by David Orrell
Of course, the comparison of economics with physics should not be taken too far, and our aim here is by no means to further mathematicize the subject or produce a quantum mechanics of the economy—but at least if we are going to draw on physics, we should draw on the right kind of physics. The wave–particle duality of subatomic particles is mirrored in the mind–body, heads–tails duality of money objects, where it leads to confounding effects. Economists have traditionally handled money by assuming that market prices and value are the same thing, which is equivalent to collapsing the two aspects of money to a single point. Money objects therefore have no special properties, they just happen to be convenient for exchange. But as discussed further in chapter 7, this Newtonian, mechanistic approach fails in economics in much the same way that it breaks down in physics. Particles are not just self-contained billiard ball–like objects, and neither is money; both embody dual properties that need to be taken into account. In particular, our failure to recognize the charged, two-sided, dynamic nature of money contributed both to the 2008 financial crisis and the ensuing eurozone crisis by blinding us to the importance of debt.
As David Graeber describes in his book Debt: The First 5000 Years, the history of money involves an “alternation between periods of virtual and metal money.”38 For chartalists, or bullionists, these phases reflect our attitudes about money, as they oscillate between clarity and confusion (though the two camps disagree on which phase is which). But another way to see it is that this behavior of money is a direct reflection of its inherently dualistic nature, and in particular the unstable relationship between number and value. During a virtual phase, money is seen primarily as mathematical debt—a score in a ledger—while in a physical phase, money is seen primarily as material wealth. However, the two sides cannot be separated, so money always retains the essential characteristics of each. The process is like a monetary equivalent of geomagnetic reversal, in which the earth’s north and south poles spontaneously swap places, which happens on average about twice every million years: the world stays the same, but the directions change.
These reversals are written like strata in the historical record, and each layer shows money in a different aspect. As we have seen, early agrarian empires were dominated by virtual credit, where the value of a clay tablet lay in the inscription and not so much in the clay (although silver was there too, out of sight). So in our scheme, that era was primarily heads. The Axial Age (800 B.C.E.–600 C.E.) saw the widespread adoption of coinage made from precious metals, so we’ll call it tails. And we will see in the next chapter, the Middle Ages, which lasted for almost the next thousand years, saw a swing back toward negative, virtual credit (heads). The reason was not because gold and silver went out of fashion but because there was just not enough to go round.
3
Virtual Money
People are often reproached because their desires are directed mainly to money and they are fonder of it than of anything else. Yet it is natural and even inevitable for them to love that which, as an untiring Proteus, is ready at any moment to convert itself into the particular object of our fickle desires and manifold needs. … Money alone is the absolutely good thing because it meets not merely one need in concreto, but needs generally in abstracto.
ARTHUR SCHOPENHAUER, “THE WISDOM OF LIFE”
Credit alone is money. Credit and not gold or silver is the one property which all men seek, the acquisition of which is the aim and object of all commerce.
A. MITCHELL INNES, WHAT IS MONEY?
A basic question of economics is how to manage the money supply. Following the collapse of the Roman Empire, for example, gold and silver were suddenly in short supply. But money could still function as an accounting device—and an advantage of numbers is that they never run out. This chapter explores the dual role of money—as an abstract signifier of debt and as a valuable physical object in its own right—and shows how, with some help from mathematicians, the balance between these two aspects shifted in the Middle Ages. Our generation is not the first to struggle with the concept of a virtual currency.
Money, as discussed in chapter 2, represents both debt and wealth at the same time. Debts are represented mathematically by negative numbers, and wealth by positive numbers. A modern banknote, for example, is created by monetizing government debt, and so is like an IOU to someone else from the state (perhaps they should carry minus signs). At the same time, while the paper itself is of no value, the note is still an object that can be physically possessed and is valuable because it can be traded for other things. Having it is a definite plus. The same is true of other types of money. In the Axial Age, though, this dual nature of money would have been less obvious, for two reasons. The first was that coins were made of precious metals that you dug out of the ground, so they obviously represented wealth (though the fact that the state handed them out, then demanded them back as tax, hinted that debt was involved as well). The second was that negative numbers hadn’t been invented. Both of these factors changed in the Middle Ages, when money rediscovered its virtual roots.
