I suppose Dennett is implying that the linear congruential generator below would take at least the number of bits in variables a, b, m, and x[0]. If those are 1-byte integers, then the bit count is at least 32 bits. Theres overhead for the actual code too. How do you measure that? Suppose the answer is 100 bits for the code including state. Then if you use it to generate a sequence of one gazillion values, that sequence would only contain the equivalent of 100 bits of information because it can be generated by a 100 bit algorithm.
I still suspect there might be circular logic here. Do we place no value on the energy needed to generate it? What if our entire universe can be described in a very simple equation that is just generated recursively or fractally by many iterations? If that equation was less than a megabyte, then would we argue that the entire works of Shakespeare must have less information? _____ From: friam-boun...@redfish.com [mailto:friam-boun...@redfish.com] On Behalf Of Roger Critchlow Sent: Thursday, April 23, 2009 12:37 AM To: nickthomp...@earthlink.net; The Friday Morning Applied Complexity Coffee Group Subject: Re: [FRIAM] random vs pseudo-random On Thu, Apr 23, 2009 at 1:05 AM, Nicholas Thompson <nickthomp...@earthlink.net> wrote: Can anybody help me understand this. (Please try to say something more helpful than the well-deserved, "Well, why do you THINK they call it pseudo-random, you dummy?")What DOES a pseudo randomizing program look like? This one is called a linear congruential generator: x[i+1] = (a * x[i] + b) modulo m x[i] is the current random number, x[i+1] is the next random number, for appropriate choice of a, b and m the sequence of numbers produced will go through all the numbers from 0 to m-1 in some order over and over again. The choice of a = 1, b = 1 enumerates in increasing order, and the choice of a = 1, b = -1 enumerates in decreasing order. Neither is a very good choice, but they aren't the only bad choices. For instance, a = 0 is probably the worst choice of linear congruential multiplier. You might try out different values for a and b in a spreadsheet with m = 17. Or just do it on paper. -- rec --
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