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.
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.