Is Randomness Real or Just Complex Predictability?

[Pythagorean]

It must be some counter-intuitive definition of randomness if my suggestion is not an example of a random event. I don't agree with it. It certainly does not just "appear to be random", thus confusing it with such things as pseudo-randomness which also appears to be random. At best it's bad wording.

The only thing that's truly random about your system (in terms of causality) would be that it's an inertially symmetric system, so it will land, with 1/6 probability, on any of the six sides.

the fact that somebody painted five sides blue and one side red doesn't change that, or change the fact that this is the underlying source of the randomness (the inertial symmetry of the die).

i.e. if you remove the underlying uniform distribution, the randomness will go away. The colors are irrelevant.

 

[Pythagorean]

supernatural vs. random discussion:

Evo:
Supernatural, I think (I hope) is not to be taken so literally. I can see the comparisons that Ivan and wulheron are drawing. I get it. But I don't think it's a complete match.

Ivan, wulheron:
quantum mechanics has examples of randomness. I wouldn't call them supernatural persay (though many physicists did seem to think it was eerie originally. Not so much today).

Atom decay is another random event (in a sample of decaying matter, any particular atom may spontaneously decay. The spatial probability distribution of which atom decays is uniform.

I wouldn't call this supernatural. It may just be fundamentally random.

 

[Evo]

Name one.

I'm carrying some dishes, one slips through my fingers and falls to the floor.

I'm not talking about systems. I'm talking about random events. Some people think that nothing can happen randomly, that everything that happens is predestined. This is the category, I believe, that wuliheron falls into. To him nothing can be random, therefore random is supernatural to him.

Below is in response to the OP.

Random, generally, can mean one of two things:
1)Unpredictable, from a given point of view.
2)Uncaused, by a previous event.

The first one is easy, random in this sense is just a description based on either a simple lack of knowledge or the impossiblity of having enough knowledge. The former being like predicting what your girlfriend will wear, whereas the latter is like predicting the weather.

The second refers to an actual event that has no preceding cause. Whether this can exist is an open question, and even if they do exist, it would be unlikely that one could distinguish it from something that is simply unpredictable.

 

[Pythagorean]

Evo, I think that example can be classically determined. It's not random, it's chaotic.

 

[wuliheron]

Where have you provided proof of this? Things can happen randomly while obeying all laws of nature. I understand if your belief is that nothing is random. But making such a claim needs backing up.

Something that is truly random, and not merely unpredictable, by definition does not follow any natural laws. To assert that something that does not have any rhyme or reason somehow follows natural law is, therefore, to utter a contradiction.

 

[apeiron]

This isn't a philosophical question, it is a scientific question and it really isn't all that difficult of a question.

Err, no one seems troubled by probablistic issues. It is the causal question that is of interest.

Rephrasing the OP: do uncaused events exist? Can something happen which had no preceding trigger?

Pythagorean suggested a way of making possible sense of this suggestion - imagining a state so pefectly poised, so symmetric, that it could break either way.

This is the old pencil balanced on its tip idea. However, a pencil would still seem to need a vibration, an unmeasured tilt, or some other triggering event to send it in some direction. A truly perfectly balanced pencil in isolation might never tip (unless we invoke QM?).

Another example given was atomistic decay. This is modeled as the probability of jumping a decay threshold - a series of fluctuations, one of which is large enough eventually. A poisson process. So is this a causeless event?

Putting mathematical models to one side, are there any convincing exampes of uncaused events, even with QM?

 

[wuliheron]

So you believe that you have a definition for what "random" actually means?

(So rigor definition, that it can be used to deal with these claims about randomness being supernatural.)

As I already stated, Words only have demonstrable meaning according to their function in a given context. The idea that anyone definition of "random" supersedes all others contradicts this observation. What I am asserting is that because the context is so broad when discussing the truly random (a metaphysical idea) its meaning becomes indistinguishable from the "supernatural".

 

[disregardthat]

The only thing that's truly random about your system (in terms of causality) would be that it's an inertially symmetric system, so it will land, with 1/6 probability, on any of the six sides.

the fact that somebody painted five sides blue and one side red doesn't change that, or change the fact that this is the underlying source of the randomness (the inertial symmetry of the die).

i.e. if you remove the underlying uniform distribution, the randomness will go away. The colors are irrelevant.

So, are you suggesting that behind every random process there is an underlying uniform distribution regardless of our ability to conceive of it?

 

[Pythagorean]

No. It's the most commonly used definition of random in the sciences when no qualification is used, as I quoted from Wolfram. The more general definition was in the first sentence of the quote, as I said when I quoted it.

 

[DrRocket]

So my definition is not completely off-base, but I think the first sentence is even more rigorous a definition.

The Wolfram definition is pretty much useless, and at best circular. It speaks of selecting a number "at random" from some "specified distribution" neatly sidestepping the basic question as to what is meant by "random" and how without such a definition there can be any meaning to a "specified distribution".

You are going n circles. You still lack any useful definition of "randomm". That is not likely to change.

 

[Evo]

What we need is to decide on a single definition of random and then argue from there. Several members have offered definitions to try to bring the thread to a point where everyone is on the same page.

Here are my 2 cents worth.

Random - Lack of predictability, without any systematic pattern.

http://www.vmlabs.com/stonline/press/news/glossary/r.htm

Random - Affected by chance

http://ec.wmich.edu/glossary/prog-glossary.htf#P-R

random (lacking any definite plan or order or purpose; governed by or depending on chance) "a random choice"; "bombs fell at random"; "random movements"

http://wordnetweb.princeton.edu/perl/webwn?s=random

Mine are simple definitions. But the Op did mention rolling dice.

 

[DrRocket]

What we need is to decide on a single definition of random and then argue from there. Several members have offered definitions to try to bring the thread to a point where everyone is on the same page.

Here are my 2 cents worth. http://www.vmlabs.com/stonline/press/news/glossary/r.htm

http://ec.wmich.edu/glossary/prog-glossary.htf#P-R

http://wordnetweb.princeton.edu/perl/webwn?s=random

The point is not that there are competing useful definitions of "random". The point is that no useful definition has ever been formulated.

Now, if people just want to argue, then go ahead ans select any combinatin of words that you choose. But if people want to apply the machinery of probability theory, then they either must accept that there is no applicable physical test to determine if that mathematical definition applies, or they will have to be the first person on the planet to formulate a useful definition and some associated test of its applicability.

