"Irreducible Randomness", what does that even mean?

[minkwe]

Isn't it possible that all these "constants" actually are the result of irreducible randomness in the very very early quantum universe at the stage when space-time itself is being born out of entangled quantum fluctuations in the initial singularity?

A spin-off from another thread, I'm hoping in this thread we will flesh out this idea of "irreducible randomness" that has been floated around quite a few times. I hope it doesn't devolve into an argument about Bell's theorem or Quantum Mechanics. The proponents of the idea 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.

The third point is crucial because without it, it would be nonsensical to even claim there is such a thing since it would be similar to the claim that there are two types of atoms "detectable atoms" and "non-detectable atoms". Perhaps just as nonsensical to claiming there are multiple universes.

[FrediFizzx]

Isn't it possible that all these "constants" actually are the result of irreducible randomness in the very very early quantum universe at the stage when space-time itself is being born out of entangled quantum fluctuations in the initial singularity?

A spin-off from another thread, I'm hoping in this thread we will flesh out this idea of "irreducible randomness" that has been floated around quite a few times. I hope it doesn't devolve into an argument about Bell's theorem or Quantum Mechanics. The proponents of the idea 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.

The third point is crucial because without it, it would be nonsensical to even claim there is such a thing since it would be similar to the claim that there are two types of atoms "detectable atoms" and "non-detectable atoms". Perhaps just as nonsensical to claiming there are multiple universes.

We sort of went down this road already,

viewtopic.php?f=6&t=386

not sure anything got settled about "irreducible".
.

[Joy Christian]

Isn't it possible that all these "constants" actually are the result of irreducible randomness in the very very early quantum universe at the stage when space-time itself is being born out of entangled quantum fluctuations in the initial singularity?

A spin-off from another thread, I'm hoping in this thread we will flesh out this idea of "irreducible randomness" that has been floated around quite a few times. I hope it doesn't devolve into an argument about Bell's theorem or Quantum Mechanics. The proponents of the idea 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.

The third point is crucial because without it, it would be nonsensical to even claim there is such a thing since it would be similar to the claim that there are two types of atoms "detectable atoms" and "non-detectable atoms". Perhaps just as nonsensical to claiming there are multiple universes.

We sort of went down this road already,

viewtopic.php?f=6&t=386

not sure anything got settled about "irreducible".

The following is what I wrote in that thread (reproduced with some editing). I should stress that I am by no means a proponent of "irreducible randomness." Quite the opposite.

The word "reducible" in this context simply means that the said randomness is epistemic in origin, like the randomness in the outcome of a coin toss. The randomness in the outcome of a coin toss is not intrinsic to the coin or to Nature, but stems from our subjective lack of knowledge of the initial state of the system; namely, of the coin. Likewise, if we know the initial state λ in [a] model ... for a given run of the experiment, then the outcome A(a, λ) for a given parameter a is completely and deterministically known. This is in sharp contrast to the irreducible randomness presumed within orthodox quantum mechanics. In the case of quantum mechanics, no matter how much information about the initial state of the system is known, the precise outcome, say, of a spin detection [or of spontaneous decay of an atom], would remain unpredictable. Therefore quantum mechanical randomness is not reducible in general.

***

[Heinera]

I think the questions posed by minkwe will mostly have answers that are philosophical in nature. But there are actually some (abstract) mathematical definitions of "irreducible randomness", see eg. Algorithmically random sequence.

[Joy Christian]

***
A concept closely related to "irreducible randomness" is "objective chance."

"Objective chance" means a chance of an event that is not due to our lack of knowledge about the system, such as a spontaneous decay of an atom within quantum mechanics.

