How Numbers Came To Rule The World

Jane Gleeson-White has worked as an editor, writer and reviewer in Sydney and London since completing her degrees in English and Australian literature, and economics, at the University of Sydney in 1987. She also worked as a student at the Peggy Guggenheim Museum in Venice, where she studied Byzantine, early Renaissance and modern art. Her first book, Classics, was published in 2005. On Tuesday 6 March 2012, Jane Gleeson White addressed The Sydney Institute on her recent book Double Entry: How the merchants of Venice shaped the modern world [Allen & Unwin].

HOW NUMBERS CAME TO RULE THE WORLD

JANE GLEESON WHITE

This evening I’m going to be talking about numbers and how they came to rule the world. So what exactly do I mean by this?

Briefly, the numbers I mean are the statistics that we generate with our national accounts, such as GDP, and the figures that we generate through our company accounts, such as annual profit. These numbers now govern the decisions we make at every level of our societies and increasingly across every sphere of our lives.

So powerful is the single GDP figure of the United States that a complex ritual has evolved around its announcement, rivalling in mystique and secrecy the selection and announcement of a new Catholic pope. Twelve times a year, chief  US statistician Steven Landefeld and his team lock themselves up in Washington without phones and the internet, draw the curtains and carry out a task refined over 50 years. They have one goal in mind: to arrive at a single number through the convergence of some 10,000 data streams from recent economic activity in the United States, including harvests, construction, manufacturers’ shipments and retail sales. So powerful is this figure that no one must speak it out loud before its official revelation at 8.30am the next morning. Why? Because this single number is capable of rocking the world. In the words of Alan Greenspan, “its premature unveiling [would] roil the global financial markets”.

And so powerful are the numbers generated by the accounts of corporations that they can cast the deciding vote between life and death. A cost benefit analysis made by the Ford Motor Company in 1977 weighed the relative merits of adding or not adding a safety device to its new Pinto car. This entailed assessing the “cost of safety parts versus the cost of lives lost”, where the “cost of lives lost” is the dollar value of men, women and children potentially killed in the unsafe vehicles. Ford’s rigorous numerical analysis reached a rather staggering conclusion – but, in the terms of the logic of cost-benefit analysis, one that was watertight.

But we’ll come back to Ford’s decision later – because the story of how I became interested in these numbers has nothing to do with numbers at all. And everything to do with falling in love at first sight with one of the most beautiful cities in the world: Venice. I lived in Venice for three months one summer as an intern at the Peggy Guggenheim Collection, where I was inducted into the mysteries and symbolic language of Italian Renaissance painting.

And so it was with some astonishment that the following year I heard my accounting lecturer utter the word Venice, a city I would once have considered to be the polar opposite of accounting.

Until that moment, I’d believed the attraction of accounting began and ended with jokes like: “Why did the accountant cross the road? To bore people on the other side.”

But it seemed it had another attraction: a relationship with my favourite city. From that moment, my lecturer had my full attention. He talked about a landmark treatise on bookkeeping that had been published in Renaissance Venice. This so seized my imagination that I decided then and there to look further into this unlikely affair between Venice and accounting.

I found their relationship went deep. Most importantly, I discovered that what had so closely bonded Venice and accounting in the annals of history was a Franciscan monk called Fra Luca Pacioli.

I then set my sights on this Renaissance monk, who’s known today – if he’s known at all – as the Father of Accounting. As I researched I began to feel that Pacioli’s life was the ultimate exemplar of Forrest Gump’s “life is a box of chocolates. You never know what you’re gonna get”.

Except that unlike most boxes of chocolates, Pacioli’s life was the metaphorical chocolate box of my dreams. I found everything in it irresistible. It contained Venice, Florence, Milan, art, commerce, religious intrigue, sexual innuendo. It included the original Renaissance man, Leon Battista Alberti, who was not only an intellectual giant but an athlete possessed of such physical prowess that he could leap over a horse from standing position with his legs tied.

It also included the Renaissance artist-mathematicians Piero della Francesca and Albrecht Durer and the new science of perspective painting. It included a communications revolution, magic, lost manuscripts, the game of chess – and, for me, the most irresistible of all: Leonardo da Vinci and mathematics.

It turned out that Luca Pacioli was Leonardo da Vinci’s teacher. The Franciscan monk taught maths to Leonardo when they were intimately acquainted in Milan in the 1490s – the time when Leonardo was painting his masterpiece, the Last Supper, whose construction required considerable mathematical training.

This little known monk, whose birth in the 1440s went unrecorded, was one of the most celebrated mathematicians of the Renaissance. In 1494 he published a gigantic encyclopaedia in Venice called Summa di arithmetica, geometria, proportione et proportionalità, or “Everything about Arithmetic, Geometry, Proportion and Proportionality”. If it were published today it would run to 1,500 pages.

