Re: [ontolog-forum] Axiomatic ontology

[Pat Hayes <phayes@xxxxxxx>]

At 1:48 PM -0500 2/12/08, Bill Andersen wrote:

> Hi Pat.
>
> On Feb 12, 2008, at 12:28 , Pat Hayes
> wrote:
> > 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.
>
> How can you tell that any variable is
> random based on a finite number of trials?

I should have said, one can gain measurable confidence in the hypothesis that it is random.

Pat

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