Bonds and Bond Insurance (basics I should understand, I think)

Bond-insurance is just a promise. When you buy it, you buy a promise. The bond is a promise in a sense, but it can also be thought of, like stock, as a part of the company’s stuff. That’s what you buy, a pound of steel, an employee’s MBA knowledge….  But insurance is a promise. Promises are performatives. So what? Shoshana Feldman might know.

A bank buys a bunch of corporate bonds. If it keeps them, it makes money in proportion to how well the companies fair. If all the companies do well and can pay, they make some interest money. If only some companies can pay and some default, the bank makes less money overall and may even lose money if a lot cannot pay.  Instead of sticking with this old-fashioned notion, the bank can pool these bonds together and re-sell them. When it re-sells them, it sells them in risk-slices. Some slice-buyers will not get any money back if a proportion of the overall pool defaults. Instead of the bank getting lower return (or loss) in this situation, the secondary investor loses everything.  So this is a way for banks to make higher profits.  Li’s formula enabled these transactions to occur because it established a way to price the slices.

In other words, if I buy into a pool of bonds, I am giving money (via an investment bank) to a bunch of companies and expecting them to pay me back with interest. It’s possible that some or all of the companies won’t be able to pay back the money (they squander the loans). A bunch of people buy into this pool in order to spread the risk of non-payment around. Collectively, the companies agree to repay 10,000. If 10 investors are going to loan money and expect to get back 1000 each, we can split it up with the most risk-hungry person paying in only, say 250 (expecting 300% return) and the most risk-adverse paying 750 (expecting 33% return). The reason the first investor is higher-risk is that if the companies can only repay 9000, the first investor gets nothing and everyone else gets their 1000.

It is difficult to figure out the price spread (between 250 and 750 in my example) unless you know the relationship between the defaults of the various companies. Li’s formula defined this relationship and gave a number to price the slices. The model takes the current prices of all the individual bonds and gives a correlation number which implies the probability of everyone defaulting all at once. Now that this probability is “fixed” or “known,” it can be used to price the pool and different sections of the pool.

In addition to re-selling bonds it bought from companies, a bank can sell bond-insurance (called a credit-default swap, CDS).  This means it collects money from investor-individuals and promises to pay if a particular bond defaults.  The bank can also pool the bond-insurance and then slice up the pool in a way similar to the bond-pool case. It then passes out the money it collected for insuring the bonds but passes out more to those who will have to compensate for default first. Li’s formula was also used to create and trade the slices of insurance.

With pools of bond-insurance (called a synthetic collateralized debt obligation, CDO), I receive money and agree to pay when companies default to a certain degree. So in that pool above, when only 9000 of the 10,000 can be repaid, I have to make up the other 1000.  If I take on this first part of the default obligation, I demand more money for my promise to pay.  The payment each insurer (investor) receives varies and the Li’s formula was used to determine the payments (prices).  This is (one of) the source(s) of the leverage people have been talking about.  Investor-insurers, like hedge funds, were able to collect huge sums from these synthetic CDOs, pools of CDSs. In return for these huge sums, they had to promise to compensate others for company defaults, but they weren’t required to have anything to prove their ability to compensate. The 100 to 1 leveraged bank had gathered 100 in CDS premiums and had to show only 1 of ability to pay.

I read something! Bruce Hunt on the two sides of math

Part of the reviewer response to my manuscript on Ideas of Math in Rhetoric was to consult this:

Hunt, B. J. ‘Rigorous discipline : Oliver Heaviside versus the mathematicians’. In Dear, Peter (ed.), The literary structure of scientific argument : historical studies (Philadelphia (PA), 1991), 72-95.

It was a pretty ugly blunder for me to leave this out of my first few drafts of this work. I’m not sure if it was poor research skills, laziness, or honest stupidity that led me to exclude it before. But I read it now and it is quite nice. But it is more of the same: math is a discipline like any other.

