The Definition of Points
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From: Lester Zick on 14 Mar 2007 21:48 On Wed, 14 Mar 2007 22:30:21 +0100, "SucMucPaProlij" <mrjohnpauldike2006(a)hotmail.com> wrote: >> If the point is defined by the intersection what happens to the point >> and what defines the point when the lines don't intersect? >> On the other hand if the point is not defined by the intersection of lines >> how can one assume the line is made up of things which aren't defined? >> > >hahahahaha you are poor philosopher. Obviously. That's why I became a mathematician. > Math can't create the world it can only >(try to) explain it. Which is probably why neomathematikers prefer to make up a world they can explain so they have something they can explain instead of something they can't. Makes them feel useful I expect. >To explain something you must fist admit that something exists. >I admit that lines and points do exist. That's nice. Does anyone care? >Every definition puts in relation two or more thing that exist. >Definition of point doesn't create point. It puts point in relation to something >else. >If you define point with intersection of two lines you put in relation: >1) point that you admit that already exists >2) two lines that you admit that already exist >3) and their intersection that you admit that already exists. Well I don't already admit points exist in the absence of line intersections. >Definition also does not create relation between thing. Relation between point, >two lines and their intersection already exists and with definition you only >admit that it exists. > >When you say "point is intersection of two lines" then you only admit that there >exist certain relation between point, two lines and their intersection. This >relation will also exist if you don't define it because definition discovers >relations, it does not create them. > >Who (beside you) claims that it is wrong to define point with lines and define >line with points? Beats me. I was hoping somebody else would. Obviously you don't. >Definition of point says that there is some relation R1 between point P and >lines L1 and L2 >R1 = {(R, L1, L2) | where blabla P bla L1 and blabla L2} > >"Line is made up of points" says that there is relation R2 between line L and >point P >R2={(L,P) | where blabla L and blabla P} > >Not all relations are in form y=f(x) nor they should be. > >It is true that you can define point without intersection of two lines and it is >true that you can define line without points but it only means that there is >certain relation between point and something that is not line, and there is >certain relation between lines and something that is not point. > >It is also true that you can't define point using nothing nor you can define >line using nothing because relation between point and nothing is just not >relation and therefore definition that defines something using nothing is just >not definition. > >Just as f(x)=x-2*f(x) if perfectly good definition of f(x), "point is >intersection of lines and line is made out of points" is ok definition if you >know how to use it. >Someone is confused with f(x)=x-2*f(x) and someone else is confused with points >and lines :))))) 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~~
From: Bob Kolker on 14 Mar 2007 21:51 Lester Zick wrote: > > > Obviously. That's why I became a mathematician. You are not now, nor were you ever a mathematician. Nor will you ever be one unless you get a brain transplant. Your postings indicate not only a profound ignorance of things mathetmicatical but a definite lack of talent for and competence in mathematics. Bob Kolker
From: Lester Zick on 14 Mar 2007 21:54 On 14 Mar 2007 11:59:42 -0700, "The_Man" <me_so_horneeeee(a)yahoo.com> wrote: >On Mar 14, 12:50 am, Lester Zick <dontbot...(a)nowhere.net> wrote: >> On Tue, 13 Mar 2007 23:40:39 +0100, "SucMucPaProlij" >> >> >> >> >> >> <mrjohnpauldike2...(a)hotmail.com> wrote: >> >> >"Lester Zick" <dontbot...(a)nowhere.net> wrote in message >> >news:2t8ev292sqinpej146h9b4t4o4n9pvr8c2(a)4ax.com... >> >> On Tue, 13 Mar 2007 20:48:34 +0100, "SucMucPaProlij" >> >> <mrjohnpauldike2...