The Virgin Birth of Points
in [Physics]
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From: Venkat Reddy on 12 Nov 2007 08:13 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
From: Hero on 12 Nov 2007 10:06 Robert wrote: > 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. > > In Euclidean space a set which has exactly one pont as a member has > measure zero. But you can take the union of an uncountable set of such > singleton sets and get a set with non-zero measure. > What measure will give a non-zero number/value? With friendly greetings Hero
From: John Jones on 12 Nov 2007 10:40 On Nov 11, 9:40?pm, Lester Zick <dontbot...(a)nowhere.net> 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. > > ~v~~ Points have zero length when construed as lying in a spatial framework. However, points have no length because points are not objects that arise in a spatial framework. Positions, not points, arise in the spatial framework, and positions are always constructions. I conclude that the question about points cannot be a logical inquiry or someone here would have been able to sort it out...
From: Randy Poe on 12 Nov 2007 10:40 On Nov 12, 10:06 am, Hero <Hero.van.Jind...(a)gmx.de> wrote: > Robert wrote: > > 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. > > > In Euclidean space a set which has exactly one pont as a member has > > measure zero. But you can take the union of an uncountable set of such > > singleton sets and get a set with non-zero measure. > > What measure will give a non-zero number/value? The Lebesgue measure of the interval [0,1] is 1. The Lebesgue measure of every finite and countable subset of that interval is 0. The Lebesgue measure of the Cantor set, which is uncountable, is also 0. Is that what you were asking? - Randy
From: Dave Seaman on 12 Nov 2007 10:42
On Mon, 12 Nov 2007 07:06:39 -0800, Hero wrote: > Robert wrote: >> 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. >> >> In Euclidean space a set which has exactly one pont as a member has >> measure zero. But you can take the union of an uncountable set of such >> singleton sets and get a set with non-zero measure. >> > What measure will give a non-zero number/value? Lebesgue measure will do so, not for all possible uncountable sets, but for some. For example, the Lebesgue measure of an interval [a,b] is its length, b-a. -- 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/> |