> > >
> > > Those "probabilities" multiply, of course. Assume only two text
variants,
> > > 24 "interesting numbers," and, say, 20 "interesting mathematical
> > > transformations." The probability of finding two of those numbers
under
> > > those circumstances is already fairly high. Add to that the concept
that
> > > "if not Gen 1 then perhaps Lev 1, etc. and the odds drop to almost
> > > certainty.
> >
> > OK, let's do the calculation.
> >
> > The agreement with the "interesting number" was to five places of
decimals,
> > so the odds of any given number on any particular text variant with any
> > particular mathematical transformation is 1e-5.
>
> Is it superfluous for me to again point out the fact, easily
provable by
> mathematical induction, that there is no "uninteresting number"?
>
I don't buy this argument at all. The gist of it as I understand it is that
there is a first "uninteresting number", therefore it's interesting because
it's the first uninteresting number, which leaves thereby makes the next
"uninteresting number" interesting.
Yes, I do I think the argument is both fallacious and superfluous. You are
constructing an "interestingness" criterion out of "lowest uninteresting",
and then use it to construct an arbitrarily long chain of uninteresting
numbers that are transformed to interesting ones via induction.
Furthermore, the argument appears to be only applicable to integers. The
argument at hand was about real numbers.
By contrast, pi and e are interesting because they turn up again and again
in physics and maths, and have real use in solving real problems. By
contrast, the 37th "uninteresting number", whatever that might be, probably
has no value at all. Furthermore, if you allow transcendental numbers such
as pi and e, you can't even enumerate the first 37 uninteresting numbers, as
there are uncountably many real numbers in any finite interval. So, while
your induction "proof" applies to integers (and I still don't think it's
relevant), it does not apply to reals.
Iain.
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