The unfortunate truth is that "random" as the term is used in probablity theory, has no definition outside the artificial context of a probability space.

 

[wuliheron]

What we need is to decide on a single definition of random and then argue from there. Several members have offered definitions to try to bring the thread to a point where everyone is on the same page.

The original post asked the simple question of whether or not anything truly random exists and made a clear distinction between the truly random (ie-acausal) and the merely unpredictable. Thus the question involves more than one single definition of "random" and to constrain ourselves to just one would defeat the original purpose of the thread.

 

[apeiron]

What we need is to decide on a single definition of random and then argue from there. Several members have offered definitions to try to bring the thread to a point where everyone is on the same page.

The essential question is about causality - efficient cause to be precise. The classical idea that every event is preceded by a cause. Or in modern physics, the principle of locality.

And the question is not about our state of knowledge, our ability to measure, but about what is really happening objectively.

We seem to need some final irreducible element of randomness in the world. Spontaneity, fluctuations and chance are frequently invoked in physical processes, especially QM ones.

So can there be events that indeed do not have a local or efficient cause?

A novel philosophical way around this traditional question is to change the dichotomy from random~determined (or classically, chance~necessity) to freedom~constraints.

That is, to claim that locally, all is free. Anything could potentially happen. However, globally, there exists constraints. And so the freedom of every location is in practice constrained.

Bottom-up, you have pure spontaneity (what CS Peirce meant by tychism http://plato.stanford.edu/entries/peirce/#anti).

Then acting top-down, you have the shaping hand of constraints. This suppresses local degrees of freedom (and then what is not suppressed, must by definition, freely happen). Peirce called this second part of his doctrine of tychism, the law of habits.

This philosophical system looks like the traditional opposition of random and determined, but has obvious subtle differences. For one, it is clearly hierarchical (chance exists locally, the "determining factors" exist globally). And it lacks the absoluteness implied by determinism (locations are constrained rather than controlled). There is an essential grain of uncertainty in the ontology (as QM generally argues).

The importance of both constraints and scale is now being explicitly recognised in modern probablistic approaches to describing nature. For example, this was my favourite paper from last year.
http://arxiv.org/PS_cache/arxiv/pdf/0906/0906.3507v1.pdf

So the OP is both a deep question, and one that does have other ways of talking about it than the familiar dichotomy of random~determined.

 

[jostpuur]

wuliheron, I believe that you have a hidden assumption, which is that laws of nature are deterministic. When you use this assumption, you can arrive at the result true randomness is supernatural. IMO this is a reasonable deduction, but I see no reason to assume that the initial hidden assumption would be true.

 

[Pythagorean]

The point is not that there are competing useful definitions of "random". The point is that no useful definition has ever been formulated.

Now, if people just want to argue, then go ahead ans select any combinatin of words that you choose. But if people want to apply the machinery of probability theory, then they either must accept that there is no applicable physical test to determine if that mathematical definition applies, or they will have to be the first person on the planet to formulate a useful definition and some associated test of its applicability.

The unfortunate truth is that "random" as the term is used in probablity theory, has no definition outside the artificial context of a probability space.

If you're looking for a mathematical test to find out whether particular aspects of nature are fundamentally random, nobody's offering that. That's why this is is a philosophical discussion.

On the other hand, if we engage in the common and useful definition of randomness from probability theory (see wolfram), which already presupposes that we don't have an exhaustive sample space, then much of it is at the heart of scientific discovery.

For instance, in acoustics, white noise can be treated no differently than random numbers (i.e. we can easily simulate white noise with a evenly distributed random number generator). Now, we know that in the real world, the noise actually has a cause (probably several causes all mishmashed together) but for all practical purposes, we call it random, because entropy has so taken effect on the signal that it's practically impossible to find a cause, so it's equivalent from our perspective (in our scheme of big, correlated signals that stand out of the noise).

So there's a divide here where people that more often use statistics for scientific observation see randomness as a lack of information and the more philosophical thinkers see random as a question of causality. Or sometimes the divide exists within a single person, which I think is sometimes my case.

I'm still not sure which kind of random you're talking about, really. You've preferred to safely criticize rather than boldly assert so far.

 

[DrRocket]

If you're looking for a mathematical test to find out whether a particular aspects of nature or fundamentally random, nobody's offering that. That's why this is is a philosophical discussion. Or sometimes the divide exists within a single person, which I think is sometimes my case.

On the other hand, if we engage in the common and useful definition of randomness from probability theory, which already presupposes that we don't have an exhaustive sample space, then much of it is at the heart of scientific discovery.

For instance, in acoustics, white noise can be treated no differently than random numbers (i.e. we can easily simulate white noise with a evenly distributed random number generator). Now, we know that in the real world, the noise actually has a cause (probably several causes all mishmashed together) but for all practical purposes, we call it random, because entropy has so taken effect on the signal that it's practically impossible to find a cause, so it's equivalent from our perspective (in our scheme of big, correlated signals that stand out of the noise).

So there's a divide here where people that more often use statistics for scientific observation see randomness as a lack of information and the more philosophical thinkers see random as a question of causality.

Nonsense.

There is a perfectly valid mathematical definition for a white noise stochastic process, and it has nothing to do with acoustics, nor does the usual scientific definition of "white noise". It is in fact a type of random process, which is considerably more general than just "random numbers". See, for instance, the classic text by Doob or any electrical engineering text on communication systems and information theory.

There are also physical models for what is called "white noise" in scientific and engineering circles, and it most certainly has an identifiable cause. Most often that cause is thermal noise, sometimes called "shot noise" in electronic devices. This is a phenomena that is understood in terms of solid state physics.

Causality and randomness do not appear to be linked in physics either. One need only consider quantum mechanics. Quantum theory is a fundamentally stochastic theory, But it does not eschew causes entirely either, and one finds that the state function evolves in a completely deterministic fashion -- that is the role of the Schrodinger equation in elementary quantum mechanics.

The definition of randomness from probability theory, (see earlier posts for the definition of a random variable) has nothing whatever to do with an "exhaustive probability space", which is actually a meaningless term.

If you just want to throw around words then feel free to do so, but don't try to attach any meaning to them from the mathematical theory of probability.

