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01 Academic Journal 2023 - 2024

02 03 FOREWORDS I’m delighted to commend this year’s Academic Journal to you all. The Journal, now in its fourth year, has become an annual piece of work, which showcases some of the best of our Sixth Formers’ research, and gives them the chance to have their work published to a wide audience. I hope that you both enjoy, and are informed by, the excellent articles in this publication and I wish you happy reading. My thanks to all students who have contributed to such a high standard – they are a credit to both themselves and the school. Phillip Wayne – Headmaster It is once again a privilege to oversee the process of this Journal and this foreword is a fitting platform to express our sincere thanks to those that have made it all happen. Firstly, to Charlie and Krish on our Senior Prefect team, who have jointly masterminded the project from its launch this year to its publication. This has meant hours of thought and practical input, for which we offer our sincere thanks. To Mrs Bignell and MrsWallace, who as ever have provided expert guidance and the means to put the Journal together in this form. To all the other Subject Ambassadors and members of staff who have helped to read and select the articles that we see in the finished Journal, please also accept our thanks and gratitude. And of course, our grateful thanks go to all the students whose articles have been selected for this Journal and also to all those students whose articles we couldn’t quite find room for this time around. You all deserve many congratulations on your efforts here. You truly are the very best of RGS and you never cease to amaze us with the breadth of your knowledge, insight and interests. Enjoy reading these articles as they showcase some of our very best talent. Mr Noyes – Director of Sixth Form

04 05 CONTENTS Forewords 3 Introduction 6 Articles 8 A dive into the paradoxical nature of the Chain rule - Richard Xu 8 An introduction to quantummechanics - ShyamYashoman 11 The economics of Universal Basic Income - Braden Greenwood 14 Can money buy happiness? - Matthew Mccall 16 The logistical nightmare of Formula One’s global circus - Seham Shah 19 How quantum computers break the internet - Ethan Tsang 22 How to tie your laces - Alex Barnes 25 The Riemann-Zeta Function - Agastya Kumar 28 Unravelling the fabric of the cosmos: exploring the wonders of StringTheory -Theham Amarasinghe 32 To what extent was medicine revolutionised during the Islamic Golden Age - Amro Elrayah 36 The theory and evaluation behind the Tulip Mania - Hugo Dighe 39 Green or greed? Finding the truth in the world of sustainable energy investments - Charles Meldrum 42 Constitutional credibility: how Covid legislation undermined our democracy - Charlie Kingsford 44 How do sharks make aviation greener? - Benjamin Watson 47 When will nuclear fusion be a viable energy source? - Archie McDougall-Hutchins 50 The short-form revolution: how short-form content is altering marketing and captivating consumer minds - Lewis Devlin 53 The spiritual metaphysics of music - Kayiza Mukasa 56

06 07 Introduction It is our pleasure to welcome you to the 2023-24 Academic Journal, which has continued strongly into its fourth year. Writing this now and looking back over the past year, there has certainly been no shortage of contemporary issues to discuss. From sustainable energy to constitutional credibility to a guide to tying your shoelaces, this Journal offers its readers a huge diversity of topics to enjoy. The opportunity to organise this year’s Academic Journal has been an incredibly fulfilling experience as, for us, it represents an outlet for the literary creativity of students across the school. We have found that when given the chance, be it through school societies or elsewhere, students are not only willing to expose themselves to new ideas and challenges, but incredibly capable once they take up this mantle. And that unique chance to display raw ability, created by this Academic Journal, is fundamentally what makes this publication so special. Finally, I must express sincere thanks to all the contributors to this year’s edition, without whom this would not have been possible. Firstly, we are grateful to Mr Noyes, Mrs Tan, Mrs Wallace and the rest of the Senior Prefect Team for overseeing the process, and giving invaluable advice at crucial moments. Secondly, huge thanks must go to the subject ambassadors who worked tirelessly to edit the articles before publication. A further thank you goes to those who wrote forewords and the massive team involved in editing and crafting this Journal. Ultimately, however, the greatest plaudits must go to the authors of the articles contained within, the bedrock of this project who spent hours carefully researching and articulating their interests to make the Journal a reality. Regardless of your interest, there is something in here for everyone, a credit to the diverse talent pool at RGS. We are proud to present this year’s Journal and hope you enjoy reading it as much as we did. Krish Chopra, Charlie Hodson and the Senior Prefect Team

08 09 A dive into the paradoxical nature of the Chain rule Richard Xu The Chain rule, as many of us know, is just the formula “dy/du * du/dx”, a simple way for us to differentiate a composite function. On the surface it appears quite logical, as the “du” part of both derivatives simply cross cancel and we are left with the fraction of “dy/dx”. For a while, that’s what I personally believed as well, that this was just a simple rule and concisely proves the feasibility of the Chain rule. However, if we take a moment to think about this conjecture more deeply, we realise that derivatives aren’t fractions. For example, “dy/dx” isn’t really a fraction but instead “d/dx *(y)” and when deconstructed, means “y” differentiated with respect to “x” or a more intuitive definition: the instantaneous rate of change of “y” with respect to “x” and therefore illustrating that “d/dx” is a notation. Why does the chain rule work then? Brief run through of how the Chain rule works: OR A more intuitive understanding of chain rule is if we imagine these functions in a real-life scenario. Let’s say in a race Adam is 3 times faster than Belial and Belial is 5 times faster