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Is Probability Real?

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Re: Is Probability Real?

#111

Post by dkersten »

ikeboy wrote: post #102

Probability is not real. Probability is subjective, it depends on what you know, and everyone has a different set of things they know. I flip a coin and look at it, then ask two other people for their probabilities. One of them knows the coin is biased towards head such that it's twice as likely to land heads than tails on any given flip. The other knows nothing about the coin. The first person guesses a 66% chance o…

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 say can never have perfect information)

Re: Is Probability Real?

#112

Post by karmakaze »

skybrian wrote: post #109
karmakaze wrote: post #65

I don't think "first forty digits of pi" should be admissible. As it depends on an external definition that's not computed by the representation. I could come up with a mathematical definition for any prefix of digits, give it a name and say the 'first x digits of C'.

That's just because it's a loose description in English. It would actually be a short computer program that calculates pi, and instead of the first 40 digits you could ask for, say, a megabyte of data, or take the limit as the amount of data grows. Transmitting a program to compute pi would be shorter than the data needed by any compression algorithm that isn't somehow based on knowing the trick. The same trick could…

Yes the point was merely 'referring to an external' isn't a good example of a minimal size description.

Re: Is Probability Real?

#113

Post by dkersten »

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!

> 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.

Re: Is Probability Real?

#114

Post by BalinKing »

dkersten wrote: post #113
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!

> 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.

Re: Is Probability Real?

#115

Post by jdc »

grandrew wrote: post #108

I have a question about how Kolmogorov complexity is related to "Human complexity" or complexity of understanding? E.g. a program may be very complex in Kolmogorov terms, like describing 1000 random numbers - easy to understand: you have a database of numbers, and a simple procedure that would scan through it. You can also imagine some real-world microservices-based program with a good architecture and a lot of code…

What is easy or useful for one person to understand is often much less so for another.

Re: Is Probability Real?

#116

Post by ikeboy »

dkersten wrote: post #111
ikeboy wrote: post #102

Probability is not real. Probability is subjective, it depends on what you know, and everyone has a different set of things they know. I flip a coin and look at it, then ask two other people for their probabilities. One of them knows the coin is biased towards head such that it's twice as likely to land heads than tails on any given flip. The other knows nothing about the coin. The first person guesses a 66% chance o…

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.

Re: Is Probability Real?

#117

Post by renewiltord »

grandrew wrote: post #108

I have a question about how Kolmogorov complexity is related to "Human complexity" or complexity of understanding? E.g. a program may be very complex in Kolmogorov terms, like describing 1000 random numbers - easy to understand: you have a database of numbers, and a simple procedure that would scan through it. You can also imagine some real-world microservices-based program with a good architecture and a lot of code…

Well, that's altering the 'language' that you're measuring the KC against. For instance, in the language that CS majors use the phrase "Kolmogorov Complexity" is sufficient to encode the concept of KC itself. And in the context of that language plus the concept of KC and adding in this entire thread, the letters KC themselves encode Kolmogorov Complexity in entirety.

So the 'real world' version isn't so easy to tell in absolute terms like that because the languages can differ. But if you were thinking of it like a compressor/decompressor pair, then moving things into the language is like moving things into the compressor/decompressor.

Naturally then you conclude that the "human complexity" depends greatly on the humans since any pair of humans creates a new universal description language that we can see as some base language plus the jargon that they are both familiar with.

Re: Is Probability Real?

#118

Post by ikeboy »

mojomark wrote: post #110
ikeboy wrote: post #102

Probability is not real. Probability is subjective, it depends on what you know, and everyone has a different set of things they know. I flip a coin and look at it, then ask two other people for their probabilities. One of them knows the coin is biased towards head such that it's twice as likely to land heads than tails on any given flip. The other knows nothing about the coin. The first person guesses a 66% chance o…

It sounds like you're argument is actually stating that probability is in fact a real attribute of physical systems, but the accuracy with which you can accurately predict a probabilistic event is dependant on the amount of information you have about the system. Interestingly, someone only observing results of a probabilistic event will eventually learn to predict events with an accuracy approaching ideal (I.e. the t…

>Interestingly, someone only observing results of a probabilistic event will eventually learn to predict events with an accuracy approaching ideal

This relies on various unstated assumptions.

I would deny the assumption that an event can be probablistic in nature. There are only ever predictions. The distinction between a probablistic world and a deterministic world is incoherent.

Re: Is Probability Real?

#119

Post by ikeboy »

xvedejas wrote: post #106
ikeboy wrote: post #102

Probability is not real. Probability is subjective, it depends on what you know, and everyone has a different set of things they know. I flip a coin and look at it, then ask two other people for their probabilities. One of them knows the coin is biased towards head such that it's twice as likely to land heads than tails on any given flip. The other knows nothing about the coin. The first person guesses a 66% chance o…

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.

Re: Is Probability Real?

#120

Post by SAI_Peregrinus »

prmph wrote: post #77
SAI_Peregrinus wrote: post #67

Earlier quoted context omitted.

> 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.

But that’s the thing: the “true“ probability is unknowable, and may even be an ill-defined concept. It is a deterministic process, so “probability“ is just a simplifying concept to describe our best guess belief about how the coin behaves in the aggregate.

The true probability requires an infinite sequence of tests, so it's by definition unknowable. But it's what any sort of statistics attempts to approximate.
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