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From: porky_pig_jr on 20 Jun 2010 20:21
On Jun 20, 5:18 pm, Arturo Magidin <magi...(a)member.ams.org> wrote:
> On Jun 20, 3:40 pm, BURT <macromi...(a)yahoo.com> wrote:
>
> > On Jun 20, 1:14 pm, purple <pur...(a)colorme.com> wrote:
>
> > > On 6/20/2010 2:34 PM, BURT wrote:
>
> > > > Lets say you accelerate; you have a starting speed and and end speed.
> > > > But you must go through every quantity of speed inbetween down to the
> > > > infinitely small. This is similar to Zeno with infinities in distance
> > > > passed through in finite time. There are transcendental quantities.
>
> > > The universe has no problems dealing with a continuum.
>
> > The math is called the Continuum Hypothesis.
>
> Ehr, no, it really is not called that.
>
> (There *is* something called "the Continuum Hypothesis" in math, but
> it has nothing to do with anything that has been mentioned or alluded
> to in this thread)
>
> --
> Arturo Magidin

Please don't spoil such a beautiful thread with some ugly facts.
From: BURT on 20 Jun 2010 23:44
On Jun 20, 2:18 pm, Arturo Magidin <magi...(a)member.ams.org> wrote:
> On Jun 20, 3:40 pm, BURT <macromi...(a)yahoo.com> wrote:
>
> > On Jun 20, 1:14 pm, purple <pur...(a)colorme.com> wrote:
>
> > > On 6/20/2010 2:34 PM, BURT wrote:
>
> > > > Lets say you accelerate; you have a starting speed and and end speed.
> > > > But you must go through every quantity of speed inbetween down to the
> > > > infinitely small. This is similar to Zeno with infinities in distance
> > > > passed through in finite time. There are transcendental quantities.
>
> > > The universe has no problems dealing with a continuum.
>
> > The math is called the Continuum Hypothesis.
>
> Ehr, no, it really is not called that.
>
> (There *is* something called "the Continuum Hypothesis" in math, but
> it has nothing to do with anything that has been mentioned or alluded
> to in this thread)
>
> --
> Arturo Magidin

The Continuum Hypothesis is about sizes of infinity of the infinitely
small. And this is a higher way for math to define finite quantities.

Mitch Raemsch
From: zookumar yelubandi on 21 Jun 2010 05:33
porky_pig_jr(a)my-deja.com wrote:
> On Jun 20, 4:14 pm, purple <pur...(a)colorme.com> wrote:
> > On 6/20/2010 2:34 PM, BURT wrote:
> > > Lets say you accelerate; you have a starting speed and and end speed.
> > > But you must go through every quantity of speed inbetween down to the
> > > infinitely small. This is similar to Zeno with infinities in distance
> > > passed through in finite time. There are transcendental quantities.
> >
> > The universe has no problems dealing with a continuum.
>
> I disagree. We *do not know* if universe is continuum. And the
> mathematical model of continuum (say, the real line) is exactly where
> Zone paradox arises. So this s not the accident the maths stays away
> from the notion of "movement" as well as "time" etc. Those are not
> math concepts, so it leaves it to physics. On the other hand, physics
> is free to apply to universe whatever mathematical model is suitable.
> Continuum is one is them, but continuum breaks down in some instances
> (so we may want to replace it with some discrete model). Zeno paradox
> is one example. But it's not maths' problem. Rather problem from
> choosing continuum model to describe some physical concepts.


Intuition tells us that the discrete and the continuous are
different orderings of the same. IOW, what is discrete is merely an
ordering of the continuum. Discrete is to particles ... as continuum is
to waves ... with waves being the reduced form of particles, as it were.
The human brain (and science) is not built to understand the discrete as
something apart from an ordering of the continuous. It connects the
gaps between points A and B by postulating all kinds of stuff in
between, e.g. strings, dark matter, vacuum, aether, etc. Granted,
there may be a case where the discrete and the continuous are separable.
But if that is the case, the human brain and science are limited from
having access to that understanding. Of course, when that happens we
are left with an article of faith, i.e. not science.

