Serpentes Issue 6

Serpentes

The Academic Journal

Issue 6 Lent Term 2021

Welcome back to Serpentes, the Radley College Academic Journal. Before you start reading, let us remind you of our aims. We aspire to change the way academic study is perceived in Radley. Due to the relatively constricted content of GCSEs and A-levels, academics becomes more about ticking a box than thinking beyond it. We would like to change this misconception because there is so much more to academics than what is written in your textbooks. Do you have an interest which you would like to write about?

Have you read an especially good book recently? Did you solve or create a challenging maths puzzle? Send it to us and it could be published in the next issue. Whether you are a Sixth former or Shell, this journal belongs to you.

Editors Contributors

Don-In-Charge

James Harrabin, Mark Lertiendumrong, Mahir Mujtaba Jan Tewes, Tommy Williams Blake Williams, Hyunjo Kim, Giorgi Gvaradze, Henry Roskill, Hamish Rimmer, Lucas Bury, Johnny Elliot, Russell Kwok, Bernardo Mercado Nithin Simanand, Toby Loftus, RDS Adam Mohammad Hilmi SR

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Contents Surrealism, The Early Years - Blake Williams . . . . . . . . . . . . . . . . . . . . . .

On the Philosophy of Quantum Theory - Hyunjo Kim . . . . . . . . . . . . . . . . .

‘Euthyphro’: Holiness and the Socratic Method - Giorgi Gvaradze . . . . . . . . . .

What makes the double pendulum chaotic? - Henry Roskill . . . . . . . . . . . . . .

Junk DNA - Hamish Rimmer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A brief history of the birth and evolution of Hip-Hop, and its significance as a modern form of literature - Lucas Bury . . . . . . . . . . . . . . . . . . . . . . . . . . . . ’Humankind is closer to anarchy than we might think’ Discuss - Johnny Elliot . . . .

Is a strong state a prerequisite or an obstacle to economic growth - Russell Kwok . .

Languistic and Change: A brief introduction - Bernardo Mercardo . . . . . . . . . .

The Acoustics of an Organ - Nithin Simanand . . . . . . . . . . . . . . . . . . . . .

Why Don’t We All Speak The Same Language - Toby Loftus . . . . . . . . . . . . .

The Pythagorean Proposition - RDS . . . . . . . . . . . . . . . . . . . . . . . . . . .

The Cure in The Root of The Predicament - Adam Mohammad Hilmi . . . . . . . .

Special Announcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3 6 10 13 18 21 25 28 32 35 37 40 43 46

Surrealism, The Early Years - Blake Williams Surrealism is the expression of the subconscious, repressed intellectual desires and especially the dream. It is the art form of true freedom of expression. Surrealism led to the careers of Salvador Dali, Freida Kahlo and Rene Magritte and to the formation of much of the art of the late twentieth and early twenty-first century. It was the defining art style of the inter war years and many of the earliest pioneers formed a substantial part of their art around their hatred of their paternal generation because they blamed them for the atrocities of the First World War. The beginnings of surrealism are as vague as the art style itself and it is impossible to pinpoint an originator from a collection of artists who all in their own right formed a substantial amount of surrealism’s early years.

surrealism. There are however two problems with this claim, the first is that there are artists that preceded Breton who write or paint in surrealist techniques and the second is that Breton and his followers only believed Poetry and its dominance and refused to accept any other art form.

The phrase surrealism was coined by Guillimare Apollinaire in 1917 in reference to a painting by Giorgio de Chirico of a street location with a hallucinatory effect.

The two men had been in correspondence for a period of two years with Guilimare effectively mentoring de Chirico. Guillimare Apollinaire was a French poet Novelist and short story writer as well as an art critic and passionate defender of cubism. As well as a passionate defender of surrealism he wrote the first surrealist novel, ‘The Breasts of Tiresias’, which became the base of Francis Poulenc’s 1947 opera les mamelles de Tiresias. He was both a defender and pioneer of surrealism but he did not do enough to launch surrealism through his own work to be considered a true originator of surrealism.

It is impossible to mention surrealism’s early years without mentioning André Breton and his surrealist manifesto. Breton was a French poet who did not fight in the First World War but treated shell shocked and other mentally ill patients in SaintDizier Psychiatric Centre. This is where Breton said that he found ‘almost all of the groundwork for surrealism’. This is because almost all of his work involved analysing patients’ dreams. In 1924 André Breton published the ‘Manifeste de surrealism’.

This is the defining document of Breton’s interpretation of surrealism and what he believed to be the only document of any worth on surrealism. However, a week prior to the release, Yvan Goll published a differing doctrine by the same name.

This led to a vicious battle for the rights to the term surrealism between both men and their devout followers which culminated with Breton winning the rights to the term Surrealism and virtually eliminating Yvan Goll from the history books. This would appear to be all the evidence that is required to make Breton the obvious originator of

However, Apollinaire’s apprentice Giorgio de Chirico could be considered an originator; he painted arguably the first surrealist painting, and went on to paint throughout the height of the surrealist era creating some of the most memorable paintings of the surrealist age. However, he clashed with Breton and his legal definition of surrealism and rocked Breton and his devout followers with his painting because they were the physical representation of their poetry and Breton detested that his ‘purest’ artform was being besmirched by lesser artists through paint and canvas. The reason for his immense success was the way that he perfectly married the dream like surrealist with famous icons of the Romantics such as his painting ‘The Disquieting Muses’ 3

If surrealism is truly a representation of the subconscious, then the only true surrealists in the late eighteenth and early nineteenth century British artists such as Fuseli, Blake, ‘mad’ John Martin and Richard Dadd because the surrealist nature of their art was in the hidden within the subconscious of their art. This is perfectly displayed in Fueli’s 1781 painting ‘The Nightmare’ which hung in replication in Sigmund Freud’s office. This subconscious surrealism manifests itself in many famous early 19th century pieces such as the extremes of emotion in De la Croit and Gericault’s works, the intensity of the spiritual nature of the German Romantics, the visions of Odilon Redon and the symbolist fanaticism of David Priedrich. These great Romantic artists were arguably the first surrealist and possibly the only surrealists to properly explore and understand the subconscious I am referring to Sigmund Freud, the through their lack of knowledge of the Austrian neurologist and founding father subconscious. of psychoanalysis. Freud’s theory of the unconscious defined surrealism as “psychic In conclusion there is no real definition of automatism”. This was a process which the early years of the surrealist movement. encouraged freeing of the mind from a There are many great pioneers and some rational train of thought but also constraints of my favourite artworks come from this such as moral and aesthetic judgement. The era. I am particularly fond of Dali’s ‘The reason why Sigmund Freud would have been Persistence of Memory’ and as well as de so influential in the Surrealist scene even Chirico’s ‘The Disquieting Muses’ and ‘The though he was not an artist was his theory Song of Love’. I believe that this is the of the unconscious mind and the conscious best way for surrealism to have formed, in mind and where the idea of surrealism sits the same subconscious manner that it was in between the two. He was the motor trying to replicate. The line of surrealist which drove the idea of surrealism into the poetry that I believe summaries the heart of public focus as an idea but not an art form. the movement comes from Braulio Arenas’ Unfortunately he was writing in German ‘So Many Moons’, “Dreams and more dreams and none of the initial surrealists knew any kisses and more kisses What will remain of German and his works were not translated so much moon”. into French until the late nineteen twenties. with classic romantics figure like the marble statue but with a balloon for it head, or ‘The Song Of Love’ with the figure of Michelangelo’s David in the foreground of the painting but surrounded in dream like obscurity and even his iconic features have been warped and distorted like in a dream.

De Chirico also wrote one surrealist novel in his time as an artist called Hebdomeros and it is widely regarded as a great and influential surrealist work. So de Chirico is undoubtedly a great surrealist and could be considered the founding father of surrealism.

However, if it wasn’t for geography there could have been a very different surrealism because a certain Austrian had been writing surrealism defining papers and theories at the same time but outside of the French central hub of surrealism’s growth and instead in Germany.

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On the Philosophy of Quantum Theory - Hyunjo Kim Introduction When the idea of quantum mechanics first emerged in the early 20th Century, there was not much consensus among physicists about the interpretation of it.

Although there are fundamental mathematical formalisms of quantum mechanics, they are uninterpreted and have many philosophical problems. These include the issue of quantum nonlocality, the ontology of quantum states, and the way we understand the structure of space-time. A lot of these propositions troubled Einstein and the view of an ‘objective reality’, which contradicted the dynamical degrees of freedom and probability of quantum theory; he famously wrote to Max Born that he is convinced that ‘[God] does not play dice1 ’.

Einstein, Podolsky, and Rosen went on to formulate a paradox concluding that the ‘wave function does not provide a complete description of the physical reality2 ’, which considered a realist’s approach to quantum mechanics. However, there was another school of thought, with physicists such as Niels Bohr who believed in the epistemic theory of the quantum world.

Despite empirical evidence, the underlying basis of quantum states remains to be debated upon. It is impossible to truly posit a philosophical definition of our physical reality based on quantum theory. No one can really understand quantum mechanics3 , however, this discussion will close in on the methodology to address its issues.

The criterion was provided: ‘If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.’ In other words, a physical reality only exists if the initial state of the system has a ‘hidden variable’, which would explain the random measurement results. This is called local realism; each element, each particle in this entangled system is predetermined when it first interacts. Most importantly, the EPR paradox did not contradict the theory of relativity.

The EPR Paradox: nonlocality and physical systems The EPR Paradox examines a physical system of a pair of entangled particles4 .

Resolving the paradox: J.S. Bell Approximately 30 years later, John Bell proposed an experiment in which any local realistic theory would contradict the

The fundamental assumption on which the EPR paradox lies on is the principle of locality. However, the EPR paradox does not reject the idea of quantum mechanics at all, but it firmly states that quantum mechanics is not a complete description of physical reality.

It concluded that some physical characteristic of each particle (electron and photon) must determine how it behaves under different experimental conditions. In other words, knowledge of our physical reality through quantum mechanics is flawed and faulty. However, Niels Bohr pointed out that the ‘peculiar individuality of the quantum effects that presents us, as regards the comprehension of well-defined evidence, with a novel situation unforeseen in classical physics and irreconcilable with conventional ideas5 ’.

