14/06/2013

midsummer miscellany

(c) Jenny Morgan, 'Midsummer Hare'



It may be that curiosity comes at the expense of commonality.


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We need a term for high-IQ people who are, nonetheless, idiots. I suggest 'arch-idiot'. Usage: "Almost the entire field of financial economics was composed of archidiots." Taleb uses nerd as a technical term for this; Marx, ein Fachidiot. The culture at large uses savant, but this is not quite right and would stick the boot in to autists yet again. We also say book-smart, but that's anti-intellectual: our problem would not cease with the banning of all poncey books, since our problem is with those that abuse the poncey books.
Archstupidity (n.): The presence of strong abstract reasoning in the absence of emotional intelligence, empirical feedback, or actual rationality. Leads to the ubiquitous, dangerous assumption that since one understands one complex theory (C++, economics, cell biology, Heidegger), one understands all complex things (love, economies, cancer, Being).

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"So in closing, fuck you pandas. If you’re too stupid to get on all that hot panda ass, well then you deserve to die."
- an angry man, speaking for you

Pandas have problems; but people too have a serious panda problem. Panda-talk is one of the remaining places it's acceptable to openly despise the weak: a cranny for social Darwinism to breed in. Mate James tried to rationalise this - saying that it's not pandas' weakness or deviance from the Darwinian script that we despise, but their conservatism, their listlessness, their inability to change. I think you know fine well what it means.


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Today we'll prove that a straight line is sometimes a circle. (This is a mad but elementary result in Euclidean geometry.) We can understand this informally with the diagram above: as circles increase in diameter, the curvature of a given arc AB decreases, with the logical endpoint being curvature zero: a straight tangent. So a circle of infinite radius is an unimaginable circ/line chimera. The proper argument can be put lots of ways; here is a simple one:

  1. From three points we can always construct their one associated circle. (Since the perpendicular bisectors of their two line segments must pass through the centre, and the radius is then trivial to find).
  2. If these 3 points are on a line, though, their perp. bisectors are parallel.
  3. If we then grant a line-at-infinity, the intersection of these bisectors - the centre they seek - exists, but infinitely far away;
  4. So their circle's radius is infinite.
  5. So the circle of three points on a line is a line. (Properly, a 'Euclidean horocycle', or 'collinear circumcircle').
Contentions abound: "Why doesn't this argument instead conclude that (1) only holds assuming the three points are not on a line? (Why isn't the circ/line a "degenerating case"?)  Obtaining curvature zero requires a division by infinity (Curv = 1/R, R=∞), and infinity isn't a number! And, don't parallel lines never meet? What on earth lets you get away with this line-at-infinity crap?" Good questions!
 
  • Why isn't this "collinear circumcircle" just dismissed as degenerative? Why add in this line-at-infinity? How can parallel lines meet?
It all began because geometers didn't like caveats. (If parallel lines never meet, then the plane they extend over is infinite and incomplete.) They also had a good reason to piss about with infinity: the real plane has problems of incidence, and one new plane ("the projective plane") can be used to solve these generally and easily. Recipe for projective geometry: take the real plane, add in one strange "point at infinity": the point that both positive and negative line directions meet at when extended to a figurative horizon. On this plane, lines are actually cyclical, and, as we'll see, circles are actually, sort of, linear. This circularity includes the line-at-infinity (the dotted line here):



If our parallel bisectors intersect at this bizarre line, then we know the centre lies on the line-at-infinity (given this again, and given that we've built this whole bloody system to ensure that incidence is universal, and that all this holds up beyond the Limit). Specifically, our infinite chimera is perpendicular to the line of the original three points: the red line (by projective logic, the centre is both of the red dots there). So, the circline's not an exception to (1), because our circline is not a limiting case: it exists, in more than one well-motivated system. (Note, if it makes you feel any better, that two infinite circles can be thought of as parallel circlines.)

  • Infinity isn't a number! How can you use it as a denominator? Why should we expect classical definitions of geometric objects to stand up to infinitudes?
There's a proof of the curvature-method that uses limits instead here. With regards to breaking Euclid: it's the same as with anything: we see what happens to the system at extremes and then talk to each other about what it means.

