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1. Robert McNees (mcnees@mastodon.social)'s status on Tuesday, 09-Jan-2024 18:52:22 UTC Robert McNees

   Bryce DeWitt, a major figure of 20th century theoretical physics who made substantial contributions to field theory, especially the field theoretic approach to quantum gravity, was born #OTD in 1923.

   Image: UT Physics History

   • Robert McNees (mcnees@mastodon.social)'s status on Tuesday, 09-Jan-2024 18:57:13 UTC Robert McNees

     in reply to

     Physics is full of beautiful bits of terminology that sit at the intersection of mathematics and poetry. DeWitt gave one of my favorite examples.

     It can he found in his book "Supermanifolds,” where he had to introduce some terminology for a concept he calls "supernumbers.”

     Supernumbers are elements of something called a Grassmann algebra. The algebras Dewitt had in mind are infinite-dimensional. One typically needs an infinite set of complex numbers to describe just one of these supernumbers.

   • Robert McNees (mcnees@mastodon.social)'s status on Tuesday, 09-Jan-2024 18:58:18 UTC Robert McNees

     in reply to

     (Complex numbers look like 𝛼 + i 𝛽, where i is the square-root of -1 and both 𝛼 and 𝛽 are just plain old real numbers. So it's sort of like that, but with a lot more numbers.)

   • Robert McNees (mcnees@mastodon.social)'s status on Tuesday, 09-Jan-2024 19:01:57 UTC Robert McNees

     in reply to

     When DeWitt described a supernumber Z, he split it into two parts: Z = Z_b + Z_s.

     The first term, Z_b, is a single complex number. It’s the simplest part of Z. But the second term, Z_s, has an infinite multitude of complex numbers hidden inside.

     He refers to Z_b as "the body," and Z_s as "the soul." It's lovely.

   • PhDog (dogfox@mastodon.social)'s status on Tuesday, 09-Jan-2024 19:04:26 UTC PhDog

     in reply to

     @mcnees

     THAT's really good.