Capitalism and Arithmetic
Swetz, Frank J.
I f ever a people demonstrated how 1 adversity could be turned into opportunity, it was the Venetians. Instead of bemoaning their marshy collection of mudbanks and islets, the refugees driven there...
...For all their financial acumen, however, the merchants of Venice were at that time still working with pretty crude tools...
...The entrepreneur is constantly driven by competition to search for ways to expand his market by making things cheaper and cheaper, which is why items that were luxuries to our grandparents—cars, cameras, and computers—are everyday essentials today...
...It is required to find in how many days they will meet . . The answer, of course, is 3 15/16 days...
...for I assure you that these things which I have set forth are necessary to anyone who would be proficient in this area, and no one can get along with less...
...From the thirteenth century onward," writes Swetz, "thousands of students at the universities had a Latin exposure to the new arithmetic, but it was not until the acceleration of commercial activities and the advent of printing that this knowledge was disseminated to the 'common man.' " This, of course, is what Marx was getting at when he spoke of the "revolutionary role" of the bourgeoisie in turning feudal society upsidedown...
...Throughout the pages of Capitalism and Arithmetic, Swetz charts how the search for profit fed the demand for knowledge, which folded back on itself in an ongoing circle of activity that characterizes free economies even today...
...It is all done, moreover, in workmanlike prose with none of the pedantry usually found when masters condescend to write for the masses...
...Even if you weren't the kind of kid who liked to figure out what time the train traveling east from Chicago would intercept the train traveling west from New York, it's hard to suppress a smile upon reading how the same word problem was put to fifteenth century Italians: The Holy Father sent a courier from Rome to Venice, commanding him that he should reach Venice in 7 days...
...Today the innovations of the Venetians are taken for granted, and most of the problems in Capitalism and Arithmetic could be handled by a fifth-grader...
...Because the scholasticism of the universities did not venture out much beyond classical theory, merchants looked to the reckoning masters for the hands-on mathematics they needed...
...The Treviso Arithmetic was after all a textbook, and proposed to instruct students in five basic skills: counting, addition, subtraction, multiplication, and division...
...Much like Donald Landes in Revolution in Time, which showed how the invention of clocks not long before had made the modern concept of productivity possible (output per measurement of time), Capitalism and Arithmetic demonstrates the interplay between fifteenth century business and fifteenth century math and the dynamismthis unleashed on Western society...
...What merchants desperately needed then (and still need today, if floating exchange rates are any key) were set standards to help them measure, compare, and assign value to disparate goods...
...With mathematics essentially confined to the university, the need for practical calculation led to the rise of "reckoning masters" to teach the sons of middle-class merchants the applied arithmetic that was fast becoming essential to Renaissance business...
...Instead of bemoaning their marshy collection of mudbanks and islets, the refugees driven there by the Lombard invasions of northern Italy linked the disparate lumps into a first-class city connected by its now famous canals...
...Such is the logic of capitalism...
...Named for the small trading town just north of Venice where it originated, it is the earliest printed book of arithmetic...
...And from Rome to Venice is 250 miles...
...Above all, Swetz reveals himself in Capitalism and Arithmetic to be one of those rare mathematical minds whose own expertise does not get in the way of passing down some of the excitement and beauty of the subject to the layman...
...In Capitalism and Arithmetic, Frank J. Swetz charts the consequent move of mathematics "from the realm of schoWilliam McGurn is deputy editorial page editor of the Asian Wall Street JournaL lastic speculation to the application of the marketplace...
...It was one of these masters who in 1478 wrote the book around which Swetz builds his own study: the Treviso Arithmetic...
...That work is nothing if not straightforward...
...During their travels, merchants were also keen observers of foreign techniques, customs, and procedures that affected their trade prospects...
...Save for the language used to explain these operations ("to multiply one number by itself or by another is to find from two given numbers a third number which contains one of these numbers as many times as there are units in the other") the book thus holds little interest for theorists...