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Einstein and the Quantum: a letter to Max Born (Scientific American) Can Quantum-Mechanical Description of Physical Reality be Considered Complete? (1935) 3 Reference to Feynman’s famous quote, ‘I think I can safely say that nobody understands quantum mechanics’ 4 https://en.wikipedia.org/wiki/Quantum_entanglement (See for reference) 5 Discussion with Einstein on Epistemological Problems in Atomic Physics (1949) 2

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by showing that when the momentum is known the coordinate would have no physical reality, thus the theory must be incomplete, and purely epistemic. Harrigan and Spekkens (2010)9 elaborate on this matter by demonstrating how the principle of locality can be held where is given ontic status. Before examining this issue, it is important to acknowledge when a quantum state is considered to be ontic or epistemic.

In Harrigan and Spekkens’ paper, this is how they define these two distinct models: ‘We call a hidden variable model -ontic if every complete physical state or ontic state in the theory is consistent with only one pure quantum state; we call it -epistemic if there exist ontic states that are consistent with more than one pure quantum state10 ’.

The epistemic theory is a representation of the observer’s reality rather than reality itself. The significance of this work is that it helped us gain more understanding about distinct quantum states and the physical reality it corresponds to. Using the classification of this paper, the PBR Theorem was established, which proved that either the quantum states are -ontic, or nonentangled quantum states would violate the assumption of preparation independence11 .

This no-go theorem showed that ‘models in which the quantum state is interpreted as mere information about an objective physical state of a system cannot reproduce

predictions made by quantum mechanics.

Instead of an ontological approach by the EPR paradox, Bell focused on the influence and the causality of the factors that are involved with locality.

As pointed out by his paper, “On the Einstein Podolsky Rosen paradox”, Bell states that the ‘statistical predictions of quantum mechanics are incompatible with separable predetermination6 ’. Bell’s theorem shows us that there is no theory that can meet the conditions of the Bell inequality and can also reproduce the statistical nature of quantum mechanics. Therefore, when Aspect, Grangier, and Roger tested Bell’s inequality7 , quantum mechanics was experimentally confirmed and realist theories were ruled out. From this, we learn that nature itself is fundamentally nonlocal; however, one must not assume that there is a causal influence8 . Yet, Bell’s theorem provides us with the boundaries of our knowledge and our existence, which leads to no logical paradox.

Ontological issues in quantum mechanics In quantum mechanics, there are sets of quantum states. The important question is whether these quantum states represent a physical reality. Einstein believed that the two-measurement complication would help him to ‘beat’ the uncertainty principle 6

https://cds.cern.ch/record/111654/files/vol1p195-200_001.pdf The Bell Inequality: by using the ‘front-panel’ description of Bell’s experiment, suppose Alice and Bob have a measuring device that has two buttons, M and N. These buttons will display either “+1” or “-1”. After obtaining data and doing correlation analysis, they can evaluate the quantity using ⌦ a↵ probability distribution.

By considering the possible set of values: {M , M , N , N } and also using S A B A B ⌦ ↵ = MA MB MA NB +NA MB +N ⌦ ↵A NB ⌦ – which is the quantity evaluated ↵ from the probability distribution – we organise the equation to S = MA (MB NB ) + NA (MB + NB ) . Because both MB and NB have values of either +1 or -1, at least one of the values inside the round brackets will equate to zero. Note that both MA and NA are either +1 or -1 as well. Hence, ⌦ we ↵ find that the value of S for that event must be either +2 or -2. Averaging over all events, we have | S |  2. This is a version of the Bell inequality (From Quantum Physics: An Introduction Based on Photons, A.I. Lvovsky) 8 This is because, in special relativity, there exist inertial frames in which a signal propagates backwards in time, which is logically impossible to describe our physical reality.

9 Einstein, incompleteness, and the epistemic view of quantum states (2010) 10 In these ontic models, there are distinct quantum states which contain only a range of disjoint probability distributions, whereas in epistemic models, quantum states contain a range of overlapping probability distributions.

11 The assumption that it is possible to prepare a pair of systems in such a way that probabilities for ontic states of the two systems are effectively independent. (Stanford Encyclopedia of Philosophy) 12 On the reality of the quantum state (Pusey, Barrett, Rudolph. Nature Physics) 7

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the predictions of quantum theory12 ’. This this theory is based on point events that are itself is not a complete theorem; the scattered through space-time, so electrons assumptions and the framework of this will have its wavefunction, but there will be argument could be easily rejected. no full physical space which signifies their existence.

The Wavefunction and Collapse Theories Commentary One of the most fundamental aspects of In this discussion, I have not fully quantum theory is the wavefunction13 . included all aspects of quantum theory.

The nature of quantum mechanics and Yet, I do not think it is necessary its dynamics have been represented by for I believe that quantum theory is deterministic equations or stochastic ones, uninterpretable.

Although I have not in which the initial state can evolve into mentioned the Copenhagen interpretation15 multiple different states.

Schrödinger’s or the Many-Worlds interpretations in the equation quite successfully reflects the collapse theories section, one thing that ‘quantum recipe’.

The philosophical is clear through close examination is that problem arises with the involvement of there is no single philosophical way to avoid Born’s rule14 . The reason is that it does assumptions. It can often be confusing not specify in which physical circumstances when reading through the different sections it applies to and what happens to the which seem to contradict each other, but wavefunction of that certain system. this is the behaviour of quantum theory. A Normally, Born’s rule is usually used complete theory is composed under three for position measurements or in different conditions: the basis of assumption follows observable properties as well.

In fact, the theory itself and possible evidence, held the ‘measurement’ is an unclear idea; in different approaches and observers with although it is often described as the collapse no colliding interpretations, and there must of the wavefunction, without a proper be formal deduction and truth in every definition, we do not completely know how structure of the theory i.e., every variable to apply it or what is applicable. The assignment. The complexity of quantum ‘measurement problem’ could be redirected theory suggests that it is impossible to to experimental characteristics, such as meet this criterion. However, it is possible collapse theories. For example, the GRW to redefine quantum theory philosophically theory suggests that the collapses occur into a ‘mixture’ of theories based on randomly with no environmental trigger, observables, ontology, measurement, noneradicating the need for an understanding locality, and epistemology. of a measurement. The ontological status of

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In order to fully understand this section, I recommend that you read about it: https://en.wikipedia.org/wiki/Wave_function 14 Born’s Rule: the probability of finding a particle at a given point is proportional to the squared of the probabilityRamplitude (magnitude of particle’s wavefunction). This rule is pointed out in the normalization 1 condition: | |2 dx = 1 1 15 The Copenhagen interpretation is full of problems (i.e., psycho-parallelism, ontological distinction)

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‘Euthyphro’: Gvaradze

Holiness and the Socratic Method - Giorgi

Plato’s Euthyphro, set in 399 BC, is one of four Socratic works which take place around the time of Socrates’ trial and death (the others being Apology, Crito and Phaedo).

More importantly, it is one of the five socalled ‘virtue dialogues’, as it explores what the Ancient Greek world considered one of the highest virtues – holiness, or piety. As such, it is one of the best displays of the ‘Socratic method’, which seeks to educate through relentless and minute questioning in a conversation. Not only do the ideas presented remain a strong challenge to anyone who believes that morality comes purely from God’s will, but, perhaps, the way in which Socrates forces his arrogant conversation partner to endlessly shift and get lost in his own argument can teach us a valuable lesson for our age.

The dialogue begins as the eponymous Euthyphro, an Athenian prophet, starts a discussion with Socrates in the Agora.

As the latter reveals that he has received notice of persecution against him from a certain Meletus, the former says that, as it happens, he is launching a persecution himself. For his father, having punished a murderous slave by binding and throwing him into a ditch (to await further action), has caused the slave’s death of exposure and thirst, leading Euthyphro, with much protest from his relatives, to take legal action against his own father. While it may seem like a curious coincidence that two people who are both due to appear in the courts just happen to have stumbled into a conversation with each other, the likelihood of such an event was actually quite high in Athens. Having just emerged from the tyrannical rule of the ‘Thirty’ and with its democracy reestablished, the city once again became very litigious in the early 4th Century BC. Jurors were paid daily and

selected annually from a pool of 6,000 adult men. In a flowering democracy, not only was this a way to exercise a right, but also a very entertaining time for spectators, as the best speakers in the law courts often appealed to the crowd with their quick wit and improvisation.

In any case, Euthyphro justifies the decision to go after his kin with the affirmation that what he is doing is ‘holy’. To Socrates’ seemingly straightforward question of what exactly ‘holiness’ means, accompanied by the philosopher’s typical snide flattery, Euthyphro brings up an example, like many of Socrates’ examinees.

This is not a satisfactory answer; an example is not the universal definition required. One is indeed offered by the prophet. He defines holiness in terms of what is approved by the gods.

But, as our knowledge of Greek mythology can tell us, the gods’ countless squabbles have ensured that it is rather difficult to pick out one thing on which they all agree.

Accordingly, Socrates points out that what one god may consider a good action, another may consider an evil one. Though this leads us into the statement that what is divinely approved is, at the same time, divinely disapproved, the philosopher concedes for the sake of argument. So, the definition that both decide to run with becomes “what all the gods disapprove of is unholy, what all approve of is holy, and what some approve of and others disapprove of is neither or both.”

Had Euthyphro been in a discussion with someone else, it is very likely the pair would have left it at that. But that is not the Socrates we know and love. It is here that we come to arguably the most famous parts of the dialogue, begun by the question “is the holy approved by the gods because it is holy, or is it holy because it’s

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approved?” The philosopher provides some examples: we speak of things ‘being carried’ and ‘carrying’, ‘being led’ and ‘leading’ and so on and so forth. So, it makes sense that there is something which is ‘approved’, and different from that which is ‘approving’.

All these examples are being something by virtue of getting that something done to them. What’s ‘being carried’ is so because it ‘gets carried’; what’s ‘being led’ is so because it ‘gets led’. Therefore, something which is ‘being approved’ is so because it ‘gets approved’. Euthyphro agrees to this.

However, when asked about the ‘holy’, he is led on by Socrates to say that “it gets approved because it is holy, it’s not holy by reason of getting approved.”

This is a direct contradiction to the earlier proposition that something is ‘approved’ because it ‘gets approved’.

With this, and the earlier definition that what’s holy is what’s approved by the gods, we have established that the opposite is true – ‘divinely approved’ does not equal ‘holy’.

excuses himself for “an urgent engagement somewhere” else, without admitting a single error. The concept of ‘holiness’ is left undefined, and Socrates is left disappointed.

