Here's how I predict your setup to work, and shame on you for chickening out:

http://sketchtoy.com/66313589

You start doing the experiment, you flip four coins, 15/16 of you memorize a sequence, 15*32 of you memorized pairwise probably different sequences. In the end, you have a probability of 15/16 to find yourself having memorized a sequence. If QI works and half of you who find a tails in a first four coins commit suicide, start-experiment-you only has a 15/17 chance to find themselves having found tails and failed to kill themselves.

Take a programing language with two characters. Assign each program a prior of 2^-length(program). If the program outputs some string, then P(string | program) = 1, else it equals 0.

This is exactly Solomonoff induction, assuming that the programming language is prefix-free.

I figure there must be some reason people don't do this already, or else there's a bunch of people doing it. I'd be real happy to find out about either.

Because it's uncomputable: there are infinitely many programs to consider, and there are programs that don't halt and for many of them, you can't prove that they don't halt.

If you set a maximum program length and a maximum execution time, then inference becomes computable, albeit combinatorially hard: maximum a posteriori inference can be easily reduced to MAX-SAT or ILP and is therefore NP-complete (optimization version), while posterior evaluation is #P-complete.

It's known that many NP-hard problems are practically solvable for real-world instances. In this case, there are indeed people (primarily at Microsoft, I think) who managed to make it work, but only for short program lengths in limited application domains: Survey paper.

In November, I donated $3000 to Against Malaria Foundation and $500 to Give Directly. I also found the answer to a question I've been researching for ~3 years.

I love this forum.

If I understand the experiment, your theory is that quantum weirdness makes it more likely to see four heads in a row because you resolved to flip many more coins if you don't.

Sounds fun. I'll flip four coins (actually use a string of 0's and 1's that's 4 bits long). If I don't get four heads, I'll generate a 10-digit sequence and memorize it. Let's explore this frontier!

I did it. It didn't work. My new favorite number is 1 1 0 0 0 0 0 0 0 1.

Reality hack failed.

Let's try again. If I don't get 4 heads, I'll memorize a 20-digit number.

It didn't work. My other new favorite number is 1 0 1 1 0 1 0 0 0 0 1 1 0 1 1 1 1 1 1 1.

I wonder if there's a better way to test this theory.

Corollaries: You expect to never try to exploit QI, because most of the anthropic weight ends up in the timelines where you didn't try to. If you are the sort of person who would try to exploit it regardless of this argument, you're likely never to come into the position to do so - for example, you, or the population of your Earth, might never think of it. If your Earth has thought of it, that is bayesian evidence QI doesn't work in the first place. (So is your being the sort of person that would exploit it.) Yay for newcomblike problems.

Minor naming feedback. You switched from calling something "supervised learning" to "reinforcement learning". The first images that come to my mind when I hear "reinforcement learning" are TD-Gammon and reward signals. So, when I read "reinforcement learning", I first think of a computer getting smarter through iterative navel-gazing, then think of a computer trying to wirehead itself, then stumble to the meaning I think you intend. I am a lay reader.

Thanks to Turing completeness, there might be many possible worlds whose basic physics are much simpler than ours, but that can still support evolution and complex computations. Why aren't we in such a world? Some possible answers:

1) Luck

2) Our world has simple physics, but we haven't figured it out

3) Anthropic probabilities aren't weighted by simplicity

4) Evolution requires complex physics

5) Conscious observers require complex physics

Anything else? Any guesses which one is right?

https://en.wikipedia.org/wiki/Wien%27s_displacement_law

white noise is caused by air molecules moving randomly at high speed

This is wrong. What you hear is sound waves, that is, rarefaction/compression zones in the air, pressure differentials. They are a phenomenon at a different scale than molecules. In particular, the energy involved is different. "White noise" means the frequencies are uniformly distributed.

Essentially, an air molecule doesn't have enough energy to register at your hearing sensors, that is, to move your eardrum (or cochlear hairs).

The peak frequency of thermal noise at room temperature is far higher than 5 GHz, it's actually closer to 30 THz. I'm not exactly sure about the biology here and whether Brownian motion of air molecules excites the hair cells in your cochlea. I'm guessing that it does, but even so, the range of frequencies you can hear (20-20,000 Hz) carries only a very, very tiny fraction of the thermal energy. Someone should do the calculations; my guess is that it's far below the detection threshold.

Another thing to keep in mind is that at equilibrium, you have thermal excitation everywhere. You might as well ask why you don't hear or see or smell the thermal excitation in your own brain.