"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?

Postby ajw » Thu Aug 29, 2019 1:43 pm

minkwe wrote:
FrediFizzx wrote: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 complimentary 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.

Aren't you be a bit off here? This explanation is often used but I think is not the complete story when it comes to subatomic particles, as can be seen by the various Heisenberg uncertainty relations. It has to do with the wave/particle duality.
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Re: "Irreducible Randomness", what does that even mean?

Postby minkwe » Thu Aug 29, 2019 2:19 pm

ajw wrote:Aren't you be a bit off here? This explanation is often used but I think is not the complete story when it comes to subatomic particles, as can be seen by the various Heisenberg uncertainty relations. It has to do with the wave/particle duality.

Please elaborate.
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Re: "Irreducible Randomness", what does that even mean?

Postby FrediFizzx » Thu Aug 29, 2019 2:20 pm

ajw wrote:
minkwe wrote:
FrediFizzx wrote: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 complimentary 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.

Aren't you be a bit off here? This explanation is often used but I think is not the complete story when it comes to subatomic particles, as can be seen by the various Heisenberg uncertainty relations. It has to do with the wave/particle duality.

Yes, all wave action has uncertainty. So I do think it is a property of Nature.
.
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Re: "Irreducible Randomness", what does that even mean?

Postby minkwe » Thu Aug 29, 2019 3:01 pm

FrediFizzx wrote:
ajw wrote:
minkwe wrote:
FrediFizzx wrote: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 complimentary 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.

Aren't you be a bit off here? This explanation is often used but I think is not the complete story when it comes to subatomic particles, as can be seen by the various Heisenberg uncertainty relations. It has to do with the wave/particle duality.

Yes, all wave action has uncertainty. So I do think it is a property of Nature.
.


There is a lot of misinformation in popular QM representations.
Here are some good quality resources for reference.
https://www.youtube.com/watch?v=MBnnXbOM5S4
https://physics.stackexchange.com/quest ... in-duality
https://en.wikipedia.org/wiki/Conjugate_variables
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Re: "Irreducible Randomness", what does that even mean?

Postby ajw » Thu Aug 29, 2019 3:02 pm

minkwe wrote:
ajw wrote:Aren't you be a bit off here? This explanation is often used but I think is not the complete story when it comes to subatomic particles, as can be seen by the various Heisenberg uncertainty relations. It has to do with the wave/particle duality.

Please elaborate.

For conjugate variables, you can take a very small delta T to measure an objects velocity, and thereby have a good estimation of it's position an momentum at T0. But on the scale of subatomic particles, Heisenberg states that there is a region where you cannot decrease delta T to get a better estimation for these variables.
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Re: "Irreducible Randomness", what does that even mean?

Postby minkwe » Thu Aug 29, 2019 4:15 pm

ajw wrote:For conjugate variables, you can take a very small delta T to measure an objects velocity, and thereby have a good estimation of it's position an momentum at T0. But on the scale of subatomic particles, Heisenberg states that there is a region where you cannot decrease delta T to get a better estimation for these variables.


This is not true. The position and momentum uncertainty is not limited to subatomic particles, although the magnitude of the uncertainty is more significant for subatomic particles, and the mathematics of QM reveals it more directly than the mathematics of classical mechanics. Yet, the uncertainty principle is about whether position and momentum are simultaneously defined to arbitrary precision. The smaller the , the larger the uncertainty in and the smaller the the larger the uncertainty in . In other words it is not possible in-principle to make a device which *simultaneously* measures both variables to arbitrary accuracy, irrespective of whether we are talking about atomic or macroscopic particles.

