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Re: Problems with Infinity?
Posted:
Feb 26, 2013 10:18 PM
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On Feb 26, 9:59 am, "Brian M. Scott" <b.sc...@csuohio.edu> wrote:
> On Tue, 26 Feb 2013 08:19:02 -0800 (PST), "Ross A.
> Finlayson" <ross.finlay...@gmail.com> wrote in
> <news:a559e5f5-7d28-46d9-a883-2e5232103382@w2g2000pbw.googlegroups.com>
> in rec.arts.sf.written,sci.math:
>
> > On Feb 25, 3:18 pm, "Brian M. Scott" <b.sc...@csuohio.edu> wrote:
> >> On Mon, 25 Feb 2013 14:11:50 -0800 (PST), Quadibloc
> >> <jsav...@ecn.ab.ca> wrote in
> >> <news:34c65c83-5bd3-4af1-9590-dda5a0c4afbb@f5g2000pbs.googlegroups.com>
> >> in rec.arts.sf.written,sci.math:
> >>> On Feb 25, 3:20 am, "Brian M. Scott" <b.sc...@csuohio.edu> wrote:
> >>>> Good grief. Is that crackpot still around?
> >>> Who, me?
> >> No, Ross Finlayson.
>
> [...]
>
> > Get used to it.
>
> No need: I've not read sci.math in years. Some idiot added
> it to this thread, and I didn't notice immediately.
>
> > Those things are true, what I wrote: nothing more,
> > nothing less
>
> What you wrote was partly false and partly just nonsense.
>
> [...]
>
> > Ross Finlayson
> > B.S., Mathematics
>
> You should ask for your money back. Or remove the comma.
But, I got a full ride.
You deserve a Ph.D. if you've contributed in your dissertation a novel
advancement of human knowledge and here mathematics. And a practicum
isn't a thesis.
Piled higher and deeper.
Then back to layman ruminations on mathematical infinity as largely
the community here might find science and speculative fiction of
particular insight and perspective, for hard science or the
fantastical in compelling themes, no, transfinite cardinals have not
yet found a particularly suited place in physics. That's not for lack
of trying.
From the unbounded to the infinite in the large, the universe, to the
microscopic and atomic and infinitesimal, the universe, physicists
today ponder how there are infinitesimal strings some as many orders
of magnitude smaller than the hydrogen nucleus as fundamental point
particle than it is to us, and how the universe is as many orders of
magnitude more grand than all our anthropocentric view can partake
around us. They confront these notions that reflect, as far as is
logical in expectation, mathematics, the Platonist of what is. And,
it is what it is. Where traditionally mathematics led physics, our
modern globalized experiments leave us more data than the mathematics,
of the day, contain.
The Universe, as set, of its elements, for all functions from things
to things, exists.
And, Zeno of Elea's archer's arrow: finds its mark.
Satisfactorially, if perhaps only partially resolved in methods of
exhaustion since even the simple consideration of potential and actual
in the infinite (and not all of Archimedes' infinities are
Archimedean): that analysis of the continuum with its perfect results
is in the countable.
The Universe exists and would be its own powerset: a contradiction to
that it is a regular, well-founded infinity. (And there are quite
modern theories with irregular infinities that have little to do with
large cardinals, which, in a well-founded universe, would simply be
cardinals already.) A paradox, some might say, but the Universe, or
via MWI or "multiverse" one and the uni-verse, exists and we are only
in it. The collection of all ordinals, would itself be an ordinal.
Russell's set of all sets not containing itself, does, exactly as what
would be the well-founded universe, would be.
So, measure theory founding real analysis uses countable (and only
countable) additivity for all results as they match results of
geometry, for evaluating area, and, though shoehorned into measure
theory (for simply the the non-measurable instead of the
polydimensional of Vitali's points), transfinite cardinals as supposed
foundation, for mathematics, find yet no edifice, as physics.
It's always one more.
Regards,
Ross Finlayson
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