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Nisan comments on Polarized gamma rays and manifest infinity - Less Wrong Discussion
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An alternative interpretation of the halting oracle hypothesis that does involve a manifest infinity: There is a program of infinite length (and infinite information content) that solves the halting problem. It contains all the digits of Chaitin's constant.
Yeah. I'm actually prepared to bite the bullet on that version of it, and say Solomonoff induction is correct in dismissing infinitely long programs as infinitely improbable. What bothers me is the version of it that gets the same results with a finite program plus infinite computing power, together with the gamma ray observations that suggest our universe may indeed be using infinite computing power.