How to Be Creative Part 2 - Mo Art Mo Problems

Show Notes

Summary

Alex explains how problem solving is central to the practise of creativity via mathematical proofs and magicians in this long awaited second part of the How to be Creative series.

Notes

• Fermat’s Last Theorem

Transcript

In 1637, French mathematician Pierre de Fermat scribbled the following in the margins of his copy of the ancient Greek mathematics tome Arithmatica:

“It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second, into two like powers. I have discovered a truly marvellous proof of this, which this margin is too narrow to contain.”

Pithy, eh?

The thing is, it turned out he had a point. What he didn’t leave us with, is that actual proof which, if it ever existed at all, he took to the grave with him. This became known as Fermat’s Last Theorem, or sometimes Fermat’s Conjecture, and it’s a problem that many of history’s best mathematicians spent the next few centuries attempting to solve.

The slightly more concise, but equally vexing form of the conjecture is usually stated as such:

No three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2.

Basically, if you take sugar 2 cubes, and glue them to 3 other cubes, the no amount of manipulating them, short of crushing them up and reforming the resulting pile of sugar, will produce a bigger cube. The conjecture states that as long as a and b are different no amount of cubes will create that megacube. This then extrapolates in to n-dimensional space as no value of n will achieve this either, and we get into some seriously mind bending territory. Simple right? OK, maybe not, just formulating those sentences made my head hurt. I’m no mathematician, but I understand from reading books and the internet that maths people thought this was a pretty important problem to solve. In maths term, find a proof for. Some thought it impossible. Possible or not, whoever came up with said proof would not do so with sugar cubes, except maybe to put in their coffee, which they would need a lot of.

Oxford Mathematics professor Andrew Wiles had been fascinated by this problem since he was a kid. In 1986 he decided that he was going to try and solve it. For the next 7 years, Wiles basically shut himself away from the world and attempted, in secrecy, to find the proof, only letting his wife in on his plan. In 1993 Wiles thought he finally had it, and unveiled his secret quest, and his ground-breaking proof to the maths world. His proof pulled in diverse, seemingly unrelated areas of mathematics into a highly original and elegant proof. Hurrah! But within months, it was pointed out by others in the maths community that there were errors in his proof. Not just little ones, either. Well, the errors were actually quite small, but their implications threatened to render Wiles’s proof worthless. Damn! Wiles was devastated, but unperturbed returned to his desk, and with the help of fellow mathematician Richard Taylor, he attempted to fix the problem, only to fail again.

In late 1994, Wiles was about to give up on the whole damn sorry business, but decided to give his work one final, forlorn look. Sitting at his desk, he had a sudden flash of inspiration, seemingly out of nowhere, that the answer lay in the fact that his final approach didn’t work meant that one of earlier approaches, from 3 years prior, would work. He later said:

“It was so indescribably beautiful; it was so simple and so elegant. I couldn’t understand how I’d missed it and I just stared at it in disbelief for twenty minutes. Then during the day I walked around the department, and I’d keep coming back to my desk looking to see if it was still there. It was still there. I couldn’t contain myself, I was so excited. It was the most important moment of my working life. Nothing I ever do again will mean as much.”

Yay for Andy!

Wiles published his final proof which was again put through its paces by the maths community, and this time found to contain no errors, and thus he had proved Fermat’s Last Theorem, 358 years after it was conjectured. Wiles became pretty famous after this. Many books have been written about his epic quest at his desk with a pen and pad, and probably a blackboard. Mathematicians love a blackboard, don’t they?

Why am I talking about maths? Well I decided this is going to be a maths podcast from now on. Suck it up!

Only joking! I did study maths for a bit, and I need some maths for my job, but I find it punishingly hard, and the road to mastery seemed impossibly long. You see, as Wiles proved, along with Fermat’s Conjecture, you can be creative with maths. Actually it’s an inherently creative field. But you need a certain type of brain and a lot of study to get to the point where you can actually be creative. There’s a couple of themes I want to pull from this story:

1. the idea of creativity as problem solving
2. creativity and mastery

The latter I’m going to cover in the next episode of this series, and I’ll no doubt, return to Wiles’s story, at least a little. But in this episode I’m going to talk about problem solving, because I think it’s one of the most important aspects of creativity.

In part one of this series, I talked about the core facets of creativity - mastery, conviction, an open mind, collaboration and focus, with a sprinkling of chaos for good measure. These are the things that need to be in place for creativity to occur. But what exactly is creativity? What things do you actually do when being creative?