As its name and size imply, the Summa contained the entire body of mathematics known to the Mediterranean of the day, which was: the recently rediscovered work of the ancient Greeks, the Latin mathematics of the medieval schoolmen and the advances of the Arabs. Importantly for my story, it also contained Pacioli’s 27-page treatise on Venetian double-entry bookkeeping.

I found that Pacioli had lived at a watershed in European mathematics, the enormity of which I think is lost to us today because its major consequence, namely the use of Hindu-Arabic mathematics, has since become the norm. It is here that the story of the rise of numbers really begins.

In the fifteenth century, Italian mathematics absorbed two significant new elements: Hindu-Arabic arithmetic and ancient Greek mathematics. And, thanks to Luca Pacioli’s rare combination of talents and training, the same century also saw the merging of two streams of mathematics which had been separated since the sixth century BC: the philosophical speculative mathematics of Pythagoras based on geometry, and the commercial arithmetic used by merchants.

According to the Greek historian Herodotus, geometry originated in Egypt and was associated with the land surveying required for the annual flooding of the Nile, hence “geo-metry” from the Greek for “earth” and “measure”. Commercial arithmetic was developed by the Phoenicians, the great merchants of the early Mediterranean. Ironically, the man who elevated geometry above the mundane needs of merchants to the realm of metaphysics was the son of a Phoenician merchant – Pythagoras.

From Pythagoras onwards, maths was split into two broad streams: the arithmetic used by merchants in their daily business transactions, and the numbers used by philosophers to express the secret harmonies of the universe.

After the fall of Rome and the rise of the Christian church, maths languished in medieval Europe. Its development was held back by the church, whose view is best expressed in this comment attributed to Augustine:

The good Christian should beware of mathematics and all those who make empty prophecies. The danger already exists that mathematicians have made a covenant with the devil to darken the spirit and confine man to the bonds of hell.

But, during the same period, maths blossomed in the Arab world. By 1200, the Arabs were the most sophisticated mathematicians of the Mediterranean, having adopted and developed the numerals, arithmetic and algebra of India, hence our name Hindu-Arabic numerals.

This new maths from the east was introduced to Europe through Muslim Spain, but the first real breakthrough in its use came with Leonardo da Pisa, whom we know today as Fibonacci. Leonardo da Pisa grew up in northern Africa, where he learnt maths from Arab merchants in the local bazaars. When he returned to Italy he wrote an influential work on Arabic mathematics called Liber abaci, which appeared in 1202.

Fibonacci’s maths was rejected by the church – for example, when English philosopher Francis Bacon attempted to promote it he was charged with magic and condemned to life imprisonment – but it found a ready audience among the merchants of Italy, where it became known as abbaco mathematics.

This new abbaco maths made possible what we now take for granted: the adding, subtracting, multiplying and dividing of Hindu-Arabic numerals on paper with a pen. This system was inscrutable to most Europeans at the time, who used counters on a board to calculate a sum and then recorded the result in Roman numerals, leaving no written trace of the calculation made.

An alternate vernacular education system based on Fibonacci developed alongside the Latin-based monastery schools of Italy. Known as abbaco schools, they taught Hindu-Arabic maths and the rules for solving common commercial problems to the sons of merchants and artisans.

While abbaco maths was transforming the way generations of Italian merchants and artisans understood the mechanics of commerce and the material world, in the rarefied atmosphere of the European universities, mathematical techniques were regarded mostly as fictions, not considered to be a language for use in daily life.

Almost uniquely in Italy, Luca Pacioli was fluent in both abbaco and university mathematics. As a boy he learnt abbaco maths from a local merchant in his home town of Sansepolcro. This perfectly equipped him to seek his fortune in Venice, the financial and commercial centre of the fifteenth century. Pacioli travelled to Venice, aged 19, to work as an abbaco teacher for the sons of a wealthy fur merchant – and it was there that he learnt bookkeeping Venetian style and studied university mathematics at its famous Scuola di Rialto.

At the age of 49, after three decades travelling through Italy teaching mathematics, Luca Pacioli put his rare mathematical knowledge to good use. He returned to Venice, by then a vibrant centre of printing, to publish the culmination of his life’s work so far, the Summa.

Pacioli’s encyclopaedia united the two streams of mathematics which had been separated since Pythagoras’s day – and the mix would prove epoch-changing. It spurred the gradual rise of mathematics to its eventual replacement of Latin as the lingua franca of Europe and ushered in a new era: the Age of Science.

The Summa made two immense contributions to the scientific and commercial life of Europe: it was the first printed book to deal with Hindu-Arabic arithmetic and its offshoot, algebra, and it contained the first printed treatise on Venetian bookkeeping. It thus bequeathed to Europe the two tools that rule the modern world: Hindu-Arabic numbers and double-entry bookkeeping.