than Charlie. Then it can be concluded that Adam is 15 times faster than Charlie. This example could then be distilled down into this: Delving into the origin of differential calculus and the chain rule: There are major debates about whether calculus was discovered by either Newton or Leibniz. However, since our focus is the chain rule, I will explore more of Leibniz’ notation of calculus but feel free to research more about this controversial debate more on your own. When Leibniz first came up with his notation of differentiation, he believed that “dy/ dx” was in fact a quotient or more commonly known as fractions. This was due to how he defined differentiation as an infinitesimal (infinitely small number) change in value of “y”, caused by an infinitesimal change in value of “x”, divided by an infinitesimal change in value of “x”. Visualized: Then, based on this idea, it would be natural for the idea of chain rule to work as both derivatives “dy/du” and “du/dx” are in fact fractions and can therefore cross cancel. Leibniz’ definition of differentiation of course makes intuitive sense but if we were to consider the actual definition of differentiation: the instantaneous rate of change of “y” with respect to “x” suggests that differentiation allows us to find the rate of change at any single point. This is where Leibniz’ definition falls apart as no matter how infinitely small the distance between two points, is there still is, a distance. However, there is a way to make Leibniz’ definition of differentiation work which I will go through later. The idea of limits and why that affects the chain rule: To get over the problems we face with the idea of infinitesimal changes, I will introduce the idea of limits which is a fundamental concept in calculus. I’ll approach this from a more intuitive point of view. Imagine, a frog at the centre of a pond which hops exactly half of the distance between itself and the edge of the pond. The frog then hops half of the distance between its new position and the edge of the pond. Now the frog keeps repeating this process forever, meaning that although the frog will never reach the edge of the pond but it will always be closer than any number we propose. A Dive into the paradoxical nature of the Chain rule The Chain rule as many of us knows it, is just the formula “dy/du * du/dx”, a simple way for us to differen<ate a composite func<on. On the surface it appears quite logical as the “du” part of both deriva<ves simply cross cancel and we are leD with the frac<on of “dy/dx”. For a while that’s what I personally believed as well, that this was just a simple rule and concisely proves the feasibility of the Chain rule. However, if we take a moment to think about this conjecture more deeply, we realise that deriva<ves aren’t frac<ons. For example, “dy/dx” isn’t really a frac<on but instead “d/dx *(y)” and when deconstructed means “y” differen<ated with respect to “x” or a more intui<ve defini<on: the instantaneous rate of change of “y” with respect to “x” and therefore illustra<ng that “d/dx” is a nota<on. Why does the chain rule work then? Brief run through of how the Chain rule works: = $ ( )) = ( ) = ( ) = × OR = ′( ) × ′( ( )) Example: = sin ( !) = 2 ( !) R A more intui<ve understanding of chain rule is if we imagine these func<ons in a real-life scenario. Let’s say in a race Adam is 3 <mes faster than Belial and Belial is 5 <mes faster than Charlie. Then it can be concluded that Adam is 15 <mes faster than Charlie. This example could then be dis<lled down into this: ℎ = × ℎ = 3 × 5 = 15 Aside: The nota.on “ ’ ” is pronounced prime and just means the deriva.ve of that func.on Delving into the origin of diff ren<al calc lus and the chain rule: There are major debates about whether calculus was discovered by either Newton or Leibniz. However, since our focus is the chain rule, I personally will explore more of Leibniz’ nota<on of calculus but feel free to research more about this controversial debate more on your own. When Leibniz first came up with his nota<on of differen<a<on, he believed that “dy/dx” was in fact a quo<ent or more commonly known as frac<ons. This was due to how he defined differen<a<on as an infinitesimal (infinitely small number) change in value of “y” caused by and infinitesimal change in value of “x” divided by an infinitesimal change in value of “x”. Visualized: Then based on this idea it would be natur l fo the idea of chain rule to work as both deriva<ves “dy/du” and “du/dx” are in fact frac<ons and can therefore cross cancel. Leibniz’ defini<on of differen<a<on f c urse makes in ui<ve sense but if w were to c nsider th actual d fini<on f differen<a<on: the instantaneous rate f change o “y” with respect to “x” suggests that differen<a<on allows us to find the rate of change at any single point. This is where Leibniz’ defini<on falls apart as no maZer how infinitely small the distance between two points is there s<ll is a distanc . However, there is a way to make Leibniz’ defini< n of differen<a<on work which I will go through later. The idea of limits and why that affects the chain rule: To get over the problems we face with the idea of infinitesimal changes I will introduce the idea of limits which is a fundamental concept in c lculus. I’ll appro ch this from a more intui<ve point of view. Imagine, a frog at the centre of a pond which hops exactly half of the distance between itself and the edge of the pond. The frog then hops half of the distance between its new posi<on and the edge of t pond. Now the frog keeps repea<ng t is process forev r meaning that although the frog will never reach the edge of the pond but it will always be cl ser than any number we propose. “dx” or an infinitesimal change in value of x “dy” or an infinitesimal change in value of y Frog Delving int the origin of differen<al calculus and the chain rule: There re m jor debates about whether calculus was discovered by either Newton or Leibniz. However, sinc our focus is the chain rule, I p rsonally will explore more of Leibniz’ nota<on of calculus but feel free to research more about this controversial debate more on your own. When Leibniz first came up with his nota<on of differen<a<on, he believed that “dy/dx” was in fact a quo<ent or more commonly known as frac<ons. Th s was due to how he defi ed differen<a<on