figure 2: Ewbank, A. (2018), ‘The Strange History of Royals Testing Food for Poison With Unicorn Horn’, Atlas Obscura. Available at: atlasobscura.com/articles/unicorn-horn-poison. Accessed 06.11.2023. Figure 3: Pyrgies, Joana (2021), ‘Qilin – a Mythical Animal in Chinese or ‘Kirin’ in Japanese’, ARCHAEOTRAVEL.eu. Available at: archaeotravel.eu/qilin-a-mythical-animal-in-chinese-or-kirin-in-japanese/

English lions, Scottish unicorns, and their combination in the history of Britain Stella W., Yara Alamad F., John C., Zorawar B., with Miss Finch The admiration and fascination for the qualities of both the lion and the unicorn is a phenomenon that dates back many centuries, and explains their use as formidable symbols in art and culture but most famously in the royal heraldry of England and Scotland. By examining the history and symbolism of both the lion and unicorn, this article seeks to inform our understanding of their contemporary significance in Britain today. The lion has been used as an English symbol since the early 12th century and has since become a metaphor for the country’s values, an essential part of the English coat of arms, and England’s national animal. Its origins lie with Geoffrey, Count of Anjou, a Plantagenet whose coat of arms featured six lions in the rampant position against a blue backdrop.1 Geoffrey Plantagenet’s son, Henry II of England, went on to experiment with the use of lions in his coat of arms as well. This ultimately inspired his sons, John and Richard I of Lionheart, to use lions in their coat of arms. Richard I was the first monarch to implement lions as the coat of arms for England at around 1200 CE. This truly cemented the lion as a part of English culture and history. However, if we step out of English tradition, we can see that lions have been prevalent in culture throughout Europe for a long period of time, and before that, in Asia. Ubiquitous within early Mesopotamian art and religion, the significance of the lion in the Middle East and India continued to grow, recurring as an important motif in the Qur’an, the hadith and classical Arabic poetry. This had a direct impact on the Bible and classical literature and from there, general European cultural consciousness, demonstrating the pervasive reach of the lion’s influence. Within Britain, the lion has been a recurrent symbol in British art, and has consistently been tailored to convey a sense of nationalism and patriotism in the British monarchy and Empire. ‘The British Lion’s Vengeance on the Bengal Tiger’ illustrates this, as the defeat of the Bengal Tiger by the British Lion symbolises the suppression of the Indian Rebellion in 1

John Gillingham, Richard I [called Richard Coeur de Lion, Richard the Lionheart] (2009), Oxford Dictionary of National Biography.

1857 against the British Empire, and reinforces the strength and ferocity of the British nation against attacks on their authority.2 Beyond the representation of Britain, in the 12th century, the symbol of the lion was combined with a sun motif on the Iranian national flag, to represent the strength and authority of the Iranian Monarchy. However this changed in 1979, when the Islamic Republic rose to power after the Iranian revolution, permanently removing this symbolism from the flag to represent the dissolution of the monarchy. Nevertheless, this reinforces the connection between the monarchy’s authority and strength and the lion.3 By contrast, the unicorn has emerged from mythology to be used as a symbol throughout Scottish history, but now sits beside the lion as a significant symbol of the United Kingdom. The first known reference of the unicorn was in the 4th century BCE, documented by the Greek physician Ctesias in his work Indica, about India. Derived from tales narrated by travellers, the unicorn was portrayed as a horse-like animal with a distinct colourful horn in the centre of its forehead, protecting those who drank from this horn from disease. Ctesias combined the unicorn with three animals indigenous to India: the rhinoceros, the horned chiru and the kiang (a wild horse), and this image continued to emerge throughout Europe, present in illustrations in the Bible that were then translated onto royal tapestries and carved ivories.4 Scotland’s choice of the unicorn as the focal point of their coat of arms in the 15th century was founded in Celtic mythology, which portrayed unicorns as a symbol of purity and innocence as well as strength and power. It was believed that they were so wild and free that the only way to capture one was if a virgin maiden, of similar purity and innocence, ventured into the woods and approached one. The unicorn was particularly revered as its horn was believed to cure poison, heal wounds and purify water. The notion of the unicorn as a pure and innocent creature can be seen further through a number of artworks created in this period. One of the most famous examples is ‘The Lady and the Unicorn’, which is a series of six tapestries found in the Musée de Cluny in Paris. The tapestries show a lady, her lady-in-waiting, a unicorn and a lion. Each of the tapestries portrays one of the 2

John Tenniel, ‘The British Lion’s Vengeance on the Bengal Tiger’, (London, 1857). Shailendra Bhandare, 'Trans-regional Connections: The ‘Lion and Sun’ motif and Coinage between Anatolia and India', Oxford University Research Archive, (2019), 1-25. 4 Chris Lavers, The History of the Unicorn, (London: Granta Publications, 2014); The Holy Bible Containing the Old and New Testaments, Authorised King James Version (Cambridge: Cambridge University Press, 1984), Psalm 22.21. 3

