The Virgin Birth of Points
in [Physics]
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From: John Jones on 12 Nov 2007 10:50 On Nov 12, 3:42?pm, Dave Seaman <dsea...(a)no.such.host> wrote: > 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/> An interval [a,b] is composed of positions, not points. But even positions are constructions, and it is not appropriate to analyse a construction in spatial terms.
From: Lester Zick on 12 Nov 2007 12:08 On Mon, 12 Nov 2007 05:13:10 -0800, Venkat Reddy <vreddyp(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. Except the main purpose of this thread is less to discuss the zero length of points than the heresy of maintaining self contradictory predicates, as in "has zero length" and "is not of zero length". ~v~~
From: Lester Zick on 12 Nov 2007 12:15 On Sun, 11 Nov 2007 20:57:47 -0800, William Elliot <marsh(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. I don't see how points "clearly" have infinitesimal length unless they're infinitesimal to begin with. Clearly Newton didn't think points were infinitesimal nor did Leibniz or they wouldn't have drafted the notations they used. And Newton's calculations of tangents were only defined at one point not at one infinitesimal. We have a certain arithmetic notation such as 5-5=0 in which the difference between 5 and itself is not infinitesimal but zero. Nor is the difference between a line and itself infinitesimal but zero. ~v~~
From: Lester Zick on 12 Nov 2007 12:15 On Mon, 12 Nov 2007 06:48:11 -0500, "Robert J. Kolker" <bobkolker(a)comcast.net> wrote: >William Elliot wrote: > > >> >> Clearly points don't have zero length, they have a positive infinitesimal >> length for which zero is just the closest real approximation. > >You don't need to resort to non-standard analysis. Within the realm of >standard real numbers, the matter is settle using measure (either Borel >or Lebesque) I wouldn't call the calculus non standard analysis. ~v~~
From: Lester Zick on 12 Nov 2007 12:17
On Mon, 12 Nov 2007 06:02:39 -0600, David C. Ullrich <ullrich(a)math.okstate.edu> wrote: >On Sun, 11 Nov 2007 20:57:47 -0800, William Elliot ><marsh(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. > >************************ Then I'm curious about this unionizing of points people talk about. ~v~~ |