The Definition of Points
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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~~
From: Lester Zick on 14 Mar 2007 22:05
On 14 Mar 2007 13:03:59 -0700, "VK" <schools_ring(a)yahoo.com> wrote: >On Mar 14, 10:13 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >> > The point is to ti en einai of the infinity. >> > If you want a definition based on something fresher than Aristotle >> > then: >> > The point is nothing which is still something in potention to >> > become everything. >> > IMHO the Aristotle-based definition is better, but it's personal. >> >> I don't want a definition for points fresher or not than Aristotle. >> I'm trying to ascertain whether lines are made up of points. > >You are bringing unacceptably too much of the "everyday sensual >experience" by placing the question like that. I do? Funny I sorta thought I'd make the question more explicit. > Why "points", why >plural? Floor by floor - a high building, foot by foot - 12 feet >stick, something like that? ;-) Neither points nor lines are really >existing, so you may think of them whatever you want - as long as it >helps you to make another step in constructing something more >complicated. Somewhere on the go you may get an intersection with the >real world - or you may not, it is always cool but not required - >unless you are on some applied contract work. So this "real world" thingie. What is that exactly? I thought my observations and questions were about the real world. I have no interest in neoplatonic mysticism. >The point is nothing with potential of becoming; that is a simplified >up to profanity hybrid or Aristotle and Hegel, my sorries to them but >it gets us started. Then the line is the point deformed (stretched) >from negative to positive infinity. > >Or let's go in the reverse order: define the point using the line. The >line is then an one-dimensional space and the point is vertical >projection of this space onto n-dimensional space. > >Both options are as good as two crossed line. The difference is in the >"mindset" they put on you, so some higher constructs are "possible" or >"not possible" here or there. > >Actually with your line with many-many(-many) points you are hitting >straight to the hands of Zenon. So can Achilles ever get the tortoise? >And - most importantly and directly relevant to your current worries - >can the bow ever flight? First answer the questions from the "reality >point of view". That will let you to relax your mind for taking non- >existing abstractions as freely as you need - for the given moment and >for the given aim. Yeah look, VK, I have a very limited interest in philosophy especially bad philosophy. If you have some conclusion to draw with respect to my observations and the question at hand please get to it and omit the philosophy. Not interested. ~v~~ |