Creation or discovery?

Is there any difference between creation and discovery? This article argues there isn’t, so Mozart did not create any music, but he discovered his symphonies. Just as Pythagoras discovered a proof of the pythagorean theorem, J.K. Rowling discovered the story of Harry Potter.

In January 2016, a new worlds largest prime number was discovered. With a whopping 22.3 mio digits, this monstrosity surely is quite the number, but as always, the search continues and it probably won’t be long before the next, even larger one will be known.

This blog post is not about prime numbers however, but about discovery. No mathematician would say that these gigantic primes were created or invented by us, no we discovered them. They already existed somewhere in the abstract universe of the natural numbers. Using our incredible computing prowess, we went out there, searching, digging through the mud of non-primes until we found the gold nugget, the next gigantic prime.

This use of language is what you find all the time in the scientific and mathematical community. Newton discovered the laws of gravity and calculus, Pythagoras discovered a proof of the pythagorean theorem, Darwin discovered the process of evolution and I could go on and on.

This is very different from the language used in the world of the arts. Mozart created his symphonies, as well as Picasso created his paintings and J.K. Rowling created the world of Harry Potter.

But I will argue that there is fundamentally no difference between discovery and creation and just as the new Mersenne Prime was found, so did Mozart found his symphonies, he did not create anything.

This idea is not at all new though. For example, Michelangelo was quoted saying “Every block of stone has a statue inside it and it is the task of the sculptor to discover it”. But I will here try to formalize this very vague intuition and make it more precise and rigorous.

Lets explore the reasoning behind this idea.

Finding the space of all possible pictures

I will use the world of mathematics as a starting point, since this is something that very clearly illustrates my point and happens to be something I understand reasonably well.

If you asked a mathematician, he would say that all the numbers on the number line already exist somehow. We invented some fundamental rules about numbers, and from them the entire number line sprang into existence, but not in the real world. It exists in the abstract world of mathematics. So even though the number 75369356452613405764 most probably has never in the history of humanity been written out before, I did not ‘invent’ og ‘create’ it. It already existed, floated out there minding its own business in, what I would call, the abstract mathematical space.

Now, so if you buy my proposition that all numbers already exist and we just use them and discover them as we move along, what if we could convert, say, the painting of Mona Lisa into a number?

Then this number would too already exist and therefore so would the painting of Mona Lisa.

This is actually a quite trivial conversion to make. Let me illustrate.

First of all, for the sake of simplicity lets approximate the real painting of Mona Lisa to a 2d and pixelated counterpart. This is the kind of image that your computer can show you. Again for simplicity, let this image have 1,000x1,000 pixels, a 1,000,000 pixels in total. Have in mind this dimension is completely arbitrary and could literally be anything. Then we give every pixel three numbers from 0 to 999 that correspond to an intensity value of the three colors red, green and blue.

This is precisely the way your computer understands images (it actually uses numbers from 0 to 255, but that’s irrelevant). It doesn’t see colors or patterns, it only understands it as all these triplets of numbers between 0 and 999.

Then, for every pixel we take these three numbers and concatenate them to a single 9-digit number. So if a pixel has the values 120, 254 and 007, it concatenates to 120254007. Now we have 1,000,000 9-digit numbers that we again can concatenate to a single enormous 9,000,000 digit number.

Alright, so what exactly have we done here? We have formulated a way to convert an image to a number, and a very precise and definite way that is. Given any pixelated image we can easily convert it.

Not only that, we have shown that every single number that can be written with up to 9,000,000 digits corresponds to one specific image of size 1,000x1,000 pixels.

But all natural numbers already exist and we have made a precise mapping from numbers to images, so every single image possible (with a certain degree of detail) now exist as well.

It doesn’t matter what the painting looks like, it could be literally anything as long as it consists of 1,000x1,000 pixels. Mona Lisa, The Scream, your holiday pictures, random meaningless noise, Donald Trump wrestling a giant toad equipped with a lightsaber, you name it. Every single one has a number encoding it.

