I have been forcing myself to read at least a few paragraphs from the second half of Becker's Denial of Death, at least every other night. Throughout my life, since childhood, the idea of mathematics and mathematicians intrigued me. Throughout high school, Physics seemed some distant destination. Encountering in university later in life renewed an interest in Calculus.

To make a long story short, the world of official physicists, to me, is like the Castle in Kafka's novel. Even in the university, I felt like a dog in the temple. That is, even though I could hold my own with math, I was not on the inside of the "priest-craft" --- I am a hobbyist who the State seems to have wasted funds on in educating, although I greatly appreciate the education, especially the community college part where I was able to focus on programming, Calculus, Physics, etc ... but as Thomas Ligotti mentions in Conspiracy, getting the A's in Calculus just did not feel as good as we might have expected it to. It was non-orgasmic.

The reason I am leaving some notes on how to find values of trigonometric functions without scientific calculators or tables is because there have been things bugging me for several decades now, beginning with high school and the introduction to these transcendental functions. We were using these functions, but had no idea the math behind defining them. In the 1980's we were to become proficient in using the scientific and graphing calculators of the day. We were also expected to know how to use the tables. Nonetheless, I became quite disillusioned with what it meant to be a mathematics or science student in the "Space Age" if we were so dependent upon the tools.

I list a handful of memorized values for sin 10, 20, 30, 40, 45, 50, cos 10, 20, 30, 35, 45, and then tan 10, 20, 30, 40, 45 ...

I use formulas I learned studying Doerfler's

Dead Reckoning: Calculating Without Instruments.

The trig stuff is toward the end of that little book.

I have noticed some weird patterns. 401/7 is used as a constant in the formulas. It serves the same purpose as 180/pi when translating radian units to degree measure. The numbers are roughly 57.2857 and 57.2958, respectively.

Well, when I was investigating how the tangent goes off into infinity as angle measure approaches 90 (pi/2 radians), I tested tan(89) = 1/tan(1).

1/tan(1) = 57.28996 degrees. It's that ratio again. That's a weird zone because from 89 to 90 degrees, the values grow exponentially. tan(89.9) = 572.957..., tan(89.99) = 5729.57789, etc

I had stumbled upon something weird and probably unrelated, but it has to give some clue to something. It can't just be a coincidence. That ratio.

So, I am working with pencil, but also with my homemade calculator, Sage, SymPy, the TI CAS ... always checking to see how many digits of accuracy my approximations have. I am honest in my documentations.

Maybe I am just living as though someone might appreciate my notes and ways of organizing "work." Who knows?

It would be poetic justice if we hobbyists, tinkerers, and burnt-out disgruntled techies end up forming our own coalitions and electronic communities. Maybe whoever is left in the future might prefer more fundamental, close to the bone, cross-platform source code, math-oriented code over the graphics-rich code demanded by video-games, corny ppporny, and Hollywood-cartoon movies.

I really think the hobbyists and their double-agent professional buddies will be able to salvage Unixland in the form of a Linux From Scratch Revolution. Maybe not everyone will be going around making their own distro, but the idea of customizing a kernel to one's particular hardware ought to be made a direct and comprehensible operation by many computer users of the future.