Okay, so it wasn't dinner, and it wasn't with André, but it was a great conversation. The following is a best efforts recollection, possibly, make that certainly, out-of-order.
[We're exercising at the University gym, returning not only from the summer hiatus, but from the pandemic, from isolation, etc.]
Me: So Andrew, what is your major again? Hey Dr. Chiang, meet Andrew, he is the next Kurt Gödel.
Dr. Chiang: Wow! Are you in Computer Science?
Andrew: Physics and Math
[That reminded me of Cedric Villani who won a Fields Medal, he worked with the Boltzmann's equation of a gas, which talks about the distribution of molecular velocities, which seemed more like chemistry than math. Dr. Villani, besides being very distinguished is very kind and approachable.]
Me: What are you taking?
Andrew: Discrete Math, Classical Electrodynamics...
Me: Discrete Math?
Andrew: Yes and I'm reading a book by Knuth on 'Concrete Mathematics' which is a [portmanteau] of the words CONtinuous and disCRETE.
Me: Clever. Time with Knuth is time well spent. What about Quantum Electrodynamics?
[10 sitting bench presses and some banter.]
Andrew: Mutters something about Dirac Delta Functions.
Me: Infinitely Narrow, Infinitely Tall
Andrew: And unit area! (An area of 1)
Me: Those are interesting basis functions.
In my head I'm seeing a pair of them and wondering how one could create a parametric expression to interpolate between them:
[This raised a sidebar where we discussed explicit, implicit and parametric functions. Visit the link if you care to explore these creatures.]
Andrew: ... and did a particularly nice view of Ohm's law in terms of flux and such.
Me: So that would be a Maxwell's Law version of R = V/I?
[It was time to put a mention of Falstad's circuit simulator which is amazingly visual and useful since it animates current flow and signal.
[Then we went upstairs to play ping pong, called 'table tennis' by those who keep score, but we don't as it violates the aesthetic of keeping the ball going in the highly echoic racquetball court. We countered the echos by turning the table at 45 degrees, which helped funnel errant shots but did little for the many copies of sound we got during our conversation.]
V = IR reminded me of F = ma which reminded me of E = mc2
Me: The problem with the last trifecta is that c is squared when maybe it should just be a thing that isn't. Consider half-derivatives which interpolate between two worlds as well. Like maybe Length, Mass, and Time are consequences of things, rather than fundamental things. Perhaps we live in a world where velocity is the fundamental value, rather than position or length - where length is the integral of velocity with respect to time, rather than velocity being the derivative of length with respect to time.
[We went on for a bit about making things non-dimensional, like lift and drag coefficients and unitizing things so for example, the speed of light, c = 1.
As the ping pong ball (note it isn't called a table tennis ball) was flying back and forth, I mentioned that simultaneity is in the eye of the beholder according to the Special Relativity Lectures by Brian Greene.
Then after a few more rounds ruled surfaces came up. They appear curved, but are built of straight lines, which at first seems paradoxical.]
Me: You know black holes can float on water right?!
Andrew: (incredulous expression)
Me: It's true, I didn't believe it myself until I did the calculation. You can check my numbers but with mass accretion in supermassive black holes there is a war between surface area and volume and the upshot is that density drops considerably as the mass of a black hole increases. You can check my math:
The moral to the story was the reminder that I too should consider wearing a floppy Oppy hat when playing ping pong in a highly echoic room to suppress the back channels.
Other Topics We Talked, Save for Later:
- Pencil and Paper vs. Computer for Mathematics
- Case in Point:
- Interval Arithmetic for Heisenberg vs.
- Maxima - A bulldozer for mathematics
- The Principle of Least Action
- The Lagrangian
- Emmy Noether's Principle and The Unassassin Trailer
- Ray Tracing Corners: Is the space Covered?
