Callow youth at Columbia and the benevolence of financiers

If you want a cynical but amusing take on finance and Wall St., I suggest the tabloid blog DealBreaker. A recent article there highlights some interviews with Columbia University seniors bound for glory and treasure in investment banking. I don’t detect much benevolence or altruism in their motivations🙂 Related posts here and here.

DealBreaker: Do you know anything about investment banking? If you answered ‘yes,’ hold on to your seat, because today’s top story in Columbia’s The Eye, “Wall Street Indiscreet,” is going to blow you away. Writer Dan Haley interviewed the pseudonymous “Paul Owen,” a senior with plans to work on the Street after graduation and the results are pretty eye-opening. You should obviously check it out for yourself, but here are a few highlights:

The majority of students who find employment in investment banks come from Ivy League-caliber schools. In the banking industry, these are referred to as “target” schools. Columbia is one. So is Cornell—but less so. Middlebury is not a target school. Don’t even think about Binghamton.

“Investment banking isn’t this advanced math, these advanced quantitative techniques. There’s Excel for that,” he tells me. “Investment banking is really just critical thinking. They way I put it, if you’re good at Sudoku, you’ll be a good investment banker.”

When you get a job in I-banking, it doesn’t matter if you were previously the biggest tool at school; the guy who always got picked last for gym, always got stuffed in his locker. You are now a certified badass.

With $145,000 in his pocket—projected earnings, it is not all actually in his pocket at the moment—Owen tells me that senior year has been “an absolute shitshow.” … “The best description of it I can give,” said Owen, “is that the third week of school I took Monday and Tuesday off from class to go to Puerto Rico.”

At first, it’ll be a lot of late hours and hard work, for sure. But once you pay your dues, it’ll be pussy, pussy, pussy. “At first, as an analyst, you’re doing grunt work,” he said. “But then, as you go on, as you get to the vice president and managing director levels, it’s all about client relations. Expensive dinners, golf trips, schmoozing. I can’t say I would mind that at all.”

When you work in I-banking, you can, like, make people do shit for you. “I was 21 and my secretary was about 15 years older,” Chan [who interned in Hong Kong last summer] said. “I could ask her to fax stuff for me, or get me coffee, or pens, or even ask her to bring me my bank account statement.”

If you work at a good enough firm, they’ll pay for your prostitutes. Of course, it wasn’t all work in Hong Kong. On Friday and Saturday nights, with no work the next day, the bankers would cut loose. This meant hitting up one of the three big expatriate bars/clubs in the city. These clubs were usually filled with two groups of people: bankers and “models.” The “models” would get in without paying the cover charge and drink for free while the bankers would have to cough up $1,000 for a table, although sometimes the firm paid for them.

Brutal, just brutal

Via Gene Expression, three essays on intelligence and education by Charles Murray. Yes, I know they appeared on the WSJ editorial page, and yes, I know what book Murray co-authored back in the 90’s. Nevertheless, there’s sometimes value in what he writes. At least, he’s willing to raise some important issues that others dare not. Some excerpts below. Warning, not for the politically correct ability egalitarians who think anyone can play basketball like Michael Jordan or compose music like Mozart if they just try hard enough. If you don’t like his continued use of IQ as a measure of intelligence, just pretend you have your own measure (or even measures) and substitute it each time he writes “IQ”, keeping in mind your measure will have an average – let’s call it “100” for simplicity – and probably be roughly normally distributed, as most human traits are.

1) What fraction of the population is capable of absorbing a university education or mastering college-level material? It might be smaller than the proportion attending college today.

To have an IQ of 100 means that a tough high-school course pushes you about as far as your academic talents will take you. If you are average in math ability, you may struggle with algebra and probably fail a calculus course. If you are average in verbal skills, you often misinterpret complex text and make errors in logic.

These are not devastating shortcomings. You are smart enough to engage in any of hundreds of occupations. You can acquire more knowledge if it is presented in a format commensurate with your intellectual skills. But a genuine college education in the arts and sciences begins where your skills leave off.

In engineering and most of the natural sciences, the demarcation between high-school material and college-level material is brutally obvious. If you cannot handle the math, you cannot pass the courses. In the humanities and social sciences, the demarcation is fuzzier. It is possible for someone with an IQ of 100 to sit in the lectures of Economics 1, read the textbook, and write answers in an examination book. But students who cannot follow complex arguments accurately are not really learning economics. They are taking away a mishmash of half-understood information and outright misunderstandings that probably leave them under the illusion that they know something they do not. (A depressing research literature documents one’s inability to recognize one’s own incompetence.) Traditionally and properly understood, a four-year college education teaches advanced analytic skills and information at a level that exceeds the intellectual capacity of most people.

