More from Pais: Einstein and bordellos?

More excerpts from the memoir (A Tale of Two Continents: A Physicist’s Life in a Turbulent World) of Abraham Pais. See earlier post.

p. 375: ... In early September we went back to Berkeley ... The physicist Otto Stern, a Nobel laureate, lived in retirement in the area. He had known Einstein well when both were in Prague, where - he told me - they would visit bordellos together, "quiet places for discussing physics." ... :-) [See also here.]

One November morning I stood in the shower when the doorbell rang... It was Don Glaser, beside himself with excitement. "I just received ... the Nobel Prize! Now I'm a free man, I can leave physics." He did not care at all for the recent style of doing experiments in large teams [modern experimental particle physics]. Indeed, soon after he returned from Stockholm he became a molecular biologist.

I met with Glaser (inventor of the bubble chamber) once when I was a grad student, about the possibility of working on computational neuroscience and vision (his focus at the time). Had I gone that route I probably would have bumped into Jeff Hawkins, who was there doing biophysics.

Goldman apologia

The following appeared as a comment on my previous post discussing Paul Krugman's anti-Goldman and anti-finance column of last week. The commenter is a (very) senior quant with a PhD in physics. His knowledge of these matters is, I would guess, superior to Krugman's and certainly superior to that of any journalist.

Is Goldman entitled to keep its recently announced gigantic profits, given that they were (perhaps) saved by the government's bailout of AIG? Hear it from the horse's mouth :-)

For more background, click the AIG tag below. [If you are going to comment on this post, please read the earlier one first. Your thoughts might be addressed in the comments there!]

...on AIG - you might wanna check out this developing story.

When large derivative dealers trade with each other they typically agree to exchange margin so that on any given day neither owes anything to the other. Sometimes dealers will disagree on the value of their trades. GS has said that AIG owed them $10bio pre-bailout (in GS's opinion), and had given GS $7.5bio (AIG's opinion of the value) against this exposure. GS had purchased insurance from other large dealers for the $2.5bio balance.

AIG deals with the public too, of course, but the public pays premiums to AIG and holds no collateral. This is all "business as usual".

Now, let's look at what would happened if AIG had defaulted. For GS, the $7.5bio of collateral is "bankruptcy remote" and GS keeps it penny for penny. The insurance contracts pay off $2.5bio to GS and the right to pursue the claim against AIG passes to the counterparties. Mom and Pop who have purchased retail insurance from AIG are left with only a bankruptcy claim. So this is all very ugly, but absent further defaults, GS is left whole - no loss. But have no doubt, someone out there will be eating a big loss.

At this point in the discourse, most people have trouble understanding collateral and that it is bankruptcy remote (is this a skill? I guess so!), but let's say we have this one down. The next point people make is that letting AIG go under would have created a financial system meltdown that would have harmed GS such that GS could not collect all its $2.5bio insurance claim. Well, this is possible, but it is equivalent to saying that a large subset of JP Morgan, DeutscheBank, BNP, SocGen, Citibank, etc... all go bankrupt. However, we probably don't believe that even a full $2.5bio hit to GS would be lethal for it, so it is hard to say that a failure by AIG would have directly taken GS down.

The next point you might make is that if all these other banks went under it might have created a large enough set of other problems for GS so as to take it out. However this final claim, which is frequently made, is specific to GS in no way at all. But if you wanna say "maybe the U.S. bailed out AIG so that the entire world banking system didn't collapse", then yes, GS benefits from that just as does anyone in the economy with any exposure at all - like anyone who purchased Auto Insurance underwritten by AIG. So maybe a smart bailout avoids a situation like the depression which followed the Panic of 1837, but the beneficiaries of the bailout are likely not dominantly the banks. This is why administrations as diverse as G.W. Bush and Barry Obama have reached for identical bailout buckets.

The Kruggy regulation question should be "would compensation reforms stop the sort of loss-making trading that went on at AIG?" - and that may be, I don't know. And might it accidentally stop economically productive trading as well? Krugs sure doesn't think so.

Against finance

Paul Krugman rails against Goldman's big quarterly numbers in yesterday's Times. He goes as far as to claim that Goldman's success is bad for America!

At the core of his argument is the following observation:

Over the past generation — ever since the banking deregulation of the Reagan years — the U.S. economy has been “financialized.” The business of moving money around, of slicing, dicing and repackaging financial claims, has soared in importance compared with the actual production of useful stuff. The sector officially labeled “securities, commodity contracts and investments” has grown especially fast, from only 0.3 percent of G.D.P. in the late 1970s to 1.7 percent of G.D.P. in 2007.

Such growth would be fine if financialization really delivered on its promises — if financial firms made money by directing capital to its most productive uses, by developing innovative ways to spread and reduce risk. But can anyone, at this point, make those claims with a straight face? Financial firms, we now know, directed vast quantities of capital into the construction of unsellable houses and empty shopping malls. They increased risk rather than reducing it, and concentrated risk rather than spreading it. In effect, the industry was selling dangerous patent medicine to gullible consumers.

This point has not received enough attention in the volumes of analysis produced by the financial crisis. Some comments.

1. Markets and capitalism are good -- overall, they benefit society by providing (mostly) efficient allocation of scarce assets (including human, as well as other, capital).

We've just been through a bubble, with resulting misallocation of resources, but perhaps bubbles are an unavoidable side effect of capital markets, and perhaps their short term negative consequences are compensated by the long term benefits of market economics. Of course, it is beyond our capabilities to address this question with high confidence, so what is left is people arguing their priors. At the bottom of this post are some previous comments of mine on this topic.

2. Concentration of the control of wealth is inevitable, given advances in communications and information technology, the complexity of our economy, and cognitive limits of average people. By control I don't mean ownership, I mean investment and allocation decisions -- think mutual fund investors of modest means, but whose money is aggregated into a billion dollar fund controlled by a few investment professionals.


Given 1 and 2, I doubt Krugman really wants to eliminate the financial sector. His outrage is really motivated by populism, and relates to the following question:

3. How should these professionals be paid? How much value do their decisions actually add to the economy?

This is the fundamental question, also unanswered. Would less extravagant pay for money managers (e.g., as a consequence of more egalitarian cultural values) lead to reduced economic growth? By how much? (By the way, I don't think we can lay all the blame for the current crisis on the professionals -- millions of Americans participated in the housing bubble.)

Personally, I think Wall St. compensation practices need to be changed. I debated this and related points with a hedge fund manager in some previous posts: On the benevolence of financiers , Money talks.


Here's what I wrote in 2008 on topic 1 above. Can anyone do better than these estimates?

Now to my heterodox heterodoxy: always estimate costs and benefits when making a decision. A little calculation is in order: suppose unfettered markets lead to systemic crises every 20 years that cost 15% of GDP to clean up. I think that's an upper bound: a $2 trillion (current dollars) crisis every 20 years. [That $2 trillion was an estimate for the direct housing bubble losses, but I can see now that the collapse of credit markets and of business and consumer confidence is going to increase that number substantially.]

Easy Question: What growth rate advantage (additional GDP growth rate per annum) would savage, unfettered markets need to generate to justify these occasional disasters?

Answer: an additional .1 percent annual GDP growth would be more than enough. That is, an unregulated economy whose growth rate was .1 percent higher would, even after paying for each 20 year crisis, be richer than the heavily regulated comparator which avoided the crises but had a lower growth rate.

Hard Question: would additional regulation decrease economic growth rates by that amount or more?

Unless you think you can evaluate the relative GDP growth effects of two different policy regimes with accuracy of better than .1 percent, then the intellectually honest answer to the policy question is -- I don't know -- no shouting, no shaking your fist, no lecturing other people, no writing op eds, just I don't know. Correct the things that are obviously stupid, but don't overstate your confidence level about additional policy changes.

