Adventures of a Mathematician: Ulam, von Karman, Wiener, and the Golem

 

Ulam's Adventures of a Mathematician was recently made into a motion picture -- see trailer above. 

I have an old copy purchased from the Caltech bookstore. When I flip through the book it never fails to reward with a wonderful anecdote from an era of giants.

[Ulam] ... In Israel many years later, while I was visiting the town of Safed with von Kárman, an old Orthodox Jewish guide with earlocks showed me the tomb of Caro in an old graveyard. When I told him that I was related to a Caro, he fell on his knees... Aunt Caro was directly related to the famous Rabbi Loew of sixteenth-century Prague, who, the legend says, made the Golem — the earthen giant who was protector of the Jews. (Once, when I mentioned this connection with the Golem to Norbert Wiener, he said, alluding to my involvement with Los Alamos and with the H-bomb, "It is still in the family!")

See also von Neumann: "If only people could keep pace with what they create"

One night in early 1945, just back from Los Alamos, vN woke in a state of alarm in the middle of the night and told his wife Klari: 

"... we are creating ... a monster whose influence is going to change history ... this is only the beginning! The energy source which is now being made available will make scientists the most hated and most wanted citizens in any country. The world could be conquered, but this nation of puritans will not grab its chance; we will be able to go into space way beyond the moon if only people could keep pace with what they create ..." 

He then predicted the future indispensable role of automation, becoming so agitated that he had to be put to sleep by a strong drink and sleeping pills. 

In his obituary for John von Neumann, Ulam recalled a conversation with vN about the 

"... ever accelerating progress of technology and changes in the mode of human life, which gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue." 

This is the origin of the concept of technological singularity. Perhaps we can even trace it to that night in 1945 :-)

More Ulam from this blog, including:

[p.107] I told Banach about an expression Johnny had used with me in Princeton before stating some non-Jewish mathematician's result, "Die Goim haben den folgenden satz beweisen" (The goys have proved the following theorem). Banach, who was pure goy, thought it was one of the funniest sayings he had ever heard. He was enchanted by its implication that if the goys could do it, then Johnny and I ought to be able to do it better. Johnny did not invent this joke, but he liked it and we started using it.

Yuri Slezkine: The Jewish Century

Yuri Slezkine of UC Berkeley, author of The Jewish Century (reviewed in The Nation).

@7 min "I was unprincipled enough to put down Russian in all my official paperwork because, obviously, it made it much easier to get into college." [ Slezkine is half Jewish; his father is Russian. See They take students like you there and I'm not Asian. ]

@29:30 The evolution of anti-semitism in the Soviet Union. From an overrepresentation of Jews in the early Soviet leadership, to (post-WWII and -Stalin) an era of quotas and overt discrimination, and an increasing identification of the Soviet state with Russian nationality.

From the introduction to The Jewish Century:

The Modern Age is the Jewish Age, and the twentieth century, in particular, is the Jewish Century. Modernization is about everyone becoming urban, mobile, literate, articulate, intellectually intricate, physically fastidious, and occupationally flexible. It is about learning how to cultivate people and symbols, not fields or herds. It is about pursuing wealth for the sake of learning, learning for the sake of wealth, and both wealth and learning for their own sake. It is about transforming peasants and princes into merchants and priests, replacing inherited privilege with acquired prestige, and dismantling social estates for the benefit of individuals, nuclear families, and book-reading tribes (nations). Modernization, in other words, is about everyone becoming Jewish.

Some peasants and princes have done better than others, but no one is better at being Jewish than the Jews themselves. In the age of capital, they are the most creative entrepreneurs; in the age of alienation, they are the most experienced exiles; and in the age of expertise, they are the most proficient professionals. Some of the oldest Jewish specialties-commerce, law, medicine, textual interpretation, and cultural mediation-have become the most fundamental (and the most Jewish) of all modern pursuits. It is by being exemplary ancients that the Jews have become model moderns. ...

