The Virgin Birth of Points
in [Physics]
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From: Lester Zick on 1 Dec 2007 12:33 On Fri, 30 Nov 2007 22:46:35 -0700, Quint Essential <QT(a)archangel.net> wrote: >On Fri, 30 Nov 2007 11:33:50 -0700, Lester Zick ><dontbother(a)nowhere.net> wrote: > >>On Sun, 11 Nov 2007 14:40:29 -0700, Lester Zick >><dontbother(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. >> >>The epistemological problem for modern math is where do an infinite >>number of points required to unionize points into lines come from? >> >>Only one solid is needed to produce one surface and one surface >>required to produce one line but an infinite number of points are >>required to produce one line. And the difficulty is that we can only >>produce finite numbers of points through tangency or intersection. So >>where are all the points supposed to come from? Imagination? Otherwise >>we can only be left with a finite number of straight line segments >>defined between points. >> >>~v~~ > >So let me give you a hypothetical. What's wrong with assuming an >infinite number of points from which we construct lines and so on? Well of course the objective of mathematics are demonstrations of truth and not merely hypothetical assumptions. And this is one of the main themes I've been trying to stress throughout these threads. However even hypothetically the problem is that lines have direction and points don't. Consequently any infinity of points that might be assumed couldn't also be assumed to lie on any line in any direction. In other words given some line, infinite subdivision is possible but those results would not be points; they would be line segments defined by points of intersection. And given any infinity of points all you could produce are various line segments not lying along any line unless the line itself is defined first regardless of the points. ~v~~
From: Lester Zick on 1 Dec 2007 12:36 On Sat, 1 Dec 2007 08:54:26 -0800 (PST), Marshall <marshall.spight(a)gmail.com> wrote: >On Dec 1, 4:43 am, Venkat Reddy <vred...(a)gmail.com> wrote: >> On Dec 1, 2:09 pm, Marshall <marshall.spi...(a)gmail.com> wrote: >> > On Nov 30, 9:56 pm, Venkat Reddy <vred...(a)gmail.com> wrote: >> > > On Dec 1, 10:46 am, Quint Essential <Q...(a)archangel.net> wrote: >> >> > > > So let me give you a hypothetical. What's wrong with assuming an >> > > > infinite number of points from which we construct lines and so on?- >> >> > > Currently there is another thread "Tea cups and elephants" where >> > > people are unable decide whether an infinite number of zero width >> > > points can make a fininte extent line. >> >> > Hmmm. It seems like you didn't answer Quint's question. >> > Unless you meant to say that what is wrong with modeling >> > lines with points is that currently there is this other thread. >> >> I meant that it is not known whether an infinite number of points can >> produce a non-zero extent, that is line. > >There is not universal agreement, you mean. If that is your >standard, then mankind knows exactly nothing. In fact, we >might then posit an individual, a scrivener maybe, who >disagrees with everything. As long as this person is alive, >then for any statement A, you can say (by your standard) >it is not known if A. > >At least, if the scrivener is on usenet. One wouldn't necessarily expect universal agreement. One might however expect demonstrations of truth and not simply captious argumentation. ~v~~
From: G. Frege on 1 Dec 2007 12:46 On Sat, 01 Dec 2007 10:33:44 -0700, Lester Zick <dontbother(a)nowhere.net> wrote: > > Well of course the objective of mathematics are demonstrations of > truth and not merely hypothetical assumptions. And this is one of the > main themes I've been trying to stress throughout these threads. > Of course you just don't know what you are talking about. "Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true." (Bertrand Russell) F. -- E-mail: info<at>simple-line<dot>de
From: Lester Zick on 1 Dec 2007 12:53 On Fri, 30 Nov 2007 21:56:16 -0800 (PST), Venkat Reddy <vreddyp(a)gmail.com> wrote: >On Dec 1, 10:46 am, Quint Essential <Q...(a)archangel.net> wrote: >> On Fri, 30 Nov 2007 11:33:50 -0700, Lester Zick >> >> >> >> >> >> <dontbot...(a)nowhere.net> wrote: >> >On Sun, 11 Nov 2007 14:40:29 -0700, 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. >> >> >The epistemological problem for modern math is where do an infinite >> >number of points required to unionize points into lines come from? >> >> >Only one solid is needed to produce one surface and one surface >> >required to produce one line but an infinite number of points are >> >required to produce one line. And the difficulty is that we can only >> >produce finite numbers of points through tangency or intersection. So >> >where are all the points supposed to come from? Imagination? Otherwise >> >we can only be left with a finite number of straight line segments >> >defined between points. >> >> >~v~~ >> >> So let me give you a hypothetical. What's wrong with assuming an >> infinite number of points from which we construct lines and so on?- > >Currently there is another thread "Tea cups and elephants" where >people are unable decide whether an infinite number of zero width >points can make a fininte extent line. Venkat, the problem I'm having with the other threads is that they seem to be couched in very abstruse mathematical terms which are frankly difficult to decipher. What we have here is an epistemological rather than mathematical problem. There are those who believe that points constitute lines through unions, lines constitute surfaces presumably through unions of some kind, surfaces constitute solids and so on whom we can call infinitists. Then there are those, finitists, who believe causation is the other way around, that solids are defined in terms of surfaces, surfaces in terms of lines, and lines in terms of points. The problem is the methodology. Infinitists have no methodology for what they claim except what they refer to as some kind of mystical union. Finitists on the other hand have a methodology of the calculus and recirpocal processes of integration and differentiation (or disintegration as I like to call it) and intersection to explain the mechanics of their concepts. But the problem is epistemological and not mathematical. ~v~~
From: Robert J. Kolker on 1 Dec 2007 13:12
Venkat Reddy wrote: > > I meant that it is not known whether an infinite number of points can > produce a non-zero extent, that is line. Nonsense. All finite intervals have the same cardinality, namely c, the cardinality of the reals. But they have various measures. For the simple case, the measure of an interval is the difference bewteen the end points. The measure (length) of the unit interval is 1. It has nothing to do with adding up the widths of points. Bob Kolker |