Randomness

@Relative,

And yet the mathematical phenominon of chaos, to which you referred earlier, involves a class of processes, many described by parabolic non linear differential equations, that are both deterministic and unpredictable. Mathematical forecasts of the details of their future states are only randomly related to what actually occurs. The wheather is a good example.

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Wow, this is an old thread Smile

But I still maintain my old view that "random" is merely unknown factors or factors calculated with inappropriate mechanics.

A good drummer is a fine example. Let's say he plays a beat in traditional 4/4 beat. It is easy to hear that the drumbeats are not random, they are all intentionally put where they are. Easy because you are measuring on the same scale as the drummer is playing. One, a two, a three, a four...
But lets say he starts playing a beat in 5/4. If you still measure on 4/4 time your prediction of where the drumbeats will bee becomes wrong. At first it will appear that he is just randomely hitting the drums, but if you keep measuring you will see that there is no randomness to it still. The cycle is just longer.

In 4/4 beat the cycle is just one count to four before the pattern repeats. For 5/4 the count is to five and then the pattern repeats.

But if he plays 5/4 and you count 4/4 the new cycle is the two old counts multiplied. 4*5=20 counts before the pattern repeats. (The song Seven Days by Sting is an example.)

Now, if the drummer is playing 13/7, and you don't know and don't have the ability to measure the correct count, you would have been unable to pick out the pattern. It would appear random to you.
And if the system in question is something much more complex than a drumbeat, and if we don't know the pattern we are attempting to predict it will seem like no pattern at all. Just randomness. To make sense of it we would apply different methods of discerning and predicting any event, making them recognizable and no longer random.
If our system of calculating this was nearly accurate, if it was 99% accurate, it would be pretty good at making predictions. But the final 1% accounts for randomness. Events we still lack the means to measure correctly.

In a drumbeat it would be one renegade sound repeating at intervals you are unable to predict even though you can predict all the other sounds in the beat.

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@georgeob1,

If Reality is deterministic predictability is always possible at least IN PRINCIPLE--when computers are strong enough and enough "data" is available. And if the table of random numbers is based on SOME kind of theoretical assumptions then CHAOS, as popularly conceived, is not likely to be the case. But I'm mathematically illiterate so these utterances are essentially idle.
Personally, the cosmos is neither orderly (deterministic) nor chaotic (random); it is both, and both are relativistic and situational expressions of human functions--not a God's absolute and objective perspective.

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@JLNobody,

Does anyone know anything about "chaos theory"?

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@JLNobody,

Can't say I know much, but I know about the butterfly effect. According to wikipedia, chaos theory is about dynamical systems that are highly sensitive to initial conditions.
Wiki:

Quote:

Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for chaotic systems, rendering long-term prediction impossible in general.

But it seems to me that if you allow these small differences like rounding errors to remain in your calculations in an initial position, where they will affect the whole system like ripples spreading through it, you yourself have introduced the chaos into the theory.
Of course, in the event that close approximation of the initial values is the best that can be had there is no choice. But again, this seeming randomness or unpredictability is a result of limitations to the mathematical system, which may not be 100% appropriate to the problem it's applied to even though it is the best alternative there is.

I still seems to me that with enough processing power, knowledge of all variables that come into play, and the right mathematical tools, we would be able to predict precicely what the effects of a butterfly fluttering by would be. But I would also say that I am mathematically illiterate, so I would like it if someone with first hand experience with chaos theory would speak up. Smile

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@Cyracuz,

Chaos theory would say that if you calculated the outcome of weather in three months using data with the butterfly's wing going down, you can and probably would get a much different outcome by just calculating the outcome using butterfly's wing going up.

Changing a small input will give you drastically different results although the results when graphed do show a spiral that appears like butterfly wings when graphed.

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@Cyracuz,

Cyracuz wrote:

And if the system in question is something much more complex than a drumbeat, and if we don't know the pattern we are attempting to predict it will seem like no pattern at all. Just randomness. To make sense of it we would apply different methods of discerning and predicting any event, making them recognizable and no longer random.

If you define "random" as "something for which we have not yet devised a pattern," then I suppose you can say that there is no randomness, or at least that we can eliminate randomness. But then that's something of a bootstrapping argument: you're defining the term in such a way that it fits your theory, and then you cite the definition as support for your theory.

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@joefromchicago,

I would say that I am defining the theory to fit the term.

I define random as that which occurs without any apparent cause. Perhaps that is a paradoxical definition made to eliminate the term. But is it wrong?

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@Cyracuz,

Cyracuz wrote:

I would say that I am defining the theory to fit the term.

I define random as that which occurs without any apparent cause. Perhaps that is a paradoxical definition made to eliminate the term. But is it wrong?

Well, yes, I'd say that's wrong. There's no effect without a cause -- at least that's how we typically view cause-and-effect. So to say that "randomness" is that which occurs without any apparent cause doesn't make a whole lot of sense. Since everything that happens has a cause, all of those things that don't have any apparent cause are nevertheless caused, and if discovering the cause eliminates the randomness, then you're essentially defining randomness away. Under that definition, there is no genuine randomness, only apparent randomness. That's definitely a bootstrapping argument.

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@joefromchicago,

But what if indeed there is no genuine randomness, only apparent randomness?

Here's how wikipedia defines randomness:

Quote:

Having no definite aim or purpose; not sent or guided in a particular direction; made, done, occurring, etc., without method or conscious choice; haphazard.

http://en.wikipedia.org/wiki/Randomness

Isn't that basically another way of saying "that which occurs without any apparent reason"?

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@Cyracuz,

Cyracuz wrote:

Isn't that basically another way of saying "that which occurs without any apparent reason"?

"Reason" isn't the same thing as "cause." Everything has a cause, but not everything has a reason. I agree that "randomness" is "that which occurs without reason or apparent reason." I can't agree that it is "that which occurs without apparent cause."

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@joefromchicago,

Oh, yes, sorry I got my words mixed up.

But I disagree with your statment that "everything has a cause, but not everything has a reason".
Cause is the word used when talking about physical observation. Reason is a human construct, right up there with god and all the other mechanisms we use to assign meaning to the world we percieve. Reason implies intention, which implies consciousness. If something doesn't have a reason it's because no one has dreamed up one.

So I still think that the definition should be "..without apparent cause"

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@Cyracuz,

Regarding the notions of cause and determinism: I agree that every condition and event has a past, a "biography", to put it loosely. I can't imagine something coming into being suddenly out of "nothing" (although contemporary physicists perhaps can). I see the world in terms of continua, not in terms of discreet causes and effects. Causes and effects are the analytical crevices we necessarily impose on our experience. FSC Northrup once said that our experience is primordially of an undifferented esthetic continuum, but we seem to only be able to deal with it as a differentiated esthetic continuum. I like to think that the meaning behind the allegory of Eve, Adam and the snake's apple (from the tree of knowledge of good and evil, or whatever) is about Man's shift from living in terms of a non-problematical perspective on life to that of a vivisected world of analytical categories like cause and effect. I don't want to be a bore, Joe, but this is one of the central points of zen buddhism.

Determinism is a useful way to THINK ABOUT the world, but it does not accurately DESCRIBE it.

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@SCoates,

Quote:

For example, flipping a coin does not generate a random result, because it is possible to calculate the outcome based on the force applied to it's shape and weight... taking account for wind resistence and so on. Everything that affects the outcome can be expressed mathematically.

You are implicitly assuming that the force, shape, weight, and wind resistance have been measured with infinite precision. Without this assumption, your mathematics have insufficient input for predicting the coin toss.

As it happens, there are physical processes for which these measurements are impossible in principle. For example, if you put a radioactive substance near a Geiger counter and use the time between clicks as your random number, I'm pretty sure that's "pure random". It's impossible to predict when an atomic nucleus will decay, even if you have measured its physical properties as precisely as theoretically possible.

Quote:

So is randomness merely the lack of that knowledge, or is there no such thing as something truly being random?

What's the difference?

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@Cyracuz,

Cyracuz wrote:

Reason implies intention, which implies consciousness. If something doesn't have a reason it's because no one has dreamed up one.

That's a non sequitur. A raindrop falling doesn't have intentionality, so it doesn't have a reason for falling where it falls. If we assign some sort of reason to it, that doesn't mean the raindrop now has a reason for falling, it means that we have imagined a reason for it falling.

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@Cyracuz,

Cyracuz wrote:

Wow, this is an old thread
But I still maintain my old view that "random" is merely unknown factors or factors calculated with inappropriate mechanics.

Some alleged cases of randomness are undoubtedly a merely convenient way to describe things not completely understood or imperfectly analyzed - just as you say. However, as others here have pointed out, there are observable pnenomena that are well understood and that obey known mathematical laws that cannot be accurately predicted, and still manifest outcomes that are indeed observably random.