The Myth of American Meritocracy

Ron Unz has performed an exhaustive analysis of elite university admissions in The Myth of American Meritocracy (December issue of the American Conservative). He finds strong evidence for de facto quotas on Asian-Americans at Ivy League universities. See below for a brief summary. I suggest reading his entire article, which is filled with additional insights, including one rather shocking surprise. Don't miss the statistical supplement.

Asian-American Quotas at Ivy League Universities?

November 28, 2012 - America’s elite Ivy League universities appear to follow a de facto Asian-American admissions quota policy according to “The Myth of American Meritocracy,”a 30,000-word cover story in the December issue of The American Conservative by publisher Ron Unz.

Unz provides detailed statistical evidence that the pattern of Asian-American enrollment over the last two decades is remarkably similar to what followed the establishment of Ivy League Jewish quotas in the mid-1920s. Soon after the U.S. Department of Justice closed its early 1990s investigation into allegations of anti-Asian admissions bias at the Ivy League:

• Asian-American numbers at Harvard, Yale, and Columbia began large declines. 

• Asian-American enrollments throughout the Ivy League strangely converged to very similar levels. 

• The college-age population of Asian-Americans doubled during 1993-2011 as did their top academic awards, but none of this was reflected in their Ivy League enrollments. 

• As one example, the percentage of college-age Asian-Americans at Harvard dropped by more than 50% during 1993-2011, a larger decline than that suffered by Jews following the 1925 establishment of ethnic quotas. 

• Meanwhile, race-neutral Caltech saw its Asian-American enrollment increase closely in line with the growth of the college-age Asian-American population. 

• Comparing the Ivy League enrollments of Asian-Americans with those of high-performing white subpopulations rules out general “diversity” factors as an explanation for these patterns.

See also Defining Merit. Guess which university produces the most Nobel prizes per student?


Some additional figures from the article (click for larger versions). Note that not only did the number of college age Asian-Americans increase in recent decades, so did (overwhelmingly) their performance at the high end of academic achievement. If admissions were race neutral (meritocratic) at Harvard, why did the percentage of Asians decrease?

The Caltech student population is demographically similar to the most intellectually talented portion of the US population (see below); the Ivy League student population is not -- there are curious distortions.

Genetic substructure of Ashkenazim

More principal components results from the huge space of human genetic variation.







Figures from the paper below (additional labeling by Razib).

A genome-wide genetic signature of Jewish ancestry perfectly separates individuals with and without full Jewish ancestry in a large random sample of European Americans

Anna C Need, Dalia Kasperaviciute, Elizabeth T Cirulli and David B Goldstein

Genome Biology 2009, 10:R7doi:10.1186/gb-2009-10-1-r7

Conclusions: Here we show that within Americans of European ancestry there is a perfect genetic corollary of Jewish ancestry which, in pinciple, would permit near perfect genetic inference of Ashkenazi Jewish ancestry. In fact, even subjects with a single Jewish grandparent can be statistically distinguished from those without Jewish ancestry. We also found that subjects with Jewish ancestry were slightly more heterozygous than the subjects with no Jewish ancestry, suggesting that the genetic distinction between Jews and non-Jews may be more attributable to Near-Eastern origin for Jewish popuations than to population bottlenecks.

Brainpower ain't free

This NYTimes article describes research on the fitness costs and benefits of increased intelligence (learning ability). The specific results are for fruit flies, C. Elegans (worms) and E. Coli (bacteria), but the theoretical basis is well understood already. Evolutionary equilibrium occurs at a local fitness maximum, which means that further increases in brainpower come with negative fitness costs in some other area (e.g., disease resistance, physical capability). If brainpower could continue to increase without negative side effects, it would have. The fact that it hasn't suggests that genes with beneficial effects on intelligence may also come with negative consequences.

Note that equilibrium is only an approximate condition -- there may be directions in gene space in which overall fitness can still increase (even substantially), but it takes time for the random mutational process of evolution to find them. In most directions one would expect to find either only a very small positive (or zero) fitness gradient or a negative gradient, assuming a population that has been genotypically stable for a long time. Recent studies suggest that humans may have experienced rapid evolution in the last 10-50 thousand years due to the advent of agriculture, population growth, etc.

