The Dependence Of Autobiography On Biography (And Vice-Versa)

A few weeks ago, I briefly spoke at a conference hosted in honor of my dissertation advisor’s eightieth birthday. In my talk I offered some personal recollections of having worked with Distinguished Professor Rohit Parikh, his intellectual influence on me, and the various lessons–personal, technical, moral–that I learned along the way from him. As I began my talk, I apologized for what I described as the ‘self-indulgent’ nature of the talk. After all, even though the talk was about Professor Parikh, it would keep me center-stage at all times; I was as much a character as him. The stories I would tell my audience were about him and me; they would describe my passage through my dissertation, my post-doctoral fellowship, and then later, my work as a faculty member of the City University of New York, all the while informed by my advisor’s presence. (And indeed, I found myself telling tales of my first encounter with my advisor, my decision to work on a dissertation topic that spun off from one of his papers, my struggles to become more mathematically proficient, the shaping of my philosophical world-view through the many discussions and conversations we had, and the various insights into mathematical method, the philosophy of Ludwig Wittgenstein, and the nature of logic and knowledge that I gleaned over the years from him. I recalled memorable lines, jokes, profundities; I briefly mentioned our political differences.)

As part of my ‘apology’ therefore, I said that in trying to provide a biography of someone I had interacted with over an extended period of time, it was necessary to provide an autobiography as well. I went on to note that this was not surprising: after all, the recountings of our autobiographies must necessarily call on the biographies of others to be made complete. Our lives are not lived in isolation; they inform, interact with, and impinge upon, many other lives. We form relationships with others; we enter into them, and move on out again; they take us from station to station. The stories of our lives, thus, are also the stories of many others’: friends, lovers, enemies, teachers.

Biography and autobiography are fickle genres of story-telling; they rely on memory, and are infected throughout by all kinds of prejudice. The interaction between the two I describe here shows how these errors may accumulate: my autobiography might distort the biography of others. I might cast myself in a more favorable light, paint myself as more virtuous when contrasted with others; if my autobiography is relied upon as a biographical source for others’ lives, these errors will be perpetuated. In the particular forum in which I was recounting my ‘autobiography’ a converse possibility existed: that I would be corrected by the very person whom I was speaking about; my advisor could have raised his hand at some point and told me that he remembered additional details that I had forgotten, or that I had gotten some quote or location or time wrong.

No man is an island and all that.

My First Academic Conference

The first academic conference I attended was the 1999 Annual Meeting of the Association of Symbolic Logic, held at the University of California at San Diego. I submitted an abstract for a presentation, which was accepted, and so off I went, hoping to gain ‘experience’ and ‘exposure.’ My paper was based on part of my then in-progress dissertation; to be more precise, it presented the first model of belief revision I was currently working on with my thesis advisor.

I  had applied for, and received, some limited funds for travel–these barely covered the flight to San Diego and did not help with car rental fees. (I had arranged housing with a philosophy graduate student at UCSD.) I arrived in San Diego, picked up my rental car, and drove to my host’s place. The next morning the conference began, and so did my disorientation.

First, I was in the wrong conference. This meeting’s attendance was mostly comprised of mathematical logicians (set theorists, model theorists, proof theorists, recursion theorists, complexity theorists, and the like) – no one was likely to be interested in the model of belief revision I was presenting. It was simply not interesting enough, at the formal and mathematical level, for this crowd. And its philosophical underpinnings and motivations were hardly likely to be of interest either; those features were not the sorts of things mathematical logicians looked for in the formal work that was being presented that weekend.

Second,  as a related consequence, I knew no one.  This was an academic community I had no previous contact with–I knew no faculty or graduate students in it. I wandered around the halls and rooms, occasionally striking up brief conversations with students, sometimes introducing myself to faculty. My thesis adviser was known to some of the faculty I introduced myself to; this fact allowed for some useful ice-breaking in conversations. (I also managed to embarrass myself by pushing copies of my paper into some hands.) But mostly, I stayed on the peripheries of these social spaces.

Third, the subject matter of the talks was utterly unfamiliar and incomprehensible. I had studied some logic, but I was an amateur yet. And the inclinations of the mathematical logicians who comprised the primary attendance at this conference were pitched entirely differently from the philosophical logic I had been exposed to: their work was almost entirely concerned with the mathematical properties of the frameworks they worked on. I attended a couple of talks, but all too soon, bewildered and bored, I gave up.

I did not feel I belonged. Not here, not at any academic conference. I was intimidated and made diffident; my doubts about my choice of career and dissertation topic grew. By the second day of the conference, this feeling had grown worse, not ideal preparation for my talk. Quaking in my boots at the thought of being exposed to a grilling by a heavy hitter in the audience, my nervousness knew few bounds. Fortunately, the worst case did not eventuate; I put up my slides, described the work underway, answered a perfunctory question or two, and walked off the ‘stage,’ relieved. 

