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Model builders will rule the world?
on 8 March 2013
The Physics of Finance was first published in the USA as 'The Physics of Wall Street', and the writing certainly reflects a corresponding USA-centric tilt. There is no 'Physics' in it of course; rather, it is a description of the mathematical modelling methods of Physics as applied to the unrelated field of Finance. But 'Physics of Finance' is a forgivably eye-catching title.
It is a very interesting and well written book that provides an in-depth look at the history of our understanding of the statistical dynamics of fluctuating financial markets, from their beginning to the catastrophic crash of 2008.
Weatherall provides the clearest explanation I have found of the reasons for that crash, arguing that those causes, at some level, still remain. He proposes that deficient mathematical models of the financial markets in the hands of inadequately informed speculators (the cause) should be replaced by good mathematical models with appropriately educated management (the cure).
He shows that the idea of predicting market fluctuations by mathematical modelling has always been rather peripheral to mainstream Economic thinking, although less so in the related world of financial trading. That and related ideas have been pursued by a long list of interesting and eccentric characters who Weatherall describes, starting with Roman poet Titus Lucretius in 60 B.C., through the 16th century Italian Physician and gambler Geralamo Cardano, to French scientist/mathematician Louis Bachelier in 1892 Paris, and beyond, to the God-father of Fractals and Chaos, Benoit Mandelbrot. In fact a large fraction of the book is devoted to short and very well written biographies of these and other fascinating characters - and the author is to be congratulated on it; they alone are worth the price of the book.
The remaining parts of the book are devoted to a description of how that cast of characters gradually provided the mathematical material to incrementally improve the mathematical model of market fluctuations, explaining and introducing the reader to the various concepts of 'Normal', 'Lorenzian', 'Cauchy' and 'Log-normal' distributions. The pattern that emerges (in my view) reveals a 'reactive' process - the modellers reacting to unexpected features of market fluctuations by changing their model principles - rather than a scientifically 'pro-active' process - where the model itself is used to *predict* unexpected features, thus verifying its underlying principles. This confirms a fundamental difference of kind between the modelling of Financial markets and the modelling of Physical systems. See the note below on Bachelier, Einstein and random-walk processes.
Now I take up four points where I feel Weatherall's arguments are flawed or where his narrative moves in the wrong direction, or hides deeper truths that he may have missed. These are not to be seen as an attempt to refute his underlying theme - they are not that - rather they concern secondary themes that, nevertheless, have substantial importance. Taken together they reduce what would have been a 4* rating to 3*.
Weatherall argues that the close collaboration between Engineers and Applied and Theoretical scientists in large scale technical projects had its early seeds in the Chemical industry in the USA; this is an interesting discussion point, and may have some truth in the USA, specifically in Plutonium production for the Manhatten Project, but it completely misses the wider R&D picture. Even in the USA the drive to large scale, cross-disciplinary, scientific collaborations had its source in the *physics* of the sub-atomic world and the well know inverse relation between the scale-to-be-probed and the probe-energy required to do so. Given that scientific requirement for high energy, large scale technical projects were an inevitable consequence. But this was empowered in the USA (and elsewhere), not by DuPont's industrial research methodology, but by two far more important and absolutely decisive factors. First; the mass-migration of the cream of European scientists; chemists, mathematicians and physicists, including Einstein, who were fleeing the horrors of Nazi Germany to a new life in the West in the 1930s. Second; E=mc2 and the discovery of nuclear fission with the consequent possibility of an atomic bomb. Western governments threw almost unlimited resources at the physics/engineering project (which is described) of creating that weapon before Nazi Germany and, even when the immediate threat had receded in 1946, they continued to fund 'High Energy Physics' generously in the hope (and fear) that it might produce the 'new physics' for the next super-weapon before their global power-balanced opponents could achieve it (this was equally true in both the USA/West and the USSR/East and continued for decades - recall Ronald Reagan's 1980s "Star Wars" initiative). This combination of scientific and political imperative, mass-migrated refugee genius and targeted high funding, were the real driving forces behind the large scale "atom smasher" projects that flourished in the second half of the 20th century, leading eventually to the 21st century LHC at CERN.
The repeated references to Bachelier's prior derivation of the equations of 'random-walk' (Brownian) motion w.r.t. Einstein's later, and more famous, 1905 paper, eventually become rather annoying and surely miss the point. It may be true that Bachelier was the first to give the correct mathematical description of 'random-walk' processes but, unlike Bachelier, Einstein saw the mathematical description of the motion not as an end-in-itself, but merely as a tool that allowed him to probe the underlying physics causing the motion. Einstein showed that the molecular-kinetic model correctly described the statistical dynamics of the liquid, thus clearly proving for the first time the physical existence of molecules *and* allowing an estimate of their size. I'm sure that Weatherall is well aware of that point so I must question why he apparently chooses to ignore it. The obvious conclusion must be that he is attempting to inflate our perception of a relatively unknown, moderately competent scientist, who was an important actor only in the chosen field of financial modelling, by comparing him favourably (and misleadingly) with a true scientific genius.
The author also writes; 'The early mathematical development of modern gauge theory [....] was largely the work of Jim Simons, the mathematical physicist turned hedge fund manager'. This is completely wrong - Simons was trained, qualified, taught, worked and achieved great distinction as a mathematician not as a physicist and he made no direct contribution to gauge theory. Modern gauge theory (as embodied in the Standard Model of Particle Physics) was principally the work of Chen Ning Yang and Robert Mills (Yang-Mills non-abelian gauge theory) with Gerard 't Hooft and Martinus Veltman providing the crucial mathematical leap - proof that it could be renormalised. Simons's contribution to gauge theory was, by comparison, peripheral and indirect, the Chern-Simons 3-form actually being introduced to gauge theory (in the context of Superstring theory) by Ed Witten. This is another example of the author artificially inflating our perception of a character important to his story by misrepresenting their importance in the actual scientific context. The attempt to re-define Simons as a mathematical 'physicist', in order to force (our perception of) Simons to fit the author's 'Physics of Finance' mould, is unfortunate to say the least! For a very good and objective summary of Gauge Theory read the 'Scholarpedia.org' online article by Gerard 't Hooft. Chern-Simons theory would be found in the link to Superstring theory (which has yet to be written by Superstring theorists - presumably too busy inventing explanations for the absence of sparticles at the LHC?).
Weatherall claims that the collapse of employment for scientists in the USA, following the successful completion of JFK's "Man on the Moon" project, provided a decisive input of scientific model-builders to the Financial sector as he describes it. But this surely begs a rather obvious question - NASA and related technical industries and academic institutes didn't suddenly disappear; they reduced their programmes and shed staff they no longer required. Now I suppose its possible that NASA kept their least able staff and released their best, but that doesn't seem very likely. And this chimes with Weatherall's later analysis of the 2008 crash, where the faulty financial modelling (inadequate modelling of crucial market correlations) sounds like the work of second-rate analysts. What's truly scary is that the Financial Services sector, which is so fundamentally important to world economic activity, has expended so little collective effort on getting their financial modelling understood. With the resources available to them they could have trained, or hired, the very best mathematical model builders available, rather than leaving the subject comparatively unsupported, on the periphery of their vision, but at the core of their (unknown but monumental) risks. We are still suffering the consequences of that collective high-level incompetence.