Saint Louis Art Museum, object number 72:1950. Public domain.
The painting only shows a tantalising glimpse of the accounts book itself: but accounts books survive in huge numbers from the sixteenth century to the nineteenth, deriving from households, businesses and individuals. Each page could be as simple as a list of items and their prices, with a total at the foot of the page (and some working by the side, providing a record of how that total had been arrived at). Other books were elaborately ruled in multiple colours, with separate columns for profits and losses, and the ‘total’ column updated after each entry: much like a modern bank statement, and manifesting the same awkward combination of dullness and importance. If something is not right here, it can mean that something is terribly wrong – fraud, theft, embezzlement – in the real world of counters and goods. Maes’s accounts book looks like the more complex kind, and the fact that there are two more volumes stacked closed on the counter suggests a business or household of some complexity, in which different categories of income and expenditure have to be tracked separately, or in which a single run of accounts has to be compared over a long period of time.
How did you learn to do such things? For this, too, a great deal of evidence has survived. Now that counting was well established as part of reading, and calculating as part of writing, you learned it wherever you learned your reading and writing. At home or at school, you made a ‘cyphering book’, in which you wrote out definitions and exercises starting with ‘numeration’ and passing through addition and subtraction, multiplication and division until you – possibly – moved on to more advanced procedures like reasoning about proportions or keeping accounts. The word ‘ciphering’ came from ‘cipher’: that is ultimately from Sanksrit sunya and Arabic sifr: a little reminder of the long heritage of this way of recording numbers, and this curriculum of study.
Hundreds of the books survive, from all over Europe and North America. They typically consisted of a quire of paper sewn together, in a generous size: often 30cm by 20cm. Children from well-to-do families might buy one ready-made, but most students would have sewn, roughly bound and decorated the book themselves. Some ruled lines to help them write: these were meant to be fair-copy books, but the students using them began as young as nine or ten and often had quite uncertain handwriting. Many, all the same, turned out careful and neat, with different inks elaborately used, headings, borders and careful management of the space on the page to make a truly personal textbook. Illustrations were common, ranging from the accomplished watercolour to the childish doodle.
The basic technique of instruction was always the same. The teacher would provide a ‘rule’ for some arithmetical process – numeration, addition or subtraction, say – which the student would copy into the book. The teacher would also provide some examples of the use of that rule, to try out as practice on slate or waste paper. The students, called forward individually, would show their exercises. If they were wrong, they had to be done again; once they were right they could be copied into the ciphering book.
Estimates varied, even at the time, as to how well this worked. Sometimes wrong sums found their way into the ciphering book if the teacher was careless; sometimes students got the answers right merely by copying from one another. And sometimes work that was correct but used a slightly different method from the teacher’s was judged wrong unfairly. It could be a frustrating system, and it was certainly a repetitious and a laborious one. A student who stayed in school for several years might produce several hundred pages of ciphering work; some students filled more than a dozen separate books. The ciphering system assumed that counting was part of reading and writing, and that the way to learn arithmetical operations was by repetitiously writing them down: that the route to the mind was through the pen and the hand. There was no mental arithmetic, and precious little speaking at all.
The curriculum started with ‘numeration’: learning to read and write the Arabic numerals fluently. Most students wrote out a table showing how to read Arabic numerals up to perhaps eight or ten digits long: hundred millions, ten millions, millions … all the way down to hundreds, tens and units. After that, practice: write eighty-five in numbers. Write one hundred and eight. Write one million, eleven hundred and one. You would do these on scrap paper until you or your teacher thought they were right, then copy them into the book.
Often there was an emphasis on large numbers. Up to nine digits was typical, but some textbooks went up to twenty or more; one went to seventy-eight digits, the perhaps ludicrous ‘duodecillion’. Large numbers provided more arithmetical work per exercise, of course; they also gestured none-too-subtly at prosperity, motivating students – or trying to – by promising that if they learned this material well they too could one day deal in hundreds of cows, thousands of barrels or millions of silver coins.
Following numeration came the four arithmetical operations: addition, subtraction, multiplication and division. The syllabus, its order, and even some of the details of the algorithms for calculation were the same as they had been in medieval Europe, in the Maghrib and Baghdad, in India itself. Next, the ‘rule of three’, which taught how to find the missing number from a set of four linked quantities. If it takes three men two days to build a certain wall, how long will it take five men to build the same wall? The same subject, with some strikingly similar examples, was covered in Bhaskara’s textbook.
Once a student had done all that, she unfortunately had to start all over again with so-called ‘denominate’ numbers: that is, numbers denoting money or weight or measure. The systems in use were numerous; just for weight there were troy weight, avoirdupois weight and apothecaries’ weight, and there were many more for volumes, lengths, areas and of course money. All of this taught the arithmetic that would enable you to keep domestic or small-business accounts in adulthood, dealing with the costs of food, clothing and equipment as well as bargains, barter and loans:
Divide twelve pounds, 17 shillings and six pence equally among four men.
