Comment by errethakbe on A full explanation to Newcomb's paradox. · 2020-10-13T02:10:29.289Z · LW · GW

Regarding the topic of your last paragraph (how can we have choice in a deterministic universe): this is something Gary Drescher discusses extensively in his book.

Firstly, he points out that determinism does not imply that choice is necessarily futile. Our 'choices' only happen because we engage in some kind of decision or choice making process. Even though the choice may be fixed in advance, it is still only taken because we engage in this process.

Additionally, Gary proposes the notion of a subjunctive means-end link (a means-end link is a method of identifying what is a means to a particular end), wherein one can act for the sake of what would have to be the case if they take a particular action. For example, in newcomb's problem one can pick just a single box because it would then have to be the case that the big box contains a million.

Putting these two things together might help make sense of how our actions affect these kind of thought experiments.

Comment by errethakbe on The Goldbach conjecture is probably correct; so was Fermat's last theorem · 2020-07-15T02:15:12.302Z · LW · GW

I don't think it's a fair deduction to conclude that Goldbach's conjecture is "probably true" based on a estimate of the measure (or probability) of the set of possible counter examples being small. The conjecture is either true or false, but more to the point I think you are using the words probability and probable in two different ways (the measure theoretic sense, and in the sense of uncertainty about the truth value of a statement), which obfuscates (at least to me) what exactly the conclusion of your argument is.

There is of course a case to be made about whether it matters if Goldbach's conjecture should be considered as true if the first counter example is larger than an number that could possibly and reasonable manifest in physical reality. Maybe this was what you are getting at, and I don't really have a strong or well thought out opinion either way on this.

Lastly, I wonder whether there are examples of heuristic calculations which make the wrong prediction about the truth value of the conjecture to which they pertain. I'm spitballing here, but it would be interesting to see what the heuristics for Fermat's theorem say about Euler's sum of primes conjecture (of which Fermat's last theorem is K = 2 case), since we know that the conjecture is false for K = 4. More specifically, how can we tell a good heuristic from a bad one? I'm not sure, and I also don't mean to imply that heuristics are useless, more that maybe they are useful because they (i) give one an idea of whether to try to prove something or look for a counter example, and (ii) give a rough idea of why something should be true or false, and what direction a proof should go in (e.g. for Goldbach's conjecture, it seems like one needs to have precise statements about how the primes behave like random numbers).