|PENN BACCALAUREATE 2007
May 22, 2007, Volume 53, No. 34
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Penn Baccalaureate Address by Dr. K. Anthony Appiah, Laurance S. Rockefeller Professor, Princeton University, Sunday, May 13, 2007.
Building Post Roads of a New Millennium
You are the smartest class to have graduated from the University of Pennsylvania since the College of Philadelphia gave its first eight baccalaureate degrees in 1757. No, I mean it. And now that I’ve said that, I’m tempted just to sit down. But I’m going to take the risk of explaining why I’m pretty sure I’m right. And when I’m done you’ll see that this is as much a reason for humility as for pride.
To explain what I have in mind, let me take you back a century before the College opened its doors, back, in fact, to 1654. We’re in France and Antoine Gombaud, chevalier de Méré, a gambling gentleman, has had a run of very large losses. Nowadays, I suppose, he’d have entered a 12-step program at Gamblers Anonymous, but that wasn’t an option then. So, instead, being a chevalier, he simply wrote to France’s two leading mathematicians, Pierre de Fermat and Blaise Pascal, and asked where he had gone wrong. That got the two great mathematicians thinking, and they wrote each other a series of letters that year, which were published a couple of years later by Christian Huygens in Holland. In those letters they invented the foundations of the modern mathematical theory of probability.
The seventeenth century was actually a pretty good period for mathematics overall. Not only do you have John Napier, Laird of Merchistoun, inventing the logarithm, but you’ve got René Descartes, in an appendix to his 1637 Discourse on Method named simply “La Géométrie,” laying out the foundations of analytical geometry (which is why those coordinates are called Cartesian). And then, in the last part of the century, Newton and Leibniz developed the calculus, pretty much independently, drawing, of course, on the ideas of Descartes and Fermat and the other leading mathematicians of the first part of the century. Logarithms, probabilities, infinitesimals, differential equations. The intellectual firmament was changed forever.
Now Fermat was usually in Toulouse, Leibniz in Hanover, Newton in Cambridge, Huygens in The Hague, Pascal in Paris, and Descartes (who served in the Dutch and Bavarian armies) was all over the place, but most often somewhere in the Netherlands. They knew Latin, but they spoke English, Dutch, French and German. And to figure out how they could nevertheless have been part of an intellectual community, you have to think about something else that happened in the seventeenth century.
In 1635, in England, a proclamation permitted the public to use the Royal Mail, which had hitherto been a means of conveying only letters between the King and members of his Court. The conveyance of private letters by the royal poste aux chevaux took off when its finances were put in order in 1627. Before long, thoughts that nobody had had before were being thought. We talk about these great thinkers as if they did it on their own, as individuals. “Nature and nature’s laws,” Alexander Pope wrote, “lay hid in night. / God said, “Let Newton be!” and all was light.” That’s highly misleading. New thoughts really emerge from collections of individuals and things. There is indeed a space where new thinking happens, but it’s not really between anybody’s ears.
What are the chances of your rolling seven with two dice? It seems that before the seventeenth century, nobody had a clue. Then, in the mid-seventeenth century, in the space between Toulouse and Paris and The Hague—a space connected by the mails as much as by stagecoaches—the answer was discovered. And now every one of you knows how to work out the answer. (Right? Ah well, it’s too late to test you now.) In the letters between Pascal and Fermat, we find glimmerings of a whole new way to understand uncertainty. Imagine what might have happened if they’d been able to IM each other as well! Fermat, scribbling in the margin of a book, wrote about the most famous theorem that bears his name, “I have discovered a truly marvelous proof of this, which this margin is too narrow to contain.” In contemporary terms, it’s as if he was Twittering his friends, and was reaching his 140-character Twitter message limit. As the mails became more accessible, midway into the early modern era, you sense a similar excitement.
The expansion of post roads continued to be a good proxy for the expansion of knowledge. The postmaster of Philadelphia was, of course, your own Benjamin Franklin. By 1775, he became this country’s first postmaster general, and put the system on excellent foundations, too. Those post-roads connected the minds of America into a web—a web that was connected, across the Atlantic, with the webs of the Royal Mail and the postes aux chevaux.
The late historian of science Derek De Solla Price devised a way of trying to quantify the growth of scientific knowledge. He saw a more or less exponential curve. Human knowledge doubles in the 1500 years between the birth of Christ and the Renaissance; it doubles again in the 250 years between the Renaissance and the French Revolution; and again, between the French Revolution and the dawn of the automotive age, 125 years later, and again between then and the start of the Cold War, another 50 years; then it doubled in the decade preceding the election of JFK. Now—by some estimates—it doubles every two years. Soon, it looks like, someone will be able to tell you that it has doubled in the course of a graduation ceremony.