The collapse of the Roman Empire put an end to the forced mining of silver and gold that had kept the army in coin and to trade routes between East and West. Cities shrank in size—the population of Rome fell from a peak of about 1 million in the second century C.E. to only about 30,000 by 550—and the markets they had nourished followed suit.1 At the same time, the religions of Christianity and Islam rose in power and influence. The precious metals that had earlier been used to pay soldiers now ended up in churches, monasteries, or other religious establishments, where they were hoarded, often after being melted down, or transformed into sacred symbols. The economy also came under increasing regulation from religious authorities. A similar pattern unfolded even earlier in India and China.2
One result of this transformation was that money became increasingly virtual—an abstract means of account rather than a piece of metal you can weigh in your hand. Money was mostly used as way to keep score, and loans were often in the form, not of a temporary transfer of physical material, but of a mark on a ledger. The leader in this process was the Islamic world, centered again on Mesopotamia. As today, Islamic finance forbade usury but allowed a range of fees, so moneylenders could still make money. Markets there flourished, but rather than being based on cash transactions, they relied on credit instruments, including the promissory notes known as sakk, or “checks.” Since transactions were backed only by a signature, rather than a government-endorsed currency, a person’s reputation—his credibility—was as important in business as his wealth.
As in ancient Greece, these financial developments both influenced and were themselves driven by advances in mathematics, the most important of which was the invention of negative numbers. When the Pythagoreans thought of numbers, they would demonstrate their ideas by arranging pebbles into different shapes. For example, the numbers 4, 9, and 16 were called “square numbers” because they could be formed into squares with sides of 2, 3, and 4 pebbles, respectively. Since there were no negative pebbles, there were no negative numbers; and for centuries afterward, negative numbers were thought to be absurd—even when they popped up as answers to equations.
The rules concerning how to deal with negative numbers, and the number 0, appeared for the first time in a book called The Opening of the Universe (628), by the Indian mathematician Brahmagupta. For example, a problem that had stumped the Greeks was equivalent to the equation 4x + 20 = 4, which has the answer x = −4. Brahmagupta thought about such seemingly nonsensical answers by putting them in monetary terms. Positive numbers he called “fortunes,” and negative numbers were “debts.” He was also the first to write about the number 0, the unique number whose negative is itself.
These concepts spread to the Islamic world through translations of Brahmagupta’s work but continued to be resisted by most European mathematicians. One of the first to accept them, along with the idea of arabic numerals (which actually originated in India), was the It
alian mathematician Leonardo Fibonacci. He is best known today for the Fibonacci sequence, which is used to describe everything from the arrangement of sunflower petals, to (less reliably) patterns in the stockmarket.3
Fibonacci, the son of an Italian merchant, grew up in Bugia (now in Algeria), where he was first exposed to the Arabic number system. Until then European mathematicians had labored under the Roman system, which made calculations such as division or multiplication almost impossible for anyone without a large amount of training. In his book Liber abaci (Book of Calculation, 1202), Fibonacci popularized the Arabic system by showing how much it aided not only mathematicians but also business people in their computations.4 Many of the examples involved activities such as money-changing, the calculation of interest, bookkeeping, and so on. For centuries, the Arabic system was viewed as less prestigious than the Roman system, and universities continued to teach the latter until the late seventeenth century. Even today, dates on important buildings are often expressed in roman numerals.
