Harmonic Justice

Economics became a separate science in the eighteenth century. Before that, the people who thought about prices, money and trade did it as philosophers, astronomers, music theorists and alchemists, and they used the tools they used on the heavens: proportion, the theory of means, and the idea that a whole holds together when its parts stand in the right ratios. The people who handled money for a living read the same books. This note follows both through the library, from Xenophon to the nineteenth-century economists who put the word “harmony” in their titles: a banker, a friar who taught merchants, an astronomer at the mint, a London exchange dealer and a financier among them.

Two earlier notes cover neighbouring ground. The Invisible Hand Has a History traces market theory from Aristotle to Bastiat, and The Nature of Harmony follows the measurers of musical ratio from Pythagoras to Kepler. This one is about the place where the two meet: the claim that a fair exchange and a well-ordered state are harmonic in the same sense a chord is.

Xenophon: the beauty of an ordered house

The word economics comes from Xenophon's Oeconomicus, a dialogue on oikonomia, the management of a household and its estate, written in the fourth century BC. Its model manager, Ischomachus, tells Socrates how he taught his young wife to run the house, and the lesson is about order. A chorus whose members do as they please is mere confusion; an army in disorder is a mob; a merchant ship stows its whole cargo so the mate can find anything in a storm. Then he turns to the storeroom. In E. C. Marchant's Loeb translation of 1923:

Yes, no serious man will smile when I claim that there is beauty in the order even of pots and pans set out in neat array, however much it may move the laughter of a wit. There is nothing, in short, that does not gain in beauty when set out in order. For each set looks like a troop of utensils, and the space between the sets is beautiful to see, when each set is kept clear of it, just as a troop of dancers about the altar is a beautiful spectacle in itself, and even the free space looks beautiful and unencumbered.

Xenophon, Oeconomicus VIII.19–20, tr. E. C. Marchant (Loeb, 1923), p. 437 →

Xenophon does not use the word harmonia here, but the Greek on the facing page is closer to music than the English. The pots look eurhythmon, well-rhythmed; things lie kata kosmon, in good order; and Marchant's “troop of utensils” is a choros, a chorus of utensils, with the empty floor in the middle like the space inside a circle of dancers. Xenophon's order is made, not found: someone has to decide where each thing goes and teach the household to keep it there.

He also saw where specialization comes from. In the Education of Cyrus he explains why food from the Persian king's table tastes better, in a passage often cited as the first account of the division of labour. In a Latin edition of 1511 in the library:

For in small cities, the same man makes a bed, doors, a plow, a table. … Therefore, it cannot be that one who uses many arts should do all things beautifully. But in great cities, because many need individual things, one art is enough for each to earn a living, and often not even an entire one.

Xenophon, Cyropaedia VIII.2, in a Latin edition (1511), p. 285. Copy: Biblioteca Nazionale Centrale di Firenze →

Aristotle: money is a mean

In Book V of the Nicomachean Ethics Aristotle treats exchange as a problem in proportion. A shoemaker and a farmer make things that cannot be compared directly, so something has to make them comparable. He sets out the chain of conditions in our copy of the Aldine Greek edition of 1495:

Currency, like a mean, makes things commensurable and equalizes them. For there would be no community without exchange, no exchange without equality, and no equality without commensurability. In truth, it is impossible that things so different can become commensurable. But with respect to need, it is sufficiently possible.

Two things in this passage matter for everything after it. Money is a mean in the mathematical sense: the middle term that lets two unlike extremes stand in a ratio. And the commensurability is not real. There must be one standard, Aristotle goes on, “and this by assumption. Therefore, it is called nomisma,” from nomos, custom or law. The measure is a convention, and it holds only with respect to need.

Oresme: the measure belongs to the community

Nicole Oresme (c. 1320–1382) worked on both ends of this problem. In a treatise on the commensurability of the celestial motions he argued that the planets' periods are probably incommensurable, and that exact astrological prediction is therefore impossible (edited by Edward Grant in 1971). In his treatise on money, written in the 1350s while the French crown was repeatedly altering the coinage, he argued that the coinage is not the prince's to alter. The library holds the 1864 edition that prints the medieval French version beside the Latin:

Since the money belongs to the community, as was stated and demonstrated in the 6th Chapter, it seems that this community may ordain concerning it at its will, and thus change it and take profit from it at its pleasure, and treat it as its own property.