That year, the final year of my dissertation work, I attended three more conferences–a graduate student meeting at Brown, and international professional conferences in Sweden and Greece. By the end of the summer, I was a little more comfortable in my skin at these spaces. One such attendance almost certainly helped secure me a post-doctoral fellowship. (Yet another saw me lost again among mathematical logicians.)

Over the years, I’ve attended many more. But I never got really comfortable with conferences; I never felt like I fitted in. Now, I don’t go to conferences any more; the travel sounds interesting, but the talks, the questions and answer sessions, the social schmoozing, the dinners, (and the conference fees!) don’t sound enticing. I prefer smaller-scale, more personally pitched interactions with my fellow academics.  But perhaps a suitable conference venue–with mountains close by–will overcome this reticence.

Teaching Wittgenstein And Making The Familiar Unfamiliar

I’m teaching Wittgenstein this semester–for the first time ever–to my Twentieth-Century Philosophy class. My syllabus requires my students to read two long excerpts from the Tractatus Logico-Philosophicus and Philosophical Investigations; bizarrely enough, in my original version of that exalted contract with my students, I had allotted one class meeting to a discussion of the section from the Tractatus. Three classes later, we are still not done; as you can tell, it has been an interesting challenge thus far.

The style of the Tractatus is notorious for the difficulties it can create for the unprepared. Many students find it its terseness, its statement in quasi-mathematical form as a series of seeming definitions, lemmas, theorems and corollaries–as part of a presentation of a grand total of seven propositions–off-putting and abstruse. Yet others find in it a curious beauty, a poetic statement, stark and austere, pregnant with meaning and suggestion. The content of the Tractatus can be forbidding too. Many philosophical doctrines–the picture theory of language, the truth-functional account of propositions, logical atomism and the correspondence theory of truth, the verification theory of meaning, the ‘no-sense’ theory of ethical and emotive statements–may be found here, varying in their level of implicit or explicit statement. A special vocabulary is employed, and the meanings of many of the special terms of art employed–‘facts’ for instance–has to be unpacked carefully.

I have read Wittgenstein before, and indeed, did my dissertation with a logician, Rohit Parikh, who doubled as a Wittgenstein scholar. (This excellent paper by Juliet Floyd explores the several dimensions of his appropriation of Wittgensteinian themes in his work.) For several years during graduate school I attended a discussion and reading group, conducted by Parikh, which often veered off into conversations on Wittgensteinian themes. Years after I completed my dissertation, I realized that many of its fundamental presuppositions and descriptions bore a similar stamp. But, I never taught Wittgenstein.

Now I have. And so, yet again, I’ve been reminded of how radically different my relationship to a philosophical text or doctrine becomes once I’ve had occasion to teach the material. I read differently; I critique differently, trying to anticipate the ambiguities my students might encounter; I notice more in the text, I seize on more. And then, in the classroom, as I work directly through the reading with my students my relationship with it changes yet again.

Sometimes, my teaching has consisted of making a few opening statements, previewing the theories and theses to be presented, and then turning to the text to find their statements within. I invite students to point me to particular propositions that they have found thought-provoking and/or difficult. At times, I have read aloud sections in class, stopping to offer and receive–along with the class–explications and exegesis. I’ve used the ‘reading-aloud-in-class’ method before; in that case, for Leibniz and Kant. What I wrote then about that particular method of approaching a philosophical text still holds:

First, more careful exegesis becomes possible, and little subtle shadings of meaning which could be brushed over in a high-level synoptic discussion are noticed and paid attention to (by both myself and my students). Second, students become aware that reading the text closely pays dividends; when one sentence in the text becomes the topic of an involved discussion, they become aware of how pregnant with meanings these texts can be. Third, the literary quality of the writing, (more evident in Leibniz and Freud than in Kant) becomes more visible; I often stop and flag portions of the text as having been particularly well-expressed or framed. The students become aware that these arguments can be evaluated in more than one dimension: analytical and artistic perhaps.

This method is exhausting, and that is an understatement. There is the obvious physical strain, of course, but doing this kind of close reading is also intellectually taxing. There is more to explain, more to place in context.

Now, with Wittgenstein and Tractatus, I am struck again, by how the seemingly familiar takes on a little of its older novelty.