(Note I'm aware that distributional issues are also important. In the most recent era gains went mostly to a small number of top earners whereas the cost of the bailout will be spread over the whole tax base.)

China market cap now #2

Yesterday, China's stock market cap ($3.21 trillion) exceeded Japan's ($3.20 trillion) slightly to become the world's second-largest.

The last time this occurred was in January 2008. As recently as early 2006, Japan's market cap was 12x the size of China's.



See earlier posts Sustainability of China economic growth (top figure) and Back to the future (bottom two figures; note these are PPP adjusted).

Autism and economics

Blogger and economics professor Tyler Cowen's latest book (Create Your Own Economy) is out, and it seems to be all about autism! If you don't believe me, here is an Editorial Review from Amazon:

In this provocative study of behavioral economics, Cowen (Discover Your Inner Economist) reveals that autistic tendencies toward classification, categorization and specialization can be used as a vehicle for understanding how people use information. Cowen spends a great deal of time dispelling autism's societal stigma, arguing that mainstream society is reaping benefits from mimicking autistic cognitive strengths. As stimulating as is the premise, the book often feels like its own long exercise in categorization, with each chapter an analysis of the human mania for classification (e.g., the obsession with ranking achievements and endeavors). According to Cowen, human brains are constantly absorbing bits of information that get smaller and are delivered faster as technology advances. The more information people receive, the more they crave—this shorter attention span is far from a flaw to the author, but a liberating mechanism that allows humans time to contemplate more ambitious, long-range pursuits. ...

Interestingly, Cowen says the idea for the book came from an email he received from a blog reader, who was convinced, based only on his writing, that Cowen was himself autistic :-)

In skimming the book (which isn't bad), I was surprised not to see any discussion about the prevalence of autistic economists -- specifically when it comes to their perspectives on human nature. (If you don't believe me, ask any non-economist social scientist.) [On further inspection, there is a reference to "economist nerds" in the context of the signaling interpretation of education, and a figure which notes that economists tend to be focus on the most "objective" kinds of human decision making, leaving aside important issues of psychology.] As far as I could tell, Cowen doesn't mention in the book that there is actually a heterodox economics organization called the Post-Autistic Economics Network (paecon), that publishes its own journal, originally known as the Post-Autistic Economic Review. Here's what's in the current issue:

How should the collapse of the world financial system affect economics? Part II

- Mad, bad, and dangerous to know
Steve Keen

- A financial crisis on top of the ecological crisis: Ending the monopoly of neoclassical economics
Peter Söderbaum

- Toward a new sustainable economy
Robert Costanza

- After the bust: The outlook for macroeconomics and macroeconomic policy
Thomas I. Palley

- A non-formal look at the non-formal economy
Sean Mallin

I'm all for cognitive diversity, especially on the geeky end of the spectrum! But to what extent are people like Cowen simply lumping all nerds together with high functioning autistics and people with Asperger's Syndrome?

For more on this topic, I recommend Simon Baron-Cohen's book The Essential Difference: male and female brains and the truth about autism.

Some things never change: Pais and Uhlenbeck

The late physicist Abraham Pais is perhaps best known for his Subtle is the Lord, the greatest of all Einstein biographies. I hadn't realized that Pais had written his own memoir (A Tale of Two Continents: A Physicist’s Life in a Turbulent World) until I came across it accidentally today in the library. If you've read any of Pais' historical writing you can probably guess that his autobiography is full of wonderful stories.

There is a condensed version of Pais' life story in his Wikipedia entry. He grew up in Holland, completing his graduate studies under Uhlenbeck in 1941 (see below). He survived the war in hiding in Amsterdam (not far from Anne Frank) and eventually immigrated to the US, becoming a member of the Institute for Advanced Study.

Here is Pais' recollection of how he became of student of Uhlenbeck's (p.31). Amazingly, I had the same experience, and so have all of my students ;-)

I ... told Uhlenbeck of my hopes to become a graduate student in theoretical physics under his guidance.

Uhlenbeck's response was unexpected. "If you like physics," he asked, "why don't you become an experimentalist? Or if you like mathematical aspects of theoretical physics, why not become a mathematician?" In explanation he noted that the practical future of a theoretical physicist in the Netherlands was extremely limited. At that time there were only five professoriates in the whole country. ... [more dissuasion] ... Furthermore, he added, theoretical physics is very difficult, it would be a life of toil with many frustrations and disappointments.

I was quite taken aback and mumbled, "But I like theoretical physics so much." Uhlenbeck's reaction was again unexpected. "If that is really true," he said, "then by all means become a theorist; it is the most wonderful subject you can imagine." As he later told me, his preliminary attempts at dissuasion were exactly like those he himself had been exposed to when he wanted to start his own graduate studies, adding that he used the same routine whenever anyone applied to study with him.

...Years later I told Uhlenbeck how that first afternoon with him had affected me. He told me with a smile that he had gone through the very same treatment, had the very same reactions, when he had visited his revered teacher, Paul Ehrenfest, for the first time. Ehrenfest in turn had received the same treatment from the great Ludwig Boltzmann in Vienna. This tradition is part of teaching in the grand old style, concentrating on but very few students. In my time I was the only student Uhlenbeck had taken on. Because of that privilege I may count myself as a spiritual great-grandson of Boltzmann. Meanwhile the old style has gone forever, I think, because of the large number of students now clamoring for higher education.

Pais wrote some important papers with Gell-Mann, including ones on Kaon oscillations and Strangeness. The result on Kaon oscillations, despite being a simple exercise in elementary two-state quantum mechanics, was not accepted by other theorists (the reactions of Racah and Dyson are recounted) until verified experimentally! (p.338: In 1956 a Columbia experimental group reported that the "rather startling properties of [neutral K's] ... predicted by Gell-Mann and Pais ... have been confirmed" :-)

Later Pais and Gell-Mann had a falling out, and Gell-Mann's hostility caused Pais some distress. In the memoir he describes reading the following inscription in St. Paul's church in Baltimore, which he liked very much (p.339).

Desiderata

Go placidly amid the noise and haste and remember what peace there may be in silence. As far as possible without surrender, be at peace with all persons.

Speak your truth quietly and clearly, and listen to others, even to the dull and ignorant; they too have their story. Avoid loud and aggressive persons; they are vexatious to the spirit.

If you compare yourself to others, you may become vain or bitter, for always there will be greater or lesser persons than yourself. Enjoy your achievements as well as your plans. Keep interested in your own career, however humble; it is a real possession in the changing fortunes of time.

Exercise caution in your business affairs, for the world is full of trickery. But let this not blind you to what virtue there is; many persons strive for high ideals, and everywhere life is full of heroism.

...

-- Max Ehrmann

History of venture capital

Some time ago I listened to this lecture by Spencer Ante, on his book Creative Capital, and have been meaning to blog about it.

Q: When did the business model for VC take shape? In other words, when did people become convinced that money should be pooled specifically to invest in small companies developing products based on new technology? What were the first VC funds?

A: Ante claims the first VC fund was Georges Doriot's ARDC founded in 1946. Judging from the size of funds raised even 40 years later, it took a long time for investors controlling large pools of money (i.e., pension funds, endowments) to become convinced about the model.

Q: What was the first "homerun" investment? A: Digital Equipment Corporation (DEC) -- ARDC made 500x on a $70k investment!

Q: How did the VC industry take root in Silicon Valley, migrating from its original home in Boston? A: Long story; listen to the lecture and consult histories of Fairchild Semiconductor, Intel, Fred Terman at Stanford, etc.

Q: What role did defense funding play in the development of VC and the tech industry in general? A: A big one. See Doriot's bio and listen to the lecture. DEC was more or less an MIT Lincoln Lab spinout.


