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Meritocracy: Almost as Wrong as Larry Summers
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Meritocracy Several years ago, Harvard President Larry Summers spoke at an academic conference on diversity issues, and casually speculated that one of the possible reasons there were relatively few female mathematics professors might be that men were just a bit better at math than women. Although his remarks were private and informal, the massive national scandal that erupted rapidly transformed President Summers into former President Summers, and coincidentally persuaded Harvard to name its first woman president as his permanent successor.

Now I am hardly someone willing to defend Summers from a whole host of very serious and legitimate charges. He seems to have played a major role in transmuting Harvard from a renowned university to an aggressive hedge fund, policies that subsequently brought my beloved alma mater to the very brink of bankruptcy during the 2008 financial crisis. Under his presidency, Harvard paid out $26 million dollars to help settle international insider-trading charges against Andrei Shleifer, one of his closest personal friends, who avoided prison as a consequence. And after such stellar financial and ethical achievements, he was naturally appointed as one of President Obama’s top economic advisors, a position from which he strongly supported the massive bailout of Wall Street and the rest of our elite financial services sector, while ignoring Main Street suffering. Perhaps coincidentally, wealthy hedge funds had paid him many millions of dollars for providing a few hours a week of part-time consulting advice during the twelve months prior to his appointment.

Still, even a broken or crooked clock is right twice each day, and Larry Summers is not the only person in the world who suspects that men might be a bit better at math than women. However, the notion that such vile and disgusting thoughts may be concealed in a few human skulls tends to agitate many ideologues, whose motives often seem to include a powerful emotional component. For example, MIT Professor Nancy Hopkins told reporters that she became physically ill at hearing Summers’ controversial remarks, and fled the auditorium, fearing she would black out or vomit if she remained. Many of the other details of Summers’ defenestration may be found in the numerous columns by bloggers such as Steve Sailer.

Perhaps Prof. Janet Mertz, a Wisconsin cancer expert, might fall into the same emotional category as Prof. Hopkins, given the peer-reviewed journal articles that she has published debunking the pernicious myth of gender differences in math ability, and rebutting the dreadful views of Larry Summers in particular. In her first article, she and her co-authors explored the distribution of top math achievers, focusing especially on the participants in the International Math Olympiad, and although the 10,000 word academic study is a bit eye-glazing, their quantitative findings are helpfully summarized in Tables 6 and 7 (pp. 1252-53).

The first of these shows the gender-distribution of the 3200-odd Math Olympians of the leading 34 countries for the years 1988-2007, and a few minutes with a spreadsheet reveals that the skew is 95% male and 5% female. Furthermore, almost every single country, whether in Europe, Asia, or elsewhere, seems to follow this same pattern, with the female share ranging between 0% and 12% but mostly close to 5%; Serbia/Montenegro is the only major outlier at 20% female. Similarly, Table 7 provides a gender distribution of results for just the United States, and we find that just 5 of our 126 Math Olympians—or 4%—have been female. Various other prestigious math competitions seem to follow a roughly similar gender skew.

Mertz and her co-authors seem to regard these results as a decisive refutation of Summers’ controversial remarks, and state as their “first and foremost” conclusion that “the myth that females cannot excel in mathematics must be put to rest” (bold-italics in the original).

In a more recent 2012 article aptly titled “Debunking Myths about Gender and Mathematics Performance,” Mertz and her co-author revisit the same topic. They open their discussion by noting in the very first paragraph that every single one of the fifty-odd winners of the Fields Medal—the “Nobel Prize” of mathematics—has been male. But this seemingly dispiriting fact is followed by 10,000 words of extremely dense verbiage, laced with mind-numbingly complex statistical analysis, ultimately allowing them to conclude that purported gender differences in math performance are largely due to differences in socialization and schooling, as well as outright bias. As a result, they end with a ringing call for the total elimination of gender-discrimination in mathematics.

 

But Prof. Mertz is hardly a narrow ideologue, focused solely on gender issues. Having successfully demolished Summers’ male-chauvinistic views by demonstrating that 95% or more of all the world’s top math students—both American and foreign—have always been male, she has recently turned her attention to similarly debunking my own claims regarding the recent pattern of ethnic performance in America. A few days ago, she produced a 3,500 word rebuttal promoted by Prof. Andrew Gelman on his blogsite.

As it happens, she and her co-authors had exhaustively researched the ethnicity of the 1988-2007 American Math Olympians in their aforementioned 2008 article, and through a combination of extensive biographical research and confidential personal interviews had determined the exact number of full-Jews and part-Jews among those 120 individuals, publishing the results in their Table 7 mentioned above, together with the broader racial categories.

Given that I had produced my own ethnic estimates for those same students based on perhaps five minutes of cursory surname analysis, while Mertz and her associates seemingly devoted five weeks of research to the same task, I readily acknowledge that her results are certain to be vastly more accurate than my own. Indeed, if we regard the Mertz figures as the “gold standard,” then comparing them with my own numbers provides a useful means of assessing the overall quality of my direct inspection technique, a technique that constituted a central pillar of my entire study. This allows us to decide whether my approach was indeed just the worthless “guesswork” that she alleges.

ORDER IT NOW

Her peer-reviewed journal article determined that the 120 American Math Olympians from 1988-2007 consisted of exactly 42 Asians, 26 Jews, and 52 non-Jewish whites. My crude surname estimate had been 44 Asians, 23 Jews, and 53 non-Jewish whites. Individual readers must decide for themselves whether these estimation errors seem so enormous as to totally invalidate my overall conclusions, but personally I would be quite satisfied if they remained in this range across the tens of thousands of surnames I had inspected throughout the rest of my paper.

Obviously, such estimation techniques may be completely incorrect for tiny handfuls of names, and should only be relied upon across substantial lists. For example, in one sentence of my 30,000 word article I stated that just 2 of the 78 names of Olympiad winners since 2000 seemed likely to be Jewish, and Mertz has repeatedly attacked me for this claim, now pointing out that I had missed the Hebrew name of winner “Oaz Nir.” She is correct, and since Nir was a double winner in 2000 and 2001, this single surname error on my part accounts for virtually the entire discrepancy between my own 1988-2007 Olympiad results and those produced by the exhaustive research undertaken by Mertz and her three academic co-authors.

