A Note on Symbols - The Great Invention: The Story of GDP and the Making and Unmaking of the Modern World - Ehsan Masood

The Great Invention: The Story of GDP and the Making and Unmaking of the Modern World - Ehsan Masood (2016)

The End of the Word. A Note on Symbols

GDP comprises six symbols. It looks like a formula from mathematics. It has the elegance and the aura of being an equation, yet it isn’t one. As we saw in Chapter 2, the idea didn’t even need to be expressed in this way. Indeed, it wasn’t, not by Simon Kuznets, not by John Maynard Keynes. National income accounting was represented by both men as a table with different columns for different kinds of spending. The symbols came later.

Had GDP remained expressed as a table, with each form of spending confined to its own column, I do sometimes wonder whether the idea of running the world’s economies through a single number would ever have taken off. That it did owes as much to the trend across the humanities and social sciences to adopt math-like notation, a way for such ideas to appear more “scientific.” The real language of science—hypothesis, experimentation, testing—was not so much the objective as was scientific notation.

And as we know, such use of specious mathematical notation has contributed to some of the most dangerous ideas in recent decades. One of these is the infamous Gaussian copula, a financial engineering formula widely used by banks and their regulators to predict the level of mortgage default. The formula was popular among finance professionals, as they believed it would enable them to predict a borrower’s creditworthiness without having to use actual financials. But until the crash of 2008, no one questioned the soundness or otherwise of the underlying data on which it was based.1

In the pre-Gaussian days a bank trying to establish whether a mortgage applicant was creditworthy would look at the applicant’s financial history. The bank manager would see what the applicant had borrowed and find out if he or she had defaulted in the past. The bank would know something about the applicant—his or her job or business, perhaps more. Only then would the bank know if it was safe to hand out a large loan.

Now, armed with the formula, banks happily lent money to people in no position to repay their loans. They did so, reassured that the Gaussian copula was telling them the chances of default would be slim. By the end of 2001 the market in mortgage-backed securities, known as credit default swaps, was $920 billion. By the end of 2007 it had shot to $62 trillion. When the following year account holders did start to default on their loans, the banks lost trillions of dollars and governments had to step in to bail them out in what we now know to have been the globe’s most serious financial crisis since the 1930s.


The use of x and y to denote unknown quantities is relatively recent, at least as deep history goes. You won’t have been taught this in school mathematics, but until the 1500s algebra was written down using words.2

Historians say that the trend for writers to use symbols for “plus” and “minus” began from around 1400. Symbols such as those used for “equals,” multiplication, and division found use between 1525 and 1687 with the publication of Isaac Newton’s Principia. Interestingly, many of the symbols we now use in everyday arithmetic were conceived and adopted in this relatively short 150-year spurt.3

That isn’t the full story, however, as it doesn’t explain how symbols became mainstream in writing, teaching, and research in the social sciences and humanities. For that we need to fast-forward another century and dive briefly into the world of university exams.

These days, we know that exams, whether in schools or universities, involve large groups of candidates, sitting hunched over desks, rapidly writing essays or, more often, completing multiple-choice questions under timed conditions under the watchful eye of a teacher. And yet this is not how students used to be assessed. Up until the early 1800s, there were few if any exams of the kind we know today. Instead, students intending to graduate from universities had to pass an oral test, known as viva voce, or “living voice.”

The viva voce consisted of a student standing in front of a class of peers and being questioned by his professors. The purpose of the test was to examine the students’ ability to reason, to construct a sound argument in support of an idea. Students were also assessed on their confidence as public speakers. Examiners would come prepared to attack a candidate’s learning, often using dubious arguments, and successful graduates had to confidently defend themselves.

There are undoubtedly many reasons why students would have been assessed in this way. One reason would have been because pen, ink, and paper were expensive and not yet being produced in enough quantities to bring prices down. Perhaps a more important reason was because of differing expectations of higher education. A university education in most countries until the 1800s was almost exclusively for the elite. If you were lucky enough to bag a place at a university, this was either in preparation for a life spent governing lesser beings in politics or in the church or to build the kind of elite network for which elite universities are still known.

Whether your destiny was to become a country parson or a member of Parliament, there was little point (then) in testing your ability to reel off a list of factoids. Examinations had to be a different kind of test, of knowledge and wit; of public speaking; of the ability to construct and defend an argument, think critically, and think on one’s feet. The viva voce was applied across the range of subjects, from theology to mathematics.

The viva voce method undoubtedly benefited those candidates who could handle and learn from an experience where their ideas would be pulled apart in public. And because the entire exercise took place in public, with other students in the audience, it benefited less able students too, as they could watch and learn from their better-performing peers.

With ever larger numbers of students entering universities, professors were demanding a more industrial-scale system. The great virtue of the modern examination is that in one three-hour sitting, hundreds of students can be assessed all at once. But there were implications for the change, and not all have been positive.

On the plus side in mathematics, for example, a largely written test meant an acceleration of the use of written symbols and a more harmonized syllabus. But on the minus side, written exams also meant that students would be assessed more on their memory and recall and less on public speaking, verbal reasoning, and being able to think quickly on their feet. A written exam was clearly testing different things than an oral one.

Equally, the move toward assessing mathematics and science with pen-and-paper exams favored a different type of learner. Someone with strong powers of recall, someone good at taking an accounting approach to mathematics, someone better suited to linear explanations, would do well. Candidates better at taking risks, comfortable with argument, able to hold different points of view at the same time, able to think more holistically, more systemically, would struggle.

Keynes as we have seen was deeply skeptical of the over-mathematization of economics. So concerned was he that, though seriously ill and with weeks to live, he took time out to plead with the Royal Statistical Society not to award a new qualification in statistics, fearing that this would institutionalize what to him was an inferior approach to making decisions.4

In recent years, a few eminent academics such as the economist Paul Krugman5 and the ecologist E. O. Wilson6 have warned against the over-mathematization of their respective fields. But they remain a minority and to some extent marginal voices. Given the explosion of data and the tools with which to manipulate data, the trend is completely in the other direction.

Our world today is what Keynes feared it would become. Most scientists and economists rely heavily on numerical and statistical models. Pick a country—any country in the world—and its economy, as well as its financial systems, is likewise built on such models. Some of these models, such as GDP, are simplistic. Others, such as those used in banking, can be far more complex. In either case, there are few practitioners who now have the ability to explain, rationalize, or critique using non-mathematical language what they do and why they do it. Of those who can, many are unable to do so using language that all of us can understand.

This is dangerous. It is dangerous for decision making and dangerous for democracy. It is well known that policy made using information accessible only to closed groups of people is often of a poorer quality compared with policy made in an open and consultative way. Moreover, if fewer and fewer of us really understand the workings of policies that affect our lives, there can be little doubt that we will have much less faith and much less trust in the process by which those decisions are made.

When Keynes died peacefully on Easter Sunday in 1946, the world lost a powerful and influential critic of linear thinking and specious symbols. It is time for a new generation to return to his cause and to win it.