Bell curves

Back at the old blog we used to occasionally chat about the notorious speech by Harvard President Larry Summers, in which he suggested that intrinsic aptitude was a more important factor than discrimination or bias in explaining the dearth of women scientists. Examples here, here, here, here, here, and here. There was a lot of posturing and name-calling and oversimplification on either side of the debate, of course, which tended to obscure the basic fact that Summers was, as far the data goes, wildly wrong. Two favorite goalpost-moving maneuvers from his supporters were first to pretend that the argument was over the existence of innate differences, rather than whether they were more important than biases in explaining the present situation, and then to claim that Summers’ critics’ real motive was to prevent anyone from even talking about such differences, rather than simply trying to ensure that what was being said about them was correct rather than incorrect.

It was a touchstone moment, which will doubtless be returned to again and again to illustrate points about completely different issues. Here’s an example (thanks to Abby Vigneron for the pointer) from Andrew Sullivan:

DAILY KOS AND LARRY SUMMERS: It’s a small point but it helps illuminate some of the dumbness of the activist left. “Armando” of mega-blog/community board, Daily Kos, takes a dig at Larry Summers, and links to a new study on gender difference. I’m not getting into the new study here, but I will address Armando’s description of Larry Summers’ position. In a bid to be fair, Armando writes:

NOTE: Yeah I know Summers didn’t say men were smarter than women, he just said they had greater aptitude in math and the sciences than women. Huge difference.

This is one of those memes that, although demonstrably untrue, still survives. Read the transcript of Summers’ now infamous remarks. His point was not that men are better at math and the sciences than women, as Armando would have it. His point was that there is a difference not in the mean but in the standard deviation:

Even small differences in the standard deviation will translate into very large differences in the available pool substantially out. I did a very crude calculation, which I’m sure was wrong and certainly was unsubtle, twenty different ways. I looked at the Xie and Shauman paper – looked at the book, rather – looked at the evidence on the sex ratios in the top 5% of twelfth graders. If you look at those – they’re all over the map, depends on which test, whether it’s math, or science, and so forth – but 50% women, one woman for every two men, would be a high-end estimate from their estimates. From that, you can back out a difference in the implied standard deviations that works out to be about 20%. And from that, you can work out the difference out several standard deviations. If you do that calculation – and I have no reason to think that it couldn’t be refined in a hundred ways – you get five to one, at the high end. (My italics.)

Summers was addressing the discrete issue of why at the very high end of Ivy League math departments, there were too few women. His point, as the Harvard Crimson summarized it was that, in math and the sciences, “there are more men who are at the top and more men who are utter failures.” Armando is wrong; and he needs to correct the item. In fact, this is a good test of leftist blog credibility. Will he correct? I’ll keep you posted.

Ah yes, the good old standard-deviation argument. It’s the absolute favorite of those in the intrinsic-differences camp, since (1) it sounds kind of mathematical and impressive, and (2) they get to insist that it’s only the width of the distribution, not the mean, that is different between men and women, so really the argument doesn’t privilege men at all, while it manages to explain why they have made all the important contributions in human history. In a debate with Elizabeth Spelke at Edge, Steven Pinker rehearses the argument somewhat pedantically.bell curves
But let’s look at what the argument actually says, both explicitly and implicitly.

  1. Standardized tests scores reflect innate ability.
  2. Boys’ scores on certain tests have a larger standard deviation than girls’ scores, leading to a larger fraction of boys at the high end.
  3. The dearth of women scientists is explained by their smaller numbers on the high end of these tests.

Now, everyone who is familiar with the data knows that point 1 is somewhere between highly dubious and completely ridiculous; Summers himself admits as much, but it would ruin his story to dwell on it, so he soldiers on. But point 3 is interesting, and deserves to be looked at. It’s a nice part of the argument, because it’s testable. Is this difference in test scores really what explains the relative numbers of men and women in science?

Summers’ data comes from the book Women in Science: Career Processes and Outcomes by Yu Xie and Kimberlee Shauman. Interviewed shortly after his remarks, both Xie and Shauman were quick to criticize them, using words like “uninformed” and “simplistic.” We were fortunate enough to have Kim Shauman herself as a speaker at our Women in Science Symposium back in May. She pointed out that the studies Summers refers to can indeed be found in her book, right there in Chapter Two. But if you wanted to know whether the standard-deviation differences were actually what accounted for the dearth of women in science, you would have to read all the way to Chapter Three.

