Super-Gaels

You can characterize a group by its gene frequencies – which can be thought of as a point in a very high-dimensional space. Another group is a different point, and the between-group difference is a vector in that space. Ignoring linkage, assuming no substructure, etc.

There’s a vector of this sort that describes the genetic differences between the Irish and Germans, or for that matter between the Irish and the average of the human race.

For Sardinians, that point is unusually distant from other Europeans, since they’re almost-pure examples of Europe’s first farmers. The Iceman genome is like that of a Sardinan, but even more so: more like Sardinia before Sardinian soaked up some genes from the mainland. More Sardinian than the Sardinians: the vector in that high-dimensional space between the Iceman and modern Italians is like the vector between Sardinians and the mainland, in the same direction, but with a greater magnitude. You would expect that the Iceman’s phenotype differed from mainland Italians in the same way that Sardinians do, only more so. Modern admixtures have produced many examples of this: mestizos differ from Spaniards in gene frequencies and traits: Amerindians (from central America, say) differ in the same general way, only more so.

With modern genetic technology, we could make these vectors even longer, while still pointing in the same direction – longer than they are in any existing population, longer than they ever were in any population that has ever existed.

So.. we could make synthetic Irishmen that were far more Irish than anyone in the emerald Isle – so Irish that they were barely human. It has been said that the Irish excel in all the qualities that make a man interesting rather than successful – compared to our new and improved product, today’s Irish would seem a nation of shopkeepers.

“The great Gaels of Ireland are the men that God made mad,
For all their wars are merry, and all their songs are sad.”

Now square that.

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92 Responses to Super-Gaels

  1. CRISPR (and equivalents) to extend the vector, so as to achieve the Platonic pure forms of the tribes of mankind.

  2. Aidan Kehoe says:

    More Brendan Behans than the world will know what to do with!

    Now, you might counter that with the point that one Brendan Behan was more than the world knew what to do with, and you would be correct. For the sake of the world and of the many people likely to be killed by their explosives, I cannot offer my support to this idea.

  3. MawBTS says:

    I’ve always been interested in people who seem like SNL parodies of their race or nation.

    Eliezer Shlomo Yudkowsky has a comically Jewish name and a comically Jewish face. He’s an atheist, but that’s a Jewish stereotype too. On the female side, you have Shula Firestone, who’s full name is Shulamith Bath Shmuel Ben Ari Feuerstein and who Wikipedia describes as “a central figure in the early development of radical feminism”. By some miracle she contrived to be born in Canada instead of the first synagogue from Ellis Island.

  4. ckp says:

    Even more fun is that “super-Irish” isn’t uniquely defined, so you could make one group of super-Irish be relative to the general human average, another relative to Europeans, yet another to the English …

  5. Garr says:

    The dopey majority of any group is as boring as the dopey majority of any other group, although certainly some dopey majorities are less dangerous than others. The brightest Irishmen don’t seem to be more interesting than the brightest Englishmen, Russians, etc., either. So maybe it’s the second-brightest chunk that’s especially interesting?

    • spottedtoad says:

      Well, maybe the brightest Irishmen have their vector pointing at “smart” rather than at “interesting…”

      • Garr says:

        I’m just thinking that WB Yeats, Laurence Sterne, and Dostoevsky are equally interesting.

        • Anonymous says:

          The way I heard it, none of the three were genetically Irish, though two were born in Ireland

          • Garr says:

            Oh … I was offering Sterne as an example of a really interesting Englishman. He’s interesting in a very English-seeming way, the way he zooms down into weird details. And I thought maybe Yeats’ dreamy other-worldly prophetic quality is typically interesting-Irish. Anyway, it occurred to me last night that maybe the idea that the Irish in general are especially interesting comes from Englishmen venturing into Irish bars for a taste of local color. I remember that when I first started going to a sort of scuzzy-bohemian bar in my hometown twenty-five years ago everyone in it seemed interesting but then I quickly realized that all the regulars were just locked into their own very narrow grooves, the same thing every night, and that the whole place was really just a day-care center for grownups.

  6. RCB says:

    So let me puzzle through this. If we define Irish as the group that is centered around the point in allele space, then we couldn’t make them more Irish: changing the allele frequencies would move them away from that point, i.e. less Irish. If you instead define Irish-ness not by the group’s center in allele space, but by the group’s vector difference from the global mean (or European mean, whatever), then that could be lengthened, so more Irish.

