# Is there a definition of randomness?

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Isn't a coin flip from the Eiffel Tower random because the effect (the yieling of the result) and the cause (the flipping of the coin) have such a complicated relationship (chaoticly), that the relationship can't be described, not conceived and not even traced back that FAPP there IS no relationship between cause and effect?
It's random because no one can predict the outcome of a flip better than 50/50. Chaos is a math concept, a coin flip is physical

No. It doesn't imply that. It just implies that we cannot make predictions using quantum mechanics alone.
If we have probabilistic definitions of events in QM, doesn't that then imply that we can't make predictions? (on that field)
Then entropy1 says:
What else would be required then?
A larger theory, that is compatible with QM within certain constraints that are satisfied by most experiments done to date.
Do you think it is possible that some grander theory than QM will avoid random (see post #108) outcomes for measurements for spin? Not even super determinism will accomplish that. However, super determinism, as a theory, does say there are no probabilities.

stevendaryl
Staff Emeritus
Do you think it is possible that some grander theory than QM will avoid random (see post #108) outcomes for measurements for spin? Not even super determinism will accomplish that. However, super determinism, as a theory, does say there are no probabilities.

The question is mixing up the two different meanings of "random". A theory may be deterministic, so that there are no intrinsically random events, but it may be practically impossible to predict some events, and so that they would appear random. But "appearing random" would be a matter of how much computational power you want to put into predicting future outcomes. I suppose that past a point, prediction would be impossible in practice.

Gold Member
It's random because no one can predict the outcome of a flip better than 50/50. Chaos is a math concept, a coin flip is physical
I mean, is being random the result of the decoupling of cause and effect? (and maybe the definition, as you suggest)

The question is mixing up the two different meanings of "random". A theory may be deterministic, so that there are no intrinsically random events, but it may be practically impossible to predict some events, and so that they would appear random. But "appearing random" would be a matter of how much computational power you want to put into predicting future outcomes. I suppose that past a point, prediction would be impossible in practice.
I have only one definition of random (given in post #108), it applies to a physical process. A theory may state that certain things are random variables.
I agree that a deterministic theory may say there are no r.v.s and as a consequence no random events, merely a lack of knowledge, but then as you say prediction would be impossible in practice.

My key objection is (are?) the words "in practice" and "intrinsically". They are unnecessary, superfluous, and misleading. When flipping a coin from the top of the Eiffel Tower or in a wind tunnel there is no information that would predict the result. Some might object and say: if one knew the position and velocities of all the entities in the air, the the position and force from the thumb, etc. the result could be predicted. I say it is a pipe dream to say that information exists. Certainly you can't prove that it does, all one can do is hypothesize its existence based on a nonexistent theory below the Planck scale. As Griffiths said, God doesn't even know.
All is random, and the Law of Large Numbers keeps us sane.

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I mean, is being random the result of the decoupling of cause and effect? (and maybe the definition, as you suggest)
In a coin flip what are the cause and effect? After you answer that tell me what decoupling means.

Gold Member
In a coin flip what are the cause and effect? After you answer that tell me what decoupling means.
What are cause and effect is a matter of preference I think; you could say that the tossing device is the cause and the effect is the read-out (heads/tails).

With "decoupling" I mean that there is, practically at least, no discernable relation between the cause and the effect - this would be randomness, that is, for the effect/readout.

Gold Member
Some might object and say: if one knew the position and velocities of all the entities in the air, the the position and force from the thumb, etc. the result could be predicted.
With no identifyable relation between cause and effect, I mean the correlation between cause and effect is just as random as the toss is, regardless of in-principle possible relations. But maybe this is circular - dunno. Probably.

stevendaryl
Staff Emeritus
My key objection is (are?) the words "in practice" and "intrinsically". They are unnecessary, superfluous, and misleading. When flipping a coin from the top of the Eiffel Tower or in a wind tunnel there is no information that would predict the result.
Well, I disagree completely. To say that something is in practice unpredictable has a clear meaning, and it’s a different meaning from a theory being stochastic, or probabilistic.

What are cause and effect is a matter of preference I think; you could say that the tossing device is the cause and the effect is the read-out (heads/tails).
So you don't think the breeze or the topography of the ground are part of the cause? Right up until the coin settles down.
With "decoupling" I mean that there is, practically at least, no discernable relation between the cause and the effect - this would be randomness, that is, for the effect/readout.
I wonder where that decoupling takes place? If the coin weren't flipped there would be no result.

If the coin weren't flipped there would be no result.
Yeah, that would be the null hypothesis.

Well, I disagree completely. To say that something is in practice unpredictable has a clear meaning, and it’s a different meaning from a theory being stochastic, or probabilistic.
Well I disagree that we disagree. I do agree with what you said.
Our difference is semantic. Saying that a coin flip is in practice unpredictable carries no more information than saying it is unpredictable, and what I call random (see #108). I think the "in practice" is a red herring and adds confusion. Determinists say it is due to lack of knowledge and that is "not even wrong".

QT says that measurements are random variables - stochastic, very different than above. But in QT or probability theory the word random or intrinsically random do not appear and not defined. And that's why they should be tossed out in that context.

Gold Member
QT says that measurements are random variables - stochastic, very different than above. But in QT or probability theory the word random or intrinsically random do not appear and not defined. And that's why they should be tossed out in that context.
If randomness is not defined, how do you predict anything that is random or derived from it?

If randomness is not defined, how do you predict anything that is random or derived from it?
You only quoted part of my post. I did define it. Please read my other posts before you reply.

Gold Member
You only quoted part of my post. I did define it. Please read my other posts before you reply.
I did read them. I must say I'm a little confused. Does QM only take place around the Eiffel tower? Or must all QM related experiments be reducible to Eiffel tower coin tosses?

bhobba
Mentor
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:

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

Thanks
Bill

Gold Member
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
Homework Helper
Gold Member
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 modelled 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 modelled. 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.

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 modelled 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 modelled. 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.

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:

So the answer is right now we cant 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
Mentor
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 cant tell if something is random - meaning it cant be modeled by some deterministic process - or not. We have deterministic sequences that pass every test we have for randomness. Even QM cant 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 cant prove it.

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

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DrClaude
Mentor
This thread has run its course. Time to close.

Thanks to all that participated.

bhobba