Jekyll2022-12-26T17:15:25+00:00https://eternalanglo.com/feed.xmlEternal Anglo weblogData about people and productThe Mathematical Reason You should have 9 Kids2022-12-19T00:00:00+00:002022-12-19T00:00:00+00:00https://eternalanglo.com/have-nine-kids<!DOCTYPE html>
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<p>In this post I propose a curious genetic question that can be modeled with a remarkably simple answer. If you have \( N \) children, what is the probability that every allele in your genome is present in at least one of your children? In other words, if you have \( N \) children, what is the probability that your entire genome has been replicated in the next generation? </p>
<p><em>Note:</em> I do not believe there is a correct number of children to have. <u>This blog post is just for fun</u>. An organism's biological purpose is not to replicate its genome. Rather, an organism's biological purpose is simply to reproduce.</br>
For an explanation of biological purpose, I invite you to read <em><a href="https://www.amazon.com/Debunking-Selfish-Gene-Van-Allen-ebook/dp/B0BPXJ85W7/">Debunking the Selfish Gene</a></em> by T. K. Van Allen.</p>
<hr>
<p>As a human, you have two sex chromosomes XY or XX, and you have 22 homologous pairs of autosomal chromosomes (autosomes) numbered 1 through 22. Your child receives 23 chromosomes from you and 23 chromosomes from the other parent. The manner in which each chromosome is transmitted to your child is independent of the manner in which the other chromosomes are transmitted to your child. Each autosome has a roughly \( \frac12 \) probability of being transmitted as a crossover of your own homologous autosome pair during cellular meiosis. And each autosome has a roughly \( \frac12 \) probability of being transmitted as an identical copy of 1 of your 2 corresponding homologs during cellular meiosis.</p>
<p style="text-align: center;"><img src="/assets/img/Meiosis_Overview_new.svg.png""></br>
<em>In this image, chromosomes of different size correspond to differently numbered chromosomes. Chromosomes of the same size and different single colors correspond to homologs of the same numbered chromosome. The H-shaped things are two chromatids attached at a centromere, and the 1-shaped things are lone chromatids. Dual-colored chromatids were generated by a crossover event during meiosis I. The end result of meiosis is 4 gamete cells. A single gamete cell from each of 2 parents fuse to form the zygote.</br>Source: <a href="https://commons.wikimedia.org/wiki/File:Meiosis_Overview_new.svg">Wikimedia Commons</a></em></p>
<p>Because chromosomes are transmitted independently, the probability that all of your autosome pairs are replicated into your children is just the probability that one of your autosome pairs is replicated into your children, raised to the power of 22.</p>
<p><a href="#calculating">Below</a>, I derive a formula for the probability that an autosome pair is replicated into your children if you have \(N \gt 0\) children.</br>
The probability is given by:
$$ 1 - \frac{N+2}{2^N} + \frac{1}{2^{2N-1}}.$$
</p>
<h2>Probability of genome replication for males</h2>
After a male has \(N\) children, it is immediately apparent whether or not the X and Y sex chromosomes were both replicated into his children. So the probability that X and Y were replicated is determinate, either 0 or 1, not probabilistic. The probability that his full genome was replicated into \(N\) children is given by the probability that each of 22 autosomes were replicated into \(N\) children:
$$ \left(1 - \frac{N+2}{2^N} + \frac{1}{2^{2N-1}}\right)^{22}. $$
Before a male has \(N\) children, it is still probabilistic whether or not the X and Y sex chromosomes will be replicated into his children. The probability that both are replicated is given by \(1-\left(\frac12\right)^{N-1}\) when \(N \gt 0\). The probability that his full genome will be replicated is given by:
$$ \left(1-\left(\frac12\right)^{N-1}\right)\left(1 - \frac{N+2}{2^N} + \frac{1}{2^{2N-1}}\right)^{22}.$$