    In terms of maximizing the difference, I see this in two possible ways, geometrically: (1) You push out the population along the vector, without changing the direction of the vector. Eventually you hit fixation for an allele at one locus (i.e. it hits 0 or 1), which means you can no longer lengthen that vector; stop there. (2) You find the new point that maximizes the dot product between the new vector and the original difference vector. I believe this is equivalent to pushing to fixation any alleles which are more common in the Irish than in the rest of the world, and the opposite for their rare alleles. The direction of the new vector will have changed.

    Taking option (2), that would mean, e.g., pushing Tay-Sachs to frequency 1 among Ashkenazis. In fact probably every group has a very deleterious allele for which they have higher frequency than the global mean. So we’d all end up in bad shape.

    • gcochran9 says:

      That’s if you maximize the vector length. I’m talking about increasing it – just to the point of lunacy, not death.

      • RCB says:

        Fair enough. Of course even very small changes across many loci will have noticeable effects. My former colleagues evidently don’t know this, hence small average Fst must imply no phenotypic divergence across groups…

        • gcochran9 says:

          Why don’t they know it? It’s ag science, not string theory: still too hard for them?

          • RCB says:

            I’m sure many of the more quantitative anthropologists do know it in the abstract, or would at least quickly grasp it if you explained it to them. But I know for certain that many still teach the classic 15% Lewontin result to intro anthro students – which is fine, except that the point of teaching it is basically to argue that race has no biological reality, etc.

          • A Erickson Cornish says:

            A few hours ago I attended a seminar by a professor up for tenure (in a bio dept.) on his work in evolutionary genetics. He had to spend around 2/3 of it explaining and re-explaining basic quantitative genetics, and the questions afterward- from biologists on the faculty at a top ten American university- were just pathetically stupid. Almost all of them were either a variant of “But what about epistasis?” or else a variant of “are the alleles found in GWAS studies actually causal for the trait in question?” I can only hope these people do not get to vote in this poor man’s tenure decision.

    • Grels says:

      There already might be a group that is further along the Irish vector, in the sense that they’re more distant from everyone else than the Irish are, while Irish remain closest to them.

      • gcochran9 says:

        That doesn’t mean they’re further along the same vector.

        • Grels says:

          If they aren’t, then there should be a population that is closer or equally close to them than to Irish along that vector. But is there?

      • Paul Conroy says:

        I’ve speculated decades ago that Irish Travellers (aka Tinkers) could be of Hiberno-Norse descent, as the Vikings were essentially itinerant traders, like the Tinkers. I made this guess based on phenotype, as to me they are usually blonder and have sallower skin than Native Irish in general.
        I read a paper over 10 years ago, that the county population they were nearest to is Leitrim, and of course Upper and Lower Lough Erne were places of extensive Viking settlement.

    • Jim says:

      For (2) yes, if there are n frequencies x1,..,xn, so 0<=xi<=1, and if v=(v1,..,vn) is the Irish Vector and w=(w1,…,wn) is the reference vector then one is trying to maximize (v-w).x where x ranges over the n-cube In in Rn defined by 0<=xi<=1. Let y be define by yi=1 if vi>wi, yi=0 if vi<wi and yi arbitrary between 0 and 1 if vi=wi. Then clearly any such y maximizes (v-w).x for x ranging over In.

      For (1) you take the last point on the ray w + lambda (v-w), lambda >= 0 which lies in In.
      Of course method (2) always produces a point at greater distance from the reference point except for very special cases where the ray with starting point w and direction v-w
      contains a vertex of In.

  7. Jerome says:

    That’s racist!!

  8. Maciano says:

    That would make the study of “national character” very interesting.

  9. ohwilleke says:

    “which can be thought of as a point in a very high-dimensions space.”

    In particular, the technical term for that is a finite “Hilbert space”.

    • gcochran9 says:

      In Hilbert space, no one can hear you scream.

    • AppSocRes says:

      Am I missing the humor? Hilbert Space are by definition infinite dimensional.

      • Space Ghost says:

        A Hilbert space is just a place where you can do dot products. It can be finite or infinite dimensional.

      • Jim says:

        A real Hilbert space H is a real vector space together with a positive definite quadratic form q such that H is complete with respect to the norm defined by q.

        A complex Hilbert space is a complex vector space with a positive definite Hermitian form q such that H is complete with respect to the norm defined by the q.

