For long before Thomas Jefferson became a Founding Father of the United States, the future president’s ambition was to be something else entirely: a mathematician. “When I was young mathematics was the passion of my life,” Jefferson wrote to his friend, the lawyer and politician William Duane, when he was approaching his 70th year and musing on a road not taken. “It was ever my favorite” study, he recalled in an 1811 letter to Benjamin Rush: “We have no theories there, no uncertainties remain in the mind; all is demonstration and satisfaction.” Jefferson never abandoned his youthful fascination with mathematics but returned to it again and again. 

In June 1783, shortly after the end of the Revolutionary War, Jefferson was elected to the Continental Congress as a member of the Virginia delegation, and he immediately plunged himself into the most mathematically challenging issues confronting the young republic. The first to come his way, and the one that had the greatest urgency for daily life, was establishing a currency for the Union. Under British rule, the official coin of the colonies was the English pound, divided into twenty shillings, each of which was worth twelve pennies. This, however, was largely a fiction, as the colonies were flooded by a vast array of European coins whose exchange rates were murky at best: half joes, doubloons, pistoles, pistareens, and rix-dollars all circulated alongside the English pound. A longtime favorite was the Dutch dog dollar, named after the canine appearance of its lion emblem, but by the 1780s the most popular coin circulating on the Atlantic Seaboard was the Spanish dollar, also known as a “piece of eight” for its standard division into reales. But the value of even this shared currency fluctuated wildly among the states, ranging from five shillings in Georgia to thirty-two and a half shillings across the border in South Carolina. To manage daily life in this chaotic state of affairs required of each citizen an uncommon level of financial wizardry and inevitably opened the way to endemic suspicions of fraud, whether real or imagined. 

By the time Jefferson got involved in devising a new currency, Congress’ superintendent of finance, Robert Morris, and his assistant, the unrelated Gouverneur Morris, had already come up with a plan. In the Morrises’ proposal, the basic currency unit was tiny — a mere 1/1140 of a Spanish dollar. The advantage of such a tiny base, they argued, was that it would be possible to convert it to each and every one of the different coins then in use. A fixed number of these units would equal every coin in circulation, making it easy for merchants to convert their old account books to the new currency.

Jefferson, however, liked neither the plan nor its authors. Robert Morris was the leading financial speculator in the colonies before the revolution and in the United States after it. A signer of the Declaration of Independence, he had put his capital and his financial talents in the service of the shared struggle, earning him the sobriquet of “financier of the revolution” and the gratitude of George Washington. Winning over Jefferson, who disliked cities and despised financiers, was a different matter. In Robert Morris he recognized the leader of what he called “that Speculating phalanx,” which was out to exploit the people and the Union for their own financial gain and destroy his dream of a virtuous agrarian America.His assistant was little better. Born to an old and respected family, young Gouverneur was a notorious rake and bon vivant of the bustling city of New York. Though not as rich as the older Morris, he was clearly on his way to joining him among the American speculating elite. 

As for the plan itself, Jefferson considered the basic unit far too small and entirely arbitrary. True, it would facilitate to some extent the bookkeeping practices of merchants, who dealt with many different circulating coins and would like a simple way to convert them to a standard American currency. At the same time, such a tiny unit would make the daily transactions of pretty much everybody else unreasonably cumbersome. Every simple purchase of a sack of flour or a farm animal would involve complex calculations with five, six, or seven figures, which would not only waste time but also hugely increase the chance of error and the opportunity for fraud. Jefferson, who considered merchants and financiers a scourge, cared nothing for their convenience. But he cared farmers, whom he considered the guardians of republican virtue. To him, a currency system that accommodated wealthy merchants at the expense of common farmers had its priorities inverted and should be rejected outright. On top of this, Jefferson had good reason to suspect that Morris was angling to run the U.S. mint that would produce his new coins, thereby taking control of the nation’s money supply. Handing such a vital national resource to the republic’s wealthiest financier was to Jefferson a nightmarish proposition that must never be allowed to pass.

