Artists, and by artists I dont mean just professional painters but anyone with an artistic temperament, people who doodle for fun, people who play instruments, people who buy macs, often talk to me in terms that make me think they have fundamentally misunderstood my life.
I count myself a scientist by temperament, and if some artists are to be believed that means I am cold and heartless. But more than that, it means I have no imagination, I dont really have the inner spark that makes one truly human, I'm an automaton, powered by laws and science and numbers. The world I live in is boring, because I cant see the beauty all around us, I just see atoms and rocks and bits of cogs. I cant appreciate music because I break it down and listen to the notes on the paper, not realising that the whole contains things that are not there in the parts. Because I'm a reductionist, that means that I break things down and refuse to believe that wholes have values and significance other than the sum of its parts. I have no sense of wonder and joy, because these things aren't in atoms and cant be written in maths. To use a biblical comparison, I'm Thomas, doubting, cynical, nasty, untrusting, unromantic all these things and worse. I dont see societies I see ruthless individuals, all trying to kill eachother, just like Darwin told them to. And I hate God, maybe because my father never loved me, but probably because I'm too evil to accept his love.
Ok, maybe I exaggerate a tad, but I've really not gone too far beyond what some people instinctively think. And you wont be surprised if I tell you that it's bullshit. Here I would normally explain the thought process of the artist and say why it's wrong. But I cant, because here I have no idea what the thought process is. So I'm just going to say why the conclusion is wrong.
An example, I was made to endure a lot of art lessons in school and you may be shocked to learn I wasn't very good. I mean that I'm not technically very good, I cant draw a structure I see well or neatly, I cant describe how an artist has achieved something because I cant see how to do it. This was described time and time again by my teachers as "it's ok, you're just not very creative" or "well I guess you just dont have as much imagination as the others". This was supposed to cheer me up, to say that it was ok, I practically had no soul or spark of humanity, but that wasn't a problem. Those teachers were woefully wrong. I have poor hand-eye coordination and a bad sense of perspective, that is not the same as having no imagination.
I have imagination, every scientist does, you need it to understand what's going on in the weird and unintuitive worlds scientists create. And yes, create, like creative. Scientists aren't Thomas, they aren't cynical doubters, that's far too simple. Scientists are Jacob. I'll let one of the 4 or 5 authors of what would later become Genesis explain:
22 That night Jacob got up and took his two wives, his two maidservants and his eleven sons and crossed the ford of the Jabbok. 23 After he had sent them across the stream, he sent over all his possessions. 24 So Jacob was left alone, and a man wrestled with him till daybreak. 25 When the man saw that he could not overpower him, he touched the socket of Jacob's hip so that his hip was wrenched as he wrestled with the man. 26 Then the man said, "Let me go, for it is daybreak."
But Jacob replied, "I will not let you go unless you bless me."
27 The man asked him, "What is your name?"
"Jacob," he answered.
28 Then the man said, "Your name will no longer be Jacob, but Israel, [the name means "he wrestles with God"] because you have struggled with God and with men and have overcome."
29 Jacob said, "Please tell me your name."
But he replied, "Why do you ask my name?" Then he blessed him there.
30 So Jacob called the place Peniel, [face of God] saying, "It is because I saw God face to face, and yet my life was spared."
Science does battle with God in a sense, we tear his creation apart and demand his secrets. Science is about probing to the heart of things, Hawking calls it "knowing the mind of God". Science is not a lowly pursuit made of doubting and being cynical of your fellow man. It means standing up to reality. It means confronting the whole universe and demanding that it tell you how it works, this is scientist as heroic figure. This story does not require a titan like Prometheus to steal the secrets from the gods, or the devil to tempt Eve. This idea of science requires Eve to not be content, it requires Eve to see knowledge and to take it, knowing the dangers, knowing the risks, because without it life is worthless. Man is not a fallen angel, he is an ape who has stood up and demanded things of the angels.