Edit: Heisenberg himself said:

W Heisenberg wrote:Any use of the words 'position' and 'velocity' with an accuracy exceeding that given by equation (1) is just as meaningless as the use of words whose sense is not defined.[footnote]

footnote: In this connection, one should particularly remember that the human language permits the construction of sentences which do not involve any consequences and which therefore have no content at all -- in spinte of the fact that these sentences produce some kind of picture in our imagination; e.g., the statement that besides our world there exists another world, with which any connection is impossible in principle, does not lead to any experimental consequence, but does produce a kind of picture in the mind. Obviously such a statement can neither be proved nor disproved. One should be especially careful in using the words "reality", "actuality", etc. since these words very often lead to statements of the type just mentioned.


Could we get back to the topic of randomness? What is your understanding of what it means, and how is the uncertainty principle relevant to the question of "irreducible randomness" in your view. I get the feeling there is a point you want to make about this that you haven't made yet.
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Re: "Irreducible Randomness", what does that even mean?

Postby ajw » Fri Aug 30, 2019 1:34 am

minkwe wrote:
ajw wrote:For conjugate variables, you can take a very small delta T to measure an objects velocity, and thereby have a good estimation of it's position an momentum at T0. But on the scale of subatomic particles, Heisenberg states that there is a region where you cannot decrease delta T to get a better estimation for these variables.


This is not true. The position and momentum uncertainty is not limited to subatomic particles, although the magnitude of the uncertainty is more significant for subatomic particles, and the mathematics of QM reveals it more directly than the mathematics of classical mechanics. Yet, the uncertainty principle is about whether position and momentum are simultaneously defined to arbitrary precision. The smaller the , the larger the uncertainty in and the smaller the the larger the uncertainty in . In other words it is not possible in-principle to make a device which *simultaneously* measures both variables to arbitrary accuracy, irrespective of whether we are talking about atomic or macroscopic particles.

Edit: Heisenberg himself said:

W Heisenberg wrote:Any use of the words 'position' and 'velocity' with an accuracy exceeding that given by equation (1) is just as meaningless as the use of words whose sense is not defined.[footnote]

footnote: In this connection, one should particularly remember that the human language permits the construction of sentences which do not involve any consequences and which therefore have no content at all -- in spinte of the fact that these sentences produce some kind of picture in our imagination; e.g., the statement that besides our world there exists another world, with which any connection is impossible in principle, does not lead to any experimental consequence, but does produce a kind of picture in the mind. Obviously such a statement can neither be proved nor disproved. One should be especially careful in using the words "reality", "actuality", etc. since these words very often lead to statements of the type just mentioned.


Could we get back to the topic of randomness? What is your understanding of what it means, and how is the uncertainty principle relevant to the question of "irreducible randomness" in your view. I get the feeling there is a point you want to make about this that you haven't made yet.

I think we agree, but this part seemed to be missing in your earlier explanation of the Heisenberg uncertainty principle.

My point to the topic is that classical QM tends to set limits on the ontology, and as it seems without proof. Postulating the existence of irreducible randomness is one example. For me it seems more natural that any seemingly random process is the result of a chaotic system, somewhat similar to waves in a sea. Another example is postulating that one cannot know the state of a particle before measurement, and QM can only be approached by probabilities.
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Re: "Irreducible Randomness", what does that even mean?

Postby gill1109 » Fri Aug 30, 2019 2:04 am

ajw wrote:My point to the topic is that classical QM tends to set limits on the ontology, and as it seems without proof. Postulating the existence of irreducible randomness is one example. For me it seems more natural that any seemingly random process is the result of a chaotic system, somewhat similar to waves in a sea. Another example is postulating that one cannot know the state of a particle before measurement, and QM can only be approached by probabilities.

Of course, it would seem more natural. Einstein had the same feeling. So does Gerard 't Hooft today. That's the whole point of the whole EPR and Bell business. Can we "explain" the randomness which QM talks about, and even puts numbers to (the numbers given by the Born rule), but which QM does not "explain", as being *merely* something so "trivial" (so familiar!) as the result of a chaotic system ... ?

