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]
<mailto:[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] <mailto:[email protected]> 505-473-9646
<tel:505-473-9646>
===================================
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