five senses (sight, smell, sound, touch, taste). For example in the sight tapestry, the lady shows the unicorn itself in a mirror, whilst in the touch tapestry, the lady is holding both the staff and the unicorn’s horn. However, there is a sixth tapestry which doesn’t fit within the same pattern as the others as the lady is shown to return her jewels to her casket as she stands underneath a tent, with the words ‘A Mon Seul Desir’ inscribed on the outside.5 This gesture might be read as a sign of her virtue, an expression of her reason over the physical sensations she experiences in other tapestries, or of her own free will. The unicorn sits beside her, a symbol of chastity and reason. Although mythical, the unicorn is believed to embody the same characteristics around the world, yet has become largely celebrated, alongside the lion, in British heraldry, and art even now in the 21st century. Overall, chosen for their uncontrollable strength and valour, the unicorn and the lion have been celebrated together on Britain’s royal coat of arms since the Union of England and Scotland in 1603. King James I endorsed the use of this beastly imagery, as it represents the harmonious, yet powerful union that emerged from two formerly warring nations, encapsulating both the complex history of the United Kingdom, but also of both the lion and the unicorn as generational symbols of courage and might.6 Bibliography and References Texts The Holy Bible Containing the Old and New Testaments, Authorised King James Version (Cambridge: Cambridge University Press, 1984), Revelations The Holy Bible Containing the Old and New Testaments, Authorised King James Version (Cambridge: Cambridge University Press, 1984), Psalm Bhandare, Shailendra, 'Trans-regional Connections: The ‘Lion and Sun’ motif and Coinage between Anatolia and India', Oxford University Research Archive, (2019), 1-25. Lavers, Chris, The History of the Unicorn, (London: Granta Publications, 2014) Stephenson, Katie, ‘The Unicorn, St Andrew and the Thistle’, The Scottish Historical Review, 215.83 (2004), 3-22

Visual sources Meister der Apokalypsenrose der Sainte Chapelle, The Lady and the Unicorn: À Mon Seul Désir (Paris: Musée national du Moyen Âge, 1500) Tenniel John, ‘The British Lion’s Vengeance on the Bengal Tiger’, (London, 1857)

Websites Gillingham, John, Richard I [called Richard Coeur de Lion, Richard the Lionheart] (2009), Oxford Dictionary of National Biography. doi.org/10.1093/ref:odnb/23498 [Accessed 1 October 2023] Welsh, James, ‘The Unicorn - Scotland’s National Animal’, National Trust for Scotland. nts.org.uk/stories/the-unicorn-scotlands-national-animal [Accessed 21 October 2023]

Meister der Apokalypsenrose der Sainte Chapelle, The Lady and the Unicorn: À Mon Seul Désir (Paris: Musée national du Moyen Âge, 1500). 6 James Welsh, The Unicorn - Scotland’s National Animal, National Trust for Scotland.

Li-ion batteries: storing the world’s renewable energy, or is a unicorn like hydrogen needed? Annabelle T., Aditi R., Joaquin S., William S., with Dr Cooper Energy storage systems are ways to store renewable energy so it is available to be used when it is needed. Being able to store renewable energy for later use solves the problem created by some forms of renewable energy, such as wind and solar, which are unreliable due to their dependency on external conditions. Currently, the most popular form of energy storage system is lithium ion batteries. However, there are less widespread alternatives in development, such as hydrogen fuel cells and other ion batteries that may be better overall than lithium ion batteries. Lithium ion batteries work using the process of electrolysis. There is an anode, which is negatively charged, on one side of the battery, and a cathode, which is positively charged, on the other. Graphite structures on the anode side keep lithium atoms trapped there, and when the appliance is turned on, the outer shell electrons of the lithium break away, creating lithium ions and free electrons. These free electrons move through the appliance to the cathode side of the battery, towards cobalt oxide structures where cobalt needs to gain more electrons. This continuous movement of electrons causes a buildup of negative charge on one side of the battery, and to solve this the lithium ions move through an electrolyte which is between the electrodes to neutralise the negative charge. This continues until the anode side of the battery is empty, which means the battery has died. When the appliance is charging, the power from the charger forces the electrons to move back to the anode side of the battery, which eventually causes the lithium ions to move through the electrolyte and become caught between the layers of the graphite structure again, until the cathode side of the battery has been emptied. This means the battery is fully charged.

Figure 1: Diagrams showing the processes in lithium ion batteries during discharging (left) and charging (right).

One alternative to lithium-ion batteries are hydrogen fuel cells: these work by passing hydrogen atoms through anodes (typically made of platinum). These anodes split the hydrogen atoms into charged protons and electrons. The protons pass through an electrolyte ‘membrane’ - into a cathode. The cathode holds a negative charge and is constantly being filled with oxygen; the protons reside here for the time being. The electrons then pass through a separate wire to rejoin with the protons due to their electrostatic force of attraction. Energy is collected from the movement of the electrons through the wire. When the hydrogen reforms along with the oxygen and electrons, water is created which is removed via the exhaust. These energy stores have the potential to significantly reduce our dependence on oil and gas, as the only byproducts of the fuel cells are water and heat. However, both hydrogen and oxygen are very flammable gases and must be stored under high pressure, creating a large explosion hazard. For mass energy storage, this has not been an issue, as the gases have been kept in very controlled environments, but as the uses of hydrogen cells increase: so do the different hazards they face (high heat, sparks, punctured gas tanks). These factors are what limit the commercial use of hydrogen fuel cells.

