The Virgin Birth of Points
in [Physics]
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From: Randy Poe on 14 Nov 2007 13:05 On Nov 14, 12:29 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: > On Wed, 14 Nov 2007 08:32:37 -0800, Randy Poe <poespam-t...(a)yahoo.com> > wrote: > > > > >On Nov 13, 10:09 pm, William Hughes <wpihug...(a)hotmail.com> wrote: > >> On Nov 13, 9:58 pm, Traveler <trave...(a)noasskissers.net> wrote: > > >> > On Tue, 13 Nov 2007 18:30:29 -0800, William Hughes > > >> > <wpihug...(a)hotmail.com> wrote: > >> > >You need to define points and line segments. > > >> > Nobody can define them in any way that does not lead to an infinite > >> > regress. > > >> Piffle. > > >Well, Hilbert didn't say exactly that, but I believe the > >point of his comment that "One must be able to say at > >all times-instead of points, lines, and planes---tables, > >chairs, and beer mugs" was that you *don't* need to > >define these things, only the axioms that define their > >properties. > > So axioms that define their properties don't define them? No, they don't. Hence the assertion that the words "tables, chairs, and beer mugs" could be substituted for "points, lines, and planes" without changing the theory. > Mirabile dictu! You are continually amazed by the most elementary things. - Randy
From: Robert J. Kolker on 14 Nov 2007 13:48 Lester Zick wrote: > > So axioms that define their properties don't define them? Mirabile > dictu! Axioms -assert- the properties possesed by the undefined objects. For exampoe: Whatever a point is, a pair of them determine a line segment (whatever that is) uniquely. Mathematics at this level of abstraction and with an axiomatic (or postulational) orientation consists of drawing conclusion from the axioms (or postulates) by means of logical inference. Bob Kolker
From: Robert J. Kolker on 14 Nov 2007 13:49 Schlock wrote: > > > Or would you say you want a size pi pair of shoes? Actually my shoe size is 3*pi with e width. Bob Kolker
From: Robert J. Kolker on 14 Nov 2007 13:50 Lester Zick wrote: > > So, Bobby, if space doesn't exist what do you plan to do with > transcendentals? What one does with any real number. Use it in proving theorems or use it in physical applications. By the way, it is Louis who insists that space does not exist, not me. Bob Kolker
From: John Jones on 14 Nov 2007 15:33
On Nov 12, 8:48?pm, Dave Seaman <dsea...(a)no.such.host> wrote: > On Mon, 12 Nov 2007 11:31:22 -0800, John Jones wrote: > > On Nov 12, 6:05?pm, Dave Seaman <dsea...(a)no.such.host> wrote: > >> On Mon, 12 Nov 2007 07:50:52 -0800, John Jones wrote: > >> > 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: > >> >> > 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. > > >> > 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. > > >> I think you need to learn some measure theory. This is a question about > >> mathematics, by the way, not philosophy. > > >> - Show quoted text - > > I think you need to distinguish between a position and a point before > > wildly conflating them in both a philosophical and mathematical > > confusion. > > In my statement that you quoted, I used neither of the terms "position" > or "point". I mentioned only Lebesgue measure, uncountable sets, and > intervals. Exactly what is your, er, point? Why do I need to distinguish > between terms that I didn't use? > > Neither of those is a precise mathematical term, by the way. The meaning > depends on context, but to me a "point" is a member of some abstract > space (possibly a vector space, or a topological space, or a metric > space, or a measure space, or a Banach space, or whatever). A > "position", on the other hand, suggests a point that is given in some > coordinate system. That doesn't always apply. Lots of times we talk > about points in situations where there are no coordinates in sight. > I consider "position" to be too limited a term for that reason. > > -- > 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/>- Hide quoted text - > > - Show quoted text - It seems you cannot understand the things you write. Let me put you straight. You said: 'I think you need to learn some measure theory. This is a question about mathematics, by the way, not philosophy.' Now then. Either you are talking about my concerns about positions or points, or you are implying by the term 'this' that Lebesque measures are really all we need to know about when doing mathematics! Play games with me and you will come off worse. Let me put you right on another point. Please, don't use the term 'abstract' in description. It indicates only the limit of understanding. |