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Is randomness = indeterminsim?

I'd say the previous post should replace "random" with "not computably determinent".

Can we agree that operations on a set with infinite elements would be "random"?
 
Nope. Don't have infinite elements to measure, infinite space to keep them in, nor infinite time to perform the measurement with.

Any set with indeterminate elements may be 'random', but that's according to what it is you're trying to measure. Is it when a particular atom of some isotope will decay, or how much a brick made of it weighs, and to what precision? Beyond a certain precision, a fly buzzing past your building will influence the measurement of weight. Are we looking for the quantum state of a single atom, or how 'warm' it is? What can we ever know about how warm ALL of an object is, when nothing is uniformly a given temperature.

What is it you're trying to draw a conclusion about? I won't draw any cosmic conclusions about the state of the universe (which is provably very, very, very big, not provably 'infinite'), or any 'infinite' set - which can only ever be hypothetical.

Finite sets, even very simple sets containing state which you don't have access to can behave unpredictably.

When you try to go beyond your available precision, you have noise.

'Randomness' is only a construct that allows us to model complex behavior. A label to slap on top of "we don't know how it will behave outside of this set of parameters".
 
evildave said:

'Randomness' is only a construct that allows us to model complex behavior. A label to slap on top of "we don't know how it will behave outside of this set of parameters".
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See. We do agree. :)
 
hammegk said:


I ask, can anything involving a set with finite elements be "random"?
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Um, yes. Rather obviously.

Consider a die, that rolls a number between 1 and 6, "randomly."

"Ah, yes," you say. "But that's not random, that's merely chaotic," as though slapping a half-understood label on anything provides an explanation. But it's fairly easy to take several radioactive samples and use them to get a QM-random number from 1 to 6.

For simplicity, I will get six individual atoms of unobtanium, and put them in individual sealed containers with geiger counters. The containers will be numbered from 1 to 6, and whichever atom decays first, that decay will be recorded, and the number of its container will be treated as the number rolled on the die. Behold, a completely random choice among a set of six elements.
 
new drkitten said:
Behold, a completely random choice among a set of six elements.
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Obviously indeterminate for each choice. Yet, certainty that 1 thing out of six will occur. Random, you say. I'd say the six element set is determinate, but not calculable.

Given an infinite number of possibilities, yup, that probably *is* random.
 
Yes, but it's not really a balanced 1:6. Even if you chopped the samples from one block of isotope, the random number generator will tend to fire one number or another more or less often because of the distribution of impurities within the sample, being a little closer to the window, being not perfectly divided, etc.

You can't really say "given a pure" sample, because even if you started out with a 'pure' isotope, it couldn't stay pure by its very nature.
 
evildave said:
Yes, but it's not really a balanced 1:6.
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Yup. Nor is it "random" when looked at as the set. Damn determinism for making us type this stuff.
 
How about "constrained unpredictability"?

I recall in reading Chaos by Glieck that when you have a system under pressure to change that a phenomena know as bifurcation occurs. For example a predator/prey ratio and something drives change in the system, such as drought. As the equations generate possible population levels for the imagined sample a wierd thing will happen. The levels of population will suddenly started fliping between two states. The level of predators will suddenly crash or boom, and the two states are considered to be mathematicaly equal. And the model can in fact be driven to bifurcate repeatedly.

The reason I bring this up is that these are very simple deterministic systems, and they can produce a multitude of states that a particular paramer can attain, all without anything else. Say that the predator level may have four states that it can just flip through, without any other parameter being changed at all. This might be an example of "constrained predictability" that appears to be random.
 
Dancing David said:
How about "constrained unpredictability"?

I recall in reading Chaos by Glieck that when you have a system under pressure to change that a phenomena know as bifurcation occurs. For example a predator/prey ratio and something drives change in the system, such as drought. As the equations generate possible population levels for the imagined sample a wierd thing will happen. The levels of population will suddenly started fliping between two states. The level of predators will suddenly crash or boom, and the two states are considered to be mathematicaly equal. And the model can in fact be driven to bifurcate repeatedly.

The reason I bring this up is that these are very simple deterministic systems, and they can produce a multitude of states that a particular paramer can attain, all without anything else. Say that the predator level may have four states that it can just flip through, without any other parameter being changed at all. This might be an example of "constrained predictability" that appears to be random.
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Its not simply change that causes the behavior; it is change that drives the system toward specific types of phase-plane attractors.
 
Originally posted by hammegk
Obviously indeterminate for each choice. Yet, certainty that 1 thing out of six will occur. Random, you say. I'd say the six element set is determinate, but not calculable.
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Huh? Something is determinate and something else is indeterminate? What are these two different things you're talking about?
 
Er, the choice of an individual element is indeterminate, yet it is 100% certain one of the six is chosen each time. That's a toughy??
 
Originally posted by hammegk
Er, the choice of an individual element is indeterminate, yet it is 100% certain one of the six is chosen each time.
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Oh. Well, of course, one of the six will be chosen. That is perfectly determinate and calculable and everything. So, what is "determinate, but not calculable", then?
 
Randomness means that the system in principle is not biased in any particular way!
A roulette wheel output random values if there is not some malfunctioning or cheating going on! A spontaneous radio isotopic decay is indeterminate phenomenon because it has no cause and cannot be predicted! But a large collection of these isotopes can be used statistically to predict their decays through half-lives, the bigger that collection is, the more certain your prediction is! The word random can be used to denote unpredictability in an unbiased system, or unpredictability in an uncaused event, the uncaused event's outcome is random because it happen by a whim!
 
hammegk said:
Er, the choice of an individual element is indeterminate, yet it is 100% certain one of the six is chosen each time. That's a toughy??
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Approximately, the choice of an individual element is determined by the dice's earlier state, approximate because the dice have no well-defined position and momentum when it comes down to billionths of millimeter known as the quantum scale! Chaos is the mechanism, which the quantum factor uses to reach the macroscopic level, according to Murray Gell-Mann's book, The Quark and the Jaguar!
 
Lord Emsworth said:
Is randomness = indeterminsim?

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


Straight forward question, no?
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What does determinism mean?
 
evildave said:
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.
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Nonsense. Randomness is innate in nature. Quantum Mechanics teaches us this.
 
evildave said:
Yes, but it's not really a balanced 1:6. Even if you chopped the samples from one block of isotope, the random number generator will tend to fire one number or another more or less often because of the distribution of impurities within the sample, being a little closer to the window, being not perfectly divided, etc.

You can't really say "given a pure" sample, because even if you started out with a 'pure' isotope, it couldn't stay pure by its very nature.
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Nonsense. I'll use individual radon molecules/atoms (extracting
individual atoms of a gas is difficult, but doable in practice),
count exactly six of them and store/measure them individually. With a half-life measured in days, I even have enough time to make the experiment physically practical.
 
Peter Soderqvist said:
Randomness means that the system in principle is not biased in any particular way!
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No. For example, the decimal digits of 1/7 are an unbiased, uniform collection of the digits 1,2,4,5,7, and 8 (all digits appear equally frequently), but they're hardly random. On the other hand, a "fair" roulette wheel has a green number come up less than 10% of the time, so it's strongly biased against green, but is still random.
 
To answer the question. In mathematics there is only determinate or random. But in the real world we also have this mysterious thing called free will which is neither random nor determined.
 
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