Oresme states this as the strongest case for altering the coin, and then argues that even the community should not do it except in real necessity, because a measure that moves breeds “innumerable perplexities, errors, and inextricable difficulties in accounts.” The historian Joel Kaye has argued that the two projects are connected: that living in a monetized economy taught fourteenth-century scholars to see nature as a field of graded, measurable quantities (Economy and Nature in the Fourteenth Century, 1998). On that reading the market did not only borrow its picture of order from cosmology. The traffic ran both ways.

The banker who put Hermes first

In the 1430s the Medici bank was the largest in Europe, and Cosimo de' Medici, who ran it, was the first citizen of Florence. When the Council of Florence brought Greek scholars to the city in 1439, Cosimo heard the Byzantine philosopher Gemistus Pletho lecture on Plato and conceived the idea of a Platonic academy. Twenty-four years later he gave the work to a young protégé, Marsilio Ficino. Ficino tells the story in the preface to his Plotinus, and the order of the commission is the surprising part:

After this, in the year 1463, when I was thirty years old, he commissioned me to translate first Hermes Trismegistus and soon after, Plato. I completed Hermes in a few months while he was still living; I then also began Plato.

The richest banker in Europe, near the end of his life, wanted the Hermetic books before the dialogues of Plato. Ficino's Latin Pimander, dedicated “to Cosimo de' Medici, father of his country,” became one of the most reprinted philosophical books of the Renaissance. The library holds the Venice edition of 1481.

Pacioli's two proportions

Luca Pacioli was a Franciscan friar and a teacher of mathematics to merchants' sons. In 1494 he printed a vast Summa of arithmetic, geometry, proportion and proportionality. Tucked inside it is a short treatise that became famous on its own: the first printed account of double-entry bookkeeping, “the system used in Venice.” Its opening chapter is about what a merchant needs. The English is John Geijsbeek's 1914 translation of Pacioli's Italian:

It has happened that many people without capital of their own but with good credit carried on large transactions. By means of their credit, which they faithfully maintained, they became very wealthy. … In the great republics, nothing was considered superior to the word of a good merchant, and oaths were taken based on that word. … This is not strange because, according to the Christian religion, we are saved by faith, and without it, it is impossible to please God.

Credit and faith are the same word, and Pacioli means the pun. The third thing a merchant needs, after cash and arithmetic, is order: books arranged so “that one may understand each of them at a glance by using the debit and credit method,” because “Where there is no order, there is confusion.” Every entry has a twin, and the two columns must balance.

Fifteen years later the same friar published De divina proportione (Venice, 1509), with woodcuts of the regular solids after drawings by his friend Leonardo da Vinci. Its subject is the ratio that divides a line so that the whole is to the larger part as the larger is to the smaller, what we call the golden ratio. Pacioli lists the ways it resembles God. The third:

The third convenience is that, just as God properly cannot be defined nor understood by us through words, so this our proportion can never be assigned by an intelligible number nor expressed by any rational quantity: but it is always occult and secret, and called irrational by mathematicians.

He goes straight on to the fourth: that like God it never changes, “holding the primacy of unity among all quantities indifferently, and never changing,” and he quotes Boethius on the unmoved mover: “Remaining stable, it gives all things to be moved.” (p. 24) So one man wrote down the two proportions an early-modern merchant lived between. The ledger's proportion must come out exactly, in whole ducats, or the books are false. The divine proportion can never be written as a ratio of whole numbers at all, and that is what makes it divine.

Copernicus at the mint

In the 1520s, while he was working out a sun-centred astronomy, Nicolaus Copernicus also wrote a treatise on coinage for the Prussian estates, where several debased currencies were circulating at once. Wolowski's 1864 volume prints it after Oresme's treatise, in the editor's French translation of the Latin:

However innumerable the plagues that ordinarily bring about the decadence of kingdoms, principalities, and republics, the following four are, in my sense, the most formidable: discord, mortality, the sterility of the land, and the deterioration of the currency. … Money is therefore, in a way, a common measure for the estimation of values; but this measure must always be fixed and conform to the established rule. Otherwise, there would, of necessity, be disorder in the State: buyers and sellers would be deceived at every moment, just as if the ell, the bushel, or the weight did not maintain a certain quantity.

The fourth plague is the dangerous one, he says, because it works “not all at once, but little by little, by a somewhat latent action.” This is Oresme's argument again, from a man with the same two subjects: the astronomer who moved the earth wanted the measure of value to stay still.

Bodin and Kepler: harmonic justice, checked against the ear

Jean Bodin ended his Six Books of the Commonwealth (1576) with a theory of harmonic justice. Arithmetic justice gives everyone equal shares. Geometric justice gives shares in proportion to merit. A well-ordered state, Bodin argued, blends the two, the way a harmonic proportion blends an arithmetic and a geometric one.

