The Definition of Points
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From: Ben newsam on 28 Apr 2007 20:06 On Sat, 28 Apr 2007 16:31:00 -0700, Lester Zick <dontbother(a)nowhere.net> wrote: >On Sat, 28 Apr 2007 21:55:51 +0100, Ben newsam ><ben.newsam.remove.this(a)gmail.com> wrote: >>The whole world except you might well be lazy or stupid, but the >>trouble remains that you are the only person allegedly to know what >>the term "truth in mechanically reduced universal terms" means, and >>you seem unable to explain yourself. > >Or, heaven forbid, you could just brush up on the relevant literature. I challenge you to show me one reference to the phrase "truth in mechanically reduced universal terms". Relevant literature indeed! >>> You're mighty long on arbiter dicta and mighty short on >>>demonstrations of truth for what you say. >> >>What does "arbiter dicta" mean? Do you mean "obiter dicta"? > >"Arbiter" not "obiter". Do you imagine you're the only person in the >world with a dictionary? I just wondered what "arbiter dicta" meant. Not the same as "obiter dictum" or "obiter dicta", I wouldn't have thought. Do you think it's the same? What's curious is that you could easily have >faulted me for "Asimov" instead of "Gamow" but you chose instead to >question a phrase which is intuitively obvious to the casual observer. > >~v~~
From: Stephen Harris on 29 Apr 2007 07:31 I came across this excellent description and modified it accordingly. > No, he can't, or won't, because he doesn't understand, or else doesn't > accept, Boolean logic. He's into Truth - some absolute something or > other out there that only Sizemore can intuit. That's why he loses > his cool when the rest of us, with our paltry operational definitions of > truth (NB the lower case) refuse to believe that he's discovered The > Secrets Of The Universe. Here he is, offering us The Truth on an > electronic platter, and we shake our heads and mutter "zealot". No > wonder he loses his cool, and indulges in picayune sarcasm and foul > mouthed insult. [The sarcasm is not always as adroit as "picayune".] > I suspect that many of the people who work themselves into rages and post, do so because the anger triggers addicted adrenalin discharges.
From: Lester Zick on 29 Apr 2007 14:28 On Sun, 29 Apr 2007 04:31:24 -0700, Stephen Harris <cyberguard-1048(a)yahoo.com> wrote: >I came across this excellent description and modified it accordingly. > >> No, he can't, or won't, because he doesn't understand, or else doesn't >> accept, Boolean logic. He's into Truth - some absolute something or >> other out there that only Sizemore can intuit. That's why he loses >> his cool when the rest of us, with our paltry operational definitions of >> truth (NB the lower case) refuse to believe that he's discovered The >> Secrets Of The Universe. Here he is, offering us The Truth on an >> electronic platter, and we shake our heads and mutter "zealot". No >> wonder he loses his cool, and indulges in picayune sarcasm and foul >> mouthed insult. [The sarcasm is not always as adroit as "picayune".] >> > >I suspect that many of the people who work themselves into rages and >post, do so because the anger triggers addicted adrenalin discharges. I couldn't agree more although Wolf's original reference was to me not Glen. Wolf frequently works himself into rages. I don't know why although I've found serial intellectual frustration often has that effect. It's one way I use to get attention by needling the ignorant until they go bonkers. When people sense there is something they should be able to spell out out can't the mind pancs and vituperation ensues. Not a pretty picture but then neither is complacent ignorance. ~v~~
From: Lester Zick on 29 Apr 2007 15:07 On Sun, 29 Apr 2007 01:06:11 +0100, Ben newsam <ben.newsam.remove.this(a)gmail.com> wrote: >On Sat, 28 Apr 2007 16:31:00 -0700, Lester Zick ><dontbother(a)nowhere.net> wrote: > >>On Sat, 28 Apr 2007 21:55:51 +0100, Ben newsam >><ben.newsam.remove.this(a)gmail.com> wrote: >>>The whole world except you might well be lazy or stupid, but the >>>trouble remains that you are the only person allegedly to know what >>>the term "truth in mechanically reduced universal terms" means, and >>>you seem unable to explain yourself. >> >>Or, heaven forbid, you could just brush up on the relevant literature. > >I challenge you to show me one reference to the phrase "truth in >mechanically reduced universal terms". Relevant literature indeed! Come, come, Ben. You could look up any number of my posts on the subject. I mean this isn't rocket science. The idea of universal truth I'm working on is that universal alternatives to anything universally self contradictory are perforce universally true. Self contradictions such as "A not A" are parochially but not universally false because they only concern "A". Self contradictions only become universally reduced when they concern the mechanism for talking alternatives in general as by "not" "contradiction" "differences" or "alternatives". Or if you want a practical applied example of mechanical reduction just look up my "Epistemology 401: Tautological Mechanics" which shows the origin of boolean conjunctions solely in terms of "not". >>>> You're mighty long on arbiter dicta and mighty short on >>>>demonstrations of truth for what you say. >>> >>>What does "arbiter dicta" mean? Do you mean "obiter dicta"? >> >>"Arbiter" not "obiter". Do you imagine you're the only person in the >>world with a dictionary? > >I just wondered what "arbiter dicta" meant. Not the same as "obiter >dictum" or "obiter dicta", I wouldn't have thought. Do you think it's >the same? Of course not. "Obiter dicta" refer to incidental remarks. "Arbiter dicta" refer to "judicial dicta" in my own estimation equivalent to "judicial fiats". However my dictionary shows no reference to the phrase "arbiter dictum" and I'm not sure where I picked up the usage. However pondering the subject of "obiter dicta" last night I decided that there is an even better neologism apropos the subject of circular definitions used in modern math and empiricism generally: "orbital dicta". At least one can infer the nature of the beast from "orbital dicta" much as one can infer the same from Tony Orlow's "per say" instead of "per se" when applied to such puzzlers as Bob's maxim "a line is the set of all points on a line" or Moe(x)'s "infinity is infinite(x)"(which only represent substantial and not literal quotes). > What's curious is that you could easily have >>faulted me for "Asimov" instead of "Gamow" but you chose instead to >>question a phrase which is intuitively obvious to the casual observer. >> >>~v~~ ~v~~
From: Rock Brentwood on 29 Apr 2007 17:29
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. In modern mathematics, lines and other manifolds are NOT defined as point sets, but rather the opposite way from top down in terms of their function spaces. The general formalism allows for "geometries" that don't even have point sets (i.e. the non-commutative geometries). The structure of modern differential geometry and the modern theory of manifolds requires only the algebra C^{infinity}(M) of the C^{infinity} functions over a given manifold M as input. The only place that any notion of point set ever enters into consideration is in providing for a representation of C^{infinity}(M). However, not even this is needed. The algebras C^{infinity}(M) for all manifolds are equivalently defined as commtative C-* algebras. In fact, one can go in reverse: given a commutative C-* algebra A, there is a well-established procedure to construct from it the manifold M for which A = C^{infinity}(M). However, the same formal apparatus underlying differential geometry, manifold theory, etc.; applies regardless of where A comes from or what kind of algebra it is -- even if A is a non-commutative algebra. |