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Sorry, but population groups are real

Back in 2015, the NIH started a longitudinal research program called All of Us with the goal of collecting genome data from a million Americans of every possible ancestry. The goal was to improve health care by figuring out how best to treat diseases in people of different backgrounds.

The program is up to 413,000 genomes and recently announced its fifth data release. Nature published a package of articles about it, including an introductory piece focused mostly on comparing All of Us with already known disease analysis. For example, the genomic markers of LDL-C cholesterol are well established, and All of Us replicated those results with very high accuracy.

So where am I going with this? It turns out that genomic analysis is typically carried out in a very high number of dimensions, and this data needs to be reduced to two dimensions to make visual sense to us limited humans. There are lots of ways of doing this, just like there are lots of ways of projecting a 3D globe onto a 2D map (the Mercator projection is one of many).

The method that's lately become a favorite in the genomic community is called UMAP, and the Nature paper included this 2D UMAP reduction of population groups constructed from its database:

On the left are the UMAP reductions, which show genetically related population groups. The colors are from self-reported race and ethnicity. This mapping, according to the authors, agrees quite well with the genetic ancestry estimates of the Human Genome Diversity Project (on the right).

Fine, but where am I going with this? Well, it turns out that a bunch of geneticists are concerned about the UMAP illustration. Why? Because UMAP is designed to be good at keeping related neighborhoods together after the 2D reduction, and this means it did a good job of showing ethnic and racial neighborhoods from the original high-dimensional data. In other words, to make a long story short, it made genetically similar population groups visible even to laymen:

The figure has reignited a long-standing debate among geneticists about how best to discuss and depict race, ethnicity and genomic ancestry, given how these terms can be misinterpreted and weaponized by extremists.

“The problem is, a lot of people will see figures like this as supporting a viewpoint” that race and ethnicity are closely aligned with genetics, says Ewan Birney, deputy director-general of the European Molecular Biology Laboratory in Cambridgeshire, UK. “And then they build castles in the air from all this.”

....To a layperson, the chart shows several distinct colourful blobs that could be misinterpreted as supporting genetic essentialism — the pseudoscientific belief that racial or ethnic groups are distinct genetic categories, and that individuals of the same group are genetically similar, Birney says.

We are in for a world of hurt if we don't get over stuff like this. Genome mapping is coming at us like a freight train, and it says what it says. We don't know what that will be yet, but we do know a few things. One of them is that there really are genetically identifiable population groups that correspond closely to common notions of race. This should hardly be a surprise since these common notions are mostly based on geography (Europe, Asia, Africa, South America, and others).

The genetic markers we're talking about are relatively minor: the difference between population groups can be measured in thousandths of a percent of the whole human genome. The vast majority of our genomes are identical no matter what our background.

Still, the differences exist, and we don't yet know what all of them are. And while we may or may not like everything we eventually discover, arguing over the minutiae of different mapping algorithms will get us nowhere. We can't allow ourselves to be hamstrung by a few creepy race extremist who are going to believe what they believe regardless. Just do the science and let the chips fall where they may.

59 thoughts on “Sorry, but population groups are real

  1. shadow

    How can you square this stance with the fact that White at one point didn't include the Irish and to many still doesn't include the Jewish? Or that Asian American was a political label invented within the last century so disparate immigrant could organize together. Or that my biracial children will undoubtedly resist being labeled Black or White.

    Race is a fully invented concept to justify whatever the current political power dynamics are, and it is you who attempting to push it on the science.

        1. dausuul

          The chart is showing the relationship of people's self-reported race and ethnicity (black, white, Hispanic, etc.) to their genetic makeup.

          Each person is a point on the chart. That point's location is based on your genetic makeup; people with similar DNA are positioned closer together. The color of that point is your self-reported race (top left) or self-reported ethnicity (bottom left).

          What the chart shows is that there is a strong relationship here. Looking at the top-left chart, for example, you can see that almost all of the folks who identify as white are genetically closer together, in the big orange blob. Those who identify as Asian are the two red blobs on the right. Those who identify as black or African-American are in the blue swath on the lower left. Et cetera.

          All of this is totally unsurprising, or should be. "Race" is a vague, fuzzy way of putting people into buckets on the basis of some mix of appearance and ancestry. Both of those are closely linked to genetics, so of course you're going to see more genetic similarity between people in the same bucket than people in different buckets.

