What a brilliant lecturer! This whole thing is a pleasure to listen to.
At 34 mins 33 secs, there is something that ought to interest cryptographers. Listen to the problem, then ask yourself "why would somebody implement a Miller-Rabin primality test using a fixed pseudo-random number generator like the "Mersenne Twister" which is based on large Mersenne primes?"
At 44 mins 43 secs the answer to the inaudible question explains something that puzzled me too, at first, because of the way John's diagrams seem to show the progressive exclusion of regions of the space. The search does not have to test every point and then choose one from the remainder of the possible points, looking for one of higher quality. All it does is guess the next point in a sequence, and if that is not of a strictly higher quality, then reject it, and so you end up with a strictly monotonically increasing sequence. And I imagine that the sequence which is the number of bad guesses between each good guess, though not monotonic, will converge to a vertical asymptote at the compression level, so if the random points are uniformly distributed in the space then the rate of increase of this number of bad guesses w.r.t. the increase in quality of successive good guesses will give you some idea of your engine's rate of convergence onto the solution. It seems possible that this could be a way to detect resonance, which would probably appear as a discontinuity in this curve.
The solution to resonance is not to use PRNGs at all (see also from 46 mins 33). I know how to do this, but I need the wherewithall to be able to design SOCs with multi-core processors. If I had sixteen of these 4-processor clusters, with one of these on each processor, and some students, then we could build a demonstration system. I had an idea that Element-14 might have actually received a response to this request of mine, so maybe they would like to help?
At 51 mins 24 secs "Don't go to a philosopher to try to get educated on how you do computer programming ... it won't work. If they could do it they would do it!" 😂
Here's part two:
At 34 mins 33 secs, there is something that ought to interest cryptographers. Listen to the problem, then ask yourself "why would somebody implement a Miller-Rabin primality test using a fixed pseudo-random number generator like the "Mersenne Twister" which is based on large Mersenne primes?"
At 44 mins 43 secs the answer to the inaudible question explains something that puzzled me too, at first, because of the way John's diagrams seem to show the progressive exclusion of regions of the space. The search does not have to test every point and then choose one from the remainder of the possible points, looking for one of higher quality. All it does is guess the next point in a sequence, and if that is not of a strictly higher quality, then reject it, and so you end up with a strictly monotonically increasing sequence. And I imagine that the sequence which is the number of bad guesses between each good guess, though not monotonic, will converge to a vertical asymptote at the compression level, so if the random points are uniformly distributed in the space then the rate of increase of this number of bad guesses w.r.t. the increase in quality of successive good guesses will give you some idea of your engine's rate of convergence onto the solution. It seems possible that this could be a way to detect resonance, which would probably appear as a discontinuity in this curve.
The solution to resonance is not to use PRNGs at all (see also from 46 mins 33). I know how to do this, but I need the wherewithall to be able to design SOCs with multi-core processors. If I had sixteen of these 4-processor clusters, with one of these on each processor, and some students, then we could build a demonstration system. I had an idea that Element-14 might have actually received a response to this request of mine, so maybe they would like to help?
At 51 mins 24 secs "Don't go to a philosopher to try to get educated on how you do computer programming ... it won't work. If they could do it they would do it!" 😂
Here's part two:
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