The following was my final report to clients in the financial industry dated December 22, 2014 when I retired and shut down my economic research firm, Leto Research, LLC in order to pursue broader questions arising from the global debt crisis. It summarizes the reasoning that prompted the explorations reflected in the occasional posting of this website, suitably named Leto Postscripts to denote a continuity of concerns from my previous professional life as an economic researcher:

On November 5, 2008, two months after the eruption of the financial crisis, Queen Elizabeth II asked the director of research at the London School of Economics “Why did nobody notice it?”

This question lingered until June 2009, when a special seminar at the British Academy convoked specifically for the purpose of answering her majesty’s question ventured an answer of sorts. In a 3-page letter signed by a member of the Bank of England’s monetary policy committee, the cream of London’s economic thinkers told the Queen that the failure to predict the crisis “was principally a failure of the collective imagination of many bright people”. That was non responsive, of course, but its authors “denied that economics as a profession had been discredited by the scale of the crisis”.

In the years after the British Academy’s non-answer, criticisms of the economic profession grew and doubts over whether economics is any kind of science were revived. On September 26, 2014 the Financial Times published an editorial, “Economics needs to reflect a post-crisis world”, admitting that “the dismal science itself is in the dock”, suffering from “a growing bias towards mathematical elegance,” and proposed that “mathematical models ought to keep their place so long as their results are not taken too literally”.

Over a month later on November 1, 2014, Jaime Caruana, the General Manager of the Bank for International Settlements, the central bank of central banks, began his address to the International Finance Forum of 2014 in Beijing by drawing attention to the FT editorial. Joining the FT’s disparagement of the role of mathematics in economic thinking, he said flat out that “I agree with the thrust of the editorial”.

The present crisis of economics – the loss of confidence in economics as a science – is centered on the misapplication of mathematics on economic problems. There is a similar loss of confidence in financial policies and investment strategies based on mathematical misapplications. 

But this conceptual crisis in economic and financial thinking is a mere tempest in a teacup compared with the crisis in the hard sciences generally, and in fundamental physics in particular, that has been raging in recent years. As it turns out, the crisis in the hard sciences is also rooted in the suspicion that there may be some kind of misapplication of mathematical techniques in physics research.

In the postwar period this issue was raised by Physics Nobel laureate Eugene Wigner in May 11, 1959 at the Courant Institute of Mathematics at NYU in a lecture titled “The Unreasonable Effectiveness Of Mathematics In The Natural Sciences”. In it Wigner argued, among other things, that our mathematically formulated “laws of nature” cover “only a small part of our knowledge of the inanimate world”, and predictions based on these “laws of nature” exclude “the overwhelming majority of the determinants of the present state of the world”. He concluded from this that because of that exclusion, the astonishing mathematical precision of these laws “may not prove their truth and consistency”.

But long before Wigner, the first to explore the implications of the use mathematical technique on natural sciences was the historian of science and philosopher Jacob Klein in his magisterial 1934 Die Griechsche Logistik und die Entstehung der Algebra (translated by Eva Brann as Greek Mathematical Thought and the Origin of Algebra and published by MIT Press in 1968). This extraordinarily difficult book had been generally neglected (‘less than half a dozen seem to have read it” by 1959, the year of Wigner’s lecture) until interest in it was revived in the 1990s and more recently in 2011 with the publication of The Origin of the Logic of Symbolic Mathematics: Edmund Husserl and Jacob Klein by Curt C. Hopkins.

Klein argues in his 1934 book that the 17^th century founders of modern mathematics – Vieta, Descartes, Stevin and Wallis – effected a fundamental shift in the way we conceive of “number” in order to develop algebra as a “universal method” based on the calculating techniques they had found in the then-recently translated ancient text of Arithmetica by Diophantus of Alexandria, a 3^rd century AD mathematician.

The concept of “number” inherited from ancient science referred to the enumerated assemblage of concrete units resulting from the counting-off of distinct objects-qua-units. It was a “number of”. By contrast, the modern concept of “number” is no longer a “number of” but rather a pure, empty symbol suitable for symbol manipulation. Klein argues (in fact, he demonstrated conclusively) that for Descartes, Vieta et al., “number is not the thing enumerated” (“numerous non est res numerata” quoting Descartes) and “a unit is not a quantity” (“unitas non est quantitas” also according to Descartes). Instead, “number” is a pure symbol and a cipher invented by the faculty of imagination to facilitate a certain type of logical, rules-based games. It is a symbol that symbolizes nothing except its own relative place in a system of logical rules for symbolic calculation.

The result of this transition of the concept of “number” from counted-off number of units to symbolic place-holder of a rules-based logical game was algebra and its subsequent offspring, calculus. This was conceived as an all-purpose power tool, a general method, a “mathesis universalis” that could serve as the analytical platform for all types of scientific investigations. It was the hammer of modernity that subsequently made all problems look like nails.

Klein wrote his book as part of a broader effort to address the sharp clash of two mathematically flawless theories of modern mathematical physics (relativity and quantum theory) that led to incompatible conclusions. It was a clash that led to the celebrated exchanges between Albert Einstein and Niels Bohr from the 1920s onward. Edmund Husserl, a philosopher of logic and arithmetic trained by the great mathematician Karl Weierstrass, characterized the situation as “the crisis of European sciences” in a celebrated series of letters, essays and lectures during 1934-37 – approximately the same time as his student’s, Jacob Klein’s work.

So long as the mathematics of quantum physics continued to be verified by experimental testing, the physics community continued to dismiss Husserl’s crisis warning and Klein’s critique. The situation began to change in the mid nineteen-seventies, when the mathematics of sub-atomic particle physics theories and experimental verification parted ways. This occurred with the attempt to resolve the gaps in the Standard Model of particle physics by developing the recondite mathematical theory of superstrings.

After forty years of effort, superstring theory has failed even to formulate predictions that can be verified by experiment. This has caused some particle physics practitioners to argue for a nearly infinite number of potential universes, a “multiverse”, leading to the conclusion that physics must now abandon the test of falsifiability. The pushback from more traditional particle physicists –Nobel Laureate David Gross (of the Kavli Institute for Theoretical Physics at the University of California) for example, among others – who are still searching for a single grand unified theory, has created unprecedented controversy within the physics community. One leading participant and opponent of Gross, Leonard Susskind, director of the Stanford Institute for Theoretical Physics and a “father” of string theory, was led to characterize the situation as a “war”, accusing his opponents of practicing “faith-based science”.

The controversy ultimately involves rival understandings of what we mean by “science”, to the point where the European Commission has sponsored the notion of “post-normal science”. This is an idea of science drawing its authority from a consensus of “stakeholders” rather than from the traditional standards of rigorous proof.

All the rival sides of this “war” among physicists ignore Klein’s hypothesis that our 17^th century transition to a symbolic concept of “number” may be the root cause of the methodological difficulties plaguing natural science today. Given that from the 17^th century to date developments in natural science had a vastly greater impact on human development than political, economic and social philosophies and movements, it is time to delve in the economic, political and broader social implications of Klein’s hypothesis.