If we look at the example of Wiles, you might conclude that it is a flash of divine inspiration. Either that or that act of locking yourself away for 7 years. But throughout that 7 years, he made countless creative leaps. Wiles’s contribution wasn’t that one inspired idea, that was just the last inspired idea required to get from A to B. Wiles’s genius was in pulling lots of seemingly unrelated areas of maths together to make something new and to solve a problem many thought unsolvable. Wiles’s solitary journey was really a string of intuitive leaps. A blanket of lilly pads in an pond the size of the universe. He simply chose the right ones to leap to. This is creativity - you pick a destination, and you figure out to get there. More specifically, you pick a problem, and you solve that problem one challenge at a time. The destination may or may not be important. You might not arrive at the destination that you originally intended, but that’s not a problem. As I’ve said countless time on this podcast, it’s the journey that matters. And this journey is pretty much always problem solving.

So how do we get from solving tough, or for that matter, easy maths problems, to the ephemeral, mercurial, mystical practise we call art?

It’s simple, Artists are problem solvers just like mathematicians! You dream up an idea of something you want to create, but that’s just where the job of being a creator starts. The real job, the 99% of perspiration to quote Thomas Edison, is problem solving. What problems are you solving?

How am I going to represent this beautiful landscape I have in front of me? How am I going to represent this picture of human? How am I going to capture the essence of what I’m looking at? How am I going to take this idea of a story in my head and turn it into a book, play or a movie? How am I going to photograph this tree and really of capture the essence and the mood and the character of the tree? How do I get my latest collection of artworks in front of some punters so that I can sell some and therefore afford to do more artworks?

And I struggle to think of any creative enterprise that isn’t mostly about problem solving. And I would argue that if you are not put in the position of having to solve a problem, you’re probably not being creative. You’re likely being fairly derivative. Even then, it’s still about solving problems.

Take those caricature artists that sit on Montmartre in Paris or on Leicester Square in London, doing caricatures of tourists. It’s all very formulaic. I’m not knocking their skills, these folk are really amazing at that they do. But it doesn’t seem particularly creative. But every time someone turns up they have to solve the problem how to characterise them in such a way that is humorous yet complimentary, but not insulting and therefore risking a punch in the face from some doting and muscular dad. This is no mean feat, especially when you consider the bizarre effect that those cities seem to have on people’s brains!

But for anyone attempting to push boundaries, either theirs or those of their medium, then problem solving constitutes the bulk of the effort, since ideas tend to come quickly. It might take them a while to develop them, but as we saw with Wiles, that’s just part of the problem solving process.

So take something that usually takes long time to develop, like a novel, perhaps a long one or a series. The arc of the thing or at least the starting point or the ending point or the meaning you’re trying to convey, tend to arrive fairly effortlessly . Maybe you had the idea many years before, and are just getting round to drafting it - you have probably been developing that ideas on or off for the intervening time. Much of it might change when you get into it, but you’re going in with a pretty good sense of what’s what. That’s the impetus to start fleshing out characters, figuring out problems with the plot, world building, all that fun stuff. And what are you doing? You’re problem solving! The problem of how to make your characters relatable so that the reader cares what happens to them. How to make the setting believable while also leaving the possibility for something out of the ordinary to happen, some drama. Figuring how to structure it to get the reader emoting in the right place for the right reasons. All this before you start solving the problem of which words to use. You then solve that problem one words at a time. And then when you do a second draft you solve the problem of the words you chose in the first draft being the wrong ones, and that your main character is a detestable twat. Oops!

In between drafts, maybe you find yourself on a hilltop in the Lake District, admiring a staggering view. You want to capture it with the watercolour paints your handily brought with you. Maybe this is the cover for your new book! But you still need to think about how you’re going to render it, what colours you’re going to use, what colour intensity, how you’re going to mix them to get the right hues to capture the ethereal light, the brush you’re going to use, where to put each blob of paint. And since you’ve only got a portable watercolour set with you and that the light is rapidly changing as the weather takes a typical English turn for the dreary, you now have to solve the problem of how to do all of that in the time you have left with the materials you have at your disposal, as well as getting back to your car before you and your artwork become a soggy mess.

I don’t think people tend to think about the creative process in this way, perhaps because framing it all as problem solving feels a little bit mechanical. A bit unromantic. Lacking magic and wonder.

And for those who don’t practise creativity but just consume it, that’s fine, and perhaps for the best. The shrouded methods a magician uses to create that spectacular illusion is always mechanical and rightly kept secret. If you look behind the curtain, the magic is lost, and you’re just left something that’s “clever”, which is no fun at all, and a sense that you’ve been had.

But from the creator’s perspective,I don’t see this process as mechanical or prosaic at all. The problem solving bit is where the magic really happens. Where the fun is to be found. This might be a problem of nomenclature. Maybe if instead of boring old problem solving we think of it as pathfinding, questing, adventuring, conquering we’d better capture the wonder and delight of it all? But it is all of these things too, it’s just that when you boil it down to its rudiments it is what it is - solving one problem after another.

