No, Aristotle Did Not ‘Create’ The Computer

For the past few days, an essay titled “How Aristotle Created The Computer” (The Atlantic, March 20, 2017, by Chris Dixon) has been making the rounds. It begins with the following claim:

The history of computers is often told as a history of objects, from the abacus to the Babbage engine up through the code-breaking machines of World War II. In fact, it is better understood as a history of ideas, mainly ideas that emerged from mathematical logic, an obscure and cult-like discipline that first developed in the 19th century. Mathematical logic was pioneered by philosopher-mathematicians, most notably George Boole and Gottlob Frege, who were themselves inspired by Leibniz’s dream of a universal “concept language,” and the ancient logical system of Aristotle.

Dixon then goes on to trace this ‘history of ideas,’ showing how the development–and increasing formalization and rigor–of logic contributed to the development of computer science and the first computing devices. Along the way, Dixon makes note of the contributions-direct and indirect–of: Claude Shannon, Alan Turing, George Boole, Euclid, Rene Descartes, Gottlob Frege, David Hilbert, Gottfried Leibniz, Bertrand Russell, Alfred Whitehead, Alonzo Church, and John Von Neumann. This potted history is exceedingly familiar to students of the foundations of computer science–a demographic that includes computer scientists, philosophers, and mathematical logicians–but presumably that is not the audience that Dixon is writing for; those students might wonder why Augustus De Morgan and Charles Peirce do not feature in it. Given this temporally extended history, with its many contributors and their diverse contributions, why does the article carry the headline “How Aristotle Created the Computer”? Aristotle did not create the computer or anything like it; he did make important contributions to a fledgling field, which took several more centuries to develop into maturity. (The contributions to this field by logicians and systems of logic of alternative philosophical traditions like the Indian one are, as per usual, studiously ignored in Dixon’s history.) And as a philosopher, I cannot resist asking, “what do you mean by ‘created'”? What counts as ‘creating’?

The easy answer is that it is clickbait. Fair enough. We are by now used to the idiocy of the misleading clickbait headline, one designed to ‘attract’ more readers by making it more ‘interesting;’ authors very often have little choice in this matter, and very often have to watch helplessly as hit-hungry editors mangle the impact of the actual content of their work. (As in this case?) But it is worth noting this headline’s contribution to the pernicious notion of the ‘creation’ of the computer and to the idea that it is possible to isolate a singular figure as its creator–a clear hangover of a religious sentiment that things that exist must have creation points, ‘beginnings,’ and creators. It is yet another contribution to the continued mistaken recounting of the history of science as a story of ‘towering figures.’ (Incidentally, I do not agree with Dixon that the history of computers is “better understood as a history of ideas”; that history is instead, an integral component of the history of computing in general, which also includes a social history and an economic one; telling a history of computing as a history of objects is a perfectly reasonable thing to do when we remember that actual, functioning computers are physical instantiations of abstract notions of computation.)

To end on a positive note, here are some alternative headlines: “Philosophy and Mathematics’ Contributions To The Development of Computing”; “How Philosophers and Mathematicians Helped Bring Us Computers”; or “How Philosophical Thinking Makes The Computer Possible.” None of these are as ‘sexy’ as the original headline, but they are far more informative and accurate.

Note: What do you think of my clickbaity headline for this post?

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.

A Small, Yet Beautiful Book Collection (And Its Scholarly Owner)

As an academic, I’m used to seeing large personal book collections in homes and offices. Many of my colleagues and friends–some very accomplished and smart folks–have, rather effortlessly, put mine to shame.  This is the story of, in contrast, a small book collection. But a very impressive one, one that revealed its owner to be a true savant–in the best and original sense of the word.  It also tells us something about a possibly lost art associated with books: quality curating and diligent reading.

During my post-doctoral fellowship at the University of New South Wales, I became friends with a mathematical logician specializing in–among other topics–computational learning theory. His work was forbiddingly mathematical and I soon developed a rather awestruck appreciation of his competence in his chosen field. Even more impressive was his attention to elegance and conciseness in both his verbal and mathematical expression; we co-authored a journal paper together and I was–for lack of a better word–blown away by his insistence on getting our written and technical formulations just right. No superfluous words, no bloated definitions, no vague sentences were to be tolerated. (Needless to say, I left the mathematics to him and concentrated on getting the exposition right.)

During this period, I had ample opportunity to visit his office. On one such occasion, I wandered over to the solitary bookshelf present. It was stacked with books, but compared to the many book collections I had seen the collection was, numerically speaking, a rather undistinguished one.

I looked closer.  Most books–hardcovers–on those few shelves were covered with a protective plastic cover; they were a historical classic or an authoritative treatise of some sort.  This was not a lightweight collection, making up with quantity for what it lacked in quality.  A discerning mind had clearly sifted the dross out and selected merely the gems.

I picked out one of the books on the shelf; a selection of papers by the Bourbaki collective in the original French. I leafed through its pages, fascinated by the history on display. I reached the end of the book. On its last page, a series of elegantly handwritten numbered notes were written on a sheet of paper and stapled there. I peered at them; the following might have been a sample entry:

Pg 33: y ‘ should read y“ in line 41

This list continued for a page or so.

I put the book down and looked at others on my friend’s shelves. Many of them had a similar erratum sheet attached to them.

I’ve never quite forgotten the feeling I experienced then, and have repeated this story many times over the years. My friend didn’t just have a book collection of exceedingly high quality, he had actually read them all. And he  had read them carefully, closely, comprehensively, and made note of any errors he had noted. Then, with a final nod to his painstaking, diligent scholarship, one that disdained ugliness in every form possible, he had refused to markup the text itself with a pen or pencil, and had instead, attached a separate sheet detailing the mistakes he had found.

A not easily emulated model.

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.)

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.