Is Randomness Real or Just Complex Predictability?

[disregardthat]

In an earlier post, I brought up the definition that refers to a situation in which all events are equally probable, then all events are random (even in the causative perspective) I think this is mathematically rigorous enough as a definition. I also tend to think it's highly unlikely that any real system has a chance of all it's states being equally probable because real systems can't be perfectly isolated from perturbation and entropy.

Why does it have to be equally probable? Suppose you are throwing a dice with 5 blue and 1 red side. Is not the outcome (side facing up) random even though it is 5 times more probable that the red side faces up?

Probability in common language is always used when we lack the ability to predict. So if something is 'really' random, does that mean it is impossible to predict, no matter what information you have? I can easily imagine that we can come up with a sort of event for which there are quantum mechanical principles which disallows us to collect the necessary amount of information to predict. But does this mean the event was 'really' random?

It's important to distinguish between 'true' causality, 'true' randomness, and just causality and randomness in models. If a phenomenon was 'really random', but behaved according to certain tendencies, we can have causal models of it (e.g. thermodynamics, given that microscopic movement is 'truly' random). And the other way, if a phenomenon is causal, we can just as well have probabilistic theories of it. Any pseudo-random phenomenon is an example of this.

So models cannot determine whether a phenomenon is 'truly' random or 'truly' causal, and I suggest that these as intrinsic properties does not even make sense. When we speak of a phenomenon, we are not merely labeling observations, we are extracting generality from individual observations. The generality extracted is a way of thinking of the phenomenon, and it is in this way of thinking terms like causal and random really make sense, and these terms are only meaningful in the sense of our ability to predict. So it is meaningless to apply these terms as intrinsic to examples of phenomena in themselves. Does this not become a question of our own ability to think of phenomena? I believe Kant argued that causality is one of our cognitive categories in which we interpret all sensory experience.

EDIT: Oh, look; this is my 777'th post. How random.

 

[russ_watters]

You're presupposing random is real, when the question of this thread is if it's real or not.

Well I'll answer that simply: random is real [sic], as far as we know. It is not a difficult question, scientifically. Much of QM is dependent on probability, behaving exactly like that dice throw.

Regarding random vs supernatural, Evo is right that she doesn't have to back up a counter to a claim that someone else made - they have to back up their claim. However, for expedience: The existence of randomness in nature does not violate physical laws, so there is no need for every random event to be considered supernatural. The proposed contradiction between "random" and "law" does not exist.

And note, repeating a throw of a die is not just a technical impossibility (I'm assuming we're not just dropping it from a height of 1" here...), but it is in fact a physical impossibility. Getting the initial conditions exactly equal every time would be a violation of physical law because the concept of "exact" violates QM.

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

 

[russ_watters]

Why does it have to be equally probable? Suppose you are throwing a dice with 5 blue and 1 red side. Is not the outcome (side facing up) random even though it is 5 times more probable that the red side faces up?

Probability in common language is always used when we lack the ability to predict.

Correct. People tend to mistake probability and randomness. That may be part of the motivation for this thread.

The fact that you can roll a die a large number of times and get a 1, 1/6 of the time does not make the roll non-random: you have no ability to predict the outcome of an individual roll greater than 1/6 of the time.

 

[russ_watters]

Some of you may find this site instructional: http://www.random.org/randomness/

It covers basically the entirety of this issue.

 

[TubbaBlubba]

I see random as something fundamentally unpredictable, that with any given a priori knowledge, one can impossibly determine the result (e.g. the position of an electron).

 

[disregardthat]

I see random as something fundamentally unpredictable, that with any given a priori knowledge, one can impossibly determine the result (e.g. the position of an electron).

There are many events which we cannot possibly determine the results of (even in principle), but for which it is entirely possible that is caused by prior events. Furthermore, we have a good ability to predict random events as well to a high accuracy. And even predictions of causal events is only up to a certain degree of accuracy anyway. The 'ability to predict' criterion is not well-defined, and is not a satisfactory criterion to establish true randomness (not to mention the impossibility of establishing that it is true for any event in practice). It is entirely plausible that we will one day find a deterministic model of the electron (and accounts for behavior on the quantum level), but which deals in other terms than today.

As to problems such as predicting of the position of the electron; consider the following analogy: What is the position of a platoon of soldiers? How accurately can we measure it in space? Do you agree that it does not entirely make sense to consider the 'position of a platoon of a battalion of soldiers' as a point in space? But even so, it does make sense to consider the position as a 0-dimensional point on the map (and so also in space) for a military tactician.

The point is that we only speak in terms of our models (e.g. a map) of nature, not of the terms of nature itself (such terms cannot exist). The 'position of the platoon' is of course not a random event, but cannot either be measured to an exact accuracy. So, a questions such as the 'true' position of the electron does not necessarily make any sense as a sort of exact position which only can be measured to a certain degree of accuracy. Hence does the complete prediction of the position make as little sense. (The analogy goes further; as the platoon is advancing it is more spread out, so you can have the position to an even less 'degree of accuracy'.)

In fact, I would argue that no claim whatsoever of nature could be true 'intrinsically' to nature for the same reason, but I won't pursue that here..

 

[DrRocket]

In an earlier post, I brought up the definition that refers to a situation in which all events are equally probable, then all events are random (even in the causative perspective) I think this is mathematically rigorous enough as a definition. not.

Nope.

First, it is not a definition of "random" but rather a definition of "uniformly distributed". Uniform distribution is a potential attribute of a random variable, but says nothing whatever about the definition of random.