Figure 2: A representation of the operation of hydrogen fuel cells. Another form of renewable energy batteries are alternative metal ion batteries, such as sodium, aluminium, and potassium. They all possess different properties that set them apart from lithium ion batteries (LIBs) in terms of cost and sustainability. Sodium ion batteries (SIBs) work in much the same way as lithium ion batteries, with reversible movement of metal ions between an anode and a cathode. SIBs are usually made using hard carbons as the anode material, as opposed to the graphite (which is considered a soft carbon) typically used for the anode in LIBs. This is due to the instability of sodium graphite intercalation compounds, which comes as a result of a mismatch in size between sodium ions and the space between graphite layers. SIBs also use aluminium current collectors, which are cheaper than the copper current collectors used by their lithium counterparts. Aluminium ion batteries work in a very similar way to SIBs and LIBs, apart from the fact that they can exchange up to three electrons per ion, while LIBS and SIBS can only exchange one (as a result of the charge of their respective ions: aluminium is Al3+, while lithium and sodium have a

charge of 1+). In theory, this means that aluminium batteries have a much larger power density than both, but the three electrons complicate the process of intercalation into the cathode. As we can infer from our discussion so far, we can identify multiple positive and negative attributes of all the battery types based on sustainability, efficiency and cost. However, when weighing the batteries against each other, we can infer that hydrogen batteries seem like a more eco-friendly method of powering society due to their high energy density, recharge efficiency and only having heat and water as waste products. However, due to hydrogen cells being a recent breakthrough in science, the technology is currently expensive (hence not easily accessible), along with containing flammable, high-pressure gas, making it quite dangerous. By contrast, lithium ion batteries are significantly cheaper, making them more accessible to public use as well as being less dangerous than hydrogen fuel cells, while still offering just as clean of an energy source. However, lithium ion batteries are less efficient because they are less energy dense and take a longer time to recharge. Lithium batteries are also hard to recycle due to the different components in the battery which have the potential to explode if not treated correctly. This makes recycling the batteries more costly than mining for new lithium which would be unsustainable. An alternate option could also include sodium ion batteries, which are relatively similar to how lithium ion batteries function, due to both being ions of alkali metals. Although they are cheaper to produce and sodium is a more abundant resource, they degrade faster and have a rechargeability of 1500 cycles compared to the 2000 to 3000 cycles of lithium ion batteries. When weighing the attributes of all the batteries, we believe that hydrogen-powered batteries are the most environmentally friendly option and the future of energy storage due to the high abundance, energy density and lack of harmful waste. However, due to hydrogen-powered batteries currently being hazardous and expensive, for now, society should continue using lithium ion batteries, as they have a higher recharge cycle compared to sodium, while scientists continue to advance hydrogen battery technology to make it suitable for commercial usage. References Scott Minos (2023), ‘How Lithium-ion Batteries Work’, US Department of Energy. energy.gov/energysaver/articles/how-lithium-ion-batteries-work David Chandler (2022), ‘A new concept for low-cost batteries’, MIT News. news.mit.edu/2022/aluminum-sulfur-battery-0824 Imperial College London, Alternative Battery Chemistries. imperial.ac.uk/electrochem-sci-eng/research/alternative-battery-chemistries/ E-Lyte Innovations, ‘Working principle sodium-ion battery’. e-lyte.de/knowledge/working-principle-sodium-ion-battery/ Innovation News Network (2023), ‘Storage capacity of aluminium-ion batteries outperforms other materials’. innovationnewsnetwork.com/storage-capacity-aluminium-ion-batteries-outperforms-other-materials/33863/

Emblem poetry: the 17th-century poet Hester Pulter Ife A., Isabel H., Hattie C., Auberon D., Timi A., with Dr Klimt Emblem poetry was a literary product of sixteenth-century Europe; a popular genre devised of unique and particular characteristics. Originating in the Renaissance period, emblem poems comprise three main components: a title, an illustration and an explanatory text in the form of verse to convey moral or religious truths. The title serves as a concise message, the image illustrating the theme and the text elaborating on the overall philosophical concept. Primarily a didactic genre, emblem poems focus on the educational and instructional aspects of literature, manipulating poetic devices and elegant language to do so. This fusion allowed authors to explore complex ideas in more depth, and to also offer commentary on the societal way of thinking in the sixteenth century. In her emblem poetry, Hester Pulter, a seventeenth-century poet and writer, suggested that matriarchal animals are far better than humans. Her works include details about the seventeenth century that provide a new insight into the history of English culture. Pulter’s manuscript was rediscovered in 1996 in the Brotherton Library, University of Leeds. By the time Pulter came to write her emblem book, the emblem genre had an established relationship with the British Monarchy, thus introducing the theme of the lion and the unicorn; the lion and unicorn are symbolic creatures and are common representations of heraldry, seen in the British coat of arms. Traditionally associated with majesty, the lion is a symbol of courage, dignity, strength and stateliness. In emblem poetry they can be seen to symbolise the virtues of valour. Alternatively, the unicorn links with ideas of purity, innocence and elegance. They can be seen also as a symbol of femininity as historically unicorns were depicted as gentle and graceful creatures, which aligned with the ideas of femininity during those periods. The representation of the unicorn extends to that of magic and fantasy, connoting a sense of wonder. Throughout ‘The Lion and The Fox’, Pulter draws a contrast between royalist opinions and the anti-monarchist views that were popular during her time. Pulter lived during the seventeenth century, a time when there was a drastic change in the constitution of England. This historical context is reflected in Pulter’s language and imagery. Pulter portrays the lion (who represents the King) as a domineering, unlikable character. Moreover, this is demonstrated in the phrase, “that of late so domineered”, which indicates a condescending tone.[1] On the contrary, in ‘The Stately Unicorn’, a more royalist attitude is evident. The unicorn is portrayed as a stately, regal creature through phrases like, “until they see the stately unicorn” and “thus he the forest governeth at his will.”[2] Pulter may have used the adjectives ‘stately’ and ‘governeth’ to indicate the unicorn’s importance, along with celestial imagery in the phrase, “Did leave the true and glorious God above.”[3] The sudden change in Pulter’s views may be because the unicorn is a symbol of Scotland and the lion of England. At the time, the Scottish may have been more sympathetic towards the monarchy than the English, as the official union of the two nations had not happened yet.

