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Is Probability Real?

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Re: Is Probability Real?

#141

Post by EbTech »

kolbe wrote: post #86

I work with probably as it relates to financial markets, and my gripe with probably is at an even lower level. Even with dice, the fact of the matter is that you will roll dice with almost entirely Newtonian forces acting on it, and it will settle on a number. This is not unknown to physics. It’s just unknown to us. And because we don’t have the data and computational power to know with any certainty where the dice w…

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 Kolmogorov complexity may be more applicable.

Re: Is Probability Real?

#142

Post by analog31 »

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…

Perhaps the most useful connection is that statistics lets us study what kind of math we can do, when we know something about a set, but not everything about it. And our experience with the world is like that too.

Re: Is Probability Real?

#143

Post by MauranKilom »

edna314 wrote: post #138
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.

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 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.

Re: Is Probability Real?

#144

Post by jbay808 »

SAI_Peregrinus wrote: post #121
jbay808 wrote: post #98

Earlier quoted context omitted.

> 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?

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?

Re: Is Probability Real?

#145

Post by jtsuken »

EbTech wrote: post #141
kolbe wrote: post #86

I work with probably as it relates to financial markets, and my gripe with probably is at an even lower level. Even with dice, the fact of the matter is that you will roll dice with almost entirely Newtonian forces acting on it, and it will settle on a number. This is not unknown to physics. It’s just unknown to us. And because we don’t have the data and computational power to know with any certainty where the dice w…

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?

Re: Is Probability Real?

#146

Post by MauranKilom »

ordu wrote: post #72
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!

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 get closer and closer.

That we can only observe, talk about and know reality in our subjective ways does not mean that there is no underlying mechanism by which reality "works". The quote points out that this "mechanism" is apparently sufficiently simple that we can effectively form and test hypotheses about it.

For example, we have no all-encompassing explanation of the universe that concludes R = U/I for electric circuits. Yet we can observe it to be accurate independently from the infinity of conceivable influences - there appears to be no influence on this observation from your lunch, the day of the week, whether your car is green or somebody was just born in Taiwan. We can't explain why these have no influence. We could imagine a reality where all of these (and infinitely many others) are confounders, in which case we could not effectively form theories about these rules. Yet the actual number of things influencing R = U/I observations in our reality are evidently very finite, allowing us to identify them and build our theories.

Re: Is Probability Real?

#147

Post by DiogenesKynikos »

ordu wrote: post #72
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!

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.

Re: Is Probability Real?

#148

Post by burrows »

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.”

Re: Is Probability Real?

#149

Post by roenxi »

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.”

It means we can't be certain. Whether the universe is random or deterministic is, ironically, a matter of probabilities.

Re: Is Probability Real?

#150

Post by nytgop77 »

ikeboy wrote: post #116
dkersten wrote: post #111

Earlier quoted context omitted.

Probability is relative to the information you have. That doesn't make it not be real. Probability is something we invented to describe systems, based on what we know about them, when we have imperfect information. If we had perfect information about the coin, its surroundings and how it was flipped, we could tell which side it will land on, but we don't. (Ignoring that there are some quantum things that physicist sa…

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 country X real? (what if it is recognised only by 1 UN nation?) Is law real? Is law real in .

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