Forty years later Kepler read this and stopped the third book of his Harmony of the World (1619) to deal with it. The section is headed “A Political Digression,” and he says plainly why it is there:

I decided to transcribe the principal points of this political discussion from Bodin himself, with the words and order mostly shaped by my own understanding of that passage. I do this both to bring some light to a place that is obscure in itself (for Bodin did not bring enough support from mathematical disciplines to this speculation) and to soothe the boredom of those peevish mathematical demonstrations (of which this whole work is composed) by interspersing pleasant, popular material, and to show a taste of its usefulness in understanding the Commonwealth.

Kepler does not reject the idea that a state can be harmonic. He rejects Bodin's arithmetic. On the next page he shows that Bodin's definition admits mixtures of ratios that are not harmonic at all, excludes ratios that plainly are, and contradicts itself. Then he names the real fault:

Bodin wrongly denies that these latter sets produce harmonic concords, rising up on the authority of the ancients against the very evidence of the sense of hearing.

This is the useful part of the episode. A model of social order borrowed from music was held to the standard of the music. If you say a distribution is harmonic, the ratios have to be consonant, and the test is the ear, not the authority.

A Rosicrucian debate on abolishing gold

The Rosicrucian manifesto Fama Fraternitatis first appeared in 1614, printed together with a piece called the General Reformation of the Whole World, a German version of a satire from Traiano Boccalini's News from Parnassus (1612). In it the sages of antiquity meet to reform humankind. One proposal is to banish “the two scentless and villainous metals, gold and silver,” for good. The library's 1616 edition prints the reply:

…people collected gold and silver because it was a measure and a counterweight of compensation for all things. And for the sustenance of the human race, it was absolutely necessary that one have a metal, or at least something else that would be held in such value, in exchange for which one could trade other things … as experience had clearly shown in India, where shells, which people use instead of money, are valued much higher than any gold and silver.

Cleobulus, one of the Seven Sages, then suggests that if a metal must go, it should be iron, which makes daggers, and that gold and silver be kept for the purpose “for which they were created by God, namely, that all other things should be valued and paid for through them.” Whatever the brotherhood was, the book that announced it to Europe came bound with Aristotle's point: money is a measure, held by agreement, that people cannot do without.

The alchemists: wealth that multiplies without being spent

Alchemy is remembered as an attempt to make gold. The texts often set the Art above gold and above trade. The English translation of Splendor Solis ends:

He is like one who had a flint from which he strikes fire and gives to whosoever he likes, without the stone getting any smaller through it. It is as good as giving superfluous fine Gold. This Art is also better than all commerce, Gold and Silver, and her fruits are better than the wealth of all the world.

The flint that gives fire without wearing down is the alchemists' “multiplication” of the Stone. Whatever one makes of the chemistry, it is an exact picture of what credit promises: a source that gives without being used up.

The people who held this picture of metals were not all recluses. Gerard de Malynes was a merchant, an adviser to the crown on trade and coinage, and the most combative writer on foreign exchange in Jacobean London (biography). In The Canker of England's Common Wealth (1601) and later books he argued that exchange rates should be held to the “par,” the true metal content of each coin. His opponent Edward Misselden, in The Circle of Commerce (1623), complained that “Malyne's Par” had been “made a Mystery in Exchange” (p. 7).

Misselden was more right than he knew. Malynes's law-merchant handbook, Lex Mercatoria (1622), includes a chapter on how metals are generated in the earth, and in 1655 Samuel Hartlib, the great London collector of reform schemes, reprinted it as an appendix to a book of chemical recipes. It opens:

All Philosophers by the light of Nature and long observation have determined, that the sperme or seed of all things created of the four elements, doth in a secret manner lowre within the two elements of water and earth; and that Nature doth continually work to produce perfect things, but is hindered therein by accidental causes.

On the next page he turns to “the operation of the Sun and Moon, and the other Planets and Stars, in the generation of all things.” For the man who wanted every coin held to its true weight in silver, the silver itself was a slow work of nature under the planets.

Johann Joachim Becher (1635–1682) carried the same mixture into the next generation. He was an alchemist, a physician, an economic adviser to the emperor in Vienna, and a promoter of manufactories and trading companies. One of his books in the library is a ledger of his own projects. Its title promises “one hundred political, physical, mechanical and mercantile concepts and propositions, some of which went well and some came to nothing” (Närrische Weißheit und weise Narrheit, “Foolish Wisdom and Wise Folly”, 1707 edition). A generation later Isaac Newton, who spent decades on alchemy, was running the Royal Mint.