At the end of the article, one of the biologists seems ready to rediscover the Cochran-Harpending hypothesis :-) See also here.

NYTimes: ... It takes just 15 generations under these conditions for the flies to become genetically programmed to learn better. At the beginning of the experiment, the flies take many hours to learn the difference between the normal and quinine-spiked jellies. The fast-learning strain of flies needs less than an hour.

But the flies pay a price for fast learning. Dr. Kawecki and his colleagues pitted smart fly larvae against a different strain of flies, mixing the insects and giving them a meager supply of yeast to see who would survive. The scientists then ran the same experiment, but with the ordinary relatives of the smart flies competing against the new strain. About half the smart flies survived; 80 percent of the ordinary flies did.

Reversing the experiment showed that being smart does not ensure survival. “We took some population of flies and kept them over 30 generations on really poor food so they adapted so they could develop better on it,” Dr. Kawecki said. “And then we asked what happened to the learning ability. It went down.”

The ability to learn does not just harm the flies in their youth, though. In a paper to be published in the journal Evolution, Dr. Kawecki and his colleagues report that their fast-learning flies live on average 15 percent shorter lives than flies that had not experienced selection on the quinine-spiked jelly. Flies that have undergone selection for long life were up to 40 percent worse at learning than ordinary flies.

... “Humans have gone to the extreme,” said Dr. Dukas, both in the ability of our species to learn and in the cost for that ability.

Humans’ oversize brains require 20 percent of all the calories burned at rest. A newborn’s brain is so big that it can create serious risks for mother and child at birth. Yet newborns know so little that they are entirely helpless. It takes many years for humans to learn enough to live on their own.

Dr. Kawecki says it is worth investigating whether humans also pay hidden costs for extreme learning. “We could speculate that some diseases are a byproduct of intelligence,” he said.

The benefits of learning must have been enormous for evolution to have overcome those costs, Dr. Kawecki argues. For many animals, learning mainly offers a benefit in finding food or a mate. But humans also live in complex societies where learning has benefits, as well.

“If you’re using your intelligence to outsmart your group, then there’s an arms race,” Dr. Kawecki said. “So there’s no absolute optimal level. You just have to be smarter than the others.”

"No scientific basis for race"

Note Added in response to 2020 Twitter mob attack which attempts to misrepresent my views:

This is not my research. The lead author affiliation for the paper discussed below is Harvard Medical School. I do not work on population structure or group differences in genomics.

This paper is from 2007. At the time even the capability to deduce ancestry ("race") from DNA was controversial. Now the technology is highly developed and used by millions of people (23andMe, Ancestry). The second part of the blog post discusses phenotype differences, not genetic causes of those differences. Genetic causes for phenotype differences could not yet be studied in 2008 and only now (circa 2020) is becoming an area of research that generates more light than heat.

Racist inferences based on the results of the paper are the fault of the reader, not the authors of the paper or of this blog.


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"It's just a social construction" -- a picture is worth a million words...




Caption: Each point is an individual, and the axes are two principal components in the space of genetic variation. Colors correspond to individuals of different European ancestry. (Via gnxp.)

The figure is from the following paper, reporting on a study of over 4000 individuals. The researchers can group most Europeans into a geographical cline (NW vs SE, that's the red band in the lower right of the figure; there are two clusters but also individuals who are in-between) + Ashkenazim (the pink isolated cluster in the upper left) using a few hundred markers. I'm sure even better resolution can be obtained with more loci.

