Chapter 9 of Bourgeois Revaluation:
Aristocratic England Scorned Measurement

One countable piece of evidence that bourgeois values were becoming dominant in England in the seventeenth and eighteenth centuries is the new, dominate role of counting in giving evidence. It is assuredly modern, and was not in fashion during Dekker’s or Shakespeare’s time. The pre-modern attitude — which survives nowadays in many a non-quantitative modern — shows in a little business between Prince Hal and Sir John Falstaff. The scene is fictional early fifteenth century. 1 Henry IV was written in London at the very end of the sixteenth century. Either time will do.

Hal disguised in stiffened cloth had been the night before one of the merely two assailants of Falstaff and his little gang of three other thieves. The two had relieved the thieves of their loot just taken. Falstaff had in fact, after token resistance, fled in terror, as had his confederates. One of them, Gadshill, and poor old Jack, re-count the episode to Prince Hal (and here among the low life the Prince, though soon to be blank-verse Henry V [ "Once more unto///"), speaks of course in prose):

Yet less than two centuries after Shakespeare’s England, Boswell says to Johnson: “Sir Alexander Dick tells me, that he remembers having a thousand people in a year to dine at his house; that is, reckoning each person as one, each time he dined there.”

Something had changed. As Johnson wrote elsewhere, “To count is a modern practice, the ancient method was to guess; and when numbers are guessed they are always magnified,” in the style of true Jack Falstaff, plump Jack Falstaff.²²⁹ Johnson the classicist knew what he was talking about. The economic historian Gregory Clark has usefully reviewed the startling evidence that wealthy if illiterate and innumerate ancient Romans, for example, didn’t even know their own ages. In the style of reported Methuselahs the innumerate among the Romans would grossly exaggerate the age at death of very old folk, with every sign of believing their own miscalculations.²³⁰ Among the ignorant it persisted. When Casanova escaped from prison in Venice in 1757 he went to Paris, where he lighted on a suitably gullible female victim, the Marquise d’Urfe. But she was already captivated by another gentlemanly scoundrel, the Comte de Saint-Germain, who had persuaded her to believe he was three hundred years old.²³¹

Numeracy was by then more advanced in Britain. Johnson laid it down that “no man should travel unprovided with instruments for taking heights and distances,” and himself used his walking stick.²³² Boswell reports a conversation in 1783 in which Johnson argues against a walled garden on calculating grounds, as not productive enough to bear the expense of the wall — the same calculation at the same time, by the way, was surprisingly important for the enclosure movement in British agriculture. “I record the minute detail,” writes Boswell, “in order to show clearly how this great man. . . was yet well-informed in the common affairs of life, and loved to illustrate them.”²³³ The point is that he loved to illustrate them quantitatively, quite contrary to the routine a century and a half before. And this was a literary man.

Because of Johnson’s friendship with Mr. and Mrs. Thrale, who ran a large London brewery, he turned his quantitative mind to their hopes. In 1778 he writes, “we are not far from the great year of 100,000 barrels [of porter brewed at the Anchor's brewery], which, if three shillings be gained from each barrel will bring us fifteen thousand pounds a year. Whitbread [a competing brewery] never pretended to more than thirty pounds a day, which is not eleven thousand a year.”²³⁴ No wonder that “by the early nineteenth century,” as Leonore Davidoff and Catherine Hall note, “foreign visitors [to England] were struck by this spirit: the prevalence of measuring instruments, the clocks on every church steeple, the ‘watch in everyone’s pocket,’ the fetish of using scales for weighing everything including ones own body and of ascertaining a person’s exact chronological age.”²³⁵

Such an idea of counting and accounting is obvious to us, in our bourgeois towns. It is part of our private and public rhetoric, and we laugh at quantitative exaggerations. But counting had to be invented, both as attitude and as technique. What we now consider very ordinary arithmetic entered late into the educations of the aristocracy and the clergy and the non-mercantile professions. Johnson advised a rich woman, “Let your boy learn arithmetic” — note the supposition that the heir to a great fortune would usually fail to do so — “He will not then be a prey to every rascal which this town swarms with: teach him the value of money and how to reckon with it.”²³⁶ In 1803 Harvard College required of course both Latin and Greek of all the boys proposing to attend. Yet only in that year did it also make the ability to figure a requirement.

