Essay on "The Best Writing on Mathematics 2012"

Writing about music, the saying goes, is like dancing about architecture. The implication is that even trying is futile and likely to make the person doing so look absurd.

The line has been attributed to various musicians over the years – wrongly, as it happens, though understandably, given how little of what they do while playing can be communicated in words to people who don’t know their way around an instrument. I don’t know if mathematicians have an equivalent proverb, but the same principle applies. Even more strictly, perhaps, since most nonmathematicians can’t even tell when things go out of tune. And in many of the higher realms, math drifts far from any meaning that could ever be expressed outside whatever latticework of symbols has been improvised for the occasion. (Kind of like if Sun Ra went back to performing on his home planet.)

Against all odds, however, there is good writing about music – as well as The Best Writing on Mathematics 2012, the third anthology that Mircea Pitici has edited for Princeton University Press in as many years. He is working toward a Ph.D. in mathematical education at Cornell University, and teaches math and writing there and at Ithaca College. A majority of the pieces come from journals such as Science, Nature, The Bulletin of the American Mathematical Society and The South African Journal of Philosophy, or from volumes of scholarly papers. But among the outliers is an article from The Huffington Post, as well as a chapter reprinted from an anthology called Dating Philosophy for Everyone: Flirting With the Big Ideas (Wiley-Blackwell, 2011)

There’s also a paper from the proceedings of the Fifth International Meeting of Origami Science, Mathematics, and Education, which opens with the sentence: “The field of origami tessellations has seen explosive growth over the past 20 years.”

Chances are you did not know that. It came as news to me, anyway, and I cannot claim to have followed every step of the presentation, which concerns the algorithms for creating fantastically intricate designs (resembling woven cloth) out of single flat, uncut sheet of paper.

The author, Robert J. Lang, is a retired specialist in lasers and optoelectronics; his standards of numeracy are a few miles above the national average, even if the math he’s using is anything but stratospheric. But Lang is also an internationally exhibited origami artist. The images of his work accompanying the article offer more than proof of what his formulas and diagrams can produce; they are elegant in a way that hints at the satisfaction the math itself must have yielded as he worked it out.

Other papers make similar connections between mathematics and photography, dance, and (of course) music. But one of the themes turning up in various selections throughout the book is the specificity of what could be called mathematical pleasure itself, which can’t really be compared to other kinds of aesthetic experience.

In his essay “Why is There Philosophy of Mathematics at All?" Ian Hacking -- retired from a university professorship at the University of Toronto – considers the hold that math has had on the imagination and arguments of (some) philosophers. Not all have been susceptible, of course. Among humans, “a high degree of linguistic competence is [almost] universally acquired early in life,” the ability “for even modestly creative uses of mathematics is not widely shared among humans, despite our forcing the basics on the young.” And as with the general population, so among philosophers.

But those who have thought carefully about mathematics (e.g., Plato and Husserl) or even contributed to its development (Descartes and Leibniz) share something that Hacking describes this way:

“[T]hey have experienced mathematics and found it passing strange. The mathematics that they have encountered has felt different from other experiences of observing, learning, discovering, or simply ‘finding out.’ This difference is partly because the gold standard for finding out in mathematics is demonstrative proof. Not, of course, any old proof, for the most boring things can be proven in the most boring ways. I mean proofs that deploy ideas in unexpected ways, proofs that can be understood, proofs that embody ideas that are pregnant with further developments…. Most people do not respond to mathematics with such experiences or feelings; they really have no idea what is moving those philosophers.”

Beyond the pleasure of proof (“Eureka!”) lies unfathomable mystery – of at least a couple of varieties. One is the problem addressed in “Is Mathematics  Discovered or Invented?” by Timothy Gowers, a professor of mathematics at Cambridge University.  Be careful how you answer that question, since the nature of reality is at stake: “If mathematics is discovered, then it would appear that there is something out there that mathematicians are discovering, which in turn would appear to lend support to a Platonist conception of mathematics….”

Or to put it another way and leave Plato out of it for a moment: If “there is something out there that mathematicians are discovering,” then just exactly where is “out there”? Answering “the universe” is dodging the question. We might naively think of arithmetic or even some parts of geometry as some kind of generalization from observed phenomena, But nobody has empirical knowledge of a seven-dimensional hypersphere. So how – or again, perhaps more pertinently, where, in what part of reality – does the hypersphere exist, such that mathematicians have access to it?