          This does not mean that every single person's genetics will match their self-identified race; you can see plenty of outliers sprinkled around the chart. And it also doesn't mean the set of buckets we've chosen is somehow the "right" set of buckets. We could group people in any number of ways that would produce a similar result.

    1. tango

      Nonsense. Of course there are a lot of social constructs that go into what people consider race.

      But the average observer sees genetically caused obvious physical differences between people whose ancestors came from Africa vs Western Eurasia vs Eastern Eurasia etc. and call these differences racial differences. And they are correct, they obviously exist. Now, of course we have more in common with each other than not and these genetic differences should not be the basis of oppressing others. But they are there.

      Geneticists and others who try to argue that there is no such thing as race are denying the obvious and risk discrediting themselves and science in general.

      (Yes I know that there are lots of gray areas and blends (like my mixed-race children) but it is a generalization and exceptions to generalizations do not disprove them because they are, well, generalizations.)

      1. shadow

        "But the average observer sees genetically caused obvious physical differences between people whose ancestors came from Africa vs Western Eurasia vs Eastern Eurasia etc. and call these differences racial differences. "

        White Americans are generally worse at telling apart the facial features of Asia/Pacific Islands descendants compared to Asian Americans, so even our ability to spot these "meaningful" differences isn't objective and likely stems from what we spend time around growing up. Goodness knows people in the Eastern part of the world wouldn't think of lumping themselves together as Asian when doing genetic research.

        Obviously there are strong genetic similarities between various people of related ethnicities, but that is not what race is and has never been historically been used for. It is foolish is try to apply it to genetics, especially with the damage race-based thinking has done to science in the past.

        1. MF

          Leaving aside the idiocy of talking about the "eastern part of the world" I can promise you without even looking at the names on the papers that lead to this study that many of the scientists involved were Asian.

          In addition, Asians also talk about Asia and Asians. The Japanese had their Coprosperity Sphere and Asia for Asians (with, of course, China at the fore) and complaints that Australians are not Asian enough are recurring themes in PRC propaganda.

          1. shadow

            Yeah, obviously Eastern / Western are social constructs as well, but there is a whole lot of different racism going on in China, Japan, India, and so forth and they very much do not consider themselves as one people in a genetic sense. But of course they can choose to use geographic label of Asian countries when it serves a purpose: just because it's an arbitrary grouping doesn't mean it doesn't have a use.

            1. MF

              One people?

              Do whites consider themselves one people?

              Do blacks? Certainly African blacks do not.

              What is this supposed to be evidence of?

              1. shadow

                That the racial labels employed in America (and this study) are based on the social history of America and would likely not be the same in Asian countries. So stop trying to apply them to "hard" sciences like genetics.

                1. MF

                  I have lived in China and speak Chinese. The racial labels used there are the same as in the US.

                  For example they call blacks 黑人 - black people - and are brutally honest about expressing their racial prejudices against them.

    2. cld

      That's a rhetorical cliche of a dead century, when people could write about 'the race of women' or ' the race of cats'.

      It meant nothing more than type or kind.

    3. Joseph Harbin

      It is one thing to say that regardless of people's genetic makeup, we should all be treated equally. It is another to say that all people have the same genetic makeup. We don't. Some of it's trivial. Height, eye color, hair color, etc. Some of it's trivial but treated by some people as important, like skin color. Sure, social constructs can be confining and unfair, or the opposite, and the groups to which we are related can mix over generations, but that doesn't negate the fact each of us has a distinct genetic makeup with certain predispositions.

      As a person of Irish heritage, I know my parents and their parents were excluded from the WASP hierarchy when they were growing up a hundred years ago. It wasn't genetics that did that. But my pale white skin (and growing up before sunblocks were routine) explains why I just finished a monthlong Fluorouracil treatment for my face. It wasn't a social construct that made me need it.

      1. shadow

        Of course not, nor did I say it was! But _White_ is not about your genetics, it is about how society has placed you in the power dynamics. If we want to discuss groups of people, why not use European/African or Germanic/Chinese/Arabian? At least those labels point to the geographic histories we pretend race does.

        1. Joseph Harbin

          The chart above from Nature uses geographic identifiers for ancestry, with White the exception. Call them European if you want. Doesn't matter to me. I'll call people whatever they like to be called.

