The Definition of Points
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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~~
From: Lester Zick on 14 Mar 2007 22:24 On 14 Mar 2007 13:02:00 -0700, "PD" <TheDraperFamily(a)gmail.com> wrote: >On Mar 14, 2:13 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >> On 14 Mar 2007 10:10:55 -0700, "VK" <schools_r...(a)yahoo.com> wrote: >> >> >On Mar 14, 1:28 am, Lester Zick <dontbot...(a)nowhere.net> wrote: >> >> Are points and lines not still mathematical objects >> >> > 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. > >Let's see if I can help. Oh that'll be refreshing for a change. >I believe Lester is asking whether a line is a composite object or an >atomic primitive. Actually I'm interested in whether vectors exist and have constituents. >One way of asking the question is whether a point sits ON a line or >whether the point is part OF the line. Like I said before you're not very good at philosophy but you're much worse at science. >Of course, since both the point and the line are idealizations, >conceptual constructions out of the human mind that don't have any >independent reality, then one could rightly ask why the hell it >matters, since there is no way to verify either statement through an >external discriminator. An external what-inator? Why don't you just call it magic and be done with it? No need to dress it up like a dog's dinner with all the philosophical badinage. You're a mystic. So what? > Lester doesn't believe in external >discriminators anyway, because that is the work of evil empirics, and >he'd rather spend his day mentally diddling away at issues like this. Whereas obviously you don't. >But to provide him with some prurient prose by which to diddle You know, sport, if you were even half as witty as I am that might indeed make you a half wit. However in this instance you're trying too hard and you wind up appearing more trying than witty. >further, let's toss him the idea that we can clearly cleave a line in >two by picking a point (either on the line or part of the line, take >your pick) and assigning one direction to one semi-infinite segment >and the other direction to the other semi-infinite segment -- >sometimes called rays. One can then take one of those rays and cleave >it again, and one of the results will be a line segment, which is >distinguished by having two end *points*. Now the interesting question >is whether those end points are ON the line segment or part OF the >line segment. Neither. The end points contain the line segment. That's how the line segment is defined. > One way to answer this is to take the geometric limit of >one end point approaching the other end point, Of course another way to answer this is to ask what defines the line segment to begin with. > and ask what the limit >of the line segment is. When it gets to zero do be sure to let us know. > That should either settle it or send Lester >into an orgasmic frenzy. Gee with another swell foop you might actually get to the calculus. Of course Newton and Leibniz and probably a thousand other wannabe's are waiting in the wings ahead of you and the other neomathematikers. >> >Now after some thinking you may decide to stay with the crossing lines >> >and hell on the cross-definition issues ;-) The speach is not a >> >reflection of entities: it is a reflection - of different levels of >> >quality - of the mind processes. This way a word doesn't have neither >> >can decribe an entity. The purpose of the word - when read - to trig a >> >"mentagram", state of mind, as close as possible to the original one - >> >which caused the word to be written. This way it is not important how >> >is the point defined: it is important that all people involved in the >> >subject would think of appoximately the same entity so not say about >> >triangles or squares. In this aspect crossing lines definition in math >> >does the trick pretty well. From the other side some "sizeless thingy" >> >as the definition would work in math as well - again as long as >> >everyone involved would think the same entity when reading it. ~v~~
From: SucMucPaProlij on 15 Mar 2007 07:11 > > 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. > I think that you think that mathematikers are stupid and it has nothing to do with lines and point. I only know that they are convergent because they are limited and monotone but this is subject for another topic :))))
From: Bob Kolker on 15 Mar 2007 08:09 Lester Zick wrote: > > Actually I'm interested in whether vectors exist and have > constituents. Yes they do, in the mathematical sense. They lead to a successful description of forces for one thing. The constituents of a vector are length and direction. > > Neither. The end points contain the line segment. That's how the line > segment is defined. That is admirably correct. And given the end points of a segment one can readily define the set of points that make up the line determined by the end points of the segment. Learn some analytic geometry to see how. > > Of course another way to answer this is to ask what defines the line > segment to begin with. A pair of points. > > >> and ask what the limit >>of the line segment is. > > > When it gets to zero do be sure to let us know. I see you are channeling Bishop Berkeley again. All of hist objections have been answered by the theory of hyperreal numbers on which non-standard analysis is based. Berkeley raised cogent objections to Newton and Leibniz which were finally and complete answered in the late 1950's by Abraham Robinson. By the way, if lines (or other curves) do not consist of the points on them, what do they consist of? Bob Kolker
From: VK on 15 Mar 2007 13:03
On Mar 14, 11:02 pm, "PD" <TheDraperFam...(a)gmail.com> wrote: > I believe Lester is asking whether a line is a composite object or an > atomic primitive. That is one of things and the most easy one. I believe I already gave the answer but not sure that he will ever accept it: it is whatever one wants it to be today thus whatever higher level constructs is one planning to study. Sometimes for instance it is more benefitial to go in definitions from surface rather than from point. The line then is an intersection of two surfaces and the point is an intersection of two lines. For the final touch it is left to define the surface as a set of points and we are back to the round of circular definitions :-) - but - in either case we don't care as we are getting the starting point we need to move on. And - hidden for an appropriate moment - he also has an implicit join of numbers and geometry, so number points and number lines are being kept close to Euclidic points and lines for the next shot :-) And what he really wants I guess as a provable definition of a basic abstraction. So he doesn't want a statement like "Got does exist" but he wants a statement like "It is rainy today outside" so Lester could just run outside to say is it true or not and provide his wet/dry umbrella as an ultimate proof. So overall it is a rather demanding gentleman :-) |