***

[gill1109]

We should also distinguish between *our* lack of knowledge or *our* inability to compute on the one hand, and the principled inability of anything in the universe to know or to compute. Now, the question does certainly, and inevitably, become a question of *meta*physics, and of philosophy. Not something that can be decided experimentally. Consider a toy universe with discrete time and discrete space, where, at each time step, each local subsystem (which has only finitely many distrinct states) acts *stochastically* depending on the state of its neighbours. Mathematically we can simulate the whole evolution of this whole universe by having a "reservoir" of countably many uniformly distributed random numbers (ie random numbers between 0 and 1). One draws one random number from the reservoir for each location at each time point in order to convert its random behaviour into deterministic (pseudo-random). Now one can en code all those uniform random numbers, each one - expressed in binary - is just an infinite sequence of fair coin flips in *one* infinite sequence of fair coin flips (lots of tricks to do that) so finally one can express the whole toy universe as a deterministic process depending on the realisation, initially (at time zero) of one uniformly distributed random number between 0 and 1. Call it the G-number. Gill's number, if you like. Or God's number, if you prefer. Now the toy universe has changed in character from being irreducibly random to being deterministic (pseudo random). Now you may say, of course, in mathematical physics we don't suppose that everything is discrete and finite (at most, countable). But in mathematics, and doing physics depends on having mathematics as a language, is very well understood (Gödel, Turing and all that), that everything in mathematics has a model [that's a technical term] in which everything is actually countable. ie the mathematical structure, from inside, has got something which it calls the real numbers and which has, internally, everything that the real numbers do have, including being uncountable; but this whole structure is embedded in a structure which is actually just a list of objects. Countable. So whatever maths we do, we cannot escape from the discrete and countable, and hence all "irrreducible randomness" which we need can be replaced by pseudo-randomness depending on one G-number.

There have been proposals to change the foundations of mathematics by adding "irreducible randomness" to the ground level, ie to the axiomatic foundations of a new,, richer formal logic. Michiel van Lambalgen wrote a fantastic, path breaking, PhD thesis on this subject about 45 years ago.

So in conclusion, it becomes, in my opinion, a *matter of taste*. What do you accept to take as the "bottom line". Do you think it is worth expending brain energy on further exploring *why* the atom decays at a particular moment of time and not another particular moment of time? I think it might be a waste of time at some stages of the evolution of science, and become a non-waste of time later. Now there are empirical aspects of all this, though they are connected again to distinctions between finite and infinite; between large and ... so large as to be effectively infinite. If the physical world does have irreducible randomness, and if we see it "in action" in, e.g., in Bell type experiments, then we can harness that randomness to create cryptographic systems which are unbreakable *because of the physical nature of the universe*, as opposed to unbreakable *because the opponent doesn't have fast enough computers and enough time*. So this is something important to those who want to *sell* cryptographic systems (and there is a big market out there!). So there is, kind of, empirical content in the distinction. Even if at the present it can only be an "article of faith" that we may perhaps say "according to current understanding of the physics of the world, this crypto system is unbreakable".

So there are also major financial interests, and national security interests, in the question. Maybe the CIA does know that irreducible randomness does *not* exist and is keeping that a secret from the rest of the world.

[minkwe]

Thanks for all the interest in this thread however, the problem with the previous discussion was that nobody really defined what "random" means in the first place leading to a bunch of "random" discussions (pun intended). Without a clear definition, it is not even possible to discuss whether "reducible" or "irreducible" adjectives even make sense. That is why I asked the three specific questions.

1. what is your understanding of the meaning of "Randomness",
2. then next explain the difference between "reducible" and "irreducible" randomness
3. then finally, explain how to distinguish the two in practice.

Since I'm the one asking, perhaps I should start:

(1) Randomness simply means "unpredictable". It is an entirely epistemic concept since predictability is not a feature of nature but a feature of states of knowledge/information and theories. If you have complete information about a system, then by definition, you have complete information about what the system has done in the past, and what it will do in the future. Anything short of this is "incomplete" information. If you have complete information, then you can predict what will happen. The idea that you might have complete information and yet not be able to predict what will happen is a contradiction of what "complete information" means, and what "unpredictable/random" means. Now, a theory only deals with information that is within the scope of that theory. While you may have all the information that is relevant to a particular theory, you may not have all the information that is relevant to the system being modeled by the theory. In that sense, the theory is incomplete. Then the theory will never be able to predict everything about the system being modeled.

(2) Therefore the suggestion that the randomness in some theory is "reducible" or "irreducible" still does not go beyond the capabilities of the theory and are both still epistemic concepts. "Reducible" if the randomness is due to lack of information that is within the scope of the theory, and "irreducible" if it is outside the scope of the theory. I have a very strong objection to anyone suggested that "reducible" or "irreducible" have to do with nature (ontology) and not the capabilities of a theory (epistemology).