 

The bulk of Mertz’s criticism relates to these surname estimation issues, and now that I have used her own data to determine the likely error rate of my own technique, let me respond to some of her other major arguments.

She claims that my Asian-American enrollment percentages at the Ivies and other elite universities are distorted by inclusion of part-time students in the governmental NCES database. However, this is completely incorrect. If she had bothered examining either the NCES database or my own description of the dataset, she would have noticed that I was quite careful to restrict my results to full-time students only. Anyway, with the notable exception of Harvard, almost none of these elite schools contain significant numbers of part-time students. She should have examined the NCES data before she made those spurious charges.

On another matter, she argues that the Jewish enrollment numbers provided by Hillel cannot possibly be correct because they are relatively constant from year to year. Now I have never claimed that the Hillel numbers are exact, and indeed have always suggested that they were probably mere estimates. But consider that the Asian enrollment figures are based on exact racial reporting as required by the federal government, and those numbers tend to be roughly as constant as the Hillel Jewish figures. Since the Asian figures are surely precise, how can the mere relative constancy of the Hillel numbers be taken as proof they are obviously fraudulent?

Next, she raises the question of whether the number of estimated Jewish NMS semifinalists is artificially depressed by their concentration in states with especially high thresholds, an issue that I had already discussed at length both in my main text and in my Appendix E. Although this issue cannot be fully resolved given our limited data, I doubt this is the case, and I actually suspect that the opposite is true, namely that the number of high-performing Jews is somewhat over-estimated. The reason is that Asians tend to dramatically outperform Jews, and a large fraction of all Asians are located in California, where they must compete against each other and face the highest state thresholds, thereby artificially restricting their numbers. For example, high school Asians in California outnumber Jews just 4.5-to-1, but are over 13 times as numerous among high-performing students. Meanwhile, a hugely disproportionate number of Jewish NMS semifinalists come from states with far lower thresholds such as Arizona, Florida, Pennsylvania, and Illinois; if a single national standard were in place, many or most of those Jews would probably have been replaced by higher-scoring Asians from California.

In any event, Mertz cites various arguments to suggest that my estimate that Jews constitute about 6% of national NMS semifinalists is too low, and that the correct figure should be 7%. Since I have already stated that I am reasonably comfortable with any figure in the 5.5% to 7.0% range, perhaps our differences are not so enormous in this particular item. But if she accepts that 7% figure, then the over-representation of Jews in elite academic institutions remains just as suspiciously high as I had originally claimed.

 

Given that two of Prof. Mertz’s greatest areas of policy interest seem to be the relative rate of elite performance by gender and by ethnicity, I notice a curious mismatch in her analysis.

She notes the large over-representation of males in math achievement, and strenuously argues that this is merely an artificial byproduct of social conditioning or even unfair gender bias, which distorts the inherently near-equal abilities of males and females. Therefore, she advocates major policy changes to bring the numbers of men and women in elite mathematics into much closer equality.

Yet at exactly the same time, she seems perfectly comfortable with Jews being over-represented at elite academic institutions by perhaps 3,000% relative to non-Jewish whites, and totally disproportionate to their apparent academic ability. I also suspect that she would be unwilling to endorse social policies aimed at bringing Jewish elite representation into much closer alignment with their 2% share of the national population.

Although I cannot explain this puzzling inconsistency in her logical positions, I can only note the curious coincidence that she herself happens to be a Jewish woman.

 

On a totally different matter I stepped off the plane in DC Tuesday evening and immediately found a message notifying me that my Wednesday Aspen Institute panel on federal minimum wage issues had been cancelled due to a looming snowstorm. Given that no ordinary snowstorm had ever cancelled a scheduled event during the years I lived in New York City, I braced myself for the blizzard of the century. Instead the next morning there were just a few very light snow flurries, without any of the scattered flakes surviving on the ground, but the government remained mostly shut down. I suppose the next step will be to close all government offices and allow workers to remain home on days that are rainy or overly warm. Such is the remarkable competence and grit of the capital city of our American World Empire.

The Aspen panel should be rescheduled for the near future, perhaps as early as March 15th, presumably subject to cancellation due to snow, rain, sleet, wind, or gloom of night.

(Republished from The American Conservative by permission of author or representative)
 
• Category: Race/Ethnicity • Tags: Meritocracy 
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  1. Yes, DC is full of weenies. For this you went to Harvard?

  2. The underlying issue isn’t I think, the veracity of a statistic, in this case, but Summers’ signature M.O.

    Ron’s description of the arc of Summers’ sly self-serving career is enough to make any fair-minded person sick. Perhaps the throwaway statements Summers made on women and mathematics, are just the straw that caused the already rising bile about his entitlement to finally overflow. And I would surmise that this self-styled, egotistical “master of the universe” is incorrigibly likely to take any statistic and color it with his own self-satisfied self-justifications as to why the status quo of his brand of crony capitalism is just as it ought to be.

    Figures don’t lie, but liars sure can figure.

    Which is the warp and woof how Summers turned the university to his own financialization ends, as Ron so succinctly points out.

    Given this guy’s signature, surely some pre-emptive strikes to protect Main Street are in order, instead of the President’s weak excuse about wanting to reform Wall Street, “but it would piss off too many powerful people.”

  3. Another reason to love the AmCon. If Summers was flogged like this every day for a decade that wouldn’t be enough to rectify his crimes.

  4. Cliff says:

    I always did well at math, in high school, college and grad school. I was a “first-rate second-rater” (I recently discovered that Somerset Maugham described himself, as a writer, in much the same way). From that background, I respond to Mertz: She’s a cancer researcher — why is she picking on math?

    More seriously, I think that fewer women than men excel in math because fewer women than men choose to go into math. I won’t bore you with my theories of why this is (I don’t think there’s an inate cause), but I do think it’s a matter of personal choice. Why should we require that women study math against their own inclinations?

    I recall a Doonesbury cartoon that pointed out that, apart from Rosemary Woods, all the major Watergate figures were men, and complained that women were denied “their equal right to obstruct justice”. Anyway, that’s what came to mind when I read about Wertz and her math campaign.

