Friday, February 6, 2009

Contemplating Mathematics

Mario Livio is contagiously passionate about his subject, a good thing.

PSU students in 53 Cramer were clearly into his rap, including the doubled slides (adjacent duplicates). During Q&A they wanted to hear more about this "intelligent jelly fish" that wasn't into natural numbers or discrete math, yet was nevertheless mathematical in its outlook -- a nice philosophical chew toy.

Mario's questions are about (a) why math proves relevant even when it's practitioners may be proudly dismissive of "the real world" and not looking for applications and (b) whether math is discovered or invented.

To the first question, he feels we're likely constituted in such a way that we can't help but reason effectively (we've been conditioned by long experience, inheriting from predecessors).

For every other-worldly geek there's another equally driven to find those practical applications. These possibly not-mathematicians act as enzymes or catalysts by connecting the dots, maybe tying knot studies -- originally proposed for atomic modeling (not so useful) -- to computing the energy required for DNA transformations (a current application).

Fuller's 10 * f * f + 2 would be another example, in connecting icosahedral numbers to the structure of the virus.

Mario's funniest joke, perhaps unintentional, is when he recapped Descartes' "cogito ergo sum" argument, then said, appreciatively, "an unbelievable guy!" (meaning "awesome brilliant" but you appreciate the irony maybe).

He focuses a lot of the "lore" of that discipline (western civ math), which fact I hope to bounce off tomorrow during our confab.

I've been invited to riff off his topics and will do so by introducing my "lore axis" then diving head first in to the 4D vs. 4D vs. 4D thread I've been developing.

He might find that fun, plus I'm guinea pigging my Chicago talk, hoping for some useful feedback.

Mario's storytelling takes us from Plato etc. to the "three worlds" of Penrose, to Bertrand Russell and his letter to Frege, pointing out a paradox. That letter wasn't really about the barber who cuts his own hair (when off duty? -- so not a barber then?), but about the set of all sets that don't contain themselves, or something similar.

Godel's Incompleteness Theorem gets touched on, reminding us of how axioms don't need to be "true" are more just "rules of the game" e.g. the rules of chess aren't "true" just give us a fun pass time (Don and I actually played most of a game of chess at Backspace, passing time until Dr. Livio's next after-dinner appearance).

Indeed, we probably shouldn't go around calling axioms "true" because that confuses them with proved theorems. Axioms are "assumed" and/or "presumed" and/or "postulated" (called "postulates" sometimes) i.e. we're allowed to make them up out of whole cloth, no proof required.

I was happy to take in this talk (and the slides) two times within the space of a few hours, the 2nd time at Powell's Technical. Terry, the consummate roadie, lugged the equipment in his van.

Once again, the audience was large and attentive and asked a lot of good questions.

Mario was generous with his time, enthusiastic with his answers, and signed quite a few books.

In Terry's van later, returning Mario to The Heathman, we yakked about the sometimes stressful aspects of jetting here and there on speaking tours, how one needs to fly through hubs in curious ways.

Mario is bothered by the turbulence out of Denver, lost a pilot friend to that sometimes unforgiving weather system (in a twin engine plane).

I didn't ask any questions out loud, was mostly thinking how the "three worlds" of Sir Roger might be reduced to two, i.e. the physical and the psychological.

I see no need for Plato to have a third special world all his own, where all the perfect stuff lives. His is just another psyche and we each have one of those (slave boys too), a private sky or private Idaho.

I have an easier time dispensing with "perfect circles" (Platonic) because of my Princeton training in Wittgenstein. Synergetics came later, with a different idea of perfection (as in "not merely imaginary").

Platonists (also called "Realists" -- versus "Nominalists" an opposing camp) depend on a mental model of naming, familiar to Python programmers. In this conventional view, names point to objects and these must be Platonic if the math is truly pure (a bias).

But what if "pointing" isn't really what's going on so much? Rorty calls Wittgenstein a "nonrepresentationalist" -- another way of saying he outgrew the Augustinian model, in turn Neoplatonist, ergo Platonist, and based on names pointing.

Instead of a Platonist, I could say I'm a Play-Doh-nist, an allusion to Claymation Station i.e. our "geometry of lumps".

The question of why math keeps syncing with nature might point us back to the fact that we we both actively invent and passively discover our own psychological namespace, mathematical to the extent that it's precise, self-consistent, and well-ordered (logical), if it is (depends on who's, how much homework, housekeeping).

While at Powell's, I snapped some pictures of really cool books, including ones about innovative dwellings and XRL (extremely remote living).

Glenn showed me a thick book called Space Structures that (a) omitted Dr. Fuller from the index (par for the course) yet (b) mentions geodesic domes and credits Fuller and his licensees for doing most of the work in that area. The U.S. Marine projects get mentioned.