Is randomness = indeterminsim?

[Lord Emsworth]

Is randomness = indeterminsim?

Or to ask differently: Is randomness (like in random decay) by definition the (only) opposite to determinism?


Straight forward question, no?

 

[espritch]

I regard random as meaning "upredictable" rather than indeterminate. A system could be completely determinate but if it is sufficiently complex, we can't really predict it's long term behaviour because we cannot acurately enough establish it's initial state. So we have to treat it, in effect, as random.

A truly random system and a very complex determinate system are effectively indestinguishable.

 

[Lord Emsworth]

I regard random as meaning "upredictable" rather than indeterminate. A system could be completely determinate but if it is sufficiently complex, we can't really predict it's long term behaviour because we cannot acurately enough establish it's initial state. So we have to treat it, in effect, as random.

A truly random system and a very complex determinate system are effectively indestinguishable.

I understand that much. But a determinate system, if all properties, the initial state etc., were known it could (and would) not be regarded as random. Right?

 

[hammegk]

You do realize a determinate system may not be computable -- that is, not predictable?

Math allows only two answers; random, or determinate. Does Reality?

 

[espritch]

But a determinate system, if all properties, the initial state etc., were known it could (and would) not be regarded as random. Right?

Yes. The point I was trying to make is that we don't know with any certainty that anything can actually meet those criteria. When you take things out to enough decimal places you start getting into the scale of quantum mechanics, and you can't measure all aspects of the system accurately no matter how accurate your measuring device. The more accurate you fix one quantity (like position), the less accurately you can know another (like velocity). From what I understand, this isn't just a limitation in the accuracy of measurements, but a fundamental aspect of quantum phenomena. So you literally can't fix all properties, initial states, etc. beyond a certain point. Therefore, it may be physically impossible to determine if a system is truly random or deterministic.

 

[T'ai Chi]

Is randomness = indeterminsim?

Or to ask differently: Is randomness (like in random decay) by definition the (only) opposite to determinism?


Straight forward question, no?

Randomness is this. One can't predict with certaintly where any one ball will go, but there is some structure.

 

[Jellby]

I regard random as meaning "upredictable" rather than indeterminate. A system could be completely determinate but if it is sufficiently complex, we can't really predict it's long term behaviour because we cannot acurately enough establish it's initial state. So we have to treat it, in effect, as random.

A truly random system and a very complex determinate system are effectively indestinguishable.

That (your understanding of random) is what's called "chaotic". A chaotic system doesn't need to be random, there's deterministic chaos, but it's unpredictable because any error, no matter how small, rapidly amplifies and becomes larger than the "signal". That's chaos. With a hypothetical perfect knowlegde of initial conditions and perfect computational capability, a chaotic system could be predictable. The rolling of a die looks random, but actually it's chaotic.

Randomness is unpredictable because it's undeterministic (so, to the original question I say "yes"). Quantum effects are usually regarded as truly random. Radioactive decay is considered fully undeterministic and random (even though open to statistical treatment). As far as I know, Heisenberg's uncertainty principle is deeper than "we can't know both", it's more like "they're not determined", it doesn't say two given quantities are not possible to measure at the same time, but they have not a determined value.

 

[espritch]

Some chaotic systems (strange attractors) can be well behaved to the point that you can predict some things about them even if you can't eliminate all the computational error. You might not be able to predict where the n'th iteration will fall, but you can predict that it will lie somewhere within the boundary of the attractor.

If quantum events can be treated in a statistical way, I am not sure you can say they are truly random. The statistical trends we observe could a kind of attractor arising from complex but fully deterministic rules. I should think a truly random behavior would not reveal any trends in a statistical treatment.

 

[hammegk]

This statement is worth repeating ....

I should think a truly random behavior would not reveal any trends in a statistical treatment.

 

[drkitten]

Some chaotic systems (strange attractors) can be well behaved to the point that you can predict some things about them even if you can't eliminate all the computational error. You might not be able to predict where the n'th iteration will fall, but you can predict that it will lie somewhere within the boundary of the attractor.

If quantum events can be treated in a statistical way, I am not sure you can say they are truly random. The statistical trends we observe could a kind of attractor arising from complex but fully deterministic rules. I should think a truly random behavior would not reveal any trends in a statistical treatment.

