Hadamard: The Mathematician's Mind

I've been meaning to discuss the book The Psychology of Mathematical Invention in the Mathematical Field, by Jacques Hadamard. It was inspired by a lecture of Poincare to the French Psychological Society entitled "Mathematical Creation". Although I always considered Hadamard a 19th century figure (born 1865), the book was published in 1945 and he lived until 1963!

Here is the Amazon description:

Fifty years ago when Jacques Hadamard set out to explore how mathematicians invent new ideas, he considered the creative experiences of some of the greatest thinkers of his generation, such as George Polya, Claude Lévi-Strauss, and Albert Einstein. It appeared that inspiration could strike anytime, particularly after an individual had worked hard on a problem for days and then turned attention to another activity. In exploring this phenomenon, Hadamard produced one of the most famous and cogent cases for the existence of unconscious mental processes in mathematical invention and other forms of creativity. Written before the explosion of research in computers and cognitive science, his book, originally titled The Psychology of Invention in the Mathematical Field, remains an important tool for exploring the increasingly complex problem of mental life.

The roots of creativity for Hadamard lie not in consciousness, but in the long unconscious work of incubation, and in the unconscious aesthetic selection of ideas that thereby pass into consciousness. His discussion of this process comprises a wide range of topics, including the use of mental images or symbols, visualized or auditory words, "meaningless" words, logic, and intuition. Among the important documents collected is a letter from Albert Einstein analyzing his own mechanism of thought.

Hadamard emphasizes a four step process of invention, consisting of

Preparation: conscious effort attacking the problem, including analysis of various methods and approaches; the outcome often appears fruitless

Incubation: a period of subconscious effort while the conscious mind is occupied with other matters

Illumination: the solution forms in the conscious mind

Verification: the solution is verified through conscious effort

This description agrees with my own experience. It seems that certain activities like walking are good for Incubation, and the shower is a good time for Illumination. Over the past weeks I've been deliberately trying to follow this method in my own research, with modest success :^) I noticed that it is also useful for overcoming writer's block -- put aside the paragraph you are struggling with and walk around for five or ten minutes before resuming. The walk often allows a small conceptual reordering, enough to proceed.

Incidentally, I often found my father and other professors and scientists I grew up around to be absent minded. I was never that way, and therefore wondered if I was fundamentally not of the scientific type (a smart kid, but not nerdy enough!). However, what I've found is that a lifetime of working on abstract problems has now given me the ability to call forth a problem of my choice and work with it in my head, leading to the tendency to occasionally detach from my surroundings. So, I appear (e.g., to my wife and kids!) to be the scientist type, but as a consequence of developing a particular functional ability rather than due to a specific predilection or tendency.

This paper contains a nice discussion of Hadamard's essay, and describes a modern study using Hadamard's original questionnaire. I liked these comments on the role of talking about problems:

... it is also clear from the mathematicians' responses that, while working in the initiation phase, they have a much higher regard for transmission of mathematical knowledge through talking than through reading. ...

Jerry: I assimilate the work of others best through personal contact and being able to question them directly. [..] In this question and answer mode, I often get good ideas too. In this sense, the two modes are almost indistinguishable.

George: I get most of my real mathematical input live, from (good) lectures or one-on-one discussions. I think most mathematicians do. I look at papers only after I have had some overall idea of a problem and then I do not look at details.

Toxic assets anyone?

You can be a vulture too :-)

Free leverage from Uncle Sam! What's not to like?

WSJ: ... New York-based fund giant BlackRock is launching a closed-end mutual fund aimed at allowing ordinary investors to put their money into the kind of toxic mortgage-backed securities that nearly brought down the financial system a few months ago. Shares are expected to go on sale in about a month.

The BlackRock Legacy Securities Public-Private Trust, which may raise up to about $1 billion, will be sold through brokers and advisers. It will try to buy mortgage-backed securities at distressed prices from banks looking to shore up their battered balance sheets. The fund will invest alongside the U.S. Treasury as part of the Public-Private Investment Partnership, or PPIP, launched earlier this year. BlackRock is among a small group of firms picked to take part in PPIP.

