Buridan’s Ass, or How the Mind Hinders Itself


Jean Buridan didn’t invent the donkey named after him as a counterexample to determinism. Since his principal contribution was in the field of mechanics, the donkey may be mods properly named in honor of Democritus, Leucippus, or Lucretius. The Stoics believed that the world was composed of atoms and that their motion and everything derived from their motion was entirely determined. The intuition was astute but the mathematics to describe their vision was lacking. The mathematical notation used by the Greeks was adequate to natural numbers of a limited size, but for huge numbers and for the fractions that fell between the natural numbers, this notation faltered. The place-value system that originated in India can represent such quantities with ease and precision, but without the benefit of these representations, quantities are much less finely set. The Stoics took their atoms to be very, very small but nevertheless of a finite size and, as their very name meant uncuttable, indivisible into smaller parts. In their description of reality, they were condemned to rely on finite quantities, and coarsely grained measurements, weaknesses exploited by their adversaries in the devising of counterexamples.


Buridan’s ass is a hungry donkey set between two piles of hay, one to the right, one to the left. The piles are exactly the same size, and they are exactly equidistant to the befuddled donkey between them. In our own age, we are so accustomed to the gargantuan numbers of astronomy, and the tiny intervals of particle physics that we find it incredible that distances or masses should be completely equal. We’ve learned to live without simultaneity, and so it’s easy for us to relinquish the precise equality of any measurements. Initial conditions are so finely set that the tiniest alteration will lead to drastically different outcomes, as Edward Lorenz discovered using the amplitude of place-value notation and computers. Montaigne suspected it without these aids.

It might rather, methinks, be said, that nothing presents itself to us wherein there is not some difference, however little soever; and that, either by the sight or the touch, there is always some choice, that, though it be imperceptibly, tempts and attracts us;

Setting chaos theory aside for a moment, there is also something peculiar about the psychology at work here. Again, in Montaigne’s words:

‘Tis a pleasant imagination, to fancy a mind exactly balanced between to equal desires.

The fancy imagines desire as having a certain mass, and it also imagines a central actor, an arbiter between these two desires and occupying some space between them. There is an ancient tradition that explains the emotions as the affects of humors, fluids which have different and sometimes contradictory influences on the mind and body. It is only a small step to take from thinking of the emotions as fluids to thinking of desire as a fluid as well. Desires may then be measured, poured into a flask and topping out at red lines with red numbers beneath. The arbiter in the middle of all this is similar to the homunculus debunked by Gilbert Ryle.


To say that somebody desires something, is to say that he will choose it over anything else. Desire isn’t some humor, some fuel that propels us toward certain objects. Desire is an act of preferring. It is impossible to think of an agent torn between two contradictory and equal desires, because desire is nothing more than choosing one thing and foregoing another. Desire can’t be quantified because it isn’t a measure but an indexing. The donkey will choose one pile of hay over the other. Some are lascivious and will pursue sex to the cost of their position. Some are avaricious and will pursue money over rank, some ambitious and will take rank and preeminence over wealth. Some are gluttonous and pick food over drink, some are drunkards and will rather drink than eat. The vain will take applause no matter what the cost, and the spiteful will forego their own acclaim for the humiliation of their enemies. These actors don’t make these choices because they are filled with twenty milliliters of rage but thirty milliliters of sloth and their sloth outweighs their rage and consequently they take no action when injured. We know them to be wrathful, slothful, envious, or greedy because of what they do and these are descriptions of their behavior and not some underlying humor.

Sumptuary Laws and Civic Virtue



In his Utopia, Thomas More wrote that in his perfect society, gold and silver were to be put to ignoble uses like chamber pots so that these precious would be despised by all citizens. Montaigne advocates similar measures for engendering a contempt for luxuries. A sympathy for sumptuary laws runs throughout the Renaissance and beyond. Not all writers believed that these laws could ever work but considered the intended effects salutary. From their reading of Plato, Livy, Plutarch and other authors, and their own understanding of ancient history, Machiavelli, Gibbon, and many more believed luxury and extravagance were the undoing of republics and empires alike.


The laws of Lycurgus were the most thorough and rigorous of all codes in curbing luxury. The Spartans used money minted of iron, on the rare occasions they handled money at all. The Spartans wore the simplest clothes, ate the coarsest food, and lived lives of hardship and privation, in order to make themselves peerless warriors. They were great fighters and Plato, Xenophon, and many more Athenian authors credited this abstemious lifestyle for their prowess on the battlefield.


