Hacking Epiphany

I

As someone who struggled in math classes and who much preferred writing papers, getting told how gifted I was, and proceeding to develop a superiority complex/motivation issues/a need for constant validation, I nevertheless find a lot of higher-level mathematics really beautiful. The Wikipedia article on "Mathematical Beauty" gives an example in Euler's Equation, eiπ + 1 = 0, the utility of which I don't really understand but which even I recognize as showing a deep, unexpected relationship between two regular numbers (0 and 1), two irrational numbers (e (which is a logarithmic thing that also has to do with compounding interest and is approximately equal to 2.71828) and π), and the imaginary number i (the square root of -1). Mathematicians love this equation very, very much; a guy named Kevin Devlin said that:

Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's equation reaches down into the very depths of existence.

Which is sort of intense but I can get there.

What makes a bit of math beautiful? When I was young I would doodle cubes in the margins of notebooks, moving through the procession of dimensions, starting with a dot and then a line and then a square, and suddenly I realized that there must be shapes of a higher dimension than the three I was used to and I got onto my parents' iMac G3 and looked at pictures of tesseracts for an hour. Is that anything? What was so interesting about that wireframe model?

In a more general philosophical sense, I think sometimes about all the natural forces and laws the scientific tradition has been able to reduce to simple, comprehensible terms. "The strength of the gravitational force exerted by one object on another is inversely proportional to the square of the distance between them." There's a sense of inevitability about statements like that, a kind of falling-into, an attractive concision that they share with equations like a²+b²=c². It's not just that truth is itself beautiful; there are lots of things that are true that don't strike me with any emotion at all. 

So, what, is it that I like simple maxims which fully express complex truths? It feels true (that is, it appeals to a bunch of preconceived notions) that humans like it when complicated, stressful problems can be reduced down to comfortable, manageable explanations, probably because of *frantic handwaving* evolutionary pressures. But do we really just like efficiency? What about the emotional rush we feel when we figure something out, when we finally see how simple the complicated problem really is? 

 

II

"Never tell a pun to a kleptomaniac. They always take things literally."

 

Not exactly sparkling comedy, but it demonstrates Basic Joke Construction well enough without relying on shock or taboo. The Setup is a simple inexplicable declarative statement, which the listener's brain immediately and without her knowledge begins to try and resolve; why shouldn't you tell a pun to a kleptomaniac? After a pause of just the right length, allowing this resolution process to run for just-so long and no longer (too long and the brain gives up frustrated, or worse, arrives at the answer before the speaker), the speaker delivers The Payoff, an unexpected, incongruous, but nonetheless fitting solution to the problem.

This produces laughter and general good feelings. Why? Great question, and judging by the number of theories, many of them from ancient Greece and most of which still sound pretty believable if perhaps incomplete, the answer is probably far more complicated than anyone really understands, least of all me. But I am nothing if not foolish and prideful.

From What are You Laughing At? by Dan O'Shannon

How funny something seems to a given listener depends first of all on them; their mood, their history with the subject matter, their relationship with the speaker, so on and so forth. It depends on a bunch of external factors, like the context in which the funny thing (O'Shannon calls it "the comedic event") is experienced, whether it is read or heard, whether it is loudly shouted in a quiet library. It is modified after the telling by any number of emotional responses; feelings of shock evoked by a dirty joke may enhance the comedic event for one listener but totally spoil it for another.

The actual joke part of the event, the gray triangle in the middle, is pleasingly summed up by Kant as
"The sudden transformation of a strained expectation into nothing," a sudden playful shift in perspective that takes your brain by surprise.

O'Shannon is big on stepping back and looking at the breadth of comedy, designing a set of rules which apply to all of it, including slapstick and schadenfreude, things that definitely make people laugh but which don't really have anything incongruous or clever about them. He goes so far as to say that "incongruity resolution theory is... one of the biggest roadblocks to understanding comedy ever created." 

Okay, Daniel. Focusing exclusively on the clever triangle misses a lot about the social and emotional miasma that surrounds it, fair enough. But a big reason that philosophers have tended to miss the forest for this one particular tree is that the tree is weird and interesting. Most people will laugh when they see a stuffy foreign dignitary fall ass over teakettle down a flight of stairs, because it tends to trigger feelings of relief and superiority and shock and so on, "thank goodness that didn't happen to me," "what a boob, good thing I'm not that clumsy and embarrassing." These are intuitive emotional responses. They make a degree of psychological sense for a species navigating complex social systems all the time. It feels like something happening deeper down in your brain, near the cerebellum or something, while incongruity resolution feels like it happens in the upper, conscious parts of the mind.

I get why someone falling down is funny. It takes a lot more work to explain why I should be so delighted by this fish meme.

III

Here is my theory. The mathematical beauty thing, our love of comedy, maybe even aesthetics, that dark and skull-lined road, are all linked in their mysterious appeal to the human brain as various ways in which we have hacked epiphany.

Evolution gave us curiosity. We see it also in many other species, like rats and dogs. The drive to investigate the novel is partially a desire to reduce uncertainty in our environment; the unknown might be dangerous, and by eliminating the possibility we eliminate anxiety. On the other hand, the novel might be hiding some resource that increases fitness, so our evolution wants us to go see if that's true.

 

Again, not an exclusively human trait. But as far as I know, the rush of joy of figuring something out, the proverbial eureka in a bathtub, is an experience unique to us. Cast your mind pastwards and try and remember a moment when everything clicked, when a thousand disparate niggling facts slid lightly into place as if moving on their own, or when a new idea suddenly took hold in your brain and after hours of struggle and work you could finally understand it. I chase after that feeling of revelation.

 

I think that part of why humor is so enjoyable is that it simulates that same mental pathway of "novel incongruity→frustration→unexpected resolution" that belies discovery. The best comedic events are ones that build from one payoff to the next, following a string of twisting insights specifically designed to appeal to the part of the brain that, a million years ago, was in charge of rewarding us for finding good hunting grounds on the other side of the mountain. Same, I think, for scientific discovery, though I think it's safe to say that figuring out how atoms work must generate greater/different feelings of awe than knock knock jokes do.

Humans have invented countless similar ways of hacking our psychological idiosyncrasies, originally evolved to improve reproductive fitness in our ancient ancestors. Modern food is maybe the most obvious example, but also look at alcohol and gambling and contraception (getting the good feelings designed to make you want to reproduce without actually reproducing), and more speculatively things like cosmetics (artificially enhanced fertility/desirability markers), the monomyth (might be the optimal story structure for generating satisfaction in listeners?), meditation (might be a way of tricking your brain into positive emotional feedback loops, see here), and so on.

It's probably too much of a simplification to say that humor and beauty and music are all just human attempts to access this same "eureka" reward pathway. As always, real psychology is probably more complicated than we think it is. But it's neat to consider; if I'm designing something, should I keep this effect in mind, try and activate it in my viewers as much as possible? I feel like it's a worthy consideration especially for games and game design.