Re: Han's startling new set theory.

Timothy Little wrote:
> imaginatorium@xxxxxxxxxxxxx wrote:
> > Han de Bruijn wrote:
> >> The decimal expansion of sqrt(2) does not repeat. You can check that
> >> by computing.
> >
> > Really?? I mean, this is finite computing, with your "microscope",
> > right? How long, very roughly, does it take to check that sqrt(2)
> > doesn't repeat?
>
> That just makes it like most scientific hypotheses: falsifiable, but
> not verifiable.


Not really. Scientific hypotheses are provisional statements *about*
the real world, so the real world has the last say on whether they are
true or not. The fact that sqrt(2) is irrational is a mathematical
statement, and doing an empirical investigation to attempt to falsify
it is just silly - like doing a search for a four-sided triangle.

Han has a point - some bits of mathematics have "engineering"
consequences in the real world, some don't at present. But predicting
what branches of maths will never turn out to have real world
consequences is a tricky business, as most famously exemplified by G H
Hardy's comments in "A mathematician's apology".

Brian Chandler
http://imaginatorium.org

.

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