Capitalism and the Zero

Numerous Financial Innovations Flowed Directly from the Discovery of Zero


John Hood is president of the John Locke Foundation, a state policy think tank in North Carolina, and author of The Heroic Enterprise: Business and the Common Good (Free Press).

In traditional discussions of the rise of free-market capitalism, great attention is paid to changes in institutions, technologies, and ideologies. We read the great philosophers and classical economists. We study the legal and political systems of England and Holland, which limited the power of government and promoted trade and economic freedom. We trace the history of kings and statesmen. But serious students of this fortunate event in human history should examine another factor with a far more ancient pedigree: the discovery of the number zero.

Our story begins in the cradle of human civilization, Mesopotamia. Historians are learning more and more about the inhabitants of this land (modern-day Iraq). Civilization began in the region not only because of farming opportunities that the Tigris and Euphrates rivers created, but because the Sumerians, Babylonians, and Akkadians were an industrious and inventive lot. They came up with a variety of agricultural, military, and cultural innovations. New archaeological discoveries suggest that their success was also due to the growth of trade and commerce, which were in many cases surprisingly sophisticated.

Primitive people had, of course, engaged in trade far back into prehistory. But merchants in Mesopotamian towns such as Uruk and Urappear to have pioneered such crucial tools as business partnerships and interest-bearing loans in the centuries before 2000 B.C. The lending of breeding stock was most likely the origin of the latter innovation. Indeed, the intimate connection between lending and livestock is easily seen in language. The ancient Sumerian word mash, which archaeologists identify as “interest,” was also the word for “calf.” The ancient Greek word for “interest,” tokos, had the original meaning “calf” too. The Latin root of the modern “pecuniary” is pecus, meaning “flock.” And the ancient Egyptian word for “interest” doubled as “to give birth.” Perhaps the rate of interest in early contracts referred to the number of calves or lambs owed the owner of a stud. Later the concept of rate of return in breeding contracts came to be applied to other business arrangements.

Certainly by the time of Hammurabi’s reign in Babylonia, in the 1700s B.C., lending must have been commonplace. Historians know this because surviving tables chronicle government regulations on the interest rate; a cap of 20 percent was frequently specified but just as frequently evaded by manipulating loan length and terms. Other records dating to the same period from Ur, the Biblical Abraham’s hometown, reveal the existence of a financial district, a sort of ancient Wall Street, where lenders congregated to make deals, compete, and finance long-range trade. These early financiers apparently experimented not only with lending at interest but also with business forms distinct from the traditional family proprietorship.[1]

One tablet tells the story of Ea-Nasir, a merchant from Ur who assembled a group of 51 investors who provided either silver or trade goods, particularly baskets. Ea-Nasir conducted trade missions southward to Persian Gulf ports, where he traded for copper, precious stones, and spices. Ea-Nasir’s business appears to be a rudimentary form of the limited-liability partnership. Investors were liable only for the money or goods they contributed up front. Losses beyond the capital investment were apparently swallowed by Ea-Nasir, as were the bulk of the profits to compensate him for this risk. In addition, the investors were compensated not strictly with interest but with a share of profits earned from Ea-Nasir’s trips south. In other words, they were equity investors—and not all large ones. Records show that ordinary citizens, investing a bracelet or two, could participate, anticipating the idea of mutual funds of small investors. “The effect of this business structure upon personal fortunes was profound,” writes Yale University historian William Goetzmann. “People were able to ‘insure’ themselves against personal failure—if their own venture collapsed, then the investment in Ea-Nasir’s might carry them through hard times.”

Still another tablet chronicles the use of interest rates to teach mathematics to young scholars, illustrating the close connection between business and numbers. The Babylonian system of counting was based on 60, rather than the decimal system we use today, and was expressed in a form of writing called cuneiform that is clumsy by today’s standards. Yet the system was sufficient to allow the Babylonians to chart the heavens, survey their property, conduct their businesses, and collect their taxes. It is likely that difficulties in charting the increasing amount of trade led the Babylonians around the third century B.C. to invent a “placeholder” number so they could calculate large quantities. But they didn’t actually come up with the concept of zero as a mathematical quantity. Nor did other ancient mathematicians.

