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Topic: Circular reasoning on a curve
Replies: 14   Last Post: Nov 11, 2013 12:40 PM

 Messages: [ Previous | Next ]
 ross.finlayson@gmail.com Posts: 2,720 Registered: 2/15/09
Re: Circular reasoning on a curve
Posted: Oct 29, 2013 10:18 PM

On Tuesday, October 29, 2013 4:36:44 PM UTC-7, fom wrote:
> On 10/29/2013 5:34 PM, Hetware wrote:
>

> > On 10/29/2013 5:20 AM, Peter Percival wrote:
>
> >> Hetware wrote:
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> >>> On 10/28/2013 9:57 PM, fom wrote:
>
> >>
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> >>>> But, your geometry without Descartes' innovation has no numbers.
>
> >>>
>
> >>> Then how do I get numbers from it?
>
> >>
>
> >> In one or other of the appendices to Hilbert's 'Foundations of geometry'
>
> >> there is an account of how various axioms of geometry imply various
>
> >> properties of numbers.
>
> >>
>
> >
>
> > I'm not familiar with that discussion.
>
> >
>
> > I believe it is impossible to completely separate our geometric
>
> > reasoning from analytical reasoning. The very notions of betweenness,
>
> > ordering, and even counting require some dimensional framework in order
>
> > to even think them. I am including time as a dimension for purposes of
>
> > this discussion.
>
> >
>
> > I find it tantalizing that our analytical mathematics can produce a
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> > number such as pi without any direct reference to any kind of geometric
>
> > object. There is some kind of supremacy of Euclidean over other
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> > geometries. For example, the geometry of general relativity is locally
>
> > Minkowskian, and at the low velocities of daily experience, Galilean.
>
> >
>
> > That is the environment in which our mind/brain evolved.
>
>
>
> Apparently, there are certain philosophers who uphold this view.
>
>
>
> For my part, I find the rejection of geometry which occurred in the
>
> late nineteenth and early twentieth century confusing. When the
>
> disputes over set theory and the paradoxes settled, Hilbert, Brouwer,
>
> and others turned to "intuitive", "a priori" notions. At the heart
>
> of these ideas is what should be called "inscriptional identity".
>
>
>
> This kind of identity is what Wittgenstein had in mind when arguing
>
> for the "eliminability of identity" from mathematical discourse.
>
>
>
> This kind of identity is what grounds the notion of number as
>
> monotone inclusive sequences of strokes:
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>
>
>
>
> |
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>
>
> ||
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> |||
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> ||||
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> These ideas, however, being grounded in inscriptional identity
>
> presume rigid motions. Geometrically, this is Euclidean geometry.
>
>
>
> Sometimes I think that all of these intelligent people have
>
> argued themselves stupid.
>
>
>
> Sometimes one must sit back and reconcile the arguments.

Curve is line from zero.

"For my part, I find the rejection of geometry which
occurred in the late nineteenth and early twentieth
century confusing. When the disputes over set theory and
the paradoxes settled, Hilbert, Brouwer, and others turned
to "intuitive", "a priori" notions. At the heart of these
ideas is what should be called "inscriptional identity".

This kind of identity is what Wittgenstein had in mind
when arguing for the "eliminability of identity" from
mathematical discourse.

This kind of identity is what grounds the notion of number
as monotone inclusive sequences of strokes: ..."

"These ideas, however, being grounded in inscriptional
identity presume rigid motions. Geometrically, this is
Euclidean geometry. "

What is this inscriptional identity?

Viete is good for your algebra. For example he discovered
the relations between sums of squares and cubes. Mitch or
fom here has him as basically inventing algebra (number
theory).

"I'm trying to recall the distinction twixt hyperbolic
geometry and hyperbola geometry, which is the geometry of
special relativity, post-Minkowski."

Minkowskian geometries have a time-like dimension as then
they have (or generally as Minkowski) three space
dimensions. In the geometric algebra, it's not always the
algebraic geometry. For Minkowski it is (the geometric
algebra). With the hyperbolic and the hyperbola in
geometry, of the space, as it is the Minkowski space, the
hyperbola (sp.) and conditions on the geometry for example
of Euclid's parallel postulate where Minkowski-space is
super-Euclidean space, of geometry, those are as to
parallel transport and the instanton.

The curve is the line through its points, the vector is
the point. Consider where the point is the curve and vice
versa. Where the vector is not the point, where the curve
goes through the points in general parallel transport, the
curve is the point. The vector is also the point as it
generally and usually is, with simply maintaining
estimation effects locally. Then, where that is transport
of effect beyond the frame, the curve is the vector
(parallel transport is uni-directional).

Regards, Ross Finlayson

Date Subject Author
10/28/13 Hetware
10/28/13 fom
10/28/13 Hetware
10/29/13 Peter Percival
10/29/13 Hetware
10/29/13 fom
10/29/13 Hetware
10/30/13 Peter Percival
10/30/13 Peter Percival
10/29/13 ross.finlayson@gmail.com
10/29/13 fom
10/29/13 ross.finlayson@gmail.com
10/30/13 Peter Percival
11/11/13 Shmuel (Seymour J.) Metz
10/29/13 Brian Q. Hutchings