  • Boo! I don't like limits! I define a tangent as that which only ever has one point of contact; so it's constant through increasing radius; so, you lose.
Feel free to move the goalposts. Make yourself at home. (There is a conflict of definitions. But since a circle is not, formally, "a very round thing", but "that plane figure that is the locus of all points equidistant from one fixed point C", I think our one wins out.)

Given all the above, we drop our intuition that "lines are never circles". Infinity is liable to do that to intuitions. So? What's the significance? Probably nothing, as usual - but it's cool to note that the medieval philosopher Nicholas of Cusa used the above argument as a Platonic gadget for seeing the outline of things we cannot really see (like, he thought, God). The infinite in the finite, and other old chestnuts.


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I wrote a thing about identity and my failing engagement to the immortal mind-queen Maths.


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Found myself in a roomful of pre-drinking clubbers talking about how much they drank last night, and were going to tonight, and how the people not currently in the room were skanks. In silent mental self-defence, I elaborated on one woman's thesis, that "Booze is awesome":
Assuredly is. Why? Because it legitimises bad behaviour. Because it levels conversation, precluding nuance. Because it exaggerates emotions. Because it alone allows you to  express said emotional state to others without enormous sanitising. Because it makes life less unentertaining (because it contrives situations for ridicule, and mutual ridicule). Because drunk people aren't alone (because booze uncovers the falsity of the Cartesian, centralised self)! Because it dulls the pain of being - a pain you never examine, for fear of what it might mean for your chances of ordinariness and cinematic happiness.

Did write this while drunk, so, y'know.


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"'He affects a large tolerance of the world - he keeps out of it. [But] I think no one can really be like that - either you're dismayed and baffled, or you reduce everything to aesthetics or politics or sex sociology or whatever.'"
- Paula Fox's Otto


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I wonder how often Yoko Ono listens to the Beatles.


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A mate recently rocked my comfortable, sneering position on postmodernism. I had made the tired point that in fact the realisms and metaphysics-of-presence that the New New Left revile have often been the oppressed's last refuge in the face of totalitarians distorting history and the present. Allowing this, he gave the following analogy, which is, I think, a third-order argument. (First-order: "is there a world?" Second-order: "are there possible worlds?" Third-order: "why do people argue that there are (or are not) possible worlds?"):
"There is a classroom. A fierce teacher stands at the head; the class work busily under his eye. What if all of Theory was just getting the teacher to leave the room? Some people predict social chaos and unchecked evil when you remove the old, objective structural rods. But maybe the class would just keep working - and that'd be the ultimate proof of the teacher's authority - the self-regulating, self-controlling class. Proof by exhaustion."
Only problem with this amazing analogy - and you can imagine the best jesters of French theory getting the joke - is that it understates the vitriol aimed at the Teacher among today's queer/eco/race Foucauldians. It's not that we are taking the teacher out for a tea break; no, we strip him naked, paint him orange and dismember him in front of his class. That's the real corollary of the academic sneer that is the mirror of mine.


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Really really good line in the otherwise stupid show Supernatural:

"Hunk #1: We make our own future.
Hunk #2: Yeah; got no choice."

(Compatibilism)


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Early class analysis missed a lot of things. A fairly minor one: the world maintains a gross inequality in the distribution of posterity. (Who pays the piper is worth a thousand words.) Posterity is that cartelised mixture of fame and honour a certain kind of person will pay vast amounts to secure. (For instance, the great works of classic poets were often bankrolled by people who wanted their moneygrubbing behaviour gilded and inset in eternity.)

It's arguable how much we currently manage to couple achievement to posterity. (Since, on the one hand, reality tv exists, but on the other: "Writers are remembered by their best books, politicians are remembered by their worst mistakes, businessmen are never remembered for anything." - Taleb.) 

Marxist history and its deradicalised form (the banally named "social history") have done quite a lot against this - and, with the internet, posterity could even be democratised a bit. But not I think, until celebrity culture dies.
 
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I used to say things like "The truth cannot be sexist." This sounds good, but isn't really true: there are many false beliefs that have made themselves contingently true by exploiting human plasticity. Consider: "Women are worse at leadership"; "There were few great female artists" (up to the C20th).

There are many countercases to these, from many slices of history. But these kinds of beliefs were beaten into generations of people, and so came to seem essential, and so no-one had time to challenge all of them. (This is how I rationalise Hume and Kant being bastard racists.)

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