Progress of this type in the field of accounting reached a climax with the development of double-entry bookkeeping. This was codified by the mathematician, Franciscan friar, collaborator with Leonardo da Vinci, and part-time magician Luca Pacioli, in his book Summa de arithmetica (1494), but by that time it had already been in use for over a century.5 The technique got its name from the fact that every transaction was entered in two different accounts, once as a debit and once as a credit. Thus an asset in one account appeared as a liability in another. The method helped detect errors, since the sum of credits over all accounts should be balanced by the sum of debits, as positives are balanced by negatives. It also gave a quick snapshot of profitability, with enduring consequences for our view of the world. As Mr. Micawber said in Charles Dickens’s novel David Copperfield (1849): “Annual income £20, annual expenditure £19.19.6, result happiness. Annual income £20, annual expenditure £20.0.6, result misery.”
Keeping Tally
During the early Middle Ages, Christian Europe was organized in the static and rigidly hierarchical system now known as feudalism. Under this system, what counted was not money, but land and power, and the ultimate source of both was God’s representative on Earth—that is, the Crown.6 The king granted land to his lords, who in turn granted plots to their vassals in exchange for loyalty, military service, work on the estate, and a portion of the land’s agricultural yield. Large areas were reserved as collectively managed commons and were used for purposes such as animal grazing and collecting firewood. The most powerful landlord was the Church, which also dominated most of the thinking about money and economics. Usury was strictly forbidden (although loopholes existed), and the pursuit of wealth for its own sake was considered a capital sin. These restrictions put a further damper on the widespread use of coins. Feudal estates were therefore relatively closed and self-contained communities in which money played little role, apart from as an accounting device, and rents and taxes were usually paid in kind or through labor rather than in cash.7 Society was bound together by a connection to the land, rather than to money.
Medieval coinage was on the whole a motley collection (box 3.1): each king and lord wanted to produce his own version, so that he could collect the “seigniorage” (from the Old French seigneur [lord]), which is the difference between the face worth of the coin and its cost of production—that is, between the coin’s numerical worth (heads) and its bodily value (tails). Unlike in Roman times, there was no central authority, with some jurisdictions covering only a city and its surrounds (an exception was England, where the king maintained a monopoly). The tendency for money to spread and unify was therefore frustrated, and its lines of force were scattered and weak.
Box 3.1
Sun and Moon
In Europe during the Middle Ages, low-value coins, known as black money and usually made of copper, served for small transactions. A more valuable but still common coin was the silver denier, denoted “d,” whose name was derived from the Roman denarius. Twelve deniers made up 1 sou, and 20 sous made up a livre. The sou and livre were units of account—no actual coins were minted—with the livre (lira in Italy) nominally equal in value to 1 pound of silver. In fact, inflation meant that the unit of account was worth much less. The livre system was originally set up by the emperor Charlemagne during his reign from 800 to 814, and deniers were minted in France and Italy through the Middle Ages. The system was later emulated by a number of European currencies. For example, the British version of the denier was the penny, denoted in the same way by the symbol “d.” Twelve pennies made up 1 shilling, and 20 shillings made up 1 pound sterling. This system remained in place until decimalization in 1971.
For larger transactions—such as international trade, financing of wars, or military ransoms—silver ingots or gold coins such as the florin and ducat were preferred. The Florentine florin was first struck in 1252 and contained 3.5 grams of gold (about $150 at current gold prices), which equated to the value of 1 lira; the similarly sized Venetian ducat (duke’s coin) was introduced in 1284. At its peak, the mint in Florence was cranking out about 400,000 gold florins per year, with most of the gold being imported from Africa.* Both coins had a number of local versions, and ducats were still in use until the early twentieth century. The French version was the gold écu, minted during the reign of Louis IX (no relation to the European Currency Unit or ECU, which was used as a unit of account before the adoption of the euro). To protect against clipping, gold coins often circulated in leather pouches that were sealed by the mint. This again raised the question of whether the value was in the gold, which you couldn’t verify without breaking the seal, or in the seal itself.
