The Virgin Birth of Points
in [Physics]
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From: Schlock on 13 Nov 2007 18:10 On Tue, 13 Nov 2007 13:34:14 -0800, John Jones <jonescardiff(a)aol.com> wrote: >On Nov 13, 10:26?am, Amicus Briefs <ami...(a)curiae.net> wrote: >> On Mon, 12 Nov 2007 14:45:25 -0800, John Jones <jonescard...(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? > >I think many problems could be solved by not conflating point and >position. A position is not a point, nor a point a position. A >position is an object in a framework or construction; while a point, >like a line, is a framework for the construction of objects such as >positions. Frameworks are incommensurables while objects (positions) >are not. So the rules for frameworks are quite different to that of >the rules for objects. Perhaps Hibert rudimentally envisaged this when >he described points and lines as 'primitives'. Well that certainly clears it all up. Primitives are undefinable self contradictory assumptions of truth. Works for me. I define you as a primitive idiot.
From: Dave Seaman on 13 Nov 2007 18:15 On Tue, 13 Nov 2007 15:48:52 -0700, Amicus Briefs wrote: > On Tue, 13 Nov 2007 16:05:12 +0000 (UTC), Dave Seaman ><dseaman(a)no.such.host> wrote: >>> The position of a point is relative to the reference coordinate >>> system. So, position is an attribute on a point to locate it with >>> reference to the given coordinate system. >> >>> Does it make some sense? >> >>What if no coordinate system is specified? The definition of a measure >>space says nothing about a coordinate system. > Well then there is no measure space to measure against. What? >> For that matter, the >>important elements of a measure space are not the points (elements of the >>space itself), but rather the measurable sets (members of the specified >>signma-algebra). > "Signma-algebra"? I must have missed that one in ninth grade algebra. Sigma-algebra, of course. If you know what a sigma-algebra is, then you should know what a measure space is, and that nothing in the definition has anything to do with coordinates. -- Dave Seaman Oral Arguments in Mumia Abu-Jamal Case heard May 17 U.S. Court of Appeals, Third Circuit <http://www.abu-jamal-news.com/>
From: psa on 13 Nov 2007 18:36 On Nov 12, 4:13 pm, Venkat Reddy <vred...(a)gmail.com> wrote: > On Nov 12, 5:02 pm, David C. Ullrich <ullr...(a)math.okstate.edu> wrote: > > > > > > > On Sun, 11 Nov 2007 20:57:47 -0800, William Elliot > > > <ma...(a)hevanet.remove.com> wrote: > > >On Sun, 11 Nov 2007, Lester Zick wrote: > > > >> The Virgin Birth of Points > > >> ~v~~ > > > >> The Jesuit heresy maintains points have zero length but are not of > > >> zero length and if you don't believe that you haven't examined the > > >> argument closely enough. > > > >Clearly points don't have zero length, they have a positive infinitesimal > > >length for which zero is just the closest real approximation. > > > Erm, no. Points (or rather singletons) have zero length. > > I agree. Also, like I said in the other post, points can only exist as > boundaries of higher dimensional regions. Lines, surfaces, solids etc > can exist as regions in their own world and as boundaries in higher > dimensions. When they are in the role of a boundary they are not part > of any regions (of higher dimension). > > We can't observe life of a point as a region in its own dimensional > space. > > - venkat- Hide quoted text - > > - Show quoted text -
From: lwalke3 on 13 Nov 2007 18:38 On Nov 13, 1:27 pm, John Jones <jonescard...(a)aol.com> wrote: > On Nov 12, 11:59?pm, lwal...(a)lausd.net wrote: > > In this model, containment is mapped to a > > more complicated matter -- one can try > > bitwise AND (or OR) to come up with the > > relation onto which containment is mapped. > > The important part is that this points > > don't have "positions" at all. > If points are not positioned, as you say, then the line that has the > minimal requirement of two points by virtue of 1.7, is a concept, or > if you like, a set. The set has fractured and unfractured lines as its > members. The set has one of its line members fractured when two points > fall on the same position. Other fractured lines arise when 'before' > and 'after' points fall contrary to their expected positions. > Interesting. Here I was giving a model of I.1 to I.7 in which lines contain only two points. Of course, this is not the standard model of Hilbert I-V, in which lines contain a point for every real number. In the standard model, lines are obviously no longer "fractured." In the standard model, the primitives "point" and "line" are mapped to certain subsets of R^3. "Points" are mapped to singletons, while "lines" are mapped to uncountable sets. The elements of these sets are ordered triples of reals. If you like, one may call these triples "positions," since they have x,y,z coordinates to determine a position. Thus (0,0,0) is a position. But {(0,0,0)} is a point. Now consider the lines y = z = 0 (the x-axis) and x = z = 0 (the y-axis). So we ask, what is their intersection? The intersection must be a subset of both sets as lines. So the intersection can only be {(0,0,0)} -- which can only be a point, not a position.
From: psa on 13 Nov 2007 18:42
On Nov 12, 4:13 pm, Venkat Reddy <vred...(a)gmail.com> wrote: > On Nov 12, 5:02 pm, David C. Ullrich <ullr...(a)math.okstate.edu> wrote: > > > > > > > On Sun, 11 Nov 2007 20:57:47 -0800, William Elliot > > > <ma...(a)hevanet.remove.com> wrote: > > >On Sun, 11 Nov 2007, Lester Zick wrote: > > > >> The Virgin Birth of Points > > >> ~v~~ > > > >> The Jesuit heresy maintains points have zero length but are not of > > >> zero length and if you don't believe that you haven't examined the > > >> argument closely enough. > > > >Clearly points don't have zero length, they have a positive infinitesimal > > >length for which zero is just the closest real approximation. > > > Erm, no. Points (or rather singletons) have zero length. > > I agree. Also, like I said in the other post, points can only exist as > boundaries of higher dimensional regions. Lines, surfaces, solids etc > can exist as regions in their own world and as boundaries in higher > dimensions. When they are in the role of a boundary they are not part > of any regions (of higher dimension). > > We can't observe life of a point as a region in its own dimensional > space. > > - venkat- Hide quoted text - > > - Show quoted text - |