A neurobiological argument could be made that the higher mathematical concepts exist in certain cognitive modules found in the brain. (And not in everyone’s, suggests Hacking’s essay.) If so, it would make sense to say that such concepts are created. But if so, the mystery only deepens. Scientists have repeatedly found the tools for understanding the physical universe in extremely complex and exotic forms of mathematics developed by pure mathematicians who not only have no interest in finding a practical application for their work, but feel a bit sullied when one is found.

Translating math’s hieroglyphics into English prose is difficult but – as the two dozen pieces reprinted in Best Writing show – not always completely impossible. Mircea Pitici, the editor, pulls together work at various levels of complexity and from authors who pursue their subjects from a number of angles: historical or biographical narrative, philosophical speculation both professional and amateur, journalistic commentary on the state of math education and its discontents.

And the arrangement of the material is, like the selection, intelligent and even artful. Certain figures (the 19-century mathematicians Augustus de Morgan and William Hamilton) and questions (including those about math as experience and mystery) weave in and out of the volume -- making it more unified than “best of” annuals tend to be.

That said, I am dubious about there being a Best Writing ’13 given the dire implications of certain discoveries (or whatever) by Mayan numerologists. This will be the last Intellectual Affairs column for 2012, if not for all time. I’d prefer to think that, centuries ago, someone forgot to carry a digit, in which case the column will return in the new year. And if not, happy holidays even so.


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Amherst College launches open-access scholarly press

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Amherst College starts publishing unit that will feature peer review and close editing -- while also making all books digital and free.

New book says campus environment plays a role in students' political identities

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New research suggests that campus environment greatly impacts conservative students' political styles, and that they can thrive on predominantly liberal campuses.

OpenStax announces first iPad version of its free, online textbooks

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OpenStax College, an open-access textbook publisher, introduces its first offering through iTunes -- and hopes the $4.99 charge will allow students to benefit from extras and the business model to grow.

Presidential (Library) Campaign Begins

With the 2012 presidential campaign complete, the campaign for the Obama presidential library (and to raise money for it) has started, Politico reported. The University of Chicago -- where Obama taught and where Michelle Obama worked -- is considered the favorite. But Politico noted that the University of Hawaii is also making a strong push. Obama was born in Hawaii, his parents met at the university and his sister teaches there.

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Survey suggests students feel satisfied but not ecstatic about library services

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Survey says students are generally satisfied with campus libraries, although a significant minority view them as irrelevant to academic success.

Student-run law reviews have much to contribute to legal education (essay)

John G. Browning’s recent essay on Inside Higher Ed fires many of the traditional bullets at student-edited law journals: They are overly theoretical, redundant, costly, and despite being edited by 20-somethings, are clumsily adapted to the digital age. I serve as editor-in-chief of Cardozo Law School’s Journal of Conflict Resolution, apparently one of these outmoded publications. Like most student editors, I’ve become accustomed to reading criticisms like these. Similar sentiments have been published in The New York Times, The Atlantic, and Legal Affairs. Browning is in good company.

Critics have their hearts in the right place. But their arguments are flawed in two ways: First, they dramatically overgeneralize the varied landscape of student-edited legal journals and the articles they publish. Second, critics view the primary mission of law journals as helping appellate judges and practicing lawyers. In fact, students are the primary beneficiaries of law reviews. Practicing lawyers and judges are important audiences too, but not as central as critics claim.

Nailing Down the Complaints

Criticism of law journals, like criticism of lawyers, is a time-honored American tradition. The common argument goes like this: Law journals publish bizarre theoretical pieces that are totally removed from real-world legal practice. As journals proliferate, they are becoming increasingly useless to practicing lawyers, and are failing in their primary mission of influencing judicial opinions. Browning makes his case, like many critics do, by citing some pompous-sounding topics of recently published pieces.

The vision of useless “theory” articles gained traction last year with a comment by U.S. Supreme Court Chief Justice John Roberts: “Pick up a copy of any law review that you see,” he said, “and the first article is likely to be, you know, the influence of Immanuel Kant on evidentiary approaches in 18th-century Bulgaria, or something which I’m sure was of great interest to the academic that wrote it, but isn’t of much help to the bar.”

This system persists, say the critics, because law professors are either innately interested in these abstruse topics or merely write under the pressure of the publish-or-perish system. More cynically, law schools themselves have a secondary incentive for subsidizing law reviews (which often operate at significant financial losses). Schools aim to build their reputations in specialty fields. “Reputation” is often code for the infamous reputational index on U.S. News & World Report -- a ranking of schools’ programs by professors in a particular field. If a school hopes to build its rank in taxation, for example, it might consider creating a tax law journal. Such a journal would allow tax scholars to publish with the school, probably bring such scholars to campus to participate in conferences, and generally increase the reputation of the school among experts in the field.

