[randomness] - A New Kind of Science: The NKS ForumA New Kind of Science: The NKS Forum
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randomness
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Posted by: Richard
I have wondered about the nature of natural randomness for some time: is radioactivity really a random process, for example?
Pseudo-random number generators have limitations and devices to generate "genuine" sequences use an external noise source. But is there such a thing as genuine randomness or is it merely irregular behaviour resulting from internal organisation?
NKS Chapter 7, page 321 says of a rule 30 automoton that "... the sequences it produces seem perfectly random, and do not suffer from any of the problems that are typically found in linear congruential generators."
This would seem to be a mathematical breakthrough with important consequences for physics. Have the sequences been rigorously analysed and do they do indeed show no regularity (or should that be the same regularity as natural sources)?
Richard Wilson
Posted by: Jason Cawley
"Have the sequences been rigorously analysed?"
Certainly. See the section on "statistical analysis" in chapter 10 of the NKS book, and the following section on cryptanalysis. The former begins on page 588, the latter follows immediately and continues through page 606. There are also relevant notes. The upshot is that standard statistical tests e.g. of block frequencies, fail to discern any regularity in rule 30.
http://www.wolframscience.com/nksonline/page-588
Richard Feynman tried to cryptanalyse rule 30 without success. Some partial progress on decrypting rule 30 sequences given enough information was made in the early 90s (see note on page 1087), but requires essentially a complete column of the rule's evolution. If you can find any significant deviation of the behavior of the center column of rule 30 from perfect randomness, it would be news.
http://www.wolframscience.com/nksonline/page-1087
The note "tests of randomness" on page 1084 reports on application of Donald Knuth's 8-fold benchmark for randomness to the various systems being discussed in the chapter at that point, one of which - (g) in the illustration on page 594 - is rule 30. "of the sequences on page 594, a through d and well as f fail every single one of the tests, e fails only the serial test, while g and h pass all the tests." See also the last paragraph of that note.
http://www.wolframscience.com/nksonline/page-1084f-text
Is radioactive decay random because of instrinsic randomness generation or because of an underlying real indeterminism in nature? That is an open issue. It is equivalent to the question whether any hidden variables model for QM (in this case, especially the weak force - decay depends on a balance in which that is relevant) is possible.
The possibility that such phenomena are "metaphysically random", "all the way down", certainly merits consideration and fits the evidence we have. It is the standard view of QM today. We cannot yet rule out all explanations that would derive that apparent randomness from an underlying deterministic system. We can place some constraints on any candidate deterministic system e.g. that it can't be completely local.
The NKS book hopes to find a deterministic network based model generating such apparent randomness by essentially the same mechanism as the randomness seen in rule 30. But this approach can't be said to have succeeded in that, yet. The NKS network approach is not the only attempt to find underlying deterministic generators for QM. If any of them works, whether there "really is" underlying indeterminism will be an open philosophical question, not decided by existing scientific theories. So one might say at present, the consensus view is that there probably is underlying indeterminism but the alternative that it is merely apparent cannot be ruled out.
One can advance definitions of randomness according to which anything produced by a simple underlying system, or satisfying definite constraints, is not to be considered as random. But such definitions shift the phenomenon of randomness away from the common sense meaning of the term, and seem to me to beg relevant questions. For example, unknown digits of pi are not random according to such definitions.
The NKS book discusses definitions of randomness in a section begining on page 552, and discusses the history of previous proposed definitions in a note on page 1067.
http://www.wolframscience.com/nksonline/page-552
http://www.wolframscience.com/nksonline/page-1067b-text
Personally (the following is simply my own view of these matters, not anything in the NKS book) I prefer a definition taken from ordinary language usage, and philosophically built on pragmatism. The test is what people are willing to do about it, not what they say about it - that is the pragmatism connection. I just use the following to distinguish between disagreements about definitions of terms, and real disagreements about the behavior of some system.
I say unknown digits of pi are random for practical purposes, because without calculating them beforehand, I would not be willing to bet (some livable amount, stipulate) a specified digit is a "4" if given only 2 to 1 odds, but I would be willing to if given 50 to 1 odds. You can narrow these ratios to a ball around "one out of ten". But the critical point is that there are odds ratios at which I would be willing to take opposite sides of the transaction.
By this sort of pragmatic definition, an analysis of rule 30 that can predict e.g. what the center column will be 100 steps beyond any point one has yet calculated, with a meaningful difference from "half 1, half 0", provides real information if the person with that analysis will take opposite sides of bets centered on some other value besides "one half", such that his "bid-ask spread" excludes "one half". (E.g. 0.55 to 0.65 that it will be a "1", would qualify. 0.45 to 0.6, would not).
Of course he might be wrong. Then someone else just consistently takes one side of such offered transactions with him. But such a willingness shows practical belief in the statement that the phenomenon is not "really random". Conversely, unwillingness to do so shows practical belief that the phenomenon is "random enough for practical purposes", whatever metaphysical hairs the disputant wishes to split, verbally.
If he claims to know what the system is going to do in the above sense, then he is disagreeing with me not about what random means, but about whether the system under consideration is (practically) random. Obviously he can do either. I just don't want to get the two confused. Some claims that a source of randomness is "pseudo" are claims that one can actually tell what it is going to do. And that is different from applying a "pseudo" just due to a preferred usage of terms or a preferred definition, without claiming one can actually tell what it is going to do.
There is a lot more in the book about it. Look in the index to explore related subjects. I hope this helps.
Posted by: Ray Donald Pratt
I bought NKS with the express purpose of learning a more fluid way of analyzing patterns in gambling games.
My one core belief is that a finite number of elements that are shuffled in a fairly routine way are never truly random and will always exhibit discernible patterns. I've seen this in every casino game I've ever taken the time to learn, watch and play.
As I go into NKS, I will ask for your thoughts about relationships between NKS and gambling games that occur to me, and I'll ask for nothing less than your most brutal honesty.
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