The Definition of Points
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From: Lester Zick on 13 Mar 2007 18:20 On 13 Mar 2007 13:30:17 -0700, "Douglas Eagleson" <eaglesondouglas(a)yahoo.com> wrote: >On Mar 13, 3:08 pm, "Douglas Eagleson" <eaglesondoug...(a)yahoo.com> >wrote: >> On Mar 13, 1:52 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >> >> > The Definition of Points >> > ~v~~ >> >> > In the swansong of modern math lines are composed of points. But then >> > we must ask how points are defined? However I seem to recollect >> > intersections of lines determine points. But if so then we are left to >> > consider the rather peculiar proposition that lines are composed of >> > the intersection of lines. Now I don't claim the foregoing definitions >> > are circular. Only that the ratio of definitional logic to conclusions >> > is a transcendental somewhere in the neighborhood of 3.14159 . . . >> >> > ~v~~ >> >> Points are rather importent things to try to get correct. I am still >> looking for some references, easy web kind, to allow topology to >> express points. >> >> And if a point was expressable, a function. And so nth topoogy is >> possible, but I need a Matlab transform that links a theorm, to the >> applied coordinate. And so the basic idea is to allow points where the >> size as infinity are expressable. >> >> This solves a symmetry problem. And resolves the question of sets of >> rationals to irrationals as true sized, infinities! >> >> So the topology of the point is a theorm I need. >> >> Any ideas? >> >> Thanks Doug > >If you think points are trivial in topology please give me your >reference. Because the Dekind Cut as the rate expresses the infinite >sequence of all. A size as absolute infinite expression was his >abstract size! > >Always was it a small little cut of exact size. > >So the appearance of the?????? > >And here we sit. > >A bunch of question marks. Abstract the Cut, no big deal? > >It is hard for me to accept Dekind's invention in the first place >until you are informed you need assitance. SO it is hard stuff. What >is a Dekind cut? > >And if you can answer, then the relation of its cause in geometric >space is apparent. SO a single little theorm I am ignorent of. >Please help. I don't see points as having any topology. That's what makes them points. Nor do I see points as making up lines. That's egregiously absurd on the face of it. And it is scarcely supportable just because mathematikers make up a pointless circular line of reasoning. ~v~~
From: Lester Zick on 13 Mar 2007 18:28 On Tue, 13 Mar 2007 20:48:34 +0100, "SucMucPaProlij" <mrjohnpauldike2006(a)hotmail.com> wrote: >> In the swansong of modern math lines are composed of points. But then >> we must ask how points are defined? However I seem to recollect >> intersections of lines determine points. But if so then we are left to >> consider the rather peculiar proposition that lines are composed of >> the intersection of lines. Now I don't claim the foregoing definitions >> are circular. Only that the ratio of definitional logic to conclusions >> is a transcendental somewhere in the neighborhood of 3.14159 . . . >> > >point is coordinate in (any) space (real or imaginary). >For example (x,y,z) is a point where x,y and z are any numbers. That's nice. And I'm sure we could give any number of other examples of points. Very enlightening indeed. However the question at hand is whether points constitute lines and whether or not circular lines of reasoning support that contention. >line is collection of points and is defined with three functions >x = f(t) >y = g(t) >z = h(t) > >where t is any real number and f,g and h are any continous functions. > >Your definition is good for 10 years old boy to understand what is point and >what is line. (When I was a child, I thought like a child, I reasoned like a >child. When I became a man, I put away childish ways behind me.....) Problem is you may have put away childish things such as lines and points but you're still thinking like a child. Are points and lines not still mathematical objects and are lines made up of points just because you got to be eleven? ~v~~
From: Lester Zick on 13 Mar 2007 18:37 On 13 Mar 2007 12:55:32 -0700, "Randy Poe" <poespam-trap(a)yahoo.com> wrote: >On Mar 13, 1:52 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >> The Definition of Points >> ~v~~ >> >> In the swansong of modern math lines are composed of points. But then >> we must ask how points are defined? However I seem to recollect >> intersections of lines determine points. But if so then we are left to >> consider the rather peculiar proposition that lines are composed of >> the intersection of lines. Now I don't claim the foregoing definitions >> are circular. Only that the ratio of definitional logic to conclusions >> is a transcendental somewhere in the neighborhood of 3.14159 . . . >> > >The modern axiomization of geometry due to Hilbert leaves >points, lines, and planes undefined. Probably just as well. I think what we have to consider however is whether lines are made up of points and the intersection of lines defined by points defines points. Or whether perhaps Hilbert and others were a little too preoccupied with problematic axioms and circular logic to ascertain the actual truth of what he didn't