The Definition of Points
in [Math]
|
Prev: Guide to presenting Lemma, Theorems and Definitions
Next: Density of the set of all zeroes of a function with givenproperties
From: Sam Wormley on 17 Mar 2007 19:21 Lester Zick wrote: > On Sat, 17 Mar 2007 03:05:26 GMT, Sam Wormley <swormley1(a)mchsi.com> > wrote: > >> Lester Zick wrote: >>> On Fri, 16 Mar 2007 04:05:59 GMT, Sam Wormley <swormley1(a)mchsi.com> >>> wrote: >>> >>>> Lester Zick wrote: >>>>> On Thu, 15 Mar 2007 13:21:19 GMT, Sam Wormley <swormley1(a)mchsi.com> >>>>> wrote: >>>>> >>>>>> Bob Kolker wrote: >>>>>>> Sam Wormley wrote: >>>>>>> >>>>>>>> Hey Lester-- >>>>>>>> >>>>>>>> Point >>>>>>>> http://mathworld.wolfram.com/Point.html >>>>>>>> >>>>>>>> A point 0-dimensional mathematical object, which can be specified in >>>>>>>> n-dimensional space using n coordinates. Although the notion of a point >>>>>>>> is intuitively rather clear, the mathematical machinery used to deal >>>>>>>> with points and point-like objects can be surprisingly slippery. This >>>>>>>> difficulty was encountered by none other than Euclid himself who, in >>>>>>>> his Elements, gave the vague definition of a point as "that which has >>>>>>>> no part." >>>>>>> That really is not a definition in the species-genus sense. It is a >>>>>>> -notion- expressing an intuition. At no point is that "definition" ever >>>>>>> used in a proof. Check it out. >>>>>>> >>>>>>> Many of Euclid's "definitions" were not proper definitions. Some where. >>>>>>> The only things that count are the list of undefined terms, definitions >>>>>>> grounded on the undefined terms and the axioms/postulates that endow the >>>>>>> undefined terms with properties that can be used in proofs. >>>>>>> >>>>>>> Bob Kolker >>>>>> Give me something better, Bob, or are you arguing there isn't a better >>>>>> definition (if you can call it that). >>>>> Well we can always pretend there is something better but that doesn't >>>>> necessarily make it so. I think modern mathematikers have done such a >>>>> first rate job at the pretense that it's become a doctrinal catechism. >>>>> >>>>> ~v~~ >>>> What's your formal education in mathemaitcs, Lester? >>> U.S. Naval Academy, Annapolis, MD. 1966 BSME. I'm sure they can >>> provide cv's to such worthy souls.Finished playing trivial pursuit now >>> and may we return to discussing the problem at hand or would you >>> prefer further essays on educational effluvia? >>> >>> ~v~~ >> Engineers should know better! > > Engineers know better. That's exactly why they're reluctant to accept > mystic explanations for Michelson-Morley etc. Are you aware Albert > Michelson was a graduate of the academy? Maybe that's partly why he > had the only sensible to comment on this experiment I've ever read: to > wit "maybe we need to understand the phenomena better before we try > these kinds of experiments.". An engineer's perspective not an > empiric's. > > ~v~~ Michelson just wouldn't believe what the data was telling him... it happens... and it might be happening to you Lester!