What is it that we can learn from all of this? What Socrates himself thought is vague. The function of these kinds of dialogues is not to teach, but to make us think of the virtues, what they are and how we may achieve them. The search for this truth is exemplified in his method of subtle questioning and manipulation of someone who not only thinks himself to be an expert on a topic but is also blindly trusted by the public. Socrates was soon to be tried and executed by people who, in accusing him, clung to the same wide and virtue-related ideas, claiming that he was “corrupting the minds of the young” and inventing his own deities. In reality, the majority who preferred to follow than to think had enough of his pestering analysis and examination of, mostly, role-model figures. It seems that the demagoguery of the few overcame Socrates Understandably, Euthyphro is frustrated, in the end. Athens lost one of its greatest and accuses Socrates of causing his ever minds through her own actions. explanations to go around in circles. After all, here he is, a religious authority, with his arguments on ‘the holy’ dismantled Today, on both sides of the political by a philosopher who claims to be much spectrum, there are those who claim that more ignorant on the topic than him. He, what they believe is so correct, that it is not with Socrates’ help, now switches to a even a matter for discussion. Either you are new definition – all that is holy is just. with them and also doing the right thing, or It logically follows that while all that is against them, doing the wrong one. This, holy may be just, not all that is just is to me, is very worrying. Instead of falling holy. Euthyphro is required to say precisely prey to the ideology of crowds, perhaps all which part of justice is holy. Going back of us could try being a bit more Socratic, to his pious standpoint, he says that holy and not be as assured in our righteousness is that part of justice which looks after as Euthyphro. We should force ourselves the gods. With some further meandering to ask questions, especially of those who and Socrates’ manipulation, we come to the not only claim to know more, but who point where ‘gratification’ is how the gods also hold largely unchallenged positions of benefit from this service of ours. Euthyphro influence, or power. Of this, Euthyphro affirms that this is what they most approve remains a perfect example. After all, as of. And so, like that, we are back to square Plato’s dialogues remind us, and as Socrates one. Holiness is once again defined as what himself said, truly the wisest man knows the gods approve of. After that, Euthyphro that he knows nothing.

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What makes the double pendulum chaotic? - Henry Roskill You might often hear about the phenomenon of mathematical chaos, often synonymous with unpredictability and randomness (although we’ll see why this isn’t quite correct).

The double pendulum is a neat illustration of this idea. Given certain initial conditions (the starting angles between the pendulum rods), the system will react erratically and wildly to even the slightest perturbation of these starting parameters. In this article, we’ll investigate the mathematical idea of chaos, and how exactly it relates to the double pendulum problem.

The diagram below gives a good visual of what exactly we’re dealing with.

We’ll consider mass and the lengths to be constant and (as always) air resistance and friction will be ignored.

In addition, we will consider the rods to be massless.

Many of you will recognise this setup and will, perhaps, be familiar with some of the wild trajectories m2 traces out.

As you can see, even the slightest difference in starting conditions, shown in Fig. 2, can lead to wildly different trajectories later on, for example in Fig. 3.

Figure 1

(a) Figure 2

(b) Figure 3

(c) Figure 4

Now that we understand the setup of the problem, we need to formulate it mathematically. In order to give this mechanical system a rigorous treatment, we need to introduce Lagragian mechanics.

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Mechanics as a whole is the mathematical study of motion. GCSE physics acquaints us with Newtonian mechanics, governed by Newton’s laws of motion, the most important of which, the 2nd law, says that force is the derivative with respect to time of momentum, or, in a closed system (i.e. mass is constant and energy is conserved1 ): F=

d dv p=m = ma dt dt

Where F is the force, p momentum, m mass and a acceleration. So far so familiar.

In mechanics, the idea of time derivative is so important is has its own notation: dx dx d2 x = x, = 2 = ẍ dt dt dt Lagrangian mechanics is based on the principle of stationary action and says that a certain equation in terms of something called the Lagrangian holds true.

The Lagrangian, L, is the total kinetic energy of the system, minus the potential energy2 : L=T

U

This seemingly innocuous quantity satisfies a very useful equation3 : d @L @L = (1) dt @qi @qi This seems very complicated, but breaking it down makes it clearer. We know what L is d and what means, and qi is just one of our parameters. As we will see, this equation dt @y holds for all our parameters (in our case, ✓1 and ✓2 ). Finally, the notation is the @x partial derivative of y with respect to x. To give an example: if y = 4x2 + xt + t2 then: @y = 8x + t. Basically, to take a partial derivative, think of everything which isn’t x as a @x constant, and differentiate normally. This means, when we come to applying this equation we will be differentiating with respect to different variables on each side, and many of the terms will be constants with respect to that variable, so differentiate away.

Therefore, if the above equation is true4 , we can begin to derive equations describing how the double pendulum will move. Specifically, we will arrive at a differential equation, an equation involving ✓i , ✓˙i , and ✓¨i , the angle, angular velocity and angular acceleration of mass mi respectively.

Firstly, let’s think about kinetic energy.

T=

1 mv2 2

1 You can’t use F=ma when you get to higher speeds as a consequence of special relativity, but force being the time derivative of momentum remains meaningful 2 Note that if we were to add these two quantities, we would have the total energy of the system.

3 I won’t explain how this follows from the principle of stationary action because it’s rather complicated.

4 It is

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dr = ṙ where r is the position of each of the swinging masses. Since each mass dt ✓ ◆ x(t) is moving in two dimensions, we can consider r to be the vector where x(t), y(t) y(t) describe the positions of the particles at time t. For simplicity, we’ll refer to them as x, y.

But v =

Figure 5 Looking at Fig. 5, it is clear, by a little trigonometry, that5 : x1 = l1 sin(✓1 ) y1 =

l1 cos(✓1 )

x2 = l1 sin(✓1 ) + l2 sin(✓2 ) y2 =

l1 cos(✓1 )

l2 cos(✓2 )

The kinetic energy of m1 will be given by T1 = 12 m1 (ẋ21 + ẏ12 ).

Likewise, the kinetic energy of m2 is T2 = 12 m1 (ẋ22 + ẏ22 ).

Differentiating each of the variables with respect to time, while remembering ✓1 ,✓2 = ✓1 (t),✓2 (t) and are dependent on time so we must use the chain rule6 , gives: 1 1 m1 (ẋ21 + ẏ22 ) = m1 ((l1 ✓˙1 cos(✓1 ))2 + (l1 ✓˙1 sin(✓1 ))2 ) 2 2 1 1 = m1 (l12 ✓˙12 (✓1 + ✓2 )) = m1 (l12 ✓˙12 ) 2 2 5

Note that the y direction is negative. This will not affect the calculations.

I’m assuming, a little unfairly, that if you’ve followed this far you know the chain rule. If not, it gives d you a way to differentiate f (g(x)) and results in dx f (g(x)) = f 0 (g(x))g 0 (x).

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Through the same process7 , we get T2 = 12 m2 (l12 ✓˙12 + l22 ✓˙22 + 2l1 l2 ✓˙1 ✓˙2 cos(✓1

✓2 ))

Taking care of the potential is much easier as the only potential energy we have in the system is gravitational potential.

GP E = mgh ) U1 = mg( y1 ) = m1 gl1 cos(✓1 ) U2 = m2 g( y2 ) =

m2 gl1 cos(✓1 )

m2 gl2 cos(✓2 )

Since U = U1 + U2 and T=T1 + T2 : If we let ✓1 =qi in equation (1) then we get:

LHS = ddtL =

d @L d = (m1 l12 ✓˙1 + m2 l12 ✓˙1 + m2 l1 l2 ✓˙2 cos(✓1 ˙ dt @ ✓ dt

d = (m1 + m2 )l12 ✓¨1 + m2 l1 l2 ( ✓˙2 (t)cos(✓1 (t) dt

✓2 ))

✓2 (t)))

Now, by the chain rule and product rule, we get8 : LHS = (m1 + m2 )l12 ✓¨1 + m2 l1 l2 (✓¨2 cos(✓1

✓2 )

˙ ✓˙2 (✓1

✓˙2 )sin(✓1

✓2 ))

Differentiating the RHS with respect to ✓1 gives: RHS =

m2 l1 l2 ✓˙1 ✓˙2 sin(✓1

✓2 )

(m1 + m2 )gl1 sin(✓1 )

Setting these equal, rearranging, cancelling terms and dividing through by l1 gives finally: (m1 + m2 )l1 ✓¨1 + m2 l2 ✓¨2 cos(✓1

✓2 ) + m2 l2 ✓˙22 sin(✓1

✓2 ) + (m1 + m2 )gsin(✓1 ) = 0 (2)

Doing the same for qi and dividing the end product through by m2 l2 yields: l2 ✓¨2 + l1 ✓¨1 cos(✓1

✓2 )

l1 ✓˙12 sin(✓1

✓2 ) + gsin(✓2 ) = 0

(3)

At the end of all this we are left with two equations of motion. These are both non-linear second order differential equations in two variables.

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Using the identities cos2 (x)+sin2 (x)=1, cos(a)cos(b) + sin(a)sin(b) = cos(a sin(b)cos(a) = sin(a b) 8 (f(x)g(x))’=f(x)g’(x)+g(x)f’(x)

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b) and sin(a)cos(b)

Given certain initial conditions, the solutions to these equations will be functions themselves, namely the functions ✓1 = f (t), ✓2 = g(t) which satisfy the above relationships between their derivatives.

To discover why this system is chaotic, we need to consider what chaos means. A chaotic behaviour is not one which is random, because randomness would imply this system is non-deterministic9 . However, the double pendulum is unpredictable, as any attempts to analytically solve equations (2) and (3) will fail, so obtaining a closed form for the angles at any desired point in time is impossible.

This means we have to resort to approximations and numerical methods to extract a solution.

However, due to the non-linearity of these differential equations, which occurs because of the presence of sine, cosine and squared terms, any uncertainty in the initial values of the system will be compounded exponentially10 .

In conclusion, having derived the equations of motion of the double pendulum, we see that the chaotic behaviour it exhibits is reflected in the complexity of the differential equations describing it, and its chaotic behaviour is explained as a consequence of the non-linearity of this dynamical system.

9

As we can see, the system’s prior behaviour will completely determine its later behaviour, making it deterministic.

10 This is made more rigorous by things called Lyapunov exponents.

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Junk DNA - Hamish Rimmer ‘Junk DNA’ may, at first glance, seem like a somewhat oxymoronic title – famously, upon discovering the double-helical shape of the DNA molecule in 1953, Francis Crick and James Watson walked into a pub in Cambridge and declared “we have found the secret to life” - surely to label any DNA as ‘Junk’ is heresy. ‘Junk DNA’, is in fact a term which refers to the sections of genetic code in an organism which do not code for proteins. The term first appeared in the 1960s, when it was mentioned only in passing in an academic paper. It was formalized by Susumu Ohno in 1972; since then, more and more discoveries have been made suggesting that so-called ‘Junk DNA’ is teeming with functions and vital roles. Hence, the term ‘Junk DNA’ has been questioned due to the provocation of a strong prior assumption of a lack of functionality – the term ‘non-coding DNA’ has been suggested to take its place.