Now that's lovely in a flowery poetic sort of way, but it doesn't answer the question. Isn't all this science done in a boring, mechanical way, isn't the brain of the scientists essentially not a creative one but a rational one? No, not at all, rationality does not constrain boundless creativity. Let me give an example. One of my favourite poems is Cadaeic Cadenza. It's written in on of the most incredibly restrictive forms of writing imaginable, each word contains as many letters as the relevant digit in the decimal expansion of pi. And yet it's a very creative and funny work, it references many other great poems, has an interesting story and would genuinely be considered good poetry by someone who had never heard of pi. And yet the restraint makes it all that much better, with the constraint the author has had to think about every word, been forced to play with the odd metre and sentence structures this produces.
But surely, thinks the artist, scientists are even more constrained than this, they cant create a new theory, they just have to look at what's there and then do maths at it, right? Wrong, of course not. There is a vast landscape of physical theories about the universe, science is not deductive, you can invent totally new ideas about the universe, there is nothing in Newton that means Einstein had to happen, in fact there's a lot to stop it, there is no reason in principle that we couldn't have gone from newton to quantum mechanics to timeless quantum mechanics to some kind of quantum gravity without needing to get relativity involved at all. There are all kinds of practical, instrumental and mathematical reasons, but fundamentally science does contain scope and freedom to create new ideas.
But you're a mathematician, sure the physicists make stuff up, but you work on the timeless platonic realities, you cant make anything up. No, I cant, but I can still create. We can create new kinds of geometry, create new ideas about infinity, create new functions and new concepts. Sure, once we have laid out an idea any given theorem is either true or false (insert standard Gödel disclaimer), but as almost every theorem has an infinity of proofs and there are an infinity of theorems given any axioms there's vast scope to be creative, to find and display the most beautiful, the most rare, the most pure. An objet trouvé is art despite no creative input from the artist, the art is in seeing beauty and displaying it.
Ok, so there's creativity, but no imagination, the whole point of science is that thing are true, so there's nothing to imagine, you just have to look. Of course, this is stupid. Because science has always worked by explaining the world in terms of (to borrow the title of a TED conference) "the structure of things unseen". Science works by explaining the world in terms of things we cannot see, either because they are too small, too large, too far away, transparent or for some other reason hidden. For example, look up at the night sky, see the moon, when I do that, I zoom out in my mind, and I see the Earth I'm standing on and the sun far behind me, and I see all 3 twirling endlessly round eachother. Can you imagine that?
And the same is true of maths. Even in geometry, the most apparently visual branch of mathematics takes an awful lot of imagination to get from paper to the true image. Take multiple dimensions, consider a universe with 4 mututaly perpendicular directions, so you could go up-down, left-right, back-forward, ying-yang. Of course there's no direction yang in this universe, but what would it be like? What would you see if something 4D travels in a yingward direction through our universe? Imagining universes this dramatically different is important if you want to have an intuitive grasp of mathematics.
So if you need creativity and imagination to do anything with science then why cant I do art? For the same reason the Newton couldn't solve the Feynman integral near the event horizon of a rotating black hole. Issac Newton was the single most brilliant mind in the history of mankind, no superior intelligences exist. But I know more physics than he did, and I know how to demonstrate more things than he did. Why? Because intelligence, creativity, imagination is not the same as being able to do specific things.
Raphael, to my knowledge, never composed a single piece of music, he was as well trained a musician as I am a painter, and yet, nobody thinks it strange that a man so clearly imaginative could have so utterly failed to have left a mark on musical history. I would wager that Einstein was an infinitely superior violinist, and yet we call only one of them creative. Richard Feynman, the great quantum physicist, often mentioned that when people talked about him as scientist, they also mentioned that he played the bongos, to show he wasn't totally scientific. But not once when he was called upon to publicly play the bongos was he introduced as a bongo player who also did physics.
Beauty in science and maths
A lot of people say there is beauty in science and then show this picture. That's bull. That's not how art works and it's not how science works either. To show a bare image like this is great as a background, but it's not comparable to a work of art, this is a mere doodle. Can I make a comparison?