The corollary to the “inspiration” fallacy, is the misconception that you have an idea, you then bust out you instrument or materials or laptop and make that thing appear. Like you plug a USB lead into your ear and a stunning sculpture is delivered via your 3D printer.

As I say, I’m going to come back to the subject of mastery as a supposed prerequisite for creativity, but for the purposes of this conversation, people seem to assume that we’re always at the level of mastery needed to achieve our musings and that we just flip a switch and the creation appears. Most folk seem to forget the sometimes long, often wonderful, sometimes painful, and usually massively rewarding bit that happens in the middle.

But the act of creation just isn’t as rewarding if there’s not some challenge involved. And if there’s some challenge, then by definition, your existing mastery needs some work to get to where you’re trying to go. And that journey might include many false starts and failed attempts that ended up in the bin. Yes, pumping out another workmanlike landscape watercolour may be mindful and relaxing and a reason to go sit on a hill with a baguette and a hip flask, but it’s not the magic bit. That just the bit where you leave your poor, overworked brain alone for a bit to simmer down.

And without that challenge, we never progress. If you want to be able to lift really heavy weights, then you need to start by lifting much lighter weights, and gradually work your way up as your muscles build. Every time you add another kilo you’re challenging yourself, your muscles, your resolve. It’s the same with creation, it’s like a muscle. Use it or lose it. The more you use it, the more powerful it gets.

And how do you know if you’ve progressed? The next thing you do is better than the last. Things take less time. Your endeavour starts to feel less like a toil, less forced, and more like a labour of love. A celebration.

And I think the consumer of your work can tell when you really challenged yourself. Not necessarily by mastery of your materials or perfection in rendering of your subject. Challenging works have an aura. A certain quality. They have the opposite feel to a Bob Ross, knock it out in 30 minute landscape by numbers. The opposite of an elaborate but soulless hodgepodge quickly rustled together using Midjourney or DALL-E.

And I know that I keep banging on about GenAI, but it really does bring into focus many facets of real creativity. I’m all for using language models or AI image generation as part of the creative process. To take the legwork out of outlining your script, or to create a mock-up for a painting you want to make. There are many ways in which AI can improve and enrich the creative process and help us more quickly solve many of those problems. But if the creativity isn’t coming from within, if you aren’t focussed on solving those really interesting problems, to bringing really delicious ideas into reality, then all that these models will do is accelerate you to a soulless and flat creation. And worse, you might feel compelled to let the AI do most of the work, which in my mind is skipping past all the fun stuff, all the stuff that really matters.

Perhaps the most important job for an artist is connecting with other humans via their medium. Art is communication. A conversation with other humans via a shared understanding of culture. If you expose your voice in a lazy artificial way, people will hear that lack care and passion, and turn their backs. You can’t connect with the world if you don’t have something compelling, or at least vaguely interesting, to say, and an effecting and engaging means to do that.

And you can’t create something compelling and engaging before having figured out the problem of having to do so. And doing so is where are the good stuff is:

It’s the part that involves the meaningful work. It’s the part that involves challenge and growth. It’s the part where you find the mindfulness and flow. It’s the part that involves a sense of fulfilment and achievement.

You don’t need to be a creative to feel the truth in that last point. If an activity didn’t take you a certain amount of mental or physical effort or a certain amount of time to produce, the results are never going to be that fulfilling. Fulfilment comes from overcoming obstacles, achievement can only occur where there is a challenge. That feeling that you’ve pushed your abilities that bit further. You’ve created something really interesting and unique and special.

Think back to where you started your last project. Recall the fact that you started with a blank canvas, and empty page, a formless slab of clay thinking:

How do I realise this idea? How do I convey this emotion? How do I tell this story so that it’s compelling and engaging? How do I make something that people can connect with emotionally?

It’s not something you get right every time, but that’s why it’s fulfilling, because it’s challenging. Any type of work you partake in has to be to some level challenging to be fulfilling. And I think that if you enjoy your work, by definition, it’s challenging. You are, by definition, spending your time solving problems. Far from being the more prosaic or mechanical part of it, of the creation process, it’s the whole thing.

It’s where the dopamine is. It’s where the excitement comes from. It’s where we get our focus and our flow from.

And these things are what are important if creativity is going to help you keep your sanity. Coming up with great ideas in itself isn’t that fulfilling if you don’t see them through to inception, because that’s the bit where you really feel good.

Thanks again for listening kiddies. As I keep alluding, there’s at least one more episode coming in this How to be Creative series. Maybe more. Will the next instalment be the next episode I release? Who knows! Tune in to find out.

In the meantime, please like and review this on whatever platform you’re listening on. This stuff really does help. Support me on Patreon at patreon.com/alexloveless and go buy my art at alexloveless.co.uk.