Art vs. Science

All intellectual human activity can be divided into one of three categories; the arts, humanities, and sciences (although these terms are not exactly fully inclusive). Art here covers everything from the painted medium to music, everything that we humans do that is intended to be creative and make our world as a whole a more beautiful place to live in. The precise definition of ‘art’ is a major bone of contention among creative types and it’s not exactly clear where the boundary lies in some cases, but here we can categorise everything intended to be artistic as an art form. Science here covers every one of the STEM disciplines; science (physics, biology, chemistry and all the rest in its vast multitude of forms and subgenres), technology, engineering (strictly speaking those two come under the same branch, but technology is too satisfying a word to leave out of any self-respecting acronym) and mathematics. Certain portions of these fields too could be argued to be entirely self-fulfilling, and others are considered by some beautiful, but since the two rarely overlap the title of art is never truly appropriate. The humanities are an altogether trickier bunch to consider; on one hand they are, collectively, a set of sciences, since they purport to study how the world we live in behaves and functions. However, this particular set of sciences are deemed separate because they deal less with fundamental principles of nature but of human systems, and human interactions with the world around them; hence the title ‘humanities’. Fields as diverse as economics and geography are all blanketed under this title, and are in some ways the most interesting of sciences as they are the most subjective and accessible; the principles of the humanities can be and usually are encountered on a daily basis, so anyone with a keen mind and an eye for noticing the right things can usually form an opinion on them. And a good thing too, otherwise I would be frequently short of blogging ideas.

Each field has its own proponents, supporters and detractors, and all are quite prepared to defend their chosen field to the hilt. The scientists point to the huge advancements in our understanding of the universe and world around us that have been made in the last century, and link these to the immense breakthroughs in healthcare, infrastructure, technology, manufacturing and general innovation and awesomeness that have so increased our quality of life (and life expectancy) in recent years. And it’s not hard to see why; such advances have permanently changed the face of our earth (both for better and worse), and there is a truly vast body of evidence supporting the idea that these innovations have provided the greatest force for making our world a better place in recent times. The artists provide the counterpoint to this by saying that living longer, healthier lives with more stuff in it is all well and good, but without art and creativity there is no advantage to this better life, for there is no way for us to enjoy it. They can point to the developments in film, television, music and design, all the ideas of scientists and engineers tuned to perfection by artists of each field, and even the development in more classical artistic mediums such as poetry or dance, as key features of the 20th century that enabled us to enjoy our lives more than ever before. The humanities have advanced too during recent history, but their effects are far more subtle; innovative strategies in economics, new historical discoveries and perspectives and new analyses of the way we interact with our world have all come, and many have made news, but their effects tend to only be felt in the spheres of influence they directly concern- nobody remembers how a new use of critical path analysis made J. Bloggs Ltd. use materials 29% more efficiently (yes, I know CPA is technically mathematics; deal with it). As such, proponents of humanities tend to be less vocal than those in other fields, although this may have something to do with the fact that the people who go into humanities have a tendency to be more… normal than the kind of introverted nerd/suicidally artistic/stereotypical-in-some-other-way characters who would go into the other two fields.

This bickering between arts & sciences as to the worthiness/beauty/parentage of the other field has lead to something of a divide between them; some commentators have spoken of the ‘two cultures’ of arts and sciences, leaving us with a sect of sciences who find it impossible to appreciate the value of art and beauty, thinking it almost irrelevant compared what their field aims to achieve (to their loss, in my opinion). I’m not entirely sure that this picture is entirely true; what may be more so, however, is the other end of the stick, those artistic figures who dominate our media who simply cannot understand science beyond GCSE level, if that. It is true that quite a lot of modern science is very, very complex in the details, but Albert Einstein was famous for saying that if a scientific principle cannot be explained to a ten-year old then it is almost certainly wrong, and I tend to agree with him. Even the theory behind the existence of the Higgs Boson, right at the cutting edge of modern physics, can be explained by an analogy of a room full of fans and celebrities. Oh look it up, I don’t want to wander off topic here.

The truth is, of course, that no field can sustain a world without the other; a world devoid of STEM would die out in a matter of months, a world devoid of humanities would be hideously inefficient and appear monumentally stupid, and a world devoid of art would be the most incomprehensibly dull place imaginable. Not only that, but all three working in harmony will invariably produce the best results, as master engineer, inventor, craftsman and creator of some of the most famous paintings of all time Leonardo da Vinci so ably demonstrated. As such, any argument between fields as to which is ‘the best’ or ‘the most worthy’ will simply never be won, and will just end up a futile task. The world is an amazing place, but the real source of that awesomeness is the diversity it contains, both in terms of nature and in terms of people. The arts and sciences are not at war, nor should they ever be; for in tandem they can achieve so much more.



One of the most endlessly charming parts of the human experience is our capacity to see something we can’t describe and just make something up in order to do so, never mind whether it makes any sense in the long run or not. Countless examples have been demonstrated over the years, but the mother lode of such situations has to be humanity’s invention of counting.

