09

Dec

"Summary of the construction of tmf" by Aaron Mazel-Gee, p. 4 in Mark Behrens’ "Notes on the construction of tmf".

Discussion: I won’t try to explain what this diagram means, but I’d like to analyze its structure. The bottom row is a diagram of various “stacks”, which are parameter spaces describing (in this case) various types of curves. These are the various worlds inhabited by the objects in the higher rows. The vertical coordinate on top is “height”, an organizational system that’s central to the modern “chromatic” view of stable homotopy theory. The goal is a new understanding of height 2 via the thing labelled “O_top” in the second column, lying over the stack “M_ell” below it. The diagram demonstrates how O_top is assembled from the other dudes by two methods:
(1) the “homotopy pullback squares” in the second and fourth columns, which serve to glue things together;
(2) more interesting because less examined, the squiggly arrows, which are not mathematical symbols but merely demonstrate that an object is sent to a different part of the diagram. What’s interesting to me is that all these “conceptual arrows” turn out to have the same mathematical meaning: they represent pushforwards of the objects on top along the maps on the bottom. This is not tautologically the same as the intuitive idea that an object lives in one place and should be moved to another one for later use! In particular, the latter concept is probably used outside math too, any time we visually organize information in solving a problem.

The question is, then: can math, which has hitherto mainly been responsible for its own philosophy, define/divine a rigorous way of talking about the squiggly arrows? Can this be applied to extramathematical concepts? Conversely, can other popular techniques for understanding thought (psychology? phenomenology? post-structuralism?) be applied to these visual, diagrammatic methods so popular in math post Mac Lane?

26

Nov

From Nicholas Katz and Barry Mazur, Arithmetic Moduli of Elliptic Curves.

The inner self is a social construct.

10

Nov

(Source: martymcphly)

09

Nov

genre shock

# Memorialization and Genre Shock

I used to do PowerPoint comedy in college, and I’m still always on the lookout for weird uses of the PowerPoint form.  It’s somehow emblematic of the artistic collapse of late-capitalist turn-of-the-millennium America: an technological marvel that was instantly dated, misguidedly intended to maximize the efficiency of information delivery at the cost of aesthetics, skeuomorphizing an older form — the slide show — that nobody ever enjoyed.  Attempts at flair — the animated transitions, the kitschy backgrounds, the overused preloaded clip art — seem as laughably old-fashioned now as they were aesthetically empty then.  The original PowerPoint makers were a quintessentially American archetype that is now rapidly disappearing in a shrinking economy: the boring-ass, white-collar, fuddy-duddy, nine-to-five Company Man.  Make a PowerPoint, then, and you, too, can tap into the Company Man’s soul, which, with its sense of ‘success’ according to an aging value system and strict insistence on mostly irrelevant social roles, is a space ripe for comedy.

Here we see another strange use of the PowerPoint.  It’s a memorial, essentially, for American mathematician Irving Kaplansky, by his student Hyman Bass.  Reading this late last night, I was acutely disturbed by the way the form seemed to trivialize the man’s life and work.  Meaningful facts and personality traits are crudely arranged in lists of bullet-points.  ”1951: Married Chellie Brenner,” we read.  ”Three children: Steven, Alex, Lucy.”  What might have been descriptive lists of students, positions, and accomplishments become boring timelines.  (In what might be more the aesthetic of Hyman Bass than the aesthetic of PowerPoint, there are even color-coded charts.)

(It’s true that we’re reading this PowerPoint without the spoken presentation that presumably accompanied it, which would no doubt have been somehow more emotional.  But the usual reader-response sorts of arguments quickly dispose of this point: this work exists, today, as a stand-alone text, and we’re within our rights to analyze it as such, i.e. within the bounds dictated by the way we’re required to read it.)

