A Fresh E-Mail for Dave tfp Hi Dave, I apologize if I miss stuff from your last e-mail, because I'm writing this offline on an AlphaSmart 3000. Have you ever seen one? It is a nifty single-purpose computer gizmo for text editing. They were originally marketed to schools before laptops/tablets became common. They get about ~400 hours to a battery and can store something like ~100 pages of text. I am glad to hear that you found a nice geometric solution to the sphere and line intersection problem. I skimmed the page that you sent and all the methods look really clean and crisp. [Using cross products, norms, and simple arithmetic is the way that I would solve the problem too.] Your situation with mathematics, how you have tried multiple times to get the hang of it and yet it remains an elusive foreign language, reminds me of how I feel about (written) music and music performance. I had no musical training as a kid, and that is one of my greatest regrets. I've made several serious attempts to learn music as an adult and made very little progress. After +200 hours of playing around with a ukulele, I can play exactly two songs shoddily ("What shall we do with a drunken sailor?" and "We shall overcome"). Formally, I know how sheet music works but the process of transforming it in to living actual music is as mysterious to me as writing was to pre-literate oral cultures. It seems utterly magical. Every time I've taken formal music lessons, on piano, ukulele, or voice, it feels awkward, clunky, and impossible. I joined a hippy choir which sang in the oral tradition, and enjoyed that for a number of number of years before the Pandemic. So, I empathize with your feelings about mathematics. I suppose that I need to find my musical analogue of your ray-tracing project. I looked in to Knuth's Literate Programming a bit by checking out the book. It is very cool. A little bit hard to appreciate what is going on due to the examples being in Pascal, but I like the idea of it. The two names of the two pre-processors, TANGLE and WEAVE, are adorable. Now I see that literate programming goes a fair bit beyond commenting and arranging code. There is a whole part about transclusion (is that the right word?) where code gets put in place according by being named by section. So, the same section of code can be included in multiple places. Very cool stuff. I looked around a bit and I don't see a strong successor to these tools. Doxygen comes close. Python has some built in stuff about docstrings. It looks like WEB and CWEB are their own limb in the tree of programming languages. I was blown away to learn that TeX and METAFONT were written in WEB. The complete programs are available as printed books. It turns out that Knuth's book, Selected Papers on Fun and Games, has a CWEB-ified version of Adventure (if you prefer lighter reading). Since getting your last e-mail, I finished reading the Old Man's War by John Scalzi. I'm confident that the whole thing is fantastic from beginning to end. This might make me sound like a prude, or a bore, but I appreciate how "clean" the plot is. There is no edge-y trauma, no complicated morally ambiguous stuff, no troubled anti-heroes, no post-modern shenanigans. Do you know what I mean? There is a place for all that, and I enjoy harder stuff, but I don't need it all the time. Old Man's War is just clean straightforward science fiction on a grand scale. The last two volumes were a nice end-of-summer binge read before I get back to work. Work is about to really ramp up. We start classes next week. I've got two sections of Calc 1 for Life Sciences, and one section of Multivariable Calc 1 plus the work of doing all the high-level administration for those courses. All told, I will have ~1000 students. My wife is also going back to day time work next week, starting as a supply teacher. She hasn't had day time work since went on maternity leave two and a half years ago. She's had some evening work teaching English after school for the last year or so, but her days were free. (As I write this, I realize that I don't know much about your family other than that you have one, love them, and read a lot with your kids.) To help get ready for back-to-school-which-is-actually-where-we-work, we spent the last month stuffing our deepfreeze with food: chili, lasagna, a bunch of soups, cookie dough, bread. Filling the deepfreeze is my most recent project. Hopefully it helps with rush of life. I love cooking and baking, but tend prefer making things en masse. Cooking an individual meal is not as satisfying (to me) as a week worth of lunches. Do you like to cook or bake? I hope that all is well with you and yours. Wish me luck as I get devoured by a thousand math-hungry undergrads. Good luck with all your projects.