The answer is *no*, unless you want to relinquish locality or realism or freedom. (Unless of course, you think that John Bell's maths or logic are wrong). In the early days of QM people like Bohr did their best to expound Michel's position: of course, if you measure position, you will disturb momentum, and so on. These were (natural) attempts to make uncertainty principles intuitively appealing. But Bohr gradually realised that this wasn't enough and he and Heisenberg came to these more or less religious statements about the meaning, or meaninglessness, of words. Schroedinger was there before them. That was post-modernism "avant la lettre". It matched their fascination with Eastern philosophy, which at that time was getting discovered and re-packaged for the consumption of Westerners. New-age hippy nonsense? Yes and no. I think that those Eastern thinkers were onto something which the rather primitive barbarians in Europe never could and never would appreciate. Then the whole thing got mixed up with the primitive adoration of the words written by a servant of God (the only true one, of course) in a book. So we got, in large parts of Europe, some kind of fusion of Nordic religion with a pantheon of Gods generally fooling about and making trouble for human beings, and so-called Judeo-Christian civilization. That (the family of semitic religions) comes from the time when a "book" was highly advanced technology and only a few guys at the top of society, Kings and/or High Priests, in the case of the UK the Queen is both, were able to say what was in it and what it meant. We in the West became even more fixated on words, especially written words. Of course they are important for civilization - justice, tax, running a stable society all depend on it. But the meaning of words tends to change over time, while systems develop which are self-perpetuating of the interests of the people on top but totally disfunctional. Just look at the UK today.
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Re: "Irreducible Randomness", what does that even mean?

Postby ajw » Fri Aug 30, 2019 3:30 am

You have way to much time to write :)
The keyword of course is 'proof', and in this case the proof that we will never be able to make a deeper mechanism plausible.
It's like postulating, let's say, in the 16th century that we will never be able to obtain any knowledge beyond the level of atoms.
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Re: "Irreducible Randomness", what does that even mean?

Postby Joy Christian » Fri Aug 30, 2019 3:42 am

ajw wrote:
You have way to much time to write :)

What matters is the signal-to-noise ratio. Look for the signals. They are often hard to find. :)

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

Postby minkwe » Fri Aug 30, 2019 8:17 am

I'm beginning to think there is active avoidance of the request for a definition for "randomness".
Take this statement for example:
gill1109 wrote:Can we "explain" the randomness which QM talks about, and even puts numbers to (the numbers given by the Born rule), but which QM does not "explain", as being *merely* something so "trivial" (so familiar!) as the result of a chaotic system ... ?


Why do we keep using words if we are reluctant to be very clear about what they mean. This is all I'm asking. Tell us what you mean by "randomness" in the above sentence and statements like it. This is what Heisenberg was talking about in the footnote I quoted above. It is very easy in human language, to string words together that sound okay but lack any content. The way to avoid this trap, which is a prevalent stumbling block, is to carefully examine the meanings of the words to see if they make sense together.

Therefore I would again kindly request that you explain your understanding of the meaning of "randomness". Assume one of your students just asked you the question: "What is randomness?", you should be able to answer immediately and confidently without any bobbing and weaving. Is the answer to this question more difficult to write than a historical excursion on the origin of Bohr's religious beliefs?
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Re: "Irreducible Randomness", what does that even mean?

Postby gill1109 » Sat Aug 31, 2019 2:51 am

minkwe wrote:I'm beginning to think there is active avoidance of the request for a definition for "randomness".
Take this statement for example:
gill1109 wrote:Can we "explain" the randomness which QM talks about, and even puts numbers to (the numbers given by the Born rule), but which QM does not "explain", as being *merely* something so "trivial" (so familiar!) as the result of a chaotic system ... ?


Why do we keep using words if we are reluctant to be very clear about what they mean. This is all I'm asking. Tell us what you mean by "randomness" in the above sentence and statements like it. This is what Heisenberg was talking about in the footnote I quoted above. It is very easy in human language, to string words together that sound okay but lack any content. The way to avoid this trap, which is a prevalent stumbling block, is to carefully examine the meanings of the words to see if they make sense together.