In the beginning of ‘The Lion and the Fox’, the lion is represented as a masculine and imperious character, yet as the passage progresses, he is shown to have fear and emotion. Likewise, there is a subtle idea that the lion is "feared" but also hated as he becomes "sick at last".[4] The lion goes from an animal "cloyed with luxury" to being sick and less powerful than previously perceived. This idea is confirmed when "the lion trembles"; the use of a caesura and lack of rhyme accentuates the lion’s cowardice and the deterioration of his masculinity.[5] Additionally, Pulter carefully uses punctuation, especially exclamation marks accentuating this idea. For example, the Fox shouts, "be not afraid!" and the narrator also writes "none like a tyrant is so 'fraid of death!”.[6] These are all attempts to develop the character of the Lion to show that it can show a level of humanity and emotion. However, as the passage ends, it is revealed that the lion has not changed his ways and even claims that the “dying groan / Of innocence” pleases him, a reference to the British monarchy.[7] Similarly to the lion, the unicorn is a masculine figure throughout the poem, a stark contrast to the now feminine connotations which unicorns hold. We see the true message of the poem and the nature of the unicorn - a “gallant beast” succumbing to and “enslavéd by a virgin’s eye”, showing how ultimately even great figures of power are corrupted by their desires. [8] This idea is reinforced by the biblical reference to those selected by God himself in Samson and Solomon being “allured by various love” regardless of being “enabled from above”, and looks at how they are ultimately human regardless of their blessings.[9] This is abnormal because within Christianity, the unicorn is often a figure of Christ. Furthermore, this is implied in verses such as Numbers 23:22 and 24:8 - in some versions it refers to an ‘ox’, whereas in the original text it speaks of the ‘unicorn’ [10]. This is additionally suggested in the painting titled ‘Virgin and Unicorn’ by Italian artist Domenichino, conveniently painted in 1605, just before Pulter wrote the poem. The painting portrays a unicorn, lying at the feet of a virgin. The virgin represents Mary, whilst the unicorn represents Jesus. This painting is an allegory for the chastity of the unicorn, demonstrating it to be a pure and noble creature, a virtue with connotations of temperance, in this specific case a being which refrains from immoral sexual activity (hence the repeated reference to a ‘virgin’ being all that can tame the creature). To conclude, ‘The Stately Unicorn’ and ‘The Lion and The Fox’ explore the relationship between the British people and their monarchy. Pulter’s poetry is of high significance in the way that it encapsulates these opinions. References

Bibliography

[1] Hester Pulter, ‘The Lion and the Fox’ (Emblem 38), l.1. [2]Pulter, ‘The Stately Unicorn’ (Emblem 14), l. 6. [3] ‘The Stately Unicorn’, l. 17. [4 ‘The Lion and the Fox’, ll. 2, 3. [5] ‘The Lion and the Fox’, l. 7. [6] ‘The Lion and the Fox’, ll. 16, 10. [7] ‘The Lion and the Fox’, ll. 28–29 [8] ‘The Stately Unicorn’, ll. 8, 12. [9] ‘The Stately Unicorn’, ll. 17, 13. [10 New International Bible, Numbers 23:22, 24.8.

All poems accessed at The Pulter Project ‘About Hester Pulter and her Manuscript’, accessed at pulterproject.northwestern.edu/about-hester-pulter-and-the-manu script.html The Bible (NIV), accessed at thenivbible.com/. ‘Emblem Literature’, University College London Department of Dutch Studies, accessed at ucl.ac.uk/dutchstudies/an/SP_LINKS_UCL_POPUP/SPs_englis h/emblems/pages/emblemlit.html. Hill, Elizabeth K. ‘What is an Emblem?’ The Journal of Aesthetics and Art Criticism, Vol. 29, No. 2 (Winter 1970): 261–65. ‘Interregnum’, Royal Family Website, accessed at royal.uk/

Orwell’s ‘The Lion and the Unicorn’. Britain and Britishness in the 1940s, and today Eleanor C-S., Zerui L., Aidan A., Katarina G., with Dr Keshavarz In this essay, we will explore the political arguments Orwell presents in ‘The Lion and The Unicorn’. In this work, Orwell attempts to fuse socialism and patriotism as firstly, a way to win the war and secondly, a long-term system for the government of England. We will discuss what it says about Britain in the 1940s, the symbolism used in the piece and how it is relevant to Britain today. In his essay ‘The Lion and the Unicorn’, George Orwell argues that it was necessary for Britain to transition from a capitalist society to a socialist (but still patriotic) society in order to produce a more successful war effort and ultimately win the war. [1] Orwell writes, “At this moment, after a year of war, newspapers and pamphlets abusing the Government, praising the enemy and clamouring for surrender are being sold on the streets, almost without interference”, telling us of his displeasure with Britain in the 1940s. [2] Being a British citizen, Orwell was eager to bring out the change he wanted for his country. He argued that the government should share profits to everyone, so citizens have the motivation to work harder, and poverty could be prevented. He believed that class division between capitalists and workers contributed to the difficulty of Britain winning the war. Orwell wanted to present how the difficulty of defeating the Nazis was a result of failed capitalism and the traditional political system of monarchy. [3] His idea of the necessity of a socialist Britain in order to defeat the Nazis was ultimately a failure, as Britain was able to win the war despite retaining a capitalist system. Orwell presented his patriotic socialism as not merely a solution to win the war, but a plan for a socialist Britain that was not totalitarian and suitable for Britain. [4] He presents the fusion of patriotism and socialism as a middle path between American consumerism and Soviet communism. [5] When Orwell talks about patriotism, he is not merely talking about some abstract love for your country, but more importantly, he is referring to the culture and heritage of England (with a focus on the working class that constitutes the majority of the population). He believed that this culture was characterised by a defence of democracy and liberty, and a preservation of moral values. Orwell claimed that there is a need to maintain democratic values in socialism to prevent totalitarianism from arising. [6] Orwell especially stressed the need for a “respect for constitutionalism and legality (and) and the belief in ‘the law’ as something above the state and above the individual.” [7] Orwell argued that these values have the power to limit corruption and hinder the development of totalitarianism. He also believed in the related liberty of the individual, in the sense of a kind of toleration towards the activities of others. [8] Furthermore, he argued that the moral attitude found in the common people of England would resist greed and corruption in the government. [9] Orwell described a patriotic socialist England as a democratic socialist nation with a deep respect for the law. Moreover, he describes it as a nation with “loose ends everywhere,” [10] maintaining many of its traditions; he would even at times refer to England as “a Christian country.” [11] 17

