= 27d567bc2d48d9f40e9ccc20ea370b15)
Eliezer_Yudkowsky comments on Demands for Particular Proof: Appendices - Less Wrong
You are viewing a comment permalink. View the original post to see all comments and the full post content.
= 783df68a0f980790206b9ea87794c5b6)
Loading…= b715d02e85f7b3b4ae65ca3d3e450868)
Subscribe to RSS Feed
Powered by Reddit
= f037147d6e6c911a85753b9abdedda8d)
You are viewing a comment permalink. View the original post to see all comments and the full post content.
Comments (60)
Why not 1/3^^^^^3?
You can't imagine anything that improbable. Unless we adopt Robin's anthropic penalty, in which case "I am in a unique position to affect 3^^^^^3 other people" is that improbable.
Actually, the beauty of mathematics is that it enables us to imagine such things -- just as surely as it tells us that there ain't nothin' we're talkin' about that's anywhere near that.
I can't imagine quarks either.
1/3^^^^^3 is a probability. A stupid probability, but a probability nonetheless. And if you declare 1/3^^^^^3 to be not a probability because of it's unimaginable uselessness then by the same standard I expect you to consider 3^^^^^3 'Not a Number'. I know you routinely use arbitrarily large numbers like 3^^^3 for decision theoretic purposes (on Halloween costumes!) and that is a number that is more or less chosen because it is already unimaginable.
log_2(3^^^^^3) heads in a row?
Coin's fixed.
Ah, so you meant: No physically possible series of Bayesian updates can promote a hypothesis to prominence if its prior probability is that low. And Peter meant: It is decision-theoretically useless to include a subroutine for tracking probability increments of 1/3^^^^^3 in your algorithm.
But the non-Bayesian source of your Bayesian prior might output 1/3^^^^^3 as the prior probability of an event -- as surely for the coin flip example as for Robin Hanson's anthropic one.
To be precise, it's impossible to describe any sense event with a prior probability that low. You can describe hypotheses conditional on which a macro-event has a probability that low. For example, conditional on the hypothesis that a coin is fixed to have a 1/3^^^3 probability of coming up heads, the probability of seeing heads is 1/3^^^3. But barring the specific and single case of Hanson's hypothesized anthropic penalty being rational, I know of no way to describe, in words, any hypothesis which could justly be assigned so low a prior probability as 1/3^^^3. Including the hypothesis that purple is falling upstairs, that my socks are white and not white, or that 2 + 2 = 5 is a consistent theorem of Peano arithmetic.
How many dustspecks in the eye are you willing to bet on that?
The log_2(3^^^^^3) consecutive binary digits of pi starting from number 3^^^^^3 are 0?
Then our minds are "fixed" too, just like the coin.