Later writers like Livy and Plutarch made a natural comparison between the early Romans and the Spartans. Those Romans from the early days of the Republic, Cincinnatus, the Horatii, and Camillus, lead lives of rude simplicity, scratching out their daily bread from the soil, strengthened by hard manual labor and inured against every privation. These sturdy forefathers conquered an empire, and this accession of wealth corrupted their descendants. The Romans became gluttonous, lazy, effeminate in manner, accustomed to lives of ease and pleasure that rendered them unfit for the legions. The fall of Rome is a story of moral degeneracy.


Although remembered as the supreme exponent of unscrupulous measures, Machiavelli was a very moral author and he thought any republic corrupted in its manners incapable of surviving. What exactly is corruption. Everything Lycurgus and Cato the Elder would despise and denounce: riding in litters, wearing silk, eating off gold plate, sleeping in soft beds. Some like Gibbon and Montesquieu have a peculiar fixation with climate. Throughout his history, Gibbon contrasts the legions hardened by the winters of northern provinces like Dacia and Britannia with those legions enervated by their heat and torpor of Syria and Egypt. Against all counterexamples, he considers shivering somehow a fortifying exercise and insists that balmy climes are fatal to martial vigor. This bias persists into modern times and Toynbee deems the town of Capua particularly emasculating.


Augustus was so alarmed by the moral decay of the Roman state that he became one of the most prolific legislators of sumptuary laws. Over the next centuries, the legions, once manned by the citizen farmers of the nearby countryside, came to depend on contingents of German mercenaries and his fears seem to be well founded. The lecheries and debaucheries of Tiberius, Nero, and Caligula, so sensationally depicted by Suetonius provide an antipode to the heroes of Livy. We picture Cincinnatus at his plow alongside his degenerate descendants writhing in their orgies or hunched over their vomitorium. Such Mediterranean sybarites can never stand up to the burly giants sweeping down from the north.


Discomfort and privation do not make good soldiers. Men accustomed to riding horses (when it was still a skill useful in war), hunting, rifles, and trained to arms since childhood will at first be better fighters than their counterparts who may be equally robust and strong in body but lack this early training. They will keep this ascendancy for some while, but their adversaries will be seasoned by training and experience and soon match if not surpass them. The Southerners were convinced that one man in butternut was worth ten in blue but in the end the factory workers of the North beat the Southern cavaliers facing them. As Sam Houston had predicted, the descendants of the heroes of Lexington and Bunker Hill were found the equals with the descendants of the heroes of Cowpens and Yorktown. The Thebans learned the art of the phalanx from the Spartans and at Leuctra although outnumbered they defeated them.


Men don’t fight well because they’re poor, or hungry, or ill-clad. They fight because they believe they have a reason to fight. They fight because they think their actions matter. Citizens believe that the state is an enterprise in which they have a share. They must be sure that they have a voice in the decisions taken and a stake in the outcome of those decisions. With this assurance they can accomplish anything, without it they’re good for nothing. The Romans were no longer willing to serve under the eagles because they didn’t believe they had a voice or a stake and they were right. The Empire was the rule of one man, whether benevolent and despotic. There were many emperors over the next centuries, so wide in their extraction, so various in their circumstance and character, that any man might aspire to become emperor. If a gigantic Thracian peasant like Maximin, or a Syrian zealot like Elagabalus might rise to become emperor, the way seems clear for anybody bold or lucky enough to attempt that dangerous climb. Yet for the ordinary citizen to take a hand in the management of the state was quite impossible.


The Roman Empire held some of the fairest portions of the earth, and this wide and fertile expanse yielded much wealth that was channeled into the recruitment and maintaining of the legions. Yet while the citizens of the Roman Empire enjoyed its benefits, they took no part in its direction. The ordinary people kept their heads down and endured whichever adventurer had risen to the purple. In the general prosperity, very few young men were compelled by poverty to enlist in the legions. There were easier and safer ways to make a living. The natives of Italy no longer aspired to become centurions, and so the empire turned to the barbarian tribesmen, trained to arms since childhood and already grouped into their warrior bands.


