Silas: @Caledonian: That’s an interesting point. But are you sure the effect you describe (at science museums) isn’t merely due to the brain now seeing a new color gradient in the image, rather than randomness as such? Don’t you get the same effect from adding an orderly grid of dots? What about from aligning the dots along the lines of the image?
Yep. Adding a set of coherent modulations will do better than noise to improve your sensor, because you’re guaranteed to get at least some modulations of a sufficiently high level, and you can subtract out the modulations afterward to arrive at a superior picture of the environment.
Remember, Eliezer_Yudkowsky’s point was not that randomness can never be an improvement, but that it’s always possible improve beyond what randomness would yield.
Lotta commenters seem to have entirely missed this.
Eliezer stated his point more precisely in the original post:
As a general principle, on any problem for which you know that a particular unrandomized algorithm is unusually stupid—so that a randomized algorithm seems wiser—you should be able to use the same knowledge to produce a superior derandomized algorithm.
I’d recommend engaging with that formulation of his point, rather than with Silas’s summary (which is what you’ve quoted).
My best guess at which uranium atom will decay next is the uniform distribution over all the atoms. (Unless of course some of them are being bombarded or otherwise are asymmetric cases). If you focus your guess on a random one of the atoms, then you’ll do worse (in terms of Bayesian log-score) than my deterministic choice of maxentropy prior.
My best guess is a uniform distribution over all the atoms. No randomness involved. If you do select one atom at random to focus your guess on, you’ll do worse than my maxentropy prior.
Yep. Adding a set of coherent modulations will do better than noise to improve your sensor, because you’re guaranteed to get at least some modulations of a sufficiently high level, and you can subtract out the modulations afterward to arrive at a superior picture of the environment.
Lotta commenters seem to have entirely missed this.
How can you improve guessing which uranium atom will blow up next?
Eliezer stated his point more precisely in the original post:
I’d recommend engaging with that formulation of his point, rather than with Silas’s summary (which is what you’ve quoted).
My best guess at which uranium atom will decay next is the uniform distribution over all the atoms. (Unless of course some of them are being bombarded or otherwise are asymmetric cases). If you focus your guess on a random one of the atoms, then you’ll do worse (in terms of Bayesian log-score) than my deterministic choice of maxentropy prior.
Give me a deterministic algorithm that performs worse than random on that problem and and I will show you how.
My best guess is a uniform distribution over all the atoms. No randomness involved. If you do select one atom at random to focus your guess on, you’ll do worse than my maxentropy prior.