So why does George Orwell mention the lion and the unicorn? Orwell is known for his symbolism across many of his works, notably Animal Farm, where he uses a farm setting to convey his ideas about the political issues in Russia during the Russian revolution. [12] The work that we researched however was ‘The Lion and the Unicorn’, and its allusions to 1940s England and the echo in today's England. He purposefully uses the symbolism of these two animals, the lion for Britain’s patriotism in WW2, and the unicorn for his socialist beliefs, to display his profound ideas and beliefs about Britain during World War II. The lion is a well-known symbol of courage, nobility, royalty, and strength. England has a historical connection with lion symbols, dating back to the English monarchy in the 12th century. Orwell uses the ties of national pride and tradition of the lion to embody the essence of patriotism. In a strong contrast, the unicorn is a symbol that traces back to the Scottish royal coat of arms during William I’s reign, and it represents purity, innocence, and power. Orwell harnesses the unicorn's rich history and uses it to symbolise socialism. George Orwell's essay during World War 2 provides valuable insights into George Orwell's thoughts and beliefs on politics during the 1940s and how they are still relevant to modern-day politics in Britain. One of the main ideas in the essay is George Orwell's belief that it is vital to have a strong sense of national identity and unison. [13] Orwell argued that the English needed to have a more patriotic spirit in order to have a better chance against external threats, for example the Nazis in the 1940s. Similarly, in Britain today, there are debates about national identity and power, most notably surrounding Brexit. The debate about whether to remain in the European Union or leave it highlighted the political divide in the country; this mirrors Orwell's concerns about conflict and national strength and identity. In his essay, he also criticises the class system in Britain and his distaste for a society divided this way. He called for a more economically equal society; these ideas are also present in modern politics. The Labour Party's promises to improve social and economic equality, as well as the recent debates on wealth distribution and access to education and healthcare, can be traced back to Orwell's socialist ideals. Moreover, Orwell's concerns about the rise of authoritarianism and its impeding on civil freedoms are also prevalent concerns in modern British politics, for example issues related to surveillance, and the government trying to control individuals’ lives. As a conclusion, Orwell argues that the fusion between patriotism and socialism is necessary for Britain to win the war and that it is a suitable political system for Britain to transition to. His belief that such a society was necessary to win the war is now proven to be false. However, his idea of the importance of national identity in times of conflict , his idea of the protection of civil liberties, and his socialist stance remain relevant today. References

Bibliography

[1] Orwell, Collected Essays, 2: 56-108 [2] Orwell, Collected Essays, 2: 67 [3] Orwell, Collected Essays, 2: 56-108 [4] Orwell, Collected Essays, 2: 56-108; Claeys, Orwell, 186-211 [5] Orwell, Collected Essays, 3: 47; Claeys, Orwell, 187-188 [6] Claeys, Orwell, 186-211; Orwell, Collected Essays, 2: 56-108 [7] Orwell, Fascism and Democracy, 206-215 [8] Orwell, Collected Essays, 2: 59 [9] Orwell, Collected Essays, 2: 60 [10] Orwell, Collected Essays, 2: 102 [11] Orwell, Collected Essays, 2: 102 [12] Orwell, Animal Farm [13] Orwell, Collected Essays, 2: 56-108

Claeys, Gregory, ‘The Lion and the Unicorn, Patriotism, and Orwell’s Politics’, The Review of Politics 47, no. 2 (1985): 186–211. doi.org/10.1017/s003467050003669x. Orwell, George, Sonia Orwell, and Ian Angus, The Collected Essays, journalism and letters of George Orwell,: Volume 2: My country right or left 1940-1943. Harmondsworth, United Kingdom: Penguin Books, 1984. Orwell, George, Sonia Orwell, and Ian Angus, The Collected Essays, journalism and letters of George Orwell: Volume 3: As I please 19431945. London, United Kingdom: Secker and Warburg, 1968. Orwell, George, Animal Farm: A fairy story, Harmondsworth, United Kingdom: Penguin Books, 1945. Orwell, George, ‘Fascism and Democracy’, The Betrayal of the Left, edited by Victor Gollancz, 206–15. Gollancz, 1941.

The so-called ‘Lion and Christian’ problem Meher G., Adeline G., Kevin Z. and Eugene S., with Ms Bowness Note that unicorns are symbolically associated with Jesus Christ. The Lion and the Christian paradox is a renowned mathematics problem that has perplexed mathematicians for years. Rado in 1925 posed the question as follows: “A lion and a Christian are in a closed arena and have equal maximum speeds. Can the man evade the lion indefinitely?”

We are more comfortable with referring to "the Christian" as "the man" for the rest of the problem. The key to the question is to establish if either: ● there is a strategy which the lion can use to guarantee catching the man in finite time, or ● there is a strategy which the man can use to evade the lion forever.