Of course, venture capital is far more than just a business model these days -- it's a source of unique American competitive advantage. It's an example of good pooling of risk (each startup is very risky, but perhaps portfolios of startups have predictable behavior and desirable risk-return ratios) that nevertheless took 50 years to transition from crazy innovation to accepted and mature financial technology.

Rumsfeld, meet McNamara

Better late than never. Rumsfeld, Bush and Cheney have a lot to learn from Robert S. McNamara.

Times obituary. Chomsky on McNamara.

They shall not grow old, as we that are left grow old:
Age shall not weary them, nor the years condemn.
At the going down of the sun and in the morning
We will remember them.

Comment posted on the Times site, from Bill Baldwin Jr. of Los Angeles:

It is "unfortunate" that three friends of mine, among a group of 58,000 other Americans of my generation, can’t shed their "let's move on" tears of forgiveness for the late Sec. of Defense, Robert S. McNamara, but they're dead. Bernard, the blond surfer looking Navy helicopter pilot, who on his second tour of duty in Vietnam, wouldn’t leave eight wounded Army guys trapped in a firefight and died along with them trying to fly out of the hot zone; John, the son of a minister in Santa Barbara, trained as a broadcast specialist as I was in 1968, but was pressed into walking patrol his first week in country and came home in a box before Mayor Daily ever hosted that friendly summer gathering of folks in Chicago; and Keith, a fellow rock & roll playing buddy from the mail room at Disney, I don’t know how he “bought the farm” down in McNamara’s little dust up, just that he never got a chance to wear pressed jeans while doing hustle to “Disco Inferno”.

...

But please feel free to label my response here as “mean spirited” or whatever the current buzz words slogan might be you have received as approved by Move On or Twittered from your personal empowerment group, because words, including my own, won’t bring back Bernard, John or Keith, but I’d feel as if I had failed in my responsibilities as a friend if I didn’t express my feelings at the passing of Robert McNamara, who made it to 93 before he left the scene. My friends never made it to their 25th birthdays.

More algorithm wars

Some time ago I posted about two MIT-trained former physicists who were sued by Renaissance for theft of trade secrets related to algorithmic trading and market making. Reportedly, Belopolsky and Volfbeyn won their court case and are now printing money at a well-known hedge fund. The Bloomberg article below is about a former Goldman employee who may have made off with code used in prop trading and market making.

The story is also covered in the WSJ (whose reporters and editors don't know the difference between "code" and "codes" -- as in software vs cryptographic keys), where it is revealed that Aleynikov was paid $400k per year at Goldman and left to join a fund in Chicago which offered him three times as much.

Goldman Trading-Code Investment Put at Risk by Theft
2009-07-06 23:18:39.529 GMT

July 6 (Bloomberg) -- Goldman Sachs Group Inc. may lose its investment in a proprietary trading code and millions of dollars from increased competition if software allegedly stolen by an ex-employee gets into the wrong hands, a prosecutor said.

Sergey Aleynikov, an ex-Goldman Sachs computer programmer, was arrested July 3 after arriving at Liberty International Airport in Newark, New Jersey, U.S. officials said. Aleynikov, 39, who has dual American and Russian citizenship, is charged in a criminal complaint with stealing the trading software. At a court appearance July 4 in Manhattan, Assistant U.S. Attorney Joseph Facciponti told a federal judge that Aleynikov’s alleged theft poses a risk to U.S. markets. Aleynikov transferred the code, which is worth millions of dollars, to a computer server in Germany, and others may have had access to it, Facciponti said, adding that New York-based Goldman Sachs may be harmed if the software is disseminated. ...

The prosecutor added, “Once it is out there, anybody will be able to use this, and their market share will be adversely affected.” The proprietary code lets the firm do “sophisticated, high-speed and high-volume trades on various stock and commodities markets,” prosecutors said in court papers. The trades generate “many millions of dollars” each year.

... “Someone stealing that code is basically stealing the way that Goldman Sachs makes money in the equity marketplace,” said Larry Tabb, founder of TABB Group, a financial-market research and advisory firm. “The more sophisticated market makers -- and Goldman is one of them -- spend significant amounts of money developing software that’s extremely fast and can analyze different execution strategies so they can be the first one to make a decision.”

Aleynikov studied applied mathematics at the Moscow Institute of Transportation Engineering before transferring to Rutgers University, where he received a bachelor’s degree in computer science in 1993 and a master’s of science degree, specializing in medical image processing and neural networks, in 1996, according to his profile on the social-networking site LinkedIn.

Feyerabend on the giants

I was struck by the following comments of Paul Feyerabend in For and Against Method. They appeared in a 1969 letter to Feyerabend's Berkeley philosophy chair Wallace Matson, which is reproduced in Appendix B of the book.

The withdrawal of philosophy into a "professional" shell of its own has had disastrous consequences. The younger generation of physicists, the Feynmans, the Schwingers, etc., may be very bright; they may be more intelligent than their predecessors, than Bohr, Einstein, Schrodinger, Boltzmann, Mach and so on. But they are uncivilized savages, they lack in philosophical depth -- and this is the fault of the very same idea of professionalism which you are now defending.

The entry on Feyerabend in the Stanford Encyclopedia of Philosophy is fascinating.

Further discussion of this topic by Sean Carroll and Lubos Motl. Lubos links to the excellent essay Against Philosophy by Steve Weinberg (chapter from his book Dreams of a Final Theory).

The Wranglers

Some time ago I came across the essay What became of the Senior Wranglers?, which describes the history of the Cambridge Mathematical Tripos examination. Interesting excerpts follow below, but I recommend the whole thing.

Difficult exams like the Tripos or present-day international Olympiads in math and science are one of the best ways to identify truly exceptional talent. As discussed below, the tests are able to distinguish between talents at the very far tail of the distribution. But even these exams are only inexact predictors of future success. It's clear that special preparation has an important impact on performance (successful Wranglers typically hired private tutors, see below), and that forcing students to focus on overly technical and narrow exam problems isn't necessarily the best way to measure (or foster) creativity or research ability (see Hardy's criticisms below).

Still, the list of Senior and Second Wranglers is an impressive one!

During the one hundred and fifty seven years (1753-1909) in which the results of the Cambridge Mathematical Tripos were published in order of merit and divided by class of degree into Wranglers (1st Class), Senior Optimes (2nd Class) and Junior Optimes (3rd Class), great prestige attached to those students who had come out in the top two or three places. The securing of the top position as Senior Wrangler was regarded, at the time, as the greatest intellectual achievement attainable in Britain and the Senior Wrangler was feted well beyond Cambridge and accorded pre-eminent status among his peers - indeed years in Cambridge were often remembered in terms of who had been Senior Wrangler in that year. It is curious therefore that no systematic study has ever been made, in so far as the author is aware, of what became of these Senior Wranglers in later years after their triumph. This article may shed a little light on the matter.

Until 1850, Mathematics in Cambridge was dominant over all other University subjects so much so that it was obligatory, astonishing as it now seems, for students who were studying for honours in Classics, first to have taken the Mathematical Tripos.

Because of the prestige attaching to the position of Senior Wrangler and the college from which the Senior Wrangler came, the students, especially the most promising, were subjected, like thoroughbred racehorses, to the most intense training for the Tripos race. The training was in the hands of private ‘coaches’ and not the University professors as often students attended very few lectures and, for example, Charles Babbage gave no lectures in the eleven years, 1828-39, during which he was Lucasian Professor. The best of the coaches, because of their reputation, were able to select the most able students thus perpetuating their reputation for success.

