Considering the discussion ongoing about mathematics and reality in another thread this disturbed me at first. We tend to think that if reality is mathematical there must be some mathematical way to describe it accurately. After all mathematics itself is very strongly quantised into the "right" or "wrong" bifurcation, "right" implying consistent with everything else in mathematics.
But I guess there's no reason to be alarmed. Mathematics still describes reality. It's just that reality itself does not conform to our human expectations. As enginerd's Professor daughter said...
Yeah, but the elegance is gone, it seems. I had the same reaction to the 70s proof of the four color theorem. Pages and pages of diagrams. Exhaustive, but hardly elegant--and requiring a computer.
Elegance schmelegance! I suppose a proof of Pythagoras' theorem would seem inelegant to a bacterium.
I'm not being offensive - just trying to say that mathematics doesn't care about how simple something has to be to be an elegant proof. But if it helps, there have been some simplifications to the four-colour proof and Wiles proof of Fermat's theorem.
The bottom line is that the grand unified mathematical theory of everything may exist, but be beyond human understanding. And even worse - the mathematics describing reality may get ever more complicated as you go deeper, without end...
The downsides for me include the inability to be shouted at by Nima for any protracted period (were his parents hard of hearing? Did they live on a construction site perhaps?) and that by the time I get around to trying to digest a particular episode, I forget a whole bunch of stuff from previous ones (what were those angle brackets again?). Still, he makes his diction clear, and I can always revisit material, so these are not important criticisms.
As for the PDF of the Geometric Algebra book I posted, I reached chapter five before beaching. Hoping to refloat shortly.
Posted By: Andrew PalfreymanAs for the PDF of the Geometric Algebra book I posted, I reached chapter five before beaching. Hoping to refloat shortly.
I've always been bothered by the duality of rotation and translation. It always seemed that the one was essentially the other. PGA, a Geometric Algebra subset, unifies them, noticing that a translation is just a rotation around infinity. https://www.youtube.com/watch?v=DOXzZZ6Bdf8
The link you posted is " Theaster Gates, and Laurie Anderson discuss art in popular culture today. " Have I missed a gem somewhere in the very large proportion I didn't watch?