(3) You can distinguish this understanding of "reducible" from the "irreducible" variant by checking if all the information possible within the scope of the theory, was taken into consideration in making the prediction. If it was then the randomness is "irreducible" within the theory, otherwise it may be "reducible" within the theory. Only after all the information possible within the scope of the theory has been taken into account can any remaining unpredictability be claimed to be "irreducible" within the theory.

As I have explained, the idea of "nature" being irreducibly random does not make sense and is an example of the Mind Projection Fallacy. "Randomness"/"Predictability" is an entirely epistemic concept. But I hope to be disproven by clear answers to the three questions from others.

[FrediFizzx]

Does that mean that you think there is a "cause" for everything in Nature? What about spontaneous symmetry breaking?
.

[Joy Christian]

***
The idea that chance is an objective property of the universe was advocated by the American philosopher Charles Sanders Peirce, who called this doctrine tychism, from the Greek word for chance. Support for the doctrine came later from orthodox quantum theory, which is often interpreted as implying that some events such as radioactive decay are inherently unpredictable.

***

[gill1109]

Thanks for all the interest in this thread however, the problem with the previous discussion was that nobody really defined what "random" means in the first place leading to a bunch of "random" discussions (pun intended). Without a clear definition, it is not even possible to discuss whether "reducible" or "irreducible" adjectives even make sense. That is why I asked the three specific questions.

1. what is your understanding of the meaning of "Randomness",
2. then next explain the difference between "reducible" and "irreducible" randomness
3. then finally, explain how to distinguish the two in practice.

Since I'm the one asking, perhaps I should start:

(1) Randomness simply means "unpredictable". It is an entirely epistemic concept since predictability is not a feature of nature but a feature of states of knowledge/information and theories
...
As I have explained, the idea of "nature" being irreducibly random does not make sense and is an example of the Mind Projection Fallacy. "Randomness"/"Predictability" is an entirely epistemic concept. But I hope to be disproven by clear answers to the three questions from others

Michel, you informed us in that post what "randomness" meant for you. For you, it simply meant "unpredictable". You think that this implies that it is an entirely epistemic concept. But I think there is a distinction between (1) "unpredictable" because we do not know enough or cannot compute enough or because of sensitive dependence on initial conditions, and (2) *unpredictable* because there are physical processes in nature which are *essentially* unpredictable. Is randomness an emergent property of the physical universe, or is it something built-in, ground level, into the very fabric of reality? You answered this question dogmatically. By stating *your* definitions. But they don't have to be everybody's definitions. In metaphysics, as in the foundations of logic and mathematics, the definitions and axioms are also up for discussion.

Notice that unpredictable (1) merely puts us into an infinite regress. Turtles all the way down? The coin toss is random because the initial conditions were random. At some point, we invoke symmetry to suppose a more or less smooth distribution over some initial conditions which translates into a uniform distribution on the outcome of the coin toss. So my objection to unpredictability (1) is that its definition is circular and/or subjective. I think that such definitions should have no place in physics! Read the Peters et al book on machine learning and causality for some serious analysis of randomness and statistical independence assumptions from a physics point of view and using algorithmic complexity theory. At some point we have some trust that nature is essentially understandable and simple (Occam's razor). We object to a theory which requires juggling of many, many free parameters to make it fit. So that can be a reason to finally prefer to hypothesize irreducible randomness. It's not for nothing that one of the assumptions of Bell's theorem is called "no conspiracy". And why it is connected to the hypothesis of "free will".

[ajw]

'irreducible randomness' incorporates the phylosophical view, like Joy says advocated in the Copenhagen interpretation, that there are limits to what can be known about physics. For me this limit has been introduced without a real reason or evidence. There is also no evidence for the opposite - deterministic - view, but all macroscopic experiments seem to point in this direction. So maybe the real question is whether or not it is proven or likely that there is somehow a fundamental limit to our understanding of physics.

[minkwe]

Does that mean that you think there is a "cause" for everything in Nature? What about spontaneous symmetry breaking?
.

No, what I said, does not imply that. Predictability does not have anything to do with causes. Causality is a completely different discussion IMHO. BTW, is spontaneous symmetry breaking a feature of a theory or a feature of nature?