<h2>Probability of genome replication for females</h2>
The female's XX chromosomes behave like autosomes during meiosis, where each gamete has a roughly \(\frac12\) probability of receiving a copy homolog and a \(\frac12\) probability of receiving a homologous pair crossover. So the probability that her full genome was replicated into \(N\) children is given by the probability that each of 23 autosomes were replicated into \(N\) children:
$$ \left(1 - \frac{N+2}{2^N} + \frac{1}{2^{2N-1}}\right)^{23}. $$
<h2>Results</h2>
The results are summarized in the following graph:
<p style="text-align: center;"><img src="/assets/img/genome_replication_individuals.png"></p>
<p>In all cases, for an individual to have better-than-even odds at replicating his/her entire genome, s/he must have 9 children.</p>
<p>Suppose that a couple wants to consider the probability that <em>both</em> of their genomes are replicated into their shared children. To determine this probability, they just multiply their individual probabilities together. The results are summarized in the following graph:</p>
<p style="text-align: center;"><img src="/assets/img/genome_replication_couples.png"></p>
<p>In both cases, for a couple to have better-than-even odds at replicating their genomes, they must have 10 shared children.</p>
<hr>
<h2 id="calculating">Calculating the probability that an autosome pair is replicated if you have \(N \gt 0\) children:</h2>
<p>We will calculate the probability that an autosome pair is replicated into your children by calculating the complement of the probability that an autosome pair is <b>not</b> replicated into your children.</p>
<p>Let us choose a particular autosome pair in your genome, and label it autosome pair \( A \). Let us give the label \( P \) to the homolog you received from your father (<em>p</em>aternal), and let us give the label \( M \) to the homolog you received from your mother (<em>m</em>aternal). If you have \( N\gt 0 \) children, there are 4 possibilities to consider:</p>
<ul>
<li><b>Possibility 1</b>: None of your children received a copy of the \( P \) homolog or a copy of the \( M \) homolog. They all received crossovers. This occurs with probability:
$$ \left(\frac12\right)^N.$$</li>
<li><b>Possibility 2</b>: None of your children received a copy of the \( M \) homolog, but \(j \gt 0\) children received a copy of the \( P \) homolog. This occurs with probability:
$$ {N \choose j} \left(\frac14\right)^0 \left(\frac14\right)^j \left(\frac24\right)^{N-j}\\
= {N \choose j} \left(\frac12\right)^{N+j}.$$
</li>
<li><b>Possibility 3</b>: None of your children received a copy of the \( P \) homolog, but \(j \gt 0\) children received a copy of the \( M \) homolog. As above, this occurs with probability:
$$ {N \choose j} \left(\frac12\right)^{N+j}.$$
</li>
<li><b>Possibility 4</b>: At least one child received a copy of the \( P \) homolog and at least one child received a copy of the \( M \) homolog. Then the probability that the autosome pair was <b>not</b> replicated into your children is \(0\), so we can ignore this case.
</li>
</ul>
<p>Each crossover event occurs at a point along the length of the chromosome. The probability that two crossover events occur at the exact same location is \(0\) (this is not exactly true, but it is virtually true). If there are \(i\) number of \(P\)-\(M\) crossovers for autosome pair \(A\), out of \(R\) total crossovers for autosome pair \(A\) among your children, then there will be \(R-i\) number of \(M\)-\(P\) crossovers for autosome pair \(A\) among your children.</p>
<h2>Possibility 1</h2>
<p>If you have \( N \) children and each receives a crossover of your autosome pair \( A \), then the following describes the criteria for which the full \( P \) homolog will <b>not</b> be replicated among your children:</p>
<p><em>If all the crossover sites for \(P\)-\(M\) crossovers occur higher along the length of the chromosome than all the crossover sites for \(M\)-\(P\) crossovers, then the full \(P\) homolog will not be replicated.
