Is Probability Real? • Hacker News Board

Re: Is Probability Real?

#21

Post by qsort » Sat, Nov 28, 2020, 2:55 PM UTC

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!

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 done on an entire model instead. Do you have any objections to that point of view?

2) I don't find the case about Kolmogorov complexity to be actually convincing, at least not as per the requirements the rest of the article sets. "3141592..." could pass as either "random digits" or "first digits of pi". The fact that it's highly unlikely a true RNG would have generated exactly those, we are back to a frequentist argument there. It's likely I'm missing something, could you elaborate more or give me a pointer?

Re: Is Probability Real?

#22

Post by [deleted] » Sat, Nov 28, 2020, 2:58 PM UTC

StavrosK wrote: post #18

st1x7 wrote: post #13

Earlier 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.

[deleted]

Re: Is Probability Real?

#23

Post by SmooL » Sat, Nov 28, 2020, 3:01 PM UTC

qsort wrote: post #21

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!

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

Re: Is Probability Real?

#24

Post by posterboy » Sat, Nov 28, 2020, 3:03 PM UTC

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…

You don't need quantum physics to formulate a philosophical standpoint that happens to agree with the Kopenhagen Interpretation.

I'm not sure if it helps, but I suppose a compromise here would be the assumption that you don't really know the starting configuration of yourself, why you draw probabilistic inferences naturally, that the sun will go up tomorrow like every day.

If that has a biologic explanation, then the top comment was not just to the illusive argument of platonic ideals.

Re: Is Probability Real?

#25

Post by xwdv » Sat, Nov 28, 2020, 3:04 PM UTC

Ultimately, 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 probability, because the particles that make up the coin could all move in such a way at any point that causes the coin to fall in a way you didn’t expect, even if that probability is very low. A small probability unlikely to happen is still a probability nonetheless.

Try computing how a dice made up of a few particles will land. Good luck...

Re: Is Probability Real?

#26

Post by nimbleal » Sat, Nov 28, 2020, 3:07 PM UTC

enriquto wrote: post #5

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!

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…

It may be deterministic, but are you sure it would be computable? One does not necessarily imply the other.

Re: Is Probability Real?

#27

Post by thread_id » Sat, Nov 28, 2020, 3:07 PM UTC

It probably depends on the p-value.

Re: Is Probability Real?

#28

Post by v64 » Sat, Nov 28, 2020, 3:08 PM UTC

enriquto wrote: post #20

Sharlin wrote: post #17

Earlier quoted context omitted.

This is basically the Bayesian interpretation of probability.

Of course. But if you pronounce a fancy word like "bayesian" there's a large amount of minds that shut irremediably.

That's also why we call it QBism [1] instead of quantum bayesianism

[1] https://en.wikipedia.org/wiki/Quantum_Bayesianism

Re: Is Probability Real?

#29

Post by peterwoerner » Sat, Nov 28, 2020, 3:10 PM UTC

rcthompson wrote: post #16

I'm glad to see a write-up of this. I've been searching recently for a way to reasonably define probability without having to invoke either hypothetical infinitely repeated experiments or placing bets (since the latter is really just implicitly invoking the former). I'm looking forward to part 2!

Check out the first chapter of Jayne's probability theory. It's the clearest take down of the frequentist interpretations that you have and introduction to the Bayesian interpretation.

http://www.med.mcgill.ca/epidemiology/hanley/bios601/Gaussia...

Re: Is Probability Real?

#30

Post by mellosouls » Sat, Nov 28, 2020, 3:10 PM UTC

xwdv wrote: post #25

Ultimately, 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…

I haven't read the article either but skimmed it briefly for a later read; I think it isn't disputing the phenomena that probability is ultimately used to describe (as you seem to claim), but how they are to be interpreted.