Consider such a modern commonplace as the graph for showing, say, how the Dow-Jones average has recently moved. (Cartoon: man sitting in front of a wall chart on which an utterly flat line is graphed declares to another, “Sometimes I think it will drive me mad.”) Aside from the “mysterious and isolated wonder” of a tenth-century plotting of planetary inclinations, Edward Tufte observes, the graph appeared surprisingly late in the history of counting. Cartesian coordinates were of course invented by Descartes himself in 1637, unifying geometry and algebra, perhaps from the analogy with maps and their latitudes and longitudes. (All this was invented in China centuries before, but the Europeans were innocent of it.) But graphical devices for factual observations, as against the plotting of algebraic equations on Cartesian coordinates, were first invented by the Swiss scientist J. H. Lambert in 1765 and, more influentially, by the early economist William Playfair in two books at the end of the eighteenth century, The Commercial and Political Atlas, 1786 (the time series plot and the bar chart) and The Statistical Breviary Shewing on a Principle Entirely New the Resources of Every State and Kingdom of Europe, 1801 (the pie chart; areas showing quantities; exhibiting many variables at one location), “applying,” as Playfair put it, “lines to matters of commerce and finance.”²³⁷ Contour lines for heights on maps were only invented in 1774 by the geologist Charles Hutton, in aid of a survey of an Scottish mountain.²³⁸

Obsession with accurate counting in Europe dates from the seventeenth century. Pencil and paper calculation by algorithm, named after the district of a ninth-century Arabic mathematician, and its generalization in algebra (al-jabr, the reuniting of broken parts),- depended on Arabic numerals, that is, on Indian, that is, on Chinese ??? Indian source? numerals, with place value and a zero (sifr: emptiness). The abacus makes rapid calculation possible even without notation, and mastery of it slowed the adoption of Arabic numerals in Europe. (Again, Needham has shown, not in China.) CHECK CHINA; FORGOTTEN? Compare the state of mental computing skills among our children nowadays, equipped with electronic calculators.

You cannot easily multiply or divide with Roman numerals. Only in the sixteenth and seventeenth centuries did Arabic numerals spread widely to Northern Europe. Admittedly the first European document to use Arabic numerals was as early as 976. The soon-to-be Pope Sylvester II (ca 940 – 1003) — or rather “the second” — tried to teach them, having learned them in Moorish Spain. His lessons didn’t take. The merchant and mathematician Leonardo Fibonacci re-explained them in a book of 1202. The commercial Italians were using them freely by the fifteenth century, though often mixed with Roman.²³⁹ But before Shakespeare’s time 0, 1, 2, 3, . . . 10, . . . 100 as against i, ii, iii, . . . x, . . . c had not spread much beyond the Italian bourgeoisie. The Byzantines used the Greek equivalent of Roman numerals right up to the fall of Byzantium in 1453. And still in the early eighteenth century Peter the Great was passing laws to compel Russians to give up their Greek numerals and adopt the Arabic.

The bourgeois boy in Northern Italy from earliest times and later elsewhere in Europe did of course learn to multiply and divide, somehow. He had to use an abacus, and skillfully, as I noted. Presumably the same was true earlier at Constantinople and Baghdad and Delhi, not to speak of ancient Chinese city and Osaka. By the eighteenth century the height of mathematical ability in an ordinary European man or a commercial woman was the Rule of Three, which is to say the solving of proportions: “Six is to two as N is to three.” In Europe centuries earlier one could hardly deal profitably as a merchant with the scores of currencies and systems of measurement without getting the Rule of Three down pat. Interest, eventually compounded, was calculated by table. We can watch Columella in 65 C.E. making mistakes with the compounding. The logarithms that permit direct calculations of compounding were not invented until 1614 by the Scotsman Napier, who by the way also popularized the decimal point, recently invented by the Dutchman Stevin — 3.5, 8.25, etc. rather than 3 ½ , 8¼ , etc. — though it would be better to say that Stevin reinvented it, since the Chinese in the fourth century B.C.E. had a full decimal system with a zero. A pity the Greeks didn’t take it in.

In England before its bourgeois time the Roman numerals prevailed. Shakespeare’s opening chorus in Henry V, two years after 1 Henry IV, apologizes for showing battles without Cecil-B.-de Millean numbers of extras. Yet “a crooked figure may /Attest in little place a million; / And let us, ciphers to this great accompt [account], / On your imaginary forces work.” The “crooked figure” he has in mind is not Arabic “1,000,000,” but merely a scrawled Roman M with a bar over it to signify “multiplied by 1000″: 1000 times 1000 is a million.