If you just look at this painting that's fine, but it's no good like that, the painting isn't very interesting, the proportions are all wrong and it's just dull dull dull. Until. Until you look at the title, the "Myth of Icarus". Until you find out what the Myth of Icarus is, remember the story of the boy who tried to fly with wings made of wax and flew too close to the sun. The wings melted and he fell into the sea. And there he is, just below the ship we see two legs sticking out. And that's the point of the painting. Icarus is a tragic heroic figure, he who tries to defy the laws of nature and who is killed by his experiment. And nobody notices, the ploughman, the shepherd, the fisherman, the entire ship, they're all looking the other way. This tragic figure dies ignored by the world, because everyone is too busy with their day to day lives to deal with this dreamer.
Now what of that can you get by putting this painting on an overhead for 30 seconds? Nothing at all! And the same is true of the works of art produced by the instruments of science. The image above is called the Hubble deep field. It was produced by pointing the Hubble space telescope at a patch of totally empty sky, as far as anyone could see with their eyes or with good telescopes there was nothing there at all. Hubble was left pointing at it like a camera doing a long exposure for 10 days. After that time the image came back to Nasa and astonished everyone. That patch of totally empty sky is in the Plough and is the same angular size as a tennis ball the other end of a football pitch. The spots you see in the image aren't dust or even stars, they're entire galaxies, each one containing hundreds of billions of stars like our sun, most of them with planets, at least some of them earth-like.
What this tells you is that the universe is massive, and there's so much in it. Behind each tennis ball the other end of a football pitch there are these thousands of galaxies, vast expanses of space, dizzyingly vast amounts of places to go and things to see. The lion king was right, there is far more to see than can ever be seen. The potential of humanity is vast, unbelievably vast. We've never left home on a cosmic scale and there's so much to do out there. That's why this image is important, this image is about human potential, about the great unknown. And just putting it up and saying "look science pretty" as much misses the point as just putting up the myth of Icarus without thinking about the meaning.
There is beauty too in maths, but again, merely staring at the Mandelbrot set isn't all of it. There's real beauty in the simplest of mathematical ideas. Take wallpaper, now people have been making patterned designs to go on walls and floors for as long as they've had walls and floors worth decorating, and there have been millions of repeating patterns. But what if you strip it down to the bare bones? What if we ignore that it's a repeated pattern of flowers and focus on the pure pattern as total abstraction? For instance, look at rotations.
Now wallpaper can have a definite orientation, so it looks different if you look at it from an angle. For instance these flowers, yo would know if someone hung this up at an angle.
Or this design, it looks the same if you rotate though half a full circle.
This design looks the same if you turn through a third of a circle.
This looks the same if you turn through a quarter of a circle
This looks the same if you turn through a sixth of a circle.
Now here's the beauty. I have to stop there. I cannot show you any more and I cannot show you five. Because we live in a world where walls are flat, 2D structures. And it is a fundamental deep property of the very space we exist in that you cannot have a regular repeating pattern that looks the same if you rotate it through one fifth of a circle. Or one seventh, or an eight, or any number at all other than 1, 2, 3, 4 and 6. We have exhausted the possibilities set, not just by our imagination or the skill of our craftsmen, but by reality itself. We can prove this rigorously, it's not hard. What we've done is learnt something fundamental, not about what is, but about what ever can be. We know some limits that are definite and absolute. We have reached into the very core of reality and discovered a limit that God himself could not overcome.
I have a problem with artists who think they understand what my world is like. Because my world is a world of beauty, of creativity, of imagination, of vast unimaginable depth. I have a problem too with the simplistic notion that you can fix this by showing some pretty patterns, you have to understand science before you can really enjoy it properly, just like art. The scientist is no more confined to lowly thoughts than the artist, we do not sit around cynically or get corrupted like Eve, we stand defiant and wrestle with God.