The Virgin Birth of Points
in [Physics]
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From: Robert J. Kolker on 12 Nov 2007 20:56 Lester Zick wrote: > Well I know enough of mathematics to have convinced you there is no > real number line. So what. The theory of real numbers can and is developed without any geometric content of all. Any geometrical associations with real numbers are merely aids to intuition, not logical necessity. In the nineteenth century a purely analytic foundations for the theory of real and complex variables was developed. Geometry was purged as a logical necessity. Of course, geometry can be very helpful for the right-brain operations associated with discovering new theorems to prove or new mathematical systems. Bob Kolker
From: Robert J. Kolker on 12 Nov 2007 20:57 Lester Zick wrote: > > > Hey it's not my problem, Bobby. I'm not the one who claims points have > zero length but are not of zero length.Modern mathematics is a heresy. Neither does any one else. You have created a straw man here. Measure is associated with certain -sets of points-, not the points themselves. Bob Kolker
From: Virgil on 12 Nov 2007 21:14 Lester Zick wrote: > > > Hey it's not my problem, Bobby. I'm not the one who claims points have > zero length but are not of zero length.Modern mathematics is a heresy. Ultra-heretic Zick accusing others of his own sin? It is to laugh!
From: Amicus Briefs on 13 Nov 2007 05:26 On Mon, 12 Nov 2007 14:45:25 -0800, John Jones <jonescardiff(a)aol.com> wrote: >A position may well not be a primitive, but the intersections of lines >construct positions, not points So if we change the name of "points" to "positions" we'll solve the problem?
From: Lester Zick on 13 Nov 2007 05:34
On Mon, 12 Nov 2007 17:39:01 -0500, "Robert J. Kolker" <bobkolker(a)comcast.net> wrote: >John Jones wrote: >> >> The intersections of lines are positions, not points. There is no >> precedent for creating a new metaphysical entity from the arbitrary >> arrangement of lines. I would have thought it obvious. But plainly I >> was mistaken. > >Take a pair of linear equations in two variables each of which define a >line. If the equations are not linearly dependent they determine a >unique solution (x,y) which is --- aha!---- the point of intersection. > >In a Euclidean Plane lines when they intersect at all, have a unique >point of intersection. And mathematical objects are not metaphysical >entities. They are brain farts the blow about in our skulls. Speak for thyself. ~v~~ |