[Question on Mechanisms of Randomness] - A New Kind of Science: The NKS ForumA New Kind of Science: The NKS Forum
Pages:1
Question on Mechanisms of Randomness
(Click here to view the original thread with full colors/images)
Posted by: Lawrence J. Thaden
On page 299 of the NKS book there begins a discussion of three mechanisms for randomness.
Suppose I have a cellular automaton with a rule that updates each cell by some algorithm that uses only one of the available neighbors, selecting which one to use by a random process that uses the Random[Integer] function.
Is the resulting randomness from the environment or intrinsic?
On the one hand this seems to fit the description of randomness from the environment for this is certainly a case in which “randomness is inserted during the evolution of a system” (p.304). Indeed at every step and at every cell the update algorithm calls upon an external mechanism to determine the neighbor that is to be used in the update process. Namely, Random[Integer].
On the other hand the Random[Integer] function is based on elementary rule 30 (page 317), the premier example of intrinsic randomness. So one might argue that intrinsic randomness is the kind manifest in such an algorithm.
Perhaps this is all a distinction without a difference.
However, I would certainly be pleased to know if it is intrinsic.
Posted by: Jason Cawley
I'd certainly consider that "from the environment". The distinction between instrinsic and environmental randomness does not depend on the final cause of any randomness in that environment (that is then imported to the system), but on whether the system's own evolution is generating randomness from its internal complexity, or merely interacting with a complicated world.
In your example, the system behaves in a complicated way because successive calls to Random are uncorrelated with each other. If, instead, you fixed this call to Random at a single value (1 say), presumably the apparently complexity would disappear. If it would not (that is, complexity remains when every call to Random is replaced by the integer, "1"), then you can say the system has the potential to generate randomness intrinsically. (If it does, but you are also tossing in randomness at every step, you can't separate the cause of any complexity seen in the outcome).
Randomness imported from beyond the boundaries of some system, can have any ultimate underlying cause. You could consult detailed initial conditions of a sensitive mechanical system by e.g. rolling dice. Or instrinsically generate randomness from a simple seed, using rule 30. Or hypothetically, measure electron spins. Or (an old fashion way) consult the nth digit of some real number in a table of logs or what have you. Anything imported just as uncorrelated with internal system elements counts as "from the environment".
Forum Sponsored by Wolfram Research
© 2004-2009 Wolfram Research, Inc. | Powered by vBulletin 2.3.0 © 2000-2002 Jelsoft Enterprises, Ltd. |
Disclaimer
vB Easy Archive Final - Created by Xenon and modified/released by SkuZZy from the Job Openings