The usual application of probability and statistics in science, as opposed to in mathematics, is as a model that compensates for lack of information, as in a description of a roulette wheel as a probability model because solving the equations of Newtonian mechanics is both too difficult and too sensitive to initial conditions that are too difficult to determine. So the ad hoc probabilistic model works in practice, despite the fact that the physics is basically deterministic. While this sort of technique works quite well in practice (that is why Las Vegas casinos make money reliably), it has nothing to do with the question posed in the OP. The macroscopic world seems to be well-described by deterministic theories, and the transition from the stochatic to the deterministic remains something that has not yet been described fully in physical theory -- see attempts made under the heading of "decoherence" and "collapse of the wave function".

The only truly stochastic physical processes of which I am aware, and that are supported by experimental data, are those of quantum mechanics at the sub-atomic level. The empirical data seems to support the tenet of quantum mechanics that it is only able to predict probabilities. There are, however, some rather serious physicists, Gerardus 'tHooft among them, who are seriously investigating deterministic theories that might mimic what we see in quantum mechanics.

So, basically your facts are at best questionable. If you simply want to "philosophize" without contact with either mathematics or physics, then you can certainly do that. But that produces only "white noise".

The problem remains one of attempting to determine if there is anything that is "truly random" while being unable to define what is meant by "truly random". If that is a meaningful philosophical discussion, then by all means go to it. I prefer to discuss the existence of something only aftere I can define what that thing is sufficiently well to be able to recognize it if it presents itself.

 

[unusualname]

a truly random event is one that has no cause.

There's no way we have of knowing if random events exist.

If they exist then free-will is enabled as long as we have the ability to influence the random events, eg if our consciousness allows us to select quantum states then, bingo! we have free-will.

 

[wuliheron]

wuliheron, I believe that you have a hidden assumption, which is that laws of nature are deterministic. When you use this assumption, you can arrive at the result true randomness is supernatural. IMO this is a reasonable deduction, but I see no reason to assume that the initial hidden assumption would be true.

We can debate metaphysics until the crows fly home, so I choose not to make assumptions about ultimate reality. It is the demonstrable meaning of words that I contest. To say that a "law" is somehow utterly "random" is a contradiction in terms. Thus it is not any metaphysical reality that I question, but the use of contradictory terminology. If we are to speak meaningfully about metaphysical issues then our words must have demonstrable meaning or we might as well spout nonsense poetry.

 

[Pythagorean]

Nonsense.

There is a perfectly valid mathematical definition for a white noise stochastic process, and it has nothing to do with acoustics, nor does the usual scientific definition of "white noise". It is in fact a type of random process, which is considerably more general than just "random numbers". See, for instance, the classic text by Doob or any electrical engineering text on communication systems and information theory.

There are also physical models for what is called "white noise" in scientific and engineering circles, and it most certainly has an identifiable cause. Most often that cause is thermal noise, sometimes called "shot noise" in electronic devices. This is a phenomena that is understood in terms of solid state physics.

Causality and randomness do not appear to be linked in physics either. One need only consider quantum mechanics. Quantum theory is a fundamentally stochastic theory, But it does not eschew causes entirely either, and one finds that the state function evolves in a completely deterministic fashion -- that is the role of the Schrodinger equation in elementary quantum mechanics.

The definition of randomness from probability theory, (see earlier posts for the definition of a random variable) has nothing whatever to do with an "exhaustive probability space", which is actually a meaningless term.

If you just want to throw around words then feel free to do so, but don't try to attach any meaning to them from the mathematical theory of probability.

The usual application of probability and statistics in science, as opposed to in mathematics, is as a model that compensates for lack of information, as in a description of a roulette wheel as a probability model because solving the equations of Newtonian mechanics is both too difficult and too sensitive to initial conditions that are too difficult to determine. So the ad hoc probabilistic model works in practice, despite the fact that the physics is basically deterministic. While this sort of technique works quite well in practice (that is why Las Vegas casinos make money reliably), it has nothing to do with the question posed in the OP. The macroscopic world seems to be well-described by deterministic theories, and the transition from the stochatic to the deterministic remains something that has not yet been described fully in physical theory -- see attempts made under the heading of "decoherence" and "collapse of the wave function".

The only truly stochastic physical processes of which I am aware, and that are supported by experimental data, are those of quantum mechanics at the sub-atomic level. The empirical data seems to support the tenet of quantum mechanics that it is only able to predict probabilities. There are, however, some rather serious physicists, Gerardus 'tHooft among them, who are seriously investigating deterministic theories that might mimic what we see in quantum mechanics.

So, basically your facts are at best questionable. If you simply want to "philosophize" without contact with either mathematics or physics, then you can certainly do that. But that produces only "white noise".

The problem remains one of attempting to determine if there is anything that is "truly random" while being unable to define what is meant by "truly random". If that is a meaningful philosophical discussion, then by all means go to it. I prefer to discuss the existence of something only aftere I can define what that thing is sufficiently well to be able to recognize it if it presents itself.

Well, this is frustrating. You've basically repeated many of the posts I've already made in this thread as if they were counterarguments.

I've done research in acoustics, and currently do research in chaos theory (i.e. nonlinear dynamics). I've also taken a full degrees worth of physics classes and some probability theory for my master's study. I said exhaustive sample space, not probability space. If you still don't know what I mean, and refuse to look in your texts on probability, I can break it down for you, but I'm hoping you were replying with animosity, thinking I was an ignorant armchair philosopher and didn't really consider what I may have meant at the moment.

In acoustic (experimental acoustics if that clears things up.. we're actually looking at real data) the word random has a statistical basis. The definition is based on a lack of information. When I used "white noise" I obviously meant the acoustics definition, which is physically defined: it has a flat power spectral density. That's not the point though. The point is that I can use a random number generator to simulate the white noise. I was demonstrating the usefulness of a definition of random in probability theory as it applies to science. This is just one example.

Consider biological sciences, who select samples "randomly" (i.e not biased).

In chaos theory, on the other hand, the discussion tends to be more philosophical. The point being that seemingly random events do actually have a cause and that apparent randomness can be traced back to a sensitivity to initial conditions. This definition of randomness is about causation. It's not an assertion as to whether all events can be random or not, it's the study of particular events that seem random, but aren't (and the study of determining whether certain events truly are random or are not).

In quantum mechanics, there are only the applications of probability theory, and whether or not it's causally linked is still a matter of debate. I like how you put it:

But it does not eschew causes entirely either, and one finds that the state function evolves in a completely deterministic fashion -- that is the role of the Schrodinger equation in elementary quantum mechanics.

