Science and America’s Founding
Newtonian physics inspires American confidence.
We in America are very fortunate to live in a country founded during the “Age of Reason,” a time, as Harvard’s History of Science professor I. Bernard Cohen has written in his book Science and the Founding Fathers, “when science was esteemed as the highest expression of human reason.”
George Washington recognized as much. As Cohen writes:
In a circular letter to the states, announcing his retirement as commander-in-chief of the army and declaring his return to private life, George Washington took note that the establishment of the new nation did not occur “in the gloomy age of Ignorance and Superstition,” but rather “at the Epocha when the rights of mankind were better understood and more clearly defined, than in any former period.” Washington attributed this change to the successful “researches of the human mind …”
Regarding the “Age of Superstition,” it’s worth noting that Benjamin Franklin’s invention of the lightning rod did much to dispel superstitions regarding that natural phenomenon. As Cohen writes, “It was an axiom of that time that the exercise of reason – expressed in its highest form in the sciences – should conquer superstition. Before Franklin, the lightning discharge was a source of terror. Many people believed the thunderbolt hurled from heaven as the action of an angry God against sinners down on Earth.” Indeed, the great Founding historian Clinton Rossiter believed “Newtonian science quickened the advance toward free government” because, as Cohen writes, one feature of the Age of Reason was “the conquering of superstition and ignorance and the parallel exaltation of the power of human reason.” Also going a long way to dispel superstitions was Isaac Newton’s Principia, and in particular his description of comets as “a sort of planet,” moving in elliptical orbits and, as Cohen writes, “returning periodically from the far reaches of outer space to the neighborhood of the Sun. Clearly, if comets move in determinate orbits, and if their appearance is a regular and therefore predictable event, a comet is not a providential sign and is not to be understood as a special warning or message from an angry God.”
Washington himself, while not a scientist, was a professional land surveyor in his youth, perhaps the most math-intensive common trade of the time: surveying involved the use of arithmetic, algebra, geometry and trigonometry.
The author of the Declaration of Independence, Thomas Jefferson, so appreciated the Age of Reason that, wherever he was, he placed three portraits in prominent places -- that of Isaac Newton, Francis Bacon, and John Locke. (Jefferson is also the only president to have read Newton’s Principia.)
While president, and steeped in politics, Jefferson reveled in escaping it. As Cohen writes:
When Jefferson wrote to Pierre-Samuel Dupont de Nemours that he had been intended for the pursuit of science, he was ending a public phase of his career, completing his second and final term as president of the United States. But for the “enormities of the times,” he added, he would never have given up a scientific career, he would never have embarked on the “boisterous ocean of political passions.” Now, at last, he was free and he felt like “a prisoner, released from his chains” … One of Jefferson’s close associates and friends, the painter and naturalist Charles Willson Peale, recorded an evening in the White House with the great naturalist and explorer Alexander von Humboldt. During “a very elegant dinner at the President’s,” he noted, “not a single toast was given or called for, or politics touched on.” Instead, the conversation was entirely on “subjects of natural history, and improvements of the conveniences of life.”
And Jefferson loved calculation. As we saw in a previous essay:
Thomas Jefferson, famous for his insistence on numerical data, “even drew on an argument based on numbers to analyze Shay’s Rebellion [an armed uprising protesting high taxes]. “The late rebellion in Massachusetts,” he wrote, “had given more alarm than I think it should have done.” He calculated that “one rebellion in 13 states in the course of 11 years” is not very great, being the same as “one for each state in a century and a half.”
Interestingly, the very first presidential veto was exercised by President George Washington based on the corrective calculations of Thomas Jefferson. Here’s how that story goes:
When the inaugural Congress first attempted to devise a system of apportionment [of seats for Members of the House of Representatives] in 1792 [based on the Census numbers from the very first Census] the proposed plan gave rise to such serious objections by Thomas Jefferson that it was vetoed by George Washington … [Jefferson’s] analysis of the proposed method of apportionment provided the grounds for Washington’s veto and determined the basis for the system that was finally adopted.
First off, the bill – the brainchild of Alexander Hamilton -- simply listed the number of House Members each state should get, without explaining the formula by which each number had been arrived at. As Cohen writes:
Since the apportionment bill did not specify the method that had been used, Jefferson had to apply his skill in computation and his experience in solving numerical problems in order to figure out just how the numbers contained in the bill had been obtained. By carefully analyzing the apportions assigned in the bill, he was able to decode the mathematical method, working backward from the results to disclose the procedural rules that had been used by the Congress, but never stated explicitly.
