Logic - 2020-10-20

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7:37 AM

Uh turns out the answer is "no" but for a simple reason I had overlooked:

I think one can still reduce regular halting problem to this; cant you just simulate the TM for “all random seeds” in parallell and you stop and give an output when one of the options reaches probability > 1/2. This does assume that the randomness is a stream of independent fair coins. — daniello 12 hours ago

The key point being that you can BFS through the entire possibility tree where branches are due to the random source outputs until at least 1/2 of them (by probability) halt and give the same answer.

8 hours later…

user21820

3:18 PM

A: Why should I believe that the real numbers model distances along a line?

Firstly, we have some geometrical intuition about what an ideal line should be like, which is based on our experience of the physical world. This ideal line satisfies: The points (i.e. possible positions) on the ideal line are closed under translation and scaling, and addition and multiplication...