  5. NB says:

    I would like to refute a couple misleading and false statements in Unz’s rebuttal.
    1. Unz’s reported %ages for the racial background of Harvard undergrads from the Harvard NCES IPEDS data DO include full-time Harvard Extension School Students. The full-time undergraduate enrollment at Harvard in Fall 2011 is listed in the IPEDS data as 3,652 males and 3,555 females, summing to 7,207 students. The enrollment at Harvard College in Fall 2011 was 6,657. The IPEDS data cannot be used to draw any conclusions about the demographics of Harvard College.

    2. Prof. Mertz did NOT state that the correct figure should be 7% for the % of Jewish NMS semifinalists. She said that when I added in Unz’s new results for MA, I got 7% *based on Unz’s data for each state.* The whole point of emphasizing that Unz underestimated by a factor of over 5 the % of Jewish IMO team members since 2000 is both that Unz’s ability to recognize Jewish names is poor and that many Jews do not have obviously Jewish names. Hence, we believe that Jews represent more than 7% of NMS semifinalists.

  6. Wesley says:

    The gender, race, or ethnicity of the winners of a contest don’t mean that people of that gender, race, or ethnicity are naturally better at that field of study. Socialization has a lot to do with it. The only way that you could really determine if people of a certain gender, race, or ethnicity were better at a certain field of study is if you administered a test as part of a scientific survey that took into account socio-economic levels.

  7. TomB says:

    NB wrote:

    ” we believe that Jews represent more than 7% of NMS semifinalists.

    Fine, fine. Got any evidence for it though? Even a molecule?

    Sorta funny, NB: Unz comes forward with statistics that he says indicate about a 3000% favoritism factor for a certain group. And your initial take on this isn’t … amazement? Flabbergastment? Outrage?

    Nope. Instead it’s that gee, you think he might be off by a mere couple of hundred percent.

    Well gee I’ll just betcha that at the end of the day with this, no matter how little violence you or anyone is able to do to Unz’s findings, you’re not gonna be in the front ranks of those condemning whatever favoritism of the sort Unz has shown no matter what its degree.

  8. NB says:

    Also, I wanted to add a bit more about Unz’s remarks on Jewish NMS semifinalists. Unz’s analysis of Jewish academic achievement is predicated on his ability to identify Jews on the basis of their names, which proved spectacularly wrong in the one data set on which there exists confirmed data about the ethnic background of the students, thus calling into question his entire analysis wrt Jews. I suspect all of Unz’s state-by-state estimates of the % of Jewish NMS semifinalists are underestimates.

    However, I’m glad Unz is drawing attention to the disparities in NMS qualifying scores by state since this is a critical issue that has a substantial impact on estimating the % of high-ability Jewish students in the Harvard applicant pool (i.e. Unz is underestimating that %). Unz recently reported that 19% of MA NMS semifinalists are Jewish (also likely an underestimate based on my perusal of the names), and MA historically has the highest NMS qualifying score. Not only that, MA is arguably the most over-represented state at Harvard. I will be discussing the flaws in Unz’s NMS data in greater detail in an upcoming blog post. I will also compare the results of Weyl Analysis on the names of NMS semifinalists and Harvard undergrads – they are very similar. I’ve recently determined that Unz did not mean Gold* when he included “Gold-” as part of his Weyl list of distinctive Jewish surnames, so I’m in the process of finalizing my figures.

  9. NB says:

    Sorry to be spamming the comments here, I just wanted to note I wrote my above comment before seeing TomB’s comment.

    Regarding your request for proof that we believe that Jews represent more than 7% of NMS semifinalists…what is Unz’s proof that Jews represent 7% of NMS semifinalists? It is based on Weyl Analysis and his subjective name inspection method, which produced gross underestimates for the recent IMO participants. I don’t expect you to trust my subjective name inspection method (though I can prove that some of the people with non-obviously Jewish names on the MA NMS list are Jewish via publicly available info), so all I can do is compare Weyl Analysis (which is an objective methodology, assuming it is clearly defined) on the names of NMS semifinalists and Harvard students. Like I said, I’ll be posting those figures once I finalize them.

    “Unz comes forward with statistics that he says indicate about a 3000% favoritism factor for a certain group. And your initial take on this isn’t … amazement? Flabbergastment? Outrage?” This absurdly misleading 3000% factor is based on Hillel’s unreliable [and I believe inflated] estimates of the % of Jewish students at Harvard divided by the % of Jews in the population. Like Asians, Jews are over-represented among high academic achievers, so the 3000% factor is misleading, as one could also post some silly favoritism factor for Asian-Americans, who represent 21% of the Harvard College Class of 2016 and ~5% of the US population. The proper question is, “What is the % of Jews, Asian-Americans, and non-Jewish whites among high academic achievers in the Harvard applicant pool?” I will address this question in my upcoming blog post.

  10. David says:

    Devastatingly funny…

  11. “Having successfully demolished Summers’ male-chauvinistic views by demonstrating that 95% or more of all the world’s top math students—both American and foreign—have always been male…”
    Unless I am missing something, doesn’t this statement not attack her position at all? You are in disagreement about the mechanism by which there is such a huge discrepancy between the male-famale ratio in the general population and the same ratio in mathematics, not whether such a discrepancy exists.

    • Replies: @Wizard of Oz
  12. TGGP says: • Website

    You mentioned Larry Summers’ controversial remarks on the representation of women in certain areas, but when I searched for “variance” or “standard deviation”, I found nothing! It is a very important point that Larry was not speaking of mean scores or ceilings for women, but that male scores are statistically more spread out, so that they make up a greater compisition of the “tails”, whether in special ed or among the very gifted.

    Your response to Mertz seems a marked improvement from your reply to Gelman, as you actually addressed some issues of fact in dispute. I look forward to seeing how Mertz responds in turn.

  13. Anonymous • Disclaimer says:

    Rusty, You are missing something. N.B., Mertz’s stenographer, is missing (almost) everything.

  14. Thos. says:

    “Her peer-reviewed journal article determined that the 120 American Math Olympians from 1988-2007 consisted of exactly 42 Asians, 26 Jews, and 52 non-Jewish whites. My crude surname estimate had been 44 Asians, 23 Jews, and 53 non-Jewish whites. “

    Astonishing how close you came. The commenters who castigated you for that rough-and-ready last name method ought to be blushing, but probably aren’t.

    Thanks again for staying with this fascinating, worthwhile subject. I too love our alma mater and hope your work results in change for the better.

  15. Mike says:

    Who would want to go to an Ivy League school with these bigoted admission standards? I think most people would want to attend a college where ability is the primary discriminator for entrance.