The most famous private tutor was William Hopkins (1793-1866) who himself had been 7th Wrangler in 1827 and was a person of distinction outside his coaching activities being President of the Geological Society 1851-53 and President of the British Association 1853. In 1849 it was said of Hopkins that in the 22 years since his degree he had taught 17 Senior Wranglers, 27 Second or Third Wranglers and 200 Wranglers in total. As William Hopkins continued to turn out Wranglers well after that date his final tally must have been much higher. Hopkins' Wranglers included Clerk Maxwell, Cayley, Thomson (Lord Kelvin), Stokes and Tait. It can be seen with the benefit of hindsight that the greatest of Hopkins' pupils was Clerk Maxwell, but remarkably Hopkins recognised this even when Maxwell was an undergraduate saying "he is unquestionably the most extraordinary man I have met with, in the whole range of my experience".

Galton, who had a nervous breakdown while preparing for the Tripos, analyzed the exam results in his book Hereditary Genius. (See after p.46 here.) In earlier discussions here and here I advanced the claim that modern selection processes are more effective than in the past, with more participants and better access to training. One can quantify this by looking at the scores on, e.g., the International Mathematical Olympiad, which is pretty much as hard an exam as one can devise. Due to the worldwide reservoir of competitors, one finds fairly tight clumping of individuals near the top -- there are often perfect scores, and many nearly perfect ones. (See 2008 scores.) Contrast this with the Tripos score distribution described below, with its outliers and large range of outcomes.

One would be tempted to classify a Senior Wrangler who far outdistanced his competition as a potential Genius, whereas a competitor who falls within the clump of IMO Gold Medalists tends not to stand out very much from his or her peers.

The actual marks were never published but Sir Francis Galton in his book 'Hereditary Genius' refers to having obtained marks in respect of three years (unspecified, but probably around the 1860's). In one of these years, out of a total possible mark of 17,000, the Senior Wrangler obtained 7634 marks, the second Wrangler obtained 4123 marks, the lowest Wrangler obtained around 1500 marks and the lowest candidate receiving an honours degree (Junior Optime) obtained 237 marks. In the second of these years the Senior Wrangler obtained between 5500 and 6000 marks, the Second obtained between 5000 and 5500 and the lowest Junior Optime received 309 marks. In the third of these years when, according to Galton, the Senior Wrangler was conspicuously eminent, he obtained 9422 marks and the Second 5642 marks. Galton makes considerable play of the large discrepancy between the marks obtained by the Senior Wranglerand by the lowest Wrangler.

It can be seen that the Senior Wrangler would typically obtain less than 50% of the marks, the lowest Wrangler less than 10% and the lowest honours candidate less than 2%! This seems to the author a rather curious result and it is not clear what conclusions are to be drawn from it. It suggests that the candidates covered a very wide ability range, that the level of the lowest Wrangler and the lowest honours man was really rather poor by to-day's standards (perhaps university life was more relaxed and the average student did not apply himself very hard?) and that the papers were too long and hard even for the best students.

Curiously, there seem to have been more great physicists among the Wranglers than pure mathematicians!

Among the Wranglers are to be found those who, along with Michael Faraday (1791-1867), William Rowan Hamilton (1805-65) and James Prescott Joule (1818-89), secured for the UK world leadership in physics and mathematical physics in the second half of the 19th century, namely:

James Clerk Maxwell viii (1831-79), 2W 1854.

William Thomson ix(1824-1907), 2W 1845, later Lord Kelvin.

George Stokes (1819-1903), SW 1841, later Sir George Stokes.

John William Strutt (1842-1919 ), SW 1865, later Baron Rayleigh, Nobel Prizefor Physics1904.

John Couch Adams (1819-92), SW 1843, predicted theoretically the existence of the planet
Neptune(also predicted independently by Le Verrier in France).

George Green x (1793-1841),4W 1837, first introduced the concept of potential in a paper of 1828.

Peter Guthrie Tait xi (1831-1901), SW 1852, author with Lord Kelvin of the epoch-making book
'Treatise on Natural Philosophy'.

J.J. Thomson (1856-1940), 2W 1880, later Sir J.J. Thomson, discoverer of the electron in 1897,
Nobel Prizefor Physics, 1906.

University professorships throughout the UK and the British Empire were commonly held by Wranglers in the top two or three places. ...

Given the great attention and prestige attaching to mathematics over the 157 years (1753-1909) we are considering it is curious that the Tripos produced, in contrast to mathematical physics, only a few world class pure mathematicians-only Cayley, Sylvester, Clifford, Hardy and Littlewood. World leadership in pure mathematics in this period remained firmly in France and Germany with each of these countries producing a plethora of world class mathematicians e.g. Gauss, Bessel, Jacobi, Dirichlet, Kummer, Riemann, Dedekind, Kronecker, Weierstrass, Cantor, Klein, Hilbert, Landau, Weyl in Germany and d'Alembert, Lagrange, Laplace, Legendre, Fourier, Poisson, Cauchy, Louiville, Galois, Hermite, Bertrand, Jordan, Poincaré, Hadamard, Cartan, Borel and Lebesguexiii in France.

It was this relative failure of British pure mathematics after the death of Professor Colin Maclaurin in 1748 that so irked G.H. Hardy and he put a large part of the blame on to the Tripos as is evident from his 1926 Address to the Mathematical Association. Hardy's thesis was that the syllabus for the Tripos was out of date and far behind the times since it did not contain any of the important ideas which were dominating contemporary thought in pure mathematics at the time. It was therefore a poor training for a pure mathematician. Furthermore the questions put too much stress on technique rather than ideas and were questions in which professional mathematicians had lost interest many years previously. While accepting these criticisms, it seems curious that those who became professional pure mathematicians apparently found difficulty in shaking off the legacy of the Tripos. After all, the Professors had spent only three years of their active lives on the Tripos during their undergraduate careers and often took little interest in the Tripos thereafter apart from setting some questions for the Smith's prizes. Given their small lecturing load, they had much free time for research, for familiarising themselves withthe latest mathematical ideas and for trying to publish work matching the originality of the papers coming from continental pens. The Cambridge Mathematical Journal had been founded in 1837 by two Scotsmen, A. Smith, SW 1836, and D. F. Gregory, 5W 1837xv. The relative failure of British pure mathematics during this period in comparison with France and Germany remains something of a paradox. A comparative study of the way mathematics was taught and research organised during this period at the Ecole Polytechnique and Ecole Normale Superieure in Paris and at the Universities of Göttingen and Berlin, the centres of European pure mathematics, would be fascinating.

Fat tails and the cubic law of returns

I came across this nice review article on power law distributions in economic and other contexts. A particularly interesting one is the following, governing short term stock price fluctuations -- surprise, it's not log normal!

6.1.1. The inverse cubic law distribution of stock price fluctuations:

The tail distribution of short-term (15 s to a few days) returns has been analyzed in a series of studies on data sets, with a few thousands of data points (Jansen & de Vries 1991, Lux 1996, Mandelbrot 1963), then with an ever increasing number of data points: Mantegna & Stanley (1995) used 2 million data points, whereas Gopikrishnan et al. (1999) used over 200 million data points. Gopikrishnan et al. (1999) established a strong case for a inverse cubic PL of stock market returns.

...Such a fat-tail PL yields a large number of tail events. Considering that the typical standard daily deviation of a stock is approximately 2%, a 10–standard deviations event is a day in which the stock price moves by at least 20%. From daily experience, the reader can see that those moves are not rare at all: Essentially every week a 10–standard deviations event occurs for one of the (few thousand) stocks in the market.28 The cubic law quantifies that notion and states that a 10–standard deviations event and a 20–standard deviations event are 5^3 = 125 and 10^3 = 1000 times less likely, respectively, than a 2–standard deviations event.

The figure below shows the probability distribution of 15 minute returns on 1000 large company stocks from data taken in 1994-1995. (Click for larger version.)