For all its intriguing innovations, the Mesopotamian economic system lacked theconcept of economic independence that fully free markets require. Most of the lending, for example, was for “emergency needs” rather than profitable investment, and the emergencies almost always involved taxes or temple requisitions, which were really the same things. More generally, Mesopotamian society simply did not allow for much large-scale economic activity outside of government, which officially owned large segments of the arable land and lorded over tenant farmers in ways more despotic than Europe’s feudal barons ever dreamed.

Individualistic Greeks

The individualistic, landowning ancient Greeks, particularly in Athens, built on the Mesopotamians’ early commercial innovations. The Greek economy, more so than in the Near East, featured long-term investment in such products as olives and wine. Stable private property rights and the decentralized, participatory government they engendered fostered long-term investment and made possible true private-sector banking, albeit on a relatively small scale. Athenian lenders invested in overseas trade, providing maritime loans as well as opportunities for equity investment. Banks accepted deposits of money from natives as well as out-of-town merchants. One successful banker was Pasion, a former slave who lived in Athens in the fourth century. His masters were bankers, too, from whom he learned the trade. At his death, his was the largest bank of at least seven operating in the city.[2]

Still, it is difficult to separate ancient investment from government, since the same lenders financing international trade were also frequently government creditors, public officials, or a hated “tax farmer.” The latter, known in Jesus’s day as “publicans,” were contractors who bought the right to collect taxes in a particular neighborhood or town, then profited by charging a higher rate, loaning money to debt-strapped farmers without other means of paying taxes, and in many cases by hiring goons to confiscate property on the flimsiest of pretenses. The ravages of the tax farmers and the financial insiders associated with rapacious governments who profited from public works and the sale of military supplies, coupled with the envy that lenders and investors have always seemed to engender in their fellow countrymen, gave ancient financiers a bad name and paved the way for much government meddling.

In both Mesopotamia and Greece, governments periodically issued debt amnesties and tried to regulate interest rates. Prophets and philosophers railed against the wealthy bankers. Socrates called government debt relief the tool of the “demagogue,” but he wasn’t above comparing moneylenders to wasps and parasites. Rome typifies the blended nature of ancient finance. By early imperial days, Rome had developed a fairly sophisticated financial sector, complete with lending, banking, (quasi-) limited-liability enterprises, and the sale of “stock” in such enterprises among Roman nobles. Unfortunately, much of this financial activity revolved around lucrative tax-farming contracts in Asia Minor and other Eastern provinces.

Even those nascent forms of monetary investment might have evolved into something more closely approaching international capitalism if the empire itself had not grown in size and cost. As economist Lawrence Reed tells the story, swelling bureaucracies and armies led emperors to attempt ever more desperate ways of financing the government and paying debts. These included hiking existing tax rates, inventing new forms of taxation, inflating the money supply, and confiscation. Ultimately, the money economy itself was driven out of the West, not to return for several hundred years. When it did, ironically enough in Italy, one of the catalysts was the zero.

Medieval Business Innovations

The first glimmers of the re-emergence of large-scale private commerce can be seen in the eleventh century. It began with an innovation that makes few millennial history lists but, small as it may seem, set the stage for capitalism itself. Double-entry bookkeeping, developed by Italian merchants in the eleventh century based on concepts borrowed from Arabic traders, wasn’t the result of some esoteric pursuit of truth. It was a practical solution to a common problem—bookkeeping errors. Particularly before the widespread use of Arabic numerals, maintaining accurate records of any large-scale operation, business or not, was a major challenge. Imagine having to keep books with Roman numerals. Commerce existed, of course, but it was inherently limited. Nor was it possible for merchants of different cultures to find common ways of valuing their enterprises and developing long-term relationships.