          Fwiw, I grew up thinking of myself as Irish Catholic or Irish American. Of course, I knew I was white. But that was a description, like saying I am medium-height, not a way to define myself. I grew up thinking I was Irish because that's the community my parents were part of. I resist this larger definition of "white" because it's meaningless to me. And it's how people like Trump want us to think.

          That said, we shouldn't deny we have distinct genetic traits and communities we are related to.

          1. shadow

            "That said, we shouldn't deny we have distinct genetic traits and communities we are related to."

            Obviously. No one is saying that. But this:

            "Call them European if you want. Doesn't matter to me. "

            It very much matters to others, and largely for not beneficial reasons. Because race isn't about ancestry, though it has strong correlation with it, and groups can fall out of the White bucket, Black bucket, Foreigner bucket, etc. as political dynamics shift.

            I recognize we're talking about differing takes on words here, but that's what Kevin and others here are missing about why this argument is happening. As elegantly said below "Ancestry is a thing. Race isn't." Talk about genetics, ancestry, the relationship between geography and our shared features. But don't use the language of race, which are made-up buckets long tainted with attempts to create divisions or hierarchies.

            1. Joseph Harbin

              “It very much matters to others…”

              I think we should use language that is accurate, informative, and respectful. But whatever words we choose, there will be others who will twist how we talk about people for their own purposes. Negro, Black, African American. Language evolves. Racism persists.

              We need to change how people think, and believing there is no such thing as race doesn’t solve the problem.

              Certainly in some contexts race is a useful concept. Anwar Sadat and Nelson Mandela were both Africans, but the term “African”
              Is helpful only to a degree. Likewise, Mandela and Charlize Theron, both South Africans.

              One problem with using geographic identifiers (Asian, African, European, e.g.) instead of racial terms for racial groups is that that causes problems too. In certain contexts, we still need words to refer to black Europeans or white Asians. Speaking of race is a bad thing only if you make it so. Adults shouldn’t let the racists dictate what we can and can’t say, lest they misuse language and ideas for ill purposes.

              1. shadow

                Absolutely agree! As a soft rule, I think race is a useful lens in social sciences. It is beneficial to have people thinking about race when discussing how society functions and the history that drives our current reality. But genetics is (at least to my knowledge) much closer to a hard science and one that should largely be expressed in non-racial terms, trying as much as possible to avoid giving ammunition to racist mindsets.

    4. MF

      The idea that "white" once did not include Irish is a myth. One simple example: anti miscegenation laws were never applied to marriages between Irish and other whites. A better claim is that the Irish were seen as inferior whites. https://en.m.wikipedia.org/wiki/Definitions_of_whiteness_in_the_United_States#:~:text=Yang%20and%20Kavitha%20Koshy%20have,that%20limited%20citizenship%20to%20%22free

      I wonder what person you think would not count me as white? I am a European Jew and obviously white. Now, there are many Middle Eastern Jews who look obviously Asiatic like Pakistanis, Iranians, and many Arabs. The racial (and skin color diversity) of both Arabs and Jews is due to mixed ancestry.

      My ancestors spent over a thousand years living in a place where "rape the Jewish women" was how you relaxed after a long pogrom. I have always assumed that half or more of my ancestry is non-jewish European. Natural selection would also have selected for whiter skin as it does for all people who live in regions with less Sun.

      For Arabs (and also Turks) the reason is the opposite. They imported European women (mostly) as slaves and interbred with them. Walking around Istanbul or Dubai I see Turks and Arabs that look totally European, totally west Asian, and every shade between.

      As for your biracial children (and mine) the existence of grey is hardly an argument that black and white do not exist.

      1. shadow

        "The idea that "white" once did not include Irish is a myth. "

        Would you prefer Finns: https://en.wikipedia.org/wiki/Definitions_of_whiteness_in_the_United_States#Finnish_Americans. As noted thoroughout that article, Whiteness/race is complicated and there is debate about. But groups (or individuals) often have their Whiteness (and thus privilege) questioned and can be excluded.

        "I wonder what person you think would not count me as white?"

        Nazis mostly.

        "As for your biracial children (and mine) the existence of grey is hardly an argument that black and white do not exist."

        I mean we can get into color theory some other time, it seems this crowd would be better off reading about race essentialism.

        1. MF

          Look again at your own sources.