The Russian peasants conscripted into the armies of the Czar in the First World War were no match for the Germans. The Germans were raised in comfort and plenty in comparison to their Russian foes, and they were the recipients of a public education which furnished them with the skills to fight a modern war and inculcated the nobility of service to the state. Growing up, the Germans had been better nourished, better educated, and more thoroughly indoctrinated. The Germans had imbibed a fervid and bellicose nationalism from the cradle, and the illiterate, confused, often unhealthy Russian serfs facing them stood little chance. The Battle of Tannenberg showed the immense might of a modern, industrial state. Schoolboys taught reading, arithmetic, and love for the Kaiser and the Fatherland throughout childhood, made terrible soldiers once grown to manhood.


It is upbringing, education, and above all, unity of purpose that makes for a citizen soldier. The Spartan fought for his companions in the mess, the Goths for a chieftain preeminent for his leadership and courage, the private in the Army of the Potomac for the union, the Roman legionary for the senate and people of Rome, and the German private in the Imperial Army for kaiser and fatherland. They fought alongside comrades and for a country or a cause that will stand and fall upon the outcome of their arms. If they become estranged from their leaders, if they consider themselves inhabitants only and not citizens, that courage will vanish.

Cuneiform Tablets, Betamax, and the Permanence of Knowledge

Letters are messy, sloppy things. They are imprecise by their very nature. The letter  R is simply a segment of a continuum of rhotic sounds that could be subdivided into two letters, or a dozen, or rather be lumped in with something nearby like the letter L. Not only are letters arbitrary in their first designation but they alter in every situation. Lenition, fortition, epenthesis, elision, Cheshirization, assimilation, and dissimilation will all change the letter spoken or written on the page based on the letters that come before or after. Numbers are clean and pure. The number two may have two integers next to it, one and three. If we include real numbers, 2.0000001 will be very close and 2.00000000000001 closer still, yet two is still entirely discrete and unpolluted.  It remains unaffected by what comes before and after. Perfect and unchangeable, numbers are not written in the book of nature; they are the book of nature. They stand above the ebb and flow of slang and borrowing, the tides of conquest and influence. Languages are born and go extinct and it is often impossible to tell when one takes up and one leaves off. At what point did Latin become Italian? Numbers have not just permanence but universality to recommend them. The symbol 2 may be spoken in hundreds of different tongues but means the same in all of them.

The attempts to base language on a perfect mapping of reality, to make language correspond to number have failed thus far. If language cannot be made perfect it might yet be made permanent by tethering it to number. If every possible sound producible by the human throat could be assigned on and only one real number, then language may inherit the eternity that pertains to number. Hitherto, all human knowledge has been borne by some corporeal vehicle. What we have learned has been traced on vellum or papyrus, scratched in clay, painted on walls, or retained in our own brains. When that vehicle is destroyed or disintegrates, that knowledge is lost forever. We look back and lament the burning of the Alexandrian Library, the immolations of Shih Huang-Ti, as well as those of Archbishops Zumarraga and Ximenes, the despoliation of anonymous barbarians, the repurposing of the ignorant and the indifferent. If numbers themselves, eternal and imperishable, could anchor our knowledge, it will be made invulnerable to mold, flame, vandalism, vermin, and even death.

In our age, our knowledge is pooled, but not stored in one gigantic reservoir but channeled among a huge number of ponds. The collected volume of all these ponds together amounts to an ocean of information, and this ocean can be reached from anywhere. There is no spot so landlocked, isolated, or benighted that it can’t be turned into a beach. This seems like welcome news. Throughout our history, we have advanced as a species but that progress has often been interrupted and sometimes been pushed back. Yet after the night has come the dawn, the winter is broken by the spring, death and desolation are followed by rebirth, and always through the rediscovery of the knowledge and wisdom of the past. These secrets, once lost are found again. We are creatures of precedent. We rely upon the discoveries and techniques so painfully achieved by our ancestors. What worked then will work just as well now. We learn that things were once better than they are now, that there is a better way of doing things, and everything changes. Our technology is algorithm, and as algorithm it is reproducible as long as it is understood. If we make tools out of stone, we learn of a metal called bronze. If groaning under tyranny, we are acquainted with the republics of the ancient world. The cure for diseases, the best usages of agriculture, the constitutions of passable if not ideal governments, the edifice of mathematics and the discoveries of science founded upon them, will all be found in this ancient knowledge. There has never been a cataclysm so great that all our accumulated wisdom has been wiped out. Some copy has always been hidden or locked away somewhere. We are the heirs to the trials and errors, the failures and the triumphs of our ancestors.

