This is an argument of the form "Suppose X were true -- then X would be true! So couldn't X be true?"
No, this is pointing out that if you provide an optimal outcome barricaded by a particular obstacle, then that optimal outcome will trivially be at least as hard as that obstacle.
You try to find a method that solves enough examples of the NP-hard problem well enough to sell the solutions, such that your more bounded ambition puts you back in the realm of P. This is done all the time -- freight scheduling software, for example. Or airline ticket price searching. Part of designing optimising compilers is not attempting analyses that take insanely long.
This is exactly the point made for computable approximations to AIXI. Thank you for agreeing.
Harder classes are subsets of NP-hard, and everything in NP-hard is hard enough to make the point.
Are you sure you want to make that claim? That all harder classes are subsets of NP-hard?
but computing the uncomputable is even more of a wild goose chase. "Omega flies up to you and hands you a box containing the Secrets of Immortality; for every digit of Chatin's Omega you correctly type in, you get an extra year, and it stops working after the first wrong answer".
Fantastic! I claim my extra 43 years of life.
Harder classes are subsets of NP-hard, and everything in NP-hard is hard enough to make the point.
Are you sure you want to make that claim? That all harder classes are subsets of NP-hard?
No, carelessness on my part. Doesn't affect my original point, that schemes for approximating Solomonoff or AIXI look like at least exponential brute force search.
...You try to find a method that solves enough examples of the NP-hard problem well enough to sell the solutions, such that your more bounded ambition puts you back in the realm of P. This is done all the t
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