Of course, I think it's somewhat cavalier to talk about causation and randomness in quantum mechanics without talking about quantum field theory, which I'm guess none of us are well versed in. I've only made it through Intro to Quantum by Griffiths. Not interested in QFT, personally.

Anyway, back to my point, which you eagerly missed. The statistical/probability definitions of random are useful to us in the sciences and are weakly connected to causation, as long as we acknowledge that our sample space is limited (i.e. not exhaustive).

A concrete example to help you with the assertion:

When I try to change the environment in different ways to produce different outputs on the microphones in my acoustic array, I can't possibly find (or practically setup) every possible combination of inputs. Everything I can possibly do has no affect on the noise. The noise remains. I don't say "eureka!" the noise is random (uncaused)! I say, "well, within the sample size I was able to attain, I can't find any causes of the noise".

If we can find a cause for something, we model it based on its dependent variables (the cause) and we no longer have a need for random data generation. That's how it's connected to causation. But this definition (lack of information) is not based on causation.

Which becomes confusing in discussions, since there is also the qualitative definition of randomness that pertains to actual causation, regardless of information. But notice, that if a system is truly random in this way, then it is also a matter of a lack of information. There's no information to be had about causation. Just the observation, statistically recorded (i.e. bose-einstein statistics and fermi-dirac statistics). i.e. Quantum Mechanics.

 

[DrRocket]

Well, this is frustrating. You've basically repeated many of the posts I've already made in this thread as if they were counterarguments.

I've done research in acoustics, and currently do research in chaos theory (i.e. nonlinear dynamics). I've also taken a full degrees worth of physics classes and some probability theory for my master's study. I said exhaustive sample space, not probability space. If you still don't know what I mean, and refuse to look in your texts on probability, I can break it down for you, but I'm hoping you were replying with animosity, thinking I was an ignorant armchair philosopher and didn't really consider what I may have meant at the moment.

I understand probability theory pretty well and it is quite frankly you who do not know what you mean. Trying to somehow appeal to authority with veiled references to unspecified degrees is not going to work. I will see all of your degrees and raise you a couple. Degree comparisons are not germane in any case. Let's stick to content.

Go ahead and break it down if you like. This should be interesting.

No animosity involved. As to anything else, I will simply form my opinion based on the content of our posts, or lack thereof.

In acoustic (experimental acoustics if that clears things up.. we're actually looking at real data) the word random has a statistical basis. The definition is based on a lack of information. When I used "white noise" I obviously meant the acoustics definition, which is physically defined: it has a flat power spectral density. That's not the point though. The point is that I can use a random number generator to simulate the white noise. I was demonstrating the usefulness of a definition of random in probability theory as it applies to science. This is just one example.

The definition in terms of a flat power spectral density it NOT physically defined, but rather mathematically defined -- via the statement that the power spectral density is constant. That is a statement about Fourier transforms. It is not physical, and in fact is not physically possible. It is an idealization that makes for simplicity in some calculations.

Just precisely how are you "demonstrating the usefulness of a definion of random in probability theory"? Remember that a random variable is nothing more and nothing less than a function that is measurable in terms of the sigma algebra of your probability space -- fpr the function to be measureable the inverse image of an open set must be a member of the sigma algebra (aka a measurable set). So, just how have you demonstrated the usefulness of this concept ?

In chaos theory, on the other hand, the discussion tends to be more philosophical. The point being that seemingly random events do actually have a cause and that apparent randomness can be traced back to a sensitivity to initial conditions. This definition of randomness is about causation. It's not an assertion as to whether all events can be random or not, it's the study of particular events that seem random, but aren't (and the study of determining whether certain events truly are random or are not).

Chaos theory has NOTHING to do with random processes. In fact, what are normally called chaotic systems are in fact completely deterministic -- as reflected in the sensitivity to initial conditions in some cases. Moreover, there are all sorts of things going under the title of "chaos theory" some not worthy of the name "theory" at all. For a good, rigorous discussion, in the context of topological dynamics one might refer to Bob Devaney's book An Introduction to Chaotic Dynamical Systems, but it is rather tangential to the discussion at hand. In fact I have no idea why you bring up this red herring.

What is heavens name is "the study of particular events that seem random, but aren't" ? Have you ever read a book on topological dynamics, or maybe ergodic theory ? You are spouting nonsense.

Try Devaney's book.

Of course, I think it's somewhat cavalier to talk about causation and randomness in quantum mechanics without talking about quantum field theory, which I'm guess none of us are well versed in.

Speak for yourself. If you want to bring in quantum field theories go right ahead. But it adds nothing to the discussion, save to eliminate direct reference to the Schrodinger equation.

There is and was nothing cavalier about the reference at all. It is quite germane.

Anyway, back to my point, which you eagerly missed. The statistical/probability definitions of random are useful to us in the sciences and are weakly connected to causation, as long as we acknowledge that our sample space is limited (i.e. not exhaustive).

I did not "eagerly miss" anything. What is your point ? This makes no sense. I suggest that you go back and review your own probability books, and in particular the definition of "sample space" and "probability space". Try Probabilty by Loeve, which is the classic text or Stochatic Processes by Doob.

A concrete example to help you with the assertion:

When I try to change the environment in different ways to produce different outputs on the microphones in my acoustic array, I can't possibly find (or practically setup) every possible combination of inputs. Everything I can possibly do has no affect on the noise. The noise remains. I don't say "eureka!" the noise is random (uncaused)! I say, "well, within the sample size I was able to attain, I can't find any causes of the noise".

Which has nothing to do with random processes. Your inability to adequately set up and shield your electronics from outside electromagnetic fields or from outside acoustic signals, or both, has nothing to do with causality. It may have something with your personal inability to locate the source of the noise, but that is completely unrelated to the question of whether a cause of the noise exists.

"Random" and "uncaused" are not the same thing. Shot noise and ordinary electromagnetic interference are caused. In fact one of the sources of noise in electronic systems is the cosmic background radiation, the discovery of which earned Wilson and Penzias a Nobel prize. I would not call that uncaused (see "Big Bang"). I think many would characterize it as random in some sense -- it matches blackbody radiation, which as a quantum effect can reasonably be called random.

You seem to have somehow confused an inability to locate a source with some unstated question involving random processes. Perhaps what we have here is some sort of random thought.

If we can find a cause for something, we model it based on its dependent variables (the cause) and we no longer have a need for random data generation. That's how it's connected to causation. But this definition (lack of information) is not based on causation.

