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JGWeissman comments on The Absent-Minded Driver - Less Wrong
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My point is that it's no more convenient than having the pseudo-random number generator available. I maintain that the generator is implementing your memory in functionally the same sense. For example, you are effectively guaranteed not to get the same number twice, just as you are effectively guaranteed not to get the same poker chip twice.
ETA: After all, something in the generator must be keeping track of the passage of the marbles for you. Otherwise the generator would keep producing the same number over and over.
That is fair enough, though the reason I find scenario at all interesting is that it illustrates the utility of a random strategy under certain conditions.
For me, finding an equivalent nonrandom strategy helps to dispel confusion.
I like your characterization above that the PRNG is "memory with the drawback that you don't understand how it works to the extent that you are uncertain how it correlates with what you wanted to remember." Another way to say it is that the PRNG gives you exactly what you need with near-certainty, while normal memory gives you extra information that happens to be useless for this problem.
What is "random" about the PRNG (the exact sequence of numbers) is extra stuff that you happen not to need. What you need from the PRNG (N numbers, of which two-thirds are less than 2/3) is not random but a near-certainty. So, although you're using a so-called pseudo-random number generator, you're really using an aspect of it that's not random in any significant sense. For this reason, I don't think that the PRNG algorithm should be called "random", any more than is the poker chip algorithm.