Superstition, Information, and Probability

Coincidence has always annoyed me, since it is not causation, and therefore, lacks a normal physical explanation. Nonetheless, it has some of the superficial elements of causation, making it particularly infuriating if it occurs often, for those that are generally scientifically minded. From what I’ve read, Bach would use random outcomes as the seeds of his compositions, and I often do something similar, which I finally took the time to think about. And upon reflection, I think there’s actually good reason rooted in information to use random exogenous signals as “inspiration” for creative works.

Causation

If I throw a ball at a window, and it breaks, there’s a narrative that can be constructed, and expressed in mathematics, that explains the transfer of momentum from my body to the ball, from the ball to the window, and ultimately, the shattering of the glass. In short, causation as a concept is really coextensive with physics, at least in my mind, which means we can construct a mathematical model that has a one-to-one correspondence to some set of measurements made on the system. In less technical terms, I can tell you how the system behaved using mathematics, and therefore, I can predict its behavior going forward.

Coincidence

But coincidence is something different. If I had to define coincidence, I would say it has two components: (a) a low probability, and (b) contextual relevance. For example, when I was on holiday during law school, I was driving with some friends through the interior of Sicily, listening to house music on the radio. Then suddenly, the station changed on its own (presumably because we had left the physical boundaries of the original radio station) and Le Tombeau de Couperin, by Ravel started playing. The event of a radio changing stations on its own is, I would say, low probability, and this piece is relevant to me, because it’s one of my absolute favorite pieces of music.

We can use these criteria to construct other examples. Imagine walking out of a store having just purchased a bright orange hat, when suddenly, someone throws an orange at you. Both events are low probability in the ordinary course, and the latter event of getting hit by an orange is relevant, because it intersects in property with the item you just purchased. And you would be completely certain the event was deliberate, even if it seemed superficially impossible for that to be the case.

Last night, in New York City, the wind was blowing extremely hard, and knocked over at least one item in the shower, and I remember immediately attaching significance to the label of the item. This is a strange thing to do, and certainly superstitious, but upon reflection earlier today, I realized it’s actually quite sensible as a mechanic. When a low probability event occurs – e.g., something loud, unusual, or bright – the brain probably treats the objects in question as likely to contain information, which is perfectly rational, since you might have to quickly size up a threat, or an opportunity in the face of a low probability event.

So I think of superstition as a sort of perversion of this perfectly reasonable instinct to treat a low probability event as a signal worthy of attention. But, I think creativity can turn this round again in a reasonable way, by using low probability signals as a seed for a creative train of thought. And this is because if something is low probability, then it should contain a lot of information, if our brains encode experiences efficiently. This could explain novelty seeking behavior as well, as the brain’s desire to consume novel information, which can in turn be used as the seed for new deterministic inferences.

Poets, musicians, artists, and even some mathematicians, are notorious novelty seekers, often degenerates because of it, which suggests that there’s probably something physically meaningful to their conduct. People generally write this behavior off as some kind of aberration typical of a creative type, but dismissing this observation turns what might actually have a scientific explanation into mere coincidence. I think creative people might have wells of information derived from random, low probability experiences, that then get restructured into novel artifacts. In short, my hypothesis is, that creative types probably have heightened senses, meaning they’ll be even more drawn to novelty, pleasure, drama, etc, precisely because they’re going to pull way more information out of those experiences than a normal person. This will in turn build up a well of information that can later be drawn upon to generate creative artifacts.

Writers do this more literally, by having unusual experiences, and sometimes simply writing about them. But painters, musicians, and even more abstractly, mathematicians, I think do the same thing, except the information becomes more and more abstract as you progress from the literal to the mathematical.

I think this is probably how it works, because deterministic thinking will never produce an original idea, since it is by definition, mechanical inference from a set of known assumptions. The truly hard part is coming up with a new and correct assumption in the first place, like F = MA. Solving for acceleration once this is known is just not as impressive, or as uncommon as stating the equation in the first instance.

As a result, creative people have to be doing something else. I think some creative people can take things even further, but I certainly use random, low probability events, as the source of inspiration for ideas, and Bach did the same, and I’m sure plenty of other people do something similar.

So whether or not the story of Newton’s Apple is true, it certainly makes a lot more sense in light of the work of Shannon.

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