Peter Wardley has pioneered for the study of numeracy in England the use of probate inventories, statements of property at death available in practically limitless quantities from the fifteenth century onward. He has discovered that as late as 1610 even in commercial Bristol the share of probates using Arabic as against Roman numerals was essential zero. By 1670, however, it was nearly 100%, a startlingly fast change.²⁴⁰ Robert Loder’s farm accounts, in Berkshire 1610-1620, used Roman numerals almost exclusively before 1616, even for dates of the month. In 1616 he started to mix in Arabic, as though he had just learned to reckon in them — he continued to use Arabic for years, probably because calendar years, like regnal years, Elizabeth II or Superbowl XVI, are not subjects of calculation.²⁴¹ English official accounts did not use Arabic numerals until the 1640s. Get Keith NNNN lecture here

Fra Luca Pacioli of Venice popularized double-entry book-keeping at the end of the fifteenth century, and such sophistications in accounting rapidly spread in bourgeois circles. The metaphor of a set of accounts was nothing new, I repeat, as in God’s accounting of our sins; or the three servants in Jesus’ parable (Matt. 25: 14-30) rendering their account [the Greek original uses logon, the word "word" being also the usual term for "commercial accounts"] of their uses of the talents, “my soul more bent / To serve therewith my Maker, and present / My true account, lest he returning chide.” Bourgeois and especially bourgeois Protestant boys actually carried it out, as in Franklin’s score-keeping of his sins.

But we must not be misled by the absence in Olden Tymes of widespread arithmetical skills into thinking that our ancestors were merely stupid. Recent neuropsychology shows that a spatial sense of a large number of trees being fewer than a very large number is hardwired in pigeons and people, regardless of whether they can do their multiplication tables. Shepherds had every incentive to develop tricks in reckoning, as in the old Welsh system of counting, perhaps from how many sheep the eye can grasp at a glance. The myth is that all primitive folk count “one, two, many,” and a much-abused tribe in Brazil has been cited as evidence, somewhat dubiously. Well, not when it matters, though some count in such a way because it doesn’t matter. Carpenters must of course have systems of reckoning to build a set of stairs. And Roman engineers did not build aqueducts with slopes of 3.4 units of fall per 10,000 units of length without serious calculation, or some very accurate analogue levels calibrated to an accuracy of 3.4 percent of 1 percent. The habit of counting and figuring is reflected in handbooks for craftsmen from the late Middle Ages on, the ancestors of the present-day ready reckoners for sale at the checkout counter at your Ace Hardware store. And you cannot build a great pyramid, or even probably a relatively little stone henge, without some way of multiplying and dividing, at least in effect, multiplying the materials and dividing the work. The first writing of any sort of course is counting, from which came eventually writing itself, such as storage accounts in Mesopotamia or Crete and calendar dates in Meso-America and reckoning knots in Peru. In Greek and then in Latin the magicians of the East were called mathematici because calculation — as against the much more elegant method of proof supposedly invented by the Greeks (though the Chinese knew most of it centuries before) — was characteristic of the Mesopotamian astrologers.

Large organizations counted perforce. Sheer counts had often a purpose of taxation — St. Luke’s story about a decree from Caesar Augustus that all the world should be taxed, for example; and in 1086 the better attested case of William the Conqueror’s Domesday Book. We owe our knowledge of medieval agriculture in Europe to the necessity in large estates to count, in order to discourage cheating by subordinates. The Bishop of Winchester’s N manors . . . .. cite Winchester Yields, and give example from it. We can see in such records the scribes making mistakes of calculation with their clumsy Roman numerals. We know less about agriculture a little later in Europe because the size of giant estates went down after the Black Death of 1348-50, and such accounting was therefore less worthwhile.

Sophisticated counting in modern times cuts through the Falstaffian fog of imprecision which any but a calculating genius starts with. Nearly universal before the common school outside the classes of specialized merchants or shepherds, the fog, I repeat, persists now in the non-numerate. Here is a strange recent example in which I have a personal interest. The standard estimate for the prevalence of male to female gender crossers in the United States is one in 30,000 born males. This is the figure in The Diagnostic and Statistical Manual of Mental Disorders, fourth edition, 1994. Let us put aside the issue of whether it is a “mental disorder,” or what purpose of gender policing would be served by claiming that the disorder is so very rare. An emerita professor of electrical engineering at the University of Michigan, Lynn Conway, a member of the National Academy of Engineering and one of the inventors of modern computer design (after IBM fired her for transitioning in 1968 from male to female), notes that the figure is impossibly low. It would imply by now in the United States a mere 800 completed gender crossers, such as Conway and me — when in fact all sorts of evidence suggests that there are at least 40,000.²⁴² My little boys’ high school in Cambridge, Massachusetts graduated only sixty boys in the two years 1959 and 1960. Two of them subsequently changed gender.

