Originally posted by royalchickenWhen you get old enough you should take your formulas to the craps table in Vegas.
The same. Pseudorandom numbers are deterministic. A few physical processes give pseudorandom numbers tht pass statistical tests with very high marks, but true "randomness" is really a statistical ideal.
Phla-
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Originally posted by royalchickenSorry, I completely disagree with you there - It is impossible to determine the initial conditions precisely enough to predict the outcome of a throw of a thoroughly shaken dice.
In theory it is possible to determine on the basis of classical physics what the outcome of a dice throw will be.
You might have some chance after I've let it go and it's tumbling towards the table (although a long enough tumble through a turbulent medium will easily defeat classical physics) - but while I am shaking it the shaking angle, strength and duration are determined by my brain!
I'm sure my brain can't be predicted by classical physics - Indeed my brain might possibly work via quantum mechanical events - which by their nature are impossible to predict via any method.
Good points. However, I'm not talking about my being able to sit down and work through it, but merely that it is in principle possible. Also, I picked the wrong phrase with "classical physics". I meant merely that it is possible to theoretically predict the behaviour of the dice to within an error small enough not to have any effect on the roll, rather than "physics as it was understood circa 1900".
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Originally posted by royalchickenI still think its as random as they come. Physics even today can't deal properly with turbulence, and quantum mechanics imposes an inherent and unescapable randomness on all tiny things. If you really want a genuine random number just use the time between two decays of a radioactive atom to generate one - it will be truly random.
Furthermore, I was stating only that the dice roll is pretty deterministic, and that randomness is really the manifestation of some statistical property to which we compare our data. Sorry about the poor phraseology of my "dice roll post #1".
Clarify what you mean by "truly random". If it is "truly random" then any set of these "truly random" numbers has any property occurring with exactly the frequency predicted by probability. For example, say these "truly random" numbers are integers. Then if they are "truly random", then for every two generated, exactly one is even. For every n numbers generated, exactly n^(1/3) will be perfect cubes, etc. Is this what you mean by "truly random"?
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Originally posted by royalchickenBy a truly random number. I mean a number selected from n in such a way that the selection cannot be predicted beforehand with a chance of greater than 1/n. I do not mean it has to be a real number or has to be selected from an infinite set. It looks to me like its impossible to select a random number from an infinite set - but I am contending that there are plenty of workable methods for randomly selecting a number from a finite set.
Clarify what you mean by "truly random". If it is "truly random" then any set of these "truly random" numbers has any property occurring with exactly the frequency predicted by probability. For example, say these "truly random" numbers are integers. Then if they are "truly random", then for every two generated, exactly one is even. For eve ...[text shortened]... ted, exactly n^(1/3) will be perfect cubes, etc. Is this what you mean by "truly random"?
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Originally posted by royalchickenI think non-predictability is the essence of true randomness. The digits of pi or sqrt(2) are not random because they can be predicted. Random numbers selected from 1 & 2 with a bia towards 2 are not completely random because I can guess 2 all the time with a probability of more than 1/2 of being right.
Randomness is the "ideal" to which the study of probability compares observations. Thus your criterion is a good one, but does it imply true randomness in all meaningful senses?
Please name a kind of randomness where the definition of non-predictability fails...