A financier's chair of music

Thomas Gresham managed the English crown's debts in Antwerp and built London's Royal Exchange. His name was later attached to Gresham's law, that bad money drives out good. When he died in 1579 his will founded a college in his house with seven professors, to lecture in divinity, law, physic, rhetoric, geometry, astronomy and music (Gresham College). Three of the four mathematical arts of the old curriculum, geometry, astronomy and music, were endowed by a financier for the City of London.

In 1651 the Gresham chair of music went to William Petty (list of professors), who went on to found what he called “political arithmetic,” the measurement of a nation's people, land and income. His work is covered in The Invisible Hand Has a History. The founder of economic statistics had first held a chair of music.

The physician's table

François Quesnay was physician to the court of Louis XV, and his Tableau économique (1758) drew the whole economy of France as a circulation: revenue passing back and forth between the farmers, the landowners and the artisans in a zigzag of lines, the kind of circulation a physician would draw. It was a diagram of an order that sustains itself if nothing blocks it.

Adam Smith: the invisible hand is a providence

A year later the phrase everyone knows first appeared, in Smith's Theory of Moral Sentiments (1759), in a passage about the land and how its produce is shared:

They are led by an invisible hand to make nearly the same distribution of the necessaries of life, which would have been made, had the earth been divided into equal portions among all its inhabitants, and thus without intending it, without knowing it, advance the interest of the society, and afford means to the multiplication of the species.

The next sentence begins “When providence divided the earth among a few lordly masters.” The hand is the hand of providence, and the claim is a claim of hidden harmony: a division nobody intended comes out close to an equal one. It is Bodin's question, whether the shares are just, answered by an appeal to design.

Smith knew how such systems work on the mind. In his essay on the history of astronomy he described a philosophical system as an “imaginary machine,” built to connect appearances and quiet the imagination's unease at what it cannot explain (published after his death, in 1795). He judged astronomical systems partly by how well they satisfied the imagination. The same test can be put to his own.

The harmony economists

In the generation after Smith, harmony stopped being a comparison and became a programme, and three rival programmes claimed it at once.

The first was Charles Fourier's (1772–1837). He called the society he was planning “Harmony,” to be built of communities called phalanxes, and his motto was that attractions are proportional to destinies: rightly arranged, people's passions would draw them to the work that needed doing, as gravity draws the planets. Fourier's own books are not yet in the library, but the way he was read is. An American summary of his system, which John Humphrey Noyes quoted in his History of American Socialisms (1870), begins:

Fourier says: There are certain Laws of Organization in nature, which are the source of order and harmony in creation. These laws human reason must discover and apply in the organization of society, if a true social order is to be established on the earth.

Fourier's system summarized, in J. H. Noyes, History of American Socialisms (Philadelphia, 1870), p. 659 →

The seer Andrew Jackson Davis took it literally. Fourier, he wrote in 1847, showed “that the world of mankind is composed of the requisite notes to play a perfect tune of peace and harmony,” and that each note needs only to be properly placed for the whole race to move “like a perfectly-tuned instrument” (The Principles of Nature, p. 586). The occultist Eliphas Lévi agreed with the motto and saw the flaw. Fourier, he wrote, “was wrong not to distinguish between fatal attractions and artificial attractions,” and he asked what Fourier would have done “with people whose attraction, proportional according to him to their destiny, would have been to disturb and demolish the phalanstery” (Le Grand Arcane, p. 35).

The second was Frédéric Bastiat's. He wrote Economic Harmonies in 1850, the year he died, against the socialists, Fourier's followers among them, and he put the whole quarrel into one question:

What radically separates the various socialist schools (I mean here those who seek the solution to the social problem in an artificial organization) from the economist school is not this or that detail of vision, or this or that governmental combination; it is the starting point, the preliminary and dominant question: Are human interests, left to themselves, harmonious or antagonistic? … It is not necessary to constrain toward harmony that which is harmonious in itself.

Frédéric Bastiat, Harmonies économiques (Paris, 1850), p. 4. Copy: Biblioteca Nazionale Centrale di Firenze →

His answer was a creed, and he wrote it as one, in the first person, addressed to the young people of France:

I believe that He who arranged the material world did not wish to remain a stranger to the arrangements of the social world; I believe that He knew how to combine and set in motion [harmoniously] free agents just as well as inert molecules. I believe that His providence shines forth at least as much, if not more, in the laws to which He has subjected interests and wills as in those He has imposed upon weights and speeds.