For 25 years it was believed that the man would be caught, until this was disproved and the correct solution was found by Besicovitch. This article will explain both solutions. This seemingly simple question requires complex mathematical skills to answer it, for example integration, as well as various circle theorems, and more. Setting up the situation and the variables We will model the scenario as follows. Let the circular arena be a circle of radius 1 with its centre at the origin, 𝑂. We will model the lion and man as taking small steps in each time interval. For the lion, he will be at point 𝐿0at the start, 𝐿1 after 1 time increment, 𝐿2 after the second time increment, and so on, with 𝐿𝑘 representing the lion's position after 𝑘 increments. This means he moves along a path 𝐿0𝐿1𝐿2… 𝐿𝑘𝐿𝑘+1… Similarly the man moves along 𝑀0𝑀1𝑀2… 𝑀𝑘𝑀𝑘+1…

The Original ‘Solution’: The lion catches the man Logically, if the man is to run away from the lion, he will end up running towards the edge of the arena. We therefore assume that his strategy is to run to a point on edge of the arena, 𝑀0, and start from there. The lion can always get to the middle of the arena, so we can assume that he starts there. From there, the man will have no choice but to run from 𝑀0 along the boundary of the arena, on the orange path, to the point 𝑀1. Since the lion and the man run at equal speeds, the lion can, at most, run the same distance as the man in its attempt to catch him. If the lion runs continuously in the direction of the man, continuously shifting his direction, he will end up running along the circumference of the small inner circle with centre 𝑆 as in the diagram. To determine if the man is able to escape, we must compare: ● the length of the orange arc along which he runs ● the length of the yellow arc along which the lion runs Looking at the angles in the diagram, we can see that: 1. by the Alternate Segment Theorem, ∠𝑀1𝑂𝑀0 is equal to ∠𝑂𝑃𝐿1, represented by φ. 2. ∠𝑂𝐿1𝑃 = 90°, as it is at the circumference of a semicircle; 3. Therefore, since angles in a triangle add to180°, the other angle will sum with φ to make 90°. We will call this angle Ѱ. The diameter of the outer circle is a tangent to the inner one, forming a right angle, ∠𝑀0𝑂𝑃, with the small circle’s radius. The smaller circle’s diameter is equal to the radius of the bigger circle. By calculating the circumference of the two circles, the larger circumference amounts to 2 times that of the smaller one. However, the man only runs ¼ of the large circumference, and the lion runs ½ of the small circumference. Therefore, the man and lion’s arcs are of equal length, and the man will be caught at point 𝑃. 20

Correct solution: The man can escape! While the first proof may seem legitimate at first, the issue with this proof is the assumption that the man would start at (or be able to be forced to) the edge of the arena. However, it is possible to prove that: ● as long as the man does not reach the edge, he will not be caught, and ● the man does not get forced to the edge. For this, it is also helpful to define: 𝑆𝑘 = segment between Mk and O 𝑑𝑘 = distance between Mk and Mk+1 (the length of the step which the man takes)

A method to achieve this is as follows. At any point 𝑘, the man runs a length 𝑑𝑘perpendicular to the line 𝑆𝑘 (between the 𝑀𝑘 and the centre), on the side of 𝑆𝑘 that 𝐿𝑘 was not on (see figure). As 𝐿𝑘𝑀𝑘+1 will always be longer than 𝑑𝑘, because 𝐿𝑘 is on the other side of 𝑆𝑘, the lion cannot reach the man in this step. Therefore, if we can repeat this process forever, the man will escape at every step and therefore never be caught.

There are two requirements for this to work: First requirement: run forever As the man travels smaller and smaller distances, it would need to be proven that he keeps moving. Mathematically, this is equivalent to saying that the total distance he runs, ∞

𝑑0 + 𝑑1 +..., or ∑ 𝑑𝑘 diverges, meaning that it goes on forever. 𝑘=0

Second requirement: stay inside the circle Additionally, we need to show that 𝑆𝑘 stays "within the boundary", and that the man's 2

distance from the centre is never more than 1. Because 𝑆𝑘+1 = 𝑆𝑘 + 𝑑𝑘 (by Pythagoras theorem), we must show that: 2

∞

𝑆0 + 𝑑0 + 𝑑1 +... 𝑑𝑘 <1, which can be written as 𝑆0 + ∑ 𝑑𝑘 < 1 . 𝑘=0

But what 𝑑𝑘 will work…? The sum of the distances approaches infinity, while squaring them somehow makes them less than 1, which may seem quite counterintuitive at first... However, as long as we find a sequence which satisfies both conditions, we would have proven that the man can survive. −3/4

Let us examine the sequence 𝑑𝑘 = 𝑐𝑘

𝑆

where 𝑐 = 20 , for all 𝑘 = 0, 1, 2, ...

This can be chosen because we know that 𝑑𝑘 can be any number, since the man can run whatever distance he wants. Does this satisfy the first requirement? When k is a natural number, then 𝑘

−3/4

−1

will be bigger than 𝑘 , because -¾ > -1.

Therefore ∞

𝑐 ∑ 𝑘

−3/4

∞

−1

> 𝑐 ∑ 𝑘 = c(1 + ½ + ⅓ + … ) → ∞

𝑘=1

This shows that the man must be able to run an infinite distance. Does this satisfy the second requirement? ∞

We wish to show that 𝑠0 + ∑ 𝑑𝑘 < 1 for the 𝑑𝑘 we have chosen. 𝑘=0

−3/4

Note that 𝑑𝑘 = 𝑐𝑘 ∞

∞

2 −3/2

so ∑ 𝑑𝑘 = ∑ 𝑐 𝑘 𝑘=1

𝑘=1

−3/2

= 𝑐 ∑ 𝑘

−3/2

⇒ 𝑑𝑘

=𝑐 𝑘 ∞

𝑘=1

The shaded green area in the figure to the +∞

left represents ∫ 𝑘

−3/2

. This shows that:

1 ∞

+∞

∑ 𝑑𝑘 < 1 + ∫ 𝑘

𝑘=1

−3/2

𝑑𝑘 ,

since the "boxes" lie beneath the curve7.