Bruce Hunt analyzed Oliver Heaviside’s encounter with “disciplinary” procedures when his work failed to meet the Royal Society’s standards for “pure mathematics.”  The third volume of his “On Operators in Physical Mathematics” was rejected by the Royal Society, even though he was a Fellow an Fellow’s work was routinely published without review. Hunt places Heaviside’s rejection in the context of the “purification” of British mathematics, a shift in intellectual orientation during which mathematics went from being understood as an approach to or tool for solving practical problems to an abstract pursuit of “formal” mathematical objects. Heaviside, having “come up” as an engineer focused on real world problems of telegraphs and other electrical circuits, did not write in the deductive form favored by pure mathematicians. William Burnside was given Heaviside’s paper instead of it being immediately entered into the Proceedings, as was typical for Fellows’ work. Burnside was an especially harsh member of the movement toward “purity” and “rigor.”  Burnside criticized, in particular, Heaviside use of numerical approximations of divergent series in his arguments. Since such entities were not deductive results of established mathematical facts, his arguments did not follow the coming-to-be-accepted rules of mathematical argument. Burnside’s negative review was the main grounds for the rejection of Heaviside’s work.

Thus, Hunt concludes, Heaviside was the victim of the establishment and reinforcement of rhetorically-constructed disciplinary boundaries, argument styles. Mathematics is a discipline like any other; it uses natural language in particular ways; these ways define members of its discourse community and the knowledge constructed in this community must use these ways. End of story.

 

Issues raised by Hunt that do not fit into the current purposes of reading:

1. Heaviside vs. Burnside

2. Heaviside took this disciplinary action to heart and “broke most of his ties with the Royal Society after 1894,” the year of the rejection (90). Math and emotions…

3. What the fuck is a “formal language?”

4. Discipline for-itself vs. practical (empirical) discipline—connection to capitalism

Rhet/math and the Financial Crisis: General statements and a first crack at David Li

Is it possible to gain a rhetorical understanding of the financial crisis? Is it possible that what went wrong, or more realistically, one part of what went wrong was a rhetorical error, a failure of discourse?  Was there a problem in the way persuasion operated? We look at things from a rhetorical perspective in order to improve the world by changing communication, changing the ways we are persuaded, by focusing closely on communication and persuasion. Was part of what went wrong in the financial collapse a failure or shortcoming in communication or persuasion. You might think I mean something like, “were borrowers lied to by lenders?” or “were investors lied to by bankers?” But leaving aside lies and dishonesty, what if there was something wrong with the communication or persuasion in the heart of the financial world, something that went wrong not by anyones choice but by the rgular operation of the language of finance. And I don’t mean the potentially obfuscating jargon like ‘sub-prime loans’ or ‘credit default swaps’, those things being too close to the lies mentioned above.

The language of finance is mathematics, or rather mathematics is one of its languages, an Other language, which supplements the jargony discipline-specific uses of English that include ‘sub-prime loans’ or ‘credit default swaps.’ There may be something going on in the regular operation of the language of mathematics that makes finance itself possible. This operation of mathematics-as-language can be addressed by those familiar with mathematics, but if it is indeed language, rhetoricians should also have some insight into it.

A very normal thing happened in the mathematics that supported the finance that “went wrong” in the recent crisis. That very normal thing was that David X. Li constructed, performed into existence, a tentative mathematical structure that gave value to assets… He constructed mathematical entity on top of mathematical entity and in the end, there came to (economic) life an entity that… there emerged a conviction that a numerical valuation of a contract was accurate.

The things he constructed:

1. A random variable: In the situation we’re concerned with, we have a bunch of loans that are paying interest. These will stop paying eventually, either because the term expires (and all is well), or because they default. The time each loan takes to stop paying is a random variable. Assuming, for the sake of simplicity that each loan has a term of tf, the time it takes for payments to stop on a loan, Ti, is a random variable with values in (0, tf]. Li calls this random variable for a given loan (asset) its survival time.
2. A distribution function for this random variable: The variable itself seems innocuous enough, but since the survival time is a random variable, it has, by mathematical necessity, a distribution function. The distribution function is a curve that tells the probability (y-axis) of payment ending at a given time (x-axis). According to Li, the curve can be constructed using “the market-agreed perception today about the future default tendency of the underlying credit” (10). This is a controversial construction, as indicated by later commentators, e.g. Janet Tavakoli.
3. A copula function that gives the joint distribution of several random variables (each related to a defaultable asset/loan) on the basis of their each random variable’s marginal distribution.
4. A correlation between the multiple survival time random variables, which is needed for the copula fuction, based on a correlation between the assets/loans in question.