The problem with this presentation isn’t an absolute one: there are no universal ethical or aesthetic laws on how to memorialize of the dead, and indeed, various cultures have invented a broad range of strategies for dealing with this transition, from worshiping ancestors’ spirits, to preserving their bodies, to making molds of their faces.  The problem, rather, is the disconnect between the PowerPoint genre, with its own aesthetic code and hidden assumptions, and the funereal genres typical to our culture.  I can think of only two: the obituary and the eulogy.  (We might add the biography, but I’d argue that this serves a distinct aesthetic purpose — for example, it can be written while its subject is alive.)

The eulogy in its current form seems a hold-over from the Victorian culture of death and mourning.  It’s delivered only once, at an emotionally charged moment, often in front of the corpse itself.  To deal with the surprising emotional needs of the moment, it’s often at least partly extemporaneous.  It’s anecdotal in form, the subject not being the broad strokes of the dead one’s life, but brief moments that they may have shared only with the eulogizer.  Of course, the true purpose isn’t to disseminate these anecdotes, but to share an emotional space with the other members of the funeral party.  Over a series of eulogies and anecdotes, the group together constructs a final memory of the departed.  One hidden assumption of the form, then, is that the group benefits from this brief resurrection — if the memorialized lived a cruel life and is better left in the grave, this assumption is challenged, lead to confrontation and the airing-out of trauma.

The obituary, at best, aims for aesthetic neutrality, and may ultimately suffer from some of the same failings as this remembrance of poor Kap.  It’s an essay-style summary of the events in a person’s life, with the added functional purpose of announcing their funeral arrangements.  For a reason I’ve never totally understood, it’s often published in the newspaper, thus reaching two audiences: loved ones, for whom the information within is redundant, and total strangers, for whom it’s irrelevant.  As with any form of such neutrality, it’s hard to get a read on its hidden assumptions, but one of them may be that the dissemination of such information serves a cultural purpose.  Again, Victorian death-culture may be relevant, as such announcements may have helped people navigate the intricate rules of mourning and long-term memorialization of the time.

The remembrance at hand is neither emotional nor aesthetically neutral.  It forces emotional data — how was Kaplansky as a father? as an advisor? — and eulogical anecdotes — here’s a song about pi he wrote — into the demands of brevity and format forced by the “efficient information delivery” aesthetic of the PowerPoint.  The result is what I’d like to call genre shockthe emotional conflict arising from the demands placed on a text by an unusual or unexpected form.  This example is particularly powerful because memorialization of the dead exists in such a small aesthetic space to begin with that any move out of this space is in some sense unexpected.

I’m having serious trouble thinking of other examples.  My brother suggested mockumentaries, which eventually became their own genre, but to me this just seems like another example of the comedy of forms (which I’ll elaborate on later): comedy is not forced into the documentary form unexpectedly, it uses the documentary form and its hidden assumptions to achieve comedic ends.  As we’ve seen here, genre shock isn’t necessarily funny, though I see no reason why it shouldn’t be funny, either.  Any other ideas?

ETA: The last slide is key.  One subtle point: “A LIFE TO BE CELEBRATED” is written in the LaTeX \mathcal font typically used in mathematical papers for cursive mathematical symbols like categories, sheaves, or families of sets.  I don’t know what to make of this.

Something Awful, as usual, gets it right.

29

Oct

From Berthelot and Ogus’s Notes on Crystalline Cohomology.

28

Oct

Christopher Wallace

08

Oct

04

Oct

John Haslam’s 1810 illustration of the “Air Loom,” a delusion of James Tilly Matthews, the first documented schizophrenic, who believed it was being used to torture him for political purposes.

From Wikipedia: ‘The torments induced by the rays included “Lobster-cracking”, during which the circulation of the blood was prevented by amagnetic field; “Stomach-skinning”; and “Apoplexy-working with the nutmeg grater” which involved the introduction of fluids into the skull. His persecutors bore such names as “the Middleman” (who operated the Air Loom), “the Glove Woman” and “Sir Archy” (who acted as “repeaters” or “active worriers” to enhance Matthews’ torment or record the machine’s activities) and their leader, a man called “Bill, or the King”.’

13

Sep

Iona Rozeal Brown, “a3 #10 down-ass emperor Quianlong”