Jefferson correctly discerned Hamilton’s method, which worked in the following way. Imagine there were only five states (as Cohen does for simplicity of exposition), the total population of the U.S. was 26,000, and Congress set a total of 26 House Members. In that case, we get one House Member for every 1,000 people, so we’d divide the total population of each state by 1,000 and get the number of House Members for each state. But of course that method is very unlikely to end up with a round number for any state. By that method, some states would wind up with, say, 3.319 Members, or 5.295 Members, and you can’t have a fractional Member. So some states would have to get less than their theoretical allotment (by rounding down), and some states more (by rounding up). Hamilton’s method gave extra seats in Congress to the eight states that had the highest decimal remainders.
But Jefferson saw several constitutional problems with this. As Jefferson wrote in his opinion on the bill:
The … clause of the constitution above cited [regarding apportionment] is express that representatives shall be apportioned among the several states according to their respective numbers. That is to say, they shall be apportioned by some common ratio. For proportion, and ratio, are equivalent words; and it is the definition of proportion among numbers, that they have a ratio common to all, or in other words a common divisor. Now, trial will shew that there is no common ratio, or divisor, which, applied to the numbers of each state, will give to them the number of representatives allotted in this bill … [F]or representatives, there can be no such common ratio, or divisor, which, applied to the several numbers, will divide them exactly, without a remainder or fraction. -- … representatives [must be divided] as nearly as the nearest ratio will admit; and the fractions must be neglected: because the constitution wills absolutely that there be an apportionment, or common ratio; and if any fractions result from the operation, it has left them unprovided for.
Jefferson then found, through a mathematical calculation, that
we must take the nearest common divisor, as the ratio of distribution, that is to say, that divisor which, applied to every state, gives to them such numbers as, added together, come nearest to 120 [the total number of House Members provided for in the bill]. This nearest common ratio will be found to be 28,858. and will distribute 119 of the 120 members, leaving only a single residuary one.
Jefferson thought that a single residuary state is better than eight, and that single residuary state getting an extra House Members should be the most populous state, which was, at the time, Virginia.
To add insult to injury, Jefferson also discovered that “The first phrase of the above citation [to the Constitution], that ‘the number of representatives shall not exceed one for every 30,000’ is violated by this bill which has given to 8 states a number exceeding one for every 30,000. to wit, one for every 27,770.”
As Cohen notes, following the veto of Hamilton’s plan, “Jefferson’s alternative to Hamilton’s plan was then adopted by the Congress and was used to determine apportionment for many decades.” It should be heartening to geeks everywhere that the first presidential veto was the result of a mathematical debate.
Jefferson, by the way, also improved the design of a plow by using calculus to shape the moldboard, calculating the path of least resistance of the soil it would overturn. As Cohen writes:
This episode is more significant than may at first appear. One of the most important applications of the Newtonian calculus has always been in problems of a “minimax” kind, that is, finding curves or solids that fulfill some kind of maximum or minimum condition. One of the public challenges made to Isaac Newton during the controversy over the invention of the calculus was whether he could use his method of fluxions [the term Newton used for calculus] to find the curve of least decent, that is, the curve along which a frictionless bead will slide from a given starting point to a given terminus in a minimum time. Even today, students learning the calculus are given minimax problems to demonstrate the extraordinary power of the calculus.
The moldboard was a very significant improvement to the plow’s efficiency. As Vaclav Smil writes in Energy and Civilization: A History, “The addition of a moldboard was by far the most important improvement. A moldboard guides the plowed-up soil to one side, turns it (partially or totally) over, buries the cut weeds, and cleans the furrow bottom for the next turn.”
Now, none of the Founders, despite some historians’ musings to the contrary, came close to showing that any particular system of government, such as that provided for in the Constitution, is based on actual physical laws such as those described by Isaac Newton. Physicist J. Robert Oppenheimer considered the question himself, and concluded as follows:
Noting that the Principia embodied a system of mathematical deductions associated with the results of careful experiments and controlled observations, Oppenheimer asserted there is no trace of the Newtonian science in either European or American politics. “What there is of direct borrowing from Newtonian physics,” he wrote, whether “for chemistry, psychology, or politics is mostly crude and sterile.”
Still, some preeminent intellects of the Founding Era may well have been broadly inspired by Newtonian gravitational principles to make novel analogies that led them to discover other phenomena from a wholly new perspective. The Scottish economist Adam Smith, for example, in his Wealth of Nations, wrote that the “natural price” of something is “the central price, to which the prices of all commodities are continually gravitating.” Smith himself wrote a history of astronomy in which, Cohen writes, “he displayed some understanding of Newton’s scientific achievements … [W]e may all the more admire Smith … for having adapted or transformed the Newtonian physical concept of gravity in a way that was of important creative use in economics.”
