The Economist | April 1, 1995

[Like most *Economist* articles, this was published anonymously. Well, almost anonymously.]

**A**lthough this newspaper has always been partial to numbers, it has not been as diligent as it could be in the reporting of mathematics. Today, to set this right, we inaugurate a new column on advances in the mathematical arts, named after the great French mathematician Siméon Denis Poisson (1781-1840). These articles will be presented, insofar as possible, in the mathematicians' own words, the better to convey the “divine rigour” of their thought. We begin with an epitome of recent work by Jon C. Chura and Jarat N. Hanouch, research fellows at the Institute of Empirical Mathematics in Boulder, Colorado

**T**HE NEW FIELD of empirical mathematics (EM), a discipline pioneered in the early 1970s by P.G. Somerset and elaborated by V.M. Singh, has already scored some notable successes. Among these are a shortened procedure for the renormalisation of transintegers and refinement of Haberlein's encryption algorithm. EM, as its name suggests, seeks advances in mathematical theory by means of counting things. As might be expected, the development of computer technology has allowed far more rapid and comprehensive counting of things than previously possible.

It is the belief of the present authors that our work in progress* may constitute EM's most important advance to date. In the course of conducting routine surveys of things counted so far, we discovered that the number of things tended generally to increase more than it decreased. Among the things that proliferated were (in alphabetical order) area of the universe, cable television channels, crime, Economist columns, four-minute milers, lawyers, persons with jobs, persons without jobs, population, potholes, tarts, torts, toxic wastes, video games and weevils. Some things did, of course, decrease. However, our statistical analysis demonstrates to a high degree of confidence that a strong element of hysteresis, or lag-induced upward stickiness, is present in the numbers of things. Put simply, on average everything is proliferating.

This would seem puzzling. Given the conservation laws of natural science, one would expect to see a rough balancing of things that became more numerous with things that became fewer. The persistent upward drift in the average number of things—or “burgeoning,” as the news media call it—suggests that what is changing is not things themselves but rather numbers. Numbers are losing their value over time; counting any given array of things requires slightly more numbers each year. We refer to this phenomenon as “number inflation”.

For EM researchers, the first order of business is of course to identify the correct deflator for numbers. Our first pass suggests a Preliminary Number Deflator (PND) of the following form:

As will immediately be evident, the scale of the inflation is directly proportionate to the size of the number. Among what arithmeticians refer to as the very small numbers (one, two, three, four, five, etc.), number inflation is detectable only with fine scientific instruments. However, the effect becomes visible among the very large numbers (eg, the millions) and grows quite pronounced indeed among the very, very large numbers (the billions), the very, very, very large numbers (the quadrillions), and the very, very, very, very large numbers (the quadroons).

A great many previously puzzling phenomena are now explained—or, more accurately, seen to be illusory. For instance, many have wondered why ever-more athletic records are broken every year. The answer is that adjusted for number inflation, human athletic performance turns out to have been roughly constant over time. Similarly, astronomers devote much attention to the apparent fact that the universe is expanding. Since the universe cannot expand forever (eventually it will run out of space and bump into something), this hypothesis seems less than satisfactory; and, indeed, when proper integer-value adjustments are performed, the expansion of the universe proves to be an artifact of number inflation.

It is, however, in the realm of human affairs and social policy that the implications are richest and most consequential. For example, in America a widely noted phenomenon is the consistent tendency of budget deficits to increase despite all efforts to reduce them. Why should something grow even when cut? Because, of course, what needs to be deflated is not the deficit but the digits.

Population provides a further example of movement from the intractable to the trivial. It is widely believed that the world's population is expanding rapidly, even exploding. However, this can hardly be the case, inasmuch as not only are more people born every year, more also die. Sure enough, application of the PND immediately shows that the world's population is actually shrinking slightly, except in Denmark. Sustainable growth, therefore, should not be a problem.

For all the other solutions it offers, though, there can be no question that number inflation in itself now poses a global challenge of the first order, displacing, for instance, global warming (a mirage created by the subtle devaluation of numbers on thermometers). We therefore recommend the convocation of worldwide number-revaluation negotiations, to be held under United Nations auspices. These negotiations will determine the rate of integer-value decay and will revalue numbers accordingly.

This job is, admittedly, no easy one. Decisions must be unanimous, because numbers can be internationally useful only if all countries assign equivalent values to them. It is much to be feared that separatist numerical regimes will be adopted by particular blocks or countries, especially France. Moreover, the most meticulous precision is essential. The same revaluation must be applied both to the numbers *and to the spaces between them*, lest the numbers all lump together at one end of the scale, followed (or preceded) by the spaces. However, the opportunities presented for enhanced global co-operation are extraordinary if all countries join hands to preserve and protect the world's precious store of integers. One of the most pressing matters for them to address will be the calendar: properly deflated, today (nominally April 1st) may in fact be February 17th of some prior year.

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* "Interim Report on Integer Hysteresis and Secular Subpolynomial Drift." In *Osiris: The Journal of Mathematics and Society* (Winter 1995).