Discerning the Ancestry of European Americans in Genetic Association Studies

Abstract: European Americans are often treated as a homogeneous group, but in fact form a structured population due to historical immigration of diverse source populations. Discerning the ancestry of European Americans genotyped in association studies is important in order to prevent false-positive or false-negative associations due to population stratification and to identify genetic variants whose contribution to disease risk differs across European ancestries. Here, we investigate empirical patterns of population structure in European Americans, analyzing 4,198 samples from four genome-wide association studies to show that components roughly corresponding to northwest European, southeast European, and Ashkenazi Jewish ancestry are the main sources of European American population structure. Building on this insight, we constructed a panel of 300 validated markers that are highly informative for distinguishing these ancestries. We demonstrate that this panel of markers can be used to correct for stratification in association studies that do not generate dense genotype data.

The money paragraph: "...Here we mine much larger datasets (more markers and more samples) to identify a panel of 300 highly ancestry-informative markers which accurately distinguish not just northwest and southeast European, but also Ashkenazi Jewish ancestry. This panel of markers is likely to be useful in targeted disease studies involving European Americans."

For previous discussion of genetic clustering of human populations, see here and here. It has been known for some time that major continental groups ("races") form distinct clusters. Improved data allow for much finer exploration of clusters within clusters.

This post is getting a lot of traffic from metafilter, and judging from the comments people are confused. I offer the following from the second link in the paragraph above:

...no matter what genetic markers you choose: SNPs, STRs, no matter how you choose them: randomly or based on their "informativeness", it is relatively easy to classify DNA into the correct continental origin. Depending on the marker types (e.g., indel vs. microsatellite), and their informativeness (roughly the distribution differences between populations), one may require more or less markers to achieve a high degree of accuracy. But, the conclusion is the same: after a certain number of markers, you always succeed in classifying individuals according to continental origin.

Thus, the emergent pattern of variation is not at all subjectively constructed: it does not deal specifically with visible traits (randomly chosen markers could influence any trait, or none at all), nor does it privilege markers exhibiting large population differences. The structuring of humanity into more or less disjoint groups is not a subjective choice: it emerges naturally from the genomic composition of humans, irrespective of how you study this composition. Rather than proving that race is skin-deep, non-existent, or unimportant, modern genetic science is both proving that it is in fact existent, but also sets the foundation for the study of its true importance, which is probably somewhere in between the indifference of the sociologists and the hyperbole of the racists.

One thing commenters seem particularly confused about is the difference between phenotypic and genetic variation. The clustering data show very clearly that, in certain subspaces, the genetic variation within a particular population cluster is less than between clusters. That is, the genetic "distance" between two individuals within a cluster is typically much less than the distance between clusters. (Technical comment: this depends on the number of loci or markers used. As the number gets large the distance between clusters becomes much larger than the individual cluster radius. For continental clusters, if hundreds or thousands of markers are used the intercluster distance dominates the intracluster size. Further technical comment: you may have read the misleading statistic, spread by the intellectually dishonest Lewontin, that 85% percent of all human genetic variation occurs within groups and only 15% between groups. The statistic is true, but what is often falsely claimed is that this breakup of variances (larger within group than between group) prevents any meaningful genetic classification of populations. This false conclusion neglects the correlations in the genetic data that are revealed in a cluster analysis. See here for a simple example which shows that there can be dramatic group differences in phenotypes even if every version of every gene is found in two groups -- as long as the frequency or probability distributions are distinct. Sadly, understanding this point requires just enough mathematical ability that it has eluded all but a small number of experts.) Update: see here for an explanation in pictures of Lewontin's fallacy. I also edited the paragraph above for clarity.

On the other hand, for most phenotypes (examples: height or IQ, which are both fairly heritable, except in cases of extreme environmental deprivation), there is significant overlap between different population distributions. That is, Swedes might be taller than Vietnamese on average, but the range of heights within each group is larger than the difference in the averages. Nevertheless, at the tails of the distribution one would find very large discrepancies: for example the percentage of the Swedish population that is over 2 meters tall (6"7) might be 5 or 10 times as large as the percentage of the Vietnamese population. If two groups differed by, say, 10 points in average IQ (2/3 of a standard deviation), the respective distributions would overlap quite a bit (more in-group than between-group variation), but the fraction of people with IQ above some threshold (e.g., >140) would be radically different. It has been claimed that 20% of all Americans with IQ > 140 are Jewish, even though Jews comprise only 3% of the total population.