Here’s where mathematics re-enters the picture. While the Babylonians (and, independently, the Mayans across the sea in present-day Central America) had come up with a “placeholder” zero, Indian scholars in the sixth or seventh centuries introduced the idea that zero represented “nothing.” It sounds banal, but it had revolutionary implications, particularly after the concept was introduced into the dynamic and adventuresome Islamic culture by famed mathematician Al-Khwarizmi in the ninth century. Al-Khwarizmi himself acknowledged that his interest in Indian numeration systems based on zero arose from the need for people to solve practical problems related to inheritances, wills, purchase and sales contracts, surveying, and tax collection. As what we now call Arabic numerals began to spread throughout the Islamic world in the ninth and tenth centuries, the traditional small-scale partnerships that characterized commerce early in Islamic history—a business form in which the Prophet Mohammed had himself participated—gave way to large-scale trading companies in which investors owned the equivalent of stock and around which a system of banking and credit evolved.

Unfortunately, Islam’s early trading institutions, though elaborate and the source of tremendous wealth, never developed into capitalism of a European sort. As was previously the case in ancient Mediterranean societies, Islam’s rulers were heavily involved in business enterprises, rarely paid their own debts, and imposed excessive costs in the form of taxes, regulations, wars, and outright confiscation. Neither Islamic law nor Islamic rulers recognized the independence of trading cities or the enterprises that populated them. And as historian Subhi Y. Labib has noted, other basic concepts such as commercial insurance “remained practically outside the scope of Islamic economic thought” during the period.[3]

Double-Entry Bookkeeping

But Arabic innovations, particularly in mathematics and bookkeeping, would find fertile ground across the sea by the eleventh century. As merchant families from Venice and other Italian trading cities began to resuscitate long-range trade in the Mediterranean after the interruptions of the Dark Ages, someone armed with the new Arabic numerals hit on a bright idea. To detect accounting errors in his business, he would enter all transactions twice, once as a debit and once as a credit. For example, the purchase of a new scale would require the entry of an asset (the value of the scale) and a liability (the cash withdrawal or debt incurred to purchase it). At the end of any recording period, typically a month, the merchant would total all debits and credits. If the two totals didn’t match, he would know to look for a flawed entry.

Double-entry bookkeeping became far more than an error-detection device, however. For the first time, it allowed managers to determine accurately the net worth of their businesses at any point. But more important, it created a conceptual doorway to what we now know as modern industrial capitalism. Here’s how. The only way for assets to equal liabilities is if the equity stake is itself considered a liability—an obligation to the owner. Double-entry bookkeeping, in other words, is based on the concept that a business is distinct and separate from its owner(s). In an eleventh-century world of family businesses, this was revolutionary, to say the least. Such separation was necessary for the future development of limited-liability partnerships and corporations, the building blocks of a modern capitalist economy. Economic historian Werner Sombart summed it up well: “One cannot imagine what capitalism would be without double-entry bookkeeping.”[4]

One further effect of this innovation was to make possible the creation of a system of international business finance far surpassing anything developed by the Mesopotamians, Greeks, Romans, or Muslims. After all, lenders in these societies had a major handicap. Outside their own circle of family and business acquaintances there were huge transaction costs in extending credit. Independent information about prospective borrowers was nearly impossible to derive. Double-entry bookkeeping gave lenders a common accounting language and a useful means of distinguishing the appearance of prosperity from the reality. The practice, write Nathan Rosenberg and L. E. Birdzell, Jr., “grew into an agreed-upon procedure for recording all economic events in a measurable and therefore calculable way. In a very real sense, economic reality became that which could be expressed in numerical terms in the books.”[5]

