Before the days of personal laptop/tablet/mobile computers, scientists kept notes in lab notebooks. I look back through my own, and marvel at the attention I paid to detail. I didn’t want to lose any thought thinked, any mountain conquered. Here are a few excerpts from several decades of handwritten notes. (After a certain time, my code itself comprised my notes.)
At first, we start with classroom notes from the Caltech and U.C. Santa Cruz days, then progress into professional notes from actual jobs.
This has something to do with the quantum mechanical energy levels of a particle in a 1-dimensional “well” or “box”. Somehow I have never (yet) used this outside the classroom.
Wave equations, the bread-and-butter stuff of certain types of physicists. I got practice writing squiggly Greek letters like xi (ξ) and eta (η).
Deriving the Lorenz force on the electron from first (relativistic) principles. I spent so much time on this (it wasn’t part of the course) that I lost track of the actual course material and my grade wasn’t so good. But I just had to see how the cross-product rule came about and how B was really just the “curly” part of a more generalized E.
Now I was studying math at U.C. Santa Cruz. In lieu of getting TA funds, one quarter I earned my keep by writing up solution sets for a book about graph theory by Gerhard Ringel. (He had written the problems but left the solutions as TBD by someone else, who turned out to be me.) That was a great way to really absorb graph theory: working out the answers to every problem in the book. (Some I couldn’t do.) This one involved coloring and numbering the vertices and edges of a 4-dimensional cube.
Now we move into professional notes from work at Cerwin-Vega, E-mu, and Philips Media, and some just personal exploration.
Here I am looking at the voltage divider equation, and pondering how the limiting value as you approach the origin can be any value at all, depending on which direction you come from. Trying to visualize the surface in the days before (easily available) computer graphics.
I was looking into just what are the constraints on the Fourier and Hilbert transforms of a function when that function is analytical, causal, or both.
On a completely different tack, I was looking at the additive and multiplicative group of integers mod 15. But true to form, this had to do with generalizing FFT software.
The only computer to which I had access that could draw a picture was my dad’s cassette-tape memory Radio Shack (or Sinclair or whatever) computer. The complete repertoire of graphics functions was plot a pixel at (x,y). But I coaxed it into giving me some useful pictures of the images of circles under the Möbius transform. Which I dutifully transcribed into my notebook before they vanished. I was using this to design digital audio filters for E-mu Systems, who built electronic pianos, aka synthesizers.
I was also getting into the most generalized kind of calculus, and trying to develop some sort of intuition for differential geometry
Here we can see the influence of the people around me at U.C. Santa Cruz, where there was a lot of good research and researchers working on chaos theory. A software version of the lower figure can be found here.
And yet another notable notebook page from 20 June. Something about that day!
Here I am trying to get a handle on the math that lets you find a good approximation to some curve using the fewest terms in an equation.
Here I “descend” into the realm of EE, and actually implement (or rather deign to design the implementation) of a filter function. Although the actual circuit must perforce be causal, so it doesn't quite model the equation.
Here I am in a quite different context. Trying to play samples of digital audio and control them by a MIDI track whose time base is not commensurable with the audio sample rate. So there will always be slippage, and you have to take care of all possibilities.
We pick up the thread fifteen years later, when I got interested in animating web pages. I met this guy who created the prime factorization web clock. I thought I could do something similar with simple graphs. So I started enumerating them. The result is here.
And here I am back at music theory, counting necklaces.