          There has been a clear and consistent consensus on who is white throughout American history with disagreement on edge cases such as Arabs and mixed race people.

          (For what it is worth, I live in Dubai and see a lot of Arabs. It is a mix. Some look white, some look Asian. Genetic heritage in this part of the world is mixed, so unsurprising.)

  2. drfood4

    I'm afraid it is no longer possible to "just do the science and let the chips fall where they may." People are tribal, and currently the tribes are based on semi-religious beliefs, not genetics. Is this better? I don't know!

    1. Jim Carey

      Is having a hammer better than not having a hammer? Depends on whether you're building something of value with it or hitting someone over the head.

  3. Jim Carey

    If genetic diversity in the average troupe of baboons is a mile, then genetic diversity in humanity as a whole is and inch.

    1. MF

      Do you have documentation for this claim?

      I would expect pedigree collapse in baboons to be more severe than in modern humans and we have more long term geographically isolated populations.

  4. Boronx

    There's no question race is determined by genetics. The danger here is that people will assume that race is a good proxy for genetics, something that probably isn't true and you can determine from a 2D projection.

  5. Doctor Jay

    The thing is that these groupings of ancestry are quite real, but nobody, but nobody is purely from one of those groups. This is all very squishy with vague borders, and the extremists want it all clear-cut with the sheep separated from the goats.

    I think it's incumbent on people write about stuff like this and who are liberal to try to come up with a way of talking about it rather than (ahem) ranting about how people need to get over .

    Ancestry is a thing. Race isn't. Discuss.

    (While we are at it, we can talk about how IQ tests and things like the SAT do pretty well at comparing people who are from similar backgrounds, but not so great on comparing people from very different backgrounds.)

    1. Special Newb

      My son is mixed race and aside from his name can easily pass as "white" .... but his genetic ancestry has about 60% europe (mom is basically an American of viking descent) and about 40% from meso-american ancestors. In a future where we tailor treatments to genetics, white is not a useful category for treatment but a more complicated genetic ancestry is.

      And this applies even among different groups from Europe.

    2. MF

      𝘞𝘩𝘪𝘭𝘦 𝘸𝘦 𝘢𝘳𝘦 𝘢𝘵 𝘪𝘵, 𝘸𝘦 𝘤𝘢𝘯 𝘵𝘢𝘭𝘬 𝘢𝘣𝘰𝘶𝘵 𝘩𝘰𝘸 𝘐𝘘 𝘵𝘦𝘴𝘵𝘴 𝘢𝘯𝘥 𝘵𝘩𝘪𝘯𝘨𝘴 𝘭𝘪𝘬𝘦 𝘵𝘩𝘦 𝘚𝘈𝘛 𝘥𝘰 𝘱𝘳𝘦𝘵𝘵𝘺 𝘸𝘦𝘭𝘭 𝘢𝘵 𝘤𝘰𝘮𝘱𝘢𝘳𝘪𝘯𝘨 𝘱𝘦𝘰𝘱𝘭𝘦 𝘸𝘩𝘰 𝘢𝘳𝘦 𝘧𝘳𝘰𝘮 𝘴𝘪𝘮𝘪𝘭𝘢𝘳 𝘣𝘢𝘤𝘬𝘨𝘳𝘰𝘶𝘯𝘥𝘴, 𝘣𝘶𝘵 𝘯𝘰𝘵 𝘴𝘰 𝘨𝘳𝘦𝘢𝘵 𝘰𝘯 𝘤𝘰𝘮𝘱𝘢𝘳𝘪𝘯𝘨 𝘱𝘦𝘰𝘱𝘭𝘦 𝘧𝘳𝘰𝘮 𝘷𝘦𝘳𝘺 𝘥𝘪𝘧𝘧𝘦𝘳𝘦𝘯𝘵 𝘣𝘢𝘤𝘬𝘨𝘳𝘰𝘶𝘯𝘥𝘴

      What do you mean by this?

      Tautologically IQ tests and the SAT do perfectly at comparing how well people do on IQ tests and the SAT whatever their background.

      Presumably you mean comparing something else, most likely the more abstract "g" - general intelligence.

      If so, what is your evidence? How are you measuring actual g in diverse populations, comparing with scores on IQ tests and SATs, and concluding that those scores are not great at comparing people from different backgrounds. Then, even more fundamentally, what is your justification for considering your measure of g superior to that of IQ tests in particular?