However, unfortunately, the name has stuck, and ‘Junk DNA’ remains widely used to refer to any genomic sequences which do not code for proteins. Nonetheless, by delving further into the dark matter of the genome, it is plain to see that ‘Junk DNA’ is far from useless.

Often, only a small percentage of a genome is responsible for coding for proteins in any particular organism. However, an increasing proportion of that which doesn’t is shown to have other functionality. It is estimated that almost 98% of the human genome is non-coding DNA, meaning only 2% codes for proteins. That 98% was assumed for a long time to be mostly, if not completely, useless. However, in 2011 the ENCODE Project, a public research project aiming to follow up from the Human Genome Project in 2001, published results suggesting that over 80% of human DNA has biochemical functions; of course, there is still some debate surrounding the validity of this

statistic as the criteria for what constitutes ‘functional DNA’ can vary.

Now that we have established that noncoding DNA contains a treasure trove of functionality, we can delve into these functions further. One function which has been determined for some non-coding DNA in general is called de novo gene birth, in which new genes are fashioned from noncoding DNA over time. This is because, due to a loss of selective pressure, pseudogenes (a sequence of DNA that once resembled a gene but has been rendered inactive through mutation) will accumulate mutations more rapidly than coding sequences.

These pseudogenes could therefore serve as raw material for genetic evolution, resulting in new genes being formed.

These pseudogenes were accordingly dubbed ‘potogenes’. On a more detailed scale, there are a range of types of non-coding DNA including: cis and trans-regulatory elements, introns, pseudogenes, repeat sequences, transposons, viral elements, and some non-coding DNA can be transcribed into functional non-coding RNA, however we don’t have time to unpack all that now. All these variations of non-coding DNA can serve separate purposes, ranging from ribozyme functionality to the control of the transcription of nearby genes. Due to the nature of much of non-coding DNA, a mutation on a regulatory section of ‘Junk DNA’ can cause a protein to be expressed in the wrong place, or at the wrong time, or can alter the expression of an important protein when it is needed, resulting in too little or too much. For example, mutations in noncoding DNA have been linked to developmental disorders such as isolated Pierre Robin sequence (a set of physical abnormalities of the face, such as a cleft palatte), which is caused by changes in enhancer elements that disrupt the activity of a gene called SOX9, altering the proteins

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it produces. As such research into this section of Junk DNA suddenly becomes much more important as it could be linked with the prevention of this syndrome.

Although non-coding DNA hosts a myriad of functions, some organisms have significantly less non-coding DNA. The classic example is bacteria, whose genomes have traditionally been viewed as very compact with around 90% of the genome consisting of proteincoding genes. Generally, prokaryotes tend to have very little ‘Junk DNA’ (often between 6-14% compared to our 98%). Another example is the pufferfish, the genome of which is only around 13% of the size of that of a human, and yet they contain a similar number of genes to us.

In experiments, (relatively) large sections of non-coding DNA have also been removed from mice before birth, this deletion of parts of their genome seemed to have little to no effect on their development, longevity, or reproduction. However, note the study doesn’t prove that Junk DNA has no function, just that removing a little over 1% of a mouse’s genome resulted in no abnormalities which they tested for in the laboratory. Clearly, it can be argued that Darwinian selection is a tougher test than surviving a single generation under laboratory conditions.

As mentioned previously, mutations in non-coding DNA can have just as serious implications in an individual as any mutation in the protein-coding DNA of a person might. As such, research into these sections of non-coding DNA could hold the key to several health problems, and even unlock a lengthier lifespan for

humans. There are many inherited genetic disorders, such as fragile X syndrome or Friedreich’s Ataxia, and there are many health problems, such as various cancers, which can arise from random mutation in your genome, especially in long non-coding RNA sequences. For example, differences in non-coding genes within a population can influence susceptibility to Ewing sarcoma, a form of aggressive bone cancer. They can also play a role in infectious disease susceptibility, such as hepatitis C. ‘Junk DNA’ can additionally serve a purpose in a more physical way, without affecting other genes. For example, at the end of each of our chromosomes, we possess "caps” of non-coding DNA called telomeres. These sections of DNA act as a sort of insulation, wearing down over the lifetime of a cell.

There is growing evidence that certain lifestyle factors may affect telomere length which, in turn, can affect the pace of aging and onset of age-associated diseases. This has led to research into reversing the effect of telomere shortening, and in the future may even hold the key to lengthening the lifespan of humans. This effect can already be observed in bats - the longest living mammals (relative to body size) - which keep their natural lives long by preserving their telomeres.

Clearly when you look past the name ‘Junk DNA’, you see that just because it does not code for proteins, does not mean noncoding DNA is useless. Far from it. It is clear then, that so called ‘Junk DNA’ will no doubt prove to be at the forefront of medical research influencing the scientific landscape of prominent fields such as oncology and genetics.

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A brief history of the birth and evolution of Hip-Hop, and its significance as a modern form of literature - Lucas Bury Introduction When covering the topic of hip-hop, the first thing worth acknowledging is that the name ‘hip-hop’ not only refers to a genre of music, but also to a whole culture.

Though it started mainly as music, hip-hop, with all its key features, soon became a characteristic way of life shared by many – a defining element of a culture. Not only did hip-hop become a way of life but it became an art when regarded collectively.

Within these collective manifestations of artistic and intellectual achievement, there is music, visual art, performing arts and literary art. Hip-hop is a modern, oral form of literature and it has arguably become the most accessible form of literature today.

America, is that it gave people a way to survive during this time of hardship through expression and communication; rap songs gave people stories and allowed them to channel and share their emotions and opinions as well as the subsequent parties which acted similarly as outlets for emotion and celebration, while murals gave people a voice. All the elements of hip-hop are artistic and art is an extremely effective means of communication and expression.

Most people can recognise that visual art is very powerful, but music is arguably more so, especially as this particular genre also inspired a visual art aspect of urban expressionism, in the form of graffiti. Its success and ability to provide such a thriving culture, was also largely down to its technicality – in both music and literature.

The start In 2014, there was a study carried out by Musixmatch called, The Largest Vocabulary in Music. The genre of hip-hop was found to have an average of 478 unique words per song. When also considering the use of slang, metaphor and dialect, one can easily become more aware of the linguistic depth of this music. A second example of the technical depth of hip-hop is its unique conciseness in expression. In the hit Broadway play Hamilton, rap is the chosen style of music which, in a musical, makes it a key feature of the production and the most significant form of expression. The creator of Hamilton, Lin-Manuel Miranda, when speaking on the most–watched news magazine ‘60 Minutes’, quoted; “I believe that rap is uniquely suited to tell Hamilton’s story because it has more words per measure than any other genre; it has rhythm, it has The reason for its success density and if Hamilton had anything in his writing, it was this density”. Therefore, it The reason hip-hop managed to initially was rap which allowed Miranda to present catch-on so successfully and spread across this density in a way which was concise Hip-hop culture emerged as an underground urban movement, encompassing what are now seen as the key features of hip-hop: DJing, rapping, breakdancing and graffiti art. The culture emerged in the South Bronx area of New York in the late 1970s.

This was a period of hardship, with the economic stagnation of the 1970s, causing high levels of unemployment and drugrelated violence in the suburbs and poorer areas of cities such as New York, which was hit particularly hard. It became the dominant cultural movement of the African American and Hispanic communities in the 1980s and it continues to be a large culture which has even spread beyond America, remaining one of the most popular music genres worldwide today.

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enough to continuously engage with the theatre and thus making hip-hop a more audience. popular form of literature (though there are clearly many other factors contributing to Hip-hop’s significance as a modern its popularity). While hip-hop may require less attention or devotion to understand and form of literature appreciate than poetry for instance, it would frankly be naïve to believe that it has any Hip-hop has arguably become one of less merit as a form of literature than any the most accessible and popular forms other form. Each of the four key features of literature today. Throughout history, of hip-hop requires a particular depth of literature has been inspired by strong skill, which has been demonstrated through thoughts and emotions on particular events countless examples of DJs, rappers, breakand aspects of life, for example, the poetry dancers and street artists, who have been which came out of World War One, or recognised as genius and have provided numerous plays and novels set during inspiration for millions of supporters and the Great Depression in America (these fans. being only two of many examples). It is often thought that the best literary themes explore human nature on a universal level, Perhaps due to its conception in such a harsh focusing on details such as love, hatred, environment, hip-hop often contains what redemption, struggle, tragedy, etc - all could be seen as a revival of romanticism of which focus on passionate emotions, - perhaps even in a heightened form. Four both positive and negative. The hardship key elements of romanticism are emotion, which was faced by those living in America imagination, nature and social class, all of during the late 1970s (especially the African which we see expressed so boldly. In many Americans and Hispanic-Americans who examples, hip-hop artists have expressed contributed to a disproportionately high emotion and nature in the context of social percentage of the slum populations) at the class in an almost Darwinian style. For time of the birth of hip-hop, is no different to example, in Mobb Deep’s song ‘Survival any other circumstances which have inspired of the Fittest’, the title makes a direct great literature, in the sense that it bred reference to Charles Darwin’s theory of these powerful feelings which demanded evolution, with the chorus (“We live in this expression. I believe that the reason why till the day that we die, survival of the fit it is so accessible, is that the ability to only the strong survive”) doing likewise and comprehend and fully appreciate its true referring to both social class and nature merit, is not exclusive to only those with a (“this”). In this case, nature does not refer particular or even basic level of education, to the beauty or danger of wild animals or which is arguably the case for much of the plants or landscapes but the natural order highest levels of poetry and novels. It is of urban existence. Run-DMC presented a also something which is performed to its similar message, and it is hard to overstate consumers, so does not require the same their impact on the trajectory of hip-hop. In level of attention or devotion to enjoy, which their song ‘It’s Like That’, they say; “money I believe may possibly be a key reason why is the key to end all your woes, your ups theatre (and film) remains such a popular your downs, your highs and your lows / form of literature as well - the key difference won’t you tell me last time love bought your being that music can be accessed anywhere clothes?”. This portrays the struggle for through radios, records or phones and does money as a means of survival as a product not require one to buy tickets or commute of recession, as well as the subsequent to a theatre at a certain time to enjoy it, evaluation of utility over all else. It is clear therefore making music more accessible than to see the effect that America’s economic 22

status had on early hip-hop through the things that happen to a negro”. This both constant portrayal of the hardships of life, reflects the hardship which many African presented in a competitive, primal image.