Bought a hogshead of molasses for twenty-one pounds and five shillings. How many gallons did it contain, valuing the gallon at two shillings and six pence?
Two merchants A and B agree to trade together. A puts in £332 for four months, and B £475 for seven months; they gained £520. What was each merchant’s part of the profits?
Many ciphering books tailed off rather than finishing neatly: students left school, and the series of definitions and examples came to a more or less abrupt halt. Nevertheless, adults frequently retained their ciphering books as personal textbooks, using them to display their competence at arithmetic and handwriting to schools, colleges or potential employers, or referring to them for the techniques of calculation that were useful in daily life. Some added to them, modified or corrected the original exercises. Some books were passed down among siblings or from parent to child; some became dense palimpsests recording the arithmetical education of a whole family. However orderly the sequence of definitions and exercises, chaos had a tendency to creep in around the edges.
Maes’s Account Keeper is a tranquil scene, invested in the details of wood and plaster, crockery and curling paper. It says something about the dignity of household work, and of accounting in particular. It speaks of the dedication it required, the time and devotion to be given to the task. Of an activity worth pursuing to the point of exhaustion. While the woman’s clothing is that of a solid, not a wealthy, householder, three separate ledgers would be a lot for a merely domestic set of accounts. The map on the wall behind her seems a clear hint that her ledgers dealt with trade beyond the borders of the Netherlands: perhaps far beyond, to the ends of the world she knew.
Did the artist intend to moralise about the woman and her labours? The picture has points in common with traditional depictions of avarice or worldliness: the prominent scatter of coins; the prominent image of, literally, the world. It would not take much to turn it into a depiction of a miser in a counting house: the resulting accounts book might look almost identical, but it would be designed to provoke a rather different response and of course tell a rather different story about what counting and the practices derived from it do to people.
Yet this woman is not a miser, and the fact that she has fallen asleep makes her look just as much like an emblem of melancholy, perhaps even of sloth. The ledgers are about to fall to the floor, the orderly scene to collapse (the woman to wake, disturbed by the crash). It was Maes’s style to look on such things with a gently humorous eye: his other pictures of people asleep invite a laugh or at least a wry smile, as dreamers have their pockets picked or risk a scolding for neglecting their chores. Here, Juno herself – the guardian of goods and wealth – also seems to have nodded off, echoing the sleepiness of the account keeper, and hinting that matters are not as well stewarded as they seem. And the world map, the sign of the woman’s ambitions and international connections, is half a reproduction of contemporary maps, half a fantasy, embellished with fantastic beasts copied from maps of the stars.
Keeping accounts – writing numbers down – always comes with a tinge of anxiety that the stability and solvency they record might one day collapse. It always has the character of an island of order and rule, threatened on every side by chaos. It was the character of the Renaissance and the Enlightenment to cultivate and expand those islands of order, bringing more and more aspects of the world under the purview of numbers, tables and facts. But a glimpse of chaos often remains at the edges.
Caroline Molesworth: Counting the weather
Monday, 1 January 1825. Cobham, Surrey. After a night of wind and rain, it is a mild day for the time of year, with the thermometer in the vestibule standing at nearly twelve degrees by nine in the morning. Quantities of furze are in bloom. Thirty-year-old Caroline Molesworth takes a clean, bound notebook and writes the first of her year’s series of weather observations.
What could be more chaotic than the weather? Yet what more tempting for the project of gathering data, tabulating, averaging and reducing that chaos to order?
One of the uses of the Arabic numerals, from a very early stage, had been the making of tables and lists: activities which of course predated the numerals themselves and had appeared in – for instance – astronomical work in ancient Mesopotamia. Lists of goods, their quantities and prices; lists of observed phenomena such as the positions of moon and planets; lists of calculated quantities such as trigonometrical ratios or predictions of planetary positions. In terms of sheer quantity, astronomical tables of the ‘Toledan’ family probably account for the majority of written number symbols in later medieval Europe. The compactness of the Arabic numerals was a help in these contexts, and their place-value feature perhaps did something to facilitate perusing the data once it was tabulated: if all the units line up vertically, all the tens will line up as well, and so will all the hundreds, making the numbers easier to read, their patterns easier to spot at a glance.
Astronomical tables began to appear in print in the later fifteenth century, and they were quickly accompanied by other kinds of printed tables: calendars, arithmetical ready reckoners, tables to work out the interest due on loans, tables to convert weights and measures from one system to another. The printed almanac became a best-selling forum for simple printed lists of all such types, typically combining a calendar with astronomical predictions in numerical form while also providing useful information of the ready-reckoner kind: rates of interest, the conversion of currency, the equivalence of local and foreign weights and measures. Johannes Gutenberg himself printed an almanac, and Europe and North America saw millions, even tens of millions printed during the long height of their popularity through the eighteenth and nineteenth centuries.