Here is a figure showing the famous power law scaling of metabolic rate with body mass in animals (click for larger version):

US Track and Field Championships in Eugene

The USATF championships were held here again last week and over the weekend. I run on the same track as these guys, only much slower :-)

The photo below is of Eugenian Nick Symmonds (Oregon Track Club Elite) winning the 800m. See also this panorama shot, which shows the 800m finish and all of Hayward Field.



If you're a track fan, keep your eye on Ashton Eaton, who placed second in the decathalon despite being only a junior at UO (he won the NCAAs earlier in the spring).



Complete results from USATF web site.

Don't cry for Michael

Yes, by the end he had become a freak, perhaps even a monster, a caricature of his younger self. But in 1983, when I was in high school, he really was the king of pop.

I remember how revolutionary MTV and music videos were for kids everywhere, especially in small towns and in states like Iowa.

I caught Michael's famous Motown 25 live performance (below) on television. My brother and I spent hours goofing around trying to figure out how to moonwalk. I was never a huge fan, but you couldn't deny the power of his music or the electricity he generated.



Considering his trajectory in later life, perhaps it was better to go out at 50. Strangely, a song by another departed pop icon comes to mind. Yes, Michael was an odd one, a brother from another planet, a stranger in a strange land. But give him his due -- he did it His Way!

My Way (audio, Frank Sinatra)

And now, the end is near;
And so I face the final curtain.
My friend, I'll say it clear,
I'll state my case, of which I'm certain.

I've lived a life thats full.
I've traveled each and evry highway;
And more, much more than this,
I did it my way.

Regrets, I've had a few;
But then again, too few to mention.
I did what I had to do
And saw it through without exemption.

I planned each charted course;
Each careful step along the byway,
But more, much more than this,
I did it my way.

Yes, there were times, I'm sure you knew
When I bit off more than I could chew.
But through it all, when there was doubt,
I ate it up and spit it out.
I faced it all and I stood tall;
And did it my way.

I've loved, I've laughed and cried.
I've had my fill; my share of losing.
And now, as tears subside,
I find it all so amusing.

To think I did all that;
And may I say - not in a shy way,
No, oh no not me,
I did it my way.

For what is a man, what has he got?
If not himself, then he has naught.
To say the things he truly feels;
And not the words of one who kneels.
The record shows I took the blows -
And did it my way!

Kids these days

Michael Chabon writes in the NY Review of Books. Parents these days are probably the most risk averse, fear driven and statistically innumerate decision makers of all. (Me included!)

Manhood for Amateurs: The Wilderness of Childhood

...Matt Groening once did a great Life in Hell strip that took the form of a map of Bongo's neighborhood. At one end of a street that wound among yards and houses stood Bongo, the little one-eared rabbit boy. At the other stood his mother, about to blow her stack—Bongo was late for dinner again. Between mother and son lay the hazards —labeled angry dogs, roving gang of hooligans, girl with a crush on bongo—of any journey through the Wilderness: deadly animals, antagonistic humans, lures and snares. It captured perfectly the mental maps of their worlds that children endlessly revise and refine. Childhood is a branch of cartography.

The thing that strikes me now when I think about the Wilderness of Childhood is the incredible degree of freedom my parents gave me to adventure there. A very grave, very significant shift in our idea of childhood has occurred since then. The Wilderness of Childhood is gone; the days of adventure are past. ...

...the kind of door-to-door, all-encompassing escort service that we adults have contrived to provide for our children. We schedule their encounters for them, driving them to and from one another's houses so they never get a chance to discover the unexplored lands between. If they are lucky, we send them out to play in the backyard, where they can be safely fenced in and even, in extreme cases, monitored with security cameras. When my family and I moved onto our street in Berkeley, the family next door included a nine-year-old girl; in the house two doors down the other way, there was a nine-year-old boy, her exact contemporary and, like her, a lifelong resident of the street. They had never met.

...But the primary reason for this curtailing of adventure, this closing off of Wilderness, is the increased anxiety we all feel over the abduction of children by strangers; we fear the wolves in the Wilderness. This is not a rational fear; in 1999, for example, according to the Justice Department, the number of abductions by strangers in the United States was 115. Such crimes have always occurred at about the same rate; being a child is exactly no more and no less dangerous than it ever was. What has changed is that the horror is so much better known. [My brainy wife, upon reading this, asked -- if parents are more vigilant, shouldn't the rate of abductions have gone *down* in recent years? If it stayed constant, isn't the world indeed more dangerous for non-vigilant parents?]

...What is the impact of the closing down of the Wilderness on the development of children's imaginations? This is what I worry about the most. I grew up with a freedom, a liberty that now seems breathtaking and almost impossible.

...Art is a form of exploration, of sailing off into the unknown alone, heading for those unmarked places on the map. If children are not permitted—not taught—to be adventurers and explorers as children, what will become of the world of adventure, of stories, of literature itself?

Genetic clustering: 40 years of progress

Represent each individual human by their DNA sequence. When aggregated, they cluster into readily identifiable groups. This has been known for 40 years now, although the technology and methods of analysis continue to improve. Below are results from 1966, 1978 and 2008.

If this seems counterintuitive to you, it might be because the space of genetic variation is of very high dimension. See here for more discussion and an illustration.

(Click images for larger version.)

Population Structure and Human Evolution
L. L. Cavalli-Sforza

Proceedings of the Royal Society of London. Series B, Biological Sciences, Vol. 164, No.995, A Symposium from Mendel's Factors to the Genetic Code (Mar. 22, 1966), pp. 362-379
http://www.jstor.org/stable/pdfplus/75457.pdf




Measurement of Differentiation: Reply to Lewontin, Powell, and Taylor
Jeffry B. Mitton

The American Naturalist, Vol. 112, No. 988 (Nov. - Dec., 1978), pp. 1142-1144
http://www.jstor.org/stable/2460361?origin=JSTOR-
pdf




Current state of the art, as discussed here. Figure: The three clusters shown below are European (top, green + red), Nigerian (light blue) and E. Asian (purple + blue).



According to the mathematical analysis given in this paper, populations with FST as low as .0001 can be resolved with current technology. (Typical FST between northern and southern Europe is about .006, between Europe and E. Asia about .1 and between Europe and Nigeria about .14 .)

Missing giants of modern science

Below is some (lightly edited) correspondence between Vanderbilt cosmologist Robert Scherrer and myself on topics related to my previous post Why are modern scientists so dull?

From: Bob
Subject: why we are all so boring

I enjoyed your posting on why we are all so boring (and I agree with the bulk of it - it is certainly easier for eccentric, brilliant types to thrive in mathematics or theoretical physics than in any other field).

The issue of genius raises an obvious question. If we are cultivating brilliant people more effectively now than at the turn of the 20th century (and I believe we are), so that everyone is brilliant, as opposed to a few outliers, then why did we get the development of quantum mechanics and relativity (or, going back even earlier, classical mechanics and electricity and magnetism) during an era when the level of effort, and the number of "brilliant" scientists, was exponentially smaller? Where are the equivalent breakthroughs of today? Is it possible that the structure of the laws of physics is such that there are basically only a few breakthroughs waiting to happen and easily accessible to an industrialized society, and we've already used them up?

Reply from Steve:

I agree with you that we may have picked a lot of the low hanging fruit. It happened to be the case that in the various "golden ages" of physics technology was available to test the new theories relatively soon after they were proposed, which is not true today. I suspect if we had table top Planck energy accelerators then progress on quantum gravity might have been much faster during our careers. In fact, some people might have revealed themselves as "geniuses" because they looked at the data stream and proposed the correct models, thereby becoming famous instead of obscure scribblers like me :-)

I have an interest in psychology and psychometrics, and have been carefully watching all the "smartest" people I have come across in our field, cross referencing as best I can between older and newer generations. (I'm sure everybody else has too.) I suspect there are plenty of smart guys around today and the old guys weren't as quite spectacular as the glow from their Nobels might suggest -- at least, not when compared to plenty of smart but relatively obscure people of later generations. Sometimes it is better to be lucky than good (an old Wall St. saying)!

