Palo Alto December 21st, 2019 ====== Hello, dearest friends and relations! Mid-morning of the solstice, and the mist has finally lifted off the San Francisco Peninsula. I'm sitting underneath the redwood in the backyard, surrounded by oxalis sprouting everywhere after two weeks of rain, running through my to-do lists trying to close the books on FY2019. (Perhaps I should have opened this letter: "Hello, auditors!") Bad news first: I again failed to stand up on a surfboard for more than two seconds, I bleached a streak in my hair (which is cool, but symbolic mainly of my continuing denial of aging and adult responsibilities), [REDACTED], [DEFINITELY REDACTED], everything involving national politics, most things involving international politics, I'm no longer living just across town from adorable cousin-niece and -nephew Olive and Leo, and Emma the corgi died in June [0] after almost fourteen years of loyal companionship. Somewhat better news: I spent January in the Balkans [1] and Asia Minor [2], ran two marathons, and went on half a dozen rock climbing trips to the Gunks and West Virginia. I visited Grandma Jean in Minneapolis twice, and 98-year-old (great-)Auntie Liz in Missouri once. I'm again sharing the Good News of mathematics with heathen youth (biking twelve miles each way to do so). The school I'm at is lovely: we offer not just the usual fancy-high-school slate of multivariable calculus and linear algebra, but also differential equations! Number theory! Complex analysis and algebraic topology in alternate years! And I got to use the school laser cutter (a/k/a "lazy cutter") to make an Etsy-ready production run of several dozen beverage coasters in the design of a Sierpinski carpet fractal [3]. I'm living in Palo Alto in a house with faded redwood shingles, owned by an electrical engineer who toured with the Grateful Dead before making ambiguous amounts of money in startups in the 90s. Chelsea Clinton's boyfriend lived in the house when she was at Stanford, and Chelsea had her graduation party here---inside is a framed photo of Chelsea, her parents, and our landlord, standing just outside the front door. I'm actually living not in the house per se, rather in the shed out back, but no need to worry---I have a roommate! Plus eight more roommates who live in the main house. This is California, so when I walk outside to go to the bathroom at night (into the house), it's usually not raining. The only thing that could have made 2019 better? Your presence, if we didn't get to commune. That, and a different President. On that note (sorta), my (unintentional) reading project this year was to juxtapose Enlightenment Now: The Case for Reason, Science, Humanism, and Progress [4], with Why Liberalism Failed [5] and two speeches by Senator Hawley [6][7]. On the one hand, our material lives have never been better. If you had to choose any place and any time in human history to live, it would be today, in America (constant doomsaying in the media notwithstanding). Fewer and fewer people are dying of disease and violence, technology is cheap and getting cheaper, entertainment is free, communication is instant. We're less and less confined by the circumstances of our birth. But all of this progress has come at a cost: everything is caught in faster and faster positive-feedback loops. A complex multidimensional landscape and search process has been reduced to the maximization of a single metric (one which isn't "virtue" or "grace"). "Late capitalism" (if you're on the left) or "modernism" (if you're on the right) is a giant emergent machine, one we all made, by accident, and that no one's in charge of, with our bodies (souls?) as the cogs. We're freeer than ever, but also more and more lost: not chained in the cave watching shadows dancing on the walls [8], but astronauts on a spacewalk, untethered, unable to see anything, shadow or not, amusing ourselves to death [9] in the darkness. In the limit of this amoral individualism, we get our current President. He acknowledges no God other than himself. Of course I'm typing all this on a gadget the richest person in the world couldn't have afforded a few decades ago, but which last year cost me less than a day's wages. I don't know how to resolve that contradiction. I know I'm part of the problem: I've spent 33 years refusing to tie myself down to a career, or a person, or a place, or even a pet, or even a single effing piece of furniture. "When the world around you goes astray," Dante writes, "in you is the cause, and in you let [the solution] be found" [10]. Goals for the 2020s: less glorification of the individual, more glorification of the numinous and transcendent. Less Smerdyakov, more Zosima; less formalism; more mysticism. ... and on THAT note, since math is fundamentally a mystical experience, I'm really excited kick off the 2020s by teaching complex numbers for the first time. The theory of complex numbers rivals calculus as the most intellectually profound topic we can talk about in high school---yet it's usually almost completely ignored. (Contra calculus, which suffers its fame by being tortured and mutilated beyond recognition.) I have a huge list of topics I want to cover---this theorem! that theorem! 100 repetitive versions of such-and-such problem to build up intuition!---and stumbled across a YouTube series by some guy that develops complex numbers all the way to Riemann surfaces, with gorgeous animations and assuming zero prior knowledge. Can we get that far?? No idea. Am I going to have any idea what I'm doing?!? Nope!!! The last day of the semester I ended class by shouting at the kids as I left the room, "Your teachers have all been lying to you! Numbers are actually two dimensional! THEY'RE ACTUALLY TWO-DIMENSIONAL!!!! SEE YOU IN JANUARY!!!" love to each of you, Andrew --------- [0] https://drive.google.com/open?id=1ol47CuiucZrSkTJ1P4ClV0Zlqm0AtX-d [1] https://medium.com/@andrewmhalexander/greece-january-2019-c87b6b8d9a7f [2] https://medium.com/@andrewmhalexander/istanbul-january-2019-58e20caded2 [3] http://andrusia.com/sierpinski-carpet-coasters.jpg [4] https://www.amazon.com/Enlightenment-Now-Science-Humanism-Progress/dp/0525427570 [5] https://www.amazon.com/Why-Liberalism-Failed-Politics-Culture/dp/0300240023 [6] https://www.christianitytoday.com/ct/2019/june-web-only/age-of-pelagius-joshua-hawley.html [7] https://www.hawley.senate.gov/senator-josh-hawleys-speech-6th-annual-american-principles-project-gala [8] http://classics.mit.edu/Plato/republic.8.vii.html [9] https://www.amazon.com/Amusing-Ourselves-Death-Discourse-Business/dp/014303653X [10] Purgatorio XVI 82-3 [11] https://www.theamericanconservative.com/dreher/the-elder-zosima-option/