There is no magic point at which a genuine college-level education becomes an option, but anything below an IQ of 110 is problematic. If you want to do well, you should have an IQ of 115 or higher. Put another way, it makes sense for only about 15% of the population, 25% if one stretches it, to get a college education. And yet more than 45% of recent high school graduates enroll in four-year colleges. Adjust that percentage to account for high-school dropouts, and more than 40% of all persons in their late teens are trying to go to a four-year college–enough people to absorb everyone down through an IQ of 104.

2) On the highly intelligent fraction and their contributions to society.

If “intellectually gifted” is defined to mean people who can become theoretical physicists, then we’re talking about no more than a few people per thousand and perhaps many fewer. They are cognitive curiosities, too rare to have that much impact on the functioning of society from day to day. But if “intellectually gifted” is defined to mean people who can stand out in almost any profession short of theoretical physics, then research about IQ and job performance indicates that an IQ of at least 120 is usually needed. That number demarcates the top 10% of the IQ distribution, or about 15 million people in today’s labor force–a lot of people.

In professions screened for IQ by educational requirements–medicine, engineering, law, the sciences and academia–the great majority of people must, by the nature of the selection process, have IQs over 120. Evidence about who enters occupations where the screening is not directly linked to IQ indicates that people with IQs of 120 or higher also occupy large proportions of positions in the upper reaches of corporate America and the senior ranks of government. People in the top 10% of intelligence produce most of the books and newspaper articles we read and the television programs and movies we watch. They are the people in the laboratories and at workstations who invent our new pharmaceuticals, computer chips, software and every other form of advanced technology.

Combine these groups, and the top 10% of the intelligence distribution has a huge influence on whether our economy is vital or stagnant, our culture healthy or sick, our institutions secure or endangered. Of the simple truths about intelligence and its relationship to education, this is the most important and least acknowledged: Our future depends crucially on how we educate the next generation of people gifted with unusually high intelligence.

How assiduously does our federal government work to see that this precious raw material is properly developed? In 2006, the Department of Education spent about $84 billion. The only program to improve the education of the gifted got $9.6 million, one-hundredth of 1% of expenditures. In the 2007 budget, President Bush zeroed it out.

Just to clarify for Murray: he’s not proposing a hard cutoff in IQ for any particular achievement (becoming a chip designer, writing a senior thesis on French literature), but merely that the fraction of people capable of that achievement with IQ below the value he gives is very small (e.g., very few medical researchers with IQ less than 120). Therefore, we can use the estimated value as a way to guess what percentage of the general population is sufficiently capable. There are of course other factors involved in success at a particular task than raw cognitive ability (motivation, organization, communication skills, …). See earler post on success vs ability.

For more on theoretical physicists, see here. This will sound terribly arrogant (so shoot me), but Murray’s estimate of few per thousand is way too high. That’s about the ability level of the average Caltech undergrad, and I would guess only the top 5-10% of students there could be theoretical physicists.

Podcast roundup

For fans of Borges, an hour long discussion on the BBC radio program In Our Time.

Scott Kriens, CEO and Chairman of Juniper, speaking at the Stanford Entrepreneurial Thought Leaders lecture series, emphasizes the role of dumb luck in startup success. Stanford students are lucky to have the opportunity to attend these lectures; thanks to podcasting we can all enjoy them. Other lectures in this series I found particularly good (available at the link above): Marissa Mayer (Google), Chong-Moon Lee (Ambex), Carol Bartz (Autodesk), Mark Zuckerberg (Facebook), Jeff Hawkins (Palm). All of these people are smart and have valuable insights to offer.