Here’s the point. By the time students are in twelfth grade, there is a substantial gap in the fraction of boys vs. girls who plan to study science in college. So it’s easy enough to ask: how much of that gap is explained by differing scores on standardized tests? Answer: none of it. Girls are much less likely than boys to plan on going into science, and Xie and Shauman find that the difference is independent of their scores on the standardized tests. In other words, even if we limit ourselves to only those students who have absolutely top-notch scores on these math/science tests, girls are much less likely than boys to be contemplating science as a career. Something is dissuading high-school girls from choosing to become scientists, and scores on standardized tests have nothing to do with it.

Now, looking at Sullivan’s post above, there’s nothing he says that is strictly incorrect. He is simply characterizing (accurately) what Summers said, not actually endorsing it. Still, he is certainly giving the wrong impression to his readers, by repeating a well-known allegation without mentioning that it is demonstrably false. It’s a small point, but it helps illustrate some of the disingenuity of the activist right. Sullivan is misleading, and he needs to correct the item. In fact, this is a good test of quasi-right-wing blog credibility. Will he correct? We’ll keep you posted.

156 Comments

156 thoughts on “Bell curves”

  1. I haven’t read primary sources on evolutionary psych. so I’m not going to pronounce judgment (although I have some suspicions based on secondary sources). Most people who I see using evolutionary psych, on the other hand, are just telling stories.

    I’m not really sure why Lubos keeps posting studies that there are intrinsic differences between men and women. I would have thought the long term studies of gender reassignment surgery made this reasonably clear. I don’t think it’s a particularly controversial position.

  2. Aaron, rather than talking about “most people”, as you do in this statement:

    “Most people who I see using evolutionary psych, on the other hand, are just telling stories.”

    Why don’t we talk about those stories that they are just telling? That’s the substance here — not some vague undefined group of “most people”. So, have there been any examples of such storytelling in this discussion?

  3. Dear Lubos,

    What can I say, but, Wow! I had no idea that I was on a crusade against evolution and trying to promote the ideas of ID. In fact, I don’t think I ever said either of those things in my posts. In fact, I suspect that your disagreement with what I said is mainly political. But, hey, calling me an anti-scientific religious crank is a pretty good rhetorical device to discredit what I was saying, so nice work there! I’m sure you won over a lot of supporters with that one.

    Since I’ve apparently been misunderstood, I’ll try to synopsize my position for you. I have no doubt in the science of evolution, and when it comes to scientific explanations for human behavior I have no doubt that both environmental and genetic factors come into play. But you seem to be advancing the hypothesis that genetic factors alone are the best explanation for why there are fewer women in the physical sciences. So yes, I do disagree with that hypothesis and I don’t think that a full accounting of the science supports it. I don’t think you can seriously dismiss the effects of gender socialization and discrimination (among others) in answering this question (as many of the posters have pointed out). I’m sure you would like to think you have already won this debate and that “science” unambiguously supports your view, however there are scientific studies that lend support to the other side that you haven’t given in your list above. So I would say the jury is still out.

    I hardly think that any of this makes me an ID proponent or a religious ideologue.

    I will admit that I am somewhat skeptical of the subfield of evolutionary psychology precisely because it seems so speculative and prone to just-so-stories. Chris Crawford has just been telling us how theories in evolutionary psychology are not even falsifiable. That sends up a red flag for me right there. The questions addressed in this subfield are indeed fascinating, but I think that there are strong criticisms to be made of some of the results. I’m sure the researchers will attempt to answer those criticisms scientifically.

  4. This particular paragraph struck me:

    The nature elements arise from evolutionary selection in favor of females with stronger social reasoning skills. Hominid females lacked the physical strength to defend themselves and their children, and so had to rely on a social network. For example, among chimpanzees this is accomplished by frequent mating with every male; this insures that any male could be the father of her children, which in turn provides an incentive for all the males to protect her children. Among hominids, this strategy can’t work because the mother also needs paternal investment in the form of protein. Therefore the mother must build a strong social support network. This has the additional benefit of adding to the enforcement of paternal commitment.