I need to spend more time with 3 and 4 and, likely 2.

Of course, the crucial thing might be that when I say there’s a failure of discourse, it’s not like anyone did anything “wrong.” It’s that this normal operation of mathematical language, the performative construction of some mathematical entities, 1) failed to do what it was intended to do and/or 2) had crazy/destructive effects in spite and in addition to doing what it was intended to do. It isn’t just about lies and deception and greed and bad people. It’s also about uncontrollable math-language.

Lines of flight and what’s the other thing?

I want words to cary me away. Or rather, that ’s what I think they’re for, what they do. How they do. The numbers can peg me in place. Peg me? REally? Is that inappropriate? because that’s what I think numbers do. They take a step, or make a step. They stand, freeze, lock. Words run. They run awway with you and/or they run you off. Like runoff and like a copy machine. Run off some copies of you.

I sit here with the numbers, but I run way with or after the words. But it’s about words and numbers for sure. My boss told me the same thing the other day. actually my boss’s boss. He loves “words (and numbers!)” he said.

And because of what numbers do, because of how they do, they perform truth procedures. Not that I even know what that means, but it sounds good. It sounds right. I’ll run after it, striate my space or whatever.

I imagine this all has to do with kung fu movies I never watch.

What is keeping me awake tonight 1: Adam Sternbergh

A few weeks back, on a listserv that I currently have no good reason to subscribe to, let alone read, someone posted a link to the Stuff White People Like blog. As a response, today someone posted a link to Adam Sternbergh’s recent critique of that blog. A link in that article led me to Sternbergh’s March 2006 piece about 30-somethings who have only sort of grown up. This eventually led me to look into the archive of his work at NY magazine, where I found a few articles about gentrification in New York and the weirdness of the whole “neighborhood X is the new neighborhood Y,” especially now that it’s been going on for over a decade.

Now I’m awake partly because 1) Although I’m glad to see a thoughtful contribution to a conversation outlining the distinctions between good and bad “edgy” comedy, I think he’s missing something about SWPL: He only glosses the fact that many people, including several that have posted comments on the blog, have pointed out that the people that actually like the things listed are “a very specific demographic sliver of left-leaning, city-dwelling white folk–in other words, people like me,” who “have previously been trapped and tagged alternately as yuppies, or Bobos, or (by yours truly in New York magazine) grups.” He sort of brushes this critique aside and adds his own, which is that nothing that is a truly cutting satire is ever accepted by the satirized as great entertainment; rather, white people laugh at SWPL only because it makes them “feel superior” (to?).

Aside from the fact that I might disagree that no true satire is acceptable to the satirized (I think Slavoj Zizek’s Welcome to the Desert of the Real! has an example of a rock band who became very popular in ethnic-conflict-torn Yugoslavia by enacting negative stereotypes about their own people), I do agree that SWPL doesn’t feel the least bit offensive, and is rarely funny. (I wonder how the laughter in response to SWPL would land on the coordinates of Diane Davis’s taxonomy?)