      1. Doctor Jay

        There is a ton of evidence of this. I started hearing about it in the 70's. It's related to, but not the same as the Flynn Effect.

        But here's one argument: IQ has a positive, though not large, effect on pretty much every social metric. Income, number of sex partners, number of friends, etc.

        Black Americans do worse on standardized IQ tests than white Americans. I don't recall the exact number, but lets say the averages are different by as much as 10 points.

        HOWEVER, Black Americans outperform their measured IQ in all the social metrics mentioned above. They do better than white people with the same measured IQ, and at a rate consistent with them having IQs about 10 points higher.

        So, something is wrong with this picture, right? Let's remember that IQ measures behavior, not a fundamental physical thing. Behavior is a learned thing. Measuring intelligence with an IQ test is a bit like measuring someone's height by having them stand by a wall and leap an touch as high up on the wall as they can. The result has something to do with height, but isn't height.

          1. Doctor Jay

            The burden of proof is not on me. It is on you.

            You are the one that appears to be making a claim that group A is inherently inferior in some aspect to group B.

            Prove it. IQ tests don't do the job by themselves. Consider the Flynn effect: IQ scores are rising over the last century. How could this be the result of genetics alone?

            So go ahead. Prove it.

            1. MF

              You made a specific factual claim.

              "HOWEVER, Black Americans outperform their measured IQ in all the social metrics mentioned above. They do better than white people with the same measured IQ, and at a rate consistent with them having IQs about 10 points higher."

              It is your obligation to back it up. You won't because you can't. You can't because you made it up.

              BTW I would expect some over performance due to affirmative action. For example, blacks can get into Harvard with lower SAT scores (closely correlated with IQ) than whites or Asians. Assuming a Harvard education actually has more value than that at a lower ranked university, we therefore expect those blacks to do better in life than whites and Asians with similar scores who do not get into Harvard.

              I do not believe the difference is remotely as large as you claim.

    3. Anandakos

      Your addendum makes an interesting point, though it's ultimately a futile one. If standardized tests have a cultural component embedded in them, and the point of the tests is to choose "the best and brightest WITHIN A CULTURE" then isn't the cultural component part of the goal?

  6. cephalopod

    For much of human history, moving long distances was very hard for humans. Only a small percentage of us actually managed it, and many of those moves were done as whole population groups. Most of our ancestry is fairly inbred - marrying 2nd, 3rd, 4th cousins.

    The result is a fair amount of consistency within geographic boundaries. It shouldn't be surprising at all.

    I would love to know how far back I have to go to share a common ancestor with random people. I think there's a very good chance it's only about 400 years with my spouse. Some people it may be a few thousand years.

    1. bouncing_b

      “I have read” (fwiw) that with few exceptions everyone everywhere is no more than about a 50th cousin of everyone else. Say 1000 years. (The exceptions are mainly Australian aborigines who have been largely isolated for roughly 50k years, and a few similar groups).

      That by no means implies that we all mixed 1000 years ago. For the most part we mixed within populations that had relatively little contact with outsiders for long periods.

      But if, say, Genghis Khan’s troops (with well-mixed ancestry within their population) raped European women, their children would then mix those genes with other Europeans, and over hundreds of years they would be fully spread. Then most Europeans would carry those genes and be distant cousins of all Mongolians (and vice versa) along with other populations (Chinese) where the troops or their cousins traveled. Only a tiny number of people needed to actually travel for this to be the case.

      My reading is shallow. Perhaps someone can shed further light. Meanwhile, nice to meet you, cuz.

  7. golack

    Now we need to do this for people from their places of origin (using that term very loosely). The waves of immigrants that settled in the US do not represent a representative cross section of the home countries. It would be interesting to see how that fills out those plots. And maybe break things down some more, e.g. Norse, Anglo, Saxon, Celt, Rus, etc.

    1. tango

      Good point @golack. We do not just get random chunks of a foreign population. This is most vivid to me when I see the many Indian and Chinese immigrants in my areas Such immigrants are highly selected for academic achievement due to US immigration laws and since intelligence is significantly heritable, Indian and Chinese Americans can arguably be considered among the smartest groups of people in the USA, arguably even the world. And if I understand what is happening in Canada, this might even MORE be the case up there.

      1. MF

        Also true for other groups. Nigerian Americans are one of the highest income immigrant groups and can be scathing when talking about African Americans.