    Males have much less dependence on social support and so faced little selection pressure in favor of social reasoning skills. The result of all this is that modern human females have much stronger social reasoning skills than modern human males. This differential explains the well-established dominance of females in careers requiring such skills.

    This is not scientific; it’s just a story.

  5. Dear Tim, the reality is not that biological differences are “alone” responsible for the differences in jobs. But they’re primary. Of course that there is always some noise that emerges also when one studies these issues – by noise, I mean various bias in education, cultural traditions, influence of parents and other people. But there is also a clear signal.

    Moreover, even the “social” influences are indirect consequences of the biological differences. Parents tend to educate girls in the “female” direction because this is the recipe that has been checked to work for millions of years. They know that in average, girls will statistically be more biologically ready to play roles that are viewed as “more typically female” roles. If there were no biological cognitive differences, the social differences would probably disappear, too.

    What I am saying is that the conjecture of many people that all the cognitive differences between the sexes are pure (social) “noise” has been ruled out. I personally find the research of the social influences – the noise – to be a much less scientific enterprise than the research of the real underlying “signal” which means biology; which does not mean that it should not be done. The research of noise will always be politicized and it will always be potentially affected by the bias of the researchers. Natural science is superior, and its insights are much more well-defined – and this holds for the gender-brain links, too.

    The reason why I say that you are anti-science is that you question the very basic thing that the properties (anatomy, physiology, cognition) of the organisms – animals and humans – are determined primarily by the long and difficult evolutionary, biological processes, instead of the influence of higher “social” factor that I generally called “intelligent design”. I understand that there are some differences between your ID and the Christian ID, but I don’t think that these differences are real physical ones. The difference is in your religion, but the actual approach to science – and the approach in which you want to humiliate serious natural science research and replace it by some “social stories” involving higher intelligence – is identical.

  6. Aaron, if you still believe that some “surgery” research has made clear that there are no differences, let me inform you that you are ignorant about very basic scientific questions of the nature of sex. On the contrary, I hope that the links to tens of articles above make it clear that there is no doubt that there are strong and easily measurable differences between the cognition of male brains and female brains that simply can’t be reduced to social bias or the mere presence of some sexual organs.

    If someone wants a surgery to change his/her sex, it’s clearly because the person believes – already before the surgery – that he/she should belong to the opposite sex. This makes it pretty easy to see that he/she will most likely be satisfied with her/his role afterwards. I doubt that someone has changed the sex of random people who did not want it. That would probably be a crime. 😉 Be sure that if that happened, the experiments predict completely unanimously that the person would probably be not satisfied with the new body and his/her thinking would not be quite compatible with it.

  7. Dear Lubos:

    Perhaps the world is fundamentally different up in the rarified air of Cambridge, and in fact, the physics dept. at your school is ruled by crazy “feminists” that hate all men and are seeking to subjugate men in their personal and professional life. I guess it’s possible.

    Where I’m at (a large public institution), things seem quite different, however. We have a rediculously high attrition (and by attrition, I generally mean people leaving with their masters, not dropping/failing out) rate amongst our female students, which, literally half the time, is caused by sexist advisors. We have several documented cases of overt sexual harassment, not to mention the general hostile environment that exists. You can cite all the studies you want, but any actual effect is just noise on top of this atmosphere.

  8. Well, Lubos, I guess we’ll just have to agree to disagree.

    I don’t share your anti-social-science chauvinism – I think that those fields are in fact scientific and that a lot can be learned from the interplay between the social and the genetic. True evolution has been acting for millennia, but we swim everday in a social sea. But I recognize that I’m not likely to convince you and I really should get some work done today.

    But for the record, equating the term “social factors” with the term “intelligent design” seems pretty non-sensical to me. I’m sure you have your reasons, but it seems more like a political broadside than a scientific argument.

    cheers,
    Tim

  9. Ummm, Lubos, I was arguing that there are intrinsic differences and that this is not particularly controversial. The surgery I was referring to (maybe it’s just gender assignment surgery?) is when children are born with ambiguous genitalia and are assigned one gender or another soon after. There is ample evidence, as I understand it, that many of these children grow up feeling that something is wrong and that they are really a different sex than they were raised.

    On the other hand, your disregard for well-established social factors (look a twin studies, for example) is completely unscientific.

