This looks great and I'm looking forward to reading it properly. But it gave me a jolt to read the following:
Weil wrote this fourteen-page letter to Simone Weil, his sister [...] Keep in mind that the letter was not written for a mathematician, even though Simone could not understand most of it.
Could not understand it? Why'd he write it to her then? (Edit: he commented on this; see below.)
Simone Weil was brilliant. She had remarkable mathematical gifts, though she decided early on that she wasn't good at math by comparing herself to her brother. (André was not only a mathematical genius, he was 3 years older. Talk about an unfortunate data point.) She ended up, in her brief life, doing remarkable philosophical, political, and spiritual work. Her intellect was as deep and as original as they come. At the time this letter was written, she would have been at the height of her powers (working for the French resistance in London, as I recall, writing a book about how to rebuild France after the war - a book which de Gaulle supposedly threw in the garbage without reading).
Simone and André Weil used to act scenes from Greek tragedy in Greek when she was 4 and he was 7. As George Grant once said, that family had intellectual culture in a way we in modern North America can't even imagine.
To make patronizing comments about what Simone Weil couldn't understand is pretty ignorant. Based on what we know about her, though, she wouldn't have minded.
(Sorry this comment has nothing to do with the actual content of the post.)
The letter itself says: "So, I decided
to write them down, even if for the most part they
are incomprehensible to you" and "you may be able to understand the beginning; you
will understand nothing of what follows that."
That shows that Andre thought Simone wouldn't understand it.
Oh, that's interesting. I probably shouldn't have commented without reading the whole thing, especially since what I said was a bit off-topic. (It's often easier to comment on tangential things, which makes a lot of discussions go awry.) I recommend upvoting mgreenbe, who actually has something on-topic to say!
Come to think of it, I vaguely remember reading this, or excerpts from it, years ago.
This notion of "analogy" is formalized in category theory. At times this is done to great effect --- the generalizing power of category theory can help a mathematician see the forest for the trees. This has been done to great effect, e.g., in programming language theory. Then again, at times category theory is shallow, nothing more than abstract nonsense. (N.B. this is a technical term.)
The strict formalist in me likes category theory because it has so many names for things, many of which are in Greek. The intuitionist in me thinks the field is pointless but likes drawings with arrows in them. All in all, it's a win-win. :)
Weil wrote this fourteen-page letter to Simone Weil, his sister [...] Keep in mind that the letter was not written for a mathematician, even though Simone could not understand most of it.
Could not understand it? Why'd he write it to her then? (Edit: he commented on this; see below.)
Simone Weil was brilliant. She had remarkable mathematical gifts, though she decided early on that she wasn't good at math by comparing herself to her brother. (André was not only a mathematical genius, he was 3 years older. Talk about an unfortunate data point.) She ended up, in her brief life, doing remarkable philosophical, political, and spiritual work. Her intellect was as deep and as original as they come. At the time this letter was written, she would have been at the height of her powers (working for the French resistance in London, as I recall, writing a book about how to rebuild France after the war - a book which de Gaulle supposedly threw in the garbage without reading).
Simone and André Weil used to act scenes from Greek tragedy in Greek when she was 4 and he was 7. As George Grant once said, that family had intellectual culture in a way we in modern North America can't even imagine.
To make patronizing comments about what Simone Weil couldn't understand is pretty ignorant. Based on what we know about her, though, she wouldn't have minded.
(Sorry this comment has nothing to do with the actual content of the post.)