## "Irreducible Randomness", what does that even mean?

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

### Re: "Irreducible Randomness", what does that even mean?

ajw wrote:
minkwe wrote:Not true. I gave you an example with one value that could not be predicted. There are lots of single occurrence events that are unpredictable, and therefore outside the scope of your definition.

Something is wrong here: For a single event randomness has no meaning. So can you please explain what you mean?

Nothing is wrong. See my definition of randomness above. You said single events are always predictable, I say that is false.
minkwe

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### Re: "Irreducible Randomness", what does that even mean?

minkwe wrote:
gill1109 wrote:Yes, I repeatedly use the word without being able to tell you its meaning.

That explains a lot. Is "non-locality" another example?

I know very well it can mean many different things. Irreducible randomness is defined as the opposite of reducible randomness. We all know lots of examples of reducible randomness. The definition of reducible randomness is randomness either which is subjective, meaning we don't know, and our probabilities are just a reflection of betting odds which we would be prepared to take. Or randomness which is reduced to the randomness of initial conditions, which is not a definition at all. What are random initial conditions.

Sorry, I'm not buying it. "reducible" and "irreducible" are adjectives which modify/categorize the type of randomness. Without a definition of randomness, you are not making any sense. If you say my definition of randomness is equivalent to "reducible randomness", then you have to explain what you understand by randomness in the first place that warrants your categorisation of my definition.

However when I am talking to someone, e,g. to you Michel, or to Albert Jan, or Joy, or Fred, or others, I do have an idea of what is in *their* mind when I use the word "random" and that means I am able to communicate - I can trigger desired associations in other people's minds to our common past experiences and instincts.

This makes no sense to me. You now know that the terms "reducible randomness" and "irreducible randomness" make no sense to me, yet you use them in our conversation. Isn't it a tad disingenuous to suggest you use them because I will understand what you mean? Come on man!

The notion of "randomness" is controversial, and has been controversial for several thousand years. The task of academics is precisely to explore controversial concepts. What is democracy, for instance?

The definitions of randomness and democracy are not controversial. If it was you would have given me a different definition that disagreed with what I provided. Instead you said, "I don't know". Ignorance is not controversy.

Bell's theorem challenges our very basic notions of randomness. That's why it is interesting.

I don't agree. But you don't even know what randomness means so how can your inexistent notion of it be challenged?

Quantum mechanics challenges our very basic notions of reality. That's why it is interesting.

I disagree. Though portrayals of the meaning of QM definitely challenge my faith in 21st century physicists. Do you know what reality means? Perhaps we need a new thread on your definition of reality.

Recent political events in the world challenge our notions of democracy.

I disagree. It may challenge your faith in democracy, not the meaning/definition of it.

Michel, I don’t have to explain anything. I use words which I know that you find meaningful. You already explained what you mean by randomness. So I can safely use the word in conversation with you, knowing what it makes you think of.

It is a still ongoing research project of humanity (been ongoing for 2000 years) to figure out what randomness means. I’m glad for you that you have already resolved this to your own satisfaction. If Kolmogorov or Poincaré or de Finetti or Jaynes could not agree on a final definition, why do you expect me to? Kolmogorov gave different definitions at different stages of his life. I think his insights were fantastic.

At the beginning of the 20th century, physicists thought that physics was essentially finished. There were just three little anomalies which needed taking care of. Those three were the seeds of Einstein’s three huge contributions in his “miraculous year”. Then he got stuck for the rest of his life.

Quantum mechanics was discovered and, it seems to me, necessitates that the whole question of what is randomness needs to be re-evaluated. I don’t believe these problems can be resolved by putting down a few clean definitions in plain English words. But sure, if you think it can be done, good luck! Certainly it is valuable to hear many opinions. I’m sorry that my opinion is pretty useless for you. Still, I am a good teacher of probability and statistics, and I have inspired many generations of really great students! It seems one can do a great deal of useful stuff without having a clear definition. It’s good enough just to have a few archetypal examples. I think that that is actually the basis of all human language.
gill1109
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### Re: "Irreducible Randomness", what does that even mean?

gill1109 wrote:Michel, I don’t have to explain anything.

True. You don't owe me anything. Though I was hoping you knew what you were talking about.
gill1109 wrote:I use words which I know that you find meaningful. You already explained what you mean by randomness. So I can safely use the word in conversation with you, knowing what it makes you think of.

You use them in ways that make no sense to me (aka meaningless).