        Real and complex Hilbert spaces are each characterized by a unique cardinal number N,
        called the Hilbert dimension, which is the cardinality of any orthonormal basis of H. Real or complex Hilbert spaces of the same Hilbert dimension are isomorphic. Any cardinality is possible as a Hilbert dimension.

        Although the above are the official definitions often the term “Hilbert space” is used to just refer to the complex Hilbert space with Hilbert dimension aleph-null.

        I heard a story that once at a seminar given by Von Neumann a member of the audience asked Von Neumann “What is a Hilbert space?”. The individual asking the question was David Hilbert.

  10. Frank says:

    I would be very interested in seeing the average “ancestral human”, that has 100% of the assumed ancestral alleles of modern humans. And, of course, the genetic average “common ancestor” of Modern Humans and Neanderthals and Denisovans.

    • melendwyr says:

      They’d probably be very boring. The flexibility of outlook that makes the most interesting of modern humans able to adapt to environments totally unlike the ancestral wouldn’t be very developed. So they’d be hyper-conservative and superstition-ridden. Basically take the vast majority of humans across all history and ignore the outliers.

  11. Yudi says:

    Whether or not race is real, we can make it so!

    I could see some crazy nationalists really getting interested in this idea, although only in places like China might they have an impact.

  12. Gunboat Diplomat says:

    Curiously, no matter whether people want to make innovatively Gaelic people or just import traditionally Somalian ones, they never offer themselves and their ancestry as perpetual bond to cover for whatever negative externalities the fruits of their whimsy should eventually produce.

  13. RCB says:

    Suppose two populations (A and B) lay on the same vector (or close enough) from the global (or continental, whatever) average, but B is further than A. Then exaggerating A will make them more like B. “A-ness” is equal to “B-ness”. (Pretty sure the probability of this happening decreases as number of dimensions increases. O(p^n).)

  14. Matt says:

    The vector would differ depending on your bag of “average” – exaggerate your Irish against your pygmies, and as the IQ pops through the ceiling, they may become not so recognizably Irish in their habits any more (but you’ve probably got the world’s newest market dominant minority… who are also possibly rather unhealthy giants). Exaggerate your Irish Travellers against a group of Jews and the end result could probably be roughly along the Paleolithic, in IQ. Again not recognizable as Irish (wither the verbal dexterity, if nothing else).

    Although with exaggerating vectors, you might quickly exhaust your variants. If you exaggerated your Irish against West Africans, would you end up with a population that burned to death when you so much as tilt a shiny menu in their direction? Or would you quickly exhaust the fair skinned variation? Whatever the vector you can only once take the variants at MC1R and IRF4 that are linked to the Irish being fair compared to their neighbours. You won’t get more lactose tolerant if you push the derived LCT variant up further, etc.

    More interesting might be to exaggerate a group against their relatives close in evolutionary time. Say take the blend of Yamnaya, Early European farmer and WHG genotypes that approximates the Irish, exaggerate them along the cline separating them from that. (Of course, you’d need to cross check against population to “build” your Yamnaya, EEF and WHG genotypes). You’d get something like an exaggerated version of their evolutionary response to their history (or an “Assume this population continued to evolve along the lines it had…”).

    Similarly Sardinians against the actual Early European Farmers alone – you’d get a curious blend of an exaggeration of their small portion of Yamnaya ancestry (taller height, etc.) and recent selection away from their ancestral blend of Yamnaya and EEF (longer lifestyle, lighter skin and at least to some extent, shorter height).

    • Grels says:

      Modern Irish are blonder and more lactose tolerant than WHG, EEF and Yamnaya so that difference would become more pronounced. If you add drift, you’ll get exaggaration against everyone, like with Ari Blacksmiths, or perhaps Travellers.

      • Matt says:

        Well, the thing is the main LP allele is at frequency of say 0.8 in Irish, and it’s a dominant trait, so that means lactase persistence is at something like 0.97-0.99 in the Irish population. So even if you increased the frequency up to 1, and exhausted the capacity to increase in frequency of that allele, then the population wouldn’t get more lactase persistent. They wouldn’t get more lactase persistent at all, unless there was some other genetic variation around that helped process lactose, that were currently at intermediate / low frequencies in their population. There has to be actual alleles that can change in frequency and effect a trait. Even then, there are biophysical limits as to how well you can functionally improve at processing lactase.