In short, critics cast law journals as nothing more than vehicles for prestige for schools and tenure for professors.

A Response: All Theory and No Practice?

To start, critics like Browning severely overgeneralize the landscape of law reviews. All student-edited legal publications are lumped together into a monolithically useless heap. In the minds of critics, these journals all publish on obscure theories of legal philosophy and hermeneutics. This is simply not the reality.

Yes, some journals are “theory-heavy”—the Yale Law Journal, William & Mary’s Bill of Rights Journal, and Washington University’s Jurisprudence Review, to name a few. But average law reviews and most specialty journals (journals that focus on particular areas, like real estate or intellectual property) are keenly interested in publishing relevant scholarship. Don’t believe me? Visit a few law journal websites and scroll through their recent tables of contents. Sure, you’ll encounter the occasional oddball pretentious titles. But you’ll also find articles firmly grounded in reality — articles that, as Sherrilyn Ifill of the University of Maryland said, “offer muscular critiques of contemporary legal doctrine, alternative approaches to solving complex legal questions, and reflect a deep concern with the practical effect of legal decision-making on how law develops in the courtroom.” Indeed, many law journal articles are written or co-written by practicing attorneys.

My own journal is a good example. We publish exclusively on arbitration, negotiation and mediation—all very practical processes for problem-solving, particularly in a world where the vast majority of cases settle out of court. To the extent that we publish “theory,” the articles discuss innovative designs for new adjudicative or dispute resolution systems.

Another rebuttal. Critics of law reviews complain that we’re failing at our key mission — being cited by appellate courts. Since when is judicial citation our raison d’être? Don’t get me wrong: I fantasize about Justice Kagan going to sleep with a copy of the Journal of Conflict Resolution on her nightstand before hearing a case arising under the Federal Arbitration Act. But contrary to the assertions of critics, I have never met a fellow law journal editor who selects articles for publication solely (or even predominantly) because of the likelihood that a judge somewhere may someday cite it. We choose articles that are thought-provoking and cutting-edge, but not merely because we desire judicial attention.

A corollary point is that law reviews do not necessarily need to be cited by courts in order to aid practicing attorneys. Attorneys facing specific legal situations often search journal databases for a starting point. Articles they discover serve as both invaluable synopses and comprehensive bibliographies of relevant precedents and statutes. That sort of impact is very difficult to measure unless the article itself is cited by a judge. (And since the great majority of cases settle before a judge ever sees them, how reliable a metric are judicial citations anyway?).

Critics underscore the role of law reviews in aiding practicing attorneys. This is surely one of their important functions. But the truth is, journals also exist for the benefit of their student editors. Students hone their legal research and writing skills by doing careful editing, citation formatting, and proposition-checking. They produce their own publishable pieces of original scholarship, usually commentaries on recent cases. Third-year students have the additional experience of managing a large team, controlling a significant budget, and interacting with leading scholars from around the world. Even if no appellate judge ever cites an article, the average student will still have grown tremendously by editing it.

Browning worries that student-edited journals are not useful for practicing attorneys. I disagree. But even adopting his assertion, attorneys still have access to innumerable attorney-edited journals published by bar associations across the country. Student law reviews are not their only resource, or even necessarily their best resource.

A Concession: An Archaic Publishing Process

Browning is absolutely right in one respect: the current model of journal publishing is entirely outdated. (I suspect this is true for non-legal academic journals too). Right now, law reviews submit content to one of the handful of specialized law review publishers. Those publishers print the content and mail our book-like volumes to subscribers. The publisher also sends that content to Westlaw and LexisNexis, the two major online legal research databases. Journals charge a small subscription fee and, sometimes, a content reuse fee if their articles are reprinted in textbooks. West and Lexis charge a great deal more. Most journals operate at a loss.

What is peculiar about this system is that many journals also publish their content as PDFs on their websites. PDFs, of course, are searchable by Google and easily findable through Google Scholar. For free. In the 21st century, I have absolutely no idea why any library or practitioner subscribes to the print edition of any law journal. (Though don’t repeat that to our valued subscribers). And I have absolutely no idea why any law school wastes money subsidizing the cost of printing and mailing them. (Though don’t repeat that to my generous dean).

The answer is probably about competition; no law school wants to be the first to go “online only.” If prestige is truly the obstacle — we are talking about lawyers here — the solution is an industrywide collusion. If deans from a collection of law schools discussed this, perhaps during an Association of American Law Schools (AALS) conference, they could reach a disarmament agreement. Depending on the number of journals a school operates, this shift could easily save five or six figures annually.

