Very cool article, Grant! Thanks. I started to get lost on page 11 with the meta-axioms that give the Bernoulli random variables. *8^( It's interesting that the wikipedia page (https://en.wikipedia.org/wiki/Continuum_hypothesis#Arguments_for_and_against_CH) mentions Feferman's semi-intuitionistic ideas in the same context as Freiling's argument against the CH.
But I was irritated by his maps from the traditional subdivisions of math to the primitive elements of human experience. The geometry one seems right to me. But either he didn't finish explaining the referents of analysis, or I disagree. Analysis (to me, of course) is all about _proximity_, the closeness of any bunch of things. Differentiation being about the determination of a locality and integration being about establishing totalities. Although it's obvious (hindsight is 20/20) how to get to analysis from the calculus and from forces. It doesn't strike me that forces (and acceleration and oscillation) are the primitive human experiences referred to by analysis, as a domain. Also, I don't really agree with the map from algebra to recipes of action. To me algebra is about the preservation of some ... "substance" _through_ transformation. So, like with forces giving us (well, Newton and Leibniz) a path into the calculus, the composition of actions in algebra is a kind of side effect. The core of it (to me, a non-mathematician!) is about the preservation of some quality through equivalence (and equivalence classes). Obviously, it would be silly for me to argue with Mumford on this sort of thing. But I'm wondering whether you (or anyone on the list) see these experience correlations more as he sees them? As usual, I have no comment on the actual topic of the paper. 8^) On 11/13/2016 10:21 AM, Grant Holland wrote:
http://www.stat.uchicago.edu/~lekheng/courses/191f09/mumford-AMS.pdf
-- glen ep ropella ⊥ 971-280-5699 ============================================================ 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-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove
