The strange properties of the infinite power tower
arxiv.org
arxiv.org
At Hampshire College in the early 90's, I took a "Math Concentrators' Seminar" which was really a free-form math club with free pizza one evening a week run by an offbeat, charismatic professor whose name I forget [edit: David Kelly[1]]. I wasn't focused on math at the time and didn't have anywhere near the foundation I should have for the class, but the professor was happy to have me.
We spent hours just informally batting around diverse, fun math concepts, and one of the topics I remember best was all the fun and counter-intuitive properties of infinite series like this. In any case, this paper is really a treat. Thank you OP.
[1] https://en.wikipedia.org/wiki/David_Kelly_(mathematician)
NS 322 MATH CONCENTRATORS' SEMINAR David Kelly This weekly gathering of students interested in mathematics and its applications will include lectures by Hampshire faculty and guests. presentations by Division III students. films, workshops. problem-solving sessions, puzzles, games. paradoxes. history, and philosophy. The seminar provides an opportunity for students to get to know each other and gain exposure to many active areas of mathematics. This class will meet once a week for two hours.
Thanks for sharing your story! :)
It's still running after almost half a century (with Kelly still in charge!). I got to attend almost 30 years ago (wait, how has it been that long already?).
Spending an entire school lifetime being taught to "solve" "problems" and then being confronted with a world where problems aren't defined and solutions are ad-hoc and piecemeal is a rude awakening.
The strategies that made us a good students and made us feel good and smart in school aren't the same strategies that make for a good employee and those strategies set new devs up to fail when they can't "see the answer" to the current jira ticket they are tasked with.