Thomas noted the radioactive decay of an atom, or nuclide whose decay process is well understood and whose average behavior (action) is known with precision, but, despite all that, the moment of decay of an individual atom is absolutely unpredictable and therrefore representable with random numbers. I noted the fine behavior of a moving viscous fluid exhibiting turbulence, as in the atmosphere: it too obeys known mathematical laws that promise absolute determinism with respect to future outcomes. However, owing to the inescapable mathematical amplification of even the smallest uncertainties in the initial state, predictions sufficiently far into the future bear only a random relationship to what accurately occurs. Neither outcome is the result of a flawed or inappropriate analysis.

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George:

Quote:

However, as others here have pointed out, there are observable pnenomena that are well understood and that obey known mathematical laws that cannot be accurately predicted, and still manifest outcomes that are indeed observably random.

Doesn anything really obey mathematical laws? Isn't it more acurate to say that our mathematical laws describe the world, not rule it.
Perhaps it is a fine point to argue, but it seems to me that such a misconception reinforces the notion of true randomness where there actually only is randomness as defined by the theory in question.
The randomness of chaos theory is caused by the inacurate representation of initial values. Long term prediction shows randomness only because these values, along with the inacuracies ripple through the system with greater and greater consequence.
Some would say that the decimals to Pi is random, since they never repeat. It starts with 3.1415, and goes on, but it doesn't ever repeat itself so we cannot devise a pattern for it. But it is not random since it is all caused by an initial mechanism that is describable.

Joe:

Quote:

That's a non sequitur. A raindrop falling doesn't have intentionality, so it doesn't have a reason for falling where it falls. If we assign some sort of reason to it, that doesn't mean the raindrop now has a reason for falling, it means that we have imagined a reason for it falling.

That is the point. When it comes to reason, wouldn't any randomness percieved also be imagined?

And I am as usually in agreement with you JL. But it seems to me that a discussion on the validity of the term random falls within the "analytical crevices we necessarily impose on our experience". The discussion perhaps isn't on the nature of the world, but the nature of the tools we have for measuring it?

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@Cyracuz,

Cyracuz wrote:

Perhaps it is a fine point to argue, but it seems to me that such a misconception reinforces the notion of true randomness where there actually only is randomness as defined by the theory in question.
The randomness of chaos theory is caused by the inacurate representation of initial values. Long term prediction shows randomness only because these values, along with the inacuracies ripple through the system with greater and greater consequence.
Some would say that the decimals to Pi is random, since they never repeat. It starts with 3.1415, and goes on, but it doesn't ever repeat itself so we cannot devise a pattern for it. But it is not random since it is all caused by an initial mechanism that is describable.

None of this hair-splitting applies to the randomness of radioactive decay. As Georgeob1 confirmed, two atomic nuclei with identical measurable properties will decay at different times, and it's unknowable when those times will be.

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@Cyracuz,

Cyracuz wrote:

Doesn anything really obey mathematical laws? Isn't it more acurate to say that our mathematical laws describe the world, not rule it.
Perhaps it is a fine point to argue, but it seems to me that such a misconception reinforces the notion of true randomness where there actually only is randomness as defined by the theory in question.
The randomness of chaos theory is caused by the inacurate representation of initial values. Long term prediction shows randomness only because these values, along with the inacuracies ripple through the system with greater and greater consequence.
Some would say that the decimals to Pi is random, since they never repeat. It starts with 3.1415, and goes on, but it doesn't ever repeat itself so we cannot devise a pattern for it. But it is not random since it is all caused by an initial mechanism that is describable.

. ... But it seems to me that a discussion on the validity of the term random falls within the "analytical crevices we necessarily impose on our experience". The discussion perhaps isn't on the nature of the world, but the nature of the tools we have for measuring it?

It seems to me that your problem is is one that arises out of your varying and self referential implied definitions of randomness. For most of us the term refers to events, and the numbers that describe them, that are (1) unpredictable and (2) posess certain statistical properties indicating the lack of correlation with external factors.

You are correct that mathematical chaos results from imperfections in the numerical representations of the initial state of the system. However the issue is that, in chaotic physical systems (and in their mathematical descriptions as well), infinite precision, not realizable in the real world, would be required for an acccurate forecast. After almost four decades of Moore's Law with respect to computing power, numerical weather forecasts still break down and diverge from real outcomes after just a few days. In some sense this can be argued as arising from the physical fact that air is not really a continuous medium, as is implied in the mathematical representation. However, both the real atmosphere and the mathematical representation manifest chaos, turbulence and fine grain unpredictability.

The inherent uncertainty in quantum theory likewise remains unresolvable with finer measurement or models.

Finally, the randomness of the decimal digits of Pi isn't confined just to that interesting number. The same phenomenon can be observed with all irrational numbers - their decimal representations involve no cyclic repetition whatever, at any period. Moreover, there are infinitely many such numbers between any two numbers.

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