Another podcast series I recommend is Bloomberg On the Economy, which is a mix of academic and “market” economists (the latter work at banks and investment funds) and the occasional portfolio manager like Bill Gross. I find it very amusing that one can easily find two “market” economists confidently stating completely contradictory predictions on the same day (e.g., right before an employment report or Fed meeting). Sometimes I listen to the podcast a day or two late, so I actually know the outcome already as I listen to the poor guy (sometimes it’s a woman) laying out their case for a prediction that turned out completely off the mark. These people must be selected for lack of Socratic self-examination, because the models they play with are so obviously lacking in predictive power, yet they never figure this out. (I suppose it’s possible they do realize this, but then they all deserve Oscars for Best Actor or Actress, since they project sincere belief in their predictions.) The academics are typically more thoughtful and, being tenured, aren’t under pressure to predict the next tick🙂

I know I’m belaboring the point, but if you forced one of these guys to give error estimates, I am sure you would find them making 3 sigma errors with regularity: e.g., my model says the jobs number is going to be low, only 90k new jobs created last month, with standard deviation of 30k — gulp, the real number is 180k! And this guy is a Sr. VP or MD at Bear/Merrill/CS/Goldman, whatever. But they never subject themselves to this discipline — if they did, they’d realize their actual one sigma error is so big that their central value is useless.

You might get the impression I’m only listening to the Bloomberg podcast for comedic value, but I find the reasoning and intuition of the various guests interesting, even if they can’t predict anything. At least it helps you understand what a sizeable fraction of market participants are actually thinking.

Finally, if you’re interested in recent progress in biotech, I suggest Futures in Biotech with Marc Pelletier (a postdoc at Yale). They cover topics ranging from protein folding to microarrays to neuroscience through interviews with leading scientists. The only problem with this show is that sometimes the real scientist being interviewed forgets the target audience is supposed to be kind of sophisticated and they resort to the usual pop science cliches.

I listen to this stuff when I’m running or at the gym. Thanks to Steve Jobs, instead of fighting boredom or replaying 80’s hits from my youth, I can learn something while sweating.

Asians at Berkeley

The Sunday Times had an interesting long article in the education section on diversity at Berkeley. Asians comprise 12% of California’s population, but now make up almost 50% of the student body at Berkeley and several other UC campuses. Nationally, they are 5% of the population, but make up 10-30% of student bodies at elite private universities (Caltech has the highest percentage at 33%, whereas Princeton has one of the lowest at 13%).

I like the use of language in the article – they refer to UC admissions in the wake of Prop 209 (which removed race-based preferences) as a strict meritocracy, as opposed to what is practiced at most other public and private colleges. In fact the lead-in to the article on the web site says:

With a mandate that says merit trumps all, Berkeley finds itself looking across the Pacific for its identity. Is this the new face of higher education?

The usual diversity double-speak refuses to acknowledge that race-based preferences are not meritocratic.

Our heroes Jian Li (Yale student suing Princeton over anti-Asian admissions policies) and Daniel Golden (WSJ writer whose recent book The Price of Admission exposes the ugly side of elite admissions) both appear in the article. The Princeton spokesperson quoted in the article provides an excellent example of politically correct obfuscation. How is awarding preference to certain ethnic groups not discriminatory towards other non-preferred groups, given that the number of students admitted each year is fixed? Innumeracy strikes again!

For earlier related discussion, see here. For the Princeton study that showed statistically how affirmative action hurts Asians (being Asian is equivalent to a 50 point penalty on the SAT), see here.

NYTimes: Little Asia on the Hill

…Spend a few days at Berkeley, on the classically manicured slope overlooking San Francisco Bay and the distant Pacific, and soon enough the sound of foreign languages becomes less distinct. This is a global campus in a global age. And more than any time in its history, it looks toward the setting sun for its identity.

The revolution at Berkeley is a quiet one, a slow turning of the forces of immigration and demographics. What is troubling to some is that the big public school on the hill certainly does not look like the ethnic face of California, which is 12 percent Asian, more than twice the national average. But it is the new face of the state’s vaunted public university system. Asians make up the largest single ethnic group, 37 percent, at its nine undergraduate campuses.

…But 10 years after California passed Proposition 209, voting to eliminate racial preferences in the public sector, university administrators find such balance harder to attain. At the same time, affirmative action is being challenged on a number of new fronts, in court and at state ballot boxes. And elite colleges have recently come under attack for practicing it — specifically, for bypassing highly credentialed Asian applicants in favor of students of color with less stellar test scores and grades.

…This is in part because getting into Berkeley — U.S. News & World Report’s top-ranked public university — has never been more daunting. There were 41,750 applicants for this year’s freshman class of 4,157. Nearly half had a weighted grade point average of 4.0 or better (weighted for advanced courses). There is even grumbling from “the old Blues” — older alumni named for the school color — “who complain because their kids can’t get in,” says Gregg Thomson, director of the Office of Student Research.