  10. Hi bitter grad student,

    let me say that I believe that the situation at other schools may be really different, and I support improvements at your place if you have sexist advisors. At Harvard, we like female colleagues and appreciate them. Modestly speaking, this is not just my opinion – the same judgement can be heard about all of us, including Summers (and me), from all their colleagues. The female colleagues have enough influence and they may have too much influence. And whatever negative I said about the task forces, of course, does not apply to all women, not even most of women, not even all women in the task force itself. 😉 What is more wrong is the system. And our debate at Harvard was about the nature of sensitive scientifical questions.

    Aaron, we seem to agree. I don’t disregard social factors. They’re a well-established noise in research of actual biology, a noise that is never quite well-defined because the behavior of the people – and the social factors – can abruptly change, especially if someone is told that he or she is an experimental apparatus used by social scientists for their research. Any research of social factors is guaranteed to be short-lived because the people’s culture and habits can change very quickly. Natural science is more long-lived.

    Al lthe best
    Lubos

  11. Aaron, the material you cite in message #104 as unscientific and mere storytelling is a good-faith representation of material appearing in many of the volumes I have earlier cited. There’s nothing unscientific about it. I suggest that you challenge any particulars that you find objectionable and I will be happy to quote my sources for you. No shotgunning, please — keep it specific.

  12. To Chris: The whole thing is storytelling. It doesn’t matter where you got the material from; it is just storytelling. If you want to cite evidence, that’s fine, but that’s not what you did. In fact, the subesequent discussion with “Sleeps with Butterflies” makes me doubt that there’s going to be much evidence to be had behind this story.

    To Lubos: “I don’t disregard social factors.” You also said:

    The reason why I say that you are anti-science is that you question the very basic thing that the properties (anatomy, physiology, cognition) of the organisms – animals and humans – are determined primarily by the long and difficult evolutionary, biological processes, instead of the influence of higher “social” factor that I generally called “intelligent design”.

    It’s the ‘primarily’ there that I don’t like. Some things are primarily innate (and not necessarily adaptive), some things are primarily environmental and some things come about from the interplay of the two. It can be very difficult to place a given trait on that continuum.

  13. I have a theory! The importance of social reasoning skills means that women are in fact much better than men at mathematics, statistically and genetically speaking. After all, counting beads clearly makes more use of arithmetic than running after a woolly mammoth. The evidence for this is the remarkably rapid increase in women in the mathematical sciences in the 20th century, as barriers have slowly been broken down.

  14. This is a poem written by the Sumerian priestess, who by the way is the world’s earliest known writer:

    “The true woman who possesses exceeding wisdom,
    She employs a tablet of lapis lazuli
    She gives advice to all lands…
    She measures off the heavens,
    She places the measuring-cords on the earth.”

  15. Lubos,

    Since it has been pointed many times that no one knows whether the observed anatomical and physiological differences between male and female brains are relevant to cognitive ability, and it has not yet penetrated your thinking, it was worth repeating that single sentence.

    The original paper on Vervet monkeys is:

    Alexander, G. M., & Hines, M. (2002). Sex differences in responses to children’s toys in a non-human primate (Cercopithecus aethiops sabaeus). Evolution and Human Behavior, 23., 467-479.

    This experiment (in a non-human primate) doesn’t seem to have been repeated yet, (and not per scholar.google.com). One of your citations is to this paper itself. The reason the experiment is important is because it subtracts away any human socialization. The experiment needs to be repeated.

  16. Arun, you deny gender differences in social intelligence and disparage my comments as storytelling — is your disparagement based on the heuristic I used or the results I present? That is, would you rather not have things explained to you in their evolutionary context, but instead just want to see the numbers?

  17. Here is the experimental protocol for the Vervet monkeys.

    A total of 88 monkeys, half male, half female were tested, in groups. A group had 17-28 monkeys in a 5 x 5 x 2.5 meter enclosure or larger. 7 groups were tested.

    “For each trial, six toys were placed in the group cage, one at a time, in random order. Each toy remained in the enclosure for 5 minutes.”

    i.e., somewhere between 11 and 17 seconds of time per monkey available.
    The animals were videotaped and independent raters rated the video tapes for approach and contact with the toys.

    The six toys were a ball, a police car, a soft doll, a cooking pot, a picture book and a stuffed toy.

    We are told that that the ball and car is a masculine toy set
    the cooking pot and doll are a feminine toy set
    the book and the stuffed animal are a neutral toy set.
    The ball was orange, the pan was red.