[minkwe]

***
The idea that chance is an objective property of the universe was advocated by the American philosopher Charles Sanders Peirce, who called this doctrine tychism, from the Greek word for chance. Support for the doctrine came later from orthodox quantum theory, which is often interpreted as implying that some events such as radioactive decay are inherently unpredictable.

***

I would say the underlined is phrase is meaningless to me at this point, without elaboration of what exactly is meant by that. How can humans "know" that something can never be "known". This is a fallacy of logic also sometimes known as "proving a negative", or "argument from ignorance".

[Joy Christian]

***
The idea that chance is an objective property of the universe was advocated by the American philosopher Charles Sanders Peirce, who called this doctrine tychism, from the Greek word for chance. Support for the doctrine came later from orthodox quantum theory, which is often interpreted as implying that some events such as radioactive decay are inherently unpredictable.

I would say the underlined is phrase is meaningless to me at this point, without elaboration of what exactly is meant by that. How can humans "know" that something can never be "known". This is a fallacy of logic also sometimes known as "proving a negative", or "argument from ignorance".

I am not defending the concept of "objective chance." I am merely reporting some facts. I very much share your misgivings about "objective chance" and "inherently unpredictable." To me, these ideas sound like magic or mysticism. But Peirce is a difficult philosopher to read or understand. I tried to, during my graduate student days at Boston University, because Peirce was the favorite philosopher of my Ph.D. mentor, Abner Shimony, who himself was a distinguished philosopher (as well as a physicist). I did not understand Peirce then and do not understand him now. But during those student days I had not yet developed an independent mind, so I had accepted the concept of objective chance on Shimony's authority, despite my unease with it.

***

[minkwe]

Thanks for all the interest in this thread however, the problem with the previous discussion was that nobody really defined what "random" means in the first place leading to a bunch of "random" discussions (pun intended). Without a clear definition, it is not even possible to discuss whether "reducible" or "irreducible" adjectives even make sense. That is why I asked the three specific questions.

1. what is your understanding of the meaning of "Randomness",
2. then next explain the difference between "reducible" and "irreducible" randomness
3. then finally, explain how to distinguish the two in practice.

Since I'm the one asking, perhaps I should start:

(1) Randomness simply means "unpredictable". It is an entirely epistemic concept since predictability is not a feature of nature but a feature of states of knowledge/information and theories
...
As I have explained, the idea of "nature" being irreducibly random does not make sense and is an example of the Mind Projection Fallacy. "Randomness"/"Predictability" is an entirely epistemic concept. But I hope to be disproven by clear answers to the three questions from others

Michel, you informed us in that post what "randomness" meant for you. For you, it simply meant "unpredictable". You think that this implies that it is an entirely epistemic concept. But I think there is a distinction between (1) "unpredictable" because we do not know enough or cannot compute enough or because of sensitive dependence on initial conditions, and (2) *unpredictable* because there are physical processes in nature which are *essentially* unpredictable. Is randomness an emergent property of the physical universe, or is it something built-in, ground level, into the very fabric of reality? You answered this question dogmatically. By stating *your* definitions. But they don't have to be everybody's definitions. In metaphysics, as in the foundations of logic and mathematics, the definitions and axioms are also up for discussion.

Notice that unpredictable (1) merely puts us into an infinite regress. Turtles all the way down? The coin toss is random because the initial conditions were random. At some point, we invoke symmetry to suppose a more or less smooth distribution over some initial conditions which translates into a uniform distribution on the outcome of the coin toss. So my objection to unpredictability (1) is that its definition is circular and/or subjective. I think that such definitions should have no place in physics! Read the Peters et al book on machine learning and causality for some serious analysis of randomness and statistical independence assumptions from a physics point of view and using algorithmic complexity theory. At some point we have some trust that nature is essentially understandable and simple (Occam's razor). We object to a theory which requires juggling of many, many free parameters to make it fit. So that can be a reason to finally prefer to hypothesize irreducible randomness. It's not for nothing that one of the assumptions of Bell's theorem is called "no conspiracy". And why it is connected to the hypothesis of "free will".

Please, if we can we avoid Bell's theorem for this discussion, that will be refreshing.