…Asians have become the “new Jews,” in the phrase of Daniel Golden, whose recent book, “The Price of Admission: How America’s Ruling Class Buys Its Way Into Elite Colleges — and Who Gets Left Outside the Gates,” is a polemic against university admissions policies. Mr. Golden, a reporter for The Wall Street Journal, is referring to evidence that, in the first half of the 20th century, Ivy League schools limited the number of Jewish students despite their outstanding academic records to maintain the primacy of upper-class Protestants. Today, he writes, “Asian-Americans are the odd group out, lacking racial preferences enjoyed by other minorities and the advantages of wealth and lineage mostly accrued by upper-class whites. Asians are typecast in college admissions offices as quasi-robots programmed by their parents to ace math and science.”

…To force the issue on a legal level, a freshman at Yale filed a complaint in the fall with the Department of Education’s Office of Civil Rights, contending he was denied admission to Princeton because he is Asian. The student, Jian Li, the son of Chinese immigrants in Livingston, N.J., had a perfect SAT score and near-perfect grades, including numerous Advanced Placement courses.

“This is just a very, very egregious system,” Mr. Li told me. “Asians are held to different standards simply because of their race.”

To back his claim, he cites a 2005 study by Thomas J. Espenshade and Chang Y. Chung, both of Princeton, which concludes that if elite universities were to disregard race, Asians would fill nearly four of five spots that now go to blacks or Hispanics. Affirmative action has a neutral effect on the number of whites admitted, Mr. Li is arguing, but it raises the bar for Asians. The way Princeton selects its entering class, Mr. Li wrote in his complaint, “seems to be a calculated move by a historically white institution to protect its racial identity while at the same time maintaining a facade of progressivism.”

…Admissions officials have long denied that they apply quotas. Nonetheless, race is important “to ensure a diverse student body,” says Cass Cliatt, a Princeton spokeswoman. But, she adds, “Looking at the merits of race is not the same as the opposite” — discrimination.

Elite colleges like Princeton review the “total package,” in her words, looking at special talents, extracurricular interests and socioeconomics — factors like whether the applicant is the first in the family to go to college or was raised by a single mother. “There’s no set formula or standard for how we evaluate students,” she says.

…Historically, Asians have faced discrimination, with exclusion laws in the 1800s that kept them from voting, owning property or legally immigrating. Many were run out of West Coast towns by mobs. But by the 1970s and ’80s, with a change in immigration laws, a surge in Asian arrivals began to change the complexion of California, and it was soon reflected in an overrepresentation at its top universities.

In the late 1980s, administrators appeared to be limiting Asian-American admissions, prompting a federal investigation. The result was an apology by the chancellor at the time, and a vow that there would be no cap on Asian enrollment.

…One leading critic of bringing affirmative action back to Berkeley is David A. Hollinger, chairman of its history department and author of “Post-Ethnic America: Beyond Multiculturalism.” He supported racial preferences before Proposition 209, but is no longer so sure. “You could argue that the campus is more diverse now,” because Asians comprise so many different cultures, says Dr. Hollinger. A little more than half of Asian freshmen at Berkeley are Chinese, the largest group, followed by Koreans, East-Indian/Pakistani, Filipino and Japanese.

He believes that Latinos are underrepresented because many come from poor agrarian families with little access to the good schools that could prepare them for the rigors of Berkeley. He points out that, on the other hand, many of the Korean students on campus are sons and daughters of parents with college degrees. In any event, he says, it is not the university’s job to fix the problems that California’s public schools produce.

Metric on the space of genomes and the scientific basis for race

Suppose that the human genome has 30,000 distinct genes, which we will label as i = 1,2, … N, where N = 30k. Next, suppose that there are n_i variants or alleles (mutations) of the i-th gene. Then, each human’s genetic information can be described as a point on a lattice of size n_1 x n_2 x n_3 … n_N, or equivalently an N-tuple of integers, each of whose values range from 1 to n_i. For the simplified case where there are exactly 10 variants of each gene, the number of points in this N dimensional space is 10^N or 10^{30k}, one for each distinct 30k digit number. It’s a space of very high dimension, but this doesn’t stop us from defining a metric, or measure of distance between any two points in the space. (For simplicity we ignore restrictions on this space which might result from incompatibility of certain combinations, etc.)