From: Sam Wormley on 17 Mar 2007 19:22 Lester Zick wrote: > On Sat, 17 Mar 2007 03:08:34 GMT, Sam Wormley <swormley1(a)mchsi.com> > wrote: > >> Lester Zick wrote: >>> On Fri, 16 Mar 2007 04:09:49 GMT, Sam Wormley <swormley1(a)mchsi.com> >>> wrote: >>> >>>> Lester Zick wrote: >>>>> On Thu, 15 Mar 2007 02:37:12 GMT, Sam Wormley <swormley1(a)mchsi.com> >>>>> wrote: >>>>> >>>>>> Lester Zick wrote: >>>>>> >>>>>>> Look. If you have something to say responsive to my modest little >>>>>>> essay I would hope you could abbreviate it with some kind of non >>>>>>> circular philosophical extract running to oh maybe twenty lines or >>>>>>> less. Obviously you think lines are made up of points. Big deal. So do >>>>>>> most other neoplatonic mathematikers. >>>>>>> >>>>>>> ~v~~ >>>>>> Hey Lester-- >>>>>> >>>>>> Point >>>>>> http://mathworld.wolfram.com/Point.html >>>>>> >>>>>> A point 0-dimensional mathematical object, which can be specified in >>>>>> n-dimensional space using n coordinates. Although the notion of a point >>>>>> is intuitively rather clear, the mathematical machinery used to deal >>>>>> with points and point-like objects can be surprisingly slippery. This >>>>>> difficulty was encountered by none other than Euclid himself who, in >>>>>> his Elements, gave the vague definition of a point as "that which has >>>>>> no part." >>>>> Not clear what your point is here, Sam. If the so called mathematical >>>>> machinery used to deal with points is nothing but circular regressions >>>>> then I certainly agree that machinery would really be pretty slippery. >>>>> >>>>> ~v~~ >>>> Here's the point where I reside, Lester: >>>> 15T 0444901m 4653490m 00306m NAD27 Fri Mar 16 04:09:09 UTC 2007 >>> But is it a circular point, Sam? >>> >>> ~v~~ >> No--it is a point (0-dimensional mathematical object) with located with >> UTM easting, northing, elevation and time (UTC). > > Like I said a circular point. > > ~v~~ Nope a 0-dimensional mathematical object.
From: Sam Wormley on 17 Mar 2007 19:23 Lester Zick wrote: > On Sat, 17 Mar 2007 03:10:15 GMT, Sam Wormley <swormley1(a)mchsi.com> > wrote: > >> Lester Zick wrote: >>> On Fri, 16 Mar 2007 04:13:10 GMT, Sam Wormley <swormley1(a)mchsi.com> >>> wrote: >>> >>>> Lester Zick wrote: >>>> >>>>> I don't agree with the notion that lines and straight lines mean the >>>>> same thing, Sam, mainly because we're then at a loss to account for >>>>> curves. >>>> Geodesic >>>> http://mathworld.wolfram.com/Geodesic.html >>>> >>>> "A geodesic is a locally length-minimizing curve. Equivalently, it >>>> is a path that a particle which is not accelerating would follow. >>>> In the plane, the geodesics are straight lines. On the sphere, the >>>> geodesics are great circles (like the equator). The geodesics in >>>> a space depend on the Riemannian metric, which affects the notions >>>> of distance and acceleration". >>> So instead of lines, straight lines, and curves, Sam, now we're >>> discussing geodesics, straight geodesics, and curved geodesics? Pure >>> terminological regression. Not all that much of an improvement. >>> >>> ~v~~ >> locally length-minimizing curve > > As opposed to a universally length minimizing curve? Or as opposed to > a locally length maximizing curve? Or as opposed to a universally > length length maximizing curve? I have no idea what this is in aid of. > Terminological regressions are a dime a dozen. In the biz they're > called buzz words. Happy to use "geodesic" instead of "line" if that's > all that's bothering you. There's nothing especially geo- about them. > > ~v~~ Geo is just historical baggage... Helio... etc.
From: Lester Zick on 17 Mar 2007 19:30 On Sat, 17 Mar 2007 09:40:03 -0400, Bob Kolker <nowhere(a)nowhere.com> wrote: >SucMucPaProlij wrote: > >> >> Mathematikers do claim that math has nothing to do with reality but if it is >> true you can't use math to prove it because math has nothing to do with reality. >> It means that there is little possibility that math has some connections with >> real world. > >Mathematics has an instrumental connection with the world. It makes >physics possible. Isaac Newton first had to invent calculus to develop a >physical theory of dynamic motion. > >Without mathematics there is no physics. True but without SOAP operas we'd still have mathematics. ~v~~
From: Lester Zick on 17 Mar 2007 19:33
On Sat, 17 Mar 2007 13:50:01 -0400, Bob Kolker <nowhere(a)nowhere.com> wrote: >alanmc95210(a)yahoo.com wrote:> >> Euclid established the foundation for our mathematical deduction >> system. As he realized from his Axioms and Postulates, you can't >> prove everything. You've got to start with some given Axioms. Lines >> and points are among those basic assumptions- A. McIntire > >The lines and points are undefined objects. It is the axioms concerning >lines and points that are the basic assumptions. "Assumptions" being the operative word. It might be nice if we could get a little closer to "truth" for a change. ~v~~ |