as an infinitesimal (infinitely small n mber) change in value of “y” caused by and infinitesimal change in value of “x” divided by an infinitesimal change in value of “x”. Visualized: Then based on this idea it would be natural for the idea of chain rule to work as both deriva<ves “dy/du” and “du/dx” are in fact frac<ons and can therefore cross cancel. Leibniz’ defini<on of differen<a<on of course makes intui<ve sense but if we were to consider the actual defini<on of differen<a<on: the instantaneous rate of change of “y” with respect to “x” suggests that differen<a< n allows us to find the rate of change at any single point. This is where Leibniz’ defini<on falls apart as no maZer how infinitely small the distance between two points is there s<ll is a distance. However, there is a way to make Leibniz’ defini<on of differen<a<on work which I will go through later. The idea of limits and why that affects the chain rule: To get over the problems we face with the idea of infinitesimal changes I will introduce the idea of limits which is a fundamental concept in calculus. I’ll approach this from a more intui<ve point of view. Imagine, a frog at the centre of a pond which hops exactly half of the distance between itself and th edg f the pond. The frog then hops half of the distance b tween its n w posi<o and the edge of the pond. Now the fr g keeps repea<ng this process forever meaning that although the frog will never reach the edge of the pond but it will always be closer than any number we propose. “dx” or an infinit si l change in value of x “dy” or an infinitesimal change in value of y Frog A Dive into the paradoxical nature of the Chain rule The Chain rule as many of us knows it, is just the formula “dy/du * d /dx”, a simpl way for us to differen<ate a composi e func<on. On the surfac it appears quit logical as the “du” part of both deriva<v s simply cross cancel a d we are leD with th frac<on of “dy/dx”. For a while that’s what I personally believ d s we l, that is was just a simple rul and concis ly pr ves the feasibility of the Chain rule. How ver, if we t ke a moment to th nk about this conjectur more deepl , we realise that deriva<ves aren’t frac<ons. For example, “dy/ x” is ’t eally a frac<on but instead “d/dx *(y)” and wh n deconstructed m a s “y” differe <ated wit r sp ct to “x” or a more intui<ve defini<on: th instantaneous rate of change of “y” with respect to “x” and therefore illustra<ng that “d/dx” is a nota<on. Why does the chain rule work then? Brief run through of how the Chain rule works: = $ ( )) = ( ) = ( ) = × OR = ′( ) × ′( ( )) Example: = sin ( !) = 2 ( !) OR A more intui<ve understan ing of chain rule is if we imagine thes func<ons in a real-life scenario. Let’s say in a race Adam is 3 <mes faster than Belial and Belial is 5 <mes faster than Charlie. Then it can be concluded that A am is 15 <mes faster than Charlie. This example could then be dis<lled down into this: ℎ = × ℎ = 3 × 5 = 15 Aside: Th nota.on “ ’ ” is pronounced prime and just means the deriva.ve of that func.on

010 011 This is essentially the idea of limits and now I’ll apply it to differentiation and illustrate why Leibniz’ definition no longer works. As the value of “h” tends to 0 (we treat it as 0 because it will always be closer to 0 than any value we imagine and therefore even smaller than infinitesimal numbers) the derivative becomes “4x” Thus, we see that a derivative of a function is no longer a fraction but a limit. This leads us back to our initial conundrum about the chain rule as cross cancelling is no longer possible due the derivatives (dy/dx) being notations and not fractions. However, despite this, the chain rule stands as somewhere along the way the limits inherit properties of fractions which allows us to treat Leibniz notation as fractions, despite them not being fractions. Infinitesimal differentiation: As I stated before, there is a way to treat derivatives as quotients in mathematics which is via non-standard analysis. I’ll provide a brief layman summary of this topic as it is very hard to grasp. First, we need to understand the definition of an infinitesimal number which is basically a number closer to 0 than any standard real number and it has some properties of standard real numbers. Now the difference between limits and infinitesimals is that with limits we can treat these infinitely small changes as 0, and basically remove them, but with infinitesimals they are hyperreal numbers. These hyperreal numbers (the small increments dx,dy,h) must be treated separately from real numbers and can only interact with other hyperreal numbers. Through this method Leibniz’ definition will work as real numbers and hyperreal numbers form fractions of their own. Hopefully this explanation made some sort of sense. Either you can just accept that limits somehow just behave with some properties of fractions or you can research more into infinitesimal differentiation which will lead you into non-standard analysis, group theory and just a lot of pure math. Source: chapter_2b.pdf (wisc.edu), Infinitesimal - Wikipedia An introduction to quantum mechanics Shyam Yashoman The vast scope of the quantum world may be too intricate for us to ever understand completely, which is ironic given that quantum mechanics is the study of matter at the smallest scale. However, just because we are unable to make sense of the quantum world, it does not mean its value or validity should be compromised. Currently, even with our limited yet undoubtedly growing understanding of quantum mechanics, we have been able to develop extraordinary technologies from fluorescent lights to quantum computers. In this article, I will outline the core principles of quantum mechanics – beginning with the dual-slit experiment. The Dual-Slit Experiment and WaveParticle Duality Perhaps the most infamous principle relating to quantum mechanics: the dual-slit experiment. The basic dual-slit experiment consists of a light source, (typically a laser beam), being fired at a plate containing two parallel slits. The light passing through the two slits is then projected onto a screen behind the plate. This experiment was first performed by Thomas Young in 1801 and demonstrated how light exhibits both wave and particle characteristics, leading to the understanding of the wave-particle