The Definition of Points
in [Math]
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From: Aaron on 14 Mar 2007 21:08 On Mar 13, 3:13 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: > On Tue, 13 Mar 2007 18:43:09 GMT, Sam Wormley <sworml...(a)mchsi.com> > 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 . . . > > >> ~v~~ > > > Point > > http://mathworld.wolfram.com/Point.html > > > A point 0-dimensional mathematical object, which can be specified in > > n-dimensional space using n coordinates. Although the notion of a point > > is intuitively rather clear, the mathematical machinery used to deal > > with points and point-like objects can be surprisingly slippery. This > > difficulty was encountered by none other than Euclid himself who, in > > his Elements, gave the vague definition of a point as "that which has > > no part." > > Sure, Sam. I understand that there are things we call points which > have no exhaustive definition. However my point is the contention of > mathematikers that lines are made up of points is untenable if lines > are required to define points through their intersection.It's vacuous. I'm like not getting it here. Are we just talking about graphing of functions? Isn't this splitting hairs or am I missing something? A point is like a spot and has the same number of information elements as there are dimensions in the space it models, right? A line is then all the spots from one spot to another. If two lines share a spot, big deal. They ahare a spot. It's just numbers in a co-ordinate system, which in tern is an abstract device to count numbers and model things we see using math functions. It it really more complicated than that? > > ~v~~- Hide quoted text - > > - Show quoted text -
From: Lester Zick on 14 Mar 2007 21:16 On Wed, 14 Mar 2007 19:37:26 -0000, "OG" <owen(a)gwynnefamily.org.uk> wrote: > >"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. And if wishes were horses you would ride. ~v~~
From: Lester Zick on 14 Mar 2007 21:23 On 14 Mar 2007 14:54:55 -0700, "Eric Gisse" <jowr.pi(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~~
From: Lester Zick on 14 Mar 2007 21:25 On 14 Mar 2007 16:12:36 -0700, "exp(j*pi/2)" <someone(a)arcanemethod.com> wrote: >On Mar 14, 12:24 pm, Lester Zick <dontbot...(a)nowhere.net> wrote: >> On Tue, 13 Mar 2007 23:28:19 -0700, Bob Cain >> >> <arc...(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~~ > >Actually, Bob Cain's fundamental problem is that when he looks into a >mirror he sees everyone except himself. Actually I'm sure when Bob looks into a mirror he sees very little. ~v~~
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~~ |