As the digital age moves along, law reviews should reject not only print publication, but also the very idea of distinct “volumes” and “issues.” What is an “issue” of a law journal but a collection of articles on a random assortment of current topics? Few issues have a single unifying theme that merits their being bound together in a book format. Law journals should move to a model of rolling deadlines more akin to digital journalism. Scholarship can be published whenever it is ready, and at a much lower cost.

Concluding Thoughts

If the goal of law journals is to influence appellate judges in their day-to-day decision-making, perhaps they are failing. But most journals don’t (or shouldn’t) adopt that as their sole metric for success. A better metric is what the students on the journal are gaining from the experience. Journals expose law students to truly complicated, confusing, complex writing. Some of that writing is terrible and pompous, some vivacious and sharp. Some is hackneyed, some is intellectually subversive and trailblazing. Thus, academic legal writing mirrors the mélange of actual writing — i.e., briefs, memos and judicial opinions — that attorneys will encounter throughout their careers.

Journals teach student editors to sharpen complex legal arguments, clarify language, format intricate citations, and work long hours to hone a final product. More sentimentally, the journal process reminds students that no legal doctrine is static. Law is subject to thinking and rethinking, argument and re-argument. Authority can not only be cited but questioned — by smart lawyers, through their writing.

There is so much to fix in modern legal education. Are student-edited law journals really so bad?

Brian Farkas is a third-year student at Cardozo School of Law and editor-in-chief of the Cardozo Journal of Conflict Resolution.

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Review of Ronald Hendel, 'The Book of Genesis: A Biography'

Intellectual Affairs

A couple of months ago it occurred to me that having a copy of the Bible on my portable reading device would be convenient, given that citations turn up in even the most secular of texts. And as William Blake wrote near the end of his life, “The Old & New Testaments are the Great Code of Art.” Which is gnomic, like most of his aphorisms, though clearly enough an encouragement to wrestle with “the book of books.”

But acquiring a classic or a public-domain book in an e-format is not so effortless as it may initially seem. Unless you find one with a fully functional table of contents, the frustration outweighs the benefits. It also helps if the text has been inspected by a copy editor at some point in the current century. Until someone invents OMR (optical meaning recognition) software, even a free digital book will seldom be worth the trouble to get. So after all due diligence, I located a good edition of the authorized translation from 1611 (better known as the King James Version) and willingly parted with 99 cents to purchase it.

When the title appeared in my Kindle queue, I saw that the slot indicating the name of the author had also been filled in: God. He has an excellent ear for English prose, to judge by the KJV, and I decided to read the whole thing from beginning to end -- my first serious engagement with the scripture in decades. Despite knowing most of the stories pretty well from childhood, the return has been an experience in constant defamiliarization. At one point, having mulled over the truly puzzling implications of Genesis 6:4 for a bit, I looked up from the screen and told my wife, “This sure is a weird book.”

The best thing about Ronald Hendel’s The Book of Genesis: A Biography (Princeton University Press) is how thoughtfully it acknowledges that strangeness, and gives it its due. Hendel is a professor of religious studies at the University of California at Berkeley and editor of Reading Genesis: Ten Methods (Cambridge University Press, 2010), a collection of essays that I intend to start reading just as soon as this column is out of the way. His new volume appears in the Lives of Great Religious Books series, which uses the biographical mode to synthesize and popularize, at a high level, the scholarship devoted to works from a variety of spiritual traditions.

Half a dozen titles have been published so far, both on scriptural texts (e.g., The Tibetan Book of the Dead and The Book of Mormon) and confessional or theological writings (most recently, Dietrich Bonhoffer’s Letters and Papers from Prison). To write the biography of a book -- portraying it as having, in effect, a personality and a career -- is a literary conceit. But it is a justified and effective one in the case of texts which seem, to a great many of their readers, almost literally alive, or at least integral to understanding life itself.

On that score, no book could be more exemplary than Genesis. “Over the generations,” Hendel writes, “the ways that people have understood Genesis tend to correlate with the ways that people have understood reality. It is not just that Genesis provides an account of the origins of reality -- which it does -- but that the kinds of meaning that people expect to find in Genesis are the same kinds that they expect to find in the outside world.”

And for good reason: “Genesis envisions a single, God-created universe in which human life is limited by the boundaries of knowledge and death. We are earth-bound, intermittently wise, often immoral, mortal creatures.” Within the first few words, the reader will encounter temptation, disobedience, sex, death, violence, and exile. It’s not necessary to believe in the historical reality of a single person named in Genesis -- nor even that God exists, let alone gets byline credit for either Genesis or the universe itself -- to recognize much of this world. De te fabula narrator. The tale is told about you.