Quantum mechanics was discovered and, it seems to me, necessitates that the whole question of what is randomness needs to be re-evaluated.

Nope, it does not. But you won't even know because you don't know what randomness means.

I don’t believe these problems can be resolved by putting down a few clean definitions in plain English words.

A lot of apparent problems can be resolved simply by use of consistent definitions, and use of precise language. Progress on actual problems will come only through clear and consistent definition of concepts, precise use of language, and sound logical reasoning.

But sure, if you think it can be done, good luck! Certainly it is valuable to hear many opinions.

Not only can it be done, it is the only way that merits the term "science". Anything else is voodoo and mysticism.

I’m sorry that my opinion is pretty useless for you. Still, I am a good teacher of probability and statistics, and I have inspired many generations of really great students!

I just spent a fraction of my life trying to understand your opinion. What are you talking about? It is you who said just above that you are not interested in explaining anything to me. Somehow, I doubt very much that if your students asked you for what randomness means, you would say "I don't know".

[quote]It seems one can do a great deal of useful stuff without having a clear definition. It’s good enough just to have a few archetypal examples. I think that that is actually the basis of all human language./quote]
Appearances can be deceiving.
minkwe

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### Re: "Irreducible Randomness", what does that even mean?

I agree 100% with this statement by Michel: "A lot of apparent problems can be resolved simply by use of consistent definitions, and use of precise language. Progress on actual problems will come only through clear and consistent definition of concepts, precise use of language, and sound logical reasoning."

But I don't think that the problem of "what is randomness" will ever be resolved that way. I think that careful use of precise language and sound logical reasoning has shown that there cannot be a simple resolution. Michel is very optimistic. I do admire his optimism and ambition. Can he do what nobody else has been able to do in several thousand years? Of course, some people, e.g. Bruno de Finetti, Richard von Mises, Ed Jaynes, and others, were ambitious enough to believe they had done it. They have dedicated followers, to this day. A lot of physicists think everything was solved by R.T. Cox, but outside of physics, no one has heard of him https://en.wikipedia.org/wiki/Cox%27s_theorem. The academic debate continues, and new physical insights give new twists to old arguments. There is renewed debate about Dempster-Shafer theory, which supposes that the usual rules of probability theory are wrong. Probability is subjective, and one *must* distinguish between degrees of belief and degrees of plausibility. Some people argue that this is the "right" theory of uncertainty for legal reasoning https://research.vu.nl/en/publications/a-new-look-at-conditional-probability-with-belief-functions, "A new look at conditional probability with belief functions" by Ronald Meester, & Timber Kerkvliet.

I explain the mathematics of probabilistic reasoning to my students by appeal to familiar examples (dice, coins, both fair and unfair; insurance, roulette; "observation roulette"). I also explain to them some of the different paradigma's which are out there. Frequentist, subjective (de Finetti), Laplace. Von Mises' collectives, Kolmogorov complexity. I gave expert evidence on behalf of a company exploiting a game with some features of roulette but, according to the company, a game of skill. The Netherlands state has a monopoly on games of chance. And makes a lot of money from the half a dozen or so legal Dutch casinos. But the legal definition of a game of chance is ... pretty meaningless, to a scientist. I showed using statistical methodology that most players were actually losing less money at the game than if they were playing with no skill at all. In other words, most players were actually employing skill to increase their chances of winning. Hence it was legally, in my opinion, a game of skill, not chance. The judges didn't agree I think the law should be rewritten so as to make it clear what it is that our lawmakers, working on our behalf, object to. They have some deep-seated instinctive objection to people making money by allowing other people to place bets, yet do admit the need for insurance companies, and a state lottery. (That was how Kolmogorov escaped the wrath of Stalin. Probability is contrary to Marxist-Leninism. Kolmogorov was summoned to explain what he was doing. He pointed out that the operation of the state lottery did depend on skilful knowledge of mathematical probability theory. He lived to tell the tale).

As a mathematician, I don't have to define randomness. I distinguish mathematical models of reality, from reality itself. The same abstract mathematical framework can have very different interpretations when applied to different fields. Presently I have the insight that independence is a more fundamental notion than randomness. There is fascinating new work reported in the recent book by Jonas Peters et. al on machine learning and causality, on an information-theoretic approach inspired by algorithmic complexity theory to the question of how to motivate statistical independence assumptions in physics. With applications to Bell's inequality. http://web.math.ku.dk/~peters/elements.html Jonas Peters, Dominik Janzing, Bernhard Schölkopf: Elements of Causal Inference: Foundations and Learning Algorithms.