Note that the genomes of all of the humans who have ever lived occupy only a small subset of this space — most possible variations have never been realized. For this reason, the surprise expressed by biologists that humans have so few genes (not many more than a worm, and far less than the 100k of earlier estimates) is no cause for concern — the number of possible organisms that might result from 30k genes is enormous — far more than the number of molecules in the visible universe.

To define a metric, we need a notion of how far apart two different alleles are. We can do this by counting base pair differences — most mutations only alter a few base pairs in the genetic code. We can define the distance between two alleles in terms of the number of base pair changes between them (this is always a positive number). Then, we can define the distance between two genomes as the sum of each of the i=1,2,..,N individual gene distances. It is natural, although perhaps not always possible, to choose the n_i labeling of alleles to reflect relative distances, so variants n_1 and n_2 are close together, and both very far from n_10.

The exact definition of the metric and the allele labeling are somewhat arbitrary, but you can see it is easy to define a meaningful measure of how far apart any two individuals are in genome space.

Now plot the genome of each human as a point on our lattice. Not surprisingly, there are readily identifiable clusters of points, corresponding to traditional continental ethnic groups: Europeans, Africans, Asians, Native Americans, etc. (See, for example, Risch et al., Am. J. Hum. Genet. 76:268–275, 2005.) Of course, we can get into endless arguments about how we define European or Asian, and of course there is substructure within the clusters, but it is rather obvious that there are identifiable groupings, and as the Risch study shows, they correspond very well to self-identified notions of race.

From the conclusions of the Risch paper (Am. J. Hum. Genet. 76:268–275, 2005):

Attention has recently focused on genetic structure in the human population. Some have argued that the amount of genetic variation within populations dwarfs the variation between populations, suggesting that discrete genetic categories are not useful (Lewontin 1972; Cooper et al. 2003; Haga and Venter 2003). On the other hand, several studies have shown that individuals tend to cluster genetically with others of the same ancestral geographic origins (Mountain and Cavalli-Sforza 1997; Stephens et al. 2001; Bamshad et al. 2003). Prior studies have generally been performed on a relatively small number of individuals and/or markers. A recent study (Rosenberg et al. 2002) examined 377 autosomal micro-satellite markers in 1,056 individuals from a global sample of 52 populations and found significant evidence of genetic clustering, largely along geographic (continental) lines. Consistent with prior studies, the major genetic clusters consisted of Europeans/West Asians (whites), sub-Saharan Africans, East Asians, Pacific Islanders, and Native Americans. ethnic groups living in the United States, with a discrepancy rate of only 0.14%.

This clustering is a natural consequence of geographical isolation, inheritance and natural selection operating over the last 50k years since humans left Africa.

Every allele probably occurs in each ethnic group, but with varying frequency. Suppose that for a particular gene there are 3 common variants (v1, v2, v3) all the rest being very rare. Then, for example, one might find that in ethnic group A the distribution is v1 75%, v2 15%, v3 10%, while for ethnic group B the distribution is v1 2% v2 6% v3 92%. Suppose this pattern is repeated for several genes, with the common variants in population A being rare in population B, and vice versa. Then, one might find a very dramatic difference in expressed phenotype between the two populations. For example, if skin color is determined by (say) 10 genes, and those genes have the distribution pattern given above, nearly all of population A might be fair skinned while all of population B is dark, even though there is complete overlap in the set of common alleles. Perhaps having the third type of variant v3 in 7 out of 10 pigmentation genes makes you dark. This is highly likely for an individual in population B with the given probabilities, but highly unlikely in population A.

We see that there can be dramatic group differences in phenotypes even if there is complete allele overlap between two groups – as long as the frequency or probability distributions are distinct. But it is these distributions that are measured by the metric we defined earlier. Two groups that form distinct clusters are likely to exhibit different frequency distributions over various genes, leading to group differences.

This leads us to two very distinct possibilities in human genetic variation:

Hypothesis 1: (the PC mantra) The only group differences that exist between the clusters (races) are innocuous and superficial, for example related to skin color, hair color, body type, etc.

Hypothesis 2: (the dangerous one) Group differences exist which might affect important (let us say, deep rather than superficial) and measurable characteristics, such as cognitive abilities, personality, athletic prowess, etc.

Note H1 is under constant revision, as new genetically driven group differences (e.g., particularly in disease resistance) are being discovered. According to the mantra of H1 these must all (by definition) be superficial differences.