</em></p>
<p>Similarly, here is the criteria for which the full \(M\) homolog will <b>not</b> be replicated among your children:</p>
<p><em>If all the crossover sites for \(M\)-\(P\) crossovers occur higher along the length of the chromosome than all the crossover sites for \(P\)-\(M\) crossovers, then the full \(M\) homolog will not be replicated.</em></p>
<p>The ordering of crossover sites along the length of a chromosome can be represented by an \(N\)-length sequence of \(p\)s and \(m\)s, where \(p\) represents a \(P\)-\(M\) crossover and \(m\) represents an \(M\)-\(P\) crossover. There are \(2^N\) possible sequences and they are all equally likely.</p>
<p>Sequences that are \(i>0\) number of \(m\)s followed by \(N-i\) number of \(p\)s fulfill the first criteria. There are \(N\) such sequences. Sequences that are \(i>0\) number of \(p\)s followed by \(N-i\) number of \(m\)s fulfill the second criteria. There are \(N\) such sequences. In total there are \(2N\) sequences in which at least one homolog will not be replicated, out of \(2^N\) equally likely sequences, so the probability that at least one homolog is <b>not</b> replicated is given by:
$$ \frac{2N}{2^N} = \frac{N}{2^{N-1}}. $$</p>
<p>Together, the probability that none of your children received a copy homolog <b>and</b> that at least one homolog is <b>not</b> replicated by the crossovers is given by:
$$\left(\frac12\right)^N\left(\frac{N}{2^{N-1}}\right) = \frac{N}{2^{2N-1}}.$$
</p>
<h2>Possibility 2</h2>
<p>Suppose \(j \gt 0\) children received a copy of the \(P\) homolog and \(0\) children received a copy of the \(M\) homolog. Let \(n\) be equal to \(N-j\). Then the following describes the criteria for which the full \(M\) homolog will <b>not</b> be replicated among your children:</p>
<p><em>If all the crossover sites for \(M\)-\(P\) crossovers occur higher along the length of the chromosome than all the crossover sites for \(P\)-\(M\) crossovers, then the full \(M\) homolog will not be replicated.</em></p>
<p>The ordering of crossover sites along the length of a chromosome can be represented by an \(n\)-length sequence of \(p\)s and \(m\)s, where \(p\) represents a \(P\)-\(M\) crossover and \(m\) represents an \(M\)-\(P\) crossover. There are \(2^n\) possible sequences and they are all equally likely.</p>
<p>Sequences that are \(i \ge 0\) number of \(p\)s followed by \(n-i\) number of \(m\)s fulfill the criteria. There are \(n+1\) such sequences, out of \(2^n\) equally likely sequences, so the probability that the \(M\) homolog is <b>not</b> replicated is given by:
$$ \frac{n+1}{2^n} = \frac{N-j+1}{2^{N-j}}. $$</p>
<p>Together, the probability that \(j\) children received a copy of the \(P\) homolog, \(0\) children received a copy of the \(M\) homolog, and the \(M\) homolog was <b>not</b> replicated by the crossovers is given by the following:
$$ {N \choose j}\left(\frac12\right)^{N+j} \left(\frac{N-j+1}{2^{N-j}}\right)\\
={N \choose j} \frac{N-j+1}{2^{2N}}.$$</p>
<p>Summing over possible values of \(j\) (see <a href=https://mathworld.wolfram.com/BinomialSums.html>https://mathworld.wolfram.com/BinomialSums.html</a> for formulae on weighted binomial sums), we have the total probability that at least \(1\) child received a copy of the \(P\) homolog, and \(0\) children received a copy of the \(M\) homolog, <b>and</b> the \(M\) homolog was <b>not</b> replicated by crossovers:
$$ \sum_{j=1}^N {N \choose j} \frac{N-j+1}{2^{2N}}\\
= \frac1{2^{2N}}\left[\left(N+1\right)\sum_{j=1}^N {N \choose j} - \sum_{j=1}^N j {N \choose j} \right]\\
= \frac1{2^{2N}}\left[\left(N+1\right)\left(2^N-1\right) - N2^{N-1}\right]\\
= \frac{N+2}{2^{N+1}} - \frac{N+1}{2^{2N}}.$$
</p>
<h2>Possibility 3</h2>
<p>As above, the probability that at least \(1\) child received a copy of the \(M\) homolog, and \(0\) children received a copy of the \(P\) homolog, <b>and</b> the \(P\) homolog was <b>not</b> replicated by crossovers is given by:
$$\frac{N+2}{2^{N+1}} - \frac{N+1}{2^{2N}}.$$</p>
<h2>Possibility 4</h2>
The probability that at least one child received a copy of the \(P\) homolog, at least one child received a copy of the \(M\) homolog, <b>and</b> either homolog is <b>not</b> replicated is \(0\).