Also fascinating is how Boole's attempt to see probability as an extension of logic ran aground on the problem of how to define prior distributions representing ignorance in situations with many variables with arbitrary dependence between them.

When I was young, I was ready to give concise clear definitions of randomness. The more I have learnt about it, however, the more I realise how little I know

Nowadays I think it is reasonable to believe that some randomness (quantum randomness) is not "merely" epistemic, not merely an expression of uncertainty and actually reducible to lack of knowledge of initial conditions or to hyper-sensitive dependence on initial conditions in what is essentially a deterministic system.

I think that that point of view is no solution at all: it is just an infinite regress. I think that Bell's theorem suggests we consider quantum randomness to be some kind of bottom line, some kind of fundamental feature of nature. Because otherwise, we have to believe in some kind of exquisite coordination between setting choices at a photo-detector and detector outcomes at another distant detector, because both are the result of purely deterministic chains of events set in motion at the time of the big bang, hence Alice's detector knows in advance what setting Bob is using.

But Tim Palmer from Oxford https://www2.physics.ox.ac.uk/contacts/people/palmer thinks this is what happens, it seems.
I have not decided yet whether or not his reasoning holds water. I'm suspicious.

https://www.mdpi.com/1099-4300/20/5/356.
Experimental Non-Violation of the Bell Inequality
T. N. Palmer
Department of Physics, University of Oxford
Entropy 2018, 20(5), 356; https://doi.org/10.3390/e20050356
Received: 7 April 2018 / Revised: 24 April 2018 / Accepted: 2 May 2018 / Published: 10 May 2018
(This article belongs to the Special Issue Emergent Quantum Mechanics – David Bohm Centennial Perspectives)

Abstract
A finite non-classical framework for qubit physics is described that challenges the conclusion that the Bell Inequality has been shown to have been violated experimentally, even approximately. This framework postulates the primacy of a fractal-like ‘invariant set’ geometry IU in cosmological state space, on which the universe evolves deterministically and causally, and from which space-time and the laws of physics in space-time are emergent. Consistent with the assumed primacy of IU , a non-Euclidean (and hence non-classical) metric gp is defined in cosmological state space. Here, p is a large but finite integer (whose inverse may reflect the weakness of gravity). Points that do not lie on IU are necessarily gp -distant from points that do. gp is related to the p-adic metric of number theory. Using number-theoretic properties of spherical triangles, the Clauser-Horne-Shimony-Holt (CHSH) inequality, whose violation would rule out local realism, is shown to be undefined in this framework. Moreover, the CHSH-like inequalities violated experimentally are shown to be gp -distant from the CHSH inequality. This result fails in the singular limit p=∞ , at which gp is Euclidean and the corresponding model classical. Although Invariant Set Theory is deterministic and locally causal, it is not conspiratorial and does not compromise experimenter free will. The relationship between Invariant Set Theory, Bohmian Theory, The Cellular Automaton Interpretation of Quantum Theory and p-adic Quantum Theory is discussed.
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### Re: "Irreducible Randomness", what does that even mean?

gill1109 wrote:Nowadays I think it is reasonable to believe that some randomness (quantum randomness) is not "merely" epistemic, not merely an expression of uncertainty and actually reducible to lack of knowledge of initial conditions or to hyper-sensitive dependence on initial conditions in what is essentially a deterministic system.

Again this is what prompted me to start this thread. You think it is reasonable but I've been trying to get you to give me any reasons behind it to no avail. You say there are two types of randomness and one from QM is of one type not the other, yet you aren't able to tell me what the difference between the two types are. How do you know that they are different in the first place?

Despite my asking, nobody has been able to tell me how to distinguish one kind from the other. So on what basis does anyone have "reason" to believe there are two kinds? You will have to do better than just make fantastic proclamations. Perhaps the difficulty arises from the fact that, there are not two types but just "randomness". So while I applaud your willingness to admit when you don't know something, I also see that this is not just a claim about not knowing, but a claim that quantum randomness is a certain way, without being able to justify/explain the reasons behind the claim.

Every time I see a claim that Quantum mechanics mandates irreducible randomness, I ask the question. What the F\$%!@* are they talking about. Nobody has been able to explain what it is they are talking about, perhaps because nobody making such a claim really knows what they are talking about. But I suspect this discussion will not dissuade you from making such claims about "irreducible randomness" in the future, since almost everybody else who is considered "relevant" in the community does it too. To hell with language/philosophy purists like us for trying to demand clarity and consistency. Isn't that right?