More from Bob:

...With regard to the relative level of "smartness", I have an interest in the history of baseball. It is certainly true that an average modern team would completely devastate an "old-time" famous team like the 1927 Yankees, given improvements in nutrition, training, (and pharmaceuticals :) However, I suspect that even if you equalized these things, the modern team might still win, as we are now much more efficient at scouring talent everywhere (the integration of baseball alone is an obvious example).

...It would be interesting to speculate if there are any areas in which we've become LESS efficient in aggregating talent than we were 50 or 100 years ago. Skilled artisans, perhaps? Marksmen?

I'm sure there is a lot of stuff that was more useful in the past than today, and for that reason we don't filter as hard anymore for those talents. But society has gotten richer and more organized, information technology has gotten cheaper, statistical techniques more widely deployed, and in some fields we now have winner-take-all economies. So we're probably overall much, much better at identifying talent, whether the field is tennis, mathematics or even American Idol crooning. I can't think of any old timers who could hang with Usain Bolt!

Why are modern scientists so dull?

On the subject of personality factors and success in science, here is a provocative essay by UK professor Bruce Charlton. (PDF version.) He claims that the modern system selects for conscientiousness over raw intelligence, with negative consequences.

Question: why are so many leading modern scientists so dull and lacking in scientific ambition?

Answer: because the science selection process ruthlessly weeds-out interesting and imaginative people. At each level in education, training and career progression there is a tendency to exclude smart and creative people by preferring Conscientious and Agreeable people. The progressive lengthening of scientific training and the reduced independence of career scientists have tended to deter vocational ‘revolutionary’ scientists in favour of industrious and socially adept individuals better suited to incremental ‘normal’ science. High general intelligence (IQ) is required for revolutionary science. But educational attainment depends on a combination of intelligence and the personality trait of Conscientiousness; and these attributes do not correlate closely.

...At each level in education, training and career progression there is a tendency to exclude smart and creative people by preferring conscientious and sociable people. As science becomes ever-more dominated by ‘peer review’ mechanisms, pro-social behaviour in scientists has been accorded primacy over the brilliant and inspired – but abrasive and rebellious – type of truth-seekers who used to be common among the best scientists.

A majority of senior professional scientists have been through a rigorous and prolonged process of education, selection and training to become professional researchers. Yet the nature of the rigour and the duration of the process in modern science ensures that those who come out at the end and attain long-term scientific employment are not the kind of people capable of top level, revolutionary science. They will very probably be extremely productive and socially compliant, but of only moderately high intelligence and likely to be lacking in imagination [2].

...Modern science is just too dull an activity to attract, retain or promote many of the most intelligent and creative people. In particular the requirement for around 10, 15, even 20 years of postgraduate ‘training’ before even having a chance at doing some independent research of one’s own choosing, is enough to deter almost anyone with a spark of vitality or self-respect; and utterly exclude anyone with an urgent sense of vocation for creative endeavour. Even after a decade or two of ‘training’ the most likely scientific prospect is that of researching a topic determined by the availability of funding rather than scientific importance, or else functioning as a cog in someone else’s research machine. Either way, the scientist will be working on somebody else’s problem – not his own. Why would any serious intellectual wish to aim for such a career? ...

Shorter Charlton: there are too many hoops, and we end up selecting for Agreeableness and Conscientiousness (hoop jumping abilities) rather than raw brainpower.

I partially agree with Charlton's claims, but the specifics vary from field to field. The area he seems most familiar with is medical science, which most physicists (after teaching premeds and biology students) might concur selects for conscientious rather than brilliant types ;-) In physics it seems we are quite tolerant of odd personalities -- hyper aggressive types, those with Asperger's Syndrome, etc., especially if the person in question displays tremendous ability. I would guess the same is largely true in math and engineering. In biology and medicine it may not be that easy to tell the really talented researchers from the rest (at least at early career stages), which would lead to more emphasis on personality traits. It's also true that in many areas of physics (specifically, but not limited to, the theoretical ones) one can work as a single investigator or small group lead investigator quite early. This may be less true in medicine and biology.

I discussed the current incentive system in science here, as well as the job prospects in theoretical physics. Given the situation I can't blame any students who find that alternative careers might be preferable. As I wrote here (in partial agreement with Charlton), this leads to a different kind of selection than in the past:

...Nowadays, success in science seems to be as much a selection for [certain] character or personality traits as it is a selection for talent.

Related posts: frauds , success vs ability .

Regarding Charlton's deeper question: Where have all the geniuses gone? I offer the following from this earlier post. See also Genius, Gleick's biography of Feynman, especially pp.325-328.

... the exact topic discussed in James Gleick's book Genius. In a field where sampling of talents is sparse [like science in its earlier days] ... you might find one giant ... towering above the others, able to do things others cannot. In a well-developed, highly competitive field like modern mathematics, all the top players are "geniuses" in some sense (rare talents, one in a million), even though they don't stand out very much from each other. In Gleick's book, Feynman, discussing how long it might have taken to develop general relativity had Einstein not done it, says "We are not that much smarter than each other"!

To put it simply, if I sample sparsely from a Gaussian distribution, I might find a super-outlier in the resulting set. If I sample densely and have a high minimum cutoff for acceptable points, I will end up with a set entirely composed of outliers, but who do not stand out much from each other. Every guard in the NBA is an athletic freak of nature [and they would destroy their predecessors from the early era of professional basketball], even though they are evenly matched when playing against each other.

Happiness

In the previous post I mentioned my scores on this Big Five personality test. Someone immediately doubted whether I (or any theoretical physicist) could really have scored at the 99th percentile for Stability (opposite of Neuroticism). Upon further reflection, I find the result a little puzzling as well!

One contributing factor I can point to is that I've been thinking about the problem of happiness and the hedonic treadmill for some time.

It's also true that my father passed away while I was still fairly young, so I had the impetus to consider his life in its entirety and to evaluate which of the things he did really mattered, and which didn't.

If you're interested in optimizing your own life satisfaction, I recommend the Happiness Project blog, written by Gretchen Rubin (she is Robert Rubin's daughter in law; I once worked with her husband who was at the time an investment banker). I especially recommend her short movie The Years Are Short (it's only a minute or so long) to any parent with small kids.

I guess I would describe myself as something of a stoic. My favorite bit of advice for academics comes from...

Marcus Aurelius

"Or does the bubble reputation distract you? Keep before your eyes the swift onset of oblivion, and the abysses of eternity before us and behind; mark how hollow are the echoes of applause, how fickle and undiscerning the judgments of professed admirers, and how puny the arena of human fame. For the entire earth is but a point, and the place of our own habitation but a minute corner in it; and how many are therein who will praise you, and what sort of men are they?"

Spent, Miller and Kanazawa

I was wandering in the bookstore today and looked through a copy of Geoffrey Miller's book Spent: Sex, Evolution and Human Behavior. (I am a cheapskate, and I read pretty fast, so I often skim through entire books at the bookstore.) If you like evolutionary psychology, you will probably enjoy the book, which is well written and covers some novel topics. One point emphasized by Miller throughout his career is that the human brain evolved not just to survive, but to survive in competition against other human brains, and particularly in the context of sexual selection. Working out the implications of this observation seems to be one of his main interests. This book concentrates on marketing, consumer behavior, signaling and related subjects.