Note that we can determine this summation to be roughly equal to 2.612 using the Riemann Zeta function. 22

This expression can be evaluated using calculus. Using the power rule of integration: +∞

1+ ∫ 𝑘

−3/2

[

𝑑𝑘 = 1 + − 2𝑘

−1/2 ∞

−2

= 1+

∞

−

−2

= 1 + 0 − (− 2) = 3

𝑆

Therefore, remembering that 𝑐 = 20 2

∞

𝑐 ∑ 𝑑𝑘

∞

= 𝑐 ∑ 𝑘

𝑘=1

𝑘=1 3

−3/2

+∞

< 𝑐 (1 + ∫ 𝑘 1

−3/2

𝑑𝑘) < 3𝑐 = 4 𝑆0

Since 𝑆0 is less than 1, 4 𝑆0 must also be less than 1, so the man will stay in the arena8. Thus, we have shown it is possible for the man to evade the lion. Forever.

This is only true for values of S0 less than 0.78, as the inequality included an additional S02 term. 23

The Paradox of Enrichment: why increasing productivity results in increased top predator biomass, but not lower down the chain Michael L., Harry B., Gaia N., Daisy S., with Dr Hayes-Smith The paradox of enrichment refers to the theory where enrichment in a predator-prey relationship leads to a collapse in the ecosystem. [1] High productivity in an ecosystem means that there will be more top predators in the ecosystem. However, this does not happen lower down the food chain because an increase in predators can lead to a decrease in prey. This natural cycle can be explained by the paradox of enrichment. Lions are apex predators; they do not have a natural predator of their own so they gain the most energy at the top of the food chain, therefore they would benefit from the paradox of enrichment. However, the unicorn can either be considered a top predator or a prey, depending on whether they are being observed from folklore or in history; the Elasmotherium, an extinct species of rhinoceros also known as the ‘Siberian unicorn’, would have been a primary consumer due to its herbivorous diet, not only a cause of its extinction but an indication that the unicorn (a prey) would not have benefited from the paradox of enrichment. The paradox of enrichment is a concept in ecology that describes a counterintuitive phenomenon in ecosystems. It arises when increasing the availability of resources, such as food, for a particular species actually leads to a decline in its population. This paradox occurs due to complex interactions within ecosystems. [2] When a resource becomes more abundant, it initially benefits the primary producers such as plants, allowing its population to grow. However, as the population increases, resources are put under more strain. For example, if we say to increase the amount of minerals, sunlight and water for the plants, due to the increase in resources, the plants will have an increased rate of growth and reproduction. However, due to the growth in population, more and more resources are required, and vital minerals and water start to run out. As a result, the once enriched population

faces a shortage of its primary resource, leading to a population crash or decline, despite the initial increase in resources. The paradox of enrichment highlights the unexpected dynamics of ecosystems, where population growth and resource availability are related, and it highlights the importance of understanding these dynamics for effective conservation and management of species and their habitats. [2] Lions are animals that have been admired for their power, strength and courage throughout history. Groups of female lions hunt together, usually preying on ungulates. [3] They are apex predators in their environment, which means they play a crucial role in keeping a healthy balance of numbers of other animals, especially herbivores such as zebras or wildebeest. [4] Top predators have profound effects throughout their ecosystems. They control the distribution, abundance and diversity of their prey and they regulate lower species in the food chain, known as trophic cascades [5] Trophic cascades are ecological interactions that are triggered by the addition or removal of top predators. If the paradox of enrichment were to take place in the habitat of lions, it would destabilise the species as their population would grow unsustainably large. [2] If the primary producer, which is grass in this case, were to increase, there would be a change in the lion’s ecosystem. Lions eat large animals such as zebras and a zebra’s diet is made up of 90% grass. [6] If there were greater biomass available to be assimilated in the next trophic level, there would be more energy available for the zebras. This would mean that the population of zebras would grow bigger and this leads to lions having more prey. The energy flow in a food chain leads to the apex predator gaining more biomass and this would mean that the lion’s population gets larger as they have more food. As the population of lions increases there is more of a danger of extinction for zebras as there are more lions that need to eat food to sustain themselves. As well as this, the lion’s population can be destabilised as the population grows unsustainably large. This is why the paradox of enrichment can lead to an unstable ecosystem where non-apex predators can suffer. Whilst unicorns are mythical creatures, appearing in both mythology and folklore, they are well known for being described as a “white horse with a single long horn on its head.” [8,9] The unicorn is considered a symbol of power and purity, not only for its white fur, but also for its horn: it has been valued and sought out for it was believed to hold magical powers as well as treating diseases like epilepsy. [7] In history, there has also existed a ‘real unicorn’: the elasmotherium (also known as the ‘Siberian unicorn’, for it roamed around Eastern Europe and Asia, and is thought to be the inspiration for the unicorn myth). It would have looked different compared to the mythical unicorn, which would be part of the Equidae family, however both of these families belong to the Perissodactyla order. The Siberian unicorns, as well as extinct rhinoceros, are primary consumers as they are both herbivores, therefore the latter can be prey to lions. Furthermore, this relationship between lion and rhinoceros reflects the predator-prey relationship in the paradox of enrichment: if there are many consumers (elasmotherium/rhinoceros), apex predators (lions) are able to grow in numbers, however as many are being consumed, there will be less prey. This is especially a concern, as not only was the elasmotherium victim to extinction due to dramatic change in climate, rhinoceros are also at high risk of extinction from being poached by humans (another apex predator) for their horn to be used for medicinal purposes. [10,11] However, comparing a European mythological unicorn’s strength to a lion’s would contrast a rhinoceros-lion relationship, as unicorns were considered to be one of the top predators, or even the strongest in folklore.

