The Judgment of Paris

Eris [Strife] tossed an apple to Hera, Athena, and Aphrodite … and Zeus bade Hermes escort them to [Paris] on Ide, to be judged … They offered [Paris] gifts: Hera said if she were chosen fairest of all women, she would make him king of all men; Athena promised him victory in war; and Aphrodite promised him Helene in marriage.
So he chose Aphrodite.
—Pseudo-Apollodorus. c. 2nd century AD.


Watching the HBO series Silicon Valley the other day, I came across a scene depicting a judged competition for venture capital dollars between different development teams—all of which promised to, for example, “make the world a better place through Paxos algorithms for consensus protocols,” or to “make the world a better place through canonical data models to communicate between endpoints.” “Making the world a better place” is a common line these days from the tech world: the language of “disruption” and “change agents” and “paradigm shifts” is everywhere. Yet, although technology is certainly having, directly or indirectly, an effect on everyone’s life, the technological revolution has had very little impact on traditional areas of political economy: for example, the productivity gains of the “New Economy” have had essentially zero effect on wages (upending a relationship that nearly every economist would have said was inherent to the universe prior to recent decades). Meanwhile, due to efforts like voter ID laws, many states are teetering perilously close to reviving Jim Crow. Still, to many, a world in which technological progress seems limitless while political progress appears impossible might not seem a matter for comment: why should technology have anything to do with politics? But to those  who first theorized that electing officials might be better than waiting around for them to be born, computers would not have been in a different category than voting. To them, voting was a kind of computing.

One of those people hailed from the island of Majorca, in the Mediterranean Sea off the Spanish coast; his name was Ramon Llull. Born in 1232, Llull lived during a time when Spain was divided between a Catholic northern part of the Iberian peninsula and a Muslim southern part. (Spain would not be unified until the Fall of Grenada, in 1492.) Not that that bothered Llull as a young man: in his autobiography, the Vita coaetanea (or “Daily Life”), he narrates that in his twenties he “was very given to composing worthless songs and poems and to doing other licentious things.” But when he was 33—a portentous age during the Middle Ages: supposedly Christ’s age at the Crucifixion, it was also the number of cantos in each part of Dante’s Divine Comedy—Llull experienced a vision of “our Lord Jesus Christ on the Cross, as if suspended in mid-air.” From that moment, Llull decided his life had three missions: to convert Muslims to Christianity even if it meant his own martyrdom (which he may—or may not—have achieved in the the city of Bougie, in what is now Algeria, in the year 1315), to found institutions to teach foreign languages (which he achieved in 1311, when the Council of Vienne ordered the creation of chairs of Hebrew and Arabic established at the universities of Paris, Oxford, Bologna, and Salamanca), and to write a book about how to convert Muslims. This last of Llull’s three missions has had profound consequences: it is the starting point that leads both to Silicon Valley—and Silicon Valley.

In order to convert Muslims Llull had, somewhere around the year 1275, the startling idea that Christianity could be broken down into constituent parts: he was a believer in what one commenter has called “conceptual atomism, the belief that the majority of concepts are compounds constructed from a relatively small number of primitive concepts.” As such, Llull thought that the Christian God possessed a certain number of relevant qualities, that God had limited the world to a certain number of what we today would call logical operations, and that the world contained a limited number of both virtues and vices. With these “primitive concepts” in hand Llull described how to construct a kind of calculator: a series of concentric wheels within wheels that could be turned so that, say, God’s attributes could be lined up with a logical category, and then with a particular vice (or virtue). By this means, a Christian missionary could reply to any objection a Muslim (or anyone else) might raise to Christianity merely by turning a wheel, which made Llull’s machine a forerunner to today’s computers—and not simply by analogy.

