right now...

wjl is giving his practice proposal talk in my living room. I'm being a distracted committee member.

mathematical bullshit: a confession

Confession time: when proving stuff, I feel the need to justify things that I consider to be intuitively obvious. In the course of this, I sometimes look up theorems in a textbook that I couldn't possibly prove, and cite them. I feel slightly dishonest when I do this.

Why? Because the proof in my head didn't need the theorem in the textbook. So why should the paper expression of my thoughts use that theorem?

I am *sure* that the statement is true but I'm unable to justify this intuitive knowledge in a formal language, without the help of the theorem in the textbook. All this talk about eigenvalues feels artificial; but it's the only way I found to connect my intuitive idea with the "objective" mathematics that "everyone" must accept.

Maybe my mind is wrong in being so secure about intuitions whose foundations it has trouble fleshing out (but I doubt it). Instead, I think that my mathematical language skills are deficient, i.e. a kind of "aphasia". If you are a visual thinker, the "informal yet rigorous" language of sentential proofs is a foreign language.

I'd say that communication is one of the hardest and most important problems faced by humanity.
See Jukka Korpela on "How all human communication fails, except by accident".

"you are like me"

Wittgensteinian problem: How can we know that we're talking about the same thing?


NOT DRAWN: cultural norms, the multiple levels of language production

Note that the information rate of English (entropy / time) is pretty low. This is a tight bottleneck in the communication between our brains.

When faced with the interpretation problem, the default working assumption is: you are like me. (Call this assumption "empathy"?)
Bob has a mechanism for generating English speech. Bob will assume that Alice's mechanism is similar enough to his, because this way it's possible to find a solution, perhaps efficiently.
But this assumption is probably the major culprit in human-human misunderstandings. I suspect that many conflicts between normal adults can be attributed to poor theory-of-mind.

It is said that autistics, by virtue of lacking in empathy, don't make this assumption. By this definition, I am very neurotypical. And I am very often wrong.

OTOH, the assumption "you are like me" sounds like a prepotent response that most people learn to suppress when they are 5 or so. If autistics have an executive dysfunction that impairs suppression of prepotent responses, this would predict that autistics, in effect, make this assumption more often than normals. What does the data tell us?

traveling in America - you're invited to invite me

I have lots of vacation days to spare. I'd like to travel around America and stay with friends (IRL or virtual) sometime in June.

Trip #1: probably going to New York in early June.

Trip #2: one of Boston, Seattle, SF Bay Area, other (Austin? San Diego?).

I am biased towards enthusiastic invitations, places where I can meet multiple people, and decent public transportation.

(The ideal trip would last 4 or 5 days. Couches are ok.)