Is probability just a construct, or is it found in nature?

Is probability just a construct, or is it found in nature?

Is stochastic modeling just a substitute for deterministic models that we haven't discovered yet?

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math.ucr.edu/home/baez/stoch_stable.pdf
en.wikipedia.org/wiki/Stochastic_electrodynamics
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the observation of particles in quantum mechanical superposition is an example of absolute probability, as opposed to probability from incomplete information

>Is stochastic modeling just a substitute for deterministic models that we haven't discovered yet?
Yes.

Wrong.

>Is probability just a construct, or is it found in nature?
Maybe, the interesting thing is that the math is basically the same as for Analysis.

how so?

Probability theory is mostly Integration of certain Functions according to certain measures.
Analysis, to be more accurate Integration theory, is basically the same, but with a different focus.

That said, the terminology isn't always the same, what a person doing Analysis would call an Integral a Probability theorist would call the expected value.

The normal distribution is essentially found in nature as evinced by the Central Limit Theorem.

If you sample any distribution X number of times, and plot X sample means in a histogram, the histogram will approach a perfect normal distribution as X goes to infinity.

probability is a construct just as numbers. you can think that probability is a way or represent some numeric measurements or think that measurements are a way to represent probability. Both ways work and nature has nothing to do with it.

Just a guess but any deterministic models found would probably be chaotic in the mathematical sense

a priori nothing is found in nature (not even the counting numbers)

Probability is a epistemological construct of partial knowledge. It exists in minds, not in nature. Some things can fundamentally only ever be known partially by minds, such as certain quantum-physical phenomena, and for those cases it can appear like the probability is part of nature. But that is a mistake: the probability is still in the minds, it's just that nature conveniently has a structure that maps well to it.

surely this applies equally to all mathematics

Nobody knows the answer to this question with 100% certainty.
We don't know if is correct, although certain people think. Other camps like disagree, but no one knows for sure. We can only philosophize at the moment, because we don't have conclusive scientific evidence on way or the other.

However, quantum theory does provide certain limitations as to what we CAN know with certainty regardless as to whether the underlying process is truly random or not, so probabilistic statements are about the best we can do.

This. Probability just wears this fact on its sleeve as opposed to other areas of mathematics/physics that try to convince you that if you open some secret panel somewhere in the universe you'll find their theories.

Bayesian Quantum Mechanics when?

Can you elaborate on that? If you are talking about a version of quantum mechanics in which all the uncertainty is in the mind rather than in the QM, that has existed for many decades.

I'm not sure how I follow the application of Bayesian methodology here. Do you mean we could, for instance, use data on the observed quantum states of particles to update and improve our ability to predict the quantum states we observe after wave function collapse of particles in the future?

I was actually thinking of what said
Really glad to see that its already a thing. I've got some reading to look forward to.

>inb4 physishits decide to make up probatons or some shit to stay relevant

All physics actually derives from probability. Stochastic mechanics will emerge as a vast new area of research, possibly even to replace quantum mechanics.
math.ucr.edu/home/baez/stoch_stable.pdf

en.wikipedia.org/wiki/Stochastic_electrodynamics

>implying those don't already exist