The Virgin Birth of Points
in [Physics]
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From: Virgil on 14 Nov 2007 18:39 In article <fhg0oe$kq3$1(a)mailhub227.itcs.purdue.edu>, Dave Seaman <dseaman(a)no.such.host> wrote: > On Wed, 14 Nov 2007 15:18:24 -0800, John Jones wrote: > > On Nov 14, 9:51?pm, Randy Poe <poespam-t...(a)yahoo.com> wrote: > >> On Nov 14, 4:20 pm, John Jones <jonescard...(a)aol.com> wrote: > >> > >> > Steenrod must be big in some arena, but to use the term 'abstract' in > >> > any context except art and everyday conversation is fudge. > >> > >> You are decreeing that we aren't allowed to use the > >> abstract concept of a number? We aren't allowed to > >> say "2"? We have to only refer to concrete things, > >> like 2 apples or 2 worms? > >> > >> - Randy > > > Abstract can be used as a get away with anything term, a sort of one > > size fits all. An abstract "2" does not fit me. > > In mathematics it is perfectly common to take ordinary words such as > "group", "ring", "set", "operator", or "manifold" and endow them with > meanings undreamed of in the ordinary world. > > "Mathematicians are a kind of Frenchman; if one says something > to them, they translate it into their own language, and it > immediately becomes something completely different." > > - Goethe
From: Marshall on 14 Nov 2007 18:44 On Nov 14, 1:27 pm, Dave Seaman <dsea...(a)no.such.host> wrote: > > > > It's not good enough to say that your reference to measure theory had > > career guidance value rather than argumentative value. > > Not good enough for what? I answered Hero's question, and I did so > without being argumentative. You are the one who is determined to start > an argument. Dave, You should know that that person you're conversing with is a troll, and is only interested in argument for argument's sake. He has no interest in mathematics or logic. Marshall
From: Lester Zick on 14 Nov 2007 19:09 On Wed, 14 Nov 2007 17:32:32 +0000 (UTC), Dave Seaman <dseaman(a)no.such.host> wrote: >On Wed, 14 Nov 2007 09:54:53 -0700, Amicus Briefs wrote: >> On Tue, 13 Nov 2007 23:15:37 +0000 (UTC), Dave Seaman >><dseaman(a)no.such.host> wrote: > >>>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. > >> You don't measure against rationals? The objective of science is not >> to confuse predicates. That was the purpose of this thread as I >> understand it. > >A measure is a real-valued function defined on a sigma-algebra of sets. >If there is confusion here, it is entirely on your end. I guess we'll just have to take your word for it. ~v~~
From: Lester Zick on 14 Nov 2007 19:10 On Wed, 14 Nov 2007 12:35:20 -0800, John Jones <jonescardiff(a)aol.com> wrote: >On Nov 13, 1:42?pm, Venkat Reddy <vred...(a)gmail.com> wrote: >> On Nov 13, 12:31 am, John Jones <jonescard...(a)aol.com> 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: >> > > >> > 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. >> >> > > I think you need to learn some measure theory. This is a question about >> > > mathematics, by the way, not philosophy. >> >> > > -- >> > > 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 - >> >> > I think you need to distinguish between a position and a point before >> > wildly conflating them in both a philosophical and mathematical >> > confusion. >> >> 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? >> >> - venkat- Hide quoted text - >> >> - Show quoted text - > >Yes, but why do we need a position to indicate a point when a position >is quite adequate by itself? To do what, pray tell? ~v~~
From: Lester Zick on 14 Nov 2007 19:12
On Wed, 14 Nov 2007 12:51:38 -0800, John Jones <jonescardiff(a)aol.com> wrote: >On Nov 13, 4:06?pm, "Robert J. Kolker" <bobkol...(a)comcast.net> wrote: >> Venkat Reddy 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? >> >> In a way. Position is a name we give to points to identify them uniquely. >> >> Bob Kolker > >You would then, propose the notion of unpositioned points, and lines >composed of unpositioned points. 'Points' are superfluous. Clearly either you or points are superfluous. ~v~~ |