Presently I have the insight that independence is a more fundamental notion than randomness.

I agree. I've been thinking a lot about independence lately. While I consider randomness as an epistemic concept, independence/dependence is more fundamental in the sense that it can be ontological and it is not always possible to characterize it. In other words, dependence might be present even if we don't know about it. That is why I've been interested in mutual information, and hypothesis testing based on it. I have some very interesting unpublished results about that as concerns some of the recent Bell-test data from Delft. Needless to say, the published conclusions do not tell the full story as some others have hinted already.

To wrap up this randomness discussion, I should mention that "randomness" and "entropy" are very closely related concepts. Some people believe entropy is ontological as well.
minkwe

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### Re: "Irreducible Randomness", what does that even mean?

minkwe wrote:
gill1109 wrote:Nowadays I think it is reasonable to believe that some randomness (quantum randomness) is not "merely" epistemic, not merely an expression of uncertainty and actually reducible to lack of knowledge of initial conditions or to hyper-sensitive dependence on initial conditions in what is essentially a deterministic system.

Again this is what prompted me to start this thread. You think it is reasonable but I've been trying to get you to give me any reasons behind it to no avail. You say there are two types of randomness and one from QM is of one type not the other, yet you aren't able to tell me what the difference between the two types are. How do you know that they are different in the first place?

I have given you my primary reason: Bell's theorem. It suggests to me, and to many others, that the randomness which we observe in experiments on small quantum systems is not reducible to ignorance of initial conditions.

A second reason is that there is strong evidence from neuroscience, and in particular neurolinguistics, that our intuitive disbelief in irreducible randomness (your unreasoned refusal to contemplate it!) has been "learnt" by our DNA through evolution. Literally, we can't think the unthinkable.

A third reason is that it has been shown by mathematical logicians (Michiel van Lambalgen and others) that it is perfectly possible to build irreducible randomness into ground level logic. We don't need to define it in mathematics - to let it "emerge" - by building on prior mathematical structures, we might just as well have put it into the axioms. Van Lambalgen showed that if regular ZFC is consistent, then so also is the modified ZFC you get by this tweak to the basement level logic.

A fourth reason is Occam's razor. The assumption of irreducible randomness makes quantum mechanics clean and complete and much less complex, than supposing there are incredibly complex deterministic mechanisms behind the apparent randomness, so exquisitely fine tuned that we can violate Bell inequalities but not see any evidence whatsoever of action at a distance. Tim Palmer's attempt looks to me an example of a ludicrously complex explanation which actually has no explanatory power at all: it does not predict new phenomena which we could look for in the lab. It is merely window dressing, to allow people like you to sleep more easily at night. The work by Peters et al which I mentioned is also based on Occam's razor. All other things being equal, simple explanations with less free parameters tend to be more effective in science than complicated explanations with so many free parameters that you can make them fit to any existing data just by freely tuning enough parameters ... in statistics, this is called overfitting. You can make an 11 th degree polynomial go perfectly through 12 (x, y) points but it won't interpolate better than joining the dots with straight lines, and it will certainly be a total failure at extrapolating beyond the observed data range.

Slava Belavkin already showed how to build irreducible randomness into conventional QM by his invention of "eventum mechanics". Later work has shown that his framework can be make relativistically invariant. People who know the right kind of mathematics should wake up and take this direction seriously! Unfortunately, "collapse theories" have remained a niche area, with not enough people exploring them further, because of prejudice and fear of the unconventional.
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### Re: "Irreducible Randomness", what does that even mean?

gill1109 wrote:
I have given you my primary reason: Bell's theorem. It suggests to me, and to many others, that the randomness which we observe in experiments on small quantum systems is not reducible to ignorance of initial conditions.

Bell's theorem implies no such thing. Your primary reason is based on Bell's oversight, which has been endlessly repeated by the followers of Bell; see https://arxiv.org/pdf/1704.02876.pdf.

Moreover, there already exists a local-realistic model of all quantum correlations, derived purely from the ignorance of initial conditions. See my peer-reviewed papers in established and reputable journals such as IJTP and RSOS (one more paper of mine is coming up soon in a reputable journal providing more details and addressing all unfounded criticisms of my model).

gill1109 wrote:
... it has been shown by mathematical logicians (Michiel van Lambalgen and others) that it is perfectly possible to build irreducible randomness into ground-level logic.

Anything can be built into ground-level logic, such as "immaculate conception", for example. That does not make it either right or meaningful, and "irreducible randomness" is no exception.

