Peter Chatain

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Does this hide the text? (Sorry just testing things out rn)

Wow

Ok so you can hide stuff by typing >! on a new line

Occam's Razor and the Universal Prior

Yep that's right! And it's a good thing to point out, since there's a very strong bias towards whatever can be expressed in a simple manner. So, the particular universal Turing machine you choose can matter a lot.

However, in another sense, the choice is irrelevant. No matter what universal Turing machine is used for the Universal prior, AIXI will still converge to the true probability distribution in the limit. Furthermore, for a certain very general definition of prior, the Universal prior assigns more* probability to all possible hypotheses than any other type of prior.

*More means up to a constant factor. So f(x)=x is more than g(x)=2x because we are allowed to say f(x)>1/3g(x) for all x.

Hammertime Day 6: Mantras

Here's some mantras I have:

That which you are aware of, you are free from.

And some variation of:

Truth comes knocking. You say "go away, I'm looking for the truth." It goes away, puzzling.

The above I rediscovered recently through reading Zen and the Art of Motorcycle Maintenance.

I was thinking something similar, but I missed the point about the prior. To get intuition, I considered placing like 99% probability on one day in 2030. Then generic uncertainty spreads out this distribution both ways, leaving the median exactly what it was before. Each bit of probability mass is equally likely to move left or right when you apply generic uncertainty. Although this seems like it should be slightly wrong since the tiny bit of probability that it is achieved right now can't go back in time, so will always shift right.

In other words, I think this will be right for this particular case, but an incorrect argument for when significant probability mass is on it happening very soon, or for when there is a very large amount of correcting done.