  8. ProgressOne

    In biology, you have species. A giraffe is one species and a lion is another. Humans are all of one species. Next you have sub-species. A Bengal tiger and a Siberian tiger are both sub-species. There are no human sub-species. And finally you have this fuzzy area where animal groups differ some but not enough to be called a sub-species. This is where the word ‘race’ comes in to use in biology. It is a word used inexactly and loosely, but it captures these physical differences. And it works for humans too. Humans with ancestral roots in Kenya look different than those with ancestral roots in Korea.

    Before modern times, people stayed in the same areas for many generations, and physical differences emerged among human population groups. Since race is loosely defined, today you can define 5 human races, or 100 humans races, depending on how small you divide up geographical regions to follow genetic similarities among various population groups.

    The US government uses just 5 racial groups, which is very small, but it serves to measure certain useful characteristics of these groups, such as for tracking social inequalities.

    However, with on-going genetic research, huge concerns have arisen with acknowledging that human population groups vary at all. Thus, there has been a major push to declare that human races do not exist at all, and that human races are actually 100% a ‘social construct’. If you are an academic studying genetic differences among different population groups, you better declare that races are purely a social construct, or you may quickly end up in hot water.

    But why is there such intense concern about the idea of the existence of human races based on biology? Here is why:

    People with ancestral roots from different parts of the world have different measured average IQs. It is not understood why this is, but certainly it is in part due to the environments and cultures that different population groups live in. With ongoing research in genetics, there are huge concerns that some scientists may at some point say that genetic factors partly explain these IQ differences. If this occurred, the sky falls, or something, and therefore it must be adamantly declared that races are 100% socially constructed. Thus, it’s a pre-emptive strike to assure that no scientist ever tries to claim that human races differ in measured IQs partly due to biology. This is an odd way to try to win an argument.

    1. Special Newb

      If this occurs there will be a genetic basis for declaring certain groups inferior. It's not hard to see why the left doesn't like this

      1. MF

        Not inferior. Just lower IQ median. This is no more evidence of inferioriority than is racial differences in height, melanin, etc.

        BTW we may find this more complicated than a simple racial split. For example, there are European and African subgroups that are clearly taller than the average human (Dutch and Masaai) and shorter (Spaniards and Bushmen).

      2. ProgressOne

        There are a lot more human qualities than just IQ when judging the worth of human beings. The world has had many monsters with above average IQs.

        Also, whites have lower average measured IQs that East Asians (Koreans, Japanese, Chinese), but I have not heard declarations about white inferiority. Ashkenazi Jews have an even higher average IQ at 112-115.

        Still, I understand the concerns about haters targeting groups like Africans to say they are inferior. But I also think you can't crush the ongoing research. It goes where it goes, and we have to deal with it.

    2. tango

      Not trying to troll here. But we all assume and PROBABLY correctly that all groups of humans are comparable in innate intelligence. And social harmony kind of needs us to.

      But best as I can tell (and I have not done an exhaustive literature review here or anything), we do not have a really good way of measuring innate intelligence and thus do not KNOW for sure. It would be interesting to see if further research down the road DOES at some point identify some innate intellectual difference among folks of different genetic backgrounds.

      In which case I hope any discoveries are completely subversive, like Aboriginal Australians in fact were on average slightly more intelligent than any other group on earth.

      1. MF

        That would seem unlikely.

        To the extent that we find ethnic genetic differences in intelligence I expect to see higher intelligence in groups with longer histories of using money, financial concepts like interest, and trading and writing. Those are the groups that works have had the strongest selective pressure for intelligence.

      1. bharshaw

        I think what strikes me is hey don't try to label "races" as the U.S. does; it's strictly ethnic groups but such fine divisions. In other words, they're "splitters", we're "lumpers". I blame it on having been and still being class-ridden.

        It's like accents, Apparently the Brits can distinguish a Manchester accent from a Liverpool accent. That's 30 miles!!

  9. D_Ohrk_E1

    Am I the only person who thinks it's unfortunate that multidimensional data is presented in two dimensions? When are we going to get interactive spatial charts?

    1. Yehouda

      It is worse than unfortunate. In many cases it is very misleading.

      Using it as a guide for further experimentation is OK, but to actually reach conclusions from two-deimensional representation is quite dangerous.

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