The Financial Revolution

Double-entry bookkeeping was followed closely by a succession of other innovations and institutions that formed the building blocks of capitalism. Armed with the ability to calculate business values accurately, merchants developed a body of commercial law to provide predictability in a world of petty tyrants, a patchwork of fiefdoms, and the ever-present threat of piracy. The ancient Greeks had pioneered the use of maritime loans to underwrite long-range trade, but by the twelfth century Italian merchants had invented more formal insurance contracts that guaranteed a trading mission against loss in return for a stated premium. Later, insurance markets in Italy, Amsterdam, and London differentiated maritime insurance, a risky product covering acts of piracy or God on the high seas, from more marketable commercial insurance, which covered the profitability of the subsequent sales. “The division between specialists in maritime risks and specialists in market risks greatly facilitated the growth of maritime trade,” Rosenberg and Birdzell write.[6]

Bills of exchange, in existence by the thirteenth century, permitted merchants to transfer the amounts they owed each other without having to exchange coin or goods directly. These early checks were themselves traded among far-flung traders, giving rise to a private system of paper money based on the credibility of the merchant families against whom the bills of exchange were drawn. Deposit banking was the next logical development, as lesser merchants deposited funds with prominent trading families whose drafts were credible money in faraway lands. The creditors found that they need not maintain the entire face value of their circulating notes and could use some of their deposits to buy other bills of exchange at discount—“that is, for lending money at interest despite the prohibition of usury.”[7]

Also in the thirteenth century, some governments began a tentative, but inexorable movement away from arbitrary taxation to a more predictable system for collecting revenue, controlled in England and later in Holland by the merchant class sitting in council rather than by kings or tax farmers. Kings put up with their diminution of the direct power to tax in exchange for a steady flow of revenue. One result in both England and Holland was that real capital assets such as vessels and trading stations could be owned and operated by private enterprises without fear of arbitrary seizure by sovereigns, a right that continental merchants—and, indeed, most of their counterparts in the Islamic world, India, and China—simply could not take for granted. This made large-scale private investment possible for the first time in markets previously the province only of governments or small-scale merchants.[8]

The final innovation needed to pave the way for the Mercantile and Industrial Revolutions of the latter half of the millennium was the development of truly private property rights and institutions. In England and other regionsof Western Europe, increasing population pressures in the thirteenth century led to robust competition for arable land and pastures, increasing enclosure of range land, and the evolution of laws governing alienation and transfers of land. States took over the administration of private property claims from feudal barons. At the same time, kings began to give exclusive franchises to private entities to operate certain economic enterprises or monopolize certain trade routes. While hardly free-market in nature, these franchises weren’t tax farms in the Roman or Muslim sense. They were honest-to-goodness trading enterprises that allowed private merchants to build up physical capital (ships and equipment) and human capital (skilled labor and knowledge of routes and markets) without as much fear of interference or confiscation of their ships or workers by governments.[9]

It is no exaggeration to say that these innovations, setting the stage for the birth of capitalism, followed directly from the discovery of zero and its introduction into European commerce. No king subsidized its invention, and no government program mandated its acceptance. Common folks, of many nationalities, had simply come up with a tool that helped them solve their problems. From such a lowly beginning, human freedom and progress took giant leaps forward.


  1. William N. Goetzmann, Financing Civilization, forthcoming.
  2. Richard Pipes, Property and Freedom (New York: Alfred A. Knopf, 1999), pp. 98-99.
  3. Subhi Y. Labib, “Capitalism in Medieval Islam,” The Journal of Economic History, March 1969, pp. 93-95.
  4. Quoted in Nathan Rosenberg and L. E. Birdzell, Jr., How the West Grew Rich: The Economic Transaction of the Industrial World (New York: Basic Books, 1986), p. 127.
  5. Ibid.
  6. Ibid., p. 118.
  7. Ibid., p. 117.
  8. Douglass C. North, Structure and Change in Economic History (New York: W. W. Norton & Co., 1981), p. 141.
  9. Ibid., p. 133.


December 2000

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