  16. “A Study in Crimson” quotes Unz’s above statement: “Her peer-reviewed journal article determined that the 120 American Math Olympians from 1988-2007 consisted of exactly 42 Asians, 26 Jews, and 52 non-Jewish whites. My crude surname estimate had been 44 Asians, 23 Jews, and 53 non-Jewish whites. “ and then says, “Astonishing how close you came. The commenters who castigated you for that rough-and-ready last name method ought to be blushing.”

    They have no reason to be blushing since they remain correct. Yes, Unz and my counting of Asian-Americans is in pretty good agreement; my number is slightly lower because I know that at least one of the Asian-Americans with an Asian surname is bi-racial. However, the fact that our Jewish numbers for the 2-decade period overall are similar does NOT indicate that Unz’s direct inspection method is accurate. Actually, it confirms what I have been saying all along, i.e., he used this subjective method rather inconsistently. Throughout the 1998-2007 decade he grossly undercounted Jews on US IMO teams. Thus, to end up overall with a similar 2-decade number, he also had to have considerably over-counted Jews for the 1988-1997 period. Unz didn’t simply miss the Hebrew Israeli name “Oaz Nir” and Jews with Anglicized names such as “Kane” during the more recent decade, he also counted as Jews during the earlier decades many students with German and Polish surnames who were Gentiles while not counting kids such as “Thomas Mildorf” and “Miller” as Jewish in the 21st century. That is how he generated incorrect data that led him to claim an “over 15-fold collapse” in Jewish very high-end achievement and a significant change in the ratio of Gentiles to Jews among US IMO team members and Putnam Fellows that, in fact, did NOT occur based upon my numbers.

    As I stated in my recent response posted by Gelman, this is exactly why Unz should have done his direct inspection analysis by hiring someone to do it who was blinded to the identity of each list of names. Given he claims direct inspection can be done quick rapidly, it should be easy to find someone he can pay to repeat the analysis in a blinded fashion for ALL of his data. That is the standard scientific method by which such studies are performed to prevent unconscious biases from creeping into the data, leading to exciting conclusions that aren’t real. There have been many famous examples of wrong “discoveries” made in just this way. I sincerely hope he will do the blinded study and publish these data so we can see what the ratio of Gentiles to Jews among the various Olympiad and Intel very high-end achievers is and whether it has actually changed significantly OR whether the dropoff in BOTH Jews and Gentiles is similar and due to changing demographics, i.e., influx of very high-achieving Asians to the US.

    p.s. N.B. is NOT my “stenographer”. She is a summa cum laude Harvard graduate with a degree in physics who decided on her own to analyze the NMS and HPY undergrad student data sets by Weyl analyis. As I have stated repeatedly, my expertise is in the IMO and Putnam data sets. These other analyses are hers, not mine.

  17. spite says:

    I highly doubt that mathematicians really are into the discrimination business, they would accept anyone into the group if it advances their field. Its a field that requires extreme focus bordering on the autistic, which biologically more males are wired to do. This is very similar as the chess world, males and females in most places in the world would have played together since children, so it cannot be blamed on the usual “socio economic” nonsense. At the very highest level men excel, you may get a Polgar once in a while (which is still a 1 to 99 ratio at the top), but the chances of a female world champion are as likely as female winning the mens 100m sprint.

  18. TomB says:

    In response to my post NB wrote:

    “Regarding your request for proof that we believe that Jews represent more than 7% of NMS semifinalists….”

    No, that won’t do. I didn’t request any such “proof.” What I asked for, very carefully, was whether you had any *evidence* to back up your belief.

    Now, almost certainly you’ll be able to come up with *some,* just as Mertz came up with some evidence that one estimate Unz used was a few individuals off.

    But that was really the point behind my comment to you: Here, after all, comes a guy with what seems very very good evidence of simply *massive* preferential treatment being given to one group in something of simply surpassing importance given the role elite universities have come to play, and what are you and Mertz doing right off the bat?

    Expressing shock at what seems a prima facie case of at least a large amount of invidious and important discrimination? Offering ideas about how to better refine that evidence no matter what way that refinement cuts? Being outraged enough to saying that Unz has at least produced enough evidence to require universities to formally collect the data necessary to “prove” things?

    No, not in my view. Instead it’s an automatic “doubting” the evidence cuts in one particular way and then at best suggesting it’s wrong around the every edges that doesn’t do any real violence to the core implication of Unz’s work: That there’s been some massive jewish favoritism going on.

    I therefore stand by my prior prophesy: No matter what the further evidence suggests I doubt that you or Mertz is going to be in the lead of demanding any action be taken. And indeed that may take the form you’ve already shown which is to start talking about how Unz has “proven” nothing, even though of course even in the courts there is no requirement for any absolute mathematical “proof” of anything, and instead just levels of proof required.

    And, if I’m not mistaken, all that it takes to “prove” a discrimination case is to produce a mere “preponderance of the evidence.”

    On that basis already it seems to me Unz has already wildly exceeded doing that, and yet you (and Mertz) might be seen as acting as if there’s only one or two anecdotal instances involved.

    Maybe I’m wrong, hope I’m wrong; But time will tell.

  19. It was unfortunate that you included the financial issues involving President Summers. That muddies the water of an otherwise interesting discussion.

    It is quite surprising that the academic community would have such ahullaballoo over a rather common area of research and discussion — gender and academic performance. Women in who engage in the emotionally charged responses to these issues are disappointing to say the least.

  20. This should not have ended Summer’s tenure.

  21. NB says:

    TomB,

    You stated, “What I asked for, very carefully, was whether you had any *evidence* to back up your belief.”
    My evidence is based on Unz’s statement that Weyl Analysis produced virtually identical results as his own subjective inspection method on the set of NMS semifinalists. I performed Weyl Analysis on the Harvard alumni directory, and I already reported that I arrived at a figure for the Jewish enrollment at Harvard that was lower than Hillel’s figures by a factor of 2.5. i.e. when using the same objective methodology on both data sets, I get similar results for both the % of Jewish NMS semifinalists and the % of Jewish Harvard students. Prof. Gelman and I have already reported this, and apparently you don’t find this convincing, so I doubt there’s anything I can do to convince you.