But I think that there’s something else going on besides a feeling of superiority. And it’s related to the simpler critique about the inaccuracy of the “White People” in the title. Basically, it seems like SWPL also allows this “very specific demographic sliver of left-leaning, city-dwelling white folk,” Bobos, grups, whatever, to be thought of as the group that defines whiteness…. This, of course, adds to… or maybe even accounts for the feeling of superiority… possibly even answering my asswholly-parenthesized question above. The “White People” described on the blog can feel superior to other people who happen to share the former’s skin tone and possibly ethnic roots because the latter are “not really white.”

partly because 2) Ugh… all I can think about lately is growing up and growing up too late and not really ever growing up.

partly because 3) Reading about the socio-economic-cultural-lifestyle-realestate dynamics of the NY metro area makes me totally anxious, in both the giddy/excited sense and the puke-y/run-for-your-life sense. Sternbergh has one article about Jersey City and one about Red Hook, a “remote” part of Brooklyn; both of these are places we’ve talked about moving. In those two articles he seems to be developing this argument about how gentrification has gotten ahead of itself (post-gentrification, obviously) and now no longer happens in stages (artsies with cheap cafes and bars-> hipsters with boutiques and fancier restaurants-> investors with developers’ plans and construction equipment-> totally rich people). Now, since the boom-to-come is so expected, the artsies and the developers land at the same time… Why do I care? I guess I’m trying to figure out at what point I’m supposed to be the one to move into the neighborhood….

partly because 4) My blog is now not only not-posted-to; it is also about neither math nor rhetoric.

Being right 1, Being wrong/Other r (current tally)

Today, Theresa said these words to me: “You’re right. I agree with you.” She seems to think she may have said these words to me before, but I’m fairly certain this was the first time. It’s not that I feel like I’m competing with her to see who’s right more often. Instead, I’m competing with myself. I’m not sure exactly how many times I’ve been something other than right.

Anyway, the context of her declaration was as follows: I was talking to her on the phone and looking at her website, which she just finished updating. Somehow, we started talking about her allergic reaction to anything that seems really cool, especially when that anything is also part of the art world. I said what I usually say when we have this conversation and, for some reason, it didn’t seem to bomb like it usually does.

Our relationship(s) to the cool (let’s call it) is one of our most common discursive (not mathematical) topoi. When we address this topic, Theresa inevitably mentions that, for the most part, I do not suffer this allergy because I have a disease that prevents it. I generally take this as a sort of veiled threat and respond with one or two defensive statements, which generally lead the conversation to an abrupt conclusion.

This time, however, she confronted her allergy in action and wondered aloud if she should just get over it and embrace the allergen. I told her, again, that the cool is part of the game and that, with this in mind, she–anyone, really–could embrace it without essentializing it. This is what I always say, more or less, but as every rhetorician and giddy schoolgirl knows: it’s not what you say; it’s how you say it.

Since I strive to talk exclusively by quoting only extremely popular movies and tv shows, I usually convey the aforementioned message about the cool by saying, you’re putting the pussy on a pedestal, but this time I said it’s all in the game. Oddly enough, Theresa seemed to like the latter version even less than the former and insisted that I never use that phrase again. Nevertheless, she approved of “it’s part of the game” and told me that I was right and that she agreed with me.

What I’ve been thinking about lately: Universals

It’s been a long time since I posted here. During that time, somethings have come and gone. Some of these things came  from very different places but wanted to be together. They float around the universal.

Last week, Theresa and I went to Miami for the art fairs (Basel, Scope, Pulse, Aqua, Nada, etc.). Our first stop was Scope. One of the first things I noticed there, in several galleries, I think, were animals made out of car tires.  They were rather realistic/representational sculptures.  Over the four days we were there, I noticed several other sculptures involving animals that were in some ways realistic, but also either very rough or else somehow fantastic/scary (e.g. realistic Siamese twin  jackals). Unfortunately, I can’t be more specific than this because given how “busy” our days in Miami were, my memory is a bit muddled.

These sculptures stuck with me primarily because on the plane on the way down there, I was reading over a debate about  “Primitivism in Modern Art” that happened in Artforum in the mid-80s. The debate began after the then-editor of Artforum reviewed a recent MOMA exhibition that interspersed a collection of Modernist paintings and sculpture with a collection of objects made in “primitive” tribal cultures.  I’m going to breeze past most of the details and most of the generalities, to focus on this point: the editor criticized the exhibition curators from a now-familiar cultural relativist point of view, arguing that they completely ignored the cultural specificity and irreducible difference of the “primitive” “tribes,” in order to prove the Western imperialist claim that beauty is universally recognizable.  Though the curators challenged the accuracy and relevance of the claim in public letters to the editor, the main criticism was that the exhibit and subsequently published catalog presented “primitive” works that happened to be formally similar to Modernist without adequately contextualizing them and highlighting differences in driving intention and cultural use. This debate took place when postmodernism was coming to dominate in intellectual and critical circles, and it is a great example of basic pomo relativism.