The relative worth of gold and silver coins needed to be kept in balance to reflect the prices of the two metals, but in Europe at least remained fairly constant at a price ratio of about thirteen, as it had since ancient times. The reason is probably that gold has long been associated with the sun and silver with the moon—as Geoffrey Chaucer wrote, “Sol gold is and Luna silver we threpe”—and thirteen corresponds to the number of lunar periods in a solar year. The number also corresponds roughly to the relative abundance of the two metals in the earth’s crust. However, the price ratio varied with location—in Asia, for example, silver tended to be valued more highly than gold—which created profitable arbitrage opportunities and helped to power East–West trade.†
*Jacques Le Goff, Money and the Middle Ages (Oxford: Polity, 2012), 86.
†Andrew Watson, “Back to Gold—and Silver.” Economic History Review, 2d ser., 20 (1967): 1–34; Joel Mokyr, The Oxford Encyclopedia of Economic History, vol. 2 (Oxford: Oxford University Press, 2003).
Around 1100 in England, King Henry I introduced a payment system that was based on wooden sticks, about ten inches long, known as tallies. The sticks, which were made of polished hazel or willow wood, were carefully notched to indicate their worth and split lengthwise; the creditor kept one half, which was known as the stock (from which “stock market”), and the debtor the other part, called the stub. As described in the twelfth-century treatise The Dialogue Concerning the Exchequer, the manner of cutting was as follows: “At the top they put 1000 pounds, in such way that its notch has the thickness of the palm; 100 pounds, of the thumb; 20 pounds, of the ear; the notch of one pound, about of a swelling grain of barley; but that of a shilling, less; in such wise, nevertheless, that, a space being cleared out by cutting, a moderate furrow shall be made there; the penny is marked by the incision being made, but no wood being cut away.”8 When the debt was retired, the stock would be matched with the stub to verify the amount and protect against tampering, and the tally would be destroyed. The system was therefore similar to ancient cuneiforms, except there the security was supplied by the clay envelope.
Such tallies, as historian Michael Clanchy notes, were “a sophisticated and practical record of numbers. They were more convenient to keep and store than parchments, less complex to make, and no easier to forge.”9 They were
initially used as receipts for taxes but soon expanded into a general form of debt that circulated as money objects. For example, the state could use its half of a tally to pay a supplier, and that person could then collect from the debtor or use it to pay taxes or sell it at a discount to a goldsmith or another broker who would collect the debt when it came due. In China, most accounts during the Middle Ages were apparently handled by a similar technique, with the difference that the tallies were made of bamboo.10
The use of tallies in England peaked in the second half of the seventeenth century, by which time they had become a general tool for raising revenue (as receipts for a loan rather than just taxes) and remained in use until 1826.11 In the history of money, however, they seem destined to remain in the shadows; old sticks lack the glamour of precious coins, and they are also easily destroyed. In 1834, the remaining sticks were collected up and burned in a stove under the House of Lords. However, the money gods had the last laugh: the fire ran out of control, resulting in what is known to history as “The Great Fire of 1834.” The existing palace of Westminster was built on its ashes in the Victorian-Gothic style.
Borrowed Time
In the twelfth and thirteenth centuries, Europe was unified not by a single currency but by the quest to capture Jerusalem from the Muslims. One of the compensations for Christian knights joining the Crusades was that it offered a way for them to plunder some of those hard-to-find coins. While these were a transportable form of wealth, they were also easy to steal, which posed a challenge given the long distances involved. Money also had to flow in the other direction to fund the Crusades, which for the states and organizations involved were a highly expensive enterprise. These security issues were addressed by the Knights Templar—a secretive, ascetic, warrior order of monks—who, stealing a leaf from their Islamic foes, set up what amounted to an early version of travelers checks. A departing pilgrim or warrior could deposit his valuables at one of its castles, pick up a letter of credit, and use it to withdraw funds from another branch along the route. Usury was officially forbidden by the Church; however, the Knights Templar managed to make money by other methods. For example, a lord could take a mortgage on one of his properties and sign the right for the rent on the property over to the Templars.