It is quite possible to know the cause of something ans still not have at hand a "model based on its dependent variables". That is precisely the situation with "white noise" or "shot noise" in communication theory. It would also apply to black body radiation, wherein one can predict the spectrum but not every bump and wiggle in the received signal.

Which becomes confusing in discussions, since there is also the qualitative definition of randomness that pertains to actual causation, regardless of information. But notice, that if a system is truly random in this way, then it is also a matter of a lack of information. There's no information to be had about causation. Just the observation, statistically recorded (i.e. bose-einstein statistics and fermi-dirac statistics). i.e. Quantum Mechanics.

All you have demonstrated here is that you don't understand quantum mechanics, whether that be ordinary quantum mechanics or quantum field theories. This is just meaningless juxtaposition of words.

This is getting silly. I'm done.

 

[Pythagorean]

you would prefer specified degrees? A Bachelor's of Science in Physics at a state university in the U.S. The point wasn't an argument from authority, the point was to give you more context. I hoped you'd be able to see the argument yourself once.

exhaustive sample space:

a sample space that includes all possible outcomes. In the sciences, we work with sample spaces that we assume are not exhaustive (i.e. we assume we haven't observed all possible outcomes).

Which has nothing to do with random processes. Your inability to adequately set up and shield your electronics from outside electromagnetic fields or from outside acoustic signals, or both, has nothing to do with causality. It may have something with your personal inability to locate the source of the noise, but that is completely unrelated to the question of whether a cause of the noise exists.

"Random" and "uncaused" are not the same thing. Shot noise and ordinary electromagnetic interference are caused. In fact one of the sources of noise in electronic systems is the cosmic background radiation, the discovery of which earned Wilson and Penzias a Nobel prize. I would not call that uncaused (see "Big Bang"). I think many would characterize it as random in some sense -- it matches blackbody radiation, which as a quantum effect can reasonably be called random.

You seem to have somehow confused an inability to locate a source with some unstated question involving random processes. Perhaps what we have here is some sort of random thought.

But this is the distinction I'm trying to make! There are two different random's being discussed here. One pertaining to causation and one pertaining to lack of information.

I can tell you right now, that nobody is really interested in the discussion about lack of information. Most people in the philosophy forums are interested in the discussion about causation.

Notice also, that I'm moving fluidly between definitions, which may cause some confusion, but I'm also trying to let you know which I'm using with parentheses. So when I say chaotic (uncaused), that's the definition I'm using.

The definition in terms of a flat power spectral density it NOT physically defined, but rather mathematically defined -- via the statement that the power spectral density is constant. That is a statement about Fourier transforms. It is not physical, and in fact is not physically possible. It is an idealization that makes for simplicity in some calculations.

This is a physical statement too, about pressure fluctuations, or electromagnetic fluctuations, or anything that oscillates over a broad spectrum of frequencies. Nobody's arguing that such a signal physically exists, that's a pretty pedantic argument. We know that our models are not reality. The map is not the territory, etc, etc... no kidding. You're completely missing the point still to go off on a tangent.

Chaos theory has NOTHING to do with random processes. In fact, what are normally called chaotic systems are in fact completely deterministic -- as reflected in the sensitivity to initial conditions in some cases. Moreover, there are all sorts of things going under the title of "chaos theory" some not worthy of the name "theory" at all. For a good, rigorous discussion, in the context of topological dynamics one might refer to Bob Devaney's book An Introduction to Chaotic Dynamical Systems, but it is rather tangential to the discussion at hand. In fact I have no idea why you bring up this red herring.

What is heavens name is "the study of particular events that seem random, but aren't" ? Have you ever read a book on topological dynamics, or maybe ergodic theory ? You are spouting nonsense.

Try Devaney's book.

Ok, once again, you've reworded what I said and repeated it as if it were a counterargument. I'm glad we agree?

You don't appreciate the philosophical aspects of this discussion, I get it. The point about chaos and causality is about the history of the philosophical discussion of determinism. Chaos theory is something determinists can draw on in arguments against anti-determinists when anti-determinists bring up apparently random (lacking causation) systems.

If we can reproduce the seemingly random (uncaused) behavior with deterministic models, then we have proven that the system isn't random (uncaused).

For instance, I'm working on the Morris Lecar model right now. Recently, Tateno (I believe, I'm out of town so I don't have publication access) wrote a paper for Chaos in which he just added a random noise term to the equation and bam! he got temporal chaos (surprise, surprise...)

So now, some philosophers are using this to say "oh look, consciousness requires noise, it's a stochastic process, the mind can't be determined, dualism, yay!"

I'm looking to produce chaos directly from the model, not by adding random noise, but by finding the parameter regime in which it actually exists in the model. I.e. I'm looking to find physiological causes for the behavior of the neuron that can be measured and verified. Tateno adding random noise to the model doesn't help us understand the causation of the behavior.

It is quite possible to know the cause of something ans still not have at hand a "model based on its dependent variables". That is precisely the situation with "white noise" or "shot noise" in communication theory. It would also apply to black body radiation, wherein one can predict the spectrum but not every bump and wiggle in the received signal.

Yeah, I said that... about "white noise" in fact! You must be fundamentally missing something I'm saying to repeat what I say so much.

 

[russ_watters]

By definition, events in a truly random system could not be predicted; they defy description, so truly random systems would qualify as being supernatural...

[separate post]

Name one.

Every measurement has a random component to it. But the easiest to use to generate a random number is probably radioactive decay.

 

[russ_watters]

Since I believe that anything real can ultimately be described by science, I maintain that the word supernatural has no meaning. It is an arbitrary concept used to dismiss concepts subjectively defined not to be real.

Ivan, as you worded that, it's just gibberish. Whether a concept can be described by science doesn't have anything to do with whether a word has a definition - heck, you should already know that as you provided the definition of the word!

Perhaps you could try that again...


...Either way, though, your basic point in providing the definition was that "supernatural" just means 'unexplainable by science'. That's a perfectly fine definition and by that definition, random/probability based processes such as radioactive decay are clearly, dealt with adequately within the realm of science.

 

[russ_watters]

Note again, what's being descirbed in this thread is just relatively simple misunderstandings about how the universe operates and what the implications of randomness are. Again, this link deals with the misunderstandings people are having here completely: http://www.random.org/randomness/

 

[Pythagorean]

But we should get back to our main point anyway.
I missed this post of yours, which goes to the heart of it.

