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The probability distribution is subjective for both parts -- because it, once again, depends on the observer observing the events in order to build a probabilit

The probability distribution is subjective for both parts -- because it, once again, depends on the observer observing the events in order to build a probability distribution. E.g. your random number generator generates 1, 5, 7, 8, 3 when you run it. It generates 4, 8, 8, 2, 5 when I run it. I.e. we have received different information about the random number generator to build our subjective probability distributions. The level of entropy of our probability distributions is high because we have so little information to be certain about the representativeness of our distribution sample. If we continue running our random number generator for a while, we will gather more information, thus reducing entropy, and our probability distributions will both start converging towards an objective "truth." If we ran our random number generators for a theoretically infinite amount of time, we will have reduced entropy to 0 and have a perfect and objective probability distribution. But this is impossible.

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canjobear 2y ago
Would you say that all claims about the world are subjective, because they have to be based on someone’s observations? For example my cat weighs 13 pounds. That seems objective, in the sense that if two people disagree, only one can be right. But the claim is based on my observations. I think your logic leads us to deny that anything is objective.
- mitthrowaway2 2y ago
  I do believe in objective reality, but probabilities are subjective. Your cat weighs 13 pounds, and now that you've told me, I know it too. If you asked me to draw a probability distribution for the weight of your cat, I'd draw a tight gaussian distribution around that, representing the accuracy of your scale. My cat weighs a different amount, but I won't tell you how much, so if we both draw a probability distribution, they'll be different. And the key thing is that neither of us has an objectively correct probability distribution, not even me. My cat's weight has an objectively correct value which even I don't know, because my scale isn't good enough.
  - bosco_mcnasty 2y ago
    All right now, here's the big question: how do you know that the evidence your sensory apparatus reveals to you is correct? What I'm getting at is this: the only experience that is directly available to you is your sensory data. And this sensory data is merely a stream of electrical impulses which stimulate your computing center. In other words, all that I really know about the outside universe is relayed to me through my electrical connections. Why, that would mean that...I really don't know what the outside universe is like at all, for certain.
mitthrowaway2 2y ago
Sorry, this is a major misinterpretation, or at least a completely different one. I don't know how to put it in a more productive way; I think your comment is very confused. You don't need to run a random number generator "for a while" in order to build up a probability distribution.
- financltravsty 2y ago
  A representative sample then? Please tell me where I went wrong -- I mean this sincerely.
  - mitthrowaway2 2y ago
    This might be a frequentist vs bayesian thing, and I am bayesian. So maybe other people would have a different view. I don't think you need to have any information to have a probability distribution; your distribution already represents your degree of ignorance about an outcome. So without even sampling it once, you already should have a uniform probability distribution for a random number generator or a coin flip. If you do personally have additional information to help you predict the outcome -- you're skilled at coin-flipping, or you wrote the RNG and know an exploit -- then you can compress that distribution to a lower-entropy one. But you don't need to sample the distribution to do this. You can have that information before the first coin toss. Sampling can be one way to get information but it won't necessarily even help. If samples are independent, then each sample really teaches you barely anything about the next. RNGs eventually do repeat so if you sample it enough you might be able to find the pattern and reduce the entropy to zero, but in that case you're not learning the statistical distribution, you're deducing the exact internal state of the RNG and predicting the exact next outcome, because the samples are not actually independent. If you do enough coin flips you might eventually find that there's a slight bias to the coin, but that really takes an extreme number of tosses and only reduces the entropy a tiny tiny bit; not at all if the coin-tossing procedure had no bias to begin with. However the objective truth is just that the next toss will land heads. That's the only truth that experiment can objectively determine. Any other doubt that it might-have-counterfactually-landed-tails is subjective, due to a subjective lack of sufficient information to predict the outcome. We can formalize a correct procedure to convert prior information into a corresponding probability distribution, we can get a unanimous consensus by giving everybody the same information, but the probability distribution is still subjective because it is a function of that prior information.

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canjobear 2y ago

Would you say that all claims about the world are subjective, because they have to be based on someone’s observations? For example my cat weighs 13 pounds. That seems objective, in the sense that if two people disagree, only one can be right. But the claim is based on my observations. I think your logic leads us to deny that anything is objective.

mitthrowaway2 2y ago
I do believe in objective reality, but probabilities are subjective. Your cat weighs 13 pounds, and now that you've told me, I know it too. If you asked me to draw a probability distribution for the weight of your cat, I'd draw a tight gaussian distribution around that, representing the accuracy of your scale. My cat weighs a different amount, but I won't tell you how much, so if we both draw a probability distribution, they'll be different. And the key thing is that neither of us has an objectively correct probability distribution, not even me. My cat's weight has an objectively correct value which even I don't know, because my scale isn't good enough.
- bosco_mcnasty 2y ago
  All right now, here's the big question: how do you know that the evidence your sensory apparatus reveals to you is correct? What I'm getting at is this: the only experience that is directly available to you is your sensory data. And this sensory data is merely a stream of electrical impulses which stimulate your computing center. In other words, all that I really know about the outside universe is relayed to me through my electrical connections. Why, that would mean that...I really don't know what the outside universe is like at all, for certain.

mitthrowaway2 2y ago

Sorry, this is a major misinterpretation, or at least a completely different one. I don't know how to put it in a more productive way; I think your comment is very confused. You don't need to run a random number generator "for a while" in order to build up a probability distribution.

financltravsty 2y ago
A representative sample then? Please tell me where I went wrong -- I mean this sincerely.
- mitthrowaway2 2y ago
  This might be a frequentist vs bayesian thing, and I am bayesian. So maybe other people would have a different view. I don't think you need to have any information to have a probability distribution; your distribution already represents your degree of ignorance about an outcome. So without even sampling it once, you already should have a uniform probability distribution for a random number generator or a coin flip. If you do personally have additional information to help you predict the outcome -- you're skilled at coin-flipping, or you wrote the RNG and know an exploit -- then you can compress that distribution to a lower-entropy one. But you don't need to sample the distribution to do this. You can have that information before the first coin toss. Sampling can be one way to get information but it won't necessarily even help. If samples are independent, then each sample really teaches you barely anything about the next. RNGs eventually do repeat so if you sample it enough you might be able to find the pattern and reduce the entropy to zero, but in that case you're not learning the statistical distribution, you're deducing the exact internal state of the RNG and predicting the exact next outcome, because the samples are not actually independent. If you do enough coin flips you might eventually find that there's a slight bias to the coin, but that really takes an extreme number of tosses and only reduces the entropy a tiny tiny bit; not at all if the coin-tossing procedure had no bias to begin with. However the objective truth is just that the next toss will land heads. That's the only truth that experiment can objectively determine. Any other doubt that it might-have-counterfactually-landed-tails is subjective, due to a subjective lack of sufficient information to predict the outcome. We can formalize a correct procedure to convert prior information into a corresponding probability distribution, we can get a unanimous consensus by giving everybody the same information, but the probability distribution is still subjective because it is a function of that prior information.