Figure 1: European mythical unicorn

Figure 2: Siberian unicorn

In conclusion, the paradox of enrichment is intertwined with the relationship between increased productivity, top predator biomass, and prey populations. This can be seen with the behaviour of lions and unicorns, both of which are known as the apex predators that rule the food chain. Overall, the paradox of enrichment shows the delicate balance needed to maintain a healthy ecosystem, with the fact that predators such as lions and unicorns (or the elasmotherium) benefit from the abundance of resources. References [1] Roy, Shovonlal and Chattopadhyay, J (2007) ‘The stability of ecosystems: a brief overview of the paradox of enrichment’ Journal of Biosciences, 32 (2). pp. 421-428. ISSN 0250-5991 doi: doi.org/10.1007/s12038-007-0040-1 Available at centaur.reading.ac.uk/36888/ [2] Wikipedia contributors. (2023, September 2). ‘Paradox of enrichment’. In Wikipedia, The Free Encyclopedia. [3] Wikipedia contributors. (2023, December 27). ‘Lion’. In Wikipedia, The Free Encyclopedia. [4] WWF UK, ‘The magnificent lion’. wwf.org.uk/learn/wildlife/african-lions. Accessed 24/09/2023. [5] Ripple, W. J. and R. L. Beschta. 2008. ‘Trophic cascades involving cougar, mule deer, and black oaks in Yosemite National Park’ Biological Conservation 141: 1249-1246. [6]Suzanne Rose and Christianlly Cena, ‘What Do Zebras Eat?’, Study.com. study.com/academy/lesson/what-do-zebras-eat-lesson-for-kids.html. Accessed 11/10/2023. [7]Benjamin Radford (2017), ‘The Lore and Lure of Unicorns’, Live Science. livescience.com/59674-unicorn-facts.html. Accessed 4/10/2023. [8]American Museum of Natural History, ‘Unicorns, West and East’. amnh.org/exhibitions/mythic-creatures/land/unicorns-west-and-east. Last accessed 4/10/2023 [9] Encyclopedia Britannica, ‘unicorn’. Accessed 4/10/2023. [10] Wikipedia contributors. (2023, December 29). ‘Rhinoceros’. In Wikipedia, The Free Encyclopedia. Accessed 5/10/2023. [11]Kosintsev, P., Mitchell, K.J., Devièse, T. et al. ‘Evolution and extinction of the giant rhinoceros Elasmotherium sibiricum sheds light on late Quaternary megafaunal extinctions’, Nat Ecol Evol 3, 31–38 (2019). doi.org/10.1038/s41559-018-0722-0

Image references Figure 1: Gessner’s Icones animalium, p. 62 (blog.library.si.edu/blog/2017/09/18/monoceros-conrad-gessners-discussion-unicorn-tells-us-natural-history-renaissance-europe/) Figure 2: Artist’s impression of a Siberian unicorn, W S Van der Merwe. bbc.co.uk/news/science-environment-46358789

Student Feedback Best aspects… “The actual presentation at the end…knowing all our hard work had paid off was amazing.” “Making new friends and collaborating with them.” “Working with people from other schools… to share ideas and cooperate.” “I learned a lot of new maths techniques that are now helping me.” “Watching the different presentations and seeing what others have discovered within the theme.” “Learning about something that is interesting and that we would not learn about in our lessons.”

What we learned… “How to effectively deliver an enticing presentation without cue cards or notes.” “Creating a good powerpoint and presenting effectively.” “Being able to work with others: it is extremely valuable and this experience honed this!” “How to Harvard reference.” “How to significantly cut down text to focus in on the most important parts of an article.” “How to do public speaking with confidence.” “Unicorns are cool.”

Audience Feedback “Very charismatic and confident presenters, who did incredibly well without notes!” “Presenters knew their subject very well, and shared their knowledge very compellingly.” “It's really not easy talking without notes in front of a big audience. Well done for taking the time to regroup and continue when you forgot what to say!” “Best by far was question-answering which allowed you all to expand on the script and showcase your impressive knowledge of the topic.” “Obviously very well-researched on some quite unusual themes!” “Excellent projection and engagement with public.” “All presenters owned the material in detail! Brilliant answers too.” “Informative and technical... not an easy topic but very nicely explained..” “Brilliant explanation that showed a true understanding of the subject” “Amazing enthusiasm to deliver such a difficult topic” “They had a very wide and in-depth understanding of their topic” “Good articulation and strong knowledge” “Lots of information, engaging speakers, really on top of content”

A final thought As this symposium takes place, Artificial Intelligence is disrupting it all, from knowledge to education to employment. Unicorns walk amongst us. It will take the courage of lions to face up to the implications. It therefore seems fitting to include a brief (if mischievous) little experiment. The image below was created in Midjourney, an app which uses AI to generate images, using the following prompt: "An academic symposium between Harrow School and Notting Hill & Ealing High School on the topic of "Lions and unicorns", for students age 15, supported by their teachers, working on questions from different subject areas, each of them loosely related to the theme of "Lions and Unicorns" in some way". What do you notice? Is it the case that more than ever, there is a role to play for education? Ms Madeleine Copin, Deputy Head Academic, Notting Hill & Ealing High School