And during the Age of Reason, both Jefferson and Hamilton analogized fundamental rules for governance as self-evident principles, akin to Euclidean axioms, with Jefferson’s preamble to the Declaration of Independence announcing, “We hold these truths to be self-evident,” and Hamilton, in Federalist Paper No. 31, stating that
In disquisitions of every kind, there are certain primary truths, or first principles, upon which all subsequent reasonings must depend. These contain an internal evidence which, antecedent to all reflection or combination, commands the assent of the mind. Where it produces not this effect, it must proceed either from some defect or disorder in the organs of perception, or from the influence of some strong interest, or passion, or prejudice. Of this nature are the maxims in geometry, that “the whole is greater than its part; things equal to the same are equal to one another; two straight lines cannot enclose a space; and all right angles are equal to each other.” Of the same nature are these other maxims in ethics and politics, that there cannot be an effect without a cause; that the means ought to be proportioned to the end; that every power ought to be commensurate with its object …
While proving nothing close to immutable laws, Enlightenment thinkers in the realm of economics and politics at least embraced the concept of timeless, fundamental principles over the practical power relations of the moment, setting America on a course based more on reason than raw force.
The esteem granted scientists during the Founding Era was perhaps illustrated best by John Adams when he wrote about what even the most powerful politicians should prioritize. As Cohen writes:
In thinking about the present and future needs of America in 1780, Adams quite correctly observed that it is “not indeed the fine arts which our country requires,” but rather “the useful, the mechanic arts,” by which he meant the arts of road and canal building, ship and factory building, bridge building, engineering, and the techniques of commerce and finance.
Beyond that, Cohen then describes how Adams related how he only engaged in politics at that crucial time of American history to make it easier for future generations to prioritize science:
[Adams] wrote, “I must study politics and war,” so that “my sons may have liberty to study mathematics and philosophy,” that is, natural philosophy or physical science. “My sons,” he concluded “ought to study mathematics and philosophy, geography, natural history and naval architecture, navigation, commerce and agriculture, in order to give their children a right to study painting, poetry, music, architecture, statuary, tapestry, and porcelain.”
James Madison, the primary author of the Constitution, himself came to embrace science after, and sometimes during, his political career. As Cohen writes, as a young student in college at Princeton, Madison was exposed to only relatively basic science instruction. Madison drew some crude science diagrams during his university studies, leading Cohen to comment “These diagrams are on so elementary a level, compared to the kind of work being done at the time by students at William and Mary or Harvard or Yale, that for a long time they were considered to have been made while Madison was in secondary school rather than in college.”
But then, Cohen writes:
Throughout his later life, Madison cultivated an interest in the sciences as a devoted amateur, as a cultivated citizen of the Age of Reason … Madison’s adult education in the sciences was influenced and even to some degree directed by Thomas Jefferson, with whom he began to be intimate in the late 1770s. One of the advantages to Madison of this relationship was that it opened to him the vast resources of Jefferson’s personal library. In 1784, when Jefferson went on his mission to France, he acted as Madison’s agent and adviser, producing for him books in French on the history and theory of government and on general philosophy, but also works on science … Madison even made careful and detailed measurements of the organs of a weasel and a mole found on his plantation at Montpelier. These were sent to Jefferson to be used as ammunition in the war against the [anti-American] theory espoused by [Georges-Louis Leclerc de] Buffon and others that animals which were similar in the Old World and the New were necessarily smaller in the New World … Madison was aware that he was ignorant of chemistry and asked Jefferson to send him “two Boxes, called La necessaire chemique,” together with “a good elementary treatise” on this subject … His own observations of the world of nature and his reading in the scientific books sent to him by Jefferson so increased his competence in science that in 1785 he was elected a member of the American Philosophical Society, in a group that included the British chemist Joseph Priestley …
In a letter to John Adams after leaving the presidency, Thomas Jefferson expressed his pleasure in having “given up newspapers in exchange for Tacitus and Thucydides, for Newton and Euclid”. Today, it’s hard to imagine a president leaving office and thinking “Excellent. Now I can read about quantum physics.” But similar sentiments prevailed among the people who framed our system of government which, when run as intended, will protect the flourishing of commerce and industry, knowledge and science.
In the next essay, we’ll look at how the love of science not only influenced America’s Founding, but also the eighteenth century’s battles over slavery in which opponents of slavery used scientific arguments to counter the pseudo-scientific arguments made in defense of slavery in America and elsewhere.