... The fund will also benefit from helpful financial engineering courtesy of the U.S. government. PPIP was set up to encourage private investors to help bail out the financial system. So for every dollar invested, Uncle Sam will provide another $2—$1 in equity and $1 in debt. The debt’s cheap, too: about two percentage points over the LIBOR interbank rate. That should boost returns.

Sources are hoping that, when you factor in the financial engineering, the fund will be able to earn maybe 10-12% annually over its ten-year life.

... “For now, the bulk of toxic assets are not going to be in play,” Harvard law professor Lucian Bebchuk, one of the intellectual architects of PPIP, told me. Changes to accounting rules and government stress tests, have taken off some of the pressure off banks, so Professor Bebchuk says banks are not as motivated to sell their toxic assets as they were when PPIP was set up in March. “For many types of toxic assets, even if the banks can get a price that’s fair, if it’s at a discount to face value they don’t have an incentive to do it,” he says.

Furthermore, thanks to the stock market rally the banks are feeling more confident—and have a lot more access to capital.

... Meanwhile, the fundamentals of MBS continue to worsen. Fitch Ratings says 6.8% of (non-agency) prime mortgages are now delinquent—twice as many as were delinquent six months ago. The figures for Alt-A are 21%, and for sub-prime, 40%. They’re still getting worse. Fitch director Grant Bailey says mortgage delinquency rates won’t stabilize until house prices and unemployment rates do.

What's another $100M among us taxpayers?

I'd be outraged, except I'm sure Mr. Hall is providing far more than $100M of value this year to US taxpayers by making sure that energy prices are set so as to optimize the functioning of the global economy. The reason I know this is the outcome of his herculean efforts is that (a) I was taught all about efficient markets by leading economists and (b) it strongly reinforces the objectivist priors I picked up from reading Atlas Shrugged ;-)

WSJ: A top Citigroup Inc. trader is pressing the financial giant to honor a 2009 pay package that could total $100 million, setting the stage for a potential showdown between Citi and the government's new pay czar.

The trader, Andrew J. Hall, heads Citigroup's energy-trading unit, Phibro LLC -- a secretive operation, run from the site of a former Connecticut dairy farm, that occasionally accounts for a disproportionate chunk of Citigroup income.

Mr. Hall's pay package puts Citigroup in a tight spot. Ripping up the contract could trigger Mr. Hall's departure and a potentially messy legal fight. But making any large payouts, even if they're based on previously agreed contracts, could subject Citigroup to political and investor fallout.

Earlier this year, American International Group Inc.'s bonus payments of $165 million to some executives caused an outcry, given the insurer's U.S.-government bailout. Citigroup has received some $45 billion in bailout money.

... It will be an early test for Kenneth Feinberg, the Treasury Department's pay czar, who was appointed last month to a new position with the power to help set pay for top executives and highly paid employees at seven firms receiving the most government financial aid. Banks and others have a mid-August deadline for submitting pay requests to Mr. Feinberg.

... Last year Mr. Hall received pay of more than $100 million, people familiar with the matter say. With this year barely half over, Mr. Hall's specific 2009 pay hasn't yet been set. Citigroup doesn't break out detailed financial reports for Phibro, but traders say the firm is having a good year.

Thomas Bouchard against group think and political correctness

Psychologist Thomas Bouchard, a leader in the field of twin and adoption studies, is retiring from the University of Minnesota. (Some Bouchard papers from Google Scholar.) He gave this farewell interview to Science. (See also this 2004 video; I think the interviewer is David Lubinski.)

Important components of today's conventional wisdom will turn out to be completely wrong. Analyze any past period and you'll find that this statement turned out to be true.

Q: What got you into twin studies?