Llull’s description of his conversion machine, that is, ended up traveling from Spain to Germany, where—three centuries later—a philosopher and mathematician found it. Llull’s work became the basis of Gottfried Leibniz’s invention of what’s become known as a “pinwheel calculator,” which Leibniz described in his Machina arithmetica in qua non additio tantum et subtractio sed et multiplicatio nullo, diviso vero paene nullo animi labore peragantur of 1685. In 1694, Leibniz was able to build a practical model of the machine, which he improved again in 1706. These models later became the basis of Frenchman Thomas de Colmar’s Arithmometer of 1851, which in turn became the basis of mechanical calculators until—in 1937—Howard Aiken convinced Thomas Watson to fund the machine known as the Automatic Sequence Controlled Calculator: in other words, IBM’s “Mark I,” the world’s first computer.

That story is not unknown of course, especially to those with an interest in both history and computing. But it is a story that is not often told in tandem with another of Llull’s interests: the creation of what today would be called electoral systems. In three different works, Llull described what is essentially the same system of voting—a system later re-invented by Marie Jean Antoine Nicolas Caritat, the Marquis de Condorcet, in the late eighteenth century. In this method, candidates—Llull used religious examples, such as the election of a monastery’s abbot—are paired off with each other, and voters decide on which is the most worthy of the pair. This continues until every candidate is paired with every other, and then the candidate with the most votes is declared the winner. (In modern political science, that winner is called the “Condorcet winner.”) In this fashion—which in one place Llull says he invented in Paris, in 1299—an election is a kind of round-robin tournament, somewhat analogous to soccer’s World Cup.

Yet it’s also possible to take the analogy in another direction—that is, towards Palo Alto. A computer, after all, is a machine, and like all machines is meant to do particular jobs; what makes the computer different from other machines is just the number of different jobs one can do. But being capable of doing so many different kinds of tasks—from assembling emails to calculating the distance of a faint star—makes computers need what are called schedulers: algorithms that tell the computer in what order to do the work it has been assigned. One kind of scheduler is called a “round-robin” scheduler: in this scheme, the algorithm tells the computer to handle each task a certain amount of time and then to move on to the next if the job is not completed by the deadline. The computer then cycles through each task, working on each for the same amount of time, until each job is done. A variant, called “weighted round robin,” more precisely makes the analogy to Llull’s electoral scheme: in this variant, each task is assigned a “weight,” which signifies just how much processing capacity the job will need—the scheduler will then assign priority according to that weight through comparing each job’s weight to every other job’s weight. To each job, the weighted round robin scheduler assigns computing power—according to its need, as it were.

In this way, in other words, democracy can be demystified, instead of being fetishized as the kind of mystical process it sometimes is. Defenders of democracy sometimes cite, for example, the Latin phrase, “vox populi, vox Dei”: “the voice of the people is the voice of God.” But democracy should not be defended by that means: democracy should not be thought of as a kind of ritual, a means of placating a suspicious and all-powerful deity. Instead, it ought to be thought of as a kind of algorithm, like a round-robin sorting algorithm. Such, at least, was how one of the earliest English uses of the “vox populi” phrase described it; in a 1709 London pamphlet—produced, coincidentally or not, just after Leibniz’s 1706 calculator—entitled “Vox Populi, Vox Dei,” the anonymous author defended the following idea:

There being no natural or divine Law for any Form of Government, or that one Person rather than another should have the sovereign Administration of Affairs, or have Power over many thousand different Families, who are by Nature all equal, being of the same Rank, promiscuously born to the same Advantages of Nature, and to the Use of the same common Faculties; therefore Mankind is at Liberty to chuse what Form of Government they like best.

To put the point another way, the author is saying that each person ought to be treated somewhat like the round-robin scheduler treats each of its tasks: as worthy of the same attention as every other. Like the computer’s jobs, every person is treated equally—on earth, as it is in Silicon Valley. The wonder, of course, is that the doyens of the Valley have not learned the lesson yet—but there is still time, as always, for a snake to disturb that Eden. When it does, perhaps the revolutionary rhetoric of the lords of California’s silicate kingdom might begin to match reality—and Silicon Valley may indeed prove a lever to “change the world.” Which, after all, might not be unprecedented in history: in one of the earliest stories about a kind of Condorcet, or Llullian, election—the Judgment of Paris—the contest between the three goddesses (Hera, Aphrodite, and Athena) is provoked by a single object.
That object?

An apple.


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