Wednesday, April 04, 2007

The Poincare Conjecture, In Our Time, and the limits of human minds

My favorite radio show (podcast) covered the The Poincare Conjecture last November. I just listened to it this week, which is the beauty of podcasting of course. I wouldn't have gotten nearly as much from a 20th century broadcast -- I lost count of how often I hit the replay button. The "lasso" analogies in particular were a bit mangled, and I think Melvyn may have skipped over what the conjecture actually is (one could decipher it by context; perhaps I failed to hit the replay button often enough).

It's a great show, but they needed another hour to do justice to Poincaré and to the lay version of his mathematics. More significantly, I think IOT hit the limits of what the medium can handle with this topic; Melvynn kept half-joking that his head was hurting. The one non-mathematician guest had to opt out of a final comment, saying "this is too hard for me". The listener comments reflect how challenging the topic was.

Which brings me to my recent readings in physics. I'm reading Gribbins on Quantum Mechanics (1994) and Brian Greene with another cosmology/string theory overview, the Gribbins book is my personal favorite, but it's a bit dated now. Together though, they make it hard to overlook that physics seems to be getting harder and harder. We have more physicists than ever, and I'd wager there's a Feynman or two in the bunch, but we've been stuck for decades now. String theory's luster is a bit tarnished (Smolin et al), special relativity doesn't fit with 'spooky action at a distance', we can't unify gravity and QM, the math keeps getting harder (or so I read) and the universe feels ever more absurd and ill-suited to the frailties of the human mind.

Sort of like Perelman's proof of the Poincaré conjecture, which teams of mathematicians are still slogging through years after its unofficial publication. Modern mathematics is said to be so complex only hyper-specialists can tackle it, but hyper-specialists can't make the kind of cross-domain breakthroughs Poincaré made.

I wonder if we'll run aground until we come up with better minds -- either human or otherwise.

PS. Firefox spell checking is very impressive. It corrected my spelling of Melvyn Bragg's first name!

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