Math note.. re recent exchanges of a seminal er, Class?

Post #421,087 by Ashton 10/27/17 4:30:38 PM 10/27/17 4:30:38 PM Reply	Math note.. re recent exchanges of a seminal er, Class? Given the {189? 289? Steps merely towards--> a sorta 'Proof' that "2 + 2 = 4"}, I believe that we should aptly re-Name this proposition as: The 2 + 2 = 4 Conjecture henceforth and forevermore, since.. As Kurt Gödel et alia have demonstrated [In every mathematical system there WILL BE certain Truths found which are not derivable from the Axioms], a statement whuch may be explained in ordinary English ~~ the word Certainty is a chimerical Idea about a situation which Shall Not Be Found by homo-saps, such as we Are in a Cosmos such as, in fact: It Is. (I would even aver that: misunderestimating the Significance of this [I claim: FACT] applied everywhere from physics to religiosity-in-all-forms: just may be the Unitary-source of very much of the World-of-'Humanity's daily, perpetual self-administered miserableness/and inability ever (OK: rarely) to achieve that high-state of mind which we call Reason. Rest case. PS Visit also: the lovely Ĉerenkov radiation /that blue glow seen in operating Reactors of water-cooled kind: where certain faster-than-light matters (in that medium) happen.
Post #421,115 by mmoffitt 10/30/17 8:30:45 AM 10/30/17 8:30:45 AM Reply	Well, we hope it is so at any rate. Specifically what I'm referring to is, "In every mathematical system there WILL BE certain Truths found which are not derivable from the Axioms." What Kurt showed was that either that (the system is Incomplete iow) OR the system is inconsistent. AFAIK (and it has been more than two decades since I last looked at this seriously) we pretend our mathematics is consistent, but there's no firm proof that it is. We know that either (a) our mathematics is incomplete (your stated observation) or (b) our mathematics is inconsistent. Kurt proved we cannot have both consistency and completeness with his (in)famous Incompleteness Theorems. To make things "just work", we claim (without proof) that (a) holds because (b) holding is really a terrible nuisance. The first time I understood this, I chuckled to myself how closely this "pretending we know that (a) is the case" was akin to other "beliefs." I think that was the source of the fire-in-the-belly I had on this topic when I was a serious student of mathematics. WE were not supposed to "believe" in anything. WE were supposed to PROVE things. Unlike scientists who can and do have "exceptions to the Rule", mathematicians don't. A single counter-example is sufficient to throw out the proposition entirely. But here, here at the base we don't do that because, well, it's disturbing. bcnu, Mikem It's mourning in America again.
Post #421,120 by Ashton 10/30/17 3:37:14 PM 10/30/17 3:37:15 PM Reply	Full agreement. Might not the matter be summarized more popularly by the oft-limned tale of the coin-dropped, then sought: Man seen peering closely at ground near a lamppost, seeking.. seeking... Woman passes by, asks "whatcha Doing?" Man replies, "looking for that Gold Sovereign I dropped." Woman asks, ~~ where did you drop it? Man responds, "over there somewhere." Woman asks, .."then why are you looking Here?" Man replies ... ... well, there's more Light here. . . . Woman joins Consciousness Raising Group: all are familiar with Men and with certain Problems akin to above. . . . Men sneer at these shameless hussies, their "proud beauties nevertheless", etc. etc.
Post #421,136 by mmoffitt 10/31/17 8:10:55 AM 10/31/17 8:10:55 AM Reply	Yes, a very nice summary. bcnu, Mikem It's mourning in America again.
Post #421,152 by Ashton 11/2/17 6:11:55 PM 11/2/17 6:11:55 PM Reply	Postlude (sorry.. my mind just has its own agenda) Woman: Whadd'ya lose? Seeker: It was this Byte-Coin, "PROOF that Math is ~~Grreat!!!~~ Complete and Error-free." It's shiny and has exquisite enameled layers from the Age of Enlightenment; see, I did come across here some differential equations (y'know, Great for making bridges, hydraulics and nuclear weapons) and even an area of Hilbert Space nearby: but my mind went blank when I peeked in; nothing but Feynman diagrams, talking it seemed .. for the longest time. What Day is this?) Sorry again, this may be an offshoot of just catching a discussion of, whether we should (consider giving) robots, as AI umm "progresses": Civil Rights-just-like-humans. [??] (I blame this on Drumpf+firestorms and the whole fucking Zeitgeist du jour. And Leibniz.)

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