        Same thing for pale / depigmented skin / hair. How close are they be to the threshold where they’ve exhausted all the functional variation? Is there the kind of variation in pigmentation alleles present in the Irish population where you can increase in frequency and eventually get the albino type of people, or would the genetic variation just not work out like that?

        (Etc for more poorly understood psychological / personality traits).

        • Grels says:

          LP and blondness are not absolutely fixed there, so there’d be some change however minor. Unknown and especially variation probably offers more room to move away from Yamnaya, but in this Greg’s thought experiment we should maximize distance to the point of lunacy, not death. If we selected some population to have a set of uniquely divergent loci including a fixed Brunner syndrome it’d be an extreme psychological change but they should be capable of survival, at least short term.

          • Matt says:

            Probably a fair amount of space left to go in blondness, not so far to go in LP.

            Interesting for you to bring up the idea of a population which is artificially fixed for something like Brunner syndrome. A population like that would have a strong selective pressure for another “anti-Brunner” mutation somewhere else on the genome.

            (As a tangent to this, I suppose that our evil future eugenics super Irish forging overlords could design outbreeding depression in through this – fix the “super Irish” for a variant that gives huge personality problems, cancel it with a compensatory mutation elsewhere. But hybrids between the thus fixed “super Irish” and normals at f2 would have an elevated chance of having two of the variants that give personality problems).

  15. Matt says:

    Another thought: Functionally, in a genetic sense, the Irish would be mixed-race between the Super-Irish and everyone else… A group of Irish doing this would retroactively make their ethnic group effectively mixed-race (and maybe the Super-Irish would see them that way).

    The complications of whether the Super-Irish naturally and obviously get super-White Privilege (because exaggerated against ethnic minorities?) or become regarded as a minority (because exaggerated against the Euro mainstream?) would be one for the identity politics crowd to chew on. (And if you exaggerated the English and Spanish against Africans, would the new groups be enriched for owing reparations? If they’re also smarter, then this is a business opportunity for the African diaspora.)

  16. it would be interesting to imagine what a uber-Brazilian would look like (since apparently we can potentially look like anyone)

  17. dearieme says:

    Christ, can you imagine the grudge-mongering from the SuperIrish?

  18. Maybe if you’re Super-Irish this actually makes sense:

    riverrun, past Eve and Adam’s, from swerve of shore to bend
    of bay, brings us by a commodius vicus of recirculation back to
    Howth Castle and Environs.
    Sir Tristram, violer d’amores, fr’over the short sea, had passen-
    core rearrived from North Armorica on this side the scraggy
    isthmus of Europe Minor to wielderfight his penisolate war:
    nor had topsawyer’s rocks by the stream Oconee exaggerated themselse
    to Laurens County’s gorgios while they went doublin their mumper
    all the time: nor avoice from afire bellowsed mishe mishe to
    tauftauf thuartpeatrick: not yet, though venissoon after, had a
    kidscad buttended a bland old isaac: not yet, though all’s fair in
    vanessy, were sosie sesthers wroth with twone nathandjoe. Rot a
    peck of pa’s malt had Jhem or Shen brewed by arclight and rory
    end to the regginbrow was to be seen ringsome on the aquaface.
    The fall (bababadalgharaghtakamminarronnkonnbronntonner-
    ronntuonnthunntrovarrhounawnskawntoohoohoordenenthur-
    nuk!)

    etc.

    • RCB says:

      It’s embarrassing that there are humans who believe that this is good literature, and that these people are considered smart and sophisticated.

  19. Greying Wanderer says:

    “So.. we could make synthetic Irishmen that were far more Irish than anyone in the emerald Isle – so Irish that they were barely human.”

    If anyone ever does this my advice is don’t make too many at once 🙂

  20. G.M. says:

    Lovely thoughts. Pretty high-dimensional space though; maybe we could break it up into subspaces where each subspace defined a trait or set of traits. Then we could mix n’ match… the body of a hyper-Australian Abo with the intellect & racial temperament of an Überswede – beauty AND brains! 😉

  21. Matt says:

    You would expect that the Iceman’s phenotype differed from mainland Italians in the same way that Sardinians do, only more so.

    Except where selection’s disrupted that signal. Using an exaggeration of Sardinian->Northern European FST along the genome, there could be signals which are absent in European hunter gatherers, and where some signatures characteristic of HGs have ceased to exist. Like the Western European HGs didn’t have SLC24A5, while a “reconstructed” HG from cline exaggeration would, because it’s at fixture across Europe (though that’s a poor example, given that most Euro HG ancestry is probably Eastern European and they probably did).

