Students of relativity should be happy that mathematicians pursued their interest in "unverifiable" non-Euclidean geometry.
Frank Sent from my Verizon Nexus 6 4G LTE Phone (505) 670-9918 On Dec 28, 2015 1:51 AM, "Grant Holland" <[email protected]> wrote: > Mathematics already went through this "crisis of confidence" in the latter > half of the 19th century when Lobachevsky and Riemann came up with > alternative, non-Euclidean, geometries. The issue that forced this new look > at the soul of mathematics was, I believe, the verifiability - consistency, > actually - of Euclid's fifth postulate with respect to his other four. This > was followed historically by the works of Dedekind and Cantor who engaged > naked logic to expose a number of counter-intuitive "truths" of > mathematics. The entire hoopla was addressed by Hilbert's program in an > attempt to put the matter to rest for once and for all. However, the work > of Russell and Whitehead to further Hilbert's program by developing > arithmetic from Hilbertian foundations was eventually stymied by Godel, > whose work was generalized by Turing. > > The result of all of this, according to my understanding, is that > mathematics ceased to see itself as a "seeker after the true nature of the > universe" (as do both science (which physics thinks it owns) and philosophy > even today); and began to see itself as a "constructor of logically > consistent models, regardless of their verifiability". Verifiability was > dropped from the program of pure abstract mathematics, and was left to the > "impure" pursuits of physicists, philosophers and applied mathematicians. > > I'm sure someone on this list can set straight my recollections of > mathematical history. But I do hold to the point that mathematics > addressed, and "kind of" resolved, its own crisis of confidence over its > assumed need for verifiability about a century ago. It's conclusion? Forget > verifiability and pursue pure mathematics as art - not science. > > Should physics give up its similar insistence on verification (seeking > "the truth") - and join the ranks as just another branch of abstract > mathematics? > > Grant > > > On 12/26/15 9:44 PM, Owen Densmore wrote: > > Abs fab! > > But amazingly, there are fantastic young grad students doing the > impossible in this field .. testing at the Planck limits. Often using the > universe itself to test its own theories. > > One of my favorites is a stream of matter flowing towards a void in space > which suggests "gravity on the other side" .. i.e. a multiverse lump hidden > from us but not by gravity. > > Why is there Something, not Nothing gets to be fascinating when the big > bang was sparked by less than a tea-spoon of matter, or so it is thought > nowadays. > > -- Owen > > On Sat, Dec 26, 2015 at 8:59 PM, Tom Johnson <[email protected]> wrote: > >> Something to keep you occupied until New Years Day. >> >> >> https://www.quantamagazine.org/20151216-physicists-and-philosophers-debate-the-boundaries-of-science/ >> >> =================================== >> Tom Johnson - Inst. for Analytic Journalism >> Santa Fe, NM >> SPJ Region 9 Director >> [email protected] 505-473-9646 >> =================================== >> >> ============================================================ >> FRIAM Applied Complexity Group listserv >> Meets Fridays 9a-11:30 at cafe at St. John's College >> to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com >> > > > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com > > > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com >
============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com