The showing of such a contradiction, like Prince Hal comments on Falstaff’s boasting exaggeration, is the kind of point a numerate person makes. The sex doctors seem not to be modern in their quantitative habits of thought. A figure of 800 completed, Conway observes, would be accounted for (note the verb) by the flow of a mere two year’s worth of operations by one doctor. Conway reckons the incidence of the condition is in fact about one in every 500 born males — not one in 30,000. It is two orders of magnitude more common than believed by the psychiatrists and psychologists who in their innumeracy write the Manual. Conway suspects that among other sources of numerical fog the doctors are mixing up prevalence with incidence — stock with flow, as accountants and economists would put it. That is, they are mixing up the total number existing as a snapshot at a certain date with the number born per year. The wrong number justifies programs like that at the NNN at Johns Hopkins and the former Clarke Institute in Toronto (now concealed in NNNN, but continuing its reparative “therapy” for misled gender crossers) to Stop Them from changing gender — after all, the real ones are extremelyrare, and the rest one may suppose, against most of the scientific evidence, are vulgarly sex-driven.

Calculation is the skeleton of prudence. But the aristocrat scorns calculation precisely because it embodies ignoble prudence. Courage, his defining virtue, is non-calculating, or else it is not courage but mere prudence. Henry V prays to the god of battles: “steel my soldiers’ hearts;/ Possess them not with fear; take from them now the sense of reckoning, if the opposèd numbers/ Pluck their hearts from them.” And indeed his “ruined band” before Agincourt, as he had noted to the French messenger, was “with sickness much enfeebled, / My numbers lessened, and those few I have / Almost no better than so many French.” Yet on the Feast Day of Crispian his numbers of five or six thousand did not prudently flee from an enemy of 25,000.

One reason, Shakespeare avers, was faith, as Henry says to Gloucester: “We are in God’s hand, brother, not in theirs.” The other was courage: “’tis true that we are in great danger; / The greater therefore should our courage be.” Shakespeare of course emphasizes in 1599 these two Christian/aristocratic virtues, those of the Christian knight — and not for example the mere prudence of the warhorse-impaling stakes that on Henry’s orders the archers had been lugging through the French countryside for a week.²⁴³ Prudence is a calculative virtue, as are, note, justice and temperance. They are cool. The warm virtues — love and courage, faith and hope — the virtues praised most often by Shakespeare, and praised little by bourgeois Adam Smith 160 years later, are specifically and essentially non-calculative.

The play does not of course tell what the real King Henry V was doing in the weeks leading up to Sunday, October 25, 1415. It tells what was expected to be mouthed by stage noblemen in the last years of Elizabeth’s England, a place in which only rank ennobled, and honor to the low-born came only through loyalty to the nobles. Before the taking of Harfleur (“Once more unto the breach, dear friends”), Henry declares “there’s none of you so mean and base, / That hath not noble luster in your eyes.” And before Agincourt, as I noted, he repeats the ennobling promise, “be he ne’er so vile, / This day shall gentle his condition.” “Vile,” too, was an idea of rank, from Latin vilis, base, cheap. (“Village” and “villein” come from a different root, as in villa, farmhouse — though in a society of rank a village “villein” [peasant], from villa becomes after all a base “villain,” too.)

Out of earshot of Henry, the king’s uncle grimly notes the disadvantage in numbers: “There’s five to one; besides they all are fresh”; at which the Earl of Salisbury exclaims, “God’s arm strike with us! `tis a fearful odds.” The King comes onto the scene, while the Earl of Westmoreland is continuing the calculative talk: “O that we now had here / But one ten thousand of those men in England / That do no work today!” To which Henry replies, scorning such bourgeois considerations, “If we are marked to die, we are enow [enough] / To do our country loss; and if to live, / The fewer men, the greater share of honor.”

Imagine how late in World War II that bit, intoned by Laurence Olivier on the stage of the Old Vic, played to British audiences. It is not bourgeois, prudential rhetoric, and counts not the cost. We will never surrender.

229. [back] A Life, II, p. 458
230. [back] Clark 2007, pp. 175-180.
231. [back] Maynial, Edouard. 1911. Casanova and His Time. Trans. E. C. Mayne. London: Chapman & Hall. Pp. 7, 10. At http://www.archive.org/stream/ casanovahistime00maynrich/casanovahistime00maynrich_djvu.txt
232. [back] A Journey 1775, p. 139.
233. [back] Journey, p. 104.
234. [back] Quoted in Mathias 1978, p. 312.
235. [back] Davidoff and Hall 1987, p. 26.
236. [back] Quoted in Mathias 1978, p. 296.
237. [back] Tufte, 1983, pp. 28, 32f, 44ff.
238. [back] Bryson 2003, p. 57.
239. [back] See for example Frederic Lane 1973, p. 142.
240. [back] Wardley 1993
241. [back] Fussell, ed., 1936, passim.
242. [back] lynnconway.com
243. [back] Keggan, SP? p. 90.

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