For his part, Hendel is telling the story of Genesis – not retelling stories from it. Much like the larger book to which it is an overture, Genesis reads more like an anthology than a single composition. The opening chapters provide two not entirely compatible accounts of how God created the world and mankind. They resemble the creation myths found in Babylonian writings, which also recount a story very similar to the one about Noah and his ark.

And beginning with Chapter 11, the narrative register of Genesis shifts from extremely condensed accounts of vast events (the flood, the Tower of Babel, the birth of giants resulting from “sons of God” hooking up with earth women) to a sprawling multigenerational family saga, complete with minor characters and complicated subplots.

Internal evidence suggests that Genesis -- like the four other books of the Pentateuch, traditionally attributed to Moses -- is the work of at least three groups of writers recording stories and customs that emerged over long periods and sometimes bore only a tangential relationship to one another. Editors later integrated the texts as much as possible, but by no means seamlessly.

On this point, Hendel is not saying anything original, simply presenting a much-condensed account of a line of analysis that has been taking shape over the past 200 years or so. But then he takes things in an intriguing direction. If Genesis is the product of various strands of cultural DNA (spliced together long ago by scribes who believed the literal truth of the material they were helping to transmit, while also needing to reconcile elements that didn’t quite fit together) then the book’s subsequent history is, in a way, encoded in its genome.

Genesis is full of enigmatic passages and unfinished stories. But if a text is the word of God -- the operating assumption of most of its careful students over the most of its history -- the puzzles are meaningful. What look like imperfections are access points to hidden truth. The interpreter has work to do, at high stakes.

And so alongside the literal significance of the text there takes shape a world of supplementary meanings – allegorical, apocalyptic, neo-Platonic, and so forth. All the better for the reader of Hebrew, who could shuffle the consonants in a word around, add some vowels, and come up with something profound -- if not, by nonmystical standards, plausible.

My favorite of the examples of creative rewriting that Hendel cites is how Philo of Alexandria handled the business with Abraham, Sarah, and Hagar. In Genesis 16, we learn that Sarah, being unable to conceive, “gave to her husband” Hagar, her handmaid, to be wife No. 2 and bear him a child.

While one must respect Abraham’s wisdom in not bringing up the idea himself, the whole “exchange of human livestock for breeding” aspect is pretty revolting.  But Philo treats it as a Platonic lesson in the “distinction between the ‘preliminary’ sciences – which study the sensible, material world – and philosophy, which studies the higher world of pure being.”

Philo’s allegorical algebra, as explained by Hendel, proves far neater than the situation itself: “The mind (=Abraham) must first be educated in the preliminary sciences (=Hagar); only then is it ready for philosophy and true wisdom (=Sarah).” No more moral ickiness! Q.E.D.

The problem with that sort of analysis is that its creativity will never be limited by questions about the literal meaning of a text, much less doubts about whether or not it is true. In an elegantly understated chapter (another author might have blown the idea up to a book) Hendel brings together Rabelais, Martin Luther, Spinoza, and the great rabbinical commentator Rashi as examples of a countertendency. They rejected interpretive inflation – a first step toward facing questions about the literal truth, moral adequacy, or overall coherence of the text itself.

Questions raised by geology and biology would eventually become critical indeed – with fundamentalism as one product of the crisis, even as Emily Dickinson and Franz Kafka found ways to inhabit the ancient book in ways that restore its true, deep otherness. “Many people don’t read Genesis anymore,” Hendel writes, “which I think is a loss – but we still fight over the meanings and consequences of the stories, and over their myriad interpretations in Western culture.” And his book documenting that truth is something of a revelation in its own right.

Ties Grow Between Drug Industry, Biomedical Research

A series of conflict-of-interest scandals have led to many attempts to limit the role of the pharmaceutical industry in supporting biomedical research. But an article in The Washington Post says that these ties remain strong and may even be growing, as the pharmaceutical industry has come to support more research than does the federal government. The Post analyzed articles on new drugs that appeared in The New England Journal of Medicine for a one-year period ending in August. Of 73 articles, 60 were funded by a drug company, 50 were co-written by people who worked for drug companies and 37 had lead authors, generally professors, who had in the past received funds from drug companies for consulting, speaking or doing research.

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New Leader for University Press Group

The Association of American University Presses on Friday named Peter Berkery Jr. as its next executive director. Berkery is currently serving as the vice president and publisher of the U.S. law division of Oxford University Press. He has previously worked as a lawyer and as an association official at the National Society of Accountants, the National Paint and Coatings Association, and the American Trucking Association.

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