Americans had been suffering throughout American history and the disproportionately As America rose out of this recession, the large percentage of them who were, and still lower socio-economic classes retained scars are, in the bottom socio-economic classes, in the forms of drug and gang culture. as well as lightly touching on the emergence Tupac addressed this saying, “Nowadays of a strong drug culture which subsequently everyone’s ashamed of the youth cos the caused the violent gang culture that is very truth look strange”. In saying this, perhaps often reflected in hip-hop music, and which he is implying that the rest of America is became a large feature of the broader hipsurprised and shocked by the cold reality hop culture. of what is happening amongst the poorer, younger generations who are growing up in Whether it is the enjoyment of the sound, the wake of this hardship and the reality the satisfaction of rhyme, the appreciation of how they cope in their environment. of skillful rapping and lyrics or the ability to The Notorious B.I.G (AKA Biggie smalls relate to the lyrics or the rapper, hip-hop can [Biggie]) rapped about his own personal appeal to anyone of any background or taste. success in stark contrast to his previous It certainly has enough variety to appeal poverty. “It’s time to get paid, blow up to all tastes, as long as one can appreciate like the world trade” - is a reflection of his the values of the music and find artists and attitude towards the bottom socio-economic songs who appeal to their preferences in at class (which he had belonged to) being left least one aspect of the culture. Hip-hop is behind by the growing wealth of the rest a culture which was borne from the passion of the country (the World Trade Centre of hardship and has therefore survived and was a symbol of America’s wealth and grown beyond the bounds of its birthplace, prosperity – this quote is not referring to and it owes this to its ability to appeal the terror attack which happened five years to so many through its many core values. after his death). Furthermore, Mob Deep’s While popularity may not be accepted as reference to Darwin’s theory of evolution evidence of genuine quality, I believe hipnot only refers to surviving poverty but also hop has presented the world with artists the threat of gang violence. They open who have demonstrated extraordinary skill ‘Survival of the Fittest’ with: “There’s a and much of their music has strong literary war going on...” and then go on to compare merit. If someone cannot directly relate to America’s urban environment to that of the many of the core themes of hip-hop yet can Vietnam war. While the gang violence was still understand the meaning of a song and a feature of slum life, the drug culture was feel as though they can relate to the person an effect of it. Cypress Hill referenced Louis rapping it, I believe there must be some Armstrong in the song ‘Insane in the Brain’, literary merit, as this passion is ultimately who, when talking about marijuana said; “It transmitted through lyrics. relaxes you, makes you forget all the bad

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’Humankind is closer to anarchy than we might think’ Discuss - Johnny Elliot Anarchy in the face of blindness. A form of chaos. A society that rejects hierarchy and curtails governments and institutions.

For Saramago it is installed into the void where once our eyes would allow us to fulfil our roles that allowed society to function.

However, I believe that, as Blindness reflects, humanity is developed beyond anarchy and as a function of evolution will fail to ever recede to such as state.

There are three levels of conscious existence that Aquinas calls the animations of the soul. We are at the Rational level and possess the power to think and reason.

Beyond this and our physical attributes developed over years of natural selection, we are born, debatably, with nothing else.

Where Aquinas or Kant might believe we have an immediate sense of inclination that guides our morality it is instead more plausible that they have mistaken biological urges to survive that are common on a Vegetative level with evolved, irrational life or the aptly named vegetation, for a priori (inherently known) inclination.

Instead humanity could conceivably be guided by these vegetative principles of survival developed through evolution, however, it is also the capacity of rational thinking that divides us from the irrational organism.

This rationality is what enables us through observation to act in a way that fulfils our base coding of survival. Hence, humanity evolves the environment as well as itself.

This is evidential in the change from a primal society reliant on hunting to that of farming where nature is manipulated more efficiently to better ends. Even now where a tertiary sector of economy provides for the most part more disposable income and a higher quality of life, we can see a global trend towards this more attractive model and have been able to all through history.

These are the fruits of rationality that allow inference through observation which develop society, and, on this basis, we can argue how humanity is incapable of settling on anarchy.

Our developed principles from inductive logic simply do not allow for the rational being to rely upon an anarchic society.

Saramago presents a societal breakdown and within it demonstrates the potential power balances that could arise. His membership of the Portuguese Communist Party can be reflected in the group within the psychiatric ward.

The nameless members are all portrayed to be different components of society yet come together to function under the unbiased and kind leadership of the doctor’s wife. A micro communist society living within the anarchic breakdown of the world. However, firstly we see Saramago has presented an ordering of society in the loose organisation of the group, a rational conclusion in the face of chaos. Secondly, in the face of a power gap, humanity will seek to fill it. From the start the army recommends appointing representatives and organising the wards. Additionally, the blind ruffian with his gun takes over without significant dispute. As Stalin said quite appropriately in this situation, “power comes from the barrel of a gun”, a power even if blindly wielded can work well enough to maintain authority.

Considering the situation, the masses of blind could have overpowered the gunman and the mob but at great undiscriminating risk. Balancing harm in the face of good or alternatively, balancing poverty with riches, humanity is arguably inclined towards a middle way which mitigates risk and reward. As a tangent, this theorem of human instinct is arguably dependent on experience inciting desperation and a willingness to gamble with life or possessions. Such a decision

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we can be easily reduced to a societal collapse but from this humanity inevitably develops into a form of order be it guided by the immoral control of authority aided by physical enforcement or the subsequent stage of a democratic institution with a hierarchy that enforces itself by benefiting the masses.

This apparent inclination towards such a society so that it is beneficial can be enforced on the observation of a universal rationality and understanding of how the inductive truth of a systemised society’s profit justifies why we would not settle for anarchy. Similarly, communism is irrational as the power gap would be filled in a way that inevitably fails to benefit the populace and even if it did, the capital incentives of the system fail to incentivise the labour and intuition that further humanities progress. But, on the basis that anarchy leaves a power gap and of rationality determining order and actions to further such a principle, whilst society may be fragile in the face of explainable or unexplainable circumstance it will install a Having developed society over the four self-reliant hierarchy and will never turn to million years since the evolution of the anarchy as the ruling principle.

Homo sapiens we can observe the benefits of a structural system. As Blindness shows, is also situational and another example of rationality determining the solution be it right or wrong. But, returning to the main point, anarchy (and communism) leaves a power vacuum. Humanity, as proven by the collapse of equal outcome and equal opportunity societies time and time again, is always incapable of not installing a hierarchy, institution or government. Be this through willingness of the participants of society who in Blindness rely on the doctor’s wife or from force or circumstance as is so often the case in a communist society as seen in Animal Farm or with Saramago’s thugs.

Order for the ruling classes benefit or for the wider society is the rational conclusion of humanities evolution to date as power is a mantle rationally taken for selfish gain or for societal benefit. A position will not be left unfilled. Furthermore, such a system may function only while the benefit is mutual to an extent where the whole is satisfied enough to not provoke a return to anarchy before settling again on a new form of government.

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Is a strong state a prerequisite or an obstacle to economic growth - Russell Kwok Note :In the interests of simplicity, we shall use the Solow-Swan Model for long-run economic growth to assess policy implications and we will define a strong state as one having a government which is able to create and enforce laws easily and stringently, which greatly influence the lives of citizens.

The implementation of unprecedented fiscal and monetary policies in conjunction with the recession caused by the Covid19 lock-down has once again brought up the discussion of economic growth.

In response to the virus, many nations have curtailed freedoms and vastly increased government control over society (Jain, 2020). This essay will demonstrate that a strong state is, in most circumstances, an obstacle to economic growth. The issues of how an authoritative government may affect productivity, investment, corruption, political stability, recession management and state-owned businesses (SOEs) will be investigated.

A government’s influence on productivity is arguably the most significant determinant of economic growth, as Roubini and Backus assert: “Productivity is the cornerstone of economic growth.” (Roubini Backus, 1998).

Since a favourable economic environment can significantly bolster innovation and diligence, the state must be vigilant about its policies. One characteristic of a strong state is efficient legislation, leading to more laws. Increased regulation often increases bureaucracy which may impair productivity; an example is the United States, which passes 2-3 million words into legislation every term (GovTrack, 2020). It is possible that certain laws may increase productivity; however, since regulations are by definition a restriction, it is more probable that such legislation will stifle economic growth by reducing the freedom needed for creativity.

Evidence of such can be found in the United States, where the Code of Federal Regulations has increased 600% from 19,335 pages to 134,261 pages from 1949 to 2011.

Dawson and Seater modelled the effect of such lawmaking and concluded: “if regulation had remained at the same level as in 1949, current GDP would have been $53.9 trillion instead of $15.1 trillion in 2011” (Dawson Seater, 2013). This is a difference of $38.8 trillion, which is approximately 13.5 times the GDP of Britain.

An apparent exception would be China, with an average growth rate of 9.1% from 1992 to 2019 according to the CEIC, with comparatively fewer regulations than most developed countries. Such impressive economic development would seem to be improbable given the powerful state present, but one should look at the details.

According to a report from the U.S. Congress: “the Chinese government decided to break with its Soviet-style economic policies by gradually reforming the economy according to free market principles. . . [to] significantly increase economic growth and raise living standards.” (Congressional Research Service, 2019) As Deng Xiaoping put it: “Black cat, white cat, what does it matter what colour the cat is as long as it catches mice?” Therefore, it was the weakening of the strong state, in the form of regulatory and bureaucratic reduction, that has provided the basis for such impressive economic growth.

Another keystone to economic growth is private investment which is, in essence, a vote of confidence in a particular country.

Given that only 18% of the world population are employed by the public sector, the role of the private sector is considerable (OECD, 2019). Therefore, the implementation of unfavourable policies will have substantially

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negative implications, especially towards SMEs since they account for 70% of the jobs around the world (Ready, 2018), and will inevitably precipitate an economic slowdown. However, some see government investment as a solution to this problem.

Such increased economic control can be identified as another way a strong state is manifested. Unfortunately, state spending is vastly inferior to its private iteration as it incentivises waste and disincentives efficiency (Folsom Folsom, 2014). This is because state spending, mostly revenue taken from the private sector via taxation and/or SOEs, displaces private investment.

In addition, government spending is not subject to the market forces that ensure efficient resource allocation in the private sector, thus increasing wastefulness that suppresses growth. (Riedl, 2010) Evidence from this can be seen in a study from the Journal of Macroeconomics that indicated that a 1% increase in government size decreases the rate of economic growth by 0.143% (Guseh, 1997). Although certain countries may have other revenue streams, such as natural resources, which reduces the displacement of private investment, the inefficiency of government spending still stands true.

