Pathological universes are ones like: where there is no order and the right answer is randomly placed. Or where the facts are maliciously arranged to entrap in a recursive red herring where the simplest well-supported answer is always wrong, even after trying to out-think the malice. Or where the whole universe is one flawless red herring (“God put the fossils there to test your faith”).

“No free lunch” demands they be mathematically conceivable. But to assert that the real universe behaves like this is to go mad.

Since we learn reason from the universe we’re in, if we were in a universe you’re referring to as “pathological”, we (well, sentients, if any) would have learned a method of arriving at conclusions which matched that. Likewise, since the universe produced math, I don’t think it has any meaning to talk of whether universes with different fundamental rules are “mathematically conceivable”.

No search algorithm beats random picking in the totally general case. This implies the totally general case must include an equal balance of pathology and sanity. Intuitively, a problem could be structured so every good decision gives a bad result.

Edit: this post gives a perfect example of a pathological problem: there is only one decision to be made, a Bayesian loses, a random picker gets it right half the time and an anti-Bayesian wins.

However we seem to be living in a sane universe.

Pathological universes are ones like: where there is no order and the right answer is randomly placed. Or where the facts are maliciously arranged to entrap in a recursive red herring where the simplest well-supported answer is always wrong, even after trying to out-think the malice. Or where the whole universe is one flawless red herring (“God put the fossils there to test your faith”).

“No free lunch” demands they be mathematically conceivable. But to assert that the real universe behaves like this is to go mad.

Since we learn reason from the universe we’re in, if we were in a universe you’re referring to as “pathological”, we (well, sentients, if any) would have learned a method of arriving at conclusions which matched that. Likewise, since the universe produced math, I don’t think it has any meaning to talk of whether universes with different fundamental rules are “mathematically conceivable”.

http://en.wikipedia.org/wiki/No_free_lunch_in_search_and_optimization

No search algorithm beats random picking in the totally general case. This implies the totally general case must include an equal balance of pathology and sanity. Intuitively, a problem could be structured so every good decision gives a bad result.

Edit: this post gives a perfect example of a pathological problem: there is only one decision to be made, a Bayesian loses, a random picker gets it right half the time and an anti-Bayesian wins.

However we seem to be living in a sane universe.