The Definition of Points
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From: mmeron on 17 Mar 2007 18:38 In article <1174170793.549628.45350(a)b75g2000hsg.googlegroups.com>, "VK" <schools_ring(a)yahoo.com> writes: >On Mar 18, 12:59 am, "SucMucPaProlij" <mrjohnpauldike2...(a)hotmail.com> >wrote: >> Cabin is symetrical and you can't distinguish between left and right. >> When you say "Left button is broken" question is "what left button?" >> There is no left or right half of circle. > >Yep, this is what I mean. That was to argue with the Hero's statement >that "left and right are geometrical concepts". Left and right are >semantical concepts appeared grace to the particular human body >symmetry. If octopuses got the intellect, I would die to see their >geometry books. And I would sell my new car for any junior-high >calculus book from a planet populated by creatures having three pods >instead of ten fingers - so they are naturally using base-3 numeral >system with base-10 system being a scientific domain obscurity. Why do you think that there is ***anything*** in calculus that depends on whether you use base 3, 10, 42 or whatever? Mati Meron | "When you argue with a fool, meron(a)cars.uchicago.edu | chances are he is doing just the same"
From: Lester Zick on 17 Mar 2007 18:40 On Sat, 17 Mar 2007 03:05:26 GMT, Sam Wormley <swormley1(a)mchsi.com> wrote: >Lester Zick wrote: >> On Fri, 16 Mar 2007 04:05:59 GMT, Sam Wormley <swormley1(a)mchsi.com> >> wrote: >> >>> Lester Zick wrote: >>>> On Thu, 15 Mar 2007 13:21:19 GMT, Sam Wormley <swormley1(a)mchsi.com> >>>> wrote: >>>> >>>>> Bob Kolker wrote: >>>>>> Sam Wormley wrote: >>>>>> >>>>>>> Hey Lester-- >>>>>>> >>>>>>> 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." >>>>>> That really is not a definition in the species-genus sense. It is a >>>>>> -notion- expressing an intuition. At no point is that "definition" ever >>>>>> used in a proof. Check it out. >>>>>> >>>>>> Many of Euclid's "definitions" were not proper definitions. Some where. >>>>>> The only things that count are the list of undefined terms, definitions >>>>>> grounded on the undefined terms and the axioms/postulates that endow the >>>>>> undefined terms with properties that can be used in proofs. >>>>>> >>>>>> Bob Kolker >>>>> Give me something better, Bob, or are you arguing there isn't a better >>>>> definition (if you can call it that). >>>> Well we can always pretend there is something better but that doesn't >>>> necessarily make it so. I think modern mathematikers have done such a >>>> first rate job at the pretense that it's become a doctrinal catechism. >>>> >>>> ~v~~ >>> >>> What's your formal education in mathemaitcs, Lester? >> >> U.S. Naval Academy, Annapolis, MD. 1966 BSME. I'm sure they can >> provide cv's to such worthy souls.Finished playing trivial pursuit now >> and may we return to discussing the problem at hand or would you >> prefer further essays on educational effluvia? >> >> ~v~~ > > Engineers should know better! Engineers know better. That's exactly why they're reluctant to accept mystic explanations for Michelson-Morley etc. Are you aware Albert Michelson was a graduate of the academy? Maybe that's partly why he had the only sensible to comment on this experiment I've ever read: to wit "maybe we need to understand the phenomena better before we try these kinds of experiments.". An engineer's perspective not an empiric's. ~v~~
From: Tony Orlow on 17 Mar 2007 18:41 Randy Poe wrote: > On Mar 17, 12:27 pm, Tony Orlow <t...(a)lightlink.com> wrote: >> Lester Zick wrote: >>> On Fri, 16 Mar 2007 16:18:53 +0100, "SucMucPaProlij" >>> <mrjohnpauldike2...(a)hotmail.com> wrote: >>>> "Lester Zick" <dontbot...(a)nowhere.net> wrote in message >>>> news:1ukbv2hq1fo7ucv8971u9qo37b48bj6a5h(a)4ax.com... >>>>> 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~~ >>>> Can you prove that non-circular definition of existence exists? >>> Well that depends on what you and others mean by "existence exists". >>> On the face of it the phrase "existence exists" is itself circular and >>> no more demonstrable than a phrase like "pointing points". It's just a >>> phrase taken as a root axiomatic assumption of truth by Ayn Rand in my >>> own personal experience whether others have used it or not I don't >>> know. >>> On the other hand if you're asking whether anything exists and is >>> capable of being unambiguously defined the answer is yes. I've done >>> exactly that on more than one occasion first in the root post to the >>> thread "Epistemology 201: The Science of Science" of two years ago and >>> more recently in the root post to the thread "Epistemology 401: >>> Tautological Mechanics" from a month ago. >>> The technique of unambiguous definition and the definition of truth is >>> simply to show that all possible alternative are false. Empirics and >>> mathematikers generally prefer to base their definitions on >>> undemonstrable axiomatic assumptions of truth whereas I prefer to base >>> definitions of truth on finite mechanical tautological reduction to >>> self contradictory alternatives. The former technique is a practice in >>> mystical insight while the latter entails exhaustive analysis and >>> reduction in purely mechanical terms. >>> ~v~~ >> So, essentially, anything that's not self-contradictory exists, or is >> "true"? In an infinite universe, perhaps.... > > Every abstract concept exists as a concept. What does the > size of the universe have to do with that? They don't > take up any space. > > - Randy > What "they" are you referring to? If the universe is finite, then only a finite number of an infinite number of possibilities can occur. For every possible event to happen requires an infinite universe, or an infinite number of "universes". - Tony
From: Lester Zick on 17 Mar 2007 18:42 On 17 Mar 2007 09:40:22 -0700, "Randy Poe" <poespam-trap(a)yahoo.com> wrote: >Every abstract concept exists as a concept. What does the >size of the universe have to do with that? They don't >take up any space. What does the space concepts take up have to do with their truth? ~v~~
From: Lester Zick on 17 Mar 2007 18:43
On Sat, 17 Mar 2007 17:51:37 +0100, "SucMucPaProlij" <mrjohnpauldike2006(a)hotmail.com> wrote: >>> So, essentially, anything that's not self-contradictory exists, or is >>> "true"? In an infinite universe, perhaps.... >> >> Every abstract concept exists as a concept. What does the >> size of the universe have to do with that? They don't >> take up any space. >> > >Wrong! >If idea doesn't have any material form and it is not even energy, magnetic field >of enything else, then you have Altzhaimer and idea is lost :))))) Well the idea certainly seems to have been lost on you. ~v~~ |