So there you have it. A (more) formal argument that any picture already exists in the abstract sense only waiting for us to discover them. We develop a mapping between numbers and paintings, and magically we have stumbled upon a vast abstract space of every conceivable image.

But there is absolutely nothing special about pictures. Sound, text, 3d-models, simulations, websites or anything that you can store on a computer we have already converted into numbers. This actually touches on a very deep topic, the topic of information. Anything that can be converted into information, you can store as numbers, and it seems like absolutely anything without exception can be converted to information. This topic is beyond the scope of this blog post though.

The difference between art and science

However, if you are like me, you will not really find this argument too satisfying. So yeah, you might be able to argue that the number corresponding to the Mona Lisa already existed and that therefore the painting already existed, somehow. But still, the process of creating a new image seems completely different to the process of discovering scientific facts about universe and exploring the fabric of reality. I will argue however that from the right perspective, they are very much alike.

For the rest of this post I will focus on music composition since music is something I understand quite a bit better than paintings. So lets have a look at the difference and similarities between composing music and discovering mathematical theorems.

We intuitively feel that there is a fundamental difference between composing a new song and finding a new prime number. But what is this difference?

When we talk about mathematical and scientific truths, they are extremely precise. Take a proof of the pythagorean theorem, make a slight random tweak, and it will most probably be completely and utterly wrong. You could imagine a lot of different explanations for why objects fall down, but only one is the correct one. When Newton began on his journey to figure out the mystery, if he succeeded there was really only one way his journey could end. With the correct explanation of gravity.

So when you want to discover hard facts about reality or mathematics, the goal is almost always predetermined.

This is also the reason why if Newton wasn’t born, someone else would have made his discoveries (and when it comes to calculus that someone was Leibniz). If Darwin had not existed, som other biologist would have solved the riddle of evolution sooner or later.

When it comes to facts there are not so many correct answers, so anyone truly trying to uncover whats real and whats not will inevitably converge to the same conclusions.

This is not at all the case for art. If Mozart had a goal of writing a beautiful symphony (whatever that means) there is a practically infinite amount of different ways he could succeed in that. There is not just one possible beautiful symphony, there is probably many, many more than the number of particles in the entire universe.

If you make slight tweaks to Eine Kleine Nachtmusik, it is still a great piece of music and would satisfy the goal of creating a beautiful symphony.

This is also the reason why if Mozart wasn’t born, nobody in the rest of the human history would ever compose Eine Kleine Nachtmusik. The number of possible symphonies is simply so vast as to make that probability zero for all practical purposes.

Try and consider these to different tasks: One is proving a mathematical theorem the other is composing a beautiful piece of music. Proving a well-formulated theorem is an incredibly precise job description with almost no wiggle room at all for what will be accepted as a solution.

Composing music however is the exact opposite. The idea of writing something that ‘sounds good’ is extremely vague and not at all well defined. What does it mean for a song to sound ‘good’? That question can have a thousand different good answers that would all be considered ‘correct’ by most people. There can be so many different ways in which music sounds good because the concept of ‘good music’ is so incredibly vague and undefined.

Not only that the evaluation of a song is non-binary. That means it is not only ‘good’ or ‘bad’. It can be a thousand things in between. A song can be a perfect use at a metal concert but a horrendous choice at a funeral and I could go on and on. A mathematical proof however is either true or it is not.

So we have established some core differences between art and science. But now that we have identified these differences, I will argue why they don’t really matter when it comes to discussing whether things are created or discovered.

Why music composition is an exploration

Lets actually get to music composition. First of all I have a proposition. Any time randomness is used it is inherently exploratory.

Imagine you have a bunch of different choices you could make, you don’t know beforehand which would be the best one, so you randomly try some of them out and chooses the best one. This is a discovery. You search through the possibilities without knowing beforehand what will work and what won’t.