The Wolfram definition is pretty much useless, and at best circular. It speaks of selecting a number "at random" from some "specified distribution" neatly sidestepping the basic question as to what is meant by "random" and how without such a definition there can be any meaning to a "specified distribution".

You are going n circles. You still lack any useful definition of "randomm". That is not likely to change.

The wolfram definition again:

A random number is a number chosen as if by chance from some specified distribution such that selection of a large set of these numbers reproduces the underlying distribution. Almost always, such numbers are also required to be independent, so that there are no correlations between successive numbers.

forgiving you for misquoting the wolfram quote, "as if by chance" means with no apriori knowledge this is a statement about lack of information.

but you completely ignored the important part:

"specified distribution such that selection of a large set of these numbers reproduces the underlying distribution"

Which should make it obvious why a uniform distribution is the first thing that comes to mind, and is an obvious, intuitive example.

This is a useful definition for physics. In acoustics, it's because this is equivalent to white noise, which is physically meaningful to us.

I went off on a tangent about how this is related to causality. This was probably largely irrelevant to you, but causality is the direction the thread is going. If we really want to 1-on-1 about mathematical definitions, nobody would be missing anything if went to PM's (which we probably don't care to do).

In quantum mechanics, we can't explain causation intuitively. Our language is inherently probabilistic (i.e. fermi-dirac and boise-einstein statistics are the experiments that "explain" the behavior of fermions and bosons). What did you do, namedrop the Schrodinger Equation? No, I don't understand causation in quantum mechanics. It's explanation isn't a mechanistic picture like Newtonian mechanics, it's probability statements.

I suspect that QFT does a lot to explain the mechanisms behind the fermi-dirac and boise-einstein statistics, but I'm on the outside looking in, really.

 

[Pythagorean]

from Russ's link:

Quantum Events or Chaotic Systems?

One characteristic that builders of TRNGs sometimes discuss is whether the physical phenomenon used is a quantum phenomenon or a phenomenon with chaotic behaviour. There is some disagreement about whether quantum phenomena are better or not, and oddly enough it all comes down to our beliefs about how the universe works. The key question is whether the universe is deterministic or not, i.e., whether everything that happens is essentially predetermined since the Big Bang. Determinism is a difficult subject that has been the subject of quite a lot of philosophical inquiry, and the problem is far from as clear cut as you might think. I will try and explain it here, but would also like to point out that Wikipedia has a concise account of the debate.

Quantum mechanics is a branch of theoretical physics that describes the universe at the atomic and subatomic levels. Random number generators based on quantum physics use the fact that subatomic particles appear to behave randomly in certain circumstances. There appears to be nothing we know of that causes these events, and they are therefore believed by many to be nondeterministic.

In comparison, chaotic systems are those in which tiny changes in the initial conditions can result in dramatic changes of the overall behaviour of the system. Weather systems are a good example of this, and you may have heard of the butterfly effect, a thought experiment in which a butterfly beating its wings in Brazil is able to affect the winds subtly but critically, just enough to cause a tornado in Texas.

Proponents of random number generators of the quantum variety argue that quantum physics is inherently nondeterministic, whereas systems governed by physics are essentially deterministic. I am personally undecided as to where I stand on the determinism-nondeterminism scale, but for the sake of argument, I will put on my determinist hat and use RANDOM.ORG as an example. You could argue that the atmospheric noise used as a source for the RANDOM.ORG numbers can be viewed as a chaotic but deterministic system. Hence, if you knew enough about the processes that cause atmospheric noise (e.g., thunderstorms) you could potentially predict the numbers generated by RANDOM.ORG.

However, to do this, you would probably need knowledge of the position and velocity of every single molecule in the planet's weather systems. This is of course infeasible, and the inaccuracy of weather forecasts is a good example of how difficult it is to give even a rough estimate of the behaviour of weather systems. For this reason, it is impractical to predict random numbers from RANDOM.ORG, even for a determinist. A similar case (on a different scale) could be made for random number generators based on lava lamps.

Now, you may think that since there's dispute about the suitability of chaotic phenomena for generating randomness, then why not just stick with quantum physics? That would seem to be the safe bet. However, quantum generators aren't safe from critique either. Hard determinists will dispute that subatomic particle behaviour is really random and instead claim that the way they behave is exactly as predetermined as everything else in the universe has been since the Big Bang. The reason we think these specific particles behave randomly is simply that no human measurement has been able to account for their behaviour. In this view, subatomic events do indeed have a prior cause, but we just don't understand it (yet), and the events therefore seem random to us. To a hard determinist, quantum physics is exactly as suited for random number generation as is atmospheric noise or lava lamps.

This is only one possible argument, and there are many others. When it comes down to it, I think the most meaningful definition of randomness is that which cannot be predicted by humans. Whether randomness originates from unpredictable weather systems, lava lamps or subatomic particle events is largely academic. While quantum random number generators can certainly generate true random numbers, it seems to me that they for all intents and purposes are equivalent to approaches based on complex dynamical systems.

Here you can see the link between randomness and causation more clearly, I hope.

 

[apeiron]

Again, this link deals with the misunderstandings people are having here completely: http://www.random.org/randomness/

Yeah that link really clears things up

Proponents of random number generators of the quantum variety argue that quantum physics is inherently nondeterministic, whereas systems governed by physics are essentially deterministic. I am personally undecided as to where I stand on the determinism-nondeterminism scale, but for the sake of argument, I will put on my determinist hat and use RANDOM.ORG as an example...

Hard determinists will dispute that subatomic particle behaviour is really random and instead claim that the way they behave is exactly as predetermined as everything else in the universe has been since the Big Bang. The reason we think these specific particles behave randomly is simply that no human measurement has been able to account for their behaviour. In this view, subatomic events do indeed have a prior cause, but we just don't understand it (yet), and the events therefore seem random to us. To a hard determinist, quantum physics is exactly as suited for random number generation as is atmospheric noise or lava lamps. This is only one possible argument, and there are many others...

Well which is then? Does QM argue for ontic randomness - as in uncaused events - or merely epistemic? Are you a hard determinist, or in some other camp as apparently there are many others?

 

[Pythagorean]

Yeah that link really clears things up

Well which is then? Does QM argue for ontic randomness - as in uncaused events - or merely epistemic? Are you a hard determinist, or in some other camp as apparently there are many others?

I believe it's a matter of your interpretation of QM (QM being the observation). My assumption is that most quantum physicists are determinists.