define. > In fact, he famously >said about this construction: "One must be able to say at >all times-instead of points, lines, and planes---tables, >chairs, and beer mugs." > >In other words, despite whatever intuition and inherent >meaning we might ascribe to these things has no effect >on the mathematical structure. > >No doubt Lester will find this approach lacking and I mainly find circular regressions pretty much meaningless and unable to support mathematikers' contention that points constitute lines. >assert he has a superior axiomization built up from "infinite >epistomological ontologies of finite tautological >regression" or something equally meaningless. Aha, Randy. As usual you lie like a flatfish. Unlike mathematikers I don't use axioms. It's just that I have an unusual penchant for truth as opposed to guesses and assumptions typifying mathematikers. ~v~~
From: Hero on 13 Mar 2007 18:37 Randy Poe wrote: > Lester Zick wrote: > > > The Definition of Points > > ~v~~ > > > In the swansong of modern math lines are composed of points. But then > > we must ask how points are defined? However I seem to recollect > > intersections of lines determine points. But if so then we are left to > > consider the rather peculiar proposition that lines are composed of > > the intersection of lines. Now I don't claim the foregoing definitions > > are circular. Only that the ratio of definitional logic to conclusions > > is a transcendental somewhere in the neighborhood of 3.14159 . . . > > The modern axiomization of geometry due to Hilbert leaves > points, lines, and planes undefined. In fact, he famously > said about this construction: "One must be able to say at > all times-instead of points, lines, and planes---tables, > chairs, and beer mugs." > > In other words, despite whatever intuition and inherent > meaning we might ascribe to these things has no effect > on the mathematical structure. > A mathematical structure, which is the same for points, lines, and planes as well as for tables, chairs, and beer mugs, seems to me not very far advanced, there is not even a difference between an object with a volume and one without. Take any object of volume, a chair. It's center of gravity is a point. Rotate the chair, the axis of rotation is a line. Let the axis spin (precession), so every part of the chair is moving with the exception of one "thing", which is at rest - a point. So points really exists, not as matter or stuff, but as an aspect of things. Just describe them. This is possible in different ways, f.e: one point is an invariant in a precessing rotation. With friendly greetings Hero PS. Lester, You claim > > ...that the ratio of definitional logic to conclusions > > is a transcendental somewhere in the neighborhood of 3.14159 . . . So definitional logic behaves like a radius extending to conclusions like half a circle. Just reverse Your way and search for the center and You have defined Your starting point. Nice. NB, why half a perimeter?
From: SucMucPaProlij on 13 Mar 2007 18:40
"Lester Zick" <dontbother(a)nowhere.net> wrote in message news:2t8ev292sqinpej146h9b4t4o4n9pvr8c2(a)4ax.com... > On Tue, 13 Mar 2007 20:48:34 +0100, "SucMucPaProlij" > <mrjohnpauldike2006(a)hotmail.com> wrote: > >>> In the swansong of modern math lines are composed of points. But then >>> we must ask how points are defined? However I seem to recollect >>> intersections of lines determine points. But if so then we are left to >>> consider the rather peculiar proposition that lines are composed of >>> the intersection of lines. Now I don't claim the foregoing definitions >>> are circular. Only that the ratio of definitional logic to conclusions >>> is a transcendental somewhere in the neighborhood of 3.14159 . . . >>> >> >>point is coordinate in (any) space (real or imaginary). >>For example (x,y,z) is a point where x,y and z are any numbers. > > That's nice. And I'm sure we could give any number of other examples > of points. Very enlightening indeed. However the question at hand is > whether points constitute lines and whether or not circular lines of > reasoning support that contention. > >>line is collection of points and is defined with three functions >>x = f(t) >>y = g(t) >>z = h(t) >> >>where t is any real number and f,g and h are any continous functions. >> >>Your definition is good for 10 years old boy to understand what is point and >>what is line. (When I was a child, I thought like a child, I reasoned like a >>child. When I became a man, I put away childish ways behind me.....) > > Problem is you may have put away childish things such as lines and > points but you're still thinking like a child. > > Are points and lines not still mathematical objects and are lines made > up of points just because you got to be eleven? > > ~v~~ hahahahaha the simple answer is that line is not made of anything. Line is just abstraction. Properties of line comes from it's definition. Is line made of points? If you don't define term "made of" and use it without too much thinking you can say that: line is defined with 3 functions: x = f(t) y = g(t) z = h(t) where (x,y,z) is a point. As you change 't' you get different points and you say that line is "made of" points, but it is just an expressions that you must fist understand well before you question it. |