Bastiat, Harmonies économiques (1850), p. 20 →

The passage ends: “Interests are harmonic, therefore the solution is entirely in this word: LIBERTY.” This is Smith's invisible hand stated as a creed. Xenophon's storeroom needed a manager; Bastiat's society is a storeroom that arranges itself.

The third was Henry Charles Carey's, in Philadelphia, and it used the same word for the opposite policy. Carey's The Harmony of Interests, Agricultural, Manufacturing and Commercial (1851; our copy is of 1868) argued for tariffs: the harmony he meant was the farmer and the manufacturer living side by side, trading with each other instead of across an ocean through middlemen. Twenty years later, in The Unity of Law (1872), he made the astronomy explicit. Society, he argued, obeys the same laws as matter, and a nation needs many local centres of attraction, as the solar system does:

To the equal action of opposing forces it is due that the celestial world is enabled to exhibit such wonderful harmony and such unceasing motion. In the application of this principle to the societary movement the people of Greece had all this yet to learn…

Henry C. Carey, The Unity of Law (Philadelphia, 1872), p. 85. Copy: University of California →

As local centres grow in number, he wrote, society tends daily toward “the same beautiful system by means of which the harmony of the universe is maintained” (p. 377). Carey and Bastiat agreed on the harmony and disagreed on the tariff. They also shared a theory of value, and Carey made sure his readers knew who had it first: a footnote to his preface quotes the Italian economist Francesco Ferrara, “Carey, and after him Bastiat, have introduced a formula à posteriori, that I believe destined to be universally adopted” (p. vi).

Free trade, protection, the phalanstery: by 1850 the word could be made to bless any of them, which is a sign it had stopped doing the work Kepler asked of it. Sixty years later Rosa Luxemburg used it as a label for a school that had stopped thinking. “If economic harmony theory,” she wrote, “had meanwhile descended from the height of Ricardo to Bastiat-Schulze, social criticism had correspondingly carried out the slide from Sismondi to Rodbertus” (Die Akkumulation des Kapitals, 1913, p. 237). Her German is ökonomische Harmonielehre: the economic doctrine of harmony.

Keynes and the last of the magicians

John Maynard Keynes bought a large part of Newton's alchemical papers at auction in 1936. In a lecture read for him at the Royal Society's Newton tercentenary in 1946, after his death, he said that Newton “was not the first of the age of reason. He was the last of the magicians” ( “Newton, the Man”). Keynes's own best-known phrase for what drives investment, “animal spirits,” has a long history behind it, through Descartes back to the spiritus animalis of Galenic medicine, though which source Keynes had in mind is disputed. The economist who did most to break the idea that markets settle into harmony on their own named what moves them with a term from the old physiology.

Two uses of harmony

There are two ways to bring harmony into talk about markets, and these books show both.

The first is apologetic. The system is already harmonious; what looks like conflict is concord at a higher level; the shares are fair because providence, or the market, set them. Bastiat is the plainest case, and Smith's invisible hand can be read that way. Carey and Fourier used the word the same way for other ends: each called harmony the state the world would reach if only his own plan were followed.

The second is critical, and it is older. Xenophon says order is beautiful and has to be made and kept by someone. Aristotle says the measure is a convention that holds only with respect to need. Oresme says it belongs to the community and should not be moved at will, and Copernicus, from the mint, says the same. Kepler says that if you call a distribution harmonic, show the ratios and test them against something other than authority. The alchemists, read soberly, describe the thing to be wary of: wealth that seems to multiply without being spent.

The people who dealt in money reached for the heavens for specific reasons. Copernicus wanted a measure that would stay fixed, like the motions he was charting. Pacioli wanted books that balance, and he set beside them a proportion so perfect it could not be written down. Malynes wanted coin held to its true metal and looked for that truth in the generation of metals. The sages of the General Reformation concluded that people will always need a measure, and the only question is what it is made of. Cosimo, who had all the money he could want, asked first for Hermes.

What all these writers shared was the assumption that an economy is one case of a general problem: how unlike things can be brought into a ratio that holds. They asked it about justice, music and the heavens at once. Modern economics kept the mathematics of the question and set aside the part about justice. The older books ask which ratios are fair in the same breath as which ones are stable.

Quotations are the library's English translations, or for English books (Malynes, Misselden, Davis, Noyes, Carey) the printed English, copied from the pages they link to. Where a book is itself a translation (Marchant's Xenophon, Geijsbeek's Pacioli, Wolowski's Copernicus), the wording is the translator's. The word in square brackets in the Bastiat creed is his harmonieusement, restored from the French. Bodin's République is not yet in the library, so his theory is given here in Kepler's account of it. Gresham's will and Petty's professorship are cited from outside the library.