Posted by
Russell Standish-2 on
URL: http://friam.383.s1.nabble.com/Model-of-induction-tp7588431p7588472.html
On Tue, Dec 13, 2016 at 08:41:12PM -0700, Nick Thompson wrote:
> Hi, Russell S.,
>
> It's a long time since the old days of the Three Russell's, isn't it? Where have all the Russell's gone? Good to hear from you.
>
> This has been a humbling experience. My brother was a mathematician and he used to frown every time asked him what I thought was a simple mathematical question.
>
> So ... with my heart in my hands ... please tell me, why a string of 100 one's , followed by a string of 100 2's, ..., followed by a string of 100 zero's wouldn’t be regarded as random. There must be something more than uniform distribution, eh?
>
Yes - the modern notion of a random string is that it is
uncompressible by a Turing machine shorter than itself.
Obviously, you can exploit nonuniformity to provide a compression - eg
the way that 'e' and 't' are represented by single . and -
respectively provides a compression of random English language
phrases. Hence why uniformity is one test of randomness
That is why non-uniform random, whilst a thing, must be defined by an
algorithmic transformation to a uniform random thing (the
algorithmically uncompressible things mentioned above).
> Is there a halting problem lurking here?
>
Absolutely.
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