***
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### Re: "Irreducible Randomness", what does that even mean?

gill1109 wrote:I have given you my primary reason: Bell's theorem. It suggests to me, and to many others, that the randomness which we observe in experiments on small quantum systems is not reducible to ignorance of initial conditions.

No it doesn't. "Suggests"? That's an empty claim, without justification. Besides, to justify such a claim you will have to explain what you mean by "randomness" in the first place.

A second reason is that there is strong evidence from neuroscience, and in particular neurolinguistics, that our intuitive disbelief in irreducible randomness (your unreasoned refusal to contemplate it!) has been "learnt" by our DNA through evolution. Literally, we can't think the unthinkable.

This is bull-crap. Don't talk about things you know nothing about. Cite a paper where this "strong evidence" is presented.

A third reason is that it has been shown by mathematical logicians (Michiel van Lambalgen and others) that it is perfectly possible to build irreducible randomness into ground level logic. We don't need to define it in mathematics - to let it "emerge"

That is BS, they too talk about "irreducible randomness" without understanding what it means? Please cite a paper.

A fourth reason is Occam's razor. The assumption of irreducible randomness makes quantum mechanics clean and complete and much less complex, than supposing there are incredibly complex deterministic mechanisms behind the apparent randomness, so exquisitely fine tuned that we can violate Bell inequalities but not see any evidence whatsoever of action at a distance.

This is astounding, anybody can invent a fantasy called "!~#\$*\$*", without the slightest clue what it means, and then claim that "!~#\$*\$*" is all we need to resolve the measurement problem and unify gravity and QM. When asked to define "!~#\$*\$*", they will dismissively say, "sorry, I don't know the meaning it just emerges. In mathematics, I don't need to know the meaning because bla, bla, bla just works." That's exactly how your responses appear to me at the moment with all due respect.

Slava Belavkin already showed how to build irreducible randomness into conventional QM by his invention of "eventum mechanics".

Translation: Slava Belavkin already showed how to build "irreducible !~#\$*\$*" into conventional QM by his invention of "eventum mechanics"

Until you define what is meant by "randomness", the above statements mean the same thing.
minkwe

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### Re: "Irreducible Randomness", what does that even mean?

Dear Michel, It's about time you carefully read a few of my papers. You will find answers to all your questions there. In particular, please read carefully my invited discussion paper of a few years ago, in a special issue on causality in the fairly prestigious journal "Statistical Science" https://arxiv.org/abs/1207.5103.

Here two other key publications, which fill in some of the mathematical details of the already mentioned paper: https://arxiv.org/abs/quant-ph/0110137, https://arxiv.org/abs/quant-ph/0301059.

And no, to justify such a claim I do *not* need first to define randomness. You already defined randomness. I take your definition as the definition of reducible randomness. Irreducible randomness is that which cannot be distinguished empirically from reducible randomness, but which does not have the same "explanation".

As I already said, your definition of randomness is not a definition or an explanation at all, since it is either subjective or an infinite regress (ie a circular definition).

If you want to attack me on this point, then: please, *you give me* your definition of randomness while making sure that it is not purely subjective and not circular. I am afraid that you will not succeed. Nobody else did, in the entire history of civilization. Many have tried. Some did gain, for a while, a large following.

Many people are happy with the notion that probability is purely in the mind of an individual person, and randomness does not need any definition. I've never been happy with those ideas. I admire de Finetti's mathematical framework which supports this point of view. But I think that Occam's razor makes it inadequate for the probabilities which we measure and the randomness which is predicted by quantum physics. The currently "best" explanation uses irreducible randomness. I understand everyone's gut-feeling opposition to this notion. I experience it myself, in my belly! My stomach turns, my mind revolts. But I think it is unscientific to take this kind of intuition as decisive.

I certainly prefer this to the solutions based on imaginary time, time reversal, or Bohmian trajectories. Mathematically they are all fine. But, IMHO, *explanations* they are not. I am pretty confident that in order to resolve the riddle of finding a grand unified theory of physics we need to reconsider some of our most basic *intuitions*. I could mention quite a few big names who completely agree with me. So don't call me an idiot for putting forward these ideas, and don't reject them without studying the arguments carefully. Instead: read the literature, ruminate on what you find there, try out some new things yourself, try to get them published. Come to our workshop/symposium. Meet some of those people "in the flesh" who have very different opinions from yours.
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### Re: "Irreducible Randomness", what does that even mean?

gill1109 wrote:Dear Michel, It's about time you carefully read a few of my papers. You will find answers to all your questions there.