Manil Suri on the Beauty and Beguilement of Mathematics

Manil Suri has an interesting Op-Ed on math–How To Fall In Love with Math–in The New York Times today. As befitting someone who is both a mathematician and a novelist, there are passages of writing in it that are both elegant and mathematically sound. The examples he provides of mathematical beauty–the natural numbers, n-sided regular polygons that become circles as n approaches infinity, fractals–are commonly used, but for all that they have not lost any of their power to beguile and fascinate.

I fear though that Suri’s message–that math is beautiful, creative, elegant, not to be confused with routine number crunching, and worthy of wonder and exaltation and careful study–will not be heard through the haze of the very math anxiety he seeks to cure. Suri needn’t feel too bad about this though; many others have tried and failed in this very endeavor in the past.  If, as Suri suggests, we are wired for math, we also sometimes give the appearance of being chronically, congenitally, incurably anxious about it.

A personal note: I came to a realization of mathematics’ beauty late myself. Like many of the math-phobic that Suri refers to in his article, through my school years my attitude toward the study of math was fraught with fear and befuddlement. I was acceptably competent in the very junior grades but a harsh teacher in the seventh grade ensured that I would earn my worst grades then. My concerned father took it upon himself to drill me in algebra and I regained a little confidence. Not enough though, to want to study it at the higher levels that were made available to us in the ninth and tenth grades. But the pressure to study engineering at the university level meant I had to return to the study of more advanced mathematics for the eleventh and twelfth grades.

In those two years, I was exposed to calculus for the first time and came to love it; its connection with motion, the slopes of curves, the use of differential equations to model complex, dynamic systems; these all spoke to me of a logical system deeply implicated in the physical world around me. Once I had learned calculus, I saw it everywhere around me: in a stone’s dropping, a car’s acceleration, a rocket’s launch, an athlete’s push off the starting block.

I majored in mathematics and statistics at university, but if I saw any beauty in mathematics in those years, it came when I saw some good friends of mine working out complex problems with some style. I had lost motivation and interest and barely survived my college years. My graduate studies in computer science didn’t help; I was able to–unfortunately–skip the theory of computation and graduate.

Years later, when I encountered mathematical logic as part of my studies in philosophy, some of my appreciation for the world of abstract symbol manipulation came back. It helped that my dissertation advisor was an accomplished mathematician whose theorems and proofs sparkled with style and substance alike. From him, I regained an appreciation for the beauty of the symbolic world.

I was never a mathematician, and don’t work in logic–mathematical or philosophical–any more. But my brief forays into that world were enough to convince me of the truths that Suri refers to in his piece:

[Mathematics] is really about ideas above anything else. Ideas that inform our existence, that permeate our universe and beyond, that can surprise and enthrall.

Of Academic Genealogies

Yesterday, in a post on this blog, I wrote about the most familiar kinds of genealogies, the familial, and the quest to uncover their details. Today, I want to make note of another kind of genealogy that sometimes obsesses folks like me: our academic ones.

Some thirteen odd years ago, shortly after I had finished my dissertation defense, I sat in the bar room of the Algonquin Hotel, enjoying a celebratory whisky or two with some friends. My dissertation adviser, Rohit Parikh, was in attendance. As we chatted, I said something like, ‘So it continues, from Hartley Rogers [Professor Parikh’s dissertation adviser]  to you to me.’ And he replied, ‘Yes, and before that, Alonzo Church.’ On hearing this, I felt absurdly pleased.  My academic lineage could be traced back to the man for whom the Church-Turing thesis was named? Nice work, dude.

It was, as I noted, an ‘absurd’ reaction. But in a community where an immediate academic ancestor had a significant impact on employment and subsequent career prospects, it wasn’t the strangest reaction to have.

A year or so later, I discovered the Mathematical Genealogy project, found an entry for myself,  duly traced my ‘academic family tree’, and came up with the following tale:

Gottfried Wilhelm Leibniz begat Nicolas Malebranche who begat Jacob Bernoulli who begat Johann Bernoulli who begat Leonhard Euler who begat Joseph Lagrange who begat Simeon Poisson who begat Michel Chasles who begat H.A Newton who begat E.H Moore who begat Oswald Veblen who begat Alonzo Church who begat Hartley Rogers who begat Rohit Parikh who begat Samir Chopra.

My initial reaction was that that is a ridiculously distinguished lineage to have.  If I had even a vanishingly small fraction of the mathematical talent on display, I would have won the Turing Award and the Fields Medal by now.

This feeling was all too quickly replaced by another feeling quite familiar to academics: I didn’t belong in there. My mathematical and logical talents are limited; I never rose above competence in my academic work in those domains. I was, you guessed it, an impostor. Indeed, after I had, in an initial burst of enthusiasm, announced the results of my quest to some colleagues and friends, I went mum. Why highlight a line of ancestry that showcased my lack of fit?