If you hate evolutionary psychology, perhaps because you feel it's unrigorous and consists of a collection of just-so stories, then you might not like the book as much. Nevertheless, much of what Miller writes remains interesting, particularly his discussion of what he calls the Central Six personality traits -- g (or IQ), Openness, Extraversion, Stability, Agreeableness, Conscientiousness. The "general factor" g is defined as the largest principal component that arises in analysis of the correlation between performance on cognitive tests. Similarly, the Big Five factors are the largest components that arise in the analysis of personality -- it is claimed that they capture most of the variation in personality (see here for more detailed discussion of Big Five). Miller argues that marketers don't make as much use of these principal components as they could.

You can take a brief Big Five test here. My scores were (percentiles): Openness 88, Conscientiousness 94, Extraversion 89, Agreeableness 74 and Neuroticism (opposite of Stability) 1.

Looking at Spent reminded me of a debate between Miller and LSE researcher Satoshi Kanazawa I read a few years ago. Each part was published separately in the journal Evolutionary Psychology (click title for PDF).

The Asian Future of Evolutionary Psychology, by Geoffrey Miller

Abstract: Asia’s population, wealth, cognitive capital, and scientific influence are growing quickly. Reasonable demographic, economic, and psychometric projections suggest that by the mid-21st century, most of the world’s psychology will be done in Asia, by Asians. Even if evolutionary psychology wins the battles for academic respectability in the United States and European Union, if it ignores the rise of Asian psychology, it will fail to have any serious, long-term, global influence in the behavioral sciences after the current generations of researchers are dead. ...

No, It Ain't Gonna Be Like That, by Satoshi Kanazawa

Abstract: For cultural, social, and institutional reasons, Asians cannot make original contributions to basic science. I therefore doubt Miller's prediction for the Asian future of evolutionary psychology. I believe that its future will continue to be in the United States and Europe.

Asian Creativity: A Response to Satoshi Kanazawa, by Geoffrey Miller

Abstract: This article responds to Satoshi Kanazawa’s thoughtful and entertaining comments about my article concerning the Asian future of evolutionary psychology. Contra Kanazawa’s argument that Asian cultural traditions and/or character inhibit Asian scientific creativity, I review historical evidence of high Asian creativity, and psychometric evidence of high Asian intelligence (a cognitive trait) and openness to experience (a personality trait) – two key components of creativity. ...

I find this debate amusing and thought provoking, although I am not at all convinced by most of the arguments presented. One wonders how careful Miller and Kanazawa are about deriving strongly held beliefs from limited data. To what extent do priors dominate their beliefs?

One interesting thing about Miller's first essay above is that he takes a quantitative stab at estimating the population of high-g (IQ > 130) individuals in different parts of the world. You can't get more un-PC than that :-) Of course, to make this estimate he needs to make assumptions not just about average IQs by population, but standard deviations as well!

Plight of the risk managers

I'd like to recommend this podcast interview with Riccardo Rebonato. Rebonato, the author of the prescient book Plight of the Fortune Tellers, written before the financial crisis, is a former physicist turned quant.

Rebonato does not mince words, pointing out the weaknesses of mathematical models, and noting that most quants, although mathematically sophisticated, often lacked deep knowledge about markets and banking (I assume he does not include himself in this group). In my experience many quants never questioned the basic efficient market assumptions underlying their models, although some certainly did -- in particular, those with trading experience.

Rebonato is polite, even urbane, but disagrees with Econtalk interviewer Russ Roberts on many important issues. The most important question, which Rebonato addresses immediately, is whether enlightened, self-interested managers of financial institutions can be relied on to properly manage risk. Regulators accepted, on faith, the self-regulating abilities and properties of a system managed by such people. Thus, one of the main ingredients in the crisis was the ideological (as opposed to political or financial) capture of regulators by efficient market proponents.

Other interesting topics covered are the divergent risk tolerances and interests of bond holders vs equity holders vs regulators of banks [1], and whether moral hazard (anticipation of a bailout) played a role in the crisis -- Russ, the anti-government libertarian, says yes. Rebonato says no, the story only makes sense if told at the institutional level, whereas individual incentives were different. I think Rebonato's logic is impeccable. It's more persuasive to me that incentive schemes which allowed huge compensation based on short term (ultimately illusory) gains were much more of a factor. (See Clawbacks, fake alpha and tail risk.)

Dr. Riccardo Rebonato

Riccardo is Global Head of Market Risk and Global Head of Quantitative Research and Quantitative Analysis for Royal Bank of Scotland based in London. Prior to joining the Royal Bank of Scotland, he was Head of Complex Derivatives Trading Europe desk and Head of Derivatives Research at Barclays Capital, where he worked for nine years.

Riccardo is a Visiting Lecturer at Oxford University in Mathematical Finance and Adjunct Professor at the Tanaka Business School, Imperial College, London.

Before joining the financial world, Riccardo was a Research Fellow in Physics at Oxford University (Corpus Christi College) and, before that, Visiting Scientist at Brookhaven National Laboratory.

Riccardo is the author of the books Plight of the Fortune Tellers ('07), The Perfect Hedger and the Fox (Wiley ’04), Modern Pricing of Interest-Rate Derivatives (Princeton University Press ’02), Interest-Rate Option Models (Wiley ’96,’98), Volatility and Correlation in Option Pricing (Wiley ’99). He has published several papers on finance (option modelling, computational techniques, risk management) in academic journals. He is a regular speaker at conferences worldwide.

[1] Footnote: see my earlier post on the vacuous Modigliani-Miller theorem. I recently learned from Vernon Smith's memoir (see pages 230-231 and 276) that he has similar opinions. Google books link; also search under "MM".

Matter and Antimatter, Angels and Demons: slides, video, audio

Below are links to slides, video and audio for the public lecture I gave on the movie Angels and Demons and related topics in high energy physics. This was part of a broader outreach effort by the high energy physics community -- about 50 such talks were given in multiple countries to coincide with the release of the film.

If you watch the video or listen to the audio, be sure to check out the last part as there were a lot of good questions from the audience.

Slides: Powerpoint file

Video: Windows Media , MP4 for Macs

Audio only: MP3

Vietnam: Strange Ground

At a dinner tonight I ended up seated next to an interesting older professor, a historian of modern SE Asia, probably in his sixties. A Yalie, he stayed in New Haven for graduate school, managing to avoid Vietnam despite being an Army officer with Ranger training. He had been a friend of mathematician Paul Olum, a highly esteemed president of the University of Oregon during the 1980's. (Olum and Feynman at Los Alamos.)

Talking with him about the Vietnam war reminded me of the oral history Strange Ground, by Harry Maurer, which I highly recommend. The recollections in the book read like the uncensored straight dope -- see, for example, this page.

Below is one of the few reviews of the book I could find online. I agree with the positive comments. As to the complaint that the book could have included interviews with Vietnamese or other participants of the war, well, the book is specifically about the American experience there.

Strange Ground is a collection of sixty seven first-hand accounts of the Vietnam war by Americans who were involved. It starts with an OSS mission to aid Ho Chi Minh against the Japanese near the end of World War II and finishes with the frantic evacuation of Saigon in 1975. The range of people included is immense — from alienated grunts in the infantry to gung-ho generals, from anti-war activists visiting North Vietnam to the wives of State Department officials in Saigon. The result is a broad sweeping view of the United States' involvement with Vietnam over three decades, but at the same time one with the feeling of immediacy that only such personal accounts can give.

My only dissatisfaction with this book was that it could have been so much better. As it stands it is like an album of photos of a tree: close up and wide-angle, black and white and colour, in sunlight and in shadow — but all taken from the same direction. Some of the Americans labelled all Vietnamese gooks and hated them, others felt the allure of Vietnamese culture and fell in love with the country. Nowhere, however, do we get any real idea about how these mysterious Vietnamese felt about the Americans. If Strange Ground had covered all the participants in the war — Viet Cong and ARVN and uncommitted peasants and French and North Vietnamese and Cambodians and even Australians — then it would have been a truly great book instead of just a very good one.

