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Is Probability Real?

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Re: Is Probability Real?

#171

Post by EbTech »

TheOtherHobbes wrote: post #10
EbTech wrote: post #2

Since 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!

OK - so apply Kolmogorov complexity to election polling. How does that work out? I think you're confusing various possible maps with the territory in a less than useful way. Given that frequentist interpretations are approximations - and understood as such - and Kolmogorov complexity isn't computable at all, what problem have you solved here?

Hm I admit it's hard to talk convincingly about election prediction, since we don't have practical algorithms to do this; a lot of it comes down to human judgment.

The philosophical point (which might be approximated algorithmically someday, or by intelligent minds today) is that your election probabilities should come out of an overall highly compressed model of the world. In theory, a Bayesian who uses the prior 2^-K(x) over all strings x should, with sufficient life experience, come up with good estimates, in a certain sense.

I'll have to think about this example more carefully when fulfilling my promise of writing about how this theory relates to everyday decision-making. Thanks for pointing out a potential weakness :)

Re: Is Probability Real?

#172

Post by EbTech »

richard_todd wrote: post #54
EbTech wrote: post #2

Since 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!

I would have liked to know what the Kolmogorov approach has to say about the examples used to deflate frequentism ("which of my friends will start a business?"). I don't see from the article how the "smallest-program" approach could say anything useful about those, either. Maybe that wasn't the point--but after poking holes in the frequentist view, it uses unrelated examples like digits of pi to illustrate the Kolmog…

Thanks! I hope to better address your concerns in Part 2.

Re: Is Probability Real?

#173

Post by EbTech »

JamisonM wrote: post #50
EbTech wrote: post #2

Since 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!

Some thoughts on the composition: * "I wrote the case arguing that frequentist interpretations don't work, but algorithmic information theory does": if that's what you are up to here then I think it would be for readers if you stated that up front in some way. And hit me with some kind of summary at the end that makes the concise version of your argument at the end, it's a long article. * Shorter might be better: The…

Thanks for the detailed critique! I'll take some time to think about how to better make the points that I wanted to convey with those sections.

Re: Is Probability Real?

#174

Post by PeterisP »

richard_todd wrote: post #54
EbTech wrote: post #2

Since 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!

I would have liked to know what the Kolmogorov approach has to say about the examples used to deflate frequentism ("which of my friends will start a business?"). I don't see from the article how the "smallest-program" approach could say anything useful about those, either. Maybe that wasn't the point--but after poking holes in the frequentist view, it uses unrelated examples like digits of pi to illustrate the Kolmog…

One aspect of Kolmogorov approach is that implicitly models things like biased probabilities through compressibility.

The shortest representation of rolls of fair dice or coins is their exact results, but if there's "less randomness" in some way (biased coin/die, sum of two dice which means non-uniform probabilities, combination of some predictable pattern with random noise) then there are more compact representations of that information, and all of that gets captured by the Kolmogorov approach without any explicit handling of the various possibilities.

Re: Is Probability Real?

#175

Post by enriquto »

Frost1x wrote: post #14
enriquto wrote: post #7

Earlier quoted context omitted.

Somebody just put the balls there carefully, and did not tell you in what order, just how many of each color.

That still boils down to a lack of prior information which I don't think removes the argument for "I don't have enough information." Probably have to use actual quantum phenomena that behave probabilistically by definition if you want a currently irrefutable physical example. I'm personally not convinced even this is fundamentally probabilistic and we currently have to rely on probability theory as a crutch for compl…

> "I don't have enough information."

My point exactly. Probability theory is a precise mathematical formalization of the concept of "not enough information".

Re: Is Probability Real?

#176

Post by dkersten »

lisper wrote: post #130
BalinKing wrote: post #114

Earlier quoted context omitted.

As I understand it: The rules are simple, but not necessarily intuitive.

Exactly right. The rules of quantum mechanics are in their essence not much more complicated than high school algebra. It is the logical consequences of those rules that are hard to wrap your brain around.

I have a couple of books on quantum field theory and it looks a lot harder than high school algebra.

Re: Is Probability Real?

#177

Post by imtringued »

st1x7 wrote: post #8
enriquto wrote: post #5

Earlier 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…

> 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. But it does talk about the coin - a weighted coin would have a different probability. Same in the example with the white/black balls - if they weren't 5 white and 5 black but 6 white and 4 black, the probability you would assign to the top one would be different. Again, the…

>Again, the probability is a way to describe the balls themselves, not just our knowledge.

Probability is about the fact that you don't know everything about the balls themselves. If you could make 100% predictions then your knowledge of the balls would be equivalent to the balls' description.

Why do you even use "describe the balls themselves" to describe this situation? From the perspective of probability you just set an upper bound to how much knowledge you could possibly have about an object, it's still knowledge.

Re: Is Probability Real?

#178

Post by imtringued »

jbay808 wrote: post #144
SAI_Peregrinus wrote: post #121

Earlier quoted context omitted.

IMO (I should have defined this) the true probability would require an infinite sequence of tests to determine.

Ok, so let's imagine you build a servo-driven flipping machine to carry out an infinite series of tests and notice, after a thousand of them, that 99% of the time, the coin flip matches the orientation of the coin when it's loaded into the machine. What have you learn about the coin's true flip probability?

>What have you learn about the coin's true flip probability?

Nothing because you only tested the coin flip machine in aggregate. If you have a different throwing mechanism the results could be completely different.

Re: Is Probability Real?

#179

Post by imtringued »

mannykannot wrote: post #52
shawnz wrote: post #45

Earlier quoted context omitted.

They didn't say that it has "nothing to do with the object it describes" though. It has to do with your knowledge, which itself has to do with the object your knowledge describes

"The probability of that coin toss being 50% does not talk about the coin." I think there is a subtle equivocation going on here.

Well, it's getting philosophical now. We do not have a way to experience the true nature of the coin. We can only experience an "image" [0] of the coin and we summarize all "images" of that object into knowledge.

[0] by image I do include your vision, but also hearing, feeling and other methods of perception.

Re: Is Probability Real?

#180

Post by edna314 »

MauranKilom wrote: post #143
edna314 wrote: post #138

Earlier quoted context omitted.

Because others already questioned the first part, I’ll question this: > the set of observations it offers is vast Actually, in an experiment there is always only one observation at a time. That we group multiple observations together is kind of arbitrary and relies on the hope that the experimental conditions are the same and therefore one experiment is analogous to the next.

Yes, that's exactly the heart of the quote to me: There is sufficiently little complexity in the causality of observable behavior that with sufficiently controlled and repeated experiments/sampling, we can uncover regularities and patterns in it to fuel our predictions (and hypothesize about these causalities). Does the reading of your multimeter depend on the digits of Arnold Schwarzenegger's phone number? Do you ha…

> Does the reading of your multimeter depend on the digits of Arnold Schwarzenegger's phone number? Do you have to repeat the experiment if his phone number changes? Indeed, we assume that this is not an "experimental condition" to take into account. There is no way to determine this a-priori, and one could conceive of a universe with an arbitrary amount of such strange influences. But we do not appear to live in such a universe, which is why we get to apply Occam's Razor.

I think this is not true for every experiment. For example if you measure the polarization of a photon it will have the same polarization in any subsequent experiment, no matter how hard you try to reduce complexity.

Also, my comment was rather directed at the fact that any experiment has a unique outcome. In that sense we we can’t have perfect control over an experiment, since at least time must have passed between subsequent measurements, such that the experimental conditions are different.

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