While brushing my teeth, thinking about this great article, Blowing Up, which I had been reading before taking a shower, which had provoked a conversation with K about predicting the stock market, a picture of a crazy mental model appeared in my head and I want to try to explain it (as much for myself as for anyone else). It brought into focus a lot of my thoughts on certainty, randomization, and decision-making... but it’s quickly slipping away. Type, little fingers, type!

Imagine that there are three people, and each of them has been given a slot machine that, each time they press a certain button, will either show a white screen or a black screen based on some unknown internal algorithm. It is their duty to try to correctly guess the color of the next button press more than 50% of the time. They will be instructed to press the button 1 million times, to give them ample time to study the system, create their own guessing algorithm using whatever means they want, in order to meet their goal.

Who has the best chances of winning?

Of course, there’s no way to know which of these three people will win because we don’t know anything about the people or the machines they’re using. They could all be using machines that alternate between white and black, at which point it will just be a test to see who is lucky enough to catch on first. Or maybe only one of them has that machine and so he will obviously win. In other words, if you and I were betting on who was going to win, we’d both have a 50% chance of winning that bet. This is really odd. Without knowing anything about the system, or about the types of machines they’re using, or about the probability of any one of these people from achieving their goals… a probability of winning our bet has been created. Something from nothing. But does this something have any real value?

Okay, now imagine that you know that person A is at a machine that, at each flip, has been programmed to have a 50% chance of showing a black screen and a 50% chance of showing a white screen. Person B is at a machine that, at each flip, will first randomly select a probability in between 0% and 100%, and then, based on that probability it will then use that percentage to determine whether or not to display black versus white. Person C is at a machine that has another person that controls the machine and tells it each time what color to display, but you know nothing about this person’s motives for displaying the color that they do.

Okay, so now you know what these people are up against. If you were to guess which person would win, would your chances of winning be any better than before? I don’t think they would. At each flip, each person still has a 50% chance (from our perspective) of being able to choose the right color. Their chance of choosing the right color may be much higher or lower than 50% actually, but we have no way of knowing, and so that makes it settle at an even 50% for us. Am I missing something here? Isn’t it odd that a 50% chance is the same as an unknown percentage chance when two choices are involved? With the person behind person C’s machine, they may fall into a pattern, but at each flip they are still equally likely to abandon that pattern as continue it, because you have no way of knowing if the pattern you’re seeing is real or imagined. Just for fun, imagine that the person behind person C’s machine would choose a color based on his ability to correctly guess what another person at a machine would guess.

Maybe this seems obvious to you, or maybe I’m completely neglecting some obvious truth… but is it the case that probability doesn’t really exist? That probability is merely a fancy way of talking about the lack of knowledge? That probability is merely a local view, from the location of any particular decision, of a completely random environment that may or may not follow your expectatations? That has a certain probability chance of following your expectations, and therefore a certain probability chance of acting any particular way at all? That a 50% chance between two things is the same as a 100% chance between two things if you don’t know to which side the 100% applies?

If this is true, then I’m pretty sure it has heavy implications about anything that we do that involves probability. Anything that is not a result of absolute certainty becomes a result of absolute randomness. Without probability to cushion us from the fall into chaos, and without the assurance of anything being certain, our only option is complete, impossible to decipher, randomness in everything.

And it turns out that everything involves probability. Can you think of anything that has a probability of 0% or 100%, or rather no probabilty at all but rather complete certainty? I was just thinking about this the last few days and then came across a huge body of prior thought by philosophers going all the way back to the invention of thinking that have pretty much ruled out certainty as a possibility. Oh, then the lack of certainty must be a certainty, you say. Well, I don’t think we’re even certain of that.

What about self-definitions—one equals one, a rose is a rose, etc. Anyone can be certain that a thing is itself. True, but that’s called circular logic, the reflexive property of equality, and it has little to no value in the field of logic that I know of unless it’s applied to other more complex notions of equality. Certainty isn’t valuable to me unless it leads to other certainties, unless it eventually leads to the transitive property of equality at some point. For example, my meta-fundamental purpose requires that I be certain that I have fulfilled my fundamental purpose, in the hopes that I could then define a fundamental purpose and know when I’ve completed it. There’s no way I can be certain of that… all I can be certain of is that my fundamental purpose is my fundamental purpose, or that my meta-fundamental purpose is my meta-fundamental purpose. Who cares?

On the other hand, if you look at it a little differently, you can say that 100% probability is everywhere. That this coin has a 100% probability of landing either heads or tails, as long as heads or tails are the only two options. And it’s this type of probability (which isn’t probability at all really, just silly word and number games) that all of science is based on. Every theory has a potential to be disproven, but the fact that there is a way to disprove them (google falsifiability for info on the value of theories being able to be disproven… damn, I just realized that Google is really just the world’s best wiki) and that so far they haven’t given them credibility of having a higher probability of being true. But that’s just not true. Imagine that you’re on coin flip number 11, and in your previous 10 flips you flipped all heads… that doesn’t mean that your coin has a higher probability of flipping heads next time. Every theory is a single flip away from being disproven, and that flip has a 50% chance of proving the theory false (or a randomly selected chance, or a God-determined chance, or a chance given to it by 1,000 monkeys that are flipping coins). Past performance has no effect on future performance. Everything is completely random at every step.

Can this be true? Am I imagining a fake scenario or a real one? I give myself a 50% chance of being right.