    Since it appeared that male animals were more likely to approach and contact toys overall, percent contact scores were computed. Percent contact score equals contact time with each individual toy divided by total contact with any of the six toys multiplied by 100. 11 males and 14 females did not make any contact with the toys.

    Eyeballing the charts, roughly, the males had percent contact times of 20% with orange ball, 18% with the police car, 8% with the doll, 18% with the red pan, 8% with the picture book and 28% with the furry dog. The females had percent contact times of 10% with the orange ball, 8% with the police car, 22% with the doll, 30% with the red pan, 7% with the picture book, 25% with the furry dog. (the not adding to 100% is because of my eyeballing). The standard error is around 5 contact time %.

    For the various analyses carried out on this data, I’ll refer you to the original paper.

  18. Chris Crawford–

    Aaron Bergman’s criticism seems to be the that you can do exactly what Kea does in 113-115–that the methodology outlined above can be used to deduce the exact opposite conclusion. Science can tell you why things as they are, sure, but it also can tell you why things are not otherwise. Above, you seem to be saying “things are how they are, let’s go back and find an ‘evolutionary’ explanation for why things are the way they are.” This sort of reasoning is very frustrating to many physicists (c.f., the debate on the anthropic principle).

    And I have to say that I agree with them. If you can never be shown wrong, you can never be shown to be correct. And if the jury is going to perpetually still be out on an issue, what is the point of even talking about the issue? Particuarly when we are talking about peoples’ livelihood and careers?

  19. Dear Arun,

    I think that your strategy for the experiments is not optimal. One verifies these things much more carefully if the experiments are repeated in slightly different contexts, with different species, and so forth. Doing exactly the same thing again without any improvement is just not what a slightly ambitious neuroscientist wants to do all the time because the credit of course goes to the first people, unless they did something wrong.

    There are many other experiments that lead to the same conclusion.

    Best
    Lubos

  20. In addition to echoing bittergradstudent’s comments, I’ll say that I have absolutely no idea whether there are innate differences in social intelligence. What I do know is that it is damn hard to measure. In the meantime, rather than being ‘provocative’, I think we’d be much better off fixing the things we know are wrong.

    By ‘we’, of course, I except Lubos, who apparently believes everything is hunky-dory.

  21. Dear Lubos,

    My strategy for the experiments? Sorry, I don’t understand what you mean.
    I described what is in the Alexander and Hines paper. The reason for describing it so that people know the conditions of that particular experiment.

    To repeat the experiment doesn’t mean do exactly the same thing. It means to do another experiment and another to see if the vervet monkey gender preference for toys found by Alexander and Hines is repeatable. It means trying it with orangutans and chimpanzees and bonobos.

    I’ll just point out some things I found a little unsettling. One is the short time per monkey the toy was available. It would seem that it passed from hand to hand rather quickly. The second is, e.g., if a monkey actually threw the ball, it would have a smaller contact time with the ball. Third, doesn’t preference require a choice? There was no choice presented in having one toy at a time.

    Anyway, Alexander and Hines are the scientists, I’m the armchair quarterback. But I do want to see more experiments. I don’t see any citations in the Alexander & Hines paper of anything similar. Nor does scholar.google.com show any more recent experiments that cite the A&H paper.

    Anyhow, in line with the way the rhetoric on these blogs go, I should be saying, see, isn’t it obvious, those 210 minutes of with vervet monkeys with toys prove beyond a doubt that the reason there aren’t more women physicists is because of biological differences.

    -Arun

  22. Aaron, I can clear up one point for you quite easily. You write:

    “I’ll say that I have absolutely no idea whether there are innate differences in social intelligence.”

    There’s not much controversy here. Here’s a quote that took me all of five minutes to find:

    “More specifically, the Bar-On model reveals that women are more aware of emotions, demonstrate more empathy, relate better interpersonally and are more socially responsible than men. On the other hand, men appear to have better self-regard, are more self-reliant, cope better with stress, are more flexible, solve problems better, and are more optimistic than women. Similar gender patterns have been observed in almost every other population sample that has been examined with the EQ-i. Men’s deficiencies in interpersonal skills, when compared with women, could explain why psychopathy is diagnosed much more frequently in men than in women; and significantly lower stress tolerance amongst women may explain why women suffer more from anxiety-related disturbances than men (American Psychiatric Association, 1994).”