Because of efficient taxation in strong states that provide large revenues, the potential benefits of managing that capital may engender political conflicts (Acemoglu, 2010).

Embezzlement and cronyism are often present in strong states; executors control an estimated $800 billion globally used for unofficial purposes (Eckert, 2007). This damages the economy grievously through the reduction of essential investment and increases in inefficient spending.

Furthermore, transparency in such administrations is reduced through bureaucracy, resulting in a system which increases the ease of cover ups for unprincipled behaviour by officials. An opposing view may argue that such conduct would be reduced if remuneration was

sufficient. However, as Lord Acton pointed out that "Power tends to corrupt", even principled public servants would be likely to succumb to the temptations of controlling a strong state.

Economic consequences of bribery are articulated by Shleifer and Vishny: “corruption is costly to economic development”. (Vishny Shleifer, 1993).

This demonstrates that the influential sway of strong states causes corruption, which obstructs economic growth.

People believe that the main advantage of a strong state is the effective implementation of policy, which can potentially enforce a strong rule of law that defends private property rights (Licht, et al., 2007) and fosters favourable commercial environments.

This is because a strong rule of law provides certainty for businesses, encouraging investment. In reality, evidence shows that a weak rule of law is more prevalent in strong states (Henderson, 1991), principally caused by excessive legislation (Somin, 2017). The implementation of new laws may precipitate an unpredictable business landscape causing a reduction in investment and dampen economic growth (Bakari, 2017). Moreover, the tight influence a strong state has over society often leads to oppression, sparking civil unrest (Mountford, 2017) which may reduce economic growth through revenue reduction leading to capital outflows. The same occurs when burdensome taxes that a strong state can impose are put into law (Haque, 2006). Since investments are the building blocks on which an economy is built (Stiglitz Shell, 1967), capital outflows from a particular jurisdiction will have a detrimental effect on the growth of the local economy. In addition, the departing owners of these monies typically have greater business expertise, also causing the flight of valuable human capital.

Another aspect in which a strong state would be an hindrance to economic growth is their response to recessions. Usually, a quick and sustainable recovery is most

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desirable so as to maximise the average GDP growth rate. The Great Depression is a good example. In 1929, the Smoot-Hawley Tariff Act was passed soon after the stock market crash on Black Tuesday, leading to a collapse in commodities, grievously affecting the large agricultural industry (Sennholz, 1969).

Moreover, there was an increase in federal, state, and local taxes from 16 percent of net private product to 29 percent in the Revenue Act of 1932, which would alone have caused a recession (Rothbard, 1963). There is a view that government intervention would have shortened the crisis. This may have seemed to be true after the institution of the New Deal, when there was a recovery, albeit an extremely weak one; the GDP in 1939 was still 27% below the GDP before Black Tuesday (Johnston, 2020). However, the recovery was unsustainable and most likely ended when the fiscal stimulus was removed.

Another view is that the Second World War stimulated an increase in government spending which lifted the US out of the Great Depression. In actuality, Roosevelt had proposed a Second Bill of Rights, which if promulgated, would have advanced a stronger state, as he believed the economic contraction would continue after the war due to massive military spending (Folsom, 2010).

However, the economy recovered sustainably due to corporate tax cuts, income tax cuts and the repeal of the excess profits tax in 1945-46 and 1948. The above examples show that poor decisions of a strong state can cause a serious impediment of economic growth, thereby suggesting that it is not a prerequisite.

wishes, affordability and other reasons, are in conflict. This is inevitable as the desire for profit is in direct opposition to unsustainably low prices. Sánchez notes that: “When an enterprise’s objectives are ambiguous or contradictory, executives and managers tend to lead the company towards their own interests.” (Sánchez, 2016) Proponents of SOEs will state that consumers will benefit from suppressed prices. However, their increased costs from inefficiencies (Greene, 2014), are borne by the taxpayer, meaning there is no net benefit.

Furthermore, their dual roles as businesses and state-controlled entities introduce the element of moral hazard, where management expects sustained financial support from the government due to weak fiscal discipline or “soft budget constraints” (Sundram, 2018).

Government backing means SOEs can gain market share by taking imprudent risks or through regulatory laxity (which regulators can ignore), putting competitors at a severe disadvantage. Buccola and McCandlish observe: “Managers of the state firm and their supervisors within the civil service form a coherent lobbying group whose interest is to defend the enterprise from competition.” (Buccola McCandlish, 1999) In addition, SOEs take a quasi-monopoly position through limiting consumer choices and suppressing prices through quality reduction, which are often due to wastefulness that arises from the mixed incentives present. Additionally, the bureaucracy and opacity in these entities encourages corruption and embezzlement.

Accordingly, an OECD survey found: “fortytwo percent of 347 SOE respondents report that corrupt acts or other irregular practices transpired in their company during the last three years” (OECD, 2018) As discussed previously, such behaviour is detrimental to GDP growth; consequently, the disruption of markets by the government creates an obstruction to development of the economy.

The intervention and resultant distortion of the free marketplace is also a trait present in strong governments, often through SOEs. Advocates of such market intervention postulate that market control ensures the beneficiaries include stakeholders and not solely shareholders.

Unfortunately, a principal-agent problem arises when the objective of management, the success of the business, and the government’s The 30

government’s

role

in

society

is

undeniably indispensable as it upholds laws that protect the free market and guarantee the validity of contracts, which are both essential for economic growth by providing stable business conditions. Although one cannot invariably assume that a strong state is always a barrier to GDP growth, proved by the example of Singapore, the

intrusive actions characteristic of strong states may incur agency dilemmas and cause the warping of free-markets that impede the development of the economy. Examples of laissez-faire successes such as Hong Kong prove that a strong state is absolutely not a requirement for economic growth.

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Languistic and Change: Mercardo

A brief introduction - Bernardo

Language is the primary way humans communicate, whether signed or spoken.

It is well-known that it affects the way we view things, from tenses, pronouns and even gender. However, language constantly changes and evolves. There are many factors which cause this, ranging across different fields, including psychology, philosophy and sociology. This is only meant to serve as an introduction into the very many effects, changes, forces and ideas have within semantics and linguistics.

the way we assign words with objects and meanings is not arbitrary. The causes are not clear, though it is speculated that it has to do with the consonants like /k/ and labial consonants like /b/, and connections between the sensory and motor areas of the brain - also relating to the potential evolutionary origins of language, with its common occurrence even among young children. This arguably represents a close similarity with the condition of synesthesia, where stimulation of one sensory or cognitive pathway causes involuntary stimulation of another - it is well-known for causing the Semantics perception of numbers, letters and days Semantics - from Greek (significant). It is of the week to be coloured. This would the field concerned with meaning. Today, further suggest a neurological basis for one can search up the etymology of words phonesthesia. in nearly all languages from Icelandic to Bengali. Both these languages belong to the Another similar thing of interest is the word Indo-European family, bringing the words for ‘mum’ and ‘dad’ around the world back to the theorised Proto-Indo-European. pronounced ‘mama’ and ‘baba’ in Chinese, Similarly, you can follow a similar path with mama and tata in Quechua, and mama and other languages outside, revealing other papa in Russian too; it is evident that they language families - Sino-Tibetan, Niger- share huge similarities, and that the word Congo, Uralic, and many more. This is for mum and dad is almost universal even the simpler way to answer - ‘Why does it outside of non-Indo-European languages.

This is given a cause however, and is mean what it does?’ attributed to the sounds a baby can first However, beyond this, why attach specific make: m, p and b - and mom from the meanings to certain sounds and the murmurs during breastfeeding, relating first corresponding sequence of signs? This is to food before mother (Jakobson, 1971, p.26the more important question within this 7). area. One of the most important effects is the Bouba/Kiki effect. The participant is shown two shapes, one rounded and one jagged, and are asked which shape is ‘Maluma (variant on Bouba)’ and which is ‘Takete (variant for Kiki),’ (Köhler, 1947). Names can vary to an extent but remain phonetically similar. There is a clear preference by participants to name the circle ‘Bouba,’ and the jagged one ‘Kiki,’ chosen by 95-98% of participants (Ramachandran Hubbard, 2001). The results have implications - primarily that

Sociolinguistics and change Meanings of words change. Examples are not hard to find - for example, the word ‘awful’ previously meant to be ‘full of awe,’ and the meaning of the word has since changed to have a decidedly negative connotation. The causes behind changes are often complex, and there have been many attempts since the 19th century to organise the way languages change and evolve, and semantic shifts too.

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A first example of semantic shift is relevant to the current status of English as the lingua franca of the world - words can experience change by widening or borrowing semantic meaning, like the word ‘star’, which in many languages, expanded to include the English meaning ‘famous/talented person.’

Other examples are more socially and culturally motivated (sociolinguistics). For example, in the realm of queer and LGBTQ+ culture, there are cases of ‘reclaiming’ words - indeed, the word queer was a case of reclaiming. It has meant strange or odd, however, this previously had always come with negative connotations and became a slur for the gay community.

The word was reclaimed starting in the late 80s in the spirit of pride and has expanded to mean anyone who is not heterosexual, or as a replacement for the LGBTQ+ label.

Similarly, the word lesbian used to mean a woman who was ‘mannish’; however, an activist group called the Lesbian avengers came about in 1992, whose actions involved showy political messages - and as a large movement, were able to change the meaning of the word lesbian. This can also have implications within linguistic theory and philosophy: the usage of queer as a broader term, whether to avoid labels or as a replacement for LGBTQ+, comes into contrast with Russell’s theory of descriptions, words being shorthand descriptions of things - as it is not necessary to know the letters and meanings within the LGBTQ+ acronym. Lesbian too during the time of its semantic shift is a clear example of the importance of context (comparing from 1992 a male politician and an activist saying: ‘Washington D.C.is full of goddamn lesbians’), which is explored in Wittgenstein’s Language-game, likening language to acting (Thorn, 2019).

Interesting other cases emerge with the evolution of language - quite clearly the English spoken today is quite different to that spoken in the time of Shakespeare -

and these shifts continue today with new words being accepted - and with the advent of the Internet and the many communities there, introducing another ‘language game,’ and new contexts, acronyms and words (e.g. whomst, lmao). It is often, and incorrectly, regarded as wrong or subverted, incorrect because through a scientific lens, we cannot say such changes are good or bad. More evolution occurs through distance, and therefore from sociocultural and geographical context - with distance separating Spanish spoken in Spain and Portuguese from Portugal from the other dialects of those languages in Latin America, and certain distinct colours not being present in some languages. The latter has also been organised into levels by Berlin and Kay in Basic Color Terms: Their Universality and Evolution (1969) - starting with just dark and light, then red, and progressing through these levels.

