The Definition of Points
in [Math]
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From: Lester Zick on 14 Mar 2007 15:24 On Tue, 13 Mar 2007 23:28:19 -0700, Bob Cain <arcane(a)arcanemethods.com> wrote: >The_Man wrote: > >> What do YOU produce, Mister Nick Ick? What have YOU accomplished? > >He's good at starting vanity threads to demonstrate his self >proclaimed and self appreciated wit. Better to be witty than witless I suppose. >He's a legend in his own mind. And in the minds of others too, Stringfellow. You seem to think these threads are one sided extemporaneous lectures on my part. You also seemed to think Ken Seto and I would have some kind of monumental donnybrook. You also pretty much just seem to think when you don't. ~v~~
From: OG on 14 Mar 2007 15:37 "Lester Zick" <dontbother(a)nowhere.net> wrote in message news:8a2fv212gphd4ndimlc9qct6ifvsrda6i0(a)4ax.com... > On Wed, 14 Mar 2007 02:22:35 -0000, "OG" <owen(a)gwynnefamily.org.uk> > wrote: > >> >>"Lester Zick" <dontbother(a)nowhere.net> wrote in message >>news:758ev21t8r8ch5sjuoasdim467bfjvk06q(a)4ax.com... >>> On Tue, 13 Mar 2007 16:16:52 -0400, "Jesse F. Hughes" >>> <jesse(a)phiwumbda.org> wrote: >>> >>>>"PD" <TheDraperFamily(a)gmail.com> writes: >>>> >>>>> Interestingly, the dictionary of the English language is also >>>>> circular, where the definitions of each and every single word in the >>>>> dictionary is composed of other words also defined in the dictionary. >>>>> Thus, it is possible to find a circular route from any word defined in >>>>> the dictionary, through words in the definition, back to the original >>>>> word to be defined. >>>> >>>>The part following "Thus" is doubtful. It is certainly true for some >>>>words ("is" and "a", for instance). It is almost certainly false >>>>for some other words. I doubt that if we begin with "gregarious" and >>>>check each word in its definition, followed by each word in those >>>>definitions and so on, we will find a definition involving the word >>>>"gregarious". >>>> >>>>Here's the start: >>>> >>>>gregarious >>>> adj 1: tending to form a group with others of the same kind; >>>> "gregarious bird species"; "man is a gregarious >>>> animal" [ant: ungregarious] >>>> 2: seeking and enjoying the company of others; "a gregarious >>>> person who avoids solitude" >>>> >>>>(note that the examples and antonym are not part of the definition!) >>> >>> An interesting point. One might indeed have to go a long way to >>> discern the circularity. However my actual contention is that this >>> variety of circularity is quite often used by mathematikers to conceal >>> an otherwise orphan contention that lines are constituted of points. >>> >> >>What you call 'orphan' is in fact 'abstract', as points necessarily are. > > You mean points are abstract from the intersection of lines? Or that > the composition of lines is abstract from points? Curious I must say. As you wish.
From: PD on 14 Mar 2007 16:02 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. I believe Lester is asking whether a line is a composite object or an atomic primitive. One way of asking the question is whether a point sits ON a line or whether the point is part OF the line. 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. 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. But to provide him with some prurient prose by which to diddle 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. One way to answer this is to take the geometric limit of one end point approaching the other end point, and ask what the limit of the line segment is. That should either settle it or send Lester into an orgasmic frenzy. > > >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: VK on 14 Mar 2007 16:03 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. 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. 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.
From: SucMucPaProlij on 14 Mar 2007 17:30
> 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. Math can't create the world it can only (try to) explain it. To explain something you must fist admit that something exists. I admit that lines and points do exist. 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. 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? 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 :))))) |