RUTA said:
First, I assume by “flipping a coin” you mean a phenomenon with an unequivocally 50-50 outcome. According to Newton’s laws, the literal flipping of a coin will produce a deterministic outcome, so the 50-50 outcome is not ontological, but epistemological.
The 50/50 probability on an individual trial is not ontological in a deterministic universe, but even in a deterministic universe, for a large set of trials where we flip a coin N times, we should expect that all possible sequences of results occur with equal frequency (for example, if we do 8 million trials where we flip the coin three times and record the result, we'd expect HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT to each occur on about 1 million of the trials). This can be justified using arguments analogous to those in classical statistical mechanics, where we assume all the possible "microstates" associated with a given "macrostate" would occur with equal frequency in the limit of a very large number of trials with the same macrostate.
Do you disagree that for some phenomena with a 50/50 outcome, regardless of whether the uncertainty is epistemological or ontological, we would expect that if a near-infinite number of civilizations were doing a sequence of N tests of that phenomena, all specific sequences of N results would occur with the same frequency relative to this near-infinite set? For example, if each civilization is doing 20 flips of a fair coin, we should expect that about 2
-20 of these civilizations get the sequence HTHHTTTHTHHHHTTHTTHT, while about 2
-20 of these civilizations get the sequence HHHHHHHHHHHHHHHHHHHH? Each
specific sequence occurs with equal frequency, but there are far more possible sequences with close to 10 heads and 10 tails then there are possible sequences with more asymmetrical ratios of heads to tails, and this explains why the average civilization is a lot more likely to see something close to a 50/50 ratio.
It would really help if you would give me a
specific answer to whether you agree that the above is statistically correct. If you don't think it's correct, do you think it would still be incorrect if we reduced N from 20 to 3, and replaced multiple civilizations with a single experimenter doing a large run of sequences of 3 tests? If a single experimenter does 8000 sequences of 3 tests, do you disagree with the prediction that about 1000 sequences will give result HHH, about 1000 will give result HHT, and so on for all 8 possible combinations?
RUTA said:
I assume we both agree that there are statistical regularities in Nature. The question is, how are they instantiated? The answer to this question tells us whether or not such regularities can be discovered scientifically. I will argue that, according the JesseM belief (what you call “pure statistics”)
But you still aren't telling me what specific statement about "pure statistics" you think is incorrect, you're just disagreeing with my argument as a whole. I laid out my argument in a step-by-step fashion so we could pinpoint where precisely you think the argument goes off the rails, rather than you just telling me you disagree with the conclusion. Can you pinpoint what specific sentences in the paragraphs above (starting with 'Do you disagree' and 'It would really help') you believe to be incorrect?
RUTA said:
it is impossible to know whether or not you have discovered any such regularity.
It is impossible to "know" with perfect 100% certainty that a given equation accurately describes nature. But science isn't about perfect 100% certainty in anything! It's just about accumulating stronger and stronger evidence for some theories, and I'd say that if we can show that if we are comparing some hypothesis to a null hypothesis, and we find that the null hypothesis would require us to believe a statistical fluctuation with probability 1 in 10^100 had occurred, that's extremely strong evidence that the null hypothesis is false. Perfect 100% certainty only occurs in pure mathematical proofs.
RUTA said:
Conclusion: Most scientists probably subscribe to the RUTA belief (either tacitly or explicitly, but at pragmatically).
I disagree, most scientists would probably agree that we can never have complete 100% certainty in any theory, only accumulate strong evidence for some theories and evidence against others. And most scientists would agree that if a given set of results would only have a probability of 1 in 10^100 according to some null hypothesis, that's very strong evidence against the null hypothesis.
RUTA said:
Consider a series of experiments designed to find a statistical regularity of Nature (SRN). Each experiment conducts many trials, each with a distribution of outcomes. Many experiments produce many distributions, so that we have a distribution of distributions at any given location in the universe (assumed infinite).
According to the JesseM belief, all conceivable distributions of distributions are instantiated in the universe
Well, only if it is in fact true that the universe is infinite in size with an infinite number of civilizations running the same type of experiment. It's possible the universe is actually finite in size. The standard frequentist view of probability is that probabilities represent the statistics that
would be seen in an infinite collection of trials of the same experiment, regardless of whether such an infinite collection is actually performed in the real physical universe.
RUTA said:
and only collectively do they yield the SRN being investigated.
According to the RUTA belief, each distribution of distributions yields the SRN being investigated.[/quote]
But a "distribution of distributions" is just a larger distribution. Do you think that the laws of statistics would work differently in these two case?
1) A single long-lived civilization does a large number of trials where each trial consists of N tests (like a coin flip), each trial giving a distribution.
2) A large number of short-lived civilizations do m trials where each trial consists of n tests, each trial giving a distribution, after which these civilizations collapse (due to nuclear war or global warming or whatever). As it so happens, m*n=N, so for each of these short-lived civilizations, their "distribution of distributions" consists of a total of N tests.
Your argument would seem to imply that in case 1), since a given series of N tests is just a single distribution from many collected by that civilization, you accept that a given series might show aberrant results; but somehow in case 2), since the "distribution of distributions" for each of the short-lived civilizations consists of N tests, not one of these civilizations will get aberrant statistics on those N tests (which consists of all tests of a given experiment in their entire history, perhaps lasting hundreds of years before they finally die off). This would be something of a statistical miracle!
If you don't think your argument would actually imply this statistically miraculous conclusion, please clarify.
RUTA said:
P1. We don’t know the SRN under investigation, that’s why we’re doing the experiment.
P2. If JesseM is right, there are distributions of distributions nowhere “near” the SRN. [Define this proximity per a number of “standard deviations” obtained over the distribution of distributions itself. Pick any number you like, since, according to JesseM, all conceivable distributions of distributions are realized.]
C1. Any particular location in the universe doesn’t (and can’t) know whether or not their distribution of distributions is “near” the SRN.
Again, they can't "know" with 100% certainty, but they can be very very confident. If some aberrant "distribution of distributions" would only occur in 1 out of 10^100 civilizations, it's reasonable for any given civilization to conclude there's only a 1 in 10^100 chance that their civilization is one of the ones that gets the aberrant statistics.
RUTA said:
P3. Most scientists believe (tacitly or explicitly, but at least pragmatically) that the distribution of distributions they discover on Earth is “near” the SRN.
P4. The scientists of P3 don’t believe Earth occupies a “special” or “privileged” place in the universe.
Yes, and according to my view of statistics, both beliefs are perfectly reasonable. You seem to think that somehow my view implies such beliefs
aren't reasonable, but you've never given a clear explanation as to why that should be the case.
RUTA said:
C2. Most scientists subscribe to the RUTA belief, not the JesseM belief.
I don't believe that. Most scientists would believe the same laws of statistics apply to collections of trials with N tests in cases 1) and 2) above, despite the fact that in 2) each trial represents a "distribution of distributions" for an entire civilization while in 1) a single civilization is doing many such trials with N tests.
RUTA said:
Now you should be able to easily and accurately infer my answer to your question about getting “all heads” when “flipping a coin” somewhere in an infinite universe.
No, I actually am not sure, so please state it outright. Do you really believe that different statistics would apply in a collection of trials with N tests each in case 1) and 2) above, even though the only difference is that in case 1) we are considering a large number of trials done by a single civilization, and in case 2) we are considering a large number of civilizations which each do N tests before dying off?