    As I said above, I’ve recently determined that Unz did not mean Gold* when he included “Gold-” as part of his Weyl list of distinctive Jewish surnames, so I’m in the process of finalizing my figures for Harvard College’s Jewish enrollment based on this new info (my figures are currently at 7-9%, though I will double-check that before writing up my results in a blog post).

    “Now, almost certainly you’ll be able to come up with *some,* just as Mertz came up with some evidence that one estimate Unz used was a few individuals off.”
    That this is how you describe a factor of 5+ error once again indicates that it’s doubtful anything I say will change your mind.

    For example, Stanford has a public student directory. You can search that and see that Weyl Analysis performed on the names of Stanford undergrad students yields the result that 4-5% of Stanford undergrads are Jewish (half of Hillel’s report). This is lower than Unz’s claim that 6% of NMS semifinalists are Jewish (which did not include his recent report that 19% of MA NMS semifinalists are Jewish; when including this result, I arrived at 7% *based on Unz’s own data for each state*). Does this prove that Stanford is discriminating against Jewish students? Of course not. Stanford draws a disproportionate number of students from the West Coast, where the Jewish population is much lower than in the Northeast, from which Harvard College draws a disproportionate number of its students.

  22. Thos. says:

    What fun! Nothing but good can come of the sorting-out taking place here, and airing of the subject is long overdue.

    (I had no idea Ron could be such a wickedly amusing polemicist.)

  23. What’s most significant in the article is that President Summers was not wrong based on the data. Now the reasons may very well be a socialogical construction — but that is one that can corrected and really did not merit the near emotional break down of men or women.

    Sad state of education. Reminds me of women who think they are entitled to special treatment while engaging in underhanded tactics or in fair exchange —- based on some notion that men should treatment with some deferrence while they themselves do not extend the same courtesies.

    Black or white women who engage in discourse and demanding to treated as equals should not complain when they are called on their academic standing. Curious that women claiming men explain away data — in this case should be subject to a job reduction.

  24. surly says:

    the 95/5 skew just illustrates that women are more tuned in to reality than men. Women who are really good at math intuit that there is a diminishing return to theory. My own daughter, who was brilliant at math and entered college as a math major, walked away from math and into the social sciences because she had all the math she needed (and she was confident in her mathiness to learn anything she didn’t have) to solve problems. It wasn’t the math in and of itself that she loved; it was the toolbox she possessed that allowed her to prove theories. She loved math because she loved to solve real problems, not because the wanted to prove who was smartest by solving theoretical problems.

    I think the imbalance comes from my theory that for 90+ percent of women, people are more important that abstractions. And more women than men don’t really care about the competitive hierarchy.

  25. DB says:

    I highly doubt that mathematicians really are into the discrimination business, they would accept anyone into the group if it advances their field. Its a field that requires extreme focus bordering on the autistic, which biologically more males are wired to do. This is very similar as the chess world, males and females in most places in the world would have played together since children, so it cannot be blamed on the usual “socio economic” nonsense. At the very highest level men excel, you may get a Polgar once in a while (which is still a 1 to 99 ratio at the top), but the chances of a female world champion are as likely as female winning the mens 100m sprint.

    Indeed. Which is why it’s so interesting that the few females who do show up for the IMO do not seem to be underrepresented among the very top performers, contrary to the pattern observed in many other male-dominated arenas. I haven’t performed a full statistical analysis, but I remember one of the other gold medalists during my final year of competition was a Japanese girl, and more recently Lisa Sauermann was effectively the world champion.

    So it’s pretty clear to me that lack of ability is not the primary reason for the dearth of females in theoretical math; instead, I’d cite lack of interest as the driver, while both discouragement/discrimination and true ability difference are rather marginal contributors today.

  26. What RonUnz is saying is so obvious it amazes me that serious people waste their time trying to disprove it. There is no question that during the Twentieth Century the children and grandchildren of Eastern European Jewish immigrants gained a foothold in the education field and they, like everyone else, used social and kinship networks to get others into the field.
    Here are some other big issues:

    Why is every place I eat lunch at run by Greeks?

    How come if you walk into a City, State or Federal office on Ash Wednesday everyone has an ash mark on their forehead?

    Why are there so many Scots-Irish in the military?

    Why are there so many Canadians in the NHL

    Why are there so many African-Americans in the NBA?

    Why are there so many Hispanics in major league baseball?

    Why does everyone in the performing arts support gay marriage?

  27. Anonymous • Disclaimer says:

    @michael n moore – I, for one, stand among those who prefer evidence and reason to unfounded assertions about what is or is not “obvious”. I don’t understand why anyone would waste their time deluding themselves that something is obvious when there is no real evidence. If you think that social networks play a larger role in uni admissions that objective measures of “merit”, then that sounds important – please prove it. Don’t just say that it is obvious. Noone serious will believe you.

  28. Anonymous • Disclaimer says:

    “I, for one, stand among those who prefer evidence and reason to unfounded assertions about what is or is not “obvious”. ”

    Absolutely. Much more evidence and reasoning is needed.

    It is puzzling that with all the intellectual power and analytical resources at their disposal (not to mention access to the actual matriculants), the schools in question have relegated this particular subject to evidential murkiness, comparatively unanalyzed, certainly not well understood. With all the attention given the minutest evidence of prejudice or discrimination elsewhere in the groves of Academe, you’d think we would know more about this, wouldn’t you?

  29. Although I cannot explain this puzzling inconsistency in her logical positions, I can only note the curious coincidence that she herself happens to be a Jewish woman.

    LOL!!!!

  30. @roland maria adler

    I am not going to re-prove what Unz has already proven to my satisfaction. My point is that this is not something unique to Jews or to the acadamy. Working your connections is a universal human art form. Most people have little faith in anything else. Where do people gravitate to on the Web, training sites or social networking sites?

    I am 64 years old and I have never gotten a job that wasn’t based on contacts and I don’t think I know anyone who has. That’s enough research for me.

  31. I will just add that if the normal working of connections by upwardly mobile people is not a play here then you’re left with 2 study options that no one is going to fund:

    A study of Jews as forming a unique body of people who are infiltrating our elites.

    An study of the NorthEast WASP elite who may be deliberatly promoting Jews to manage their unruly empire.

    If you have other ideas I would be glad to hear them.