A couple of years later, there was even less occasion to talk up my mathematical genealogy: I wasn’t writing papers in logic any more and had moved on to other topics of interest. And besides, I had figured out the only relevant part of my academic genealogy was the node that preceded me; little else mattered. That connection is one I remain proud of for the right reasons: the relationship was, and is, a friendly and intellectually enriching one. And that, I think, is all that should matter.

Note: The following chart–produced by Yifan Hu of the AT&T Shannon Laboratory–shows the second largest tree in the Mathematical Geneaology Project. It shows a total of 11766 mathematicians, with the hundred most prolific dissertation advisers circled: plot_comp2_p2.2_font8. Interestingly enough, ninety-eight percent of the nodes on this tree are leaves i.e., they have no students.  (I thank Noson Yanofsky for sending me this reminder of my incongruous location in this luminous bunch.)

Strategic Voting and Election Season Polls

I am linking to a paper of mine (‘Knowledge-Theoretic Properties of Strategic Voting’, co-authored with Eric Pacuit and Rohit Parikh) of possible relevance in the context of the just-decided elections and the importance of election season polling. Here is the abstract. (I am traveling and so unable to write a longer comment at this time).

Results in social choice theory such as the Arrow and Gibbard-Satterthwaite theorems constrain the existence of rational collective decision making procedures in groups of agents. The Gibbard-Satterthwaite theorem says that no voting procedure is strategy-proof. That is, there will always be situations in which it is in a voter’s interest to misrepresent its true preferences i.e., vote strategically. We present some properties of strategic voting and then examine – via a bimodal logic utilizing epistemic and strategizing modalities – the knowledge-theoretic properties of voting situations and note that unless the voter knows that it should vote strategically, and how, i.e., knows what the other voters’ preferences are and which alternate preference P′ it should use, the voter will not strategize. Our results suggest that opinion polls in election situations effectively serve as the first n–1 stages in an n stage election.

This is a technical paper and so unlikely to be readable to plenty of folks so I will try to provide a quick summary and discussion next week. The last sentence of the abstract though, should give you some indication of what its implications are and why they should be of interest to voters, politicians and pollsters alike.

Flying Solo, As Author, For a Change

Sometime this week or the next, my fourth book, Brave New Pitch: The Evolution of Modern Cricket (HarperCollins India 2012), will make its way to bookstores and online book-sellers. My fourth book differs in one crucial regard from those that have preceded it: I have not co-authored it with anyone; its jacket lists but one name, mine, as the author. (Summing up, the blurb says: ‘In Brave New Pitch, Samir Chopra takes a hard look at cricket’s tumultuous present, and considers what could and should lie ahead.’)

This is a novel feeling, a journey to a strange land. Flying solo?

I like collaborators. Not dastardly Vichy-types but the diverse set of co-authors that have brought my writing projects,  thus far, before Brave New Pitch, to fruition. While working on my doctorate I carefully managed my awe of my Putnam Prize-winning adviser while drawing upon his genius to help me navigate the complexities of mathematical logic. My dissertation–on new models of belief revision that accommodated inconsistent beliefs and relevance-sensitivity–bore my name on its spine but the stamp of his exacting attention to detail.

And then there was the military aviation historian whom I did not meet until after the publication of our book (a history, the first, of the India-Pakistan air war of 1965).  We talked on the phone and generated a blizzard of emails (he lived in India, I in the US and Australia); his presence was always palpable in constantly redefining my notion of good history. We used no sophisticated file sharing software; we simply maintained a repository of book chapters, and sent the other an email when we edited a file. It worked; somehow, at the end of it all, we had a book, a good one.

Later, while working on a book about the liberatory potential of that gigantic collaboration called the ‘free software phenomenon’,  I found a co-author four floors down from me; we went biking, drank beers, went on double-dates, and squabbled endlessly over writing. Every single sentence was negotiated, an exhausting experience essential to the form and content of the final work. We stored our files online, worked on them together. And I mean ‘together’; we put four hands on the keyboard, and miraculously, managed to write that way.

Later, while working on a book on how current legal theory could and should accommodate artificial agents, I negotiated with a collaborator who often preferred long periods of autonomous activity in isolation. For the first time, I used software for writing collaboration; it wasn’t perfect but it introduced some much-needed structure to the writing process. I became an expert at change-tracking software; I became used to repeated iterations and pass-throughs of chapters in response to close readings by my co-author.

I’ve negotiated many power relationships in these partnerships; from dissertation advisers to good friends (deleting either’s sentences requires sensitivity and tact). Each collaborator has enriched and complemented me, and, in becoming part of my cognitive resources, has been an essential agent in my self-realization. The muses only visit while we work; mine include my collaborators.