I noticed that you did not provide a definition for "randomess". What is your definition? Without that, it is difficult to even understand what you are trying to say or engage in anything else you are describing. Since you do not make any clear distinctions in between theories and reality.

FYI, nature does not predict so anything that deals with prediction is the domain of epistemology.

[minkwe]

'irreducible randomness' incorporates the phylosophical view, like Joy says advocated in the Copenhagen interpretation, that there are limits to what can be known about physics. For me this limit has been introduced without a real reason or evidence. There is also no evidence for the opposite - deterministic - view, but all macroscopic experiments seem to point in this direction. So maybe the real question is whether or not it is proven or likely that there is somehow a fundamental limit to our understanding of physics.

Epistemology deals with knowledge. If "irreducible randomness" deals with limits to what can be known, then it is epistemic. First of all, I would take issue to any claims that there are limits to what can be known as it is again an "argument from ignorance" fallacy. But even granting that, to say something can not be known implies that the thing exists but you can't know it. So then, there is information about the thing that is out-of-reach, and therefore we have incomplete information about the thing.

[FrediFizzx]

'irreducible randomness' incorporates the phylosophical view, like Joy says advocated in the Copenhagen interpretation, that there are limits to what can be known about physics. For me this limit has been introduced without a real reason or evidence. There is also no evidence for the opposite - deterministic - view, but all macroscopic experiments seem to point in this direction. So maybe the real question is whether or not it is proven or likely that there is somehow a fundamental limit to our understanding of physics.

Epistemology deals with knowledge. If "irreducible randomness" deals with limits to what can be known, then it is epistemic. First of all, I would take issue to any claims that there are limits to what can be known as it is again an "argument from ignorance" fallacy. But even granting that, to say something can not be known implies that the thing exists but you can't know it. So then, there is information about the thing that is out-of-reach, and therefore we have incomplete information about the thing.

I think what Albert Jan is referring to is how do you get around the uncertainty principle?
.

[Heinera]

Thanks for all the interest in this thread however, the problem with the previous discussion was that nobody really defined what "random" means in the first place leading to a bunch of "random" discussions (pun intended).

You asked a philosophical question. Why would you then expect to get sensible answers?

[minkwe]

Thanks for all the interest in this thread however, the problem with the previous discussion was that nobody really defined what "random" means in the first place leading to a bunch of "random" discussions (pun intended).

You asked a philosophical question. Why would you then expect to get sensible answers?

I don't know of you are deriding the question or the answers but there is a trend these days in theoretical physics in which people deride philosophy as an excuse to practice faulty logic. As soon as you point out erroneous reasoning, they say "that's philosophy" and ignore anything you say.

Unfortunately that will not cut it, because philosophy is intertwined in every scientific endeavor. We have to reason about data. We make arguments using logical structures. Every scientist should have a basic understanding of philosophy. Usually when somebody brings up the word "philosophy" dismissively, it is a sign that they are not a scientist or they are naive about science.

Is it too much to ask you to explain your understanding of the meaning of a word you have been using frequently?

[minkwe]

I think what Albert Jan is referring to is how do you get around the uncertainty principle?
.

I don't think you need to "get around" it. The uncertainty principle is not a feature of nature but a feature of the theory. It arises from the complementary definition of the "properties". Whenever there is an uncertainty principle, look for complementarity in the definitions within the theory. It has nothing to do with uncertainty in nature.

Take position and momentum for example. It states that the more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa. But this is obvious if you think about what "position" and "momentum" mean. Position has dimensions L, while momentum has dimensions MLT^-1. The definition of momentum (in the theory) involves an important component which is "change of position" over time. Obviously this implies that momentum is undefined at a given position since " position" is undefined at a fixed position. Therefore mathematically, the definition of position and momentum are such that they become pontryagin duals, or conjugate variables. This is the origin of the uncertainty principles.

Another example is "time" and "frequency" which are also pontryagin duals and therefore have an uncertainty relationship between them. Note how "frequency" is defined using " time" in such a way that instantaneous frequency is meaningless.

BTW: Pontryagin duals are also known as "conjugate variables".

Therefore the uncertainty principle is not something that needs to be gotten around, it just is because of the way we have chosen to create concepts such as "position" and "momentum" and defined them in certain ways mathematically. It's all completely epistemic.