...48 THE AMERICAN SPECTATOR JANUARY 1989...
...The printing press had been invented only the century before, Columbus was about to discover the New World, and the internationalization of trade was forcing a quantum leap in business practices...
...By the time the fifteenth century rolled around, it was the trading capital of Europe...
...It is no mere coincidence that Fibonacci, one of the principal conveyors of a knowledge of the Hindu-Arabic numeral system to Europe, was also a merchant...
...The Polos were Venetian merchants seeking to advance their fortunes but, as a result of their adventures and travels, European society learned of foreign lands and strange people...
...Although Swetz concedes the Treviso Arithmetic is "neither elegant nor necessarily outstanding by the standards of the fifteenth century," it is nonetheless significant for what it reveals about the dramatic changes in society wrought by the rise of mercantile capitalism...
...The changes in math, he is ever reminding us, were not conceived in a vacuum...
...They were also able record-keepers and compiled detailed logs of personal impressions and empirical facts relevant to commerce...
...Swetz relays all this with the enthusiasm of an amateur but the expert's eye for that telling anecdote...
...Swetz talks too of how the Venetian Republic would cut off the right hand of anyone found debasing the currency (coins were frequently chipped or sweated for the gold or silver in them), a salutary practice that if applied today would see most of the world's central bankers shaking hands lefty...
...LaSalle, IL)/$16.95 William McGurn THE AMERICAN SPECTATOR JANUARY 1989 47 the Treviso Arithmetic into English, the late Professor Smith...
...There's more to mathematics than theory," writes Swetz, "for theory by itself, without a mode of expression or articulation, remains impotent...
...Unlike the new math, moreover, it did not skirt the need for memorization: "We should not complain . . . at having to learn these things by heart in order to acquire readiness...
...He explains, for example, how the word "bankruptcy" comes from the punishment meted out to a moneylender of this time...
...Ironically Swetz, a math professor at Pennsylvania State University, is at his most persuasive when he is talking about capitalism...
...On top of this, trade with ever more exotic parts of the world was presenting new problems in the form of setting exchange rates, dealing with different units of weight and measurement, working out profit shares, not to mention finding enough capital to fund foreign ventures whose benefits would not be realized for months, perhaps even years...
...try dividing CLXVIII by XIV and you have some idea what this change alone meant...
...when found guilty of fraud he was publicly discredited by having his bench (banco) broken (ruptus...
...And the most illustrious Signoria of Venice also sent another courier to Rome, who should reach Rome in 9 days...
...There is finally a touching tribute to the man who first translated CAPITALISM AND ARITHMETIC: THE NEW MATH OF THE 15th CENTURY Frank J. Swetz/Open Court Publishing Co...
...They then turned their maritime skills outward, and it wasn't long before Venice became a power to be reckoned with...
...It happened by order of these lords the couriers started their journey at the same time...
...So much do we take the existing system as natural (and indigenous) that we forget, for example, that the Hindu-Arabic numerals now in use were imported and did not gain widespread acceptance until the fourteenth century...
...Like the revolution that brought computers into the home, the social consequences of that fifteenth century commercial ferment was a democratization of knowledge that hitherto had been confined to a relatively small elite...
...More than anything else, says Swetz, foreign trade was the catalyst that set off the whole shebang: The driving force that brought Marco Polo, and his father and uncle before him, to the court of Kublai Khan was a search for profit...
...This is, in short, the voice of a teacher...
...Included in the book is a complete translation of the Treviso Arithmetic made by David Eugene Smith at the turn of the century...
...Wading through the same pages today, one readily imagines the frustration of a student grappling with these seemingly meaningless tables, followed by the kindling of interest as the master began to show how to apply this knowledge to divide profits, figure out foreign exchange, barter wool for silver without the medium of money, and so forth...
...It is the same with knowledge...
Vol. 22 • January 1989 • No. 1
