This is very useful.

Upon reading this, I immediately synthesized the following practical advice (with offline conversations in mind):

1) To be a better talker, you need to know off the top of your head what to do with a "what's new" or similar invitation. Being prepared for likely specific inquiries (e.g. "How was your weekend" on a Monday) is also wise, keeping in mind that a certain amount of redirection is acceptable ("Not too much--I was resting after [interesting intense thing] last weekend").

2) To be a better listener, you need to be able to ask specific questions. I, for one, would be highly interested in a list of conversation items to drill this on, since generating these on the spot has been my failure point more times than I can count. (I don't mean trying to prepare follow-ups to everything someone might say, but rather practicing to get better at generating.)

I don't think it is strictly true that Grothendieck didn't rely on examples. Here is a quote from a letter from Luc Illusie, who was a grad student under Grothendieck. Quote:

“In his filing cabinets, located behind his desk, Grothendieck kept many handwritten notes, where he had studied specific examples: he sometimes told me that he was weak on surfaces, but as everybody knows, he was not so weak in local algebra, and he knew enough of curves, abelian varieties and algebraic groups to be able to test his ideas. Also, his familiarity (and constant interest) in analysis and topology was a strong asset. All these examples appeared when you discussed with him."

Slightly related ... there is a recent philosophy of mathematics book (albeit a work of continental philosophy, but it is still interesting). I say slightly related, because firstly it has an entire chapter on Grothendieck and creativity, and secondly the entire book is about the interplay between examples and theory. It goes into the way mathematics moves up and down a ladder of abstraction (from particulars to universals, local to global, specialization to generalization). It focuses on the last 100 years of mathematics, concentrating on algebraic geometry, category theory, model theory, and others. The author splits up the abstractions into:

• Eidal mathematics, or "transfusions of form." This is mathematics that moves up the ladder from the particular to the universal. In this part of the book it focuses on the work of Serres, Langlands, Lawvere, Shelah.
• Quiddital mathematics, or "transfusions of reality." This is abstractions made concrete moving down the ladder. Here the book focuses on Atiyah, Lax, Connes, Kontsevich.
• Archeal mathematics, or "decantations of the universal." This is mathematics that studies the invariants while one moves up and down the ladder. Here it focuses on Freyd, Simpson, Zilber, Gromov.

Now you could say this philosopher is just dressing up stuff already known to mathematicians (Both Kevin Houston's How to think like a mathematician, and Mason/Burton's Thinking Mathematically talk about generalization and specialization). But it is still interesting, as I think it may be the only philosophy of mathematics book out there that does an indepth treatment of 20th and 21st Century mathematics that goes beyond Russell and Frege.

Is there a better expression for the "my enemy must be the friend of my other enemy" fallacy, or insistence on categorizing all your (political or ideological) opponents as facets of the same category?

Short Online Texts Thread

Short Online Texts Thread

You may remember early in the Arabian revolutions in Libya, an American student took the summer off college to fight in the revolution.

Adding to this, there is an entire online community of these people at the Black Flag Cafe. Outsiders label them as "war tourists," but the majority of them are journalists, war photographers, businessmen, and humanitarians/activists. The website was founded by Robert Young Pelton (whose wikipedia page is worth reading). He wrote a great book, that is filled with practical information.

RE: how / why distinction.

John Whitmore's book Coaching for Performance goes into this. Snippit from the book:

If commanding a person to do what they need to do does not produce the desired effect, what does? Let's try a question.

• "Are you watching the ball?" How would we respond to that? Defensively, perhaps, and we would probably lie, just as we did at school when the teacher asked us if we were paying attention.

• "Why aren't you watching the ball?" More defensiveness -- or perhaps a little analysis if you are that way inclined. "I am," "I don't know," "because I was thinking about my grip," or, more truthfully, "because you are distracting me and making me nervous."

These are not very effective questions, but consider the effect of the following:

• "Which way is the ball spinning as it comes toward you?"
• "How high is it this time as it crosses the net?"
• "Does it spin faster or slower after it bounces, this time, each time?"
• "How far is it from your opponent when you first see which way it is spinning?"

These questions are of an altogether different order. They create four important effects that neither the other questions nor commands do:

• This type of question compels the player to watch the ball. It is not possible to answer the question unless he or she does that.

• The player will have to focus to a higher order than normal to give the accurate answer the question demands, providing a higher quality of input.

• The answers sought are descriptive not judgmental, so there is no risk of descent into self-criticism or damage to self-esteem.

• We have the benefit of a feedback loop for the coach, who is able to verify the accuracy of the player's answers and therefore the quality of concentration.

Short Online Texts Thread

Nonfiction Books Thread

Nonfiction Books Thread