TB: I was teaching the psychology of individual differences, and in 1979, two different people put a copy in my mailbox of a story about twins reared apart and their similarities when they met. [These were the "Jim twins," Jim Springer and Jim Lewis, who had been separated at birth and reunited at age 39. Both married women named Linda, divorced, and remarried women named Betty. They named their sons James Allan and James Alan, respectively, and both had dogs named Toy.] They sounded interesting, so I asked a few of my colleagues to help me study them. We ended up studying twins reared apart—126 pairs including 74 pairs of identical twins—for 20 years. [The twin study wound down in 2000.] I found that I loved working with twins. They're still amazing and a major mystery to me.

Q: What were attitudes toward behavioral genetics in the early years of your career?

TB: In graduate school at UC [the University of California] Berkeley, I was reading a book edited by psychiatrist D. D. Jackson on the etiology of schizophrenia. The first chapter, by a geneticist, was on twin studies. Then Jackson refuted it all with just the kind of crap you hear now against twin studies. He said families are the cause of schizophrenia. I remember saying in a graduate seminar, "Most of this stuff [in Jackson's argument] is junk"—I crawled out of the seminar room a bloody pulp. The reaction [from seminar members] was my first absolutely clear-cut demonstration that psychologists believed correlation is causation, ... and many still do.

In the '70s, when I was teaching research by [IQ researcher Arthur] Jensen and [twin researcher Francis] Galton, people picketed me, called me a racist, tried to get me fired. The progressive student association sent members in to ask hostile questions. ... So I put a tape recorder on the podium and said: "I'm going to tape my lectures." I never heard from them again. They knew what they were saying was nonsense and I would be able to prove it.

Q: Do you think perceptions have changed dramatically since the '70s now that twin research has revealed genetic bases for many disorders, such as autism (which had been blamed on cold mothers) and ADHD (for which many blamed food dyes)?

TB: Within the university—at least at U. Minnesota—the cumulative impact of behavioral genetics findings has had a lot of effect. There's a lot more tolerance for the idea of genetic influences in individual differences.

But we still have whole domains we can't talk about. One of the great dangers in the psychology of individual differences is self-censorship. For example, when I was a student, it was widely accepted that black self-esteem was much lower than white self-esteem, and that was a cause of differences in achievement between the two groups. Now that's been completely overturned—there is virtually no racial difference in self-esteem. But people had enormous amounts of data [showing this] that they didn't publish because it did not fit the prevailing belief system. How much wasted effort was generated by the flawed self-esteem work as an explanation of the black-white IQ difference? Now a days, I'm sure there are people who are not publishing stuff on sex differences. Look what happened to Larry Summers [who resigned as president of Harvard University after suggesting that discrimina tion alone doesn't account for women's lower representation in math-based disciplines]. I talk about those things in my class all the time—that males and females have different interests; ... in a sense, females have a broader and richer view of life. There are a lot of people who simply won't talk about those things. Academics, like teenagers, sometimes don't have any sense regarding the degree to which they are conformists.

Nicholas Wade also writes about this in a guest post on the NYTimes TiernyLab blog:

... You’re an expert because all your peers recognize you as such. But if you start to get too far out of line with what your peers believe, they will look at you askance and start to withdraw the informal title of “expert” they have implicitly bestowed on you. Then you’ll bear the less comfortable label of “maverick,” which is only a few stops short of “scapegoat” or “pariah.”

A remarkable first-hand description of this phenomenon was provided a few months ago by the economist Robert Shiller, co-inventor of the Case-Shiller house price index. Dr. Shiller was concerned about what he saw as an impending house price bubble when he served as an adviser to the Federal Reserve Bank of New York up until 2004.

So why didn’t he burst his lungs warning about the impending collapse of the housing market? “In my position on the panel, I felt the need to use restraint,” he relates. “While I warned about the bubbles I believed were developing in the stock and housing markets, I did so very gently, and felt vulnerable expressing such quirky views. Deviating too far from consensus leaves one feeling potentially ostracized from the group, with the risk that one may be terminated.”

