The Definition of Points
in [Logic]
|
Prev: On Ultrafinitism
Next: Modal logic example
From: Randy Poe on 13 Mar 2007 15:55 On Mar 13, 1:52 pm, 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 . . . > The modern axiomization of geometry due to Hilbert leaves points, lines, and planes undefined. In fact, he famously said about this construction: "One must be able to say at all times-instead of points, lines, and planes---tables, chairs, and beer mugs." In other words, despite whatever intuition and inherent meaning we might ascribe to these things has no effect on the mathematical structure. No doubt Lester will find this approach lacking and assert he has a superior axiomization built up from "infinite epistomological ontologies of finite tautological regression" or something equally meaningless. - Randy
From: Clifford Nelson on 13 Mar 2007 16:14 In article <et6v6r$1ov$1(a)ss408.t-com.hr>, "SucMucPaProlij" <mrjohnpauldike2006(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. > > 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.....) Primary means like prime, first. First things first, second things second, third things third, etc.. Bucky Fuller's kindergarten teacher gave her class semi-dried peas and toothpicks to build "structures". All of the kids built structures that had 90 degree angles like squares and cubes except Bucky. He could not see because he didn't have a pair of glasses yet, and felt that the triangle and tetrahedron were strong, but the square and cube did not hold their shape. He got a patent for the structure he made about 60 years later. He thought like a child for about 60 years and started to write Synergetics. 15 years later the first volume was published. See: http://bfi.org/node/574 Cliff Nelson Dry your tears, there's more fun for your ears, "Forward Into The Past" 2 PM to 5 PM, Sundays, California time, http://www.geocities.com/forwardintothepast/ Don't be a square or a blockhead; see: http://bfi.org/node/574 http://library.wolfram.com/infocenter/search/?search_results=1;search_per son_id=607
From: Douglas Eagleson on 13 Mar 2007 16:30 On Mar 13, 3:08 pm, "Douglas Eagleson" <eaglesondoug...(a)yahoo.com> wrote: > On Mar 13, 1:52 pm, 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 are rather importent things to try to get correct. I am still > looking for some references, easy web kind, to allow topology to > express points. > > And if a point was expressable, a function. And so nth topoogy is > possible, but I need a Matlab transform that links a theorm, to the > applied coordinate. And so the basic idea is to allow points where the > size as infinity are expressable. > > This solves a symmetry problem. And resolves the question of sets of > rationals to irrationals as true sized, infinities! > > So the topology of the point is a theorm I need. > > Any ideas? > > Thanks Doug If you think points are trivial in topology please give me your reference. Because the Dekind Cut as the rate expresses the infinite sequence of all. A size as absolute infinite expression was his abstract size! Always was it a small little cut of exact size. So the appearance of the?????? And here we sit. A bunch of question marks. Abstract the Cut, no big deal? It is hard for me to accept Dekind's invention in the first place until you are informed you need assitance. SO it is hard stuff. What is a Dekind cut? And if you can answer, then the relation of its cause in geometric space is apparent. SO a single little theorm I am ignorent of. Please help.
From: Lester Zick on 13 Mar 2007 17:44 On 13 Mar 2007 11:20:47 -0700, "Ross A. Finlayson" <raf(a)tiki-lounge.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~~ > >You should ask me. Why? ~v~~
From: Lester Zick on 13 Mar 2007 18:06
On 13 Mar 2007 11:34:56 -0700, "PD" <TheDraperFamily(a)gmail.com> wrote: >On Mar 13, 12:52 pm, 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~~ > >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. Well see the problem here, PD, is that most dictionaries of language would be embarrassed to give a circular definition outright. In other words I should be quite surprized to find a definition of "gregarious" along the lines of "gregarious is gregarious" or "gregarious means gregarious people". Mathematikers however are not quite so timid. They routinely resort to tight loops in their definitions adding very little of substance anywhere along the line. In this particular case mathematikers feel quite comfortable defining points as "intersections of lines making up lines". Quite lame. Nor does one find dictionary definitions arbitrarily drawn to support various contentions they can't support logically. The question here is not whether there are mathematical objects we call points but whether in fact they compose lines. Obviously mathematikers are too lazy or stupid to demonstrate that contention so they just define it that way. >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. Scarcely the point, sport. Ostensible definitions often wind up being particular rather than general. It's just unfortunate mathematikers prove comparably inept. >That being said, perhaps it is in your best interest to find a way to >write a dictionary that eradicates this circularity. Or mathematikers might consider defining their objects in somewhat more general terms which don't just assume what they should prove. > That way, when >you use the words "peculiar" and "definitional", we will have a priori >definitions of those terms that are noncircular, and from which the >unambiguous meaning of what you write can be obtained. Well I've certainly made more progress in that direction with generic language than mathematikers seem to have made in theirs. Kinda makes one skeptical whether mathematikers claim that lines are made up of points is in fact true. I see no evidence to support that claim in the definition of points. It appears to be nothing but an arbitrary claim. ~v~~ |