5 ms·

What does that mean, "you can tell this sequence is not random"? If you show me a blue hat, and ask me if it's blue, I'll say yes, I can say it's blue. But ther

What does that mean, "you can tell this sequence is not random"? If you show me a blue hat, and ask me if it's blue, I'll say yes, I can say it's blue. But there is always a chance it's not actually blue. It's very conceivable that I'm in a situation where I say with confidence that something is blue, but it isn't. You always only ever speak in probability. Of course you can't say the sequence isn't random, because every sequence can be the result of a random process. "can you tell which is random" to me is equivalent as asking "is one of the sequences such that it is rational to choose it over the other as being random". It's about rational decisions. Consider the frequentist view, where a probability p for an event A means that out of k trials, pk will show A (in expectation), and fruthermore if k -> infty, then the portion of events that show A will converge to p. If you want to choose the right sequence as being random as often as possible, it is rational to choose the one I described above, because it will, overall, be the one that is MORE OFTEN the random one compared to the other.

denton-scratch 4y ago
For a blue hat, it either is or isn't blue (and there's some rather strong evidence - whether or not it looks blue). Like, with a sequence of 6 digits, if you don't know whether the source was random or not, then that's like NOT showing me your hat, and asking me whether it's red or blue. For a single sequence of six digits, it might or might not have come from a random source. You can't get any edge on that judgement by just inspecting the sequence. Only inspecting the source (the hat, if you like) can give you an advantage. Perhaps you're colour-blind, or the lighting is weird; so there's still uncertainty. But that's equivalent to examining the source of the digits, determining that it's really a random source, but making a mistake in your determination. That's uncertainty on a different level. Red-pill blue-pill is a sort of meta-uncertainty. > "is one of the sequences such that it is rational to choose it over the other as being random" Most people don't care about this shit; it doesn't matter to them what random means, nor whether it's sequences or sources that can be said to be random. But for some people it does matter, and they have to try to use language precisely. All [red|blue] hats are either red or blue. But no sequence is random or non-random; it's the source of the sequence (the process, if you like) than can be random or non-random. If 111111 is emitted by a random process, then you can call that a "random sequence" if you like. If I emit 126692 from my ass (not a random process), that's not a "random sequence" in any sense, whatever statistical properties it has. You can't tell which is of random origin by inspection. The experimental subjects face an impossible challenge, and I can't see what conclusions you can draw from their responses.
- denton-scratch 4y ago
  Regarding "random process": (and sorry for commenting to myself) I'm not taking a position on what a "random process" is; for these purposes, a PRNG, a LFSR or even the last three bits of the system-clock would do as well as radioactive decay.

denton-scratch 4y ago

For a blue hat, it either is or isn't blue (and there's some rather strong evidence - whether or not it looks blue). Like, with a sequence of 6 digits, if you don't know whether the source was random or not, then that's like NOT showing me your hat, and asking me whether it's red or blue. For a single sequence of six digits, it might or might not have come from a random source. You can't get any edge on that judgement by just inspecting the sequence. Only inspecting the source (the hat, if you like) can give you an advantage. Perhaps you're colour-blind, or the lighting is weird; so there's still uncertainty. But that's equivalent to examining the source of the digits, determining that it's really a random source, but making a mistake in your determination. That's uncertainty on a different level. Red-pill blue-pill is a sort of meta-uncertainty. > "is one of the sequences such that it is rational to choose it over the other as being random" Most people don't care about this shit; it doesn't matter to them what random means, nor whether it's sequences or sources that can be said to be random. But for some people it does matter, and they have to try to use language precisely. All [red|blue] hats are either red or blue. But no sequence is random or non-random; it's the source of the sequence (the process, if you like) than can be random or non-random. If 111111 is emitted by a random process, then you can call that a "random sequence" if you like. If I emit 126692 from my ass (not a random process), that's not a "random sequence" in any sense, whatever statistical properties it has. You can't tell which is of random origin by inspection. The experimental subjects face an impossible challenge, and I can't see what conclusions you can draw from their responses.

denton-scratch 4y ago
Regarding "random process": (and sorry for commenting to myself) I'm not taking a position on what a "random process" is; for these purposes, a PRNG, a LFSR or even the last three bits of the system-clock would do as well as radioactive decay.