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.

National Meteorological Library and Archive C_1825–1832. Open Government Licence v3.0.

The series continued in all for over forty years. After about 1850, though, the gaps due to illness became more frequent, and other hands than Molesworth’s filled in an increasing proportion of the entries. The latter volumes of the series gradually petered out, the last full observation being made early in October 1867. A final, terse note came on Wednesday, 9 October 1867: ‘rain’.

Molesworth’s tables of data and of number symbols were the outcome of a variety of processes: observation, measurement, counting and calculation. At the end of each year, she prepared summaries which relied particularly on both computation and counting. At the fullest, there was a summary for each month of the year, for which she counted the number of days on which rain had fallen and the number of days on which the wind had stood in each of eight directions, as well as computing the month’s total rainfall and the mean and ranges for the barometer and three thermometers. There was also a summary for each whole year, for which Molesworth provided a similar set of totals and means. On occasion she even prepared multi-year summaries. Francis Bacon would have been proud.

Molesworth did not just collect data; she also corresponded with a number of other weather observers and meteorologists, owned and read books on the subject, and published in periodicals some of her summaries of the weather of Cobham. On her death, her collection of dried plants was presented to the herbarium at the Royal Gardens at Kew, and her weather diaries were presented, at her request, to the Meteorological Society in London. In 1880, a volume of summaries extracted from them was published. Their editor picked up on the statistical side of the work, writing that

Miss Molesworth’s labours will not have been … useless if they add anything to the amount of information which we may look forward to from the careful observations now being carried on in the same field of research, promising – it is not too much to say – to be of infinite value to the country agriculturally, by showing the bearing of weather influences on the growth of our food crops.

Caroline Molesworth’s work illustrated both the pleasures and the frustrations of systematically observing the natural world. On numerous occasions, observations had to be reported as missing or questionable because of breakages or other difficulties among her instruments. Every trip away from home occasioned a gap in the series of observations that could never be made up or substituted for. And the very process of dividing winds into eight points of the compass, rounding temperatures and pressures to the nearest whole number, and so on, emphasised that turning observations into numbers must always involve simplification and, therefore, loss.

The process of aggregation at the end of each year possessed something of the same ambiguity. On the one hand, it promised to transform a series of isolated observations into something bigger; a series of atoms into a coherent picture. On the other hand, though, the summing and averaging effected a real loss of texture and granularity compared with the original observations. And even on the scale of a whole year, the result could still feel like a series of details rather than a description of a climate. In 1827, Caroline Molesworth counted one hundred and forty-one days with rain or snow or frost, twenty-three of them in December; forty-two days of northerly wind, eleven of them in September. There were fifty-six days of southerly wind, spread across every month of the year. The most common wind over the year was from the northwest … It fell to her posthumous editor to note certain relationships between the dates at which plants flowered and variations of temperature and rainfall from year to year. Perhaps it would not have been possible to turn the numbers into a bigger picture during Molesworth’s lifetime.

By the nineteenth century, and still more by the twentieth, Arabic numerals were everywhere, carried to most of the countries in the world, their family tree now dense with branches. Generations of textbooks along the lines of Bhaskara’s and Al-Khwarizmi’s presented ‘numeration’ as the reading, writing and visualising of Arabic numerals on dust boards, blackboards, parchment or paper. It had become common in ordinary speech and writing to say ‘numbers’ and mean the Arabic number symbols, as though the two were the same: as though there were no conceivable or at least worthwhile other way of representing numbers. (The neat way to expose the paradox here is to observe that many people would say 2,543 is a four-digit number, but no one would say Mary is a four-letter girl. Arabic numerals become identified with the thing they represent far more readily than words do.)

Meanwhile, the number concept itself was being steadily expanded beyond the ‘natural’ numbers possible with beads, fingers or tallies. Fractions and ratios had been written down in the ancient Near East; irrational numbers like certain square roots – which cannot be expressed by any fraction – were already of interest in ancient Greece. The many writers of ciphering books studied negative numbers, and Molesworth used them to record temperatures. In the context of mathematical research, ‘real’, ‘imaginary’ and ‘complex’ numbers would be defined during the nineteenth century, and in the twentieth, ‘hyperreal’ and ‘surreal’ numbers too. Much of this was supported by the power and flexibility of the Arabic number symbols, steadily extended using negative signs, decimal points and other devices.

This may seem like an end point; it may seem, even, as though the rise of the Arabic numerals is the story of counting. But it is in reality only one branch among many. Writing numbers down as symbols is only one of many ways of counting; and indeed the distinctive structure of the Arabic numerals is only one of several ways a set of number symbols can be organised.

INTERLUDE

Number symbols

As the other examples in this book illustrate, counting symbols have displayed a range of different systems at different times and places. The basic choice is between having one symbol repeated several times (|, ||, ||| …) and having a set of different symbols to symbolise the different numbers (α, β, γ, …). The first system is that of the simplest tallies, whether ancient or modern; the second that by which the books of Homer’s Iliad and Aristotle’s Metaphysics are numbered to this day. But as with counting words – and number symbols very often imitate their structure from the counting words in the language of their first users, albeit frequently with some tidying up – a system with no more structure than this quickly becomes unusable for larger counts.