A standard argument against H2 is that the 50k years during which groups have been separated is not long enough for differential natural selection to cause any group differences in deep characteristics. I find this argument quite naive, given what we know about animal breeding and how evolution has affected the (ever expanding list of) “superficial” characteristics. Many genes are now suspected of having been subject to strong selection over timescales of order 5k years or less. For further discussion of H2 by Steve Pinker, see here.

The predominant view among social scientists is that H1 is obviously correct and H2 obviously false. However, this is mainly wishful thinking. Official statements by the American Sociological Association and the American Anthropological Association even endorse the view that race is not a valid biological concept, which is clearly incorrect.

As scientists, we don’t know whether H1 or H2 is correct, but given the revolution in biotechnology, we will eventually. Let me reiterate, before someone labels me a racist: we don’t know with high confidence whether H1 or H2 is correct.

Finally, it is important to note that any group differences are statistical in nature and do not imply anything about particular individuals. Rather than rely on the scientifically unsupported claim that we are all equal, it would be better to emphasize that we all have inalienable human rights regardless of our abilities or genetic make up.

[See here (Economist’s View blog) for more comments.]

[See Gene Expression for more discussion and references.]

Gregory Chaitin on physics and mathematics

I stumbled on this interesting discussion with Gregory Chaitin, one of the discoverers of algorithmic information theory, on the relationship between physics and mathematics. Some excerpts below.

Cristian Calude: I suggest we discuss the question, Is mathematics independent of physics?

Gregory Chaitin: Okay.

CC: Let’s recall David Deutsch’s 1982 statement:

The reason why we find it possible to construct, say, electronic calculators, and indeed why we can perform mental arithmetic, cannot be found in mathematics or logic. The reason is that the laws of physics “happen” to permit the existence of physical models for the operations of arithmetic such as addition, subtraction and multiplication.

Does this apply to mathematics too?

GC: Yeah sure, and if there is real randomness in the world then Monte Carlo algorithms can work, otherwise we are fooling ourselves.

CC: So, if experimental mathematics is accepted as “mathematics,” it seems that we have to agree that mathematics depends “to some extent” on the laws of physics.

GC: You mean math conjectures based on extensive computations, which of course depend on the laws of physics since computers are physical devices?

CC: Indeed. The typical example is the four-color theorem, but there are many other examples. The problem is more complicated when the verification is not done by a conventional computer, but, say, a quantum automaton. In the classical scenario the computation is huge, but in principle it can be verified by an army of mathematicians working for a long time. In principle, theoretically, it is feasible to check every small detail of the computation. In the quantum scenario this possibility is gone.

GC: Unless the human mind is itself a quantum computer with quantum parallelism. In that case an exponentially long quantum proof could not be written out, since that would require an exponential amount of “classical” paper, but a quantum mind could directly perceive the proof, as David Deutsch points out in one of his papers.

…

[GC:] But mathematicians shouldn’t think they can replace physicists: There’s a beautiful little 1943 book on Experiment and Theory in Physics by Max Born where he decries the view that mathematics can enable us to discover how the world works by pure thought, without substantial input from experiment.

CC: What about set theory? Does this have anything to do with physics?

GC: I think so. I think it’s reasonable to demand that set theory has to apply to our universe. In my opinion it’s a fantasy to talk about infinities or Cantorian cardinals that are larger than what you have in your physical universe. And what’s our universe actually like?

a finite universe?
discrete but infinite universe (ℵ0)?
universe with continuity and real numbers (ℵ1)?
universe with higher-order cardinals (≥ ℵ2)?
Does it really make sense to postulate higher-order infinities than you have in your physical universe? Does it make sense to believe in real numbers if our world is actually discrete? Does it make sense to believe in the set {0, 1, 2, …} of all natural numbers if our world is really finite?

CC: Of course, we may never know if our universe is finite or not. And we may never know if at the bottom level the physical universe is discrete or continuous…

GC: Amazingly enough, Cris, there is some evidence that the world may be discrete, and even, in a way, two-dimensional. There’s something called the holographic principle, and something else called the Bekenstein bound. These ideas come from trying to understand black holes using thermodynamics. The tentative conclusion is that any physical system only contains a finite number of bits of information, which in fact grows as the surface area of the physical system, not as the volume of the system as you might expect, whence the term “holographic.”