Therefore I would again kindly request that you explain your understanding of the meaning of "randomness". Assume one of your students just asked you the question: "What is randomness?", you should be able to answer immediately and confidently without any bobbing and weaving. Is the answer to this question more difficult to write than a historical excursion on the origin of Bohr's religious beliefs?

Yes, a good answer to this question is extremely difficult to write. In fact, it is impossible for me to write. You want an answer which is both correct and short. I think such an answer does not exist. It is a nice example of complementarity. As you wrote, quoting (I think) Heisenberg: "It is very easy in human language, to string words together that sound okay but lack any content. The way to avoid this trap, which is a prevalent stumbling block, is to carefully examine the meanings of the words to see if they make sense together."

A good answer is not short and it does involve meta-physics and perhaps even what some people would call "religion". I am actually rather interested in "answers" which come from modern neuro-linguistics and other present day neuro-sciences. What does it mean to us, when we think we "understand" something? I have earlier written about the "systems of core knowledge", the basic modules of thought which we use already as newly born infants to make sense of the sensory inputs which we are getting. In our brains is already encoded some "physical" picture of the world. In particular, our brains *know* that everything that happens does have a cause. Randomness is something horrific. Our brains do "know* that there are agents in the world and objects which agents can act on. Our brains actually "know" that action at a distance, by an agent, is possible. Our brains already "know* that the world is populated by gods and devils. Randomness must be the work of devils. We instinctively know the destructive side of chance, but we don't understand quite so well the creative, constructive side. However, Jung did describe it well.

So, Michel, to answer your question: my present understanding is "I don't know". Just as one should distrust anyone who claims to understand quantum mechanics, I distrust equally anyone who claims to understand randomness. There are lots of fascinating approaches. They all seem to me to be somehow circular, or at least, to lead to an infinite regress. I have been thinking very hard indeed about randomness for more than 50 years, and reading everything I could find about it, and the more I think about it, the less I know.

I am very interested in the answers of anyone who thinks that there is a short, correct answer! Personally, I think that invoking Pontryagin and claiming that the uncertainty principle is just obvious, certainly explains why we should not be surprised that this principle exists. But in a (so-called) loophole-free Bell experiment something else is going on. Some people here claim that we have to invoke retro-causality to explain it. Sure, that is a mathematical picture which works, but I would not call it an "explanation". Those experiments of recent years were successful because the experimenters' freedom to choose measurement settings is completely illusory? The "stuff" in the detectors and in the source already "knows" what the settings are going to be?

Call that an explanation? I don't. I don't even see how it could be useful. But if some people find it so useful that they can do new physics with these ideas, then I would start to be impressed. There are lots of mathematical tricks which one can use to do difficult calculations in quantum mechanics. Converting time to imaginary time, or even reversing time, are tricks which have been shown to be powerful mathematical tools. They don't qualify as "explanations of what is really going on" in my mind. But if they work for other people, fine.
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Re: "Irreducible Randomness", what does that even mean?

Postby ajw » Sat Aug 31, 2019 9:14 am

Is it really so difficult? From the top of my head: A system that is capable to produce between 2 and infinite values for a property at some step or interval, where each next value does not depend on previous values and cannot be determined or guessed in advance by other information (except the chance of an outcome by the distribution of the values).

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

Postby minkwe » Sat Aug 31, 2019 11:01 am

Thanks! Finally,
Shoot :)

Believe me, I'm not here to "shoot" down other's points of view. Just trying to understand it, which is not easy to do if we use words we don't understand the meanings of. All I'm asking is for others to tell me what they mean when they use the word "randomness" so let me try to understand your definition and distill it to its essential bits.

ajw wrote:A system that is capable to produce between 2 and infinite values for a property at some step or interval

I was just asking for the definition of "randomness". So to begin with, you are talking about a system. I don't see the connection, please make it clear. Do you mean randomness is a system, or a property of a system? I'll appreciate more clarity here.

