Re: [ontolog-forum] Axiomatic ontology

[Pat Hayes <phayes@xxxxxxx>]

At 10:14 AM +0000 2/12/08, Barker, Sean (UK) wrote:

> Pat's claim "The definition of a random sequence is that no
> matter how
> much of it you have, there is no way even in principle to compute
> any
> information about the next item." is true only where you
> exclude
> probabilistic estimates (which you might do depending on how you
> interpret "information"). For example, if you encode the
> tosses of a
> coin as a bit stream, as you continue to observe the bit stream,
> you
> will be able to make increasing accurate estimates of the
> probability
> that the next bit will be a 1. Given the additional knowledge that
> this
> is the encoding of coin flips, you will also be able to estimate
> the
> probability that it is a fair
> coin.

No, wait. A series of tosses of an unfair coin is not a random sequence. One gets randomness just when the actual probability of each toss being a head is 0.5 precisely.

What you say above is correct, of course, but it can be translated as: if a series of bits is not random, this can be detected with increasing accuracy as the series gets longer. Also, of course, if it is random, this can also be detected (if it were previously unknown), but that does not mean that any particular toss can be predicted.

Pat

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