But, a "truly random behavior" that didn't reveal any trends would
fit the very definition of a uniform random behavior. A "truly random" coin flip would reveal a trend of having 50% heads.

Trying to define "random" as "not having trends" is like trying to buy opaque paint that doesn't have any color.

 

[drkitten]

.

Randomness is unpredictable because it's undeterministic (so, to the original question I say "yes").

That's an argument-by-definition, not by evidence. The usual metaphors in probability class (coin flips, throwing dice, shuffling cards) are deterministic, and yet unpredictable --- but no one
objects to calling the roll of a fair die "random."

 

[Jellby]

That's an argument-by-definition, not by evidence. The usual metaphors in probability class (coin flips, throwing dice, shuffling cards) are deterministic, and yet unpredictable --- but no one
objects to calling the roll of a fair die "random."

Yes, but you have to know the definition of whatever you're talking about ;-)

I realize that might not be very satisfactory, but that's my opinion. Apparent randomness is either lack of knowledge (or computational abilities) or "true" randomness. Whether this true randomness really exists is subject to debate. Most things I've read point to quantum events being truly random, but there may be a better explanation waiting for us to find it.

Originally posted by espritch
If quantum events can be treated in a statistical way, I am not sure you can say they are truly random. The statistical trends we observe could a kind of attractor arising from complex but fully deterministic rules. I should think a truly random behavior would not reveal any trends in a statistical treatment.

Don't confuse "random" with "uniform". A loaded die may not be uniform (some numbers are more likely than others), but it's still random (let's forget about "chaotic" now), there's no way of knowing in advance which number will be rolled, you can talk about probabilities, and that's powerfull, but doesn't make it less random (unless brought to the extreme of 1 & 0 probabilities).

 

[Dancing David]

I would counter that a truely random system may still behave in a probable fashion.

We can say that a coin (More on that below) has a fifty/fifty chance of landing heads/tails. This does not mean that that probabilty is in any way determined. That is the fallacy of many gamblers, say you toss a coin six times, and the first five tosses it land on heads. Some people would try to compute the aggregate odds of that event and would mistakenly say that the coin will only have a .5 to the sixth power chance of landing heads. But that is wrong, the chance is till 50%.

Even with the knowledge that an event has in the past had a given probability does not mean that you can predict it's particular state. Thank goodness otherwise the sun wouldn't shine.


I heard a story on NPR about a mechanical cointosser that could be adjusted to be random or determined, in that it could be rigged to always land the same way.

 

[69dodge]

Well, I think that this statement is worth repeating:

Originally posted by new drkitten
Trying to define "random" as "not having trends" is like trying to buy opaque paint that doesn't have any color.

Seriously, espritch and hammegk, what's a "trend," exactly? Something has to happen, after all.

It's possible to imagine an infinitely long sequence of coin flips where the proportion of heads never settles down to a limiting probability, but if you think about what that really entails, I bet you'll conclude that such a sequence is much less random than one that does settle down. There will have to be stretches where heads dominate, alternating with stretches where tails dominate, and the length of the stretches will need to increase without bound as the coin continues to be flipped. How can the coin possibly know how long it's supposed to come up mostly heads before switching to coming up mostly tails (or vice versa)? It can't unless it has an infinite amount of memory. It would be quite a stretch (ha, ha) to call a coin random that remembers all its previous flips and decides based on that information what to do on its next flip.

 

[espritch]

Something has to happen. But when? And why?

Consider atomic decay. This is generally described as a truly random event. You can't predict when any given atom is going to decay. But you can talk about half life; the amount of time it takes for half the atoms in a sample to decay. Does the fact that a particular atom has been around for a million years change the likelyhood that it will decay in the next million years? If so, what has changed? If not, then why should their be half lives? And more importantly, why should the half life vary so greatly from one isotope or element to another?

The very fact that different types of atoms decay at different rates suggests that their is some principal related to atomic structure governing rate of decay. If so, how can decay be truly random?

 

[evildave]

Not random, just no way known (at the moment) to determine the state that will cause an atom to pop at a given time.

'Randomness' is only a model of what is unpredictable due to insufficient information.