    Source: http://www.eiconsortium.org/research/baron_model_of_emotional_social_intelligence.htm

    So let’s not kid ourselves about the *existence* of such differences — they’re quite real, and the fact that they are cross-cultural eliminates the hypothesis that they are cultural in origin. My concern was to provide you with some understanding of how this came to be, but since your only concern is the actual result, here it is: women have better social intelligence than men. Period.

    But there’s a larger issue and much more difficult issue that I’d like to delve into. I’ll begin by telling a story. I was raised, as you were, as a physicist, and I once thought as you did. I can still do that kind of thinking, but back then I thought that it was the ONLY way to think, that everything else was self-indulgent intuitive nonsense. But then, many years ago, I struck up a friendship with a crazy Frenchwoman named Vero. She and I were utter opposities: I was all rationalism and logic, where she was all intuition. She loved astrology, aromatherapy and all the other superstitions that we dismiss.

    But I was at a stage in my life where I was willing to look more closely at alternative thinking styles, and she was interested in my rigorous style. We’d go on long walks, talking about differences of opinion. We never argued; for some reason, we treated each other with respect even though we each felt the other stark raving mad.

    One day we were discussing reincarnation. I, obviously enough, considered it wishful thinking, where she believed firmly in it. I decided I would walk Vero down the primrose path to logical obliteration, and so I initiated a Socratic dialogue, asking one question after another, building my case. My plan was quite clever, involving dozens of logical steps before reaching its inevitable conclusion. Moreover, Vero has no talent for logical thinking, so I knew that she would never see it coming until it was too late. I spent nearly two hours laying the perfect trap, steadily removing every possible exit path until I was ready to snap the trap closed. There was, however, one small weakness in my logic: a small assumption that, while reasonable, was not actually provable. Moreover, the nature of this chink in the argument was so subtle that I was sure that Vero would never notice it. I made the point rather hastily and hurried on to the next step. About fifteen minutes later, I triumphantly sprung the trap door and turned to Vero, expecting her face to turn ashen.

    She smiled right back at me and said, “Yes, but there’s one problem” and then proceeded to put her finger on precisely the weakest point in my chain of logic. I was flabbergasted — this lady couldn’t logic her way out of a paper bag, and yet she saw right through my weakest spot. I asked her how she had figured that out. “It just came to me” was her only answer.

    From that day forward, I have recognized that there are other ways of thinking that can be every bit as effective as the standard Aristotelian logic that we live and breathe. I don’t really understand them, but I no longer dismiss them as inferior.

    Now I would like to turn to the problem of how scientists come to accept scientific theories. You can disprove any hypothesis, but you can never prove one. There’s always the possibility of some unanticipated factor that would later disprove the hypothesis. So how is it that scientists come to accept theories? For example, what led physicists to accept special relativity? Sure, it made predictions that were later borne out by experiment — but even a demonstrably false hypothesis can do that. We like to point out that it is falsifiable and that none of its predictions have been disproven, but that doesn’t constitute proof — it establishes only that the hypothesis has not yet been disproven.

    So, why do physicists accept special relativity when it has never been proven? Well, we like to think that there have been “enough” tests that it has passed. People have shot at it for a century and every bullet has bounced off, so it MUST be correct, right? But that’s not Aristotelian logic. Nothing has been rigorously proven. We believe it because, well, we just kinda have this good feeling about it.

    This is not sequential reasoning, this is pattern-based reasoning. There is no set of calculations in the universe that can prove that special relativity is correct. But we believe because we don’t rely on proof, we rely on pattern-based reasoning. We look at the overall pattern of experiments, Michelson-Morely and Cerenkov radiation and magnetism and Hiroshima, and when we put the whole pattern together, each of us says, “good enough for me”, and we accept it.

    And then physicists turn around and dismiss evolutionary psychologists for doing exactly the same thing. The reason, of course, is that physicists don’t know the vast array of facts that evolutionary psychologists bring to bear on their problems. Kea in message #113 offers some absurd poppycock that in no way comports with the huge mesh of facts that have been developed, and proclaims her results to be just as valid as the efforts of people who have absorbed volumes of information.

    I believe that the best term to describe this behavior is “sophomorism”.

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