... If the brightest minds on Wall Street got suckered by group-think into believing house prices would never fall, what other policies founded on consensus wisdom could be waiting to come unraveled? Global warming, you say? You mean it might be harder to model climate change 20 years ahead than house prices 5 years ahead? Surely not – how could so many climatologists be wrong?

What’s wrong with consensuses is not the establishment of a majority view, which is necessary and legitimate, but the silencing of skeptics. “We still have whole domains we can’t talk about,” Dr. Bouchard said, referring to the psychology of differences between races and sexes.

Look for Wade to take a huge beating from climate conformists.

Bitter geeks

From Googler Mark Chu-Carroll, a post and ensuing 600+ comments on how horrible high school is for some geeks. Mark writes the blog Good Math, Bad Math and seems fairly well adjusted now, despite the lingering bitterness. My main advice is to get his kid studying MMA/BJJ/Judo/Wrestling rather than Karate ;-)

Original post (with 400+ comments), follow up post (with 200+ comments).

... I graduated from high school in 1984. Which means that this year is my graduating class's 25th year reunion. As a result, a bunch of people from my high school class have been trying to friend me on facebook, sending me email, and trying to convince me to come to the reunion.

I don't feel like replying to them individually, which is why I'm writing here.

As pretty much any reader of this blog who isn't a total idiot must have figured out by now, I'm a geek. I have been since I was a kid. My dad taught me about bell curves and standard deviations when I was in third grade, and I thought it was pretty much the coolest damn thing I'd ever seen. That's the kind of kid I was. I was also very small - 5 foot 1 when I started high school, 5 foot three my junior year. Even when I shot up in height, to nearly 5 foot eleven between junior and senior year, I weighed under 120 pounds. So think small, skinny, hyperactive, geek.

Like most geek kids, I had a rough time in school. I don't think that my experience was particularly unusual. I know a lot of people who had it worse. But I think that it was slightly worse than average, because the administration in the school system that I went to tolerated an extraordinary amount of violent bullying. Almost every geeky kid gets socially ostracized. Almost all get mocked. In fact, almost all face some physical abuse. The main determinant of just how much physical abuse they get subjected to is the school administration. And the administration at my school really didn't care: "Bruises? He must just be uncoordinated and bumps into things. Broken fingers? Hey, it happens. We're sure it must have been an accident. What do you want, an armed guard to follow your kid around?"

In high school, I didn't have a single real friend in my graduating class. I had a very few friends who graduated a year before me; I had a few who graduated one or two years after me. But being absolutely literal, there was not a single person in my graduating class who came close to treating me like a friend. Not one.

Like I said before, the way I was by my classmates in high school was pretty typical for a geek. At best, I was ignored. At worst, I was beaten. In between, I was used as a sort of status enhancer: telling people that you'd seen me doing some supposedly awful or hysterical thing was a common scheme for getting ahead in certain social circles. ...

... Now it's twenty five years since I got out of that miserable fucking hell-hole. And people from my high school class are suddenly getting in touch, sending me email, trying to friend me on Facebook, and trying to convince me to bring my family to the reunion. (It's a picnic reunion, full family invited.) Even some of the people who used to beat the crap out of me on a regular basis are getting in touch as if we're old friends.

My reaction to them... What the fuck is wrong with you people? Why would you think that I would want to have anything to do with you? How do you have the chutzpah to act as if we're old friends? How dare you? I see the RSVP list that one of you sent me, and I literally feel nauseous just remembering your names.

The only positive thing that ever came out of my time with you people is that my children are studying karate. My son will, most likely, have his black belt by the time he finishes fourth grade. He's a hyperactive little geek, just like me. ...

Luckily for me my high school years were among the best of my life. My 20th reunion was a blast -- it went by way, way too fast!

Optimism

I love this picture, perhaps because I am slightly hypomanic (see old post below) and associate myself with the smiley ball.

How do I know I'm hypomanic? Because I've twice been diagnosed as such -- once by a research psychologist who lived next door to me in New Haven, and the second time by a very precise Japanese colleague who was my host for several months in Tokyo. ("Are you familiar with the term Hypomania?" he asked.) This was years before I started a tech company.

