|To:||"[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>|
|From:||Pat Hayes <phayes@xxxxxxx>|
|Date:||Tue, 12 Feb 2008 15:19:01 -0600|
At 12:08 PM -0600 2/12/08, Schiffel, Jeffrey A wrote:
A series of unfair coin tosses can easily be random. The distribution of the random variable will not be uniform (as is the case of a fair coin), but it may still be random.
It may be a random variable in the mathematical sense, of course. (http://en.wikipedia.org/wiki/Random_variable)
But this rather begs the question, as this definition already incorporates the notion of probability. For example, a completely unfair dice which always gives '1' is a random variable in this sense.
But OK, let me accede to my own strictures. You are right, any variable which incorporates a degree of chance may be called 'random'; and Sean is right that a sampling of such values may well provide statistical information about likelihoods. Nevertheless, my original point still holds. When we are talking about what is usually called a 'random sequence' of numbers or bits, as spoken of in Kolmogoroff theory, what makes such a sequence have maximal information density is that there is no way to compute any one of its values from all the others.
It is just that the probabilities must be described by a different distribution. Pink noise is a simple example, since the randomness compared to white noise is red-shifted.
-- Jeffrey Schiffel
40 South Alcaniz St.
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