    You could correct for this using the Singleton Density Scores method – if there’s a signal from that of strong recent selection in one or both populations, then decrease weight at that region. If you’ve got a signal for increased height in mainland Italians and decreased in Sardinians, give lower weight to those variants when creating the cline (or reverse, if the signals are strong enough).

    (Btw – https://ep70.eventpilot.us/web/page.php?page=IntHtml&project=ASHG16&id=160123376 – PgmNr 208: Global shared natural selection for increased stature in recent human history – “We use SDS to analyze whole-genome-sequencing data for additional populations…we find that selection for increased height has recently elevated in Northern Europe. However, surprisingly, we find that all examined populations, independently across continents, had experienced detectable selection for taller stature. This apparent global shared selective pressure could not have been detected with earlier comparative approaches.”)

    That would get worse with time. If you used a more CRISPR-y version of Razib Khan’s “Neanderthal Kwisatch Haderach” (https://www.geneticliteracyproject.org/2013/01/31/bringing-back-the-neanderthal-genome-the-old-fashioned-way/) idea (as taken up by Neal Stephenson in sevenEves, I note), then the outcome product of extending the Neanderthal cline wouldn’t work so well at recreating actual Neanderthals because of Neanderthal gene deserts and Neanderthal variants fixed in moderns (as I think noted by Razib).

    Trying to reconstruct “Basal Eurasian” in this way would be intermediate the Neanderthal and EEF case. You’d get a “Basal Eurasian” like people by extending the cline from North->Southern Europe (a very, very, very long way) but the result might lack variants that were present in the Basal but have since been selected out, and lack or have low frequency of variants present in Basal but which have reached higher frequency elsewhere.

  22. Anchises says:

    These super-Gaels might even successfully make it all the way through to The Session to End All Sessions:

    • BB753 says:

      Since 10% of the irish population is alcoholic ( even accounting for 20% teetotalers), per national health statistics, would a super-irish population be 100% alcoholism prone or pretty close, like Amerindians?

      • Matt says:

        OTOH, if 20% of the Irish population were teetotalers, and you exaggerated that up the cline x10 against a population with 0% alcoholism, 0% teetotalling, seems like you’d have 100% teetotalers… Assuming teetotalling and alcoholism are both totally under genetic control.

        But there’s no population with genetic 0% alcoholism and 0% teetotalling.

        Genetic differences in propensity to alcoholism probably are not that large for most groups, so exaggeration along the cline would have to be huge to get a large measurable difference in propensity to alcoholism. (Other problems would start kicking in way before alcoholism for your exaggerated group.)

        Now, I’d imagine since you’re smart, you’re thinking “What about the Ashkenazis and the Chinese, who are pretty measurably likely to be less alcoholic? Exaggerate Irish against them and…”. Well, yes in part, but remember that’s because those populations have those derived ALDH variants that basically make them sicker when they drink (http://patagoniamonsters.blogspot.co.uk/2014/05/alcohol-genes-and-human-migrations-part.html). What Greg has previously described as in built Antabuse.

        Now those variants are already basically at 0% in the Irish, so exaggerating the Irish further down a cline would do nothing to the frequency of those variants; You can’t fall further than the floor.

        Conversely though, you could probably make Jews (and more generally the Near East) and Chinese (and more generally East Asians) less alcoholic (or at least, more likely to die by liver cancer if alcoholic) by exaggerating them against other world groups, like the Irish, because those derived variants that are protective against alcoholism aren’t near 100% yet in either Jewish or Chinese groups. The reverse operation though, wouldn’t work nearly so well.

  23. c23 says:

    There was something like that in Neal Stephenson’s Seveneves – in a far flung future in which everyone is descended from seven women after a population bottle neck.

    “…Caricaturization: selective breeding, pursued consciously in some cases and unconsciously in others, that had the effect over many generations of intensifying racial differences. The example cited most often was a gradual change in eye color among Moirans. Eve Moira’s eyes had been hazel: relatively light in color by the standards of black people, but not all that unusual. By the end of the Second Millennium, many Moirans had eyes so pale in color as to appear golden in strong light. On the walls of the Great Chain’s fashion stores, blown up to ten times life size, Moiran fashion models still gazed at you through shockingly yellow, catlike eyes.”

