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Is Probability Real?

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Re: Is Probability Real?

#151

Post by thisiszilff »

burrows wrote: post #148
roenxi wrote: post #140

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…

> There is, philosophically speaking, nothing that we can guarantee looks random from all perspectives. Does this imply that the universe is deterministic? I believe it is false to claim “Humans have knowledge that the universe is deterministic.”

I think this is related to the bayesian/frequentist approach to statistics. Bayesian statistics revolves around incorporating knowledge to update beliefs and probabilities express degrees of belief. IE, bayesian probability is the logic of uncertainty and how we should reason with imperfect information.

The most famous example of this is the "draw a ball from an urn" example, and how we frequently day we "shake" the urn after we add the balls to "randomize" it. There is a lot of wordplay going on in stats to effectively forget certain information so that the problem I'd workable

Re: Is Probability Real?

#152

Post by ikeboy »

nytgop77 wrote: post #150
ikeboy wrote: post #116

Earlier quoted context omitted.

Generally we use the term real to refer to objective claims and consider subjective claims not to be real. You can certainly use the term real in a broader sense if you'd like. I don't think the concept of reality is particularly useful or coherent, but to the extent others use the term, probability is not real in the sense it's being used in.

Nitpick on definition of "real" and "objective" follows. Proceed at your own risk :-) Would you agree that given exact info of conditions one can objectively assign concrete probability? That would give objectivity to it. Definition of "real" for daily life is hard (impossible?). I would say "probabilities" are as real as other useful constructs that impact our lifes. Examples would be "countries" and "laws". Is coun…

Sure, it's as real as those other examples, i.e. not particularly except insofar as it affects peoples' expectations.

I don't think "exact info of conditions" is objective or coherent. This pre-supposes there's an external universe with exact conditions that produces our experiences, but there's no way to distinguish this possiblity from other possibilities (like a multiverse, for instance.) This lack of ability to distinguish, in my ontology, makes the distinction meaningless. Yours may differ.

Re: Is Probability Real?

#153

Post by loup-vaillant »

Koshkin wrote: post #97
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.

No mental construct can exist without a cognition engine to run it. No idea can be thought without a mind to think it. Information has to be stored somewhere, and that somewhere is ultimately physical: a nervous system, a hard drive, a piece of paper…

Re: Is Probability Real?

#154

Post by kgwgk »

loup-vaillant wrote: post #153
Koshkin wrote: post #97

Earlier quoted context omitted.

> 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.

No mental construct can exist without a cognition engine to run it. No idea can be thought without a mind to think it. Information has to be stored somewhere , and that somewhere is ultimately physical: a nervous system, a hard drive, a piece of paper…

When everything is real, the word doesn't mean anything anymore.

Re: Is Probability Real?

#155

Post by ordu »

MauranKilom wrote: post #146
ordu wrote: post #72

Earlier quoted context omitted.

It is a funny statement, I like it. But due to a different reason: all we know about reality is our theories. How we could state, that rules of the universe are simple? As I see it, we could state, that our theories are full of simple rules. But the universe have no theories nor rules outside of human's mind. It is completely our inventions, our dreams, our hopes that the universe have some rules. We could state that…

I think there is a disconnect between the "rules of the universe" that the quote talks about and the "our simple rules" that your comment focuses on. Without getting too philosophical, I think we can agree that there are "rules" how the universe works (which is what the quote talks about), which are not necessarily the same as the rules that our theories postulate (what you talk about), although we of course try to g…

> Without getting too philosophical, I think we can agree that there are "rules" how the universe works...

Well, maybe I am too philosophical, because I feel myself reluctant to agree. I accept science method because I know nothing better. But I doubt the idea, that there are no possibility to invent something better.

> we have no all-encompassing explanation of the universe that concludes R = U/I for electric circuits

I'm not a physicist to argue with it. But somewhere deep inside me I see R = U/I as a tautology too. R, U and I was defined by a way, that made R=U/I true. There is some information about the universe encoded in this rule, but there also information about us there. How to separate information about the universe from information about us?

Re: Is Probability Real?