Next, you have a restriction of between 2 and infinity. Why 2, why not 1. In my definition, if you are given exactly one electron moving towards a SG set of magnets, and two observers, one of them (A) without any other information, and a second (B) with full information about the properties of the electron and the apparatus, the result of the single measurement will be random according to A and completely predictable with respect to B. In your definition, it is not random to either, because it is just a single outcome.

where each next value does not depend on previous values

Here, you imply that the Markov order of the random variable must be zero for it to be random. In my definition, the Markov order is not important, it is the knowledge of any Markov order that is important for determining randomness. If you know about it, then it may be predictable but if you don't know about it then it may not be. Keeping in mind that knowing that a dependence exists, without knowing the details still results in unpredictability.

and cannot be determined or guessed in advance by other information
.
So here, you imply that there is in principle, no information that will allow the sequence to be predicted. Is that a correct understanding?

If I may paraphrase, you essentially are saying:

"A random [process] is one which produces a sequence of values with Markov order zero, which is in-principle impossible to predict"


So then given your definition of "randomness" above, what would you understand by "reducible randomness" as compared to "irreducible randomness".
Finally, unassuming "reducible randomness" and "irreducible randomness" are concepts that make sense in your definition, how will you be able to distinguish them in practice. Imagine a sequence of values coming at you, (a) how can you tell if it is random or not and (b) how can you tell which of the two types of randomness it is (again assuming the two types make sense in the definition).
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Re: "Irreducible Randomness", what does that even mean?

Postby minkwe » Sat Aug 31, 2019 11:20 am

gill1109 wrote:
minkwe wrote:
gill1109 wrote:Can we "explain" the randomness which QM talks about, and even puts numbers to (the numbers given by the Born rule), but which QM does not "explain", as being *merely* something so "trivial" (so familiar!) as the result of a chaotic system ... ?

...
This is all I'm asking. Tell us what you mean by "randomness" in the above sentence and statements like it.
...

...
So, Michel, to answer your question: my present understanding is "I don't know".
...

Really, you use the word repeatedly without knowing it's meaning?

viewtopic.php?f=6&t=399&p=9809&hilit=irreducible+randomness#p9809
viewtopic.php?f=6&t=318&p=9677&hilit=irreducible+randomness#p9672
viewtopic.php?f=6&t=318&p=9334&hilit=irreducible+randomness#p9330
viewtopic.php?f=6&t=318&p=9168&hilit=irreducible+randomness#p9168
viewtopic.php?f=6&t=318&p=9163&hilit=irreducible+randomness#p9163
viewtopic.php?f=6&t=377&p=9001&hilit=irreducible+randomness#p9001
viewtopic.php?f=6&t=377&p=8995&hilit=irreducible+randomness#p8995
viewtopic.php?f=6&t=70&p=3335&hilit=irreducible+randomness#p3335

http://arxiv.org/pdf/1207.5103.pdf (Page 3 & 4)
In this way, we can keep quantum mechanics, locality and freedom. This position does entail taking quantum randomness very seriously: it becomes an irreducible feature of the physical world, a “primitive notion”; it is not “merely” an emergent feature.
...
However, there is no such explanation for quantum randomness. Quantum randomness is intrinsic, nonclassical, irreducible


http://arxiv.org/pdf/math/0610115.pdf
According to Bell’s theorem, the randomness of quantum mechanics is truly ontological and not epistemological: it cannot be traced back to ignorance but is “for real.” It is curious that the quantum physics community is currently falling under the thrall of Bayesian ideas even though their science should be telling them that the probabilities are objective.
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Re: "Irreducible Randomness", what does that even mean?

Postby ajw » Sat Aug 31, 2019 12:47 pm

From my earlier posts it should be clear that I very much doubt whether irreducible or 'true' randomness exists, and, if so, can be proven to exist.

