The Definition of Points
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From: Lester Zick on 22 Mar 2007 13:54 On Wed, 21 Mar 2007 20:43:22 -0400, Bob Kolker <nowhere(a)nowhere.com> wrote: >This view of mathematics as empirical content free is a relatively >modern view. So what about the axioms, Bob? Are they empirical or just false? > In the beginning, mathematics was thought to be talking >about the world. It still is. > But Euclidean geometry can't be -true- in the factual >sense since there are non-Euclidean. And is Euclidean geometry a limiting case and without Euclidean geometry are non Euclidean geometries true? > Euclidean geometry is readily >-applied- to flat spaces with a straightforward pythagorean metric. And without Euclidean geometry non Euclidean geometries aren't applicable to anything. ~v~~
From: Lester Zick on 22 Mar 2007 13:56 On Wed, 21 Mar 2007 22:42:11 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On Tue, 20 Mar 2007 23:47:48 -0500, Tony Orlow <tony(a)lightlink.com> >> wrote: >> >>> Bob Kolker wrote: >>>> Tony Orlow wrote: >>>> >>>>> You know that's not what I mean. >>>> I do? Then what do you mean. >>>> >>>> >>>> How do you measure the accuracy of the >>>>> premises you use for your arguments? You check the results. That's the >>>>> way it works in science, and that's the way t works in geometry. If some >>>> But not in math. The only thing that matters is that the conclusions >>>> follow from the premises and the premises do not imply contradictions. >>>> Matters of empirical true, as such, have no place in mathematics. >>>> >>>> Math is about what follows from assumptions, not true statements about >>>> the world. >>>> >>>> Bob Kolker >>> If the algebraic portions of your mathematics that describe the >>> geometric entities therein do not produce the same conclusions as would >>> be derived geometrically, then the algebraic representation of the >>> geometry fails. Hilbert didn't just pick statements out of a hat. >>> Rather, he didn't do so entirely, though they could have been >>> generalized better. In any case, they represent facts that are >>> justifiable, not within the language of axiomatic description, but >>> within the spatial context of that which is described. >> >> Well Hilbert seems to have had a penchant for tables and beer bottles >> in his non definitions of lines and points. >> >> ~v~~ > >Beer bottle are better on the table than the floor, that's for sure. Hilbert mostly wound up on the floor I expect. ~v~~
From: Lester Zick on 22 Mar 2007 14:02 On 22 Mar 2007 06:24:46 -0700, "PD" <TheDraperFamily(a)gmail.com> wrote: >On Mar 21, 6:00 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >> >> Well I can tell as soon as boobirds like Stephen come out the cause is >> hopeless. At least I'm witty. > >Just keep telling yourself that, Lester. Actually others say it. >Oh, and perhaps you might ask yourself why you are exercising your >self-acclaimed wit on a *science* group, where wit is not particularly >of value. Wit like motions to adjourn is always in order. Nor is truth apparently of value to empirics. In fact they can't handle the truth. They proclaim it never and mock it ever. > Wouldn't you be having more fun at rec.humor.arent.I.clever >or alt.witty.perceived.self? As previously noted brevity is the soul of wit and you're neither. ~v~~
From: PD on 22 Mar 2007 14:12 On Mar 22, 12:28 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: > On Wed, 21 Mar 2007 22:24:22 -0500, Tony Orlow <t...(a)lightlink.com> > wrote: > > > > > > >Lester Zick wrote: > >> On Wed, 21 Mar 2007 07:40:46 -0400, Bob Kolker <nowh...(a)nowhere.com> > >> wrote: > > >>> Tony Orlow wrote: > >>>> There is no correlation between length and number of points, because > >>>> there is no workable infinite or infinitesimal units. Allow oo points > >>>> per unit length, oo^2 per square unit area, etc, in line with the > >>>> calculus. Nuthin' big. Jes' give points a size. :) > >>> Points (taken individually or in countable bunches) have measure zero. > > >> They probably also have zero measure in uncountable bunches, Bob. At > >> least I never heard that division by zero was defined mathematically > >> even in modern math per say. > > >> ~v~~ > > >Purrrrr....say! Division by zero is not undefinable. One just has to > >define zero as a unit, eh? > > A unit of what, Tony? > > >Uncountable bunches certainly can attain nonzero measure. :) > > Uncountable bunches of zeroes are still zero, Tony. > Why no, no they're not, Lester. Perhaps a course in real analysis would be of value. Ever consider reading, rather than just making stuff up? PD
From: Brian Chandler on 22 Mar 2007 14:13
Lester Zick wrote: > On 22 Mar 2007 06:24:46 -0700, "PD" <TheDraperFamily(a)gmail.com> wrote: > >On Mar 21, 6:00 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: <snip-snop> > As previously noted brevity is the soul of wit and you're neither. Neither what? I mean, if neither this nor that, what are this and that? (Don't bother to answer if it takes too much time out of your lecturing schedule...) Brian Chandler http://imaginatorium.org |