 

[Dancing David]

The very fact that different types of atoms decay at different rates suggests that their is some principal related to atomic structure governing rate of decay. If so, how can decay be truly random?

This seems to be along the lines of 'order exists' and therefore it can't be random. But it is still unpredictable! And therefore meets the criteria for the common usage of random which is ' equally likely to attain one of certain states'.

You are correct there is an underlying priciple to what cause radioactive decay and certain atoms have different halflifes, but that is an aggregate phenomena , the fewer the number of atoms the less it holds true.

In fact under the current theory you can not predict when a single atom will decay, so you can not assign probabilty to the unfortunate cat in the bocx being alive.

There is an apparent order in the universe but it overlies something that appears to be chaotic. The repulsive force of electrons is 'constant' but one electron may still materialize next to another , in defiance of the repulsive force. So while there may be an 'order' in the geometric ratio of repulsion, the electrons don't care.

As I said before, this is a good thing otherwise we would never have nuclear fusion in the sun, if it were not for the random behavior of protons, there would be no sun shine.

 

[69dodge]

Originally posted by espritch
Consider atomic decay. This is generally described as a truly random event. You can't predict when any given atom is going to decay. But you can talk about half life; the amount of time it takes for half the atoms in a sample to decay. Does the fact that a particular atom has been around for a million years change the likelyhood that it will decay in the next million years? If so, what has changed? If not, then why should their be half lives?

No. Nothing changed. Half-lives are what naturally happens when you have lots and lots of atoms that don't remember their past, don't know about each other, and each have the same probability of decay per unit time. It's the same reason why you won't end up with 90 heads if you flip a coin 100 times. You might end up with 90 heads, strictly speaking, but the probability of that happening is very small. Similarly, you might end up with 90 % of a radioactive sample remaining after its half-life, but the probability of that happening is smaller still, if the sample consists of more than 100 atoms.

Neither the coin nor the atoms actively try to make things work out that way; it's just what happens. If the coin, for example, did try to come up heads exactly half the time, then you'd never get 55 heads either; but, in fact, sometimes you do.

And more importantly, why should the half life vary so greatly from one isotope or element to another?

The very fact that different types of atoms decay at different rates suggests that their is some principal related to atomic structure governing rate of decay. If so, how can decay be truly random?

Something determines the probability of decay, yes. And the something, whatever it is, differs between different types of atoms. But nothing coordinates the activities of the various atoms in a sample, nor the activity of a single atom over time. Nothing needs to.

I guess I don't understand what you mean by "truly random." Can you give me an example of something, or of some behavior, that you consider random? Not necessarily something that actually exists, even. Just something that, if you did happen to observe it, you'd say, "yes, this appears to be truly random."

 

[hammegk]

Re, "trends" and "what *is* "random" ...

Let me agree that:

'Randomness' is only a model of what is unpredictable due to insufficient information.

I ask, can anything involving a set with finite elements be "random"?

 

[evildave]

It's according to how well understood these 'elements' are, and how well you control their environment.

Poor controls will yield unpredictable results as readily as unpredictable elements will. Indeed, there are probably additional forces and/or techniques we're not aware of that could be isolated from or applied to an experiment that would control the outcome of formerly 'unpredictable' elements.

As an example, a means of getting radioactive decay to happen in a precise way would make fission power a lot safer and more economical, as so much less fuel would be wasted forming 'byproducts'. It's not inconceivable that some technique might 'pop' heavy nucleii on demand, rather than building a critical mass of them that allows for spontaneous breakdowns to cause chain reactions that don't economically continue to produce much of the potential energy that should be there.

And that's another lesson about 'randomness'. Although you can't rely on certain things on the atomic or sub-atomic scale to happen predictably (mainly because there isn't any way to get information about a given particle without changing its state, or losing it), you can rely on things on a macro scale. With enough of this 'random' stuff going on, some statistical patterns emerge that makes a larger pattern based on this 'noise' predictable, ergo we can get a chain reaction based on what is likely to occur when enough enriched nuclear fuel is brought together. With enough fuel, the outcome is a guarantee, even though we can't predict which atoms will specifically split, absorb, or remain unchanged.