#156

Post by 6gvONxR4sf7o »

lisper wrote: post #131
6gvONxR4sf7o wrote: post #93

Earlier quoted context omitted.

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…

I assume you’re taking about the Bell experiments. Imagine that it’s the nonlocality side of things that ends up being correct. In that case, a full foundation of QM could be a nightmare.

Regardless, we don’t have a full unified theory of everything, so it seems premature to say we know how complex it’ll end up needing to be.

Also, the universe isn’t just an time evolution differential equation. It’s that, plus all the initial/boundary conditions. Saying the Kolmogorov complexity of the universe is small while only looking at the side that’s simplifiable seems circular.

Re: Is Probability Real?

#157

Post by ordu »

DiogenesKynikos wrote: post #147
ordu wrote: post #72

Earlier quoted context omitted.

It is a funny statement, I like it. But due to a different reason: all we know about reality is our theories. How we could state, that rules of the universe are simple? As I see it, we could state, that our theories are full of simple rules. But the universe have no theories nor rules outside of human's mind. It is completely our inventions, our dreams, our hopes that the universe have some rules. We could state that…

Science has an empirical aspect that you're ignoring here. Our theories are tied to nature through experiment. They are more than just inventions of the human mind. People come up with new ideas about nature all the time. Most of them are wrong, and we find that out by doing experiments.

Yes. If we take a look at social sciences struggling with experimental method, we'll see, that they get better with time. When experiments do not work, people somehow figure out how to do experiments better, and it changes things. It gives a hope that experimental method could falsify itself, so when it stops working we will be able to notice it. So if we do not see it to fail, we could assume that it works.

Re: Is Probability Real?

#158

Post by EbTech »

jtsuken wrote: post #145
EbTech wrote: post #141

Earlier quoted context omitted.

Fair enough! I'd like to point out that the Kolmogorov complexity approach can make sense of subjective probability too. Since you lack precise enough information to predict the dice roll, the most compressed way to write down your observations will involve a Shannon-style code with your subjective probabilities. If you have enough information but not enough computational power, the resource-bounded variants of Kolmo…

Can you please define Shannon-style code? (Obviously, you don't have the shannon code, the compression method, in mind). Also, isn't Kolmogorov complexity uncomputable and you run into multiple "who shaves the barber" issues, when trying to determine it?

The compression code can be specified first. If you have a lot of data, the specification will be negligible in length, compared to the code itself. Together, the specification and the Shannon code give an upper bound on the Kolmogorov compmlexity. If this is the shortest known program, we may consider the Shannon code probabilities as our "best explanation" of the data.

You can also get posterior probabilities using a universal prior such as 2^-K(x), but of course, this can only be approximated in the limit of infinite runtime.

Re: Is Probability Real?

#159

Post by sxzxs »

jbeam wrote: post #85
sxzxs wrote: post #82

Earlier quoted context omitted.

For me, it comes down to what kinds of these risky models are most interesting. Some can be interesting because of potential profit or minimizing loss (financial or actuarial) and others are inherently (theoretical physics). To add to your tail risk point - I wonder how many people foresaw the Venezuelan oil crisis way back when, or even less likely, the Saudi Arabian oil complex attack in 2019. And of course, the cu…

>as an aside, do insurance companies significantly alter their policies when such a cat-5 hurricane is imminent? What preparations would they make in the face of that sort of event? You cannot retroactively alter a policy, for obviously good reasons. The main preparation policy-wise is that insurance companies do not knowingly write new policies in the affected area when disaster is ongoing or imminent. Reinsurers wi…

Thanks for the link, I'll check it out.

Re: Is Probability Real?

#160

Post by xvedejas »

ikeboy wrote: post #119
xvedejas wrote: post #106

Earlier quoted context omitted.

Your example suggests to me the opposite: Probability is a real and objective way to describe the information you have. "Garbage in, garbage out" still applies when you have no information.

The distinction between objective and subjective collapses under your usage.

No, the distinction is clear. If your assigned probability is something that someone else can reproduce using the same steps given the same information, then it is objective (yet contextual). Your examples each have a clear reasoning behind the assigned probabilities, they're not just opinion-based assertions.
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