Is there a definition of randomness?

[bhobba]

I don't know why this thread has gone on for so long. At present for many pseudo random number generators we have tests that tell us its not random - but many is not all - some pass the lot:
file:///C:/Users/William/Downloads/tuftests.pdf

So the answer is right now we can't tell if a sequence is really random or not - that may change of course.

Thanks
Bill

 

[entropy1]

What I'm wondering: we can't predict an individual outcome of a random variable, but we make assumptions about ensembles of oucomes of a r.v. that in practice can be approached arbitrarily accurate by theory. So is that a property of randomness/probabilistics?

I am thinking of entanglement and correlations, where the correlations seem to have a tangible regularity.

 

[andrewkirk]

Do you think it is possible that some grander theory than QM will avoid random (see post #108) outcomes for measurements for spin?

I can imagine there being such a theory. Whether humans can ever come to know such a theory is a different question, to which I suspect the answer is No.

Not even super determinism will accomplish that.

It sounds like you're thinking of 'super-determinism' as a Theory. In my experience, when that phrase is used, it is not referring to a complete theory, but at most an aspect of a theory.

A theory may state that certain things are random variables.

I don't know of any theory that says that. What the theories I have seen say is that, under the theory, a certain measurable quantity is modeled as a random variable, which is a very different thing. It is not the business of science to say what things 'are', only how they can be modeled. And thank goodness for that, or scientists would get bogged down in unresolvable arguments about the nature of Kantian noumena. There'd be no time left for inventing useful stuff like QM or GR.

 

[Zafa Pi]

Your response to my statement: A theory may state that certain things are random variables. is

I don't know of any theory that says that. What the theories I have seen say is that, under the theory, a certain measurable quantity is modeled as a random variable, which is a very different thing. It is not the business of science to say what things 'are', only how they can be modeled. And thank goodness for that, or scientists would get bogged down in unresolvable arguments about the nature of Kantian noumena. There'd be no time left for inventing useful stuff like QM or GR.

QT says that. My favorite text (Nielsen & Chuang) states as it's 2nd postulate that measurements are random variables (plus details). There are many other sources.
Theories are models.

 

[Zafa Pi]

I don't know why this thread has gone on for so long. At present for many pseudo random number generators we have tests that tell us its not random - but many is not all - some pass the lot:
file:///C:/Users/William/Downloads/tuftests.pdf

So the answer is right now we can't tell if a sequence is really random or not - that may change of course.

The reason why is that there is a great deal of confusion over what random means. Most people on this thread agree that a sequence produced by an algorithm is not random since its values are predictable, regardless of satisfying randomness tests.
Random is not a defined notion in probability theory. I am attempting to define it in terms of a physical process, see post # 108. So far I have not found coherent objections.

 

[bhobba]

The reason why is that there is a great deal of confusion over what random means. Most people on this thread agree that a sequence produced by an algorithm is not random since its values are predictable, regardless of satisfying randomness tests.
Random is not a defined notion in probability theory. I am attempting to define it in terms of a physical process, see post # 108. So far I have not found coherent objections.

That post looks fine.

My issue is simple. Give someone some data, even how you obtained it, such as you did in in the mentioned post eg Most would agree that a "fair" coin flipped from the Eiffel Tower or in a wind tunnel is a physical device that is modeled by the theory. I now define that processes/result as random.

So you can PROVE some future test for true randomness may not tell us its not really random? I think it highly unlikely - but we are speaking of matters of principle here.

As of now you can't tell if something is random - meaning it can't be modeled by some deterministic process - or not. We have deterministic sequences that pass every test we have for randomness. Even QM can't be assured of that - even though the consensus is it truly is random - just like there would be the same consensus for what you mentioned - we can't prove it.

Added Later:
You would think a roulette wheel is random - I know I would have - except for one thing:
https://www.amazon.com/dp/0140145931/?tag=pfamazon01-20

The only thing that looks, in light of things like the above, truly random is QM - but we have no way to prove it.

Thanks
Bill

 

[DrClaude]

This thread has run its course. Time to close.

Thanks to all that participated.