…

CC: Maybe in the future mathematicians will work closely with computers. Maybe in the future there will be hybrid mathematicians, maybe we will have a man/machine symbiosis. This is already happening in chess, where Grandmasters use chess programs as sparing partners and to do research on new openings.

GC: Yeah, I think you’re right about the future. The machine’s contribution will be speed, highly accurate memory, and performing large routine computations without error. The human contribution will be new ideas, new points of view, intuition.

CC: But most mathematicians are not satisfied with the machine proof of the four-color conjecture. Remember, for us humans, Proof = Understanding.

GC: Yes, but in order to be able to amplify human intelligence and prove more complicated theorems than we can now, we may be forced to accept incomprehensible or only partially comprehensible proofs. We may be forced to accept the help of machines for mental as well as physical tasks.

CC: We seem to have concluded that mathematics depends on physics, haven’t we? But mathematics is the main tool to understand physics. Don’t we have some kind of circularity?

GC: Yeah, that sounds very bad! But if math is actually, as Imre Lakatos termed it, quasi-empirical, then that’s exactly what you’d expect. And as you know Cris, for years I’ve been arguing that information-theoretic incompleteness results inevitably push us in the direction of a quasi-empirical view of math, one in which math and physics are different, but maybe not as different as most people think. As Vladimir Arnold provocatively puts it, math and physics are the same, except that in math the experiments are a lot cheaper!

CC: In a sense the relationship between mathematics and physics looks similar to the relationship between meta-mathematics and mathematics. The incompleteness theorem puts a limit on what we can do in axiomatic mathematics, but its proof is built using a substantial amount of mathematics!

GC: What do you mean, Cris?

CC: Because mathematics is incomplete, but incompleteness is proved within mathematics, meta-mathematics is itself incomplete, so we have a kind of unending uncertainty in mathematics. This seems to be replicated in physics as well: Our understanding of physics comes through mathematics, but mathematics is as certain (or uncertain) as physics, because it depends on the physical laws of the universe where mathematics is done, so again we seem to have unending uncertainty. Furthermore, because physics is uncertain, you can derive a new form of uncertainty principle for mathematics itself…

GC: Well, I don’t believe in absolute truth, in total certainty. Maybe it exists in the Platonic world of ideas, or in the mind of God—I guess that’s why I became a mathematician—but I don’t think it exists down here on Earth where we are. Ultimately, I think that that’s what incompleteness forces us to do, to accept a spectrum, a continuum, of possible truth values, not just black and white absolute truth.

In other words, I think incompleteness means that we have to also accept heuristic proofs, the kinds of proofs that George Pólya liked, arguments that are rather convincing even if they are not totally rigorous, the kinds of proofs that physicists like. Jonathan Borwein and David Bailey talk a lot about the advantages of that kind of approach in their two-volume work on experimental mathematics. Sometimes the evidence is pretty convincing even if it’s not a conventional proof. For example, if two real numbers calculated for thousands of digits look exactly alike…

CC: It’s true, Greg, that even now, a century after Gödel’s birth, incompleteness remains controversial. I just discovered two recent essays by important mathematicians, Paul Cohen and Jack Schwartz.* Have you seen these essays?

*P. J. Cohen, “Skolem and pessimism about proof in mathematics,” Phil. Trans. R. Soc. A (2005) 363, 2407-2418; J. T. Schwartz, “Do the integers exist? The unknowability of arithmetic consistency,” Comm. Pure & Appl. Math. (2005) LVIII, 1280-1286.

GC: No.

CC: Listen to what Cohen has to say:

“I believe that the vast majority of statements about the integers are totally and permanently beyond proof in any reasonable system.”

And according to Schwartz,

“truly comprehensive search for an inconsistency in any set of axioms is impossible.”

GC: Well, my current model of mathematics is that it’s a living organism that develops and evolves, forever. That’s a long way from the traditional Platonic view that mathematical truth is perfect, static and eternal.

CC: What about Einstein’s famous statement that

“Insofar as mathematical theorems refer to reality, they are not sure, and insofar as they are sure, they do not refer to reality.”

Still valid?

GC: Or, slightly misquoting Pablo Picasso, theories are lies that help us to see the truth!

Money talks

The anonymous commenter who inspired my post on the benevolence of financiers has identified himself as David Kane, Harvard PhD and former US Marine Corps officer (!), who runs Kane Capital Management, a quantitative, market-neutral, global equity hedge fund. David takes me to task in further comments here (copied below).