Pacioli became famous in his day for his knowledge of mathematics and his passion for disseminating its secrets via the printing press. But his lasting fame would rest on his 27-page bookkeeping treatise called Particulars of Reckonings and Writings.

As with Hindu-Arabic maths, the Venetian bookkeeping system Pacioli codified is so natural to our modern way of thinking that we take it for granted. But in 1494 it was exceptional – and in his treatise Pacioli recommended it above all others. In their system, Venetian merchants separated debits and credits in their ledgers, dividing them into two columns. As Pacioli says, this is the most important thing to note in Venetian bookkeeping: “All the creditors must appear in the Ledger at the right hand side, and all the debtors at the left. All entries made in the Ledger have to be double entries – that is, if you make one creditor, you must make someone debtor.” Pacioli also makes it clear that the purpose of every business was to make a lawful and reasonable profit, which can be calculated with Venetian bookkeeping.

Pacioli was the first to codify Venetian bookkeeping – and because he used the printing press to record and disseminate this important commercial information, it was his version of Italian bookkeeping that spread across Europe during the next two centuries, through Germany to Holland, England and then to America.

By the eighteenth century, double-entry bookkeeping had become so pervasive that it had spread beyond the realm of business and commerce and into European culture more generally, as we can see in the literature of the time. Daniel Defoe famously applied it in his novel Robinson Crusoe, published in 1719, when the shipwrecked Crusoe uses double entry to assess his life, drawing up his “State of Affairs” and stating “very impartially, like Debtor and Creditor, the Comforts I’d enjoyed, against the Miseries I suffered”.

Goethe refers to double-entry bookkeeping in his novel Wilhelm Meister’s Apprenticeship when his character Werner extols the spirit of “a genuine merchant” and asks: “What advantages does he derive from the system of bookkeeping by double entry? It is among the finest inventions of the human mind.”

Goethe was writing in the 1790s, a time when Europe was undergoing a massive transformation. Italian bookkeeping would be swept up in the energy of this new industrial age and be likewise transformed. With the flourishing of a new form of business organisation, the joint stock company, bookkeeping morphed into a brand new profession: accounting.

The financing and management of the vast investments required to build railways during the nineteenth century brought new issues of accounting and accountability. Most other successful industries of the time – pottery, cotton, wool, iron – had started small and grown through the reinvestment of their own profits. But in the case of railways this was not possible. Huge amounts of capital expenditure were required at the outset and they were raised not through profits but from private investors on stock exchanges and managed by joint stock companies.

Repeated cases of fraud and corporate failure put pressure on the British government to protect creditors and investors on the new stock markets. The British parliament did eventually force companies to keep publicly available financial statements based on reliable accounting records, starting with the Joint Stock Companies Act of 1844. By the 1860s accountants were legally required at every phase of a company’s life: at its formation, during its operation and at its liquidation. Needless to say, their numbers increased accordingly. In 1811 there were 24 accounting firms listed in the London directories; by 1883 there were 840.

In 1800, financial statements were an incidental product of an enterprise’s bookkeeping system. By 1900, and increasingly thereafter, annual financial statements had become bookkeeping’s raison d’etre.

Venetian bookkeeping proved to be the perfect mechanism for generating these financial statements. Luca Pacioli’s double entry with its Hindu-Arabic numerals could accurately record capital and income as required by law and investors, it could distinguish between private expenses and corporate costs, and it could produce data that helped to evaluate past investment decisions. By 1900, most businesses across the planet were keeping their books in Pacioli’s double entry.

And so double-entry bookkeeping and the numbers it generates became essential to the workings of the modern corporation. In the twentieth century they became equally essential to the machinery of the modern nation.

With the crash of the New York Stock Exchange in 1929, the laissez-faire principles that had previously guided government approaches to national economic affairs suddenly lost their lustre. Over the next four years, in the United States 11,000 banks failed, production collapsed by more than half and unemployment rose to nearly half the workforce.

To guide their policy responses to the crisis, the administrations of Herbert Hoover and Franklin D Roosevelt commissioned Russian-born economist Simon Kuznets to develop comprehensive estimates of the income of the United States. In 1934 the British economist John Maynard Keynes went to America to see Roosevelt’s New Deal in action. In Washington he said: “Here, not in Moscow, is the economic laboratory of the world.”

This signified a momentous change in both government practice and economic theory, prompted by the Depression. If Roosevelt’s response to the Depression was the New Deal, the first full-scale, systematic government intervention in a capitalist market economy, then Keynes’ response was his “theory of effective demand”, which provided a theoretical basis for the measurement of national income, consumption, investment and savings.

