This is a non-random algorithm that you can use with confidence, but which requires no memory.
You mean it does not require memory in your brain, because you implemented your memory with the poker chips. It is quite convenient they were available.
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.
Rather than using a PRNG (which, as you say, requires memory), you could use a source of actual randomness (e.g. quantum decay). Then you don’t really have extra memory with the randomized algorithm, do you?
I thought of this as well, but it does not really matter because it is the ability to produce the different output in each case event that gives part of the functionality of memory, that is, the ability to distinguish between events. Granted, this is not as effective as deterministically understood memory, where you know in advance which output you get at each event. Essentially, it 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.
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.
Randomness ‘degenerates’ (perhaps by action of a malicious daemon) into non-randomness, and so it can do better and no worse than a non-random approach?
(If the environments and agents are identical down to the source of randomness, then the agent defaults to a pure strategy; but with ‘genuine’ randomness, random sources that are different between instances of the agent, the agent can actually implement the better mixed strategy?)
I’m having trouble parsing your questions. You have some sentences that end in question marks. Are you asking whether I agree with those sentences? I’m having trouble understanding the assertions made by those sentences, so I can’t tell whether I agree with them (if that was what you were asking).
The claim that I was making could be summed up as follows. I described an agent using a PRNG to solve a problem involving painting marbles. The usual way to view such a solution is as
deterministic amnesiac agent PLUS randomness.
My suggestion was instead to view the solution as
deterministic amnesiac agent
PLUS
a particular kind of especially limited memory
PLUS
an algorithm that takes the contents of that memory as input and produces an output that is almost guaranteed to have a certain property.
The especially limited memory is the part of the PRNG that remembers what the next seed should be. If there weren’t some kind of memory involved in the PRNG’s operation, the PRNG would keep using the same seed over and over again, producing the same “random” number again and again.
The algorithm is the algorithm that the PRNG uses to turn the first seed into a sequence of pseudo-random numbers.
The certain property of that sequence is the property of having two-thirds of its terms being less than 2⁄3.
I maintain that the generator is implementing your memory in functionally the same sense.
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.
You mean it does not require memory in your brain, because you implemented your memory with the poker chips. It is quite convenient they were available.
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.
Rather than using a PRNG (which, as you say, requires memory), you could use a source of actual randomness (e.g. quantum decay). Then you don’t really have extra memory with the randomized algorithm, do you?
I thought of this as well, but it does not really matter because it is the ability to produce the different output in each case event that gives part of the functionality of memory, that is, the ability to distinguish between events. Granted, this is not as effective as deterministically understood memory, where you know in advance which output you get at each event. Essentially, it 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.
Have you read this comment of mine from another branch of this conversation?
Randomness ‘degenerates’ (perhaps by action of a malicious daemon) into non-randomness, and so it can do better and no worse than a non-random approach?
(If the environments and agents are identical down to the source of randomness, then the agent defaults to a pure strategy; but with ‘genuine’ randomness, random sources that are different between instances of the agent, the agent can actually implement the better mixed strategy?)
I’m having trouble parsing your questions. You have some sentences that end in question marks. Are you asking whether I agree with those sentences? I’m having trouble understanding the assertions made by those sentences, so I can’t tell whether I agree with them (if that was what you were asking).
The claim that I was making could be summed up as follows. I described an agent using a PRNG to solve a problem involving painting marbles. The usual way to view such a solution is as
My suggestion was instead to view the solution as
The especially limited memory is the part of the PRNG that remembers what the next seed should be. If there weren’t some kind of memory involved in the PRNG’s operation, the PRNG would keep using the same seed over and over again, producing the same “random” number again and again.
The algorithm is the algorithm that the PRNG uses to turn the first seed into a sequence of pseudo-random numbers.
The certain property of that sequence is the property of having two-thirds of its terms being less than 2⁄3.
OK, that’s clearer. And different from what I thought you were saying.
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.