None of the disasters of the past has destroyed that heritage. Yet it is possible for some catastrophe so widespread and overwhelming to befall us that every book, every text, every record, every picture and image is effaced and we are hurled back to the very beginning. We will not stumble across any signpost to lead us out of this longest and most terrible of our dark ages. The chances of this are small but they aren’t null. What is more likely, in fact probable, is another painful regression. We flatter ourselves that this could never happen, not to us. Would the inhabitants of the Roman World under the Antonines believe that their empire will be smashed, their capital ruined and depopulated, and their world carved up into tribal fiefdoms ravaged by barbarian incursions? Could the sages of the Tang Dynasty ever imagine Genghis Khan?


In each of these cases, a civilization succumbed to a period of violence, poverty, and ignorance that was only slowly and agonizingly banished, but our own knowledge is ubiquitous and ever present, and without ignorance, violence and poverty cannot hold sway. Our art and science are written on clouds, nebulous and indestructible. Our wisdom is reposed safely in binary code to be rendered back into shape, color, letter, or image whenever called upon. We are proof against the exigencies that plagued our more primitive and vulnerable predecessors.

Our knowledge is reposed in binary but not even ones and zeroes can be set in some Platonic firmament. They most have some embodiment. They must be written on something solid. Early computers used large floppy disks to hold information. These evolved into smaller hard plastic disk with a metal slide. These disks gave way to CD-ROM’s. More recently the flash drive has appeared. Each new vessel is a marked improvement on what has come before, but each renders its predecessor unreadable and useless. Information is recorded in strings of ones and zeroes but these must be organized by some rule, some syntax that governs how their output is to appear. The modes by which we store, retrieve, and display that information change, and they are whizzing by faster and faster with every generation. The Parmenidean cloud turns out to be a Heraclidean river that can never be drawn from twice to yield the same mouthful.

Throughout history, whatever was recorded could be read unless its vehicle was damaged or obliterated. Archaeologists dig through the deserts of Iraq and unearth cuneiform tablets from the city-states of Sumeria. These tablets have lain under the sands for thousands upon thousands of years but their wedge-shaped imprints are still quite visible and can still be read ages later. Buy a Betamax copy of Mad Max at a garage sale for a nickel, and you’ve struck a bad bargain because you’ll never be able to view it. Even if the tape it was recorded on was still pristine, the means of displaying it have vanished forever. These storage devices are prisons for the knowledge held within.

Kings of old used to lock away their enemies in oubliettes, cells in which they were held until death, forgotten ever after. The prisoners were transitory, soon crumbling to dust, while their stone cells remained to entomb the next occupant. We lock away our school projects, films, videos, photos, documents, and writings in these plastic oubliettes. Unlike granite and iron, these plastic and polyester components soon degrade. Even if they didn’t the treasures within would be lost forever. If the prison remained intact, the key to unlocking it vanished long ago.

We cannot stop this frantic rush, and perhaps there is no need. The internet is a flow of information, and like all global processes it is fluent, vast, and chaotic. And like all processes, it can be studied and recorded. We must attempt to take a snapshot of the entire internet at a given moment at certain intervals, to rescue its contents from the annihilation sure to ensure from its turbulence, to map and diagram what is jumbled and incoherent, and to document the evolution of the mightiest force of our age.

Lucius Cornelius Sulla and the Wages of Sin

In the year 79 AD. Lucius Cornelius Sulla retired from public life. He’d twice been elected consul of Rome and had been appointed dictator for an unlimited term. He’d marched his armies on Rome, won a civil war, and violated the sacred boundary of the city. His power supreme and unchallenged, he forcibly remade the constitution, and massacred his enemies. Every day he posted the lists of his proscriptions, those declared public enemies, whose deaths were to be rewarded with a large sum of money. After hundreds if not thousands had been killed, and his reforms had been accomplished to his satisfaction, he laid down his office and went back to his farm to write his memoirs.

It is not only Sulla’s public record that is remarkable but perhaps more so is this quiet and peaceful exit. Historians may explain, excuse, exonerate his actions at the remove of millennia, but the friends and relatives of those he’d killed must have burned with a simple and implacable hatred. A man who’d butchered his fellow citizens and given over Athens to sack and slaughter was permitted to withdraw from the fray and live in peace. Where were his enemies? Were there none left alive to take vengeance? He went unguarded. There was no troop of armed bodyguards about his person. He walked the streets unattended and yet perfectly safe. Was there no orphaned firebrand, no vengeful father, no bitter widow to strike down the tyrant? It is difficult to understand this immunity. Perhaps he was so feared that none dared strike at him, even when he seemed so helpless. Maybe he was just lucky. Good fortune had always attended his endeavors and he had always boasted of his proverbial and unbroken good luck.

