The Definition of Points
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From: Lester Zick on 20 Mar 2007 20:50 On 20 Mar 2007 14:09:33 -0700, "Hero" <Hero.van.Jindelt(a)gmx.de> wrote: > Lester Zick wrote: > >> >> >And another question: is the trace, left by a movement, not part of >> >static geometry? It is an invariant of dynamic geometry. >> >> You know, Hero, there are some extraordinarily subtle considerations >> involved here which need to be considered for any exact analysis of >> static rac versus dynamic non rac construction methods. However I'd >> rather not get into them just at present because they really aren't >> germane to the basic topics we're considering here at the moment. >> > >It's a pity. Well as I mentioned above there are some extraordinarily subtle considerations here which I prefer not to get into at the moment mainly because I'm not really confident I fully understand them myself. So anything I said would be more speculative in nature than I'd feel comfortable speculating on with such a hostile audience. > (just one more comment, when You can get to exact >algebraic lengths on the real line and because of an open window the >temperature did change a bit and with it Your compass, so You have a >chance of an exact transcendental). Well you always have chance encounters with points which are on a straight line but that doesn't mean there is any point on a straight line which corresponds with a transcendental, the proof being that every point on a straight line corresponds with some rac construction and no straight line rac construction corresponds to transcendentals. >Okay, back to points and lines. There's topology, just the simple >beginning: > A space (mathematical) is a set with structure. >A point is a geometrical space without geometrical structure, but it >can give structure to geometry. >Think of a vertex or a center and so forth. >A line is made up of points and sets of points ( the open intervalls >between each two points),which obey three topological rules. Hero, exactly what makes you think the foregoing observations are true? >What i learned recently: >With adding a point to an open (open in standard topology) flexible >surface one can enclose a solid, with adding a point to an open line >one can enclose a figure, and two points are the boundary of an >intervall on a line. But there is no point at or beyond infinity. All very interesting but I still have no idea why any of this is supposed to be true. ~v~~
From: Bob Kolker on 20 Mar 2007 20:53 Virgil wrote:> > > Read up on Pontryagin and his ilk before making such idiotic claims. For those who do not know it, Leon Pontrfyagin was a blind topologist. Bob Kolker
From: stephen on 20 Mar 2007 20:57 In sci.math Tony Orlow <tony(a)lightlink.com> wrote: > PD wrote: >> >> No one says a set of points IS in fact the constitution of physical >> object. >> Whether it is rightly the constitution of a mentally formed object >> (such as a geometric object), that seems to be an issue of arbitration >> and convention, not of truth. Is the concept of "blue" a correct one? >> >> PD >> > The truth of the "convention" of considering higher geometric objects to > be "sets" of points is ascertained by the conclusions one can draw from > that consideration, which are rather limited. How is it limited Tony? Consider points in a plane, where each point is identified by a pair of real numbers. The set of points { (x,y) | (x-3)^2+(y+4)^2=10 } describes a geometric object. In what way is this description "limited"? Can you provide a better description, and explain how it overcomes those limitations? Stephen
From: Lester Zick on 20 Mar 2007 21:12 On 20 Mar 2007 15:20:55 -0700, "PD" <TheDraperFamily(a)gmail.com> wrote: >On Mar 20, 2:33 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >> On 19 Mar 2007 11:51:47 -0700, "Randy Poe" <poespam-t...(a)yahoo.com> >> wrote: >> >> >> >> >> >> >On Mar 19, 2:44 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >> >> On 19 Mar 2007 08:59:24 -0700, "Randy Poe" <poespam-t...(a)yahoo.com> >> >> wrote: >> >> >> >> > That the set of naturals is infinite. >> >> >> >> Geometrically incorrect. Unless there is a natural infinitely greater >> >> >> than the origin, there is no infinite extent involved. >> >> >> >The naturals don't have physical positions, since they are not >> >> >defined geometrically. >> >> >> They are if they're associated with points and points define line >> >> segments. >> >> >By "associated with points" I assume you mean something >> >like using points to model the naturals. In that case the points >> >in your model have positions, but nevertheless the naturals >> >themselves don't have physical positions or exist as geometric >> >entities. >> >> >Do you have any idea what I'm saying? >> >> I'm a physicist, Randy, not a psychologist. > >By whose standard and measure are you a physicist, Lester? You know, Draper, you're an incredibly stupid person for such a fond member of the physics community. No sooner do I pull the same stunt on Bob Kolker than you take exactly the same bait. How about if I just define Lester(x)=physicist(x) where x=Michelson-Morley or x=frequency dilation? At least I understand that is the preferred method of mathematical definition these days. Unless you intend to complain Michelson-Morley and frequency dilation aren't physics. Which I wouldn't put past you considering some of your other proclivities. >There are certain categorizations, like "expert", which one does not >self-attach. One earns certain labels through attribution by others. I know; that's why I let the terms themselves speak for me. >This is also a fact that one cannot circumvent by willful abstinence >or simple refusal to abide. This sounds more like a priestly sermon than scientific observation. > That you don't like that, is completely >irrelevant. And who exactly died and elevated you to the papacy? And keeper of the public morals no less? For someone who can't even explain which two frames of reference he claims are required to calculate fringe shifts for Michelson-Morley, when my version of the experiment fails you can talk to your heart's content. Otherwise I just might consider keeping my mouth shut if I were you until you have something constructive to say, princess. ~v~~
From: Randy Poe on 20 Mar 2007 21:25
On Mar 20, 8:17 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: > On 20 Mar 2007 12:39:37 -0700, "Randy Poe" <poespam-t...(a)yahoo.com> > wrote: > >> >Is my guess wrong? Fine. I assume you know what > >> >you meant (oops, there I go making assumptions again). > >> >If so, then explain it. > > >> "Associated with points". > > >That would not be "alternate terminology". > > No it would be the question I asked in the terms I asked it. Do those terms have meaning? If so, what? It's a simple question. Every other human being has the capability of rephrasing questions. Why don't you? The answer, of course, is that you yourself have no idea what you were asking. You were just stringing words together. - Randy |