duality of light. Primarily, the dual-slit experiment illustrates how when only one of the slits is open, the electrons and photons that pass-through form a pattern on the screen in approximately the same shape as the slit (pretty obvious right). However, when both slits are open, they form an interference pattern on the screen - and not two separated rectangular strips as you might expect. Interference patterns are known to arise from the superposition of waves (where two or more waves that cross paths interact to either combine or cancel with one another). For example, if a crowd of people were to all shout simultaneously, their individual sound waves undergo superposition and result in a combined sound wave with a greater amplitude (therefore increasing the volume of the perceived sound). Coming back to the dual-slit experiment, one argument to explain this phenomenon is that before reaching the two slits, the electron splits in some way and hence passes through both slits simultaneously. The two parts of the electron then undergo superposition, before recombining and hitting the screen as a localised particle. Now, this theory could easily be evaluated by placing a detector just before the two slits. This detector would either observe which slit the electron passes through, or whether the electron passes through both slits simultaneously. However, this is where Th is e sen<a l i ea of limits and ow I’ll apply it to differen<a<o and illustrate why Leibn z’ defini<o n lo ger works. First Principle: lim "→$ ( + ℎ) − ( ) ℎ Example: f(x) = 2 ! + 1 lim "→$[2( + ℎ)! + 1] − [2 ! + 1] ℎ lim "→$2 ! + 4 ℎ + 2ℎ! + 1 − 2 ! − 1 ℎ lim "→$ℎ(4 ℎ + 2ℎ) As the value of “h” tends t ( e treat it as 0 because it will always be clos r to 0 than any v lue we imagine and therefore even smaller than infinitesimal umb rs) the derivaFve becomes “4x” Thus, we see that a deriva<ve of a func<on is no longer a frac<on but a limit. This leads us back to our ini<al conundrum about the chain rule as cross cancelling is no longer possible due the deriva<ves (dy/dx) being nota<ons and not frac<ons. However, despite this the chain rule stands as somewhere along the way the limits inherit proper<es of frac<ons which allows us to treat Leibniz nota<on as frac<ons despite them not being frac<ons. Infinitesimal differen<a<on: As I stated before, there is a way to treat deriva<ves as quo<ents in mathema<cs which is via non-standard analysis. I’ll provide a brief layman summary of this topic as it is very hard to grasp. First, we need to understand the defini<on of an infinitesimal number which is basically a number closer to 0 than any standard real number and it has some proper<es of standard real numbers. Now the difference between limits and infinitesimals is that with limits we can treat these infinitely small changes as 0 and basically remove them but with infinitesimals they are hyperreal numbers. These hyperreal numbers (the small increments dx,dy,h) must be treated separately from real numbers and can only interact with other hyperreal numbers. Through this method Leibniz’ defini<on will work as real numbers and hyperreal numbers form frac<ons of their own. Hopefully this expla a<on m de some sort of sense. Either you can just accep that limits somehow just behave with some proper<es of frac<ons or you can research more into infinitesimal differen<a<on which will lead you into non-standard analysis, group theory and just a lot of pure math. Reference: chapter_2b.pdf (wisc.edu), Infinitesimal - Wikipedia An Introduc+on To Quantum Mechanics The vast scope of the quantum world may be too intricate for us to ever understand completely, which is ironic given that quantum mechanics is the study of ma:er at the smallest scale. However, just because we are unable to make sense of the quantum world does not mean its value or validity should be compromised. Currently, even with our limited yet undoubtedly growing understanding of quantum mechanics, we have been able to develop extraordinary technologies from fluorescent lights to quantum computers. In this arCcle, I will outline the core principles of quantum mechanics – beginning with the dual-slit experiment. The Dual-Slit Experiment and Wave-Par7cle Duality Perhaps the most infamous principle relaCng to quantum mechanics: the dual-slit experiment. The basic dual-slit experiment consists of a light source (typically a laser beam) being fired at a plate containing two parallel slits. The light passing through the two slits is then projected onto a screen behind the plate. This experiment was first performed by Thomas Young in 1801 and demonstrated how light exhibits both wave and parCcle characterisCcs, leading to the understanding of the wave-parCcle duality of light. Primarily, the dual-slit experiment illustrates how when only one of the slits is open, the electrons and photons that pass-through form a pa:ern on the screen in approximately the same shape as the slit (pre:y obvious right?). However, when both slits are open, they form an interference pa:ern on the screen - and not two separated rectangular strips as you might expect. Interference pa:erns are known to arise from the superposiCon of waves (where two or more waves that cross paths interact to either combine or cancel wi h on another). For example, if a crowd of p ople were to all shout simul an ously, their individual s und w ves undergo s perp siCon and result in a combin d sou d wave with a grea er amplitude (therefore increasing the volume f the perceived sound). Coming back to the dual-slit experiment, one argument to explain this phenomenon is that before reaching the two slits, the electron splits in some way and hence passes through both slits simultaneously. The two parts of the electron then undergo superposiCon, before recombining and hiQng the screen as a localised parCcle. Now, this theory could easily be evaluated by placing a detector just before the two slits. This detector would either observe which slit the electron passes through, or whether the electron passes through both slits simultaneously. However, this is where the profound peculiarity of quantum mechanics begins. By acCvely observing the path of each electron, you will find that they will no longer form the interference pa:ern shown above but will instead form two individual strips.