This debate caught my attention because a few days before we left, I finished reading Alain Badiou’s book on St. Paul and Universalism. Badiou is engaged in a very ambitious project of resuscitating concepts like “Truth,” “Universal,” and “Infinity,” that have become more or less taboo thanks to almost 40 years of post-thought criticism. The more I learn about this project, the more excited I get. I still don’t know much about it, but it seems to be just what I’ve been hoping for: it “brings back” concepts that certainly haven’t really gone away, but does so in a way that affirms and builds on post-thought, rather than dismissing it.  All I have to say at this point is that one of types of truth Badiou theorizes is “art.” Whether or not that’s the same as beauty, I don’t know.

About a week before we left for Miami, Theresa and I went to a gallery talk at which the artist explained his former devotion to breaking the conventions and rules of painting, his move to collecting objects when that got tiresome, and his recent return to painting with a newfound acceptance of all its humble conventions. He seemed completely unaware that a devotion to breaking conventions (in the pursuit of some absolute-perfection) is, itself, a classic modernist convention and that, by accepting the more humble conventions of painting–for instance, putting attractive colors on rectangular stretched canvases and hanging them at eye-level in a comfortable white-walled room–he had, in a sense, simply become a post-modern relativist who accepts the contingency and limitations of his specific cultural practices.

Before the plane landed, Theresa and I started talking about some of these things (those that had happened) and she brought up this question: Can the conventions of painting serve as something Universal in Badiou’s sense? Could they be something event-like, to which a Truth procedure could apply and a subject could be committed and constituted?

She also asked if the Universal is just an individual, personal thing or if it is “for everyone” or something…

unmanlyfesto for teaching writing next time, part 2

• Make it a practicum. Write and workshop in class more often.
• Work on several different “types” of writing simultaneously.
• Make students write short things more often.
• Have more one-on-one conferences with me.
• Make workshops/peer reviews shorter and involve less commitment.
• Call it a “creative thinking” course, but say that you can’t create just by thinking. You have to do something, and what you’ll do in this class is create writing. You’ll create creative thoughts by making texts (i.e. writing). There are plenty of other ways to make creative thoughts and in an important sense, writing is old fashioned. But people still think it’s so important, so we’re going to stick with it for now. Say: “Thinking is worthless without writing.”
• Read Wayne Booth’s “The Rheotircal Situation” on days one and two. Have students read it aloud in class and talk through confusing things and have them read it at home in between the first two classes so they can really engage it. Splice this reading in with brief intros and getting-to-know-you type stuff. This will be a struggle we can all endure together, in order to form a community… like the people in that movie Alive.
• Begin the semester with a simple, easily accessible and easily get-mad-about-able essay that makes a serious (that is, not ironic/too tongue-in-cheek) argument about a non-serious issue (that is, not directly political or with obviously grave consequences), e.g. Amy Gross’s article offering dating advice. Have students summarize and rebut this argument. Then have students read these two arguments (the original essay and one classmate’s rebuttal) “across” each other, compare-contrasting them to gain some insight into one or both. Also have them write a more “free” response to their classmate’s paper, giving it a “critique” from their own perspective. Part of the point of this is to, with any luck, show them that a critique based on the framework of another text is more easily kept controlled, balanced, organized, and coherent than a critique based on their own vague, unarticulated position. The latter type of critique also, oddly or not, tends to seem like a critique “in general” or from an “objective” perspective….
• Not focus on what my students do wrong… I mean wrong. I sometimes tend to focus on things that I can easily say are just wrong because these things are easier to deal with.
• More emphatically emphasize that the point of critique is to say something non-obvious, “come to a deeper understanding,” as Behrens and Rosen say, about a text. Add that the non-obvious thing is a construction. It’s something they, as authors, invent.
• Emphasize that I’m not going to chase them down about stuff. I don’t want to have to worry excessively about who handed in what….