Answers to the questions you have already told me you don't know the answer to?
minkwe

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### Re: "Irreducible Randomness", what does that even mean?

gill1109 wrote:And no, to justify such a claim I do *not* need first to define randomness. You already defined randomness. I take your definition as the definition of reducible randomness. Irreducible randomness is that which cannot be distinguished empirically from reducible randomness, but which does not have the same "explanation".

So now we get some admission that in fact, you do have definitions. You just don't want to share them. For example, you now claim that my definition of "randomness" is your definition of "reducible randomness". Note that in my definition of randomness, the phrase "irreducible - " or "reducible -" randomness is meaningless. So it can't be my definition you are relying on.

Secondly, as I've already explained, the words "irreducible" and "reducible" are adjectives which modify the meaning. But what is the meaning exactly that is being modified? This is what I've been asking, what exactly is it that you claim is reducible or irreducible. You claim not to know so why are we even continuing this discussion.

As I already said, your definition of randomness is not a definition or an explanation at all, since it is either subjective or an infinite regress (ie a circular definition).

Or so, now it is not a definition any more but yet it is the definition you use for "reducible randomness"? Come on!
minkwe

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### Re: "Irreducible Randomness", what does that even mean?

gill1109 wrote:And no, to justify such a claim I do *not* need first to define randomness. You already defined randomness. I take your definition as the definition of reducible randomness.

minkwe wrote:So now we get some admission that in fact, you do have definitions. You just don't want to share them. For example, you now claim that my definition of "randomness" is your definition of "irreducible randomness".

For God's sake minkwe, at least read a post twice before you start trolling. He wrote "reducible".
Heinera

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### Re: "Irreducible Randomness", what does that even mean?

Heinera wrote:
gill1109 wrote:And no, to justify such a claim I do *not* need first to define randomness. You already defined randomness. I take your definition as the definition of reducible randomness.

minkwe wrote:So now we get some admission that in fact, you do have definitions. You just don't want to share them. For example, you now claim that my definition of "randomness" is your definition of "irreducible randomness".

For God's sake minkwe, at least read a post twice before you start trolling. He wrote "reducible".

Obviously you did not take your own advice. Or is it just the typo that got you so worked up? If you have a contribution to make, I will be happy to hear your own definition for "randomness".
minkwe

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### Re: "Irreducible Randomness", what does that even mean?

minkwe wrote:
Heinera wrote:
gill1109 wrote:And no, to justify such a claim I do *not* need first to define randomness. You already defined randomness. I take your definition as the definition of reducible randomness.

minkwe wrote:So now we get some admission that in fact, you do have definitions. You just don't want to share them. For example, you now claim that my definition of "randomness" is your definition of "irreducible randomness".

For God's sake minkwe, at least read a post twice before you start trolling. He wrote "reducible".

Obviously you did not take your own advice. Or is it just the typo that got you so worked up? If you have a contribution to make, I will be happy to hear your own definition for "randomness".

Michel, take a leaf out of Ludwig Wittgenstein's Blue Book. "The idea that in order to get clear about the meaning of a general term one had to find the common element in all its applications has shackled philosophical investigation; for it has not only led to no result, but also made the philosopher dismiss as irrelevant the concrete cases, which alone could have helped him to understand the usage of the general term."

At this stage we can better discuss examples and problems; asking for definitions is just making things worse.

Here's some more Wittgenstein: "I am saying that these phenomena have no one thing in common in virtue of which we use the same word for all — but there are many kinds of affinity between them. (...) we see a complicated network of similarities overlapping and criss-crossing: similarities in the large and in the small. I can think of no better expression to characterize these similarities than “family resemblances”; for the various resemblances between members of a family — build, features, colour of eyes, gait, temperament, and so on and so forth — overlap and criss-cross in the same way." (Philosophical Investigations)
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### Re: "Irreducible Randomness", what does that even mean?

minkwe wrote:
gill1109 wrote:Dear Michel, It's about time you carefully read a few of my papers. You will find answers to all your questions there.

Answers to the questions you have already told me you don't know the answer to?