012 013 the profound peculiarity of quantum mechanics begins. By actively observing the path of each electron, you will find that they will no longer form the interference pattern shown above but will instead form two individual strips. It is as if the electrons know they are being observed and do not want to be caught in the act of quantum mischief, resulting in the electrons behaving as ordinary particles. This seemingly magical phenomenon, which has been aptly named ‘nature’s conjuring trick’ by physicist Jim Al-Khalili, appears to have no rational explanation and comprises the ‘measurement problem’ of quantum mechanics. We will come back to this ‘measurement problem’ later, but for now we need to have a clear understanding of certain key concepts surrounding the quantum world. Indeterminism and Heisenberg’s Uncertainty Principle Have you ever wondered whether some things are just meant to be? You may believe in the idea of fate, or that all actions taken are pre-determined right down to the quantum level. This ideology is known as determinism and is commonly associated with Isaac Newton. Newton argued that every particle in the universe should obey the laws of motion, and that no matter the intricacy of the system, all processes should follow a predictable path. This appears to be a plausible argument, however, Newton later accepted the fact that the future can be pre-determined only if we have complete information on the present (i.e. information on the current location and momentum of every particle in the universe). This, in practice, is of course impossible and so led to the idea of indeterminism (the opposing view to determinism). But what has all this got to do with quantum mechanics? Well, to be able to explain this all, we need to have an idea of what a wavefunction is. Taking its definition from ‘Britannica,’ it is stated that a wavefunction is a variable quantity that mathematically describes the wave characteristics of a particle. For all we are concerned with, these wave characteristics can solely be its momentum and position. Now the groundwork has been laid out, it can be stated that a significant consequence of the indeterminism of a wavefunction is the concept of indeterminacy. Ok, please bear with me here. I know that there are quite a few fancy terms being thrown around that may seem incomprehensible, but I assure you that this idea is quite simple. Although indeterminacy and indeterminism appear to be remarkably similar, it is vital to not confuse them with one another. Indeterminism relates to the notion that the knowledge of certain characteristics of a particle at one point in time does not mean that its future characteristics can be known with certainty. On the other hand, indeterminacy states that we can never know with total precision all the characteristics of a system simultaneously. All clear so far, right? This is where Heisenberg’s uncertainty principle comes in. In essence, it states that we cannot simultaneously know the position and velocity of an electron at any point in time. To expand upon this, let us imagine we have an electron trapped in a room of microscopic scale. As we know with certainty that this electron lies somewhere in this small area, we can say that the position wavefunction of this electron is ‘localised in space.’ Moreover, using a mathematic method known as the ‘Fourier Transformation,’ we can use the position wavefunction of the electron to calculate its momentum wavefunction. Now, the catch is that a localised position wavefunction will always bring about a spread-out momentum wavefunction, and vice versa. This links back to the idea of indeterminacy, and how we can never know with total precision all the characteristics of a system simultaneously. To end, perhaps Heisenberg’s uncertainty principle could help to uncover the magic of the dual-slit experiment. By observing the precise location of the electron during the dual-slit experiment, we greatly narrow down its position wavefunction. Hence, we necessarily cause the momentum wavefunction of the electron to become more spread out – leading to uncertainties in its velocity. Although this explains why observing an electron may alter its initial path, it certainly does not explain why the electron behaves like a particle after it has been observed. Bibliography Jim Al-Khalili, Quantum: A Guide For The Perplexed Brittanica: Science & Tech - wave function https://www.britannica.com/science/wave-function Physics in a minute: The double slit experiment https://plus.maths.org/content/physics-minute-double-slit-experiment-0 he electron then undergo superposiCon, before recombining and hiQng the screen as a localised Ccle. w, this theory could easily be evaluated by placing a detector before the two slits. This detector would either observe ch slit the electron passes through, or whether the electron es through both slits simultaneously. However, this is where profound peculiarity of quantum mechanics begins. By vely observing the path of each electron, you will find that will no longer form the interference pa:ern shown above will instead form two individual strips. known with certainty. On the other hand, indeterminacy states that we can never know wi precision all the characterisCcs of a system simultaneously. All clear so far, right? This is where Heisenberg’s uncertainty principle comes in. In essence, it states that we simultaneously know the posiCon and velocity of an electron at any point in Cme. To expand up let us imagine we hav an electron trapp room of micros o ic scale. As we kno certainty that this lectron lies somewher small area, we can say that the p wavefuncCon of this electron is ‘local space.’ Moreover, using a mathemaCc known as the ‘Fourier TransformaCon,’ use the posiCon wavefuncCon of the elec calculate its momentum w vefuncCon. N

014 015 working at its full capacity and isn’t achieving its market goals; to achieve the best allocation of scarce resources. In theory, providing UBI would create a disincentive to work. But is this a bad thing? This could instead encourage people to pursue education, training, entrepreneurship, and unpaid care workers, positively benefiting society as a whole. The main concern is increasing unemployment; however, the evidence does not support this. A number of pilot studies have been conducted, including the Canadian and Alaskan Mincome experiment, that found minimal reductions in work effort associated with cash transfers. Thirdly, we must assess the macroeconomic effect of UBI on the economy. According to the U.S. bureau of economic analysis, in 2021, consumer spending made up 68% of GDP in the United States. Simulation models tell us of the positive multiplier effect UBI has on GDP, giving people more disposable income to spend, thereby increasing aggregate demand, which is the cause behind economic growth, one of the main macroeconomic objectives. This shows us that implementing a universal basic income may be able to stimulate economic growth in our society, benefitting everyone. By contrast, we must also look at the fiscal implications of financing a universal basic income policy, the greatest issue behind creating a UBI policy. How could UBI be funded you might ask? Taxation is the only way we can finance UBI and provides one of the biggest disadvantages of providing UBI. Whether that be through progressive income taxation, wealth taxes, carbon taxes, this is the only way of providing UBI. Governments