 

[russ_watters]

I believe it's a matter of your interpretation of QM (QM being the observation). My assumption is that most quantum physicists are determinists.

Really? It seems clear to me that someone who accepts QM must not be a determinist!

 

[Pythagorean]

Well, my sample size is small, but my QM professor taught it as a determinist.

 

[Fuzzystuff]

I still don't think we could account for everything and measure something so precisely, so perfectly, that mother nature reveals all of her secrets to us. The ones that appear to our observations and measurements, the unknown, and to give it all cause. Top-down or Bottom-up.

 

[russ_watters]

Yeah that link really clears things up

What that link best makes clear is the proper framing of the question. There are still matters of opinion in there, but it clearly explains the positions and the definitions. That's the main purpose of the link.

Well which is then? Does QM argue for ontic randomness - as in uncaused events - or merely epistemic? Are you a hard determinist, or in some other camp as apparently there are many others?

I wouldn't call a nuclear decay an "uncaused event". What it is is an event who'se exact timing cannot be determined: it is random/non-deterministic and governed by probability.

I would have thought it was clear from my other posts that I see physics - particularly QM - as being absolutely positively non-deterministic. The only way to be a scientist and be deterministic is to believe there is another yet-to-be-discovered theory/law governing these events that currently appear random. That seems unlikely.

 

[russ_watters]

Well, my sample size is small, but my QM professor taught it as a determinist.

That seems very odd to me: how did he reconcile the HUP with determinism?

 

[russ_watters]

From the wiki on QM:

The Copenhagen interpretation, due largely to the Danish theoretical physicist Niels Bohr, is the interpretation of quantum mechanical formalism most widely accepted amongst physicists. According to it, the probabilistic nature of quantum mechanics is not a temporary feature which will eventually be replaced by a deterministic theory, but instead must be considered to be a final renunciation of the classical ideal of causality.

That makes it pretty clear that most physicist studying QM consider QM - and the universe - to be non-deterministic.

 

[Pythagorean]

It was a she. SelfAdjoint (R.I.P.) was apparently a determinist too:

https://www.physicsforums.com/showthread.php?t=127525

Anyway the point is not that there is no cause, but that we can never know what the cause was (which is where the probability comes in).

I don't think QM unseats determinism. It's a statement about what we can know, fundamentally, no matter how good technology gets. One could follow form that that the universe is undeterministic, but it's an extra step (and not a large one).

 

[russ_watters]

It was a she. SelfAdjoint (R.I.P.) was apparently a determinist too:

https://www.physicsforums.com/showthread.php?t=127525

It isn't clear to me that SA is actually saying there that he's a determinist.

Anyway the point is not that there is no cause, but that we can never know what the cause was (which is where the probability comes in).

Why can't we know the cause? Aren't we smart enough?

I don't think QM unseats determinism. It's a statement about what we can know, fundamentally, no matter how good technology gets. One could follow form that that the universe is undeterministic, but it's an extra step (and not a large one).

So... you're saying that there's a deterministic law of physics that we can never know? Why? It doesn't make a whole lot of sense to me.

Further, why bother with making the distinction? If it is fundamentally impossible to know the answer to a question, then how is that functionally different from the answer not existing? That seems like a pure religious belief to me.

 

[russ_watters]

It isn't clear to me that SA is actually saying there that he's a determinist.

Ok, I found a better quote:

My point was that if you assume the UP is epistemic, i.e "We can't observe the particle perfectly because our observation disturbs it", this ignores the possibility that we could, perhaps using entanglement as Einstein, Posolski, and Rosen suggested, observe it without disturbing it.

He's saying that the HUP is a technological limitation, not actually a fundamental principle. I would argue that that is neither the intent of the HUP nor the prevailing view (as per the quote above). It's basically a religious belief.

 

[Pythagorean]

It isn't clear to me that SA is actually saying there that he's a determinist.
Why can't we know the cause? Aren't we smart enough?
So... you're saying that there's a deterministic law of physics that we can never know? Why? It doesn't make a whole lot of sense to me.

Further, why bother with making the distinction? If it is fundamentally impossible to know the answer to a question, then how is that functionally different from the answer not existing? That seems like a pure religious belief to me.

sA pointed to causality and indicated that QM does not lack causation, but that we can't determine the source of causation. This is the heart of the discussion, no? Determinism relies on causation.

And no, I'm not saying there's deterministic law of physics we can never know, the CI interpretation of QM says that.

I think a new framework will eventually be developed, that, just like QM did with CM, will match QM in the limit, and we'll go "oohhhh!"

 

[russ_watters]

So basically, it comes down to accepting/believing one of the following two ideas:

1. Current scientific theory incorporates non-deterministic/random/probabilistic concepts. IOW, randomness exists and is adequately dealt with in scientific theory. This theory has so far been spectacularly successful in making accurate predictions.

2. There are other laws (currently unknown) governing the universe that explain events that currently appear to be random. If we can find these, we'll have a deterministic explanation for how the universe works. If these laws are inherrently unfindable, then this view is functionally equvalent to #1 and believing it without evidence therefore is a religious viewpoint, not a scientific one.

"Supernatural" is unnecessary for either of these ideas.

If #1 is correct - and again, all available theory and evidence says it is - then "random" is real. If #2 is correct, then nothing really is random - it just appears random because we don't know what's going on behind the clock face.

 

[Pythagorean]

Ok, I found a better quote: He's saying that the HUP is a technological limitation, not actually a fundamental principle. I would argue that that is neither the intent of the HUP nor the prevailing view (as per the quote above). It's basically a religious belief.

I agree with you, here.

And, btw, my mind isn't made up about determinism in QM. But QM would be useless if it wasn't deterministic wouldn't it? I mean, that's the point of theories. You have some chain of causality that explains a phenomena, then you can exploit that chain of causality and manipulate the system. How would we be able to make use of QM if it wasn't deterministic? If there's no chain of causality, what's the point? It may as well be a random number generator you're playing with.

 

[DrRocket]

Note again, what's being descirbed in this thread is just relatively simple misunderstandings about how the universe operates and what the implications of randomness are. Again, this link deals with the misunderstandings people are having here completely: http://www.random.org/randomness/

Not only does that link not deal with the misunderstandings "completely" it simply reiterates the misunderstandings themselves -- in short the author offers no understanding but only a boat load of platitudes, culminating in no useful definition of "random" whatever.