No, answers to all the other questions which you asked. Please read (or re-read) those three papers of mine. Maybe this time you'll pick up some new information from them. Take your time. And come to our workshop and symposium!

https://arxiv.org/abs/1207.5103 Statistics, Causality and Bell's Theorem
https://arxiv.org/abs/quant-ph/0301059 Time, Finite Statistics, and Bell's Fifth Position
https://arxiv.org/abs/quant-ph/0110137 Accardi contra Bell (cum mundi): The Impossible Coupling
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### Re: "Irreducible Randomness", what does that even mean?

gill1109 wrote:
minkwe wrote:
gill1109 wrote:Dear Michel, It's about time you carefully read a few of my papers. You will find answers to all your questions there.

Answers to the questions you have already told me you don't know the answer to?

No, answers to all the other questions which you asked. Please read (or re-read) those three papers of mine. Maybe this time you'll pick up some new information from them. Take your time. And come to our workshop and symposium!

https://arxiv.org/abs/1207.5103 Statistics, Causality and Bell's Theorem
https://arxiv.org/abs/quant-ph/0301059 Time, Finite Statistics, and Bell's Fifth Position
https://arxiv.org/abs/quant-ph/0110137 Accardi contra Bell (cum mundi): The Impossible Coupling

LOL, those are some of your worst works IMHO. But if they do not address the meaning of randomness, then they are irrelevant to this topic and can't answer my questions. BTW, I'm well aware of the rhetorical tactic of listing papers and/or pointing to a library and saying -- "go study, you'll find your answers there" .

BTW, I was surprised by your lack of curiosity about my earlier statements on mutual information and Bell's theorem.
minkwe

Posts: 1128
Joined: Sat Feb 08, 2014 10:22 am

### Re: "Irreducible Randomness", what does that even mean?

minkwe wrote:
gill1109 wrote:...
https://arxiv.org/abs/1207.5103 Statistics, Causality and Bell's Theorem
https://arxiv.org/abs/quant-ph/0301059 Time, Finite Statistics, and Bell's Fifth Position
https://arxiv.org/abs/quant-ph/0110137 Accardi contra Bell (cum mundi): The Impossible Coupling

LOL, those are some of your worst works IMHO. But if they do not address the meaning of randomness, then they are irrelevant to this topic and can't answer my questions. BTW, I'm well aware of the rhetorical tactic of listing papers and/or pointing to a library and saying -- "go study, you'll find your answers there" .

In this case, it was not a rhetorical tactic. I don't think it was polite of you to suppose that I was merely performing a cheap debating trick, like British politicians in the House of Commons.

But OK, if you have already read them and discarded them as junk, you are obviously not likely to learn anything at all from talking to me today. I'm not ready to give a definition of randomness. I agree with a number of scientists and scholars who think this would be premature. I can give you what I believe are many examples of reducible (epistemic) randomness, and a few examples of irreducible (ontological) randomness. I think that the "reducible" kinds do not help us to define probability. You seem to take it as axiomatic that probability is epistemic. So you don't define randomness, you just talk about an agent's uncertainty. Maybe it is then *unnecessary* to define randomness!

De Finetti's definition of probability in terms of a consistent person's acceptable betting odds is the foundation of the modern-day interpretation of QM called QBism. It is also invoked by David Deutsch in his many-worlds interpretation. Reducing randomness to uncertainty about initial conditions is either circular or the beginning of an infinite regress. You haven't responded to this remark by me. Did you just reject it without thought as junk?

Certainly, it is possible to take this approach to *explain* why most people think that fifty-fifty are the correct odds for a physically fair coin. This fits to the Laplace definition: take "equally likely" to be a primitive concept, which does not have a definition. By our own intuition we are supposed to know when it is applicable or not. Then look for the "equally likely" atomic configurations and just count them.

Christian Huygens defined probability in terms of fair betting odds, by reducing all problems to atomic equally likely initial configurations and counting them. His book was *the* textbook on probability for several hundred years, during which time insurance companies and the stock exchange came into being as part of the hand-in-hand development of modern capitalism and European colonialism, and a mass move of humanity from the country to cities. In fact this was his own scientific motivation - the brand new Dutch State (one of the only republics in Europe, at a time of autocratic monarchies) badly needed to raise money. And the merchants, who had the power in the cities, needed to insure their ships and their cargoes.

I don't like the intrusion of the economic motives of a human being into physics.