already struggle with funding basic essentials, take, for example, the UK government and its problems funding the NHS. The lack of funding for the NHS has had huge impacts on the UK, failing to provide adequate healthcare for everyone, something the NHS promises. Perhaps the government needs to figure out its problems with healthcare first, before thinking about providing universal basic income to everybody. However, if UBI is used to replace inefficient social welfare programs and tax expenditures, it has been shown during UBI simulations that financing UBI through progressive taxation could possibly be money saving, but only if provided at the most efficient level. Designing a sustainable and equitable funding mechanism for UBI requires careful consideration of distributional impacts, taxes, political acceptability, and constant administration. But providing an incremental approach to UBI implementation, such as beginning with targeted cash transfers towards the disabled, specific poverty issues such as child poverty, or the elderly, and then working towards expanding the coverage may mitigate these risks. To conclude, UBI is a regular amount of money given to every adult citizen, with the goal of reducing poverty, and stimulating economic growth. Overall, I believe the benefits outweigh the negatives, as the possibility to significantly reduce poverty is immense, and the macroeconomic benefits are generally positive with the possibility to stimulate growth. However, there would still be many problems with implementing this, primarily the funding, but also the effect on labour market participation. The economics of Universal Basic Income Braden Greenwood Universal basic income. Many of us have heard the term, but what actually is it? What effect would it have on the economy, how do we finance it, and what the issues with it? Should it be implemented, and if so, why would it be implemented? Universal basic income, or UBI, is a government policy in which every adult citizen is given a regular amount of money as a basic income. This means that every week, month, or year (depending on the policy), you would essentially receive a cheque from the government to do with as you please. Sounds great! But why would the government do this? The government’s primary reasoning behind providing UBI is to reduce poverty, but additionally it can have other benefits such as stimulating economic growth. But, in order to determine whether we should or shouldn’t input a universal basic income, we must first determine the impacts of introducing one. Primarily, the potential to provide a fairer distribution of income. In the United States alone, according to the U.S. Census Bureau in 2021, the official poverty rate in 2020 was 11.4%, with 34 million people living below the poverty line. This is a huge number and is clear evidence that there is need for something to counteract this. A study by the Roosevelt Institute estimated that providing $1,000 per month for all U.S. adults could reduce the poverty rate by over 40%, and significantly increase the quality of life of the other 60%. This means that many of these people can have regular, healthy eating habits, pay off bills and begin to pay back debts, afford electricity and heating, and gain many essential benefits that the rest of us take for granted. Applying this to a grander scale, the world bank states that approximately 700 million people today live in absolute poverty, where they are living on less than $2.15 per day. We have been working hard to reduce this number, with taxes, education, minimum wages, and benefits, but often it just isn’t enough. But perhaps introducing a universal basic income is a way to reduce this inequality, providing a regular income floor for vulnerable populations, thereby reducing the risk of absolute/partial poverty. If we could apply the same poverty reduction rate of 40% to this, we could save up to 280 million people from living in absolute poverty. On the other hand, we must also look at the effect on labour market participation, wages, and productivity. There is a worry that providing a UBI would produce disincentives to work, negatively effecting the economy by increasing unemployment rates, leading to market failure, as the economy is not producing at its best rate. In the UK, labour participation rate in May 2023 for people above the age of 16 was at 62.8%, meaning much of the population is unemployed, tied up in education, or retired. This tends to be bad for the economy, as it means that the population is not

016 017 Can money buy happiness? Matthew Mccall A fundamental challenge faced by all societies is the economic problem. The problem of which that humans, by nature, have unlimited wants yet this is compromised by the fact that there are limited resources. Due to this scarcity of land, labour and capital, people are forced to make decisions on how to allocate them. Since the dawn of this problem, the key focus of allocation was an increase in GDP otherwise known as Gross Domestic Product. Now this may seem like the obvious solution, yet as economies grow, and incomes rise it is becoming evident that these increases do not have a corresponding increase in happiness which raises the question: Is this really what we should be measuring? In 1972, the 4th King of Bhutan, King Jigme Singye Wangchuck created GNH – Gross National Happiness and declared that “Gross National Happiness is more important than Gross Domestic Product.” Encouraging a paradigm shift towards a more holistic approach that considers the contentment of society as an equal to pure economic growth. This concept was internationalised in 2011 where the UN General Assembly passed resolution 65 – “Happiness: towards a holistic approach to development”, urging members of the UN to follow suit from Bhutan methodologies. Now many people would presume that by nature, countries with larger, more flourishing economies would have a higher level of happiness because the common view is that money does in fact buy happiness. However, this figure taken from the pre-COVID World Happiness Report released by the United Nations demonstrates that happiness and GDP have no correlation. Now this figure portrays the statistics of America, therefore leading onto the point that it could be argued that this highly political nation is an outlier to the trend due to internal issues. Yet it can be disproven through analysis of what are considered the happiest nations across the globe. According to the UNs latest report, the top 5 ranking nations on happiness are Finland, Denmark, Iceland, Israel, and Netherlands. Although in terms of GDP they rank 48th, 37th, 111th, 29th and 18th, which clearly follows the trend stated earlier of no correlation. Even the other largest economies like China and Japan only rank 61st and 47th in the happiness index. This would suggest that the state of an economy is not a factor of happiness, thus proving money cannot in fact buy happiness. On the other hand, in terms of GDP per capita, with the relative prices in each nation considered (Purchasing Power Parity) to make the comparison more equitable, the top 5 ranked respectively 21st, 9th, 12th, 34th and 10th, in happiness. This would imply a slightly closer correlation between the living conditions in certain nations compared to the level of satisfaction as all 5 countries ascended the rankings. Moreover, another important factor to consider is inequality, as