  32. My evidence is based on Unz’s statement that Weyl Analysis produced virtually identical results as his own subjective inspection method on the set of NMS semifinalists. I performed Weyl Analysis on the Harvard alumni directory, and I already reported that I arrived at a figure for the Jewish enrollment at Harvard that was lower than Hillel’s figures by a factor of 2.5….

    Umm, don’t you mean a “divisor” of 2.5? A “factor” of 2.5 would have made the number higher.

    More generally, you haven’t provided evidence; you’ve made an argument based on conclusions in support of which you’ve again presented no evidence.

    And if you conclude that that only 7-9% of Harvard College’s students are Jewish, your methodology is terribly flawed. That number is less than half the number for the class of 1927, which

    Let’s see the names for Harvard College’s students, so we can visually inspect them.

  33. The research as presented doesn’t indicate any issues of competition. It is a rather simple observation based on a established set of numbers.

    Why the disparity is probably based on sociological practices as opposed to some vie of intution verses biology.

    Given that men by and large carried the weight of protection, production, building, it makes some sense that they would have excelled in mathmatics. I am sure history would clearly establish that modality. A female architect is no less inclined to use math than a male in same field. The stress on a strut is the stress on a strut. Those stresses wouldn’t change as the result of a woman’s skill verses a man’s.

    Mathmatics and with most sciences is grounded in rules. It took me about twenty years to figure that simple process — follow the rules — they don’t have to make sense save as to the rule. I think it is unfortunate that so much of what has been role assignment and practice has been turned into some gender dominance discussion.

    Perhaps, I should have walked the sixty yards and erased the blackboard when asked by a female co-worker. Not.

  34. Now that women are able to serve in combat ars, it will be interesting to see how that is palyed out. Will the exams be eased? Will passing require a lower score?

    Will women take up the task? Is it time for men to cease bearing the brunt of dangerous duty? Are women going to register?

    The standard of recruitment will be means tested. It will be interesting to how they are going to structure the mean?

  35. Mr. Unz,

    if in fact, you’d like to spread the meritocratic wealth in education by spreading it around. Here’s mysuggestion:

    Provide each school from Kindergarten up with an instructor of equal skill, expertise and committment as one might find at La Jolla Country Day.

    Each student would be required to learn the same material using the same syllabi.

    Sanitize the neighborhoods of drugs, crime, etc. Sanitize and hypnotize the parents, so they model the value of education. Ensure that every institution have the same tecnological tools.

    Cease all extra study programs for those that can afford them or require them for everyone.

    Perhaps dump the ACT, SAT and similar such testing models and each meritcratic institution provide their own across the board for every student so desiring to get in.

    I have no idea how to end legacy placements. It is a method of compensation to faculty. But it may be taking up a neccessary slot for some test worthy student.
    Did I mention the redesign of the economic structure.?

  36. There has been much a do about a woman’s worth. While I certainly want to honor women in their role as equal members of a society. If that role means that some other member in this case males are to scarificed so as to appease the emotional burden of working through the issues to operate in the work place,

    No women is worth a sacrificed economy. No woman is worth the displacement of another’s family and certainly no woman is worth a lie leading to the same. That women are discovering that work comes at a price of personal fulfillment — welcome to the club.

  37. NB says:

    william wright said:
    “Umm, don’t you mean a “divisor” of 2.5? A “factor” of 2.5 would have made the number higher.”
    Umm, what I said was correct. I’m using definition 4 here:

    http://www.ahdictionary.com/word/search.html?q=factor

    In mathematics, the term divisor refers to an integer, so 2.5 isn’t even a divisor of 25:

    http://www.math.niu.edu/~beachy/abstract_algebra/study_guide/11.html

    “More generally, you haven’t provided evidence; you’ve made an argument based on conclusions in support of which you’ve again presented no evidence.”
    Obviously I can’t post a list of the names of Harvard students. When I spoke to Unz in person, I asked him to look at the Yale alumni directory with me, precisely so that he would cease to describe my data as unverifiable (Unz has access to the Harvard alumni directory too). Unz declined my request, but he did say that I should publish my counts for each surname from the alumni directories, so I will do that when I write up my blog post. You can also perform Weyl Analysis on Stanford’s public directory, so you can see that yields a result half as large as Hillel’s report and lower than Unz’s figure for the % of Jewish NMS semifinalists.

    “And if you conclude that that only 7-9% of Harvard College’s students are Jewish, your methodology is terribly flawed.”
    I never said that only 7-9% of Harvard College students are Jewish. I said that Weyl Analysis [using a restrictive list of Gold- names rather than Gold*; see my previous comment] performed on the Harvard alumni directory names yielded that result. As I have stated previously, I believe that Weyl Analysis yields underestimates of the % of Jews (given a reasonably large sample size). Hence, I believe Unz’s result for the % of Jewish NMS semifinalists is an underestimate. The point is that using the same methodology on both the names of NMS semifinalists and the names of Harvard students produces similar results.

  38. My conclusion is that the female-lobby is more powerful than the jewish-lobby, at least in this case.

  39. Anonymous • Disclaimer says:

    @NB – ” This absurdly misleading 3000% factor is based on Hillel’s unreliable [and I believe inflated] estimates of the % of Jewish students at Harvard “

    I would hope and expect that Hillel’s numbers are reasonably accurate. At most of the Ivies organizations that deliberately or negligently misrepresent material facts are subject to sanction, including loss of official standing.

    That doesn’t mean it doesn’t happen, of course. But the implication of what you are saying is that Hillel has been reporting “unreliable” and “exaggerated” numbers over a period of years. I find this hard to believe, not least because the “exaggeration” you describe is not a few percentage points, but closer to 100 percent. Surely someone would have noticed this by now and called it before a relevant board of inquiry?

  40. NGPM says:

    I didn’t read the study in question, but if Mertz seems to think that what is at stake is the need to “put to rest” “the myth that females cannot excel in mathematics,” then she is fighting the wrong battle, because one excellent female mathematician will suffice to refute that notion, and it is in fact NOT what Larry Summers claimed.

    It is well known, among people who are not afraid of “inequality” as a persistent element of human society and human life, that the median I.Q. for men and women is the same, but the standard deviation is greater for men than it is for women. The bell curve for male intelligence is much more spread out, and the practical consequences of this are that one is much more likely to find a man than a woman among super-geniuses, but also among super-cretins.