Both Roosevelt’s program and Keynes’ theory entailed the construction of national accounting systems, a massive undertaking that was carried out using the principles of double-entry bookkeeping. The first US national accounts were made during the Depression, the first British accounts during Second World War.

But Keynes was suspicious of statistics and considered these quantitative expressions of the national economy to be temporary, emergency measures demanded by the times. The British Chancellor expressed the same view, stressing that they were an exceptional measure made necessary by war.

But, instead, these national accounts became an annual event in the United Stated and Britain. And, following the war, national accounts were constructed in countries across Europe as part of the framework of the Marshall Plan. Under the aegis of the newly created United Nations, standardised forms of national accounts were compiled and have since the 1950s been implemented in most nations on earth.

GDP measures are now used by governments to calculate budgets and assess the impact of fiscal and monetary policy on an economy. They are used by politicians in campaign strategies, and by corporations for investments decisions and Wall Street takeovers and they have a profound influence on markets. GDP, this one miraculous figure, apparently “compresses the immensity of a national economy into a single data point of surpassing density” – and governments and many people believe that only this one statistic “can really show whether things are getting better or getting worse”.

But the GDP was not designed for this purpose. It was not conceived to be the primary gauge of the economic health of a nation, it was not created to be a key tool for policymakers and investors, it was not born to govern the global financial markets. As a measure of national wellbeing, the GDP is a deeply flawed rule. Simon Kuznets himself warned of the limitations of GDP measures, especially their exclusion of household production and other non-market activity, as well as their failure to count the many costs of economic development. Kuznets’s concerns have been reiterated ever since, most famously by Senator Robert Kennedy in a speech he gave in 1968 just months before his assassination. He said:

Too much and for too long, we seemed to have surrendered personal excellence and community values in the mere accumulation of material things. Our Gross National Product, now, is over $800 billion a year, but that Gross National Product – if we judge the United States of America by that – that Gross National Product counts air pollution and cigarette advertising, and ambulances to clear our highways of carnage. It counts special locks for our doors and the jails for the people who break them. It counts the destruction of the redwood and the loss of our natural wonder in chaotic sprawl. It counts napalm and counts nuclear warheads and armored cars for the police to fight the riots in our cities. It counts Whitman’s rifle and Speck’s knife, and the television programs which glorify violence in order to sell toys to our children.

Yet the Gross National Product does not allow for the health of our children, the quality of their education or the joy of their play. It does not include the beauty of our poetry or the strength of our marriages, the intelligence of our public debate or the integrity of our public officials. It measures neither our wit nor our courage, neither our wisdom nor our learning, neither our compassion nor our devotion to our country, it measures everything, in short, except that which makes life worthwhile.

It is not just the numbers generated by national accounts which are flawed. They’ve also proven fallible in the case of corporate accounts, most spectacularly in the case of Enron, but more recently and closer to home in the demise of ABC Learning. There two sets of auditors found two completely opposing stories in the company accounts. One of impending disaster, the other of a viable business. The third party brought in to arbitrate could fault neither of the radically different conclusions.

Luca Pacioli’s double entry has morphed into an exacting global calculus and created a culture that makes possible reasoning which generates ruthless decisions such as the one made by the Ford Motor Company. Which brings us back to its Pinto dilemma. So, what did the Ford Motor Company decide? An internal company memorandum estimated that “if the Pinto was sold without the $11 safety feature, 2,100 cars would burn every year, 180 people would be hurt but survive, and another 180 would burn to death”. The calculus revealed that the money saved by a safer car would be $49.5 million. But the cost would be $137.5 million.

Clearly, the costs of the safety device far exceed its benefits, in numerical terms. And so, naturally, Ford decided not to spend money on the safety feature, based on the inexorable logic of these two simple numerical equations. According to the journalist who broke the story, Mark Dowie, in the six years from the introduction of the Pinto to 1977 when his analysis of the case was published, at least 500 people burnt to death in Pinto crashes.

And so I ask you: do you believe the numbers denominated in money that we’ve allowed to rule our lives are really our best possible arbiters? These same numbers that tell us to risk people dying rather than installing a safety device on a car? That tell us to cut down a forest of Redwood rather than leaving it alive?

I’ll leave you with John Maynard Keynes, who made a radical remark in 1933. He was in Ireland, so perhaps whiskey or leprechauns had loosened his tongue, but in that year Keynes spoke the following truth: “Once we allow ourselves to be disobedient to the test of an accountant’s profit, we have begun to change our civilisation.”

So, merchants of Venice I can give you. Gnomes of Zurich I cannot offer you, but I hope the monk of Sansepolcro will do in their place. It is he and the merchants of Venice who have given us the tools that rule the modern world.