"All models are wrong, but some are useful"
Is Probability Real?
31–40 of 227 posts
Re: Is Probability Real?
#32Earlier quoted context omitted.
A simple sentence that I've found useful for pedagogy: "the probability of that coin toss being 50% does not talk about the coin; it talks about you , and about your partial knowledge of the universe." You can add: "The coin toss itself is deterministic and the result can be computed if you know the initial position and speed." They will inevitably bother you about the physical impossibility to measure the starting p…
This is basically the Bayesian interpretation of probability.
Saying that "the probability of a coin toss of 50% talks about you" is not an interpretation of probability. Saying that we are "50% sure" is also not an interpretation of probability. It's a nonsensical statement. It's like saying we are "50% angry". It doesn't really mean anything.
Re: Is Probability Real?
#33Earlier quoted context omitted.
The article is excellent, congratulations. A couple observations/questions. 1) You didn't comment on the bayesian viewpoint that probability reflects a subjective idea about the state of the world. One might argue, for example, that probability isn't measurable, and that therefore, strictly speaking, a statement about the objective probability of an event isn't meaningful. Experimental evaluation would have to be don…
Isn't that what the occam's razor argument was for? Sure, both an RNG and the "40 digits of pie" program can produce that output, but the "40 digits of pie" program is shorter, therefore having less kolmogorov complexity
Yeah but is it? They are both programs with logarithmic Kolmogorov complexity, and Kolmogorov complexity is only defined up to constant factors unless you commit to a computational model.
If you do commit to one, which is the shortest is just a function of what are the specifics of the model you chose, which isn't really interesting, it's literally code golf at that point.
Re: Is Probability Real?
#34Since this topic isn't so well-known, I wrote the case arguing that frequentist interpretations don't work, but algorithmic information theory (Kolmogorov complexity) does. I want to make this accessible and persuasive, so thoughts, questions, and arguments would be appreciated!
A simple sentence that I've found useful for pedagogy: "the probability of that coin toss being 50% does not talk about the coin; it talks about you , and about your partial knowledge of the universe." You can add: "The coin toss itself is deterministic and the result can be computed if you know the initial position and speed." They will inevitably bother you about the physical impossibility to measure the starting p…
Forget the coin and the balls — does the nucleus decay? You're not missing any knowledge; there isn't any.
Re: Is Probability Real?
#35Since this topic isn't so well-known, I wrote the case arguing that frequentist interpretations don't work, but algorithmic information theory (Kolmogorov complexity) does. I want to make this accessible and persuasive, so thoughts, questions, and arguments would be appreciated!
A simple sentence that I've found useful for pedagogy: "the probability of that coin toss being 50% does not talk about the coin; it talks about you , and about your partial knowledge of the universe." You can add: "The coin toss itself is deterministic and the result can be computed if you know the initial position and speed." They will inevitably bother you about the physical impossibility to measure the starting p…
Wigner's friend might have something to say about this...
I don't have a specific argument to make here, only the feeling that if it were all just a matter of what a given observer knows, no-one would be talking about there being a QM measurement problem.
Re: Is Probability Real?
#36Earlier quoted context omitted.
Isn't that what the occam's razor argument was for? Sure, both an RNG and the "40 digits of pie" program can produce that output, but the "40 digits of pie" program is shorter, therefore having less kolmogorov complexity
Yeah but is it? They are both programs with logarithmic Kolmogorov complexity, and Kolmogorov complexity is only defined up to constant factors unless you commit to a computational model. If you do commit to one, which is the shortest is just a function of what are the specifics of the model you chose, which isn't really interesting, it's literally code golf at that point.
> They are both programs with logarithmic Kolmogorov complexity
In the case of true random numbers, how is that so?
Very few random sequences can be generated by a logarithmic-sized program, since most strings are not significantly compressible [1]. A simple counting argument shows that: there are 2^n strings of n bits, but only 2^(lg n) = n logarithmic-sized strings, a much smaller number!
[1] http://theory.stanford.edu/~trevisan/cs154-12/kolcomplexity-...
Re: Is Probability Real?
#37[deleted]
Re: Is Probability Real?
#38Ultimately, probability must be real, because if you zoom in to a low enough level, the movement of particles is basically random, and this randomness is enough to poison any deterministic explanations for which side a coin flip will land. You could calculate which side a coin will land if you knew all the variables and thus arrive at a higher probability that it will land on a certain side, but it’s still a probabil…
Philip McShane expressed this nicely: "...a thing is defined by... systematizations of coincidental aggregates of the properties of lower things". Probability theory "allows for the emergence of the systematic from the non-systematic".
Re: Is Probability Real?
#39Since this topic isn't so well-known, I wrote the case arguing that frequentist interpretations don't work, but algorithmic information theory (Kolmogorov complexity) does. I want to make this accessible and persuasive, so thoughts, questions, and arguments would be appreciated!
A simple sentence that I've found useful for pedagogy: "the probability of that coin toss being 50% does not talk about the coin; it talks about you , and about your partial knowledge of the universe." You can add: "The coin toss itself is deterministic and the result can be computed if you know the initial position and speed." They will inevitably bother you about the physical impossibility to measure the starting p…
As a caveat, while this intuition works for classical mechanics, it does not work for quantum mechanics. All observations are consistent with wave function collapse being fundamentally random. Any hidden variables would need to be transmitted many times faster than the speed of light (~10000x, last time I checked the experiments), and are therefore inconsistent with our understanding of special relativity.
Re: Is Probability Real?
#40Earlier quoted context omitted.
Sure, I just can't agree with the parent statement that probability has nothing to do with the object it describes, which is demonstrably false.
I don't think it's demonstrably false: If you don't know that the coin is weighted, the probability is 50%. Probabilities are predictions and estimates, not fundamentally about the thing itself, but about what we know about the thing.
The principle of indifference? I know that it is a commonplace assumption, but feels to me as though one is assuming one has more information than is justified. Coming back to the article's "economist's wager", is it rational to bet with even odds on something you know nothing about? If the assumption is interpreted as a testable hypothesis about outcomes, why would complete ignorance imply any particular result? On the other hand, if it is interpreted strictly as a statement about one's knowledge, why present it exactly as if one had sufficient knowledge of the situation to know that the probability is 0.5? Maybe the author will have an answer in part 2.