    This seems fairly consistent with other realities of human life, that men are more likely than women to spontaneously react heroically, but also to commit heinous crimes.

    Of course, credible psychometricians also freely acknowledge that I.Q. is not 100 percent heritable – far from it. Mertz is perfectly free to argue that the gender gap in standard deviations of various gauges of intellectual ability and achievement (I.Q., math wizardry, success in engineering and the natural sciences) is entirely due to conditioning and not to biological factors, but the onus is on her to demonstrate evidence to that end.

  41. Sometimes an old text is very instructive. And I am again reminded of the Myth of Male Power by Warren Farrell

  42. NGPM,

    In short men are risk takers on either end of the spectrum . . .

    I appreciated the data on the spread. I am not a big fan of the Bell curve analysis on intellegence — but your comments were informative

  43. NGPM says:

    @EliteCommInc.: thank you for your kind words. Statistics themselves don’t lie, but it is easy enough to lie with statistics, whether by falsifying them outright, showing only part of the data or equivocating among variables.

    In short men are risk takers on either end of the spectrum

    I don’t think it’s “all” that simple, but what you say is basically true. Biologically, men have less to lose from taking a risk – our gametes are smaller, as is our physical investment in the reproductive process. It would make sense that this would translate into behavioral patterns that are not so (immediately) obviously linked with reproduction.

    However, we need to be careful about searching for “the math whiz” gene or “the machissimo gene” or whatever. Human culture grew up around genetic and environmental realities, and the one tends to enforce the other. Asking whether a trait is environmental or genetic is not quite as futile as asking whether the chicken or the egg came first, but even a genetically-loaded trait such as eye color still assumes certain inputs of water, oxygen, nutrients, et. al. for expression. Conversely, even such an environmentally-induced ability as the knowledge of the location of Russia on the globe assumes one or more neurologically valid configurations for learning such information at all.

    For behavior and intellectual abilities in particular, we may never find perfectly causative genes, but we can find strong enough correlations to give us an idea of why certain inequalities tend to persist–and insight into whether it is possible or desirable to eradicate them. So far as social sexual dimorphism is concerned, I confess to being among those who does not believe that it is possible or desirable to eradicate, and this was my primary beef with Warren Farrell’s work. But while I disagree with the advocacy latent in The Myth of Male Power, the facts he cites are incontrovertible, and his analysis, if in my opinion flawed (and not particularly enlightened historiographically with regards to feminism), seems to be carried out in basically good faith.

  44. NGPM says:
    “I didn’t read the study in question, but if Mertz seems to think that what is at stake is the need to “put to rest” “the myth that females cannot excel in mathematics,” then she is fighting the wrong battle, because one excellent female mathematician will suffice to refute that notion, and it is in fact NOT what Larry Summers claimed.”

    From the founding of Harvard in 1636 to the day Summers gave his talk in January 2005, there had been a total of ZERO women who had ever been tenured research (as opposed to teaching) professors in their math department.
    When Nancy Hopkins had chaired in 1995 MIT’s “Study on the status of women faculty in the school of science at MIT”, there were zero women professors at that time in their math department. Zero at Stanford. Zero at U of Chicago, a school that at one time had been the leading producer of female Ph.D.s in mathematics (so they could become professors at the top all-female colleges such as Smith). Yes, a primary point of my 2008 Notices article was to show that there did, indeed, exist some women mathematicians of truly outstanding caliber. Even if their numbers were small, why didn’t these departments have ANY on their faculty?

    A 2nd major point of this article related to the fact that some countries such as the USSR and East Germany have produced numerous world-class female mathematical problem solvers (as measured by being among the very top scorers in the IMO) throughout the past 1/2 century while the US didn’t have a single female on its IMO teams until 1998. Lisa Sauermann of Germany had the only perfect score at the 2011 IMO. She had placed 3rd and 4th in the world in the IMO in 10th and 11th grade and had already qualified for the German team in 8th grade! The tiny country of Romania has produced more female Putnam Fellows than the US. How can this be? In my 2012 Notices article, I show that a strong, statistically significant correlation exists between % females on a country’s IMO team and its gender gap index as determined by the World Economic Forum. In other words, countries with greater gender equity, especially with respect to economic equity in the paid labor force, also tend to produce a higher % of top-notch mathematicians who are females. By the way, the US does not rank among the top countries with respect to gender equity.

    A third major point I make in my 2012 article relates directly to Summers’ argument of greater male variance in math performance being the primary reason for the scarcity of top female mathematicians. I show that while the US and most other countries have greater male variance in math, there are some countries that do not. In fact, there exist some countries where the entire distribution of math scores are essentially identical. If greater male variance is a biologically determined difference between the sexes, such countries should not exist!

    I further show that there is a very strong, statistically significant correlation between gender gap in mean math performance and ratio of male variance to female variance. In other words, both the gender gap in math performance and variance ratio are likely both artifacts of the same sociocultural factors.

    In summary, Larry Summers WAS wrong about the primary reasons he gave for the extreme scarcity of tenure women math professors in top-ranked US math departments at the January 2005 NBER conference, just like he was wrong about many other things where I actually agree with Unz. I’m not saying that innate gender differences can’t play any role in there being fewer women than men among top mathematicians. I’m simply saying that the US could be producing lots more female (AND male) outstanding mathematicians given there are some European and Asian countries that produce many more than we do. Read my articles and decide for yourself what you think. (Yes, they contain some heavy-duty statistics, especially the 2012 article where the data sets contain hundreds of thousands of students.)

  45. A possible weakness in Unz’s study is the Hillel House participation numbers. Non-profits use these numbers to report to funding sources and have an incentive to inflate them.

  46. SGT Caz says: • Website

    Mr. Unz, your sarcasm has won me over. Well done.

  47. NGPM says:

    I’m not saying that innate gender differences can’t play any role in there being fewer women than men among top mathematicians. I’m simply saying that the US could be producing lots more female (AND male) outstanding mathematicians given there are some European and Asian countries that produce many more than we do.

    Madame, if that’s the case, then with all due respect, why simply harp on the fact that there is a dearth of strong female mathematicians at Harvard? To me it’s like arguing that female Wal-Mart employees are underpaid. So are the men. The U.S. rewards underachievement. What’s your point?

  48. Anonymous • Disclaimer says:

    @surly

    “Women who are really good at math intuit that there is a diminishing return to theory.”

