> In the computational proof, independence is between the probability of computational error affecting the calculation. (To be sure, you'd want to run the proof on different hardware!)
But i don't think that is the concern at hand. Yes, re-running can reduce probability of failures due to soft-memory errors and such. But does nothing against logic errors (or non-transient hardware errors). My understanding is the main concern with the proof is not that a cosmic ray hits RAM and flips a bit, but that either the logic may be wrong or a general epistimitic unease that no human directly inspected the cases of the proof.
In any case i said as much in my original comment. To quote: "excepting cosmic ray induced errors of course"
> Wait, what? Your original comment[1] was specific alleging that the absence of a randomizer completely broke the analogy:
Yes, i stand by that (although accept your point that independence not randomization is the salient property). I also maintain that whether or not it is theoretically possible to do independent tests without a randomness is irrelavent to the matter at hand. What matters is if rerunning the code was an independent experiment, not what could theoretically be possible. Even if there exists some non-random way to do that, its irrelavent to whether or not any method was used.
> Sorry, are you really saying that you see no parallel whatsoever between:
>
>a) Run the 4-color computer proof multiple times to increase your confidence that the result wasn't just luck, and
>
>b) Run additional rounds of an interactive ZKP to increase your confidence that the prover wasn't just lucky?
Yes.
Although for greater clarity, i would clarify (a) to say i don't see the connection to non-negligibly increasing your confidence the result of the 4 colour is correct. I agree (and said this in my very first comment) that it would increase your confidence that you didn't get an incorrect result due to a soft-memory error. I would say that relative to all the possible reasons why you might get an incorrect answer, transient hardware failure is very low, so the increase in confidence from rerunning is negligible because the meat of the question is programming error.
In the analagous situation, re-running the zkp gives an extremely high increase in confidence the answer is correct, usually at least halving the possibility of error.
> If you were disputing that additional runs of the 4-color computer proof could increase your epistemic confidence in it
Sure, although the original comment was a bit vauge as to exactly what they meant.
But i don't think that is the concern at hand. Yes, re-running can reduce probability of failures due to soft-memory errors and such. But does nothing against logic errors (or non-transient hardware errors). My understanding is the main concern with the proof is not that a cosmic ray hits RAM and flips a bit, but that either the logic may be wrong or a general epistimitic unease that no human directly inspected the cases of the proof.
In any case i said as much in my original comment. To quote: "excepting cosmic ray induced errors of course"
> Wait, what? Your original comment[1] was specific alleging that the absence of a randomizer completely broke the analogy:
Yes, i stand by that (although accept your point that independence not randomization is the salient property). I also maintain that whether or not it is theoretically possible to do independent tests without a randomness is irrelavent to the matter at hand. What matters is if rerunning the code was an independent experiment, not what could theoretically be possible. Even if there exists some non-random way to do that, its irrelavent to whether or not any method was used.
> Sorry, are you really saying that you see no parallel whatsoever between: > >a) Run the 4-color computer proof multiple times to increase your confidence that the result wasn't just luck, and > >b) Run additional rounds of an interactive ZKP to increase your confidence that the prover wasn't just lucky?
Yes.
Although for greater clarity, i would clarify (a) to say i don't see the connection to non-negligibly increasing your confidence the result of the 4 colour is correct. I agree (and said this in my very first comment) that it would increase your confidence that you didn't get an incorrect result due to a soft-memory error. I would say that relative to all the possible reasons why you might get an incorrect answer, transient hardware failure is very low, so the increase in confidence from rerunning is negligible because the meat of the question is programming error.
In the analagous situation, re-running the zkp gives an extremely high increase in confidence the answer is correct, usually at least halving the possibility of error.
> If you were disputing that additional runs of the 4-color computer proof could increase your epistemic confidence in it
Sure, although the original comment was a bit vauge as to exactly what they meant.