Strange Ground will be compulsory reading for anyone interested in the American experience in Vietnam.

University rankings: research and faculty quality

University rankings are a complicated subject; see this Wikipedia entry for an overview of various methodologies. Two common problems with ranking algorithms are:

1. Reliance on reputational surveys -- reputation is a lagging indicator, and often inaccurate (see below).

2. Failure to normalize performance measures to size of institution (i.e., number of faculty). A bigger institution should, all things being equal, produce more research papers and grant dollars. Normalizing to size yields a better indicator of average quality.

The only analysis I could find which corrects for these problems appears in the book The Rise of American Research Universities, a detailed study by two academics, Hugh Davis Graham and Nancy Diamond. The authors construct 3 research productivity indices for the period 1980-1990. The natural and social science indices are computed by counting publications in top journals, while the humanities index is computed by counting awards from the National Endowment for Humanities, American Council of Learned Societies, Guggenheim Foundation, etc. (humanists tend to publish books rather than articles). Graham and Diamond normalize the scores to the number of faculty, providing a true per capita measure of average quality.

The following figure shows the combined results for public research universities. Note the divergence between reputation (right column, from NRC rankings of graduate programs) and actual per capita scholarly productivity. (Click for larger version.)



The natural science index result is also interesting (natural science includes math, engineering, computer science as well as physics, chemistry, biology, etc.). Caltech's score is 3.36, followed by Stanford 1.21, MIT 1.16, Harvard .93, Berkeley .92, Princeton .83. So far, according to reputation, but note UC San Diego is ranked 4th (just below MIT) at 1.07! UC Irvine (.56), UCSB (.53), UCLA (.51) and Colorado (.55) are all in the top 20, comparable to Ivies like Yale (.65), Cornell (.60) and Columbia (.49) and ahead of Big 10 powers Illinois (.45), Wisconsin (.42) and Michigan (.32). Hmm... according to these results Caltech researchers were 3 times as productive per capita (in these subjects, normalized to total faculty size) as their counterparts at MIT and Harvard, and 10 times as productive as those at Michigan. Part of this must be the relatively smaller social science and humanities departments, but that can't explain the whole effect.

Graham and Diamond's results establish that reputation is often a misleading indicator. They identify a number of "rising" public research universities -- often in the west (California, Colorado, Oregon) -- whose reputation rankings are not commensurate with their research quality. It reminds me of the way that traditional east coast sports media underrates Pac-10 football year after year. Sure, Ohio State and Michigan look great playing against other slow as mud teams, until they get to the Rose Bowl :-)

Princeton Companion to Mathematics

I finally got a copy of The Princeton Companion to Mathematics. PCM is over 1000 pages of extremely well written, self-contained essays on a variety of topics in pure and applied mathematics. The book aims to be comprehensive in its coverage, an amazing ambition that seems to have been achieved, at least at the level of overview for non-specialists. Modern mathematics is such a broad and deep subject that PCM will be of use to students and experienced researchers alike. Every essay I have looked at is a pleasure to read.

Because the essays can be read independently, I think the ideal form for this book would be as an online document. Perhaps the publishers could work out a system for granting online access to people who buy the book (copy control issues notwithstanding)?

For hard core researchers, the alternative is the Japanese Encyclopedic Dictionary of Mathematics (EDM), which was prepared by the Mathematical Society of Japan. This book is highly compressed (even at 2000 pages) and is not the place to look for a cursory overview or readable introduction. One reviewer wrote:

EDM is an astonishing achievement. The result of an extraordinary, decades-long collaboration among literally hundreds of celebrated Japanese mathematicians, it will not only never be equalled but in all probability will never be challenged. In two massive volumes, the EDM surveys the whole of the mathematical sciences, both pure and applied, through a series of pithy articles containing the key definitions, methods, and results of every mathematical subdiscipline sufficiently coherent to have a name. It also tabulates vast amounts of information -- homotopy groups of spheres, symmetries of ordinary differential equations, characters of finite groups, class numbers of algebraic number fields, and so forth, seemingly, ad infinitum -- available, as far as I know, in no other single reference work.

...It is likewise only fair to point out that the EDM is a tool for serious research mathematicians. To keep its component articles brief, it makes full, unapologetic use of a wide variety of notational and expositional economies. The EDM seldom if ever provides a heuristic explanation of anything; although it often gives a bare outline of the historical development of a subject area, it resolutely eschews Toeplitz's "genetic" exposition, in which the crucial problems and examples that engendered a field are placed in the foreground. Only those persons comfortable with a very considerable level of compactness and abstraction in the exposition of mathematical ideas will find the EDM easy reading.

This lack of heuristic background and examples has made the EDM very difficult for me to use. It's OK for looking up results, but not for getting a feel for a completely new area. Perhaps there are people who are sufficiently strong that they can just pick up and read the EDM the way I can read the PCM, but probably not very many!

PCM was edited by Fields Medalist Timothy Gowers, who recently posted the latest errata on his blog.

Below are the contents:

I. What is Mathematics?
II. Ideas of Mathematics
III. Mathematical Objects
IV. Branches of Mathematics
V. Mathematicians
VI. Theorems and Problems
VII. The Influence of Mathematics
VIII. Miscellaneous

The following sample articles can be accessed as described below. Enter Username “Guest” and Password “PCM” at this site, then click “Resources” in the sidebar, then “Sample articles” in the sidebar.

Section Title

I Some Fundamental Mathematical Definitions
I The Language and Grammar of Mathematics
II Geometry
III Braid Groups
III Designs
III Determinants
III Distributions
III The Exponential and Logarithmic Functions
III Function Spaces
III Hilbert Spaces
III Knot Polynomials
III Metric Spaces
III Normed Spaces and Banach Spaces
III Permutation Groups
III Riemannian Metric
III Quaternions
III The Exponential and Logarithmic Functions
III The Euclidean Algorithm and Continued Fractions
III The Simplex Algorithm
III The Spectrum
IV Algebraic Geometry
IV Algebraic Numbers
IV Arithmetic Geometry
IV Differential Topology
IV Dynamics
IV Enumerative and Algebraic Combinatorics
IV High-Dimensional Geometry and Its Probablistic Analogues
IV Moduli Spaces
IV Operator Algebras
IV Probabilistic Models of Critical Phenomena
IV The Fourier Transform
V George Birkhoff
V János Bolyai
V Arthur Cayley
V Pierre Fermat
V Kurt Gödel
V Jacques Hadamard
V David Hilbert
V Sonya Kovalevskaya
V Nicolai Ivanovich Lobachevskii
V Pierre-Simon Laplace
V Isaac Newton
V Emmy Noether
V Jules Henri Poincaré
V Karl Weierstrass
VI Dvoretzky's Theorem
VI Gödel's Theorem
VI Liouville's Theorem and Roth's Theorem
VI The Atiyah–Singer Index Theorem
VI The Banach–Tarski Paradox
VI The Classification of Finite Simple Groups
VI The Fundamental Theorem of Algebra
VI The Fundamental Theorem of Arithmetic
VI The Insolubility of the Quintic
VII Analysis, Mathematical and Philosophical
VII Mathematical Biology
VII Mathematics and Chemistry
VII Mathematics and Economic Reasoning
VII Reliable Transmission of Information
VII Routing in Networks
VII The Mathematics of Algorithm Design
VII The Mathematics of Money
VIII Advice to a Young Mathematician
VIII Mathematics: An Experimental Science
VIII The Art of Problem Solving