According to Wittgenstein, the smartest thing to do at present could well be simply to collect examples and to think about them. I think that Bell's theorem does show us that QM demands irreducible randomness. Incidentally, so did Feynman, who proved a version of Bell's theorem himself, a few years later (1981). See https://aapt.scitation.org/doi/full/10.1119/1.4948268.
RICHARD FEYNMAN AND BELL'S THEOREM
American Journal of Physics 84, 493 (2016); https://doi.org/10.1119/1.4948268
Andrew Whitaker
"One of the questions he [Feynman] asked was, 'Can quantum systems be simulated probabilistically by a classical computer with local connections?' Feynman's answer was in the negative, and he explained this answer by analyzing what he called the two-photon correlation experiment, which was designed to check the possibility of using hidden variables to produce the quantum mechanical results for an entangled system. Feynman explains the crucial element of his analysis that causes it to fail: it requires some probabilities to be negative. He emphasizes that the experiment has been performed and that the results agree with the quantum predictions."

So you think that Richard Feynman was wrong, too? He may have heard about Bell but he preferred to figure out everything for himself. He was aware of the first Bell type experiments. "Experimental Test of Local Hidden-Variable Theories", Stuart J. Freedman and John F. Clauser, Phys. Rev. Lett. 28, 938 – Published 3 April 1972. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.28.938

minkwe wrote:BTW, I was surprised by your lack of curiosity about my earlier statements on mutual information and Bell's theorem.

I was already aware of the connection and interested in it. I'm waiting patiently for you to tell us more.

PS Feynman's paper: Richard P. Feynman, International Journal of Theoretical Physics, June 1982, Volume 21, Issue 6–7, pp 467–488. "Simulating physics with computers". Both Joy and I have published in this journal. The editorial board consists almost entirely of Nobel Prize winning physicists. Most of them are not very young. One wonders if they do much work, or if it is all left to the Managing Editor.
gill1109
Mathematical Statistician

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### Re: "Irreducible Randomness", what does that even mean?

By the way, George Boole also wanted an epistemic foundation of probability (hence no need for a definition of randomness!). His project ran aground on the issue of finding the proper prior probabilities on probability structures. Suppose you have four binary variables. The joint probability distribution of the four depends on 2 to the power 4 which is 16 probabilities, which have to add up to one. OK, we could put the uniform distribution on the 15-dimensional simplex. But this does not do justice to our prior knowledge that possibly there are lower dimensional structures in the relationships between those 4 variables. For instance, there could, a priori, be some deterministic relations between those variables. Or conditional independence relations. Some conditional probabilities might be identically zero. He could not figure out how to solve this problem.

This is the kind of problem which is now being tackled for instance by people like Jonas Peters, whose 2018 book "Elements of Causal Inference: Foundations and Learning Algorithms", published by MIT, (authors: Jonas Peters, Dominik Janzing, Bernhard Schölkopf) I already mentioned a few times. Check out Jonas Peters' own home page http://web.math.ku.dk/~peters/ to track down the free pdf. If, like me, you love reading printed letters on real paper, here's the Amazon link:
https://www.amazon.co.uk/Elements-Causal-Inference-Foundations-Computation/dp/0262037319
and here's the MIT link:
https://mitpress.mit.edu/books/elements-causal-inference
gill1109
Mathematical Statistician

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Location: Leiden

### Re: "Irreducible Randomness", what does that even mean?

minkwe wrote:...should probably explain:
1. what they understand by "Randomness",
2. then next explain the difference between "reducible" and "irreducible" randomness
3. then finally, explain how to distinguish the two in practice.

Just in case the point of this thread is forgotten.
If you don't know what randomness means and don't know how to distinguish reducible from irreducible randomness in practice, and yet claim to have examples of each type. Do you expect me to take anything you say on the subject seriously? You are essentially claiming to have knowledge you've previously told me you don't have. Look up the meaning of "knowledge".

Once you answer "I don't know" to question 1, you can't claim to know anything about the rest of the questions.
minkwe

Posts: 1128
Joined: Sat Feb 08, 2014 10:22 am

### Re: "Irreducible Randomness", what does that even mean?

minkwe wrote:
minkwe wrote:...should probably explain:
1. what they understand by "Randomness",
2. then next explain the difference between "reducible" and "irreducible" randomness
3. then finally, explain how to distinguish the two in practice.

Just in case the point of this thread is forgotten.
If you don't know what randomness means and don't know how to distinguish reducible from irreducible randomness in practice, and yet claim to have examples of each type. Do you expect me to take anything you say on the subject seriously? You are essentially claiming to have knowledge you've previously told me you don't have. Look up the meaning of "knowledge".

Once you answer "I don't know" to question 1, you can't claim to know anything about the rest of the questions.

Your definition "unpredictable" seems fine to me for randomness. I don't know why anyone would not accept that. ???
.
FrediFizzx
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