Whatever the reason, Sulla lived on to die of natural causes. Yet leaders who were kind, benevolent men, later revered by their countrymen if misunderstood by their contemporaries, were struck down by assassins while the Roman dictator, a man only a biographer could love, escaped any retribution for his crimes. Abraham Lincoln had presided over a long and terrible war, and as commander in chief, he had sent the mighty armies of the Union against men who believed that they were fighting for their freedom. He had not sought this war, and had done everything he could to avoid it but in the end, he accepted the war rather than let the nation perish while his enemies made war rather than let it survive. He did not himself condemn men to death, and he is remembered for pardoning the guilty rather than proscribing the innocent yet his enemies believed him a tyrant and a butcher. One of these adversaries later assassinated him. Having won the war, he was struck down before he could make the peace. John Wilkes Booth left the South to the mercy of  those who would remake her in the swiftest and roughest way possible.

Henry of Navarre reigned over both Protestants and Catholics in an age when adherents of the two faiths had been slaughtering one another for decades. Himself a survivor of the Saint Bartholomew’s Day Massacre when thousands of Protestants were butchered, he granted freedom of faith to both sides and ended the Wars of Religion. With the aid of his brilliant finance minister, and the opportunity of peace, he brought forth an age of prosperity to France and laid the foundation for her future power. All of this naturally made him widely hated and many tried to assassinate him. Another incorrigible pardoner, he frequently spared men who’d just attempted to murder him. One of these men ultimately succeeded, and by killing Henry Francois Ravaillac put himself beyond the reach of his mercy. The assassin was executed in the gruesome manner reserved for traitors and regicides.

Mahatma Gandhi and Martin Luther King Jr. practitioners of nonviolent social protest, were likewise assassinated by men who weren’t constrained by the same scruples. The Kennedy brothers both came to violent ends before their time and with their work unfinished. Although the list is lamentable and all too long, not every wise and compassionate leader is murdered by a madman or fanatic, and not every tyrant survives to die in bed. Yet we are troubled that this happens at all. We want to believe in a cosmic justice, where the good are rewarded and the wicked punished. We hope that wisdom really leads to happiness. We pray that suffering may find its consolation.


Maybe none of this is true. Maybe the wicked live happily and die contented. If happiness consists in one’s achievements coinciding with one’s hopes, there is no reason to think the vilest among us don’t lead wonderful, fulfilling lives. Maybe the wicked aren’t afflicted with Dostoyevskian torments. Maybe the conscience atrophies from disuse. Maybe the voice of guilt grows fainter and fainter and fades away entirely. The man who murders his friend to seduce his wife, may marry her and go on to live in marital bliss with an unsuspecting partner. The clever embezzler may get away with his plundered riches, living in comfort and plenty while his victims pine in misery and poverty.

Some have said that virtue is its own reward, and sages from the beginning of history have extolled the blessings of virtue and given dire warnings of the penalties of vice. Yet none of them has offered virtue as sufficient to itself. There is always some attendant benefit to good and some inescapable sting to evil. The religious promise that this short vale of want and suffering will be followed by an eternity of bliss and plenty. The philosophic promise that wisdom brings contentment and joy while the vicious are torn and savaged by their basest passions. The idyllic allegories of Plato and the graphic descriptions of Dante hold out prizes and punishments, to be enjoyed or suffered in this world or the next. Is anyone strong enough to hold onto the good, come what may, with the same grim determination that Milton’s Satan embraced evil? Must wisdom, justice, and virtue always be coated in sugar for us to find them desirable?

Game theory teaches that tit for tat is an exemplary strategy. We are a social species and by nature work together. Those who abide by the rules, return benefits with gratitude, and prove trustworthy, are accepted and promoted while those who do not are despised, penalized, and cast out. The vicious and the criminal sometimes do escape punishment and reap the fruits of their misdeeds but not often. We must be made aware of this probability and reminded of it because sin can be all too tempting. Those who break the rules and caught, are themselves broken to serve as an example to the rest of us. Sulla was lucky and he was exceptional in his luck. Most lives of blood and violence end in blood and violence. Caesar was mobbed and borne down in front of the statue of Pompey. Macbeth met his doom in a man not born of woman. Gilles de Rais died on the gallows. Kindness, consideration, and moderation are not the only courses to a long and happy life but they are the most likely. This truth has served us in the past and must guide us through the future.