In his remarks he says “There are many confusions here, so it is tough to know where to start”, “D’uh!”, and “Unconvincing!”

David, I respect your opinions, and if you ever want to guest blog here, send me an email and I’ll post it for my readers🙂 Since I’m a truth-seeking idealist, I’m displaying your comments where they can be seen.

A couple of thoughts:

1) No disagreement that the market works through the self-interested actions of participants. But I don’t see how this contradicts my original comment that “not all financial games that make money for a hedge fund necessarily lead to more efficient resource allocation in the overall economy.” Although selfishness is crucial to the operation of markets, let us not mistake selfishness for altruism🙂

2) Of course it’s based on an unscientific sample (i.e., people I know), but yes, I would say that people who join startups tend to be more idealistic than people who join hedge funds. Would anyone differ if I replaced the word “startups” with “the Peace Corps” or something similar (like “academic science” ;-)? There are generalizations about groups that are statistically true.

A lot of people are in startups as much for the chance to “do something cool” or improve the world, as for the stock option lottery ticket. I can’t think of a single person I know who is in finance primarily because of the good it does in the world. Perhaps, as David mentions, they are looking ahead to their future days as a philanthropist, but I think that consideration is dominated by near term remuneration.

Comment 1: I was the original commentator but forgot to sign. There are many confusions here, so it is tough to know where to start.

1) You write:

“For example, many people in startups are idealistic, and part of the attraction of their work is that they are changing the world for the better. The same goes for academic scientists.”

Do you have any, you know, evidence that the average person in a start-up is more idealistic than the average person in a hedge fund? (By the way, is it useful to compare hedge funds as a class, including big ones and small ones, against start-ups? You think everyone at Cisco and Microsoft is an idealist? A more fair comparison would be tech start ups (like the firm you started) with hedge fund start ups (like the firm that I started). What makes you think that you (and your buddies) are more idealistic than me and my buddy?

2) The purpose of a hedge fund is not to allocate capital more efficiently. D’uh. But that is the effect of a hedge fund’s activities. We can go into specific examples, if you like, but every time I short a stock it is because I think it’s price will go down. But, by shorting it, I drive the price down a bit and therefore bring closer the day when it is accurately valued.

3) “Although financial activities play an important role in the economy, as I have emphasized, I suspect the prime motivation for finance as a career choice is maximization of remuneration, not altruism :-)”

And you start a tech company because, what, you are an altruist? I assume that this is a joke. All of us make career decisions for a variety of reasons. Salary, security, people, intrinsic interest all play a part. How much time would you spend on your current start up if you were certain that the financial reward to you would be zero?

Comment 2: I asked you for a specific example and the best that you can do is some ramble about the tech bubble? Unimpressive!

1) What should a hedge fund have done in 1998 with Yahoo at $4 (split-adjusted)? Is this a “bubble,” so you should short it? Or is it too low, so you should buy it?

That was a really hard question in 1998 and — guess what? — it is an equally hard question today with YHOO at $25. It is a fantasy to think that you (or anyone) knew in 1998 or 2006 or any other specific time what a fair price of YHOO should be, or what the price of YHOO will be in 6 months.

You mention some hedgies or traders who “knew” that it was a bubble (YHOO goes lower in 6 months) or “knew” that the bubble was going on (YHOO goes higher in 6 months) without any sense of how this identifies a class of strategies widely used by hedge funds that fails in increase economic efficiency.

The economy is more efficient of capital is better allocated, relative not to some utopian ideal of perfect allocation, but compared to some other plausible world. All the equity trading done by hedge funds as a class makes the price of YHOO go more quickly to its real stable value, relative to what the price would have done in the absence of that hedge fund activity.

Can you imagine what the bubble would have looked like were it not for the billions of dollars of shorts done by hedge funds?

Comment 3: You write:

“I know from personal contacts that hedge funds actually behaved this way, and it is supported by subsequent academic studies.”

Baloney! If you can site these “studies” then please do so! The one you do (in the linked post) is not worth more than the 5 minutes I spent with it. The authors have no information on short positions, so how can they know what was going on?

Who do you think made all that money shorting stocks in 2000-2003? Some old lady in Des Moines?

There is no evidence that the bubble would have been less severe in the absence of hedge funds. Indeed, since the S&P is at about the same level that it was in 1999, just how much of a bubble was there?