This should remind you of Moore’s Law, which suggests that, holding unit costs steady, the processing power of an integrated circuit doubles every two years. The computer can be thought of as a cognitive prosthesis. Since Moore’s law was coined, it has been observed that per-person productivity improvements in DNA sequencing follow more or less the same plot. Likewise when it comes to how long it takes, in man-hours, to determine a protein structure. So biological technology has gone into overdrive, too. In theory, the time it takes to go from “bug to drug”—from identifying a pathogen to devising a treatment for it—can be reduced from a decade to a matter of weeks. 1
Given all this, given the acceleration of connectivity and computational power, yours will be the smartest generation so far: the most networked, the most cosmopolitan, the most intellectually powerful. Your computer connects you with millions of gigabytes of data; but equally importantly it connects you with millions of human minds. In the space among all of you, amazing things are going to happen. Not because you’re individually smarter than Newton, but because you have better tools and you’re better linked up than he was. The intellectual capital tied up in the brains of each human being can now potentiate the capital in all the others. The genius of modern science isn’t that we’ve figured out how to make more scientific geniuses. It’s that we’ve worked out how to take normal human beings and link them up in institutions where they can develop new understandings by challenging old ideas. You’re the smartest generation because other people have built the tools and the resources that make you smarter: the world wide web, the cell phone that allows you to ask a question by IM or access a news site or a blog; the databases and the instruments that will make you productive in all you do at work and at home in the life ahead of you. And in that life you’ll be creating things that will help other people to be smarter, too—even smarter than you, if that’s possible to imagine. You’ll be building the post roads of a new millennium.
But to make the best use of your shared resources you have to keep yourself open to the possibility that you’re wrong. That web of information that you tap into everyday is a web of misinformation, too: and you’ll need to remember not just that every time the Internet challenges you with a new idea, it may be right; but also that every time it confirms what you already thought, it’s possible that you and it are both wrong. Human knowledge, it has been suggested, is itself a Wiki, a collective, ever changing edifice: constantly expanding, constantly being corrected, and constantly in need of correction. Part of why a rigorous education, such as you’ve received at Penn, matters so much, is that it aids the self-correcting function. Education is as much about teaching you to identify falsehoods as it is about teaching you truths. Bad ideas—not least, violent fanaticisms—can travel along the post roads of our postmodernity, too. They have done so. But such ideas hate to be exposed to the rough-and-tumble of debate; they fear exposure to other ideas, other beliefs. Apocalyptic fantasies will persist, I have no doubt; but there’s reason to hope they will not prosper.
When I was an undergraduate, my biochemistry tutor gave me a print of one of Carpaccio’s great murals of St. Jerome. Years later, looking at the original in Venice, it struck me that the shelf of books behind the saint—his library—contained almost everything that he would have thought worth reading, and he would surely have read all of them. Now, a single web site may contain millions of times the number of pages that St. Jerome could have read in his lifetime. Once, to have heard the range of music that you can scan on your radio, you would have had to travel thousands of miles, hoping to be on time for the right performances. Your DVD collections may well contain more hours of acting than Samuel Pepys—that devoted seventeenth century theatergoer—saw in his entire lifetime. There used to be a time when the proof of a new mathematical theorem was a rare and noteworthy event; and now? Well not so long ago, a distinguished mathematician suggested that more than one hundred thousand new mathematical theorems were now being proved each year.2 The next Enlightenment is yours for the making, together.
The gains I’ve talked about so far are mathematical, scientific, and technological. What about moral gains? Given everything our species has learned about historiography, literature, engineering, sociology, molecular biology, algebraic topology, and the rest, why haven’t our ethical attainments kept pace? If we’re so good at math, why haven’t we become whizzes at morality? Certainly, it can be discouraging to think about the persistence of cruelty and carnage in our own day. Yet here, too, there are reasons for hope. Two hundred years ago, on March 25, 1807, the British Parliament passed the Abolition of the Slave Trade Bill. Within a single generation, Britain went from being the world’s leading slave traders, with more than 50,000 slaves shipped every year, to banning the trade, and then the practice of slavery across its empire—and it did so at a time when there was still a great deal of profit to be made. It was a startling turn-around within one generation. Or think of foot-binding in China: a practice that was entrenched for a millennium but was, in one generation straddling the turn of the past century, essentially eradicated. Our own country lived with routine everyday legal apartheid for most of its history; but then, in the 1950s, the Supreme Court insisted that the very idea of enforced separation was repugnant, and in the decade that followed, federal laws promulgated that core idea. People born since Brown v. Board of Education—even if they came from families with long histories of racism—now almost all accept that racism is wrong. But, as with the scientific advances, the work here has always been a social endeavor: not the possession of a solitary mind, but something that emerges out of an extended human horizon. People didn’t learn that forcible segregation was wrong by sitting alone and pondering the question: they learned it was wrong by arguing about it together, by seeing together what it meant in a social world they shared. And by making arguments, together, they changed the world.
And so the challenge is not only to create a smart society, with smart institutions, which can be organized to bring more and more of the population of this world on-line, so to speak. It is also to advance the great collective project of moral understanding. We each have a part to play. If the great conceptual breakthroughs of the seventeenth and eighteenth-centuries, the West’s first Enlightenment, were partly to do with an expanded postal service, then the people who helped build a post road—the surveyors, the engineers, the fellows who designed the shovel, the plow, and the rake, and the fellows who wielded them—all were part of that revolution of thought, too.
One mark of the dawn of our modernity, I suggested at the start, was a new way of understanding uncertainty. The results helped gamblers like Antoine Gombaud lay down bets that still had no guarantee of success but at least enjoyed better odds. Yours will be an age of intellectual abundance, such as the world has never seen, and you face challenges such that the world as never known—problems that, alas, your elders have bequeathed you as well. There’s no guarantee of success. But, in the spirit of the chevalier de Méré, and speaking for my own generation, I’d like to say, “We are betting on you.”
2R. W. Hamming, “Mathematics on a Distant Planet,” The American Mathematical Monthly, Vol. 105, No. 7. (Aug. - Sep., 1998), pp. 649.