There are other distributions besides the uniform distribution and in many situations a uniform distribution is impossible.

Mathematics avoids actually defining the term "random" and a "random variable" is nothing more and nothing less than a measurable function defined on a probability space. In turn a probability space is simply a set with a sigma algebra of subsets and a positive measure that measures the whole space as 1. So, you see therein lies no useful test for "randomness".

Thus you still need a viable definition for "random".

 

[Pythagorean]

This was from wiktionary, which is hardly a reliable source, but it is fundamentally speaking about causality, which is more physical than mathematical:

Having unpredictable outcomes and, in the ideal case, all outcomes equally probable; resulting from such selection; lacking statistical correlation.

Here's what wolfram, a more reliable source, says about random numbers (i.e. random in mathematics):

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. Computer-generated random numbers are sometimes called pseudorandom numbers, while the term "random" is reserved for the output of unpredictable physical processes. When used without qualification, the word "random" usually means "random with a uniform distribution." Other distributions are of course possible. For example, the Box-Muller transformation allows pairs of uniform random numbers to be transformed to corresponding random numbers having a two-dimensional normal distribution.

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

Why does it have to be equally probable? Suppose you are throwing a dice with 5 blue and 1 red side. Is not the outcome (side facing up) random even though it is 5 times more probable that the red side faces up?

but you're kind of playing games, you're not confront the causality. If it was a truly random system, than each of the six sides would have equal probability of coming up. In that case, you would know exactly why blue is more probable than red (because it's a truly random die and more sides are painted blue than red). The randomness still only exists in the equal distribution of the probability of the faces turning up themselves. The distribution of colors in your system is no longer random (remember? you made blue more probable than red so they're not equally probable), but which face turns up still is.

the fact that you can roll a die a large number of times and get a 1, 1/6 of the time does not make the roll non-random: you have no ability to predict the outcome of an individual roll greater than 1/6 of the time.

I don't think anyone implied that. It depends, of course, what definition of random you're operating under, but the reason dice are non-random is because they're chaotic. A dice roll is classically deterministic, it just has a lot of figures to fiddle with in four dimensional variable space and n dimensional parameter space.

I'm still not sure though, whether your definition of random pertains to unpredictability of lack of causation. When I say that outcomes are equally probable, I mean fundamentally lack causation.

also, from your link:

When discussing single numbers, a random number is one that is drawn from a set of possible values, each of which is equally probable, i.e., a uniform distribution. When discussing a sequence of random numbers, each number drawn must be statistically independent of the others.

 

[disregardthat]

but you're kind of playing games, you're not confront the causality. If it was a truly random system, than each of the six sides would have equal probability of coming up. In that case, you would know exactly why blue is more probable than red (because it's a truly random die and more sides are painted blue than red). The randomness still only exists in the equal distribution of the probability of the faces turning up themselves. The distribution of colors in your system is no longer random (remember? you made blue more probable than red so they're not equally probable), but which face turns up still is.

You must not confuse the information of the system with the information of the results. In my example we still have no information whatsoever what the result will be. The point is that it is a random process. It is still random, even though the distribution is not uniform.

 

[Ivan Seeking]

I understand the reference to supernatural and I think it is applicable. I have made arguments related to this idea before. Part of the problem is the interpretation of the word. As has been mentioned, "supernatural" is often associated with specific concepts like God, ghosts, or magic. But those concepts are really secondary to the definition. We assume that a God would be supernatural, but the word supernatural is not limited to the concept of a God.

Again here are the primary definitions. from several sources.

Of or relating to existence outside the natural world.
Attributed to a power that seems to violate or go beyond natural forces.
http://education.yahoo.com/reference/dictionary/entry/supernatural [American Heritage]

1 : of or relating to an order of existence beyond the visible observable universe; especially : of or relating to God or a god, demigod, spirit, or devil
2 a : departing from what is usual or normal especially so as to appear to transcend the laws of nature b : attributed to an invisible agent (as a ghost or spirit)
http://www.merriam-webster.com/dictionary/supernatural

supernatural adjective /ˌsuː.pəˈnætʃ.ər.əl//-pɚˈnætʃ.ɚ-/ adj
caused by forces that cannot be explained by science
http://dictionary.cambridge.org/dictionary/british/supernatural

1.existing or occurring outside the normal experience or knowledge of man; not explainable by the known forces or laws of nature; specif., of, involving, or attributed to God or a god
http://www.yourdictionary.com/supernatural [Webster New World]

To say that true randomness is supernatural, is only to say that any underlying process eludes description. It is beyond the ablity of science to describe it. It is simply a matter of definition.

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

 

[Pythagorean]

You must not confuse the information of the system with the information of the results. In my example we still have no information whatsoever what the result will be. The point is that it is a random process. It is still random, even though the distribution is not uniform.

So then you're talking about a definition of random that only pertains to your subjective state of knowledge. This is what I would call something "appearing random". I covered this definition already. I'm talking about the causality. You seem to be talking about predictability.

 

[Evo]

the random and supernatural. Both are said to not obey natural law.

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.

 

[Ivan Seeking]

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 Seeking]

Things can happen randomly while obeying all laws of nature. .

Name one.

 

[disregardthat]

So then you're talking about a definition of random that only pertains to your subjective state of knowledge. This is what I would call something "appearing random". I covered this definition already. I'm talking about the causality. You seem to be talking about predictability.

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.

 

[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.