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Is Probability Real?

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Re: Is Probability Real?

#121

Post by SAI_Peregrinus »

jbay808 wrote: post #98
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.

> 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.

Re: Is Probability Real?

#122

Post by _v7gu »

jbay808 wrote: post #98
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.

> 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?

Of course not. If you're a frequentist you can say your best estimate is 100% heads with an unknown variance, and if you're a Bayesian you work out p(a|b) = p(b)p(b|a)/p(a) and update your priors (which will not give 100% heads). The more coins you flip, the better you can estimate the true probability

Re: Is Probability Real?

#123

Post by jhayward »

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.

I've always taken the Feynman quote to mean: just because you understand the rules doesn't mean you understand the implications, which are varied, vast, and counter-intuitive.

Re: Is Probability Real?

#124

Post by kgwgk »

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.

https://www.youtube.com/watch?v=X5cQcmAtjJ0

Re: Is Probability Real?

#125

Post by Igelau »

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.

> The scientific method only works because the rules of the universe happen to be simple

It's simple in the sense that the universe seems to be the kind of place where inductive reasoning mostly works. For the most part we seem to be able to expect things like predictability and causality at the scale of the objects and processes in our everyday life. If it wasn't like that, things would be a lot more complicated.

Re: Is Probability Real?

#126

Post by feanaro »

ikeboy wrote: post #118
mojomark wrote: post #110

Earlier quoted context omitted.

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.

How do you resolve the problems raised by Bell's theorem?

Re: Is Probability Real?

#127

Post by XuMiao »

ikeboy wrote: post #118
mojomark wrote: post #110

Earlier quoted context omitted.

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.

If quantum reality is objective, then probabilistic reality is objective.

Deterministic probability like Chaos or second law of thermodynamics imply the existence of incomplete information. This type of probabilistic reality might be subjective.

Re: Is Probability Real?

#128

Post by ikeboy »

feanaro wrote: post #126
ikeboy wrote: post #118

Earlier quoted context omitted.

>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.

How do you resolve the problems raised by Bell's theorem?

Bell's theorem rules out local realism. I view realism as incoherent, so I'm certainly not committed to local realism.

Re: Is Probability Real?

#129

Post by ikeboy »

XuMiao wrote: post #127
ikeboy wrote: post #118

Earlier quoted context omitted.

>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.

If quantum reality is objective, then probabilistic reality is objective. Deterministic probability like Chaos or second law of thermodynamics imply the existence of incomplete information. This type of probabilistic reality might be subjective.

I don't think that's a coherent concept. It's not clear how one can assert that a particular model of reality is "correct" outside of any predictions than it makes.

Re: Is Probability Real?

#130

Post by lisper »

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.

Exactly right. The rules of quantum mechanics are in their essence not much more complicated than high school algebra. It is the logical consequences of those rules that are hard to wrap your brain around.
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