Closely linked is African American Vernacular English (AAVE), which has a history of being misunderstood as incorrect English or slang. It is associated with and spoken by black people in America, though most are also bi-dialectal and can ‘codeswitch’ with General American English. Its roots are theorised - however, it is suggested it either originated from Early Modern English - and diverged as slaves brought from Africa would have spoken with each other far more than with other groups, a situation which has changed. However, this remains with American cities as segregated as they still are. This dialect would have been spread all over the country with the events of the Great Migration. The other suggests it was formed from a creole of African languages spoken by those brought over (Yoruba, Igbo, etc.) with English, and continued to be influenced by English.

However, it still has its own rules, and is not English ‘with mistakes’. For example, it treats double negatives in a different way, reinforcing the negative, rather than cancelling out (this is a feature shared

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in other languages, including in earlier forms of English). It also introduces the habitual be: indicating a habit or something someone might ordinarily do and is why Cookie Monster ‘be eating’ cookies, even if not shown to be (Jackson and Green, 2005). It is this dialect of English that has also backed up racism and the assertion that Black people are less intelligent and contributed to the eugenics debate in the early 20th century - and language, along with socioeconomic factors, were forgotten largely in these studies.

Concluding In ending this introduction, I should remark that there are still many more regions to discover within linguistics - this has covered social and cultural areas more; however, there are huge amounts of research into grammar and more practical parts of languages as well - and languages remain a crucial component of this, therefore having experience with them too is incredibly useful for communicating over barriers and wider research. And the field will remain of interest, as current political events continue to unfold, and the Internet continues its existence.

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The Acoustics of an Organ - Nithin Simanand At Radley college, we have all heard the organ and have had various degrees of experience with it; some only ever hearing it in chapel, some attending the recitals and some learning to play the instrument.

Whichever category you may fall in, it is easy to appreciate that as an instrument, the organ is sophisticated, and its complex tone is dependent on a multitude of factors.

The characteristics of the building plays a massive role as it affects the sound that finally reaches the listener. However, it is no surprise that acoustics is a precise science and in fact to achieve the perfect tone, many factors must be considered. These include the volume of air in the building per person, materials used in the construction of the building and where the different materials are, the shape of the different planes that Let’s first consider it’s past. The organ make up the building etc. “One general rule was invented around 280BC and was used to achieve this is to allow a minimum of 250 widely in the ancient Greek and Roman cubic feet of volume for every person.” world. However, this was a very different instrument to the modern pipe organ. It The tone is so easy to affect that we can used water (as opposed to electricity) as the notice the change as the season changes, source of power to blow the air in the pipes. and we go into summer dress. Listen out It was used predominantly during games and for it and you will notice that 700 boys plus races such as chariot racing and the gladiator dons wearing two layers of sound dampening fights. Over time the instrument became layers fewer makes a difference. The tone popular in Europe and organs were installed is also altered by changes to temperature in churches, town halls, synagogues, and and humidity in the building. Both factors other performance venues such as in the change the pressure of the air and by extension affect the sound wave travelling royal albert hall in London. through them.

The organ is built and tuned depending on the building it is in. The first thing to consider is the use case of the organ. An organ built in a hall for performances will be different to that accompanying a choir.

Even then, one accompanying a small chapel choir will vary vastly with one accompanying a large cathedral choir.

Figure 1: Example of different organ designs

However, the biggest factor lies in the instrument itself. The organ has three key components that need to be placed strategically for the best possible sound: The console, the blower and the pipes. The console has the manuals, footboard and stops. The ‘manuals and footboard’ control which note is played and the ‘stops’ are used to select which pipes the air needs to 35

flow through. A large stop simply means that the pipes are longer, the actual stops themselves are the same size. The blower is a pump that blows air through the pipes specified by the notes played and the stops used. Different sets of pipes have different sounds and volume which are governed by the length and shape. They can be flutes or reeds. In flutes, the sound is produced from air flowing past an opening, whereas in reeds, it’s created by a vibrating piece of brass. The length of the pipes controls the octave of the notes. They can be 2, 4, 8, 16, 32 and even 64 feet in length (0.6, 1.2, 2.4, 4.8, 9.6 or 19.2 meters). Some stops cause air to flow through a mixture of pipes and are therefore called ‘mixtures’.

A combination of these give the organ it’s unique yet instantly recognizable tone.

The tone will be chosen by the organist by selecting appropriate stops and varies from piece to piece, often changing during a piece. It is not hard to imagine how much space such an instrument will take, the biggest of which is shown occupying 310(W)x137(H)x456(L) feet.

This begs the question: where does it all go? The answer, however, is not what one would expect. Some Chapels, churches, etc, have the luxury of space and simply have massive sets of pipes that are 64 feet in height, the longest in the world.

at Atlantic City; the other is a Contra Trombone at the Sydney Town Hall.

Therefore the answer to the question above is simply: it doesn’t. This is where the element of acoustics plays its best card, the illusion of deeper sound. When two pure tones (a sound with a sinusoidal waveform) are played, they combine to create two more sounds, with frequencies which are the sum and difference of the first two. This means that stops that are much smaller can be used to produce lower frequency tones that usually require a bigger set of pipes. This bass is called resultant bass and the new organ in Radley will have a stop with a resultant 32 feet bass though it is “only” 16 feet in length. This occurs at all frequencies but is most prominent at the lower, bass register.

So to summarize, the organ is the largest instrument in the world and is very old.

It has been used in a variety of different locations across the world and can create a vast variety of tones and sounds that are distinct and instantly recognizable.

However, there is a decline in the number of organists as there is a decline in the number of functioning organs, due to the cost, size and maintenance of the organ. As an example, during warden’s music every year you see how long it takes for the orchestra to tune using one note. Now imagine tuning There are only two true 64 foot stops in every single note on every single instrument existence. One is the Diaphone Profundo one at a time!

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Why Don’t We All Speak The Same Language - Toby Loftus If the Bible is to be believed, everyone did once speak the same language. However, after constructing a tower in Babylon that glorified their achievements, God punished them by ensuring they all spoke different languages, so that they could never work together again.

said that although this is why languages originally differ, it proves no hindrance today against us combining them all into one. But the foremost principle of language is communicating efficiently and articulately, and new unnecessary words prove not much immediate use, and with no sense of immediacy or necessity, a universal To go with a more scientific theory, humans language is unlikely to catch on. originally communicated in different tongues as a result of long-term geographical Humans have a desire for tribalism, separation. We are said to have appeared naturally. We like organising ourselves into in Africa about 200,000 years ago, but only groups, and by extension, creating walls developed a capacity for language 50,000 of communication.

It’s this philosophy years ago, and so as the first humans that led to even more varying dialects dispersed around the globe, different for the earlier groups, and still today it’s language evolved in different areas. We what counteracts the movement towards are genetically wired with primitive forms a more global way of communication that of communication such as a smile or a the internet and long distance travel have laugh, and every language contains the same brought about. Not everyone wants to parts of speech. It’s only the words and lose what makes their background unique, their order that distinguish all 6500 which which explains increasing efforts to retain have active speakers today - an impressive dying languages such as Welsh. So it’s now figure considering we all have the same vocal that we must consider the value of today’s apparatus for speech. many languages, and whether a modern world would benefit from an artificially Geographical separation dividing up constructed universal language. A unified languages is still seen on a reduced scale humanity sounds appealing, so why isn’t today.

The UK’s official language is there such a language already in existence?

English, but the distance between different regions means it has split into many Esperanto is a 19th century attempt to different dialects, and someone with a actualise this concept, and was created traditionally Cornish accent may have from a mixture of Romance and Slavic trouble understanding someone with a languages, with a goal of serving as the typical Glaswegian accent, even though they universal second language. But although are supposedly speaking the same language. there have been experiments like this, none of them have been genuinely recognised But there is still the question of why as the international auxiliary language languages didn’t emerge slightly more (one meant for communication between similar and interconnected. This is largely people who don’t share a common first due to the contrasting nature of the world, language) as they simply haven’t caught and the popular myth that the Eskimos on. So despite Esperanto having an active have 100 words for snow demonstrates the community of possibly 2 million speakers same point. We all have such different worldwide with increasing opportunities to daily experiences that it’s not surprising learn online, it hasn’t achieved its goal of we have dissimilar vocabulary. It could be becoming the universal second language, 37

and its users are regarded by critics as a ‘stateless diasporic linguistic group’. This essentially means the population of speakers is thinly dispersed and not ruled by a state or government. It offers little hope for the future, because as the founder described himself, no language can survive without a closely supportive community of speakers.

These proposals of encouraging the world to speak the same language haven’t worked due to the combined reasons of a suitable language being too difficult to create, and people either being unable or unwilling to learn it. There must be a desire to learn a new language, and currently, no language is perfect or completely regular which is something that appeals to speakers, surprisingly. There is a desire to play with language, which is satisfied by abnormal turns of phrase and peculiarities which give a language character. Idioms and similar verbal oddities that have accumulated over millennia cannot be replicated in an artificially constructed language. There is an absence of history and culture behind an artificial one, and so the appeal of learning it suddenly disappears. We cannot possibly assimilate the world’s 6500 languages, and by extension heritages and values, into one immense universal one, not only because it would be impossible to capture all the detail, but because it wouldn’t be right to concentrate what makes this planet so impressively diverse into one dialect.

Even if everyone agreed with the idea of reducing the number of languages, no one would readily surrender their own, which leads to an impossible situation. So instead, we’re seeing that linguistic diversity is on the increase, and more UK schools encouraging Welsh to be learnt as a second language is an example of diversity being praised in all areas, which for languages such as Esperanto, is a movement in the opposite direction. Finland is a model example of a country with two equal national languages (Swedish and Finnish) whilst Manchester is proud to call itself Britain’s city of

languages, with an estimated 200 spoken by long-term residents there. The admirable qualities of multilingualism are widely recognised.

Politically, there is trouble with a universal language, as world leaders in countries like China would be abandoning an important part of their culture in favour of something that would likely have a Latin alphabet resembling European languages, which would consequently become unquestionably dominant. Esperanto speakers were widely persecuted under Stalin and Hitler too.

Moreover, an international body inventing a language and demanding that it be taught in schools worldwide would require an immense amount of global cooperation, unexampled in human history. This vast scale of coaction would be implausible if many nations weren’t in favour of the idea anyway.

All in all however, this is about the individual.