  24. Stephen W says:

    There a multiple directions you could take a super ethnicity. For example if you exaggerated the Spanish compared to the global average they would give them all the white alleles but if you exaggerated them compared to other Europeans they would become very swarthy.

  25. Halvorson says:

    Speaking of European genetics, there’s a lot of interesting dirt buried in the big Lazarides paper that hasn’t been commented on yet. For example, it turns out that there are several European populations whose Fst value is 0. This is true of Poles/Czechs, and more surprisingly to me, Greeks/Bulgarians/Albanians (Magna Graecia?). I’m not sure what history I can invoke to explain this. Ancient Greek colonies don’t really work because Genetically Modern Greeks only seem to have emerged after the Slavs arrived in the 7th century or so and mixed with a population similar to today’s Cypriots.

    • Matt says:

      The populations don’t seem totally identical and convergent even with Fst 0 between them though, as Bulgarians vs Greeks vs Albanians or Poles vs Czechs each have slightly different Fst with other European populations. You can see this when you project those Fsts onto MDS scaling, and they get given different positions:

      • Halvorson says:

        Yeah, here Bulgarians are clearly distinct and there is some noticeable wiggle room between Poles and Czechs. Albanians still look like Greeks roleplaying as a different ethnicity, though.

        • Matt says:

          Though Albanians are pretty distinct when it comes to IBD (Identity by Descent) where out of all Europeans they seem to have the highest within population haplotype sharing (although not sure if that’s true when compared to the Ashkenazis or Finns and small groups like Orcadian and Shetland Islanders and alpine mountain villages) and are quite distinct from Greeks.

          http://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.1001555

          “By far the highest rates of IBD within any populations is found between Albanian speakers—around 90 ancestors from 0–500 ya, and around 600 ancestors from 500–1,500 ya (so high that we left them out of Figure 5; see Figure S12). Beyond 1,500 ya, the rates of IBD drop to levels typical for other populations in the eastern grouping.” (Within population IBD rates are higher in most Eastern European than Western European populations; possibly expansions more recent in history).

          That does speak against them being just Greek cosplayers (or Greeks being Albanian cosplayers) rather than coherent separate population. It seems like the Albanians have undergone a large population expansion from a pretty small base in the last 1500-500 years. The Albanian language is believed to have evolved from an ancient Balkan branch of Indo-European, apparently from a mountainous region, so kind of an odd thing, to have this pocket of Paleo-Balkan speaking survivors from a mountain region who have expanded for unknown reasons.

          Like you say, they really don’t seem very distinct from mainland Greeks here at the pairwise Fst scale.

        • Matt says:

          There’s also should be a difference in Fst to the Middle East for Greeks vs Albanians:

          (Greek more geneflow with ME / Cypriots?).

          Though if the more you include the Middle Eastern groups, the less informative the plots are for the precise structure among the Europeans (the two plots above are more informative for capturing the distance of the Europeans from one another while these are sort of restricted in where they can place the Europeans by their relatedness to the ME).

  26. deuce says:

    Kudos for the Chesterton quote. I mention that and examine Robert E. Howard’s attitude toward the Irish Gaels here: http://leogrin.com/CimmerianBlog/if-nobody-but-a-pure-celt-wore-the-green/

  27. Paul Conroy says:

    As a Super-Gael myself – being higher in Irish percentage than anyone else on 23andme or Ancestry.com that I’ve compared with – I’d imagine that Super-Gaels would exhibit the following qualities in spades:
    1. Phenotype – mixture of Colin Farrell and Gabriel Byrne.
    2. Demeanor – Maximum Alpha: could nonchalantly pickup any girl, single, married, poly or otherwise.
    3. Career1 – become political leader of any country they wished.
    4. Career2 – become the greatest prose writer the world has ever known, higher quality than Shakespeare and more prolific than Goethe.

    Betas beware!

  28. By the same argument, you could take the Irish vector and put a negative sign on it, and get an anti-Irishman, or even lengthen the negative vector to produce a super-anti-Irishman. As before, the actual result would depend on your reference population.

    This is similar to how you can have negative coefficients of relatedness. (r is just F-with-a-change-of-variables). In fact you get them automatically in a finite population, although they’re just barely less than 0 for large N.

    And, no, contra some authors, this doesn’t mean you can expect either ethnic nepotism or ethnic spite. But that’s an argument for another day.

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