    Well, then they “intuit” incorrectly. (And this would be news to the numerous female professors I learned from while pursuing my math degree.) Proclamations that any given mathematical theorem will never have a practical application in “the real world” are usually on par with the old claims that heavier than air flight was impossible or that the sound barrier would never be broken.

    There’s also the appreciation of well-done theoretical math for its inherent aesthetic elegance. One of my graph theory classmates (a woman and now a Ph.D in mathematics) used to proclaim “math is beautiful” a lot. Just because your daughter did not share that shame appreciation (at least not enough to finish a math major), does not mean the people who do are all disconnected from reality or engaged in a contest to “prove who is the smartest.”

    You can take everything you said about math and apply it to lots of other fields, and see how ridiculous it sounds. “People who decide not to devote their entire lives to the theoretical study of music are just more in touch with the real world. They learn just enough theory to be able to make music that real people enjoy, and then get on with the business of making it.”

  49. Gaeranee says:

    I am curious as to why Ms. Mertz did not include the bi-racial person with an Asian surname in the Asian-American category. Does this mean that when Ms. Mertz came across a person with a Jewish surname but with a Jewish mom, he wasn’t counted as Jew?

  50. Janet Mertz.

    I was going to respond to your research specifically, but I thoiught it best to reread Pres. Summers speech. In so doing. I find that he has been taken out of any reasonable context. Certainly, if one chooses to single out a particular phrase or thought expressed, one could twist the context into something akin to the complaints. But in placing those complaints in content and context of the entire speech.

    These complaints are found wanting. And the academic community should be ashamed of itself. He maes no clear definitive conclusions as has been attributed to him. He has some idea. But he repeatedly says, no one knows, and he doesn’t know. He has some ideas, but they are just ideas based on experience, research, discussion, etc.

  51. NGPM,

    I take Farrell’s work at face value. I think his motive is simple and clear. Where as men have been indicted on their abuse of women. The historical data as he presents it, and I agree is quite the opposite. That men have paid a fair price on behalf of women and in protection of women.

    I won’t go further, because what prompted his text was his work with men on anger issues. And I would not deny, it is a defense of manhood being a man and what that means.

    I appreciated your comments. I don’t think it is simple as it is played out, but a quick anecdotal observation. From the moment male issue ascends the pathway to egg. It is on a very risky journey frought with benign and unbenign attempts to prevent success.

  52. [...] focus of her article was a worldwide gender analysis of top performing math students aimed at refuting the controversial speculations of former Harvard President Larry Summers, who had suggested that men might be better at math than women, at least at the very high end of [...]

  53. [...] focus of her article was a worldwide gender analysis of top performing math students aimed at refuting the controversial speculations of former Harvard President Larry Summers, who had suggested that men might be better at math than women, at least at the very high end of [...]

  54. I have now posted my official 3-page response to Unz’s above March 9th post. It is available at:

    http://andrewgelman.com/wp-content/uploads/2013/03/Mertz-response-to-Unz-March-9-post-final.pdf

  55. Anonymous • Disclaimer says:

    Mertz’s response to this latest defense eviscerates Unz’s argument. It is now difficult to believe that Unz in debating in good faith and it is rather ironic that Unz accuses Mertz of being emotional. Unz states that his count of Jewish Math Olympians from 1988-2012 was only wrong by 2. Well, yes. But what he doesn’t mention is that he accidentally stumbled on the right answer by grossly over-counting Jewish representation on the 1970 teams and gross under-counting representation on the 2000-2012 team. After you adjust for Unz’s errors, the change in representation is only about 5%, very far from the collapse in Jewish achievement that Unz claimed. His thesis completely falls apart.

    It is telling that Unz, who claims to objectively follow the statistics, refuses to acknowledge these errors and reconsider his findings in light of the new evidence.

    Andrew Gelman, the highly respected Columbia University statistician who was originally favorable inclined to Unz’s argument has reversed course after reviewing the numbers and the Mertz rebuttal. And no wonder – Unz’s errors are devastating.

  56. Anonymous • Disclaimer says:

    Mertz’s work is flawed at best, as it does not take biological factors into account at all. This constant drivel of words like “social conditioning” and “gender bias” stems purely from emotion with an insistence that masks biological affinities. The male and female brains (and bodies) evolved differently and are built for different things. This is one of the more recent documentaries that exposed the paradox: http://www.youtube.com/watch?v=KQ2xrnyH2wQ.

    The national “outrage” that followed Summers is no different from the feminist tactics of bullying institutions and attacking men in order to feed emotional failures. It is the same tactic that skews domestic violence or sexual harassment reports: http://www.dvmen.org/dv-30.htm#pgfId-1000404 or http://www.sba.oakland.edu/faculty/schwartz/Scenes%20from%20a%20Sexual%20Holy%20War.pdf. Mertz’s work follow the same forced, unscientific method of appealing to feelings rather than facts. Just like most feminist “research”, this is just another card to the pile of rubbish that insults the scientific method. Stop trying to reform biology.

  57. Anonymous • Disclaimer says:

    Research has found that male and female brains are ‘essentially’ the same (Cordelia Fine). Unfortunately ‘essentially’ is a weasel word because it doesn’t preclude one gender having a very slight edge in a particular area – and that is all it takes to dominate in the very highest echelons. In tennis, the absolute difference between Djokovic and the player ranked 50 in the world is, in absolute terms, miniscule and the latter is a superlative player by all but the very highest standards. However, in an intensely competitive situation, the tiny edge which Djokovic possesses is sufficient to ensure that he will prevail the great majority of the time.

  58. Just stumbled on this interesting set of comments.
    Here is a response:

    I am constantly astonished by people who wish to claim and imply that men’s and women’s brains are different and therefore women can reasonably be expected to be less good at math. If these people had any interest whatsoever in understanding the biological basis of math ability, they would be interested in comparing the brains of women who are great mathematicians to women who aren’t, or the brains of men who are great mathematicians to men who can’t do math at all. But they never do, Why?

    I assume for the same reason that Mr. Unz selects only data that fits his preconceived ideas (while Mertz – a scientist – feels obliged to get every data point correct before making her conclusions.) ps Mr. Unz, Larry Summers was just as wrong when his ideas DON”T agree with yours, as he was when they do. He is one of those very smart people who lack common sense and wisdom.

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