But there is a lot of randomness in composition. You just try a lot of random things until you find something that works out. Imagine if not. Imagine if no randomness was involved at all. Then the entire process will be completely predetermined and every time you would try to compose a new piece, you would always end up with the exact same thing.

Let me illustrate how randomness can be used. Imagine a person who has never touched a piano before, played any kind of music and has no musical knowledge. If this person tried to compose something on a piano, the only thing one could do is to just randomly press some keys and discover what sounds good or not. At this point the creation process is nothing but a blind search. What note should follow the preceding? The person has no idea, tries a bunch of different ones and choses the best one. That is, the person discovers the next note to use.

Now lets say this blossoming composer learns some music theory and remembers musical patterns that work well.

He now has an understanding of chord progressions and scales and remember certain notes that fit well together.

The composing process is now much more guided and much less arbitrary, but it is still a discovery. Which note should follow the preceding one? Well, there are 88 keys on the piano, but the composer knows heuristically that perhaps 6 of the 88 notes has the highest probability of fitting in well. Which of the 6 notes should be used? The composer tries them out and choses the one he likes the most. Again, randomness.

A composer will very often just ‘play around’ with the instruments until he finds something he likes. Randomness and exploration.

But just because the process is dominated by randomness and discovery doesn’t mean at all that skill isn’t absolutely critical.

Remember the beginner musician who just completely randomly pressed some keys? What is the probability that his process would generate anything meaningful with any kind of structure? It is unfathomably low and just about non-existing.

The skilled musician however has developed very powerful heuristics and has remembered a wide variety of different patterns that work well. So the skilled musician can not only compose a piece of music note by note, but also discover the overarching structure of the entire piece before hand, imagine the different dynamics and harmonics of different parts of the composition before he has pressed a single key on the piano.

But the process of creating this is dominated by exploration in much the same was as the individual notes. The filtering process may just be happening all inside the head of the composer. He doesn’t need to press every key to know what it sounds like, he can simulate it in his own mind to boost the discovery.

Now when he has an idea of the overall structure and harmonies, his search space for notes is much more narrow and focused. He doesn’t need to press all the keys to find the best one, he only needs to press a few of the best candidates to find something that fits.

He also has the advantage over the novice that he can sample from his memory pool of whole patterns of successive notes to find entire small passages that work well at once, and not only searching note for note.

His intuition will guide him, where this intuition works by accessing already discovered heuristics and rules unconsciously to streamline the search even more.

All these things make the searching process so much more intelligent, focused, effective and powerful than the novice’s, but it is still a search. It is still a discovery.

So how is all of this related to the number representations argument? We start by trying to imagine every single piece of theoretically possible piece of music as a space you can wander about in and search through. However, we need to first convince ourselves that this space even exists in any meaningful way. This we accomplish by converting music to numbers and accepting that numbers already exists in an abstract mathematical space. In our particular example it was pictures we converted, but that was only because that mapping is easy to explain and understand. You can do the same with music.

So the music space exists in some kind of meaningful way. Then we can intuit the composing process as a walk through this space. For a novice, this walk is just a completely unguided random tumbling about. But as the novice becomes more musically mature, he remembers patterns and develop tools to get a handle of this sprawling, never-ending landscape of music.

The tumbling about becomes more sophisticated. He can now identify dead ends before becoming trapped in them and learns to spot the well hidden promising roads. He develops tools to jump around and see larger sections of this landscape at once. He may not need to painstakingly follow every twisted path in detail to know where it ends, but he can see it from above. All of this guides the search. But it is still a search, it is still dominated by randomness, by exploration and a bit of luck to stumble upon the pieces to the masterpiece.

This explanation is not limited to music composition however. It can be modified to almost any area of interest and the arguments are not difficult to generalize (but this post is long enough as it is). So if you are convinced that the composition of music can be seen not as creation, but as discovery, you should accept this holds true for many other areas like painting, storytelling, architecture, engineering etc.

When every single step in a creation can be described as a discovery, then the entire process must be a discovery as well.