I think you make a good point about the continuum model perhaps
being just one model among others. Who really knows? Still, my best
intuition tells me that space and matter are attributes of the same,
i.e. different aspects of the continuum; moreover, that our
understanding of the "same" ("continuum") is as elusive as our
understanding of "infinity", "the infinitesimal", "the limit of
fractals", etc.

To wit, if things are connected to each other, they are part of
a continuum. As best can be discerned, everything in the Universe is
connected to everything else, however small the connection. MHO,OC.


Uncle Zook


From: Arturo Magidin on 24 Jun 2010 00:47
On Jun 20, 10:44 pm, BURT <macromi...(a)yahoo.com> wrote:
> On Jun 20, 2:18 pm, ArturoMagidin<magi...(a)member.ams.org> wrote:
>
>
>
> > On Jun 20, 3:40 pm, BURT <macromi...(a)yahoo.com> wrote:
>
> > > On Jun 20, 1:14 pm, purple <pur...(a)colorme.com> wrote:
>
> > > > On 6/20/2010 2:34 PM, BURT wrote:
>
> > > > > Lets say you accelerate; you have a starting speed and and end speed.
> > > > > But you must go through every quantity of speed inbetween down to the
> > > > > infinitely small. This is similar to Zeno with infinities in distance
> > > > > passed through in finite time. There are transcendental quantities.
>
> > > > The universe has no problems dealing with a continuum.
>
> > > The math is called the Continuum Hypothesis.
>
> > Ehr, no, it really is not called that.
>
> > (There *is* something called "the Continuum Hypothesis" in math, but
> > it has nothing to do with anything that has been mentioned or alluded
> > to in this thread)

> The Continuum Hypothesis is about sizes of infinity of the infinitely
> small.

Again, no, it's not really that.

> And this is a higher way for math to define finite quantities.

I have no idea what "this" may be, higher, lower, or co-planar, but I
do know that it is *not* "the Continuum Hypothesis", just like I know
that it is also not "A Hearbreaking Work of Staggering Brilliance."

--
Arturo Magidn
From: BURT on 30 Jun 2010 14:05
On Jun 23, 9:47 pm, Arturo Magidin <magi...(a)member.ams.org> wrote:
> On Jun 20, 10:44 pm, BURT <macromi...(a)yahoo.com> wrote:
>
>
>
>
>
> > On Jun 20, 2:18 pm, ArturoMagidin<magi...(a)member.ams.org> wrote:
>
> > > On Jun 20, 3:40 pm, BURT <macromi...(a)yahoo.com> wrote:
>
> > > > On Jun 20, 1:14 pm, purple <pur...(a)colorme.com> wrote:
>
> > > > > On 6/20/2010 2:34 PM, BURT wrote:
>
> > > > > > Lets say you accelerate; you have a starting speed and and end speed.
> > > > > > But you must go through every quantity of speed inbetween down to the
> > > > > > infinitely small. This is similar to Zeno with infinities in distance
> > > > > > passed through in finite time. There are transcendental quantities.
>
> > > > > The universe has no problems dealing with a continuum.
>
> > > > The math is called the Continuum Hypothesis.
>
> > > Ehr, no, it really is not called that.
>
> > > (There *is* something called "the Continuum Hypothesis" in math, but
> > > it has nothing to do with anything that has been mentioned or alluded
> > > to in this thread)
> > The Continuum Hypothesis is about sizes of infinity of the infinitely
> > small.
>
> Again, no, it's not really that.
>
> > And this is a higher way for math to define finite quantities.
>
> I have no idea what "this" may be, higher, lower, or co-planar, but I
> do know that it is *not* "the Continuum Hypothesis", just like I know
> that it is also not "A Hearbreaking Work of Staggering Brilliance."
>
> --
> Arturo Magidn- Hide quoted text -
>
> - Show quoted text -

There is now a higher way to think of the finites.

Mitch Raemsch
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