To prevent such a calamity, Jefferson in early 1784 presented Congress with his own currency plan. Instead of inventing a new unit, as the Morrises had done, he proposed relying on the most familiar coin then in use, the Spanish dollar, which would henceforth be called the U.S. dollar. And while this seemed to be a move to preserve the status quo, Jefferson’s innovation lay in the way he proposed to divide new currency. Like practically all coins of the era, the Spanish dollar was commonly divided into halves, which were in turn halved, halved, and halved again, leading to half-dollars, quarter-dollars, eighth-dollars (or “reales”), and so on. Jefferson, however, proposed to divide the U.S. dollar into tenths, hundredths, and thousandths, arguing that such divisions are mathematically simpler and would lead to fewer mistakes. This seems self-evident to us today but was far less so to eighteenth-century Americans who since childhood had been used to repeated divisions by two. Nevertheless, Jefferson’s proposal carried the day, perhaps more because of concern about the Morrises’ intentions than because of the persuasiveness of the Virginian’s argument. On July 6, 1785, Congress decreed that “the money unit of the United States of America shall be one dollar” and that “the several pieces shall increase in decimal ratio.”  It would be several more years and numerous congressional committees and recommendations before a mint was established and the first U.S. dollar went into circulation, but the resolution of 1785 proved decisive. Thanks to Jefferson, the U.S. dollar became the first decimal currency in the world, serving as a model for all modern currencies. And thanks to the enduring power of old habits, the Spanish dollar nevertheless had its subtle revenge: the U.S. dollar is among the very few currencies in the world whose most common division, to this day, is into quarters. 

The second issue to which Jefferson devoted his mathematical talents in the 1780s — and which would continue to occupy him for another decade — was the reform of weights and measures, which were in as chaotic a state as the currency at the time. To us, the two issues are entirely unrelated: weights and measures refer to actual physical objects and territories in the world, whereas the value of a coin is an arbitrary convention, which people agree upon for their convenience. This seems so natural that we sometimes forget just how novel and recent this notion of currency is. Because in fact, from the earliest uses of coinage in the ancient Mediterranean right up until the United States fully abandoned the gold standard in 1971, the value of a currency was ultimately dependent on the weight of precious metals. For Jefferson, as for his contemporaries, setting a clear value and standard divisions for coinage was inseparable from doing precisely the same for units of weight, as well as the related ones of length, area, and volume. 

Ever the Enlightenment universalist, Jefferson was determined to establish his units of measurement on the natural structure of the Earth. This was not an entirely novel idea. Back in 1671, in his book Mesure de la Terre, the French astronomer and cartographer Jean Piccard  suggested basing a system of measurements on the circumference of the Earth. Piccard had used triangulation to measure the length of a degree of latitude with unprecedented accuracy. By multiplying his result by 360, he arrived at a figure for the circumference of the Earth that is less than half a percent smaller than the true figure. His results were later improved upon by four successive generations of astronomers named Cassini, all of whom served the French kings as directors of the Paris Observatory, as well as by measurements made on expeditions to Lapland and South America in the 1730s, sponsored by the Paris Academy of Sciences. On the basis of their accumulated results, Jefferson calculated that the length of one minute (i.e., one-sixtieth of a degree of latitude) is 6,086.4 feet, a unit that he referred to as the “geographical mile” and, more optimistically, the “American mile.” He then proposed to redefine traditional measures as decimal fractions of the new unit: A “furlong” would be 608.64 feet, a “chain” 60.864 feet, and a “pace” 6.0864 feet.

This was as far as things went in 1784, though Jefferson never abandoned his hopes of reforming American measures and setting them as a rational example to the world. During the five years he spent in Paris, from 1784 to 1789, he consorted with French scientists who were working on their own reform of weights and measures, and in particular with his friend the Marquis de Condorcet, permanent secretary of the Paris Academy. The Earth, the French savants argued, was not a true sphere but a very imperfect one, beset by irregular bulges and depressions. This means not only that the precise circumference is extremely difficult to measure but also that it is very difficult to define: it varies considerably depending on which great circle is measured. Consequently, the dimension of the Earth is not a reliable basis for a universal system of measurement. 