In practice of course we work with reducible or 'pseudo' randomness, deriving random values from complex deterministic systems, like a coin or roulette table.(I can't imagine randomness without something producing a random value)

My definition leaves no room for observer dependent randomness, like you seem to use in your example, because it excludes the existence of information from which the outcome can be known. I mentioned 2 as the minimum amount of values for randomness, because 1 value can of course always be predicted.
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Re: "Irreducible Randomness", what does that even mean?

Postby gill1109 » Sat Aug 31, 2019 10:51 pm

minkwe wrote:Really, you use the word repeatedly without knowing it's meaning?

viewtopic.php?f=6&t=399&p=9809&hilit=irreducible+randomness#p9809
viewtopic.php?f=6&t=318&p=9677&hilit=irreducible+randomness#p9672
viewtopic.php?f=6&t=318&p=9334&hilit=irreducible+randomness#p9330
viewtopic.php?f=6&t=318&p=9168&hilit=irreducible+randomness#p9168
viewtopic.php?f=6&t=318&p=9163&hilit=irreducible+randomness#p9163
viewtopic.php?f=6&t=377&p=9001&hilit=irreducible+randomness#p9001
viewtopic.php?f=6&t=377&p=8995&hilit=irreducible+randomness#p8995
viewtopic.php?f=6&t=70&p=3335&hilit=irreducible+randomness#p3335

http://arxiv.org/pdf/1207.5103.pdf (Page 3 & 4)
In this way, we can keep quantum mechanics, locality and freedom. This position does entail taking quantum randomness very seriously: it becomes an irreducible feature of the physical world, a “primitive notion”; it is not “merely” an emergent feature.
...
However, there is no such explanation for quantum randomness. Quantum randomness is intrinsic, nonclassical, irreducible


http://arxiv.org/pdf/math/0610115.pdf
According to Bell’s theorem, the randomness of quantum mechanics is truly ontological and not epistemological: it cannot be traced back to ignorance but is “for real.” It is curious that the quantum physics community is currently falling under the thrall of Bayesian ideas even though their science should be telling them that the probabilities are objective.


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

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.

I think that if we think carefully about it there are not many words we use which we can define. I can point to chairs, I can point to non-chairs. We can teach a deep neural network to reproduce most people's notion (most people within a given cultural group, excluding infants and advanced Alzheimer patients) of what is a chair and what isn't, in internet images. Some artists' impressions of chairs would be challenging, both to the neural network and to real people. Many artists are working very hard at the task of challenging concepts. Jokes have the same technique.

The notion of "chair" is not [at present] controversial. 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?

Bell's theorem challenges our very basic notions of randomness. That's why it is interesting. Quantum mechanics challenges our very basic notions of reality. That's why it is interesting. Recent political events in the world challenge our notions of democracy. Recent climate events challenge many basic notions. I'm fascinated by randomness and uncertainty and that is why I became a ... data scientist.
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Re: "Irreducible Randomness", what does that even mean?

Postby minkwe » Sun Sep 01, 2019 6:57 am

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

Postby minkwe » Sun Sep 01, 2019 7:24 am

ajw wrote:From my earlier posts it should be clear that I very much doubt whether irreducible or 'true' randomness exists, and, if so, can be proven to exist.

Okay.

In practice of course we work with reducible or 'pseudo' randomness, deriving random values from complex deterministic systems, like a coin or roulette table.(I can't imagine randomness without something producing a random value)

But by your definition, this is not randomness at all.

My definition leaves no room for observer dependent randomness,

Exactly, there is no room for "reducible randomness" in your definition. But you admit that you doubt the existence of "randomness" (your definition).

like you seem to use in your example, because it excludes the existence of information from which the outcome can be known.

Knowledge of the sequence is enough information to be able to predict the sequence. So in principle, there is information that will allow the sequence to be predicted. Whether that information can be obtained is a different question.
I mentioned 2 as the minimum amount of values for randomness, because 1 value can of course always be predicted.

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

Postby ajw » Sun Sep 01, 2019 9:06 am

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?
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