...The imbalance continues to increase for still higher IQ’s. New York City’s public-school system used to administer a pencil-and-paper IQ test to its entire school population. In 1954, a psychologist used those test results to identify all 28 children in the New York public-school system with measured IQ’s of 170 or higher. Of those 28, 24 were Jews.

There is no strong evidence for specific gene variants (alleles) that lead to group differences (differences between clusters) in behavior or intelligence, but progress on the genomic side of this question will be rapid in coming years, as the price to sequence a genome is dropping at an exponential rate.

What seems to be true (from preliminary studies) is that the gene variants that were under strong selection (reached fixation) over the last 10k years are different in different clusters. That is, the way that modern people in each cluster differ, due to natural selection, from their own ancestors 10k years ago is not the same in each cluster -- we have been, at least at the genetic level, experiencing divergent evolution. In fact, recent research suggests that 7% or more of all our genes are mutant versions that replaced earlier variants through natural selection over the last tens of thousands of years.

Mamet on Asperger's, Ashkenazim and the movies

The excerpt below is from his book Bambi vs Godzilla. Is he talking about movie directors, or physicists? :-)

Trivia question: what do David Mamet, Greg Cochran, Steve Pinker and Gregory Clark (author of A Farewell to Alms) have in common?

Glengarry Glen Ross is one of my favorite movies; the scene below is an all time classic. PUT THAT COFFEE DOWN!

DAVID MAMET

I think it is not impossible that Asperger’s syndrome helped make the movies.

The symptoms of this developmental disorder include early precocity, a great ability to maintain masses of information, a lack of ability to mix with groups in age-appropriate ways, ignorance of or indifference to social norms, high intelligence and difficulty with transitions, married to a preternatural ability to concentrate on the minutiae of the task at hand.

This sounds to me like a job description for a movie director. Let me also note that Asperger’s syndrome has its highest prevalence among Ashkenazi Jews and their descendants. For those who have not been paying attention, this group constitutes, and has constituted since its earliest days, the bulk of America’s movie directors and studio heads.

Neal Gabler, in his An Empire of Their Own points out that the men who made the movies – Goldwyn, Mayer, Schenck, Laemmle, Fox, - all came from a circle with Warsaw at its center, its radius a mere two hundred miles. (I will here proudly insert that my four grandparents came from that circle).

Widening our circle to all of Eastern European Jewry (the Ashkenazim), we find a list of directors beginning with Joe Sternberg’s class and continuing strong through Seven Spielberg’s and he youth of today.

...There was a lot of moosh written in the last two decades about the “blank slate”, the idea that since each child is theoretically equal under the eyes of the law, each must, by extension be equal in all things and that such a possibility could not obtain unless each child was, from birth, equally capable – environmental influences aside – of succeeding in all things.

This is a magnificent and majestic theory and would be borne by all save those who had ever had, observed, or seriously thought about children.

Races, as Steven Pinker wrote in his refutational The Blank Slate, are just rather large families; families share genes and thus, genetic disposition. Such may influence the gene holders (or individuals) much, some, or not at all. The possibility exists, however, that a family passing down the gene for great hand-eye coordination is likely to turn out more athletes than without. The family possessing the genes for visual acuity will likely produce good hunters, whose skill will provide nourishment. The families of the good hunters will prosper and intermarry, thus strengthening the genetic disposition in visual acuity.

Among the sons of Ashkenazi families nothing was more prized than genius at study and explication.

Prodigious students were identified early and nurtured – the gifted child of the poor was adopted by a rich family, which thus gained status and served the community, the religion, and the race.

The boys grew and regularly married into the family or extended family of the wealthy. The precocious ate better and thus lived longer, and so were more likely to mate and pass on their genes.