Anyone who knows me is welcome to add their diagnosis :-)

hy·po·ma·ni·a: A mild form of mania, characterized by hyperactivity and euphoria.

From the intro to The Hypomanic Edge by J. Gartner, professor of psychiatry at JHU medical school.

"The 1990s will be remembered as the age of Internet mania, a time when entrepreneurs making grandiose claims for their high-tech companies swept up millions of Americans with their irrational exuberance, inflating the biggest speculative bubble in history. The idea that some entrepreneurs may be a little manic is hardly new. A Google search for "manic" and "businessman" yields more than a million hits. Entrepreneurs, as well as the markets they energized, were commonly described in the media as "manic." Yet, until now, there has never been a serious suggestion that the talent for being an entrepreneur and mania, the genetically based psychiatric disorder, are actually linked. Perhaps because I am a clinical psychologist, it was clear to me that "manic" was more than a figure of speech in this case.

I called several reporters who had written profiles of these "manic" entrepreneurs and asked them, "Do you think he really was manic?" None said yes. "Not really manic; not clinically," was a typical response. They resisted applying the psychiatric diagnosis because the entrepreneurs they had interviewed were boastful, hyperenergized, and zany, but they "weren't crazy." And the journalists were right. Their subjects were not manic. They were hypomanic. Hypomania is a mild form of mania, often found in the relatives of manic depressives. Hypomanics are brimming with infectious energy, irrational confidence, and really big ideas. They think, talk, move, and make decisions quickly. Anyone who slows them down with questions "just doesn't get it." Hypomanics are not crazy, but "normal" is not the first word that comes to mind when describing them. Hypomanics live on the edge, betweeen normal and abnormal.

...My new hypothesis became that American entrepreneurs are largely hypomanic. I decided to undertake what social scientists call a pilot study: a small-scale, inexpensive, informal investigation meant to test the waters. I placed announcements on several Web sites devoted to the technology business, expressing my interest in studying entrepreneurs and requesting volunteers. I interviewed a small sample of ten Internet CEOs. After I read them each a list of hypomanic traits that I had synthesized from the psychiatric literature, I asked them if they agreed that these traits are typical of an entrepreneur:

* He is filled with energy.
* He is flooded with ideas.
* He is driven, restless, and unable to keep still.
* He channels his energy into the achievement of wildly grand ambitions.
* He often works on little sleep.
* He feels brilliant, special, chosen, perhaps even destined to change the world.
* He can be euphoric.
* He becomes easily irritated by minor obstacles.
* He is a risk taker.
* He overspends in both his business and personal life.
* He acts out sexually.
* He sometimes acts impulsively, with poor judgment, in ways that can have painful consequences.
* He is fast-talking.
* He is witty and gregarious.
* His confidence can make him charismatic and persuasive.
* He is also prone to making enemies and feels he is persecuted by those who do not accept his vision and mission.

I feared they might find the questions insulting. I needn't have worried. All of the entrepreneurs agreed that the overall description was accurate, and they endorsed all the hypomanic traits, with the exceptions of "paranoia" and "sexual acting out" (these traits in particular are viewed as very negative and thus may be more difficult to admit to). Most expressed their agreement with excitement: "Wow, that's right on target!" When I asked them to rate their level of agreement for each trait on a standard 5-point scale, many gave ratings that were literally off the chart: 5+s, 6s. One subject repeatedly begged me to let him give a 7."

Letter from China

I've been meaning to recommend Letter from China, the blog of Evan Osnos, China correspondent for the New Yorker.

Here are some good posts:

Xinjiang reckoning

On the intersection of the Arab and Chinese worlds

Photos from the cultural revolution

Leapfrog to 3G in China, comments from Google's Kai-Fu Lee (600M internet-ready handsets!). TD-SCDMA?

Republishing vintage expat books about China

Green tech in China

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.