Just 84% of the world’s adults are literate, and it’s very easy for the developed world to set this giant goal, but many who don’t have access to learning resources cannot be expected to learn a whole new language. Perhaps a new language is unnecessary anyway, because we already have popular solutions in overcoming the language barrier, such as English as an auxiliary language. It’s already used by over half of Europeans in everyday life, with many terms currently adopted by other languages, and a vast architecture of support behind it. New translating technology also renders a universal language slightly more unavailing.

But supposing that despite it all, a perfect international language is created.

It’s now that the critical issue is discovered.

Language evolves far too quickly for just one. In a few decades, we’d find the language divided up into numerous different ones anyway, because as long as the human population live on different sides of the

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Earth, we will not communicate identically.

Our language is influenced by culture.

Fragments of indigenous slang would slip into ordinary language (as happened in the case of French slang, Verlan, with words appearing in the dictionary) and soon, these different dialects would become separate languages.

There are a number of reasons why we don’t speak the same language overall, and today,

a universal one is hindered by the same fallacy that has prevented so many other movements: we cannot create an entirely new start, and hope that the new effort will proceed by its own momentum. Each current language is supported by its native speakers, its history, and the locations where it’s spoken, but for an artificial language, there’s an absence of such a foundation.

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The Pythagorean Proposition - RDS In mathematics we like to prove things. And if something has been proved then we like to look for other, neater ways of proving it.

In 1940 Elisha Scott Loomis published a book called The Pythagorean Proposition containing 370 different proofs of Pythagoras’ theorem. Here are five of my favourites.

Proof 1: Leonardo da Vinci (1452 - 1519) We start with a right angled triangle ABC with squares BDEC, ACKH and AGFB drawn on the sides. We then add a rotated copy LED of ABC and also the lines AL, FA, AK, GH. Note that FAK is a straight line as ∠ FAK = 45° + 90° + 45° = 180° Also note that triangle AGH is congruent to triangle ABC (AB = AG, AC = AH, ∠ BAC = ∠ GAH).

Now the diagram has four congruent quadrilaterals: FGHK is congruent to FBCK (reflection in FK) which is congruent to LECA (rotation about C) which is congruent to ABDL (rotation about midpoint of AL).

Taking these in pairs it follows that area BCKHGF equals area ABDLEC. Taking away two copies of triangle ABC from each gives area ABFG + area ACKH = area BCED. So AB2 + AC2 = BC2 H G K

A F

B

C

D

E

L

Proof 2 This is one of the nicest. Four copies of a right angled triangle make up the shape below. b

a

b

a

c

c

It is easy to show that the centre shape is a square so the area can be calculated in two ways: 1

(𝑎𝑎 + 𝑏𝑏)2 = 𝑐𝑐 2 + 4 × 𝑎𝑎𝑏𝑏 2

c

c

b

a

∴

𝑎𝑎 + 2𝑎𝑎𝑏𝑏 + 𝑏𝑏 = 𝑐𝑐 + 2𝑎𝑎𝑏𝑏

∴

𝑎𝑎2 + 𝑏𝑏 2 = 𝑐𝑐 2

2

2

2

a

b

A proof very similar to this is attributed to James Abram Garfield, 20th president of the United States. I am not aware of any mathematical proofs associated with more recent presidents.

Proof 3: Atscharja Bhaskara (1114 - 1185) Alternatively we could arrange the triangles as follows Now

c

1

4 × 𝑎𝑎𝑏𝑏 + (𝑏𝑏 − 𝑎𝑎)2 = 𝑐𝑐 2

a

c

2

b

b a

a b

2𝑎𝑎𝑏𝑏 + 𝑏𝑏 2 − 2𝑎𝑎𝑏𝑏 + 𝑎𝑎2 = 𝑐𝑐 2

∴

𝑎𝑎2 + 𝑏𝑏 2 = 𝑐𝑐 2

b c

a

c

∴

Proof 4: Thānit (826 – 901) The following diagrams illustrate a neat way of cutting up two small squares to make larger one. It is not difficult to show that this fits together correctly. Pythagoras’s theorem is proved in the process.

c

b

a

c

a

b

Proof 5: Using similar shapes and area ratios Take a right-angled triangle and draw an altitude (line from the vertex C which is perpendicular to the base AB).

C.

b

a

A c

D

B

Triangles CBD, ADC and ABC are similar and their length ratio is a : b : c Therefore their areas are in the ratio a 2 : b 2 : c 2 So we can call the areas ka 2 , kb 2 and kc 2 for some constant, k.

But clearly area CBD + area ADC = area ABC, so ka 2 + kb 2 = kc 2 and a 2 + b 2 = c 2 .

RDS

The Cure in The Root of The Predicament - Adam Mohammad Hilmi Introduction The 21st Century saw the world plunge into the beginning of a frightful chapter; global warming and our heightened consciousness of the deteriorating environment as well as the political and economic difficulties that affect human rights. Delving deeper into the conundrum, it is easy to see that the roots of these issues trace all the way back to the ‘Tyger’ of the 18th Century.

The industrial revolution took the world by storm as coal became the primary energy source used to power the heavy machinery that drove industrial growth. Alongside that growth came unforeseen costs that humanity continues to pay till this day.

The Root In the 18th Century, levels of manufacturing were reached that were never before thought possible and with the progress came the potential to carve a fortune; a motivation that far overshadowed the calamitous effects of exponential development in industry. The utilization of the steam engine, through the combustion of coal and petrol was the flint that sparked the unsustainable amount of greenhouse gasses that, even until now, is being released into the atmosphere. Massive booms in industry accompanied by the limited regulations of the 18th Century translated to the ingraining of irresponsible behavior, the negligence of social costs in production, within firms for generations to come.

It was common practice for waste to be dumped into rivers and for ashes to be scattered across the streets.

Humanity progressed forward in commerce and technology, but the global ecosystem paid the price.

It is also theorised, that although child labour had historically existed for thousands of years usually in the case of children helping their parents on farms, it was the large up-scale of production during the Industrial Revolution that propagated the use of children in industry in ways which were far more dangerous than their agrarian work. Some historians even suggest that the 19th century was when child labour ‘peaked’ in the United States. This could simply be due to an increase in population but could also be the result of greater demand for work in the exponentially growing industry, which would be positive, if it was not imposed on children who would then be exploited as ‘cheap labour’ by manufacturing firms.

Children took on roles in the mining industry which were highly dangerous including ‘hurriers’, who were tasked with pushing carts weighing up to 400kg in the precarious settings of the mines. They risked being trapped in mines and consequently dying of hunger. Additionally, children were potentially exposed to toxic gasses and also risked drowning in groundwater or being buried alive. The conditions in factories weren’t much better with children being exposed to boiling hot machinery and hazardous equipment. Children were forced to work unbearably long hours resulting in potential injuries and accidents which were routinely neglected by firms without

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any compensation. It’s obvious that the immoral practices of the past have resulted in current day issues regarding child abuse in labor. This is because practices in Britain at the time were also abominably used in the colonies ranging from Malaysia to Jamaica. In addition, the still persisting use of children for labor prevents their engagement in education which directly correlates to income inequality as children are unable to escape the cycle of poverty.

The Cure Ironically however, the latter half of this article aims to present the argument that technological advancement, though argued to be the root of the problems, is the best process to cure the issues of the SDGs. Technological advancement can mean a plethora of things. However, in the context of this article, it may loosely be defined as improving machinery today, through innovation and scientific methods to become more efficient in their own rights and to be able to perform more tasks. It can be argued that technological advancement may be able to positively impact up to 70% of the SDG aims.

The aforementioned statements are made to suggest that many of the current day problems that humanity faces, as reflected in the United Nations Sustainable Development Goals (hereby: SDG), can be traced back to their origins which is argued to be the Industrial Revolution of the 18th Century.

The Industrial Revolution was only made possible by the advancement of technology and thus one may even go so far as to claim that technological advancement is the root of our global issues to date.

Take the issue of global warming, arguably the biggest crisis that the current generation will face.

Governments are forced to decide between implementing tax policies or proposing advertising campaigns or other alternative methods but it can be

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argued that investing in STEM research is the best foot forward. More investments in research increases the likelihood of successfully developing new technologies, such as solar power and wind power, to become more efficient. This would result in an increase of their application in the energy industry which would be the most significant way of reducing CO2 emissions through the replacement of combustion in energy generation. Changing social habits would take far too long and is unlikely to produce significant impact with the exponentially growing global population.

The world needs energy; taxes and social campaigns simply are not enough to deter the consumption of fuel thus the best solution is the establishment of a more sustainable alternative, the 7th SDG. Furthermore, the decrease in pollution that would result from the transition of using the greener energy will also help in protecting life below water and life below land, the 14th 15th SDG. This could be attributed to preventing suffocation in animals from debris as well as simply slowing down the increasing global temperature which directly impacts biodiversity.

abundant sea water. Furthermore, investing into STEM Research and Education can provide the prospect of the establishment of lucrative businesses that will market the newly found, more efficient, more beneficial, technologies. This may create more jobs globally allowing for more economic growth, the 8th SDG. Finally, investing into STEM Education will obviously increase the quality of its deliverance and the impact of the knowledge taught, likely resulting in a more innovative demographic in the long run, both the 4th 9th SDG.

More scientific research in endeavors such as bio-insulation and composting alongside the development of new technologies to facilitate them can lead to their wider scale use, due to their new ease of implementation which can in turn be pivotal in creating more sustainable cities; the 11th SDG. Greater research into optimizing water purification systems, combined with more sustainable energy alternatives could provide a solution to the lack of clean water world-wide, the 6th SDG. This would be through utilizing a more efficient and sustainable aqua-distillation system that would use the condensation of steam sourced by the

Conclusion The potential for technology to create an everlasting impact is substantial however it is important that humanity moves forward with caution, in reflection of the past.

Technological advancements, in the right direction, is certainly the cure to many global conundrums. Nevertheless, traversing into more contentious and dangerous technologies, like artificial intelligence or CRISPR, though baring the prospects of being incredibly useful and profitable, should still be done carefully or humanity may find itself in yet another difficult predicament.

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Special Announcement This edition of the Serpentes comes with three £100 prizes to the best article as judged by the Academic Prefects and the Editorial Team. We are happy to announce the following winners: 6.1/6.2: Giorgi Gvaradze(J) Remove/Vth: Hyunjo Kim(J) Shell: Blake Williams(A) Special Commendation: Russell Kwok(C)

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Thank you for reading this edition of Serpentes If you wish to submit an article for the next edition please send it to: mark.lertiendumrong2016@radley.org.uk