If a number base is used – say, a special symbol for the number ten – it can be combined with the smaller numbers simply by juxtaposing it: XI meaning ten-and-one, for instance. For multiples of the base, the choice must then be made again, between simply repeating its symbol the required number of times, and adopting a whole series of symbols to denote the different multiples. In Roman numerals, for instance, ten, twenty and thirty may be shown by X, XX and XXX; in Greek by Ι, Κ and Λ. Another alternative is to reuse the original set of number symbols with some sort of modification: a, b, c becoming a', b', c', say, to show that they now mean ten, twenty and thirty. Or, finally, you can make no modification, but rely on the relative position of the symbols to show that some mean units and others mean multiples of the base. This last is the system of the Brahmi numerals that became the dust numerals, the Toledan numerals, and finally the Arabic numerals.

Each of these ways of structuring a system of number symbols has been used over long periods; each is capable of remaining stable over hundreds or even thousands of years: none has in fact any very strong tendency to evolve into – or be replaced by – any of the others. The advantages and disadvantages of different kinds of system depend very much on what you want to use it for. Some are quicker to learn, some quicker to write; some use a smaller set of symbols overall, others tend to represent any given number with a shorter string of symbols. Says Stephen Chrisomalis, historian of number symbols, ‘There is no ideal numerical notation system; rather, each system is shaped by a set of goals that its users and inventors seek to attain, and that they can achieve only by compromising on other factors.’

About a hundred different sets of number symbols have appeared throughout history; from the dawn of writing until about 1500 CE, their number steadily increased. But number symbols – like alphabets – have a marked tendency to be reused by more than one culture; the successful ones have been particularly successful at travelling, perhaps particularly successful as tools for communication between different communities, cultures, languages and places. The cuneiform numbers, the Egyptian demotic and Greek systems, the Roman numerals, and of course the Brahmi numerals all travelled widely, as did many more. The Arabic numerals were eventually carried around the world with – mainly – the European languages and cultures; other systems meanwhile became extinct. In the last five hundred years the number of distinct systems has fallen, on the whole.

As recently as the 1990s, it was not uncommon to hear it suggested that the decimal place-value system effectively represented the end of history as far as number representations, counting and arithmetic were concerned, no significant improvement being likely or even possible. Yet such certainties are no sooner stated than they begin to crumble. There have always been other ways to count, and there will always be other systems of number symbols. And there was an element of chance in the meteoric rise of the Arabic numerals: place-value systems have been invented at other times and places without overrunning the world. For the specific purpose of doing arithmetic in writing, the Arabic numerals have real advantages: but spare a moment to consider how long it takes most children to learn the forty-five addition facts and thirty-six multiplication facts in the base-10 tables, and how long to become fluent at even a limited set of operations on larger numbers: addition, subtraction, multiplication and division. (The extraction of roots, present in many medieval and Renaissance textbooks, seems to have largely dropped out of view in modern classrooms.) How easy it is to make a mistake, after all, despite the vaunted advantages of the system: and what a relief it is nowadays to outsource the whole thing to a calculator. Similar effort devoted to analogous tasks with different ways of representing numbers – the counting board, say – can make them, too, feel efficient and seem natural. Chrisomalis again: ‘We do not stand at the end point of a linear historical sequence, but in the midst of a branching and complex yet patterned and explainable world of written numbers.’

So, not an end point after all; and at most times and places the history of counting has not been written at all, but has involved other ways of keeping track. The drift of the last century has been that way even in the parts of the world dominated by Arabic numerals. In Molesworth’s own lifetime, there came the first hints that the era of performing large tabulations, calculations and even counts by hand, using Arabic numerals on paper, would not last for ever. Machines were beginning to appear that could perform some of those functions automatically, and whose descendants would eventually transform the way humans related to counts, numbers and data. Over the last few decades, the prevalence of number representations in the world has increased exponentially, but the overwhelming majority of them are not Arabic numerals on paper but something quite different: binary representations encoded in electrical impulses.

Another hugely important branch on the tree of counting must surely be the story of physical devices – manual, mechanical and eventually electrical and electronic – that assist with the counting process: the story, in other words, of counting machines. Like the Arabic numerals, they have swept the world, making their story into a global one; but nowhere is their deep history more richly recorded than in East Asia.

6

Machines that count

: Around East Asia

From African roots, the story of counting spread its branches through the Fertile Crescent, Europe and India. East Asia is home to another branch, one that has undergone its own evolution for millennia. Here the number words are also decimal for the most part, as in the large language families further west. Here number symbols are powerfully in play even in some of the earliest extant texts. But here counting also involves a distinctive set of counting devices. Everybody has seen an abacus – the suanpan in Mandarin, the soroban to the Japanese and the jupan to Koreans – whose operators became famous far beyond East Asia for the skill and speed with which they worked.

After the abacus, electrical machines. Right up to the 1950s it was a matter of comment that they worked more slowly than the most skilled abacus operators. But eventually the machines overtook the humans, and it is now in the form of electrical and magnetic signals that most of the world’s counting is done: the binary representations deep inside modern digital devices. This is a global story, with early technical innovations coming from the USA in particular. Today, East Asia is a leader in both the manufacture and the consumer uptake of the products that make the digital revolution.

And before the abacus? Before the abacus, East Asia was home to a different technology for recording and manipulating counts, whose operators also attained astounding dexterity and efficiency. It was in use for centuries, and the patterns it made provided the shapes of the classical Chinese number symbols. That technology was the counting rods.

Hong Gongshou: Counting with rods

Zhili, Qimen district, Huizhou prefecture, China. The fourteenth year of the Chongzhen emperor (1641 CE). Hong Gongshou is being assessed for tax liability.