Numbers do not, in and of themselves, exist- they are simply a construct designed by our brains to help us get around the awe-inspiring concept of the relative amounts of things. However, this hasn’t prevented this ‘neat little tool’ spiralling out of control to form the vast field that is mathematics. Once merely a diverting pastime designed to help us get more use out of our counting tools, maths (I’m British, live with the spelling) first tentatively applied itself to shapes and geometry before experimenting with trigonometry, storming onwards to algebra, turning calculus into a total mess about four nanoseconds after its discovery of something useful, before just throwing it all together into a melting point of cross-genre mayhem that eventually ended up as a field that it as close as STEM (science, technology, engineering and mathematics) gets to art, in that it has no discernible purpose other than for the sake of its own existence.

This is not to say that mathematics is not a useful field, far from it. The study of different ways of counting lead to the discovery of binary arithmetic and enabled the birth of modern computing, huge chunks of astronomy and classical scientific experiments were and are reliant on the application of geometric and trigonometric principles, mathematical modelling has allowed us to predict behaviour ranging from economics & statistics to the weather (albeit with varying degrees of accuracy) and just about every aspect of modern science and engineering is grounded in the brute logic that is core mathematics. But… well, perhaps the best way to explain where the modern science of maths has lead over the last century is to study the story of i.

One of the most basic functions we are able to perform to a number is to multiply it by something- a special case, when we multiply it by itself, is ‘squaring’ it (since a number ‘squared’ is equal to the area of a square with side lengths of that number). Naturally, there is a way of reversing this function, known as finding the square root of a number (ie square rooting the square of a number will yield the original number). However, convention dictates that a negative number squared makes a positive one, and hence there is no number squared that makes a negative and there is no such thing as the square root of a negative number, such as -1. So far, all I have done is use a very basic application of logic, something a five-year old could understand, to explain a fact about ‘real’ numbers, but maths decided that it didn’t want to not be able to square root a negative number, so had to find a way round that problem. The solution? Invent an entirely new type of number, based on the quantity i (which equals the square root of -1), with its own totally arbitrary and made up way of fitting  on a number line, and which can in no way exist in real life.

Admittedly, i has turned out to be useful. When considering electromagnetic forces, quantum physicists generally assign the electrical and magnetic components real and imaginary quantities in order to identify said different components, but its main purpose was only ever to satisfy the OCD nature of mathematicians by filling a hole in their theorems. Since then, it has just become another toy in the mathematician’s arsenal, something for them to play with, slip into inappropriate situations to try and solve abstract and largely irrelevant problems, and with which they can push the field of maths in ever more ridiculous directions.

A good example of the way mathematics has started to lose any semblance of its grip on reality concerns the most famous problem in the whole of the mathematical world- Fermat’s last theorem. Pythagoras famously used the fact that, in certain cases, a squared plus b squared equals c squared as a way of solving some basic problems of geometry, but it was never known as to whether a cubed plus b cubed could ever equal c cubed if a, b and c were whole numbers. This was also true for all other powers of a, b and c greater than 2, but in 1637 the brilliant French mathematician Pierre de Fermat claimed, in a scrawled note inside his copy of Diohantus’ Arithmetica, to have a proof for this fact ‘that is too large for this margin to contain’. This statement ensured the immortality of the puzzle, but its eventual solution (not found until 1995, leading most independent observers to conclude that Fermat must have made a mistake somewhere in his ‘marvellous proof’) took one man, Andrew Wiles, around a decade to complete. His proof involved showing that the terms involved in the theorem could be expressed in the form of an incredibly weird equation that doesn’t exist in the real world, and that all equations of this type had a counterpart equation of an equally irrelevant type. However, since the ‘Fermat equation’ was too weird to exist in the other format, it could not logically be true.

To a mathematician, this was the holy grail; not only did it finally lay to rest an ages-old riddle, but it linked two hitherto unrelated branches of algebraic mathematics by way of proving what is (now it’s been solved) known as the Taniyama-Shimura theorem. To anyone interested in the real world, this exercise made no contribution to it whatsoever- apart from satisfying a few nerds, nobody’s life was made easier by the solution, it didn’t solve any real-world problem, and it did not make the world a tangibly better place. In this respect then, it was a total waste of time.

However, despite everything I’ve just said, I’m not going to decide that all modern day mathematics is a waste of time; very few human activities ever are. Mathematics is many things; among them ridiculous, confusing, full of contradictions and potential slip-ups and, in a field whose age of winning a major prize is younger than in any other STEM field, apparently full of those likely to belittle you out of future success should you enter the world of serious academia. But, for some people, maths is just what makes the world makes sense, and at its heart that was all it was ever created to do. And if some people want their life to be all about the little symbols that make the world make sense, then well done to the world for making a place for them.

Oh, and there’s a theory doing the rounds of cosmology nowadays that reality is nothing more than a mathematical construct. Who knows in what obscure branch of reverse logarithmic integrals we’ll find answers about that one…