Condorcet had a better idea: instead of using a fraction of the circumference of the Earth as a basic unit of measurement, he proposed using the length of the “second’s pendulum” — the length of a pendulum that completes a full cycle every second. The standard is based on Galileo’s observation that a pendulum’s period of oscillation is dependent on its length alone. Newton had proved it and calculated that the length of a pendulum that completes a cycle in exactly one second is 39.2 inches. Jefferson was immediately converted: since the length of the pendulum could be measured directly anywhere in the world, this seemed to Jefferson an ideal basis for a natural and universal system of measurements. 

In 1790, back from France and serving as Secretary of State, Jefferson believed the time for reform had finally come. On July 13, he submitted to Congress a detailed “Plan for Establishing Uniformity in the Coinage, Weights, and Measures of the United States,” which was based on the length of a second’s pendulum at a latitude of forty-five degrees (thereby slightly shorter than Newton’s number for London’s latitude of fifty-one degrees). Since a perfect pendulum—in which the string is weightless and all weight is concentrated at a single point—is impossible to produce, Jefferson replaced it with a pendulum made of a uniform swinging rod of 58.8 inches. One-fifth of this, or slightly less than 12 traditional inches, he called a “foot,” which served as the basic unit of his system. One cubic foot would be designated the new “bushel,” the basic unit of volume, and a bushel of water would weigh a thousand new “ounces.” And the weight of the dollar was to be adjusted so that it came to be exactly one ounce of silver.

Jefferson’s proposal of 1790 was a perfect Enlightenment reform plan. Derived from nature itself, it was based not on human tradition but on the deep order of the universe. It was rational and systematic, replacing all the arbitrary, variable, and confusing units then in use with a single universally applicable system. It was comprehensive, tying together measures of length, volume, weight, and coinage in a single interconnected rational system, and it was decimal, making it easy to convert the various units into one another. Such a simple and rational system would wrench the units of measurement from the hands of the aristocratic elites, who had used them to exploit their underlings, and make them accessible to common people everywhere. In its ambition it captured Jefferson’s desire to start anew, demolish an old world built on irrational tradition and superstition, and replace it with one founded on the clear light of reason. 

If Jefferson’s proposal had passed in Congress, then the United States today would likely be known as the birthplace of the metric system rather than as one of the last (and by far the most significant) nonmetric holdouts. But Jefferson held back: reports from revolutionary Paris indicated that Jefferson’s old friends, including Condorcet, Lagrange, and the chemist Antoine Lavoisier had been appointed to a committee for the reform of weights and measures. Confident that the recommendations of the committee would closely parallel his own,  Jefferson asked Congress not to vote on his proposal but to wait to hear the details of the French report. Much better, he reasoned, to tweak his system to correspond with the Parisian one than to end up with two competing systems, each claiming to be “universal.” 

But when the committee’s report finally arrived in America, Jefferson was stunned. His French friends, who a few years before had convinced him to abandon the circumference of the Earth as the basis of measurement in favor of the second’s pendulum, had inexplicably reversed course. In their report, published on March 19, 1791, they discuss the advantages of the second’s pendulum at considerable length, praising its certainty and accuracy. Then, with little warning, they add: “However we ought to observe that the unit thus derived contains something arbitrary”—the second itself. A second, they explain, is the 86,400th part of the length of a day, which is an arbitrary division and therefore not sufficiently “natural.” The fact that any unit of measurement based on the meridian would require an equally arbitrary division of a natural magnitude—the circumference of the Earth— troubled them far less for some reason. And so they abandoned the pendulum and instead set about once again to determine the precise length of a meridian, dispatching astronomers Pierre Méchain and Jean-Baptiste Delambre to triangulate the meridian between Dunkirk and Barcelona.

The French savants’ sudden abandonment of the pendulum standard pulled the rug from under Jefferson’s proposal. The supposedly universal proposal that would set the standard for the entire world turned out to be nothing of the sort. It now appeared to be just an overly ambitious reform effort that would disrupt the work and the daily habits of all Americans and wreak havoc on commercial transactions, all to no obvious gain. And so, much to his chagrin, Jefferson’s reform of weights and measures was never adopted by Congress, leaving the country with a dizzying array of incompatible units for years to come. 

Adapted and excerpted from Liberty’s Grid: A Founding Father, a Mathematical Dreamland, and the Shaping of America by Amir Alexander, published by the University of Chicago Press. Copyright © 2024 by Amir R. Alexander. All rights reserved.

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