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Is Probability Real?

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Re: Is Probability Real?

#91

Post by adrianN »

yters wrote: post #64
smallnamespace wrote: post #55

Earlier quoted context omitted.

> the amount of error a perfect Bayesian makes as they observe event and bet on the next one, ad infinitum, is finite. There's a little assumption that you're leaving out, namely that the Kolmogorov complexity of the data generating process is finite . From Wikipedia: > expected cumulative errors made by the predictions based on Solomonoff's induction are upper-bounded by the Kolmogorov complexity of the (stochastic)…

If quantum is really random, then our universe has infinite Kolmogorov complexity.

No, just because a process is probabilistic, in does not immediately follow that it has infinite Kolmogorov complexity. For example the probabilistic effects could cancel out.

Re: Is Probability Real?

#92

Post by [deleted] »

loup-vaillant wrote: post #75
smallnamespace wrote: post #55

Earlier quoted context omitted.

> the amount of error a perfect Bayesian makes as they observe event and bet on the next one, ad infinitum, is finite. There's a little assumption that you're leaving out, namely that the Kolmogorov complexity of the data generating process is finite . From Wikipedia: > expected cumulative errors made by the predictions based on Solomonoff's induction are upper-bounded by the Kolmogorov complexity of the (stochastic)…

> Whether the universe (or our observations of the universe) have finite complexity is very much an unresolved philosophical question. Every time there was a significant advance in physics, it tended to go towards simplification and unification. Geocentrism required epicycles. Then Keppler came up with his ellipses. Then Newton unified celestial and terrestrial laws. Maxwell & Einstein allowed us to view time as less…

[deleted]

Re: Is Probability Real?

#93

Post by 6gvONxR4sf7o »

MauranKilom wrote: post #11

> The scientific method only works because the rules of the universe happen to be simple, while the set of observations it offers is vast. Kolmogorov complexity captures this defining characteristic of our reality. I've never seen this spelled out so beautifully!

I disagree that the rules just happen to be simple. Thinking in dynamical systems or evolutionary terms, a language and mental model of the universe just won’t stick around unless it’s useful. Imagining that the universe happens to be horribly complex, but has some emergent phenomena that happen to be simple, we’re almost inevitably going to think in those simpler terms and go “wow the universe is simple!”

Then if the foundation underlying those simple emergent concepts turns out to be horrible complex, maybe we get stuck with the foundations at some point. Or maybe simplicity is relative and a visitor from a different hypothetical universe would be astounded at all the shit we have to simulate because the answer isn’t just obvious.

Like how macroscopic objects are an emergent phenomenon, but they’re simple. Maybe the universe at a fundamental level follows some ultra convoluted string theory. Doesn’t matter for us, the same way that flipping a coin is 50-50 regardless of questions about foundational physics.

It’s taken a long time to develop the hierarchy of physical and mathematical concepts in which we can usefully describe much of the universe as simple. And those concepts, the best we have so far, still don’t tell the whole story.

Re: Is Probability Real?

#95

Post by CraneWorm »

yters wrote: post #64
smallnamespace wrote: post #55

Earlier quoted context omitted.

> the amount of error a perfect Bayesian makes as they observe event and bet on the next one, ad infinitum, is finite. There's a little assumption that you're leaving out, namely that the Kolmogorov complexity of the data generating process is finite . From Wikipedia: > expected cumulative errors made by the predictions based on Solomonoff's induction are upper-bounded by the Kolmogorov complexity of the (stochastic)…

If quantum is really random, then our universe has infinite Kolmogorov complexity.

quantum is not the same as random, this analogy breaks down quickly as you try to explain the experimental results

Re: Is Probability Real?

#96

Post by jbay808 »

st1x7 wrote: post #13
wearsshoes wrote: post #12

Earlier quoted context omitted.

This is still a partial knowledge situation - you have the information that there are a certain proportion of colored balls in the chamber, but not the information about their order. The probability includes the information we do know and allows inferences about information we don’t know.

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.

It has to do with your knowledge of the object. To that extent, it has something to do with the object it describes.

Re: Is Probability Real?

#97

Post by Koshkin »

loup-vaillant wrote: post #49

Tow things. First, probability is real: it's a construct in one's mind, and minds are just as real as dice or coins. https://www.lesswrong.com/posts/f6ZLxEWaankRZ2Crv/probabilit... Second, (and the author may be leading up to this), there's Solomonoff's theory of inductive inference, which he has proven complete : when we apply Occam's razor (where the prior probability of each possible theory drops exponentially wit…

> is real: it's a construct in one's mind, and minds are just as real

This is a weird thing to say. Not all mental constructs are "real" in a meaningful sense.

Re: Is Probability Real?

#98

Post by jbay808 »

SAI_Peregrinus wrote: post #67
StavrosK wrote: post #18

Earlier quoted context omitted.

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.

> If you don't know that the coin is weighted, the probability is 50%. No, if it's weighted it's not 50%. Your prior probability is 50%, but neither a Bayesian nor a frequentist would claim the true probability is known before testing.

> the true probability

Interesting expression.

After testing, it turned out that you flipped it and it landed on heads.

Does that mean that you've discovered that the "true probability" for that flip should have been 100% heads?

Re: Is Probability Real?

#99

Post by jbay808 »

kps wrote: post #34
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…

Forget the coin and the balls — does the nucleus decay? You're not missing any knowledge; there isn't any.

This is definitely the most interesting example, but it's not obvious that a situation where the relevant information is fundamentally inaccessible is a situation where you aren't missing any information.

It's your best bet for a scenario where you can be sure that nobody else has more information than you do, though.

Re: Is Probability Real?

#100

Post by Koshkin »

abdulhaq wrote: post #94

Surely you have to define reality before approaching this question?

I wonder if it is even possible. In math, science, and philosophy some (basic) terms are necessarily left undefined and their meaning is either left open to interpretation or assumed to be evident based on common experience or convention.
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