Is there a video that provides intuition about why countable subsets of R (even dense ones) have outer measure zero, by zooming in on a cover of such a set by a union of countably many intervals?
Last night I dreamed that I accidentally triggered a mass movement in which mathematicians attending a talk would rise to their feet sarcastically clapping and cheering if the speaker was disorganized and incomprehensible
@christianp I was not the speaker; I was in the audience, asking questions that I hoped would steer the speaker back into the realm of comprehensibility. He welcomed my questions but his answers were just as incomprehensible as everything else he said.
Slowly getting through my backlog of emails and tasks that built up while I was away for #G4G15. It was an extended trip this time, but #G4G was fabulous.
what do provability, decidability, consistency, and completeness mean?
how do we work with equality in set theory?
I don't know articles that explain topics like this to non-mathematicians, clearly and crisply, without becoming overlong or heavy with notation. Do you?
I looked around and found this "Introduction to First-Order Logic":
but that's more like a course than what I'm thinking of here: a collection of essays that explain different topics in plain English.
I also liked Hofstadter's "Gödel, Escher, Bach", but that's a massive quirky elaborate tale, not a simple clear explanation.
Wikipedia articles are packed with information but they aren't self-contained, clearly written essays. Articles in the Stanford Encyclopedia of Philosophy are better in some ways, but they often "show off" by including more advanced material.
@johncarlosbaez What about “A Panorama of Logic” by Joel Hamkins? It’s intended to be “an introduction to all aspects of logic, for philosophers, mathematicians, and computer scientists”. I know nothing about the book but I like Hamkins’ writing so I’m guessing it’s good.
In this month's Mathematical Enchantment essay, you'll learn what Cauchy thought complex numbers really were and what Kronecker thought irrational numbers really were, and how mathematicians learned to stop worrying. https://mathenchant.wordpress.com/2024/02/17/plus-and-times-set-free/
@johncarlosbaez@csk@stevenstrogatz Radiolab has established a lot of credibility, so I hate to see them lend prestige to goofy stuff that layfolk might mistake for the latest revolution in mathematical thought. (Especially since “All Is One” vs. “Everything Is Different from Everything Else” is not a new duality; goes back to ancient Greece if not beyond.)
Dismayed to notice that in 2003 I published an article containing a sentence with an unmatched left parenthesis so that everything I’ve published in the last twenty years has been part of one extremely long parenthetical remark.
A garbled version of my essay appears at https://show-hn.com/2023/10/22/apt-arithmetics-of-distance/ . It looks like it was translated into another language before being translated back into English. Anyone know who would create such a thing and why? (And am I risking anything by Approving it via WordPress?)
I seem to recall that Mr. Spock bungles the definition of exponentiation in some Star Trek episode (incorrectly defining 10^n as TEN followed by n zeroes). Can anyone provide details? Or am I thinking of some other sci-fi series?
Why does the cover art for “Music for 88” by Tom Johnson leave out the “1 3 3 1” row of Pascal’s triangle? Did the graphic designer mess up, or is a deliberate artistic choice that relates to the music?