with any statistic or ranking it is important to consider the nation-wide level and account for the top 1% bringing up the average. However, looking at this graph portraying the happiness gap in the top 137 countries, it becomes evident that the inequality in terms of happiness has been accounted for with the previous research, as our top 5 can all be found in the top 10 of this data for the happiness gap. Linking onto this, by comparing the Gini coefficients, it is evident to see that 3 of the 4 countries available from this specific research support the conclusion that low income-inequality is an obvious basis for the low happiness gaps. The comparison between these two graphs allows us to recognise that money has an undeniable impact on the happiness of a population. By analysing data that represents the differences in wealth and income within countries alongside the differences in happiness, it is clear how money is the underlying key factor in determining the happiness of citizens. Can Money Buy Happiness? By Ma&hew Mccall A fundamental challenge faced by all socie4es is the economic problem. The problem of which that humans, by nature, have an unlimited wants yet this is compromised by the fact that there are limited resources. Due to this scarcity of land, labour and capital, people are forced to make decisions on how to allocate them. Since the dawn of this problem, the key focus of alloca4on was an increase in GDP otherwise known as Gross Domes4c Product. Now this may seem like the obvious solu4on, yet as economies grow, and incomes rise it is beco ing evident that th se increases do not have a corresponding increase in happiness raises the ques4on: Is this really what we should be measuring? In 1972, the 4th King of Bhutan, King Jigme Singye Wangchuck created GNH – Gross Na4onal Happiness and declared that "Gross Na4onal Happiness is more important than Gross Domes4c Product." Encouraging a paradigm shiS towards a more holis4c approach that considers the contentment of society as an equal to pure economic growth. This concept was interna4onalised in 2011 where the UN General Assembly passed resolu4on 65 – “Happiness: towards a holis4c approach to development" urging members of the UN to follow suit from Bhutan methodologies. Now many people would presume that by nature countries with larger, more flourishing economies would have a higher level of happiness because the common view is t at money does in fact buy happiness. However, this figure taken from the pre-COVID World Happiness Report released by the United Na4ons demonstrates that happiness and GDP have no correla4on. Now this figure portrays the sta4s4cs of America, therefore leading onto the point that it could be argued that this highly poli4cal na4on is an outlier to he trend due to nternal issues. Yet can b disproven through naly is of what re considered the hap iest na4ons acros the globe. According to he UNs latest report, the top 5 ranking na4ons on happiness are Finland, Denmark, Iceland, Israel, and Netherlands. Although in terms of GDP they rank 48th, 37th, 111th, 29th and 18th which clearly follows the trend stated earlier of no correla4on. Even the other largest economies like China and Japan only rank 61st and 47th in the happiness index. This would suggest that the state of an economy is not a factor of happiness thus proving money cannot in fact buy happiness. On the other hand, in terms of GDP per capita, with the rela4ve prices in each na4 considered (Purchasing ower Parity) to m ke the comparison mo equi able, the top 5 ranked respec4vely 21st, 9th, 12th, 34th and 10th in happiness. This would imply a slightly closer correla4on between the living condi4ons in certain na4ons compared to the level of sa4sfac4on as all 5 countries ascended the rankings. Moreover, another important factor to consider is inequality, as with any sta4s4c or ranking it is important to consider the na4onwide level and account for the top 1% bringing up the average. However, looking at this graph portraying the happiness gap in the top 137 countries it becomes evident that the inequality in terms of happiness has been accounted for with the previous research as our top 5 can all be found in the top 10 of this data for the happiness gap. Linking onto this, by comparing the Gini coefficients it is evident to see that 3 of the 4 cou tries available from this specific research support the conclusion that low incomeinequality is an obvious basis for the low happiness gaps. The comparison between these two graphs allows us to recognise that money has an undeniable impact on the happiness of a popula4on. By analysing data that represents the differences in wealth and income within countries alongside the differences in happiness, it is clear how mon y is the und rlying key factor in determining the happiness of ci4zens. While Denmark, Finland and Netherlands follow the expected results of rela4vely lowincome inequality, which is demonstrated by a lower Gini Coefficient, Israel is an outlier to not only this sta4s4c but also could be argued of our earlier sta4s4c on GDP per capita in terms of purchasing power parity. So, with a rela4vely high level of income inequality, a low level of average income in terms of the living’s condi4ons, and currently ac4vely par4cipa4ng in war, how does Israel manage to stay among the top 5 happiest countries as of 2024? It is first important to declare how the happiness index is determined, which is through social support, income, health, freedom, generosity, and the absence of corrup4on. Now while one would assume that this na4on scores a mediocre score throughout all categories, the one main outlier is social support. With 73.8 percent of the popula4on wide level and account for the top 1% bringing up the average. However, looking at this graph portraying the happiness gap in the top 137 countries it becomes evident that the inequality in terms of happiness has been accounted for with the previous research as our top 5 can all be found in the top 10 of this data for the happiness gap. Linking onto this, by comparing the Gini coefficients it is evident to see that 3 of the 4 countries available from this specific research support the conclusion that low incomeinequality is an obvious basis for the low happiness gaps. The comparison between these two graphs allows us to recognise that money has an undeniable impact on the happiness of a popula4on. By analysing data that represents th differen es in wealth and i come within countries alongside the differences in happiness, it is clear how money is the underlying key factor in determining the happiness of ci4zens. While Denmark, Finland and Netherlands follow the expected results of rela4vely lowincome inequality, which is demonstrated by a lower Gini Coefficient, Israel is an outlier to not only this sta4s4c but also could be argued of our earlier sta4s4c on GDP per capita in terms of purchasi g power parity. So, with a rela4vely high level of income inequality, a low level of average income in terms of the living’s condi4ons, and currently ac4vely par4cipa4ng in war, how does Israel manage to stay among the top 5 happiest countries as of 2024? It is first important to declare how the happiness index is determined, which is through social support, income, health, freedom, generosity, and the absence of corrup4on. Now while one would assume that this na4on scores a mediocre score throughout all categories, the one main outlier is social support. With 73.8 percent of the popula4on

