Is Probability Real? • Hacker News Board

Re: Is Probability Real?

#131

Post by lisper » Sat, Nov 28, 2020, 8:57 PM UTC

6gvONxR4sf7o wrote: post #93

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 th…

> if the foundation underlying those simple emergent concepts turns out to be horrible complex

That is extremely unlikely. The simplicity of the universe is not just an artifact of our best theories, it appears to be baked into the very structure of those theories. If our current theories are even in the ballpark, then there are very few places that hidden complexity could possibly hide.

Take quantum randomness, for example. It used to be thought that the apparent randomness could just be papering over our ignorance of some hidden underlying mechanism, but it turns out that we can prove that this is not the case. We can eliminate entire classes of theories based on finite observations, and one of the classes that we can eliminate (with very high probability) is theories with high Kolmogorov complexity.

Re: Is Probability Real?

#132

Post by moosinho » Sat, Nov 28, 2020, 9:01 PM UTC

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.

There is no such thing as "true probability" in Bayesian interpretation, it only exists in frequentist world.

Notice that it is possible to build a robot which flips a coin in such a way that it's always heads - sure you might need to build a different robot if the coin is "biased"(you probably mean its weight distribution is uneven) but it's still possible.

Re: Is Probability Real?

#133

Post by lottin » Sat, Nov 28, 2020, 9:02 PM UTC

alisonkisk wrote: post #101

lottin wrote: post #32

Earlier quoted context omitted.

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.

I don't understand your claims that these statements are are meaningless. They are commonly uttered and understood.

I can understand expressions such as "pretty sure" or "completely sure". I do not understand the expression "to be X% sure". If someone says they're "37% sure" tomorrow will rain, what does that mean exactly?

Re: Is Probability Real?

#134

Post by carapace » Sat, Nov 28, 2020, 9:10 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!

This is awesome! Good work!

Are you going to touch on Chaitin's Omega?

Re: Is Probability Real?

#135

Post by dinosaurdynasty » Sat, Nov 28, 2020, 9:15 PM UTC

lottin wrote: post #133

alisonkisk wrote: post #101

Earlier quoted context omitted.

I don't understand your claims that these statements are are meaningless. They are commonly uttered and understood.

I can understand expressions such as "pretty sure" or "completely sure". I do not understand the expression "to be X% sure". If someone says they're "37% sure" tomorrow will rain, what does that mean exactly?

37% of the time that someone says they are 37% sure of a statement X the statement X is true (assuming they're calibrated correctly/etc).

Re: Is Probability Real?

#136

Post by [deleted] » Sat, Nov 28, 2020, 9:19 PM UTC

BalinKing wrote: post #114

dkersten wrote: post #113

Earlier quoted context omitted.

> The scientific method only works because the rules of the universe happen to be simple Are they simple though? That's not the impression I get from physicists, eg, the famous Richard Feynman quote: If you think you understand quantum mechanics, you don't understand quantum mechanics. We haven't even managed to find a unifying theory yet, but the current contenders, like Loop Quantum Gravity are anything but simple.

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

[deleted]

Re: Is Probability Real?

#137

Post by kgwgk » Sat, Nov 28, 2020, 9:28 PM UTC

lottin wrote: post #133

alisonkisk wrote: post #101

Earlier quoted context omitted.

I don't understand your claims that these statements are are meaningless. They are commonly uttered and understood.

I can understand expressions such as "pretty sure" or "completely sure". I do not understand the expression "to be X% sure". If someone says they're "37% sure" tomorrow will rain, what does that mean exactly?

Can you understand expressions like "more sure of A than B" or "as sure of A as of B"? Then, they are as sure that tomorrow will rain as they are sure that throwing three dice the sum will be 9 or less (37.5%).

Re: Is Probability Real?

#138

Post by edna314 » Sat, Nov 28, 2020, 9:33 PM UTC

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!

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.

Re: Is Probability Real?

#139

Post by pizza » Sat, Nov 28, 2020, 9:33 PM UTC

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…

I think this is just semantics; whether you read the parent comment as describing a hypothetical and fair coin with 50% chance for each state, versus saying that a god-like entity could reduce this to a deterministic computation via replaying the coin flip exactly (eg. same ambient air conditions, position of coin on finger, exact sequence of muscle nerve activations..) and that because that's impossible for you to do you just assign the minimum-information-content-probability to the coin flip (50%)

Re: Is Probability Real?

#140

Post by roenxi » Sat, Nov 28, 2020, 9:42 PM UTC

Nice article, there is an even easier interpretation though:

The mathematics of probability defines a bunch of objects that do not exist, anywhere. Random variables, expectations, probabilities, maybe a few others. Then there are situations in the real world that look a lot like those objects from certain perspectives.

It is a bit like Escher's Ascending and Descending - sometimes people make things in the real world that look like the infinite staircase when viewed from the right spot. Similarly, sometimes we find things that look probabilistic (dice rolls, coin flips) when viewed in ignorance of the sum totality of the entire universe. That is why there are a bunch of statistical tests that determine if outcomes are distinguishable from a hypothetical process generating that outcome.

tl; dr; I like the article, but it seems to answer it's own headline with "yes" and it is much easier to answer it with "no". There is, philosophically speaking, nothing that we can guarantee looks random from all perspectives.