(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. > >O.K. Tell us, Icky-po: What do YOU think lines are made of? Itsy bitsy little dots. > What do >YOU think is a "suitable" definition for point, line, plane, etc.. I'm >sure Gauss, Euler, Cantor, Cauchy, Riemann, and Hilbert are rolling >over in their graves with anticipation. Straight lines are derivatives of curves. At least according to Newton and his method of drawing tangents. Tell Euler et al. they can stop rolling. Euler couldn't even get the definition of angular mechanics right. >Maybe the crew of my local Burger King will redefine QM next week, and >the Friendly's will unify all the forces of nature in one theory. Why bother? I already have. That was the first point of my collateral thread "Takin Out the Trash". >> >>>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. >> >> Which is all just swell. So now the question I posed becomes are >> abstract lines made up of abstract points? >> >> >Is line made of points? >> >If you don't define term "made of" and use it without too much thinking you can >> >say that: >> >> Why don't you ask Bob Kolker. He seems to think lines are "made up" of >> points, abstract or otherwise. I'm not quite clear about how he thinks >> lines are "made up" of points but he nonetheless seems to think they >> are. >> >> >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. >> >> Frankly I prefer to question things before I waste time learning them. > >Yes -learning things is such a "waste". That's why you know so little. Well I agree learning erroneous things is such a waste. That's why you know so much that's wrong. ~v~~
From: Eric Gisse on 14 Mar 2007 21:57 On Mar 14, 5:23 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: > On 14 Mar 2007 14:54:55 -0700, "Eric Gisse" <jowr...(a)gmail.com> wrote: > > > > >On Mar 14, 11:15 am, Lester Zick <dontbot...(a)nowhere.net> wrote: > >> On 13 Mar 2007 23:21:54 -0700, "Eric Gisse" <jowr...(a)gmail.com> wrote: > > >> >On Mar 13, 9:54 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: > >> >> On 13 Mar 2007 17:18:03 -0700, "Eric Gisse" <jowr...(a)gmail.com> wrote: > > >> >> >On Mar 13, 9:52 am, 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, lines, etc aren't defined. Only their relations to eachother. > > >> >> So is the relation between points and lines is that lines are made up > >> >> of points and is the relation between lines and points that the > >> >> intersection of lines defines a point? > > >> >No, it is more complicated than that. > > >> Well that's certainly a relief. I thought you said "only their > >> relations to each other". It's certainly good to know that what lines > >> are made up of is not "only a relation" between points and lines. > > >> ~v~~ > > >No, I said "it is more complicated than that." > > No what you said is "Points, lines, etc aren't defined. Only their > relations to eachother". Your comment that "No, it is more complicated > than that" was simply a naive extraneous appeal to circumvent my > observation that relations between points and lines satisfy your > original observation. Your trivial ideas on complexity are irrelevant. > > ~v~~ *sigh* It isn't my fault you cannot read for comprehension. Points and lines are undefined - it is as simple as that. Every question you ask that is of the form "So <idiotic idea> defines [point,line]" will have "no" as an answer.
From: Lester Zick on 14 Mar 2007 21:58
On 14 Mar 2007 12:20:35 -0700, "Hero" <Hero.van.Jindelt(a)gmx.de> wrote: > Lester Zick wrote: >> Hero wrote: >> >Randy Poe wrote: >> >> Lester Zick wrote: >> >> >> > The Definition of Points >................ >> >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? >> >> Who said anything about half a perimeter, Hero? I believe the ratio pi >> is between the full circumference of a circle and its diameter. >> > >Accepted. By Your own reasoning You've got already three points: >A center, from which definitional logic starts out into two >directions,and two points, where it changes into conclusions. And You >can go in circular way in Your picture from conclusions to conclusions >( NB there is more than one diameter and it can be extended to a >sphere). >Historical, axioms are not the beginning of geometry. You start with >full, complex life, understand here a bit and there, proceed from >simple things to complex ones and than You look for the most simple >and common structure underlying the geometry you have done so far. >F.e. You shrink a sphere to it's infinitesimal minimum, which is >radius ( and diameter ) zero - and like the smile of Cheshire cat - >there You have, what You've looked for. I guess. Was that what I was looking for? Sure coulda fooled me. ~v~~ |