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Fibonacci and Mises

May 25, 2006

Mises has emphasized the central role of calculation in a developed economic order. This is not an allegorical term but quite literal. He means adding, subtracting and otherwise calculating with numbers... Numbers that are money prices arising from private property.

But the theoretical relationship that Mises points out, the dependance of rational economic decision making on mathematical calculation, is not historically a one way street. In Rodney Stark's recent book The Victory of Reason: How Christianity Led to Freedom, Capitalism, and Western Success we see that the spread of math in Europe, at least what we think of as math now, was closely related to the rise of early Italian capitalism.

Leonardo of Pisa (c1170-1250), more famously known as Leonardo Fibonacci, is credited with a central role in the introduction of Hindu-Arabic numerals and the concept of zero to Europe through the 1202 publication of his book Liber Abaci (Book of the Abacus). The Italian merchants took little time to understand the practical importance of these new numerals:

[Liber Abaci] was seized upon eagerly all across northern Italy as it provided new, efficient techniques for multiplication and division, tasks that are extraordinarily complicated when using Roman numerals - even addition and subtraction were daunting chores for Romans. Perhaps indicative of his true genius, Fibonacci did not simply present arithmetic in abstract form but carefully made it accessible and relevant by applying basic arithmetic techniques to primary business concerns, such as computing profit margins and interest, converting weights and measures, dividing profits or costs among partners, and the like.

Abacus schools spread rapidly across northern Italy, and soon nearly half of all boys enrolled in them after completing grammar school. By the 1340s there were at least six abacus schools in Florence alone, and similar schools flourished in all of the major Italian capitalist centers. Keep in mind that these schools were not training mere clerks and bookkeepers. Their graduates dominated the ranks of senior executives... Companies placed such value on abacus school training that they not only sought their graduates but often sent new employees to be trained in such a school. (108-9)

Many of the earliest archeological examples of writing we have are related to tax records. But in a wonderful twist, the introduction of modern numerals into Europe seems to have been driven by free markets!

One final quote from Stark's discussion... On the almost unbelievable success of this early training in the use of the new numerals:

As for the effectiveness of instruction, the great economic historian Armando Sapori took the trouble to check all of the computations made in the surviving ledgers of many medieval bookkeepers and found not a single error. Moreover, unlike their modern counterparts, medieval bookkeepers "avoided rounding off figures even in transactions bearing on thousands and hundreds of thousands of pounds." For example, the Bardi company of Florence once reported an immense current balance as totaling 1,266,775 pounds and 11 shillings.

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