018 019 While Denmark, Finland and Netherlands follow the expected results of relatively low-income inequality, which is demonstrated by a lower Gini Coefficient, Israel is an outlier to not only this statistic but it can also be argued of our earlier statistic on GDP per capita in terms of purchasing power parity. So, with a relatively high level of income inequality, a low level of average income in terms of the living’s conditions, and currently actively participating in war, how does Israel manage to stay among the top 5 happiest countries as of 2024? It is first important to declare how the happiness index is determined, which is through social support, income, health, freedom, generosity, and the absence of corruption. Now while one would assume that this nation scores a mediocre score throughout all categories, the one main outlier is social support. With 73.8 percent of the population consisting of Jewish people, Israelis are known for their tight, close-knit communities with high levels of religious affiliation. Whether it be Jews or Muslims, it is clear how important a sense of community is through the spread of small villages known as ‘Yishuvim’, outside the main congregation within cities. The factors explaining the nation’s unusual level of happiness could be enough to debate that happiness is not simply about money, but also a factor of community and family. Many experts in the field presume that this level of happiness was simply due to the statistics being taken before the democratic protests. Although money will continue to be instrumental in modernity, it cannot be solely relied on in the pursuit of happiness. The logistical nightmare of Formula One’s global circus Seham Shah Formula 1 is not just the pinnacle of motorsport, but also a huge logistical demonstration that combines global coordination, speed, and accuracy to bring the show to spectators all over the world. Teams face very tight turnarounds to pack, move, and set up in a new country within days. These operations are critical, and often overlooked, with every minute of planning and execution contributing to the team’s success on race day. Beyond the adrenaline of racing, the silent, relentless effort of logistics ensures the orchestra of F1 continues to function harmoniously across continents. The sport’s nine-month schedule, which includes 24 races in 21 different countries on five continents, is a chaotic ballet, utilising land, air, and sea to traverse 10 distinct time zones, and this article will scrape the surface of showing how this military-like operation is achieved. Within a season, 1,500 tonnes of cargo are sent flying for 240 hours and covering 75,000 miles to move equipment, vehicles and team garages, hospitality spaces, and broadcast media equipment. Precision engineering and speed are vital, as if one component is eliminated from a race, the team may be at a significant disadvantage. To give some context of the scale of the items that are sent from race to race, each team has a motorhome in the paddock - a building which is erected at every race, then taken down and moved to the next location before being reconstructed. Red Bull’s motorhome is three-storeys, 13,000-square feet, with offices, a coffee bar and a private chef. The logistics of the season can be divided into two categories: the races held in Europe, where road travel is convenient and economical, and the more challenging races held abroad, known as fly-away races, when air and sea transport is required. Typically, races are held every other week, and there is a ten-day buffer for travel and transportation. However, if there are back-to-back races, this proves a much more daunting logistical challenge as there are only three days left to get everything set up at the next location. To assist with this, DHL has a high level of involvement, as the official logistical partner of F1. DHL operates with three dedicated teams - inbound, on site customer service, and pack-up - working together to guarantee a smooth operation, especially crucial when there are back-to-back events. The team will pack priority pallets for each Grand Prix, which include all the essentials to set the garages up, such as computers and garage walls. These arrive first at the site, allowing the logistics setup team to begin constructing work quarters before the rest of the personnel and equipment arrive. For The logis*cal nightmare of Formula One’s global circus. Formula 1 is not just the pinnacle of motorsport, but also a huge logis7cal demonstra7on that combines global coordina7on, speed, and accuracy to bring the show to spectators all over the world. Teams face very 7ght turnarounds to pack, move, and set up in a new country within days. These opera7ons are cri7cal, and o?en overlooked, with every minute of planning and execu7on contribu7ng to the team's success on race day. Beyond the adrenaline of racing, the silent, relentless effort of logis7cs ensures the orchestra of F1 con7nues to func7on harmoniously across con7nents. The sport's nine-month schedule, which includes 24 races in 21 different countries on five con7nents, is a chao7c ballet, u7lising land, air, and sea to traverse 10 dis7nct 7me zones, and this ar7cle will scrape the surface of showing how this military-like opera7on is achieved. Within a season, 1,500 tonnes of cargo re sent flying for 240 hours and covering 75,000 miles to move equipment, vehicles and team garages, hospitality spac s, and bro dcast media equipment. Precision engineering and speed are vital, as if one component is eliminated from a race, the team may be at a significant disadvantage. To give som context of the scale of the items that are sent from r ce to race, each t am has a motorhom in the paddock- a building which is rected at every race, then take own and mo ed to the next loca7on before being reconstructed. Red Bull’s otorhome is three-storeys, 13,000-square fe t, with offices, a c ffee bar nd a private chef. The logis7cs of the season can be divided into two categories: the races held in Europe, where road travel is convenient and economical, and the more challenging races held abroad, known as fly-away races, when air and sea transport is required. Typically, races are held every other week, and there is a ten-day buffer for travel and transporta7on. However, if there are back-to-back races, this proves a much more daun7ng logis7cal challenge as there are only three days le? to get everything set up at the next loca7on. To assist ith this, DHL has a high level of involvement, as the official logis7cal partner of F1. DHL operates with three dedicated teams- inbound, on site customer service, and pack-up- working together to guarantee a smooth opera7on, especially crucial when there are back-toback events. The team will pack priority pallets for each Grand Prix, which include all the essen7als to set the garages up, such as computers and garage walls. These arrive first at the site, allowing the logis7cs setup team to begin construc7ng work quarters before the rest of the personnel and equipment arrive. For the races with the 7ghtest turnarounds, before the chequered flag of a race is even waved, the DHL crew is already taking apart and packing away equipment. The cars are completely stripped down and each component is placed in its own foam slot, a?er being wrapped with bubble wrap.

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