Almanacs and astronomical tables of this sort generally contained, in the main, predictions based on theory. But tables of data as actually observed also acquired a new range and visibility in the world of print, contributing to the long rise of a statistical mindset in European and North American populations through the eighteenth century and beyond. Francis Bacon, to whom modern empirical science looked as founder, had urged the collecting and tabulating of observations – the gathering of facts – as a key activity in the creation of knowledge: effectively as a way of understanding the world in its own right. Under the impetus of scientific societies like the Royal Society of London from the later seventeenth century, such harvesting of facts became increasingly widespread, a favoured activity of amateurs wishing to contribute their mite to the store of knowledge. Many of the facts thus gathered were – or could be made – numerical, the outcomes of counting or measuring the natural world; their publication in many cases amounted to tables of number symbols. Tables of mortality, for instance: the numbers of people dying each week from various causes. Tables of population, of national wealth, of government spending. Tables of patients successfully or unsuccessfully treated, of success and failure in controlled experiments.
Indeed, counting successes and failures in experimental trials was a crucial step in the development of the idea that by observing the frequency of events and outcomes you can make reliable predictions about what will happen in the future: statistical inference, in other words, one of the foundations of modern science. Enumerating events in this sense was surely the most important innovation the Enlightenment brought to counting.
Weather predictions, for example, had long appeared in printed almanacs. Weather observation was promoted by the learned societies and became a widespread enthusiasm from the late seventeenth century, a form of what would now be called citizen science. During the eighteenth and nineteenth centuries, weather journals were kept across Europe, from Ireland to Portugal to Czechoslovakia, in China and Japan, around the USA and the Caribbean, in New Zealand and Australia. Their authors included clerics and schoolteachers, merchants, landowners, physicians and gardeners, whose motivations ranged from the study of climate and its effects on human health to anxiety about crop performance and consistency in planting and harvesting times.
By the 1720s, the Royal Society alone was receiving dozens of weather journals from around Britain, Europe and North America, to the point that there was more data to hand than could be either printed or synthesised, and many remained unpublished and unused in the Society’s archive. Other British publications such as the Gentleman’s Magazine carried accounts of the weather from various contributors, and the tradition was taken up by local societies of natural history who maintained it well into the nineteenth century. There were even book-length publications of the weather records of particular observers or locations.
The unsystematic character of both observations and publications became a matter of comment, and institutions occasionally attempted to impose more order and routine on the collecting of weather data. Robert Hooke, a founding fellow of the Royal Society, had published a specimen format for weather journals as early as 1667. Enterprising printers offered blank weather-report forms for sale. A favoured model was the ship’s log, which was subject – at least in national navies – to a literally military discipline and typically recorded a consistent set of information including eventually the air’s temperature and pressure as well as more general observations, generally at regular times of day and night.
Caroline Molesworth, born in England in 1794, was descended both from the Baronets of Pencarrow and from French immigrants, and after a childhood spent in Cornwall and London she moved with her mother to Cobham Lodge, in Surrey. There, in October 1823, she began the series of weather observations she would continue for the rest of her life. She collected and cultivated rare plants, and one of her reasons for an interest in the weather was its effect on her garden.
Molesworth acquired – perhaps to some degree sought – a reputation for benign eccentricity: ‘brusqueness and originality’, in the words of one commentator, as well as ‘good sense and feeling’. She retained for the rest of her life the style of dress current around 1800. ‘Very kind to the poor and generous to her relatives’, she was described by those who knew her well as a ‘most entertaining companion’.
She acquired various instruments to aid her observations of the weather. Outdoor thermometers for the maximum and minimum temperatures, and two more thermometers for different positions inside the house. A rain gauge made in London, which amounted to a bottle sunk in the ground with a funnel in its top. A barometer by the well-known instrument maker George Adams. She also had a ‘storm glass’: a bubble of glass containing air and water, whose appearance responded to both temperature and pressure. The reputation of this scientific toy as an instrument for serious observation was never high, and in April 1843 Molesworth silently stopped reporting its behaviour in her weather journal. The house must also have had a wind-vane, but nowhere in her observations did she say so, merely reporting the direction of the wind (never its speed). For some, this collection of instruments would have been an object of pride, even of conspicuous consumption: but for Molesworth they were instruments of use far more than of display.
Her journals became slightly battered over their years of service, with covers of marbled board and yellowed pages occasionally spotted with ink or – perhaps – rainwater. Superficially, they looked very like a set of household accounts. The pages were ruled in red and blue, and Molesworth recorded up to nineteen columns of data each day, filling a two-page spread twice a month: the day and date, the times of sunrise and sunset, the phase of the moon and the hour(s) of observation. Temperatures at various locations, atmospheric pressure, cloud cover, wind direction, inches of rainfall, general observations about the weather, about the plants and animals in her garden.
The discipline of daily and twice-daily observations was evidently congenial to Molesworth. In a sense, it became part of her persona. Where some diarists defined themselves through their acute study of human nature, of political affairs or of their own minds and bodies, she used her neatly ruled pages to record a self that was pure scientific observer. Travel, illness or accident she reported only when they affected the series of weather records.
A typical page from Caroline Molesworth’s weather diary.