These students grew into acclaimed rabbis and Hassidic masters, and founded generations of rabbis; the progeny of these rabbinic courts intermarried, as does any royalty, and that is my amateur Mendelian explication of the prevalence of Asperger’s syndrome in the Ashkenazi.

What were the traits indicating the nascent prodigy? Ability to retain and correlate vast amounts of information, a lack of desire (or ability) for normal social interaction, idiosyncrasy, preternatural ability for immersion in minutiae; ecco, six hundred years of Polish rabbis and one hundred of their genetic descendants, American film directors.

Pinker pulls no punches

From the Edge.org Web site. It will be a good sign for science if Pinker isn't burned in effigy like Larry Summers. I imagine in some quarters he is already the bogey man of the 21st century.

Groups of people may differ genetically in their average talents and temperaments

The year 2005 saw several public appearances of what will I predict will become the dangerous idea of the next decade: that groups of people may differ genetically in their average talents and temperaments.

In January, Harvard president Larry Summers caused a firestorm when he cited research showing that women and men have non-identical statistical distributions of cognitive abilities and life priorities.

In March, developmental biologist Armand Leroi published an op-ed in the New York Times rebutting the conventional wisdom that race does not exist. (The conventional wisdom is coming to be known as Lewontin's Fallacy: that because most genes may be found in all human groups, the groups don't differ at all. But patterns of correlation among genes do differ between groups, and different clusters of correlated genes correspond well to the major races labeled by common sense. )

In June, the Times reported a forthcoming study by physicist Greg Cochran, anthropologist Jason Hardy, and population geneticist Henry Harpending proposing that Ashkenazi Jews have been biologically selected for high intelligence, and that their well-documented genetic diseases are a by-product of this evolutionary history.

In September, political scientist Charles Murray published an article in Commentary reiterating his argument from The Bell Curve that average racial differences in intelligence are intractable and partly genetic.

Whether or not these hypotheses hold up (the evidence for gender differences is reasonably good, for ethnic and racial differences much less so), they are widely perceived to be dangerous. Summers was subjected to months of vilification, and proponents of ethnic and racial differences in the past have been targets of censorship, violence, and comparisons to Nazis. Large swaths of the intellectual landscape have been reengineered to try to rule these hypotheses out a priori (race does not exist, intelligence does not exist, the mind is a blank slate inscribed by parents). The underlying fear, that reports of group differences will fuel bigotry, is not, of course, groundless.

The intellectual tools to defuse the danger are available. "Is" does not imply "ought. " Group differences, when they exist, pertain to the average or variance of a statistical distribution, rather than to individual men and women. Political equality is a commitment to universal human rights, and to policies that treat people as individuals rather than representatives of groups; it is not an empirical claim that all groups are indistinguishable. Yet many commentators seem unwilling to grasp these points, to say nothing of the wider world community.

Advances in genetics and genomics will soon provide the ability to test hypotheses about group differences rigorously. Perhaps geneticists will forbear performing these tests, but one shouldn't count on it. The tests could very well emerge as by-products of research in biomedicine, genealogy, and deep history which no one wants to stop.

The human genomic revolution has spawned an enormous amount of commentary about the possible perils of cloning and human genetic enhancement. I suspect that these are red herrings. When people realize that cloning is just forgoing a genetically mixed child for a twin of one parent, and is not the resurrection of the soul or a source of replacement organs, no one will want to do it. Likewise, when they realize that most genes have costs as well as benefits (they may raise a child's IQ but also predispose him to genetic disease), "designer babies" will lose whatever appeal they have. But the prospect of genetic tests of group differences in psychological traits is both more likely and more incendiary, and is one that the current intellectual community is ill-equipped to deal with.

The point about costs associated with benefits from certain genes is a bit off the mark. Even if it is so, there are still desirable combinations of genes, just as there are some people who are above average over a broad range of abilities. (Or, some parents will accept associated problems in order for their child to be the next Michael Jordan or Einstein.) I would be surprised if market-driven technologies did not arise to satisfy the demand for genetic engineering.