unmanlyfesto for teaching in the future, part 1

The next time I teach freshman writing, I will:

• Use the Learning Record;
• Add a description of “independence” to the description of the dimension of learning called “confidence and independence”;
• Grade individual assignments on A-F scale but clearly indicate to the students that I will NOT tally these grades to determine their final grades. Instead, the student will still present an argument for their grade based on the framework provided by the Learning Record, and they will receive a grade from me based on their LR. This way, I can be as honest, clear, and direct as possible about the quality of students’ work (because I will tell them in the familiar language of letter grades) but can still insist that very high quality doesn’t guarantee an A and below-average, barely acceptable work doesn’t guarantee a D.
• I will have questions to respond to for each assignment students complete, like the questions I used to respond to the LR.
• When students write multiple drafts of an essay, one of the questions I will respond to will have to do with the way the students responded to my comments on their earlier draft(s). I might even give a separate grade to indicate the quality of revision. The goal here is to evaluate the (evidence of) effort and thought that went into revision separately from the quality of the essay.

Brian Rotman and Shoshana Felman: mathematical objects and referents

Though it may surprise most people who know me, I have actually read all of Brian Rotman’s book. Nevertheless, for several posts now, I have been dwelling in the first chapter, “Toward a Semiotics of Mathematics.” I just haven’t gotten through all I want to get through yet. In particular, I haven’t gotten to the semiotic account of mathematical objects he moves toward in the first chapter. I hope that this post will get there.

I think I’ve taken a while to get there because, as I said in an earlier post, Rotman essentially skips over the part of semiotics that deals with the referent.

Early in the chapter, Rotman explains the perils of approaching math by each of the three axes of semiotic investigation: beginning with signifiers leads to a roughly formal approach (see Hilbert); beginning with signifieds leads to a roughly psychological approach (see Brouwer); and beginning with referents leads to a realist approach (see Frege) (4-5). Though he says each approach is problematic, he seems to begin with signifiers. But he doesn’t fall into the trap of old-fashioned pure formalism because he deals with signifiers only as material things used by and existing in relation to embodied semiotic subject-agents. He then proceeds from the signifiers used, to the signifieds imagined by these subject-agents.

Rotman doesn’t get “more specific about the semiotic answer to the fundamental question of what (in terms of sign activity) the whole numbers are or might be” until about pg. 38. Like Ruben Hersh, Brouwer, Kronecker, and most others who pursue foundational projects, Rotman approaches a description of mathematical objects, in general, via the natural numbers, in particular. And, like Hersh, who says that they are “social institutions,” Rotman suggests that mathematical objects are “social, cultural, and historical artifacts” (38). But I find Rotman’s account much more exciting. I want to move through his description a bit at a time:

• “numbers do not arise, nor can they be characterized, as single entities in isolation from one another: they form an ordered sequence, a progression” (38 emphasis in original)
  • Doesn’t this conception of whole numbers being an ordered sequence presume that the whole numbers are already there…? Doesn’t there have to be whole numbers for anything to be “ordered”?

• “It seems impossible to imagine what it means for ‘things’ to be the elements of this progression except in terms of their production through a process of counting. And since counting rests on the repetition of an identical act, any semiotic explanation of the numbers has to start by invoking the familiar patter of figures [...] created by iterating the operation of writing down some fixed but arbitrarily agreed upon symbol type” (38 italics original, bold mine).
  • For all Rotman says about Deleuze later in the book, I don’t think he’s thinking repetition here in a Deleuzean way. Repetition, in Deleuze’s Difference and Repetition, isn’t about identity…. Rotman goes somewhere else with Deleuze. I’m sure I’ll get back to that.