That is not particularly surprising since no one else on this planet has formulated a satisfactory physical definition of "random" either. Thus you are stuck with either the everyday definition which is neither testable nor scientifically useful or else you are stuck with the mathematical treatment which also is not testable.

What the mathematical treatment does offer is a rather detailed theory of probability and stochastic processes, suitable for use in physical models. However, the connection between the models and the physical processes being described lies solely in the apparent empirical connection between predictions and observations. Again this is not surprising as the connection between mathematics and physics of necessity lies solely in the empirical evidence. There is no particular reason why mathematics should be as effective as it apparently is -- see Eugen Wigner's essay "The Unreasonable Success of Mathematics in the Natural Sciences."

There is no misunderstanding as to how the universe operates, although there is the possibility of ignorance. So far as anyone knows, the physical processes of the universe, other than those concerning gravity, are governed by one or another quantum field theory and those theories are inherently stochastic. So, insofar as our current understanding of
physics goes, the universe is indeed governed by probabilistic laws. However, and the mechanism behind this is not fully understood, at the macroscopic level the stochastic laws of quantum theory give way to predictions that are apparently deterministic. This may well be due to the law of large numbers, but again the research in this area is incomplete -- if you like "Google" the subjects of "quantum decoherence" or "collapse of the wave function".

The author of your link gives a rather superficial treatment of the relationship between quantum theory, probability, and macroscopic phenomena. But the bottom line is that, according to the best available theory, radioactive decay is actually a stochastic process. Thus his counter-arguments to the efficacy of radioactive decay as a means of generation of random numbers relies on decidedly speculative physical theories. Those specualtions may or may not eventually prove valid, but at this juncture there is not the slightest experimental evidence for them.

Of course you can always take the philosophical approach, ignore the science and mathematics, and just talk. That seems to be what is going on here.

 

[apeiron]

I wouldn't call a nuclear decay an "uncaused event". What it is is an event who'se exact timing cannot be determined: it is random/non-deterministic and governed by probability.

I would have thought it was clear from my other posts that I see physics - particularly QM - as being absolutely positively non-deterministic. The only way to be a scientist and be deterministic is to believe there is another yet-to-be-discovered theory/law governing these events that currently appear random. That seems unlikely.

If a decay is not uncaused, then does that mean you believe it is caused?

Your wording is very unclear here as you make an ontic statement, then qualify it with epistemological facts (an observer lacks the necessary information, must rely on probablistic modelling, etc).

And if you really believe in ontic randomness, then surely this in turn does justify deeper enquiry into our deterministic conception of physical law, which you seem to agree is the basis of standard science.

My argument here has been 1) QM is hard evidence for something like ontic randomness, 2) to then say nothing further leaves the door open to woo-woo talk about supernatural causation, 3) we can in fact look to other models of causality which reframe both determinism and randomness as global constraint and local spontaneity.

And I have seen no arguments yet against a Peircean approach.

 

[russ_watters]

But QM would be useless if it wasn't deterministic wouldn't it? I mean, that's the point of theories. You have some chain of causality that explains a phenomena, then you can exploit that chain of causality and manipulate the system. How would we be able to make use of QM if it wasn't deterministic? If there's no chain of causality, what's the point? It may as well be a random number generator you're playing with.

That is the point! Certain things can be known, certain things can be predicted as a matter of probability and certain things are just random number generators we're playing with (which is why they are used as random number generators!). QM tells us which is which and how to properly deal with each.

 

[Pythagorean]

That is the point! Certain things can be known, certain things can be predicted as a matter of probability and certain things are just random number generators we're playing with (which is why they are used as random number generators!). QM tells us which is which and how to properly deal with each.

So then, you mean to say that QM has both deterministic and non-deterministic elements? And the question of determinism and applying it to the whole universe is fundamentally flawed? This isn't much different from naive classical mechanics.

 

[russ_watters]

If a decay is not uncaused, then does that mean you believe it is caused.

Lets take it slow:

QM can predict that a decay will happen.

QM can predict a probability distribution of when it might happen.

QM cannot predict exactly when it will happen.

 

[russ_watters]

Not only does that link not deal with the misunderstandings "completely" it simply reiterates the misunderstandings themselves -- in short the author offers no understanding but only a boat load of platitudes, culminating in no useful definition of "random" whatever...

For all that, I see lilttle in your post that characterizes the issue differently!

 

[russ_watters]

So then, you mean to say that QM has both deterministic and non-deterministic elements?

Sure - the HUP tells us that the more accurate your measurement needs, the less accurate your results. If you just need to do a rough-estimate of your weight with Newton's law, you do fine to ignore sources of error and assume it is deterministic and 100% accurate. If you need to know the position of an electron, you can't.

And the question of determinism and applying it to the whole universe is fundamentally flawed? This isn't much different from naive classical mechanics.

I don't understand what you meant there, but it may be just what I said above...


...to expand a little, though, early scientists had no reason to believe they couldn't get whatever measurement accuracy they wanted - that the universe was deterministic. Their measurements weren't accurate enough to find that their measurments had a fundamental accuracy limit.

 

[DrRocket]

I agree with you, here.

And, btw, my mind isn't made up about determinism in QM. But QM would be useless if it wasn't deterministic wouldn't it? I mean, that's the point of theories. You have some chain of causality that explains a phenomena, then you can exploit that chain of causality and manipulate the system. How would we be able to make use of QM if it wasn't deterministic? If there's no chain of causality, what's the point? It may as well be a random number generator you're playing with.

QM is NOT deterministic, period.

The only thing in QM that is deterministic is the evolution of the state function, which is in fact nothing more than a deterministic evolution of probability measures.

This is basic quantum theory, whether you choose elementary quantum mechanics or quantum field theories.

The WHOLE POINT of quantum theories is that they predict only probabilities, not specific events.

 

[Pythagorean]

Sure - the HUP tells us that the more accurate your measurement needs, the less accurate your results. If you just need to do a rough-estimate of your weight with Newton's law, you do fine to ignore sources of error and assume it is deterministic and 100% accurate. If you need to know the position of an electron, you can't.

I don't understand what you meant there, but it may be just what I said above...

Ok, we're on the same page. I guess I assumed you were speaking in absolutes, and you might have assumed the same about my comments.

My argument was basically that there are deterministic events in the universe (and in QM), your argument is that there are non-deterministic events in the universe (and in QM).

These aren't mutually exclusive.