• “Such a pattern achieves mathematical meaning as soon as the type ‘1′ is interpreted as the signifier of a mathematical sign and the ‘etc.’ symbol as a command, an imperative addressed to the mathematician, which instructs him to enact the rule: copy the previous inscription then add to it another type. Numbers, then, appear as soon as there is a subject who counts. [...]. With the semiotic model I have proposed, the subject to whom the imperative is addressed is the Subject, while the one who enacts the instruction, the one who is capable of this unlimited written repetition, is his Agent” (38-9 bold mine).

• Here it comes: “Seen in this way, numbers are things in potentia, theoretical availabilities of sign production, the elementary and irreducible signifying acts that the Subject, the one-who-counts, can imagine his Agent to perform via a sequence of iterated ideal marks whose paradigm is the pattern 1, 11, 111, etc. [...]. Thus, the numbers are objects that result-that is, are capable of resulting-from an amalgam of two activities, thinking (imagining actions) and scribbling (making ideal marks), which are inseparable: mathematicians think about marks they themselves have imagined into potential existence. In no sense can numbers be understood to precede the signifiers that bear them; nor can the signifiers occur in advance of the signs (the numbers) whose signifiers they are” (Rotman 39 italics original; bold mine).
  • So numbers are signs or (if this is different and I think it is) the signified parts of signs…. More precisely, numbers are potential signifying acts, which are signified by numerals, which are signifiers. This begins to come into line with Felman’s performative referent, which is always an act, “a dynamic movement and modification of reality” (77).
• The objects of math–”the things which it countenances as existing and can be said to be ‘about’–are unactualized possibilities, the potential sign productions of a counting subject who operates in the presence of a notational system of signifiers. [...]. And moreover, what is true of numbers is in fact true of the entire totality of mathematical objects: they are all signs-thoughts/scribbles-which arise as the potential activity of a mathematical subject” (Rotman 40-1 bold mine).
  • One the one hand, this makes the objects of math “mappings” in the Deleuzean sense. Mathematical things must always be made.
  • At the same time that they must be made, however, they are also never actually made; they are always going to be made, in the future that never comes to pass. This is a second connection to Felman, whose performative “referentiality [...] can be reached and defined only through the dimension of failure: on the basis of the act of failing” (82 emphasis hers).
• “Thus, mathematics, characterized here as a discourse whose assertions are predictions about the future activities of its participants, is ‘about’–insofar as this locution makes sense–itself. The entire discourse refers to, is ‘true’ about, nothing other than its own signs. And since mathematics is entirely a human artifact, the truths it establishes–if such is what they are–are attributes of the mathematical agency of Agent/Subject/Person who reads and writes mathematical signs and suffers its persuasions” (41 bold and italics mine).
  • The italicized phrase reiterates the connection between Rotman and Hersh. And the sentence it appear in reiterates the rhetorical nature of mathematical languge.
  • More importainingly, for me at least, the bold-face phrases make another connection with Felman’s performative referent: “the performative has the property of subverting the alternative, the opposition, between referentiality and self-referentiality” (79-80). This connection between Rotman and Felman is less direct and it is a connection that runs through Rotman to the beyond. That is, Rotman, as I’ve said, is not exactly, explicitly talking about reference and referents. (PS–It’s no mistake that the endings of these two words–the former naming an act and the latter multiple objects–have similar pronunciations.) He skips over reference/ents early on and is now talking about mathematical objects. His point here is that, on a semiotic account, math is about math, mathematical language is about mathematical language. (Can we say that the latter formulation is purely formalist? Rotman insists that language is material….) So, for Rotman, math is self-referential, but it is not necessarily referential. It may only be by considering math on the model of the performative, the performative as worked (out) by Felman, that math can be referential too.
• Rotman goes on from here to conclude that “truth” is basically useless in mathematics. This is also due to the fact that mathematical objects are always deferred objects. Mathematical assertions are predictions, so it makes no sense to ask if the are true. “A prediction-about some determinate world for which true and false make sense-might in the future be seen to be true, but only after what is foretold has come to pass; for only then can what was predicted be dicted” (41). Thus, mathematics is about belief… but belief based on persuasion. So it’s rhetorical… but it’s more.