<h2>Combining Possibilities 1-4</h2>
<p>If \(N \gt 0\), the probability that autosome pair \(A\) was <b>not</b> replicated into \(N\) children is given by:
$$ \frac{N}{2^{2N-1}} + 2\left[\frac{N+2}{2^{N+1}} - \frac{N+1}{2^{2N}}\right] \\
= \frac{N+2}{2^N} - \frac{1}{2^{2N-1}}. $$</p>
<p>If \(N \gt 0\), the probability that autosome pair \(A\) <b>was</b> replicated into \(N\) children is given by:
$$ 1 - \frac{N+2}{2^N} + \frac{1}{2^{2N-1}}. $$</p>
</body>Contra Jared Taylor: Blacks are not 35 Times as Likely to Attack Whites as the Reverse2022-11-20T00:00:00+00:002022-11-20T00:00:00+00:00https://eternalanglo.com/contra-jared-taylor<!DOCTYPE html>
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This is a response to Jared Taylor's <a href=https://www.amren.com/videos/2022/11/latest-interracial-crime-stats>article and video</a> in which he claims that blacks are 35 times more likely to attack whites than the other way around in the United States. I will use hypothetical scenarios and county-level crime data to motivate and substantiate an alternative claim: that if the black population were equal to the white population in the United States, then blacks would be 7.63 times as likely to attack whites as the reverse.
<h3>Hypothetical Scenario 1: All violence is random</h3>
<p>Consider a hypothetical town with 100 green-eyed people and 900 blue-eyed people. In this town, 1 out of every 10 people attacks a random person.</p>
<p>Simple calculations determine the expected outcome: 90 blue-eyed people commit attacks; their victims are 81 blue-eyed people and 9 green-eyed people. 10 green-eyed people commit attacks; their victims are 9 blue-eyed people and 1 green-eyed person.</p>
<p>
At first it seems that blue-on-green violence is in parity with green-on-blue violence. Nothing is amiss in this town in terms of inter-ocular violence. But consider this perspective: A green-eyed person is 9 times as likely to attack a blue-eyed person as a blue-eyed person is to attack a green-eyed person. This claim is indisputably true, but intuitively it feels like nonsense. What went wrong? It is not an incorrect claim, it is an <b>incoherent claim</b>.</p>
<p>Incoherence creeps into the claim at the ambiguity of the phrase <em>"a person"</em>. The phrase <em>"a person"</em> either means <em>"any of the persons of a group"</em> or it means <em>"one particular person of a group"</em>.</p>
<p>The claim above is only true when it is interpreted as follows:</p>
<ol>
<li><em>One particular</em> green-eyed person is 9 times as likely to attack <em>any of the</em> blue-eyed persons as <em>one particular</em> blue-eyed person is to attack <em>any of the</em> green-eyed persons.</li>
</ol>
<p>Alternative true claims are as follows:</p>
<ol start="2">
<li><em>One particular</em> green-eyed person is 9 times as likely to <em>be attacked</em> by <em>any of the</em> blue-eyed persons as <em>one particular</em> blue-eyed person is to <em>be attacked</em> by <em>any of the</em> green-eyed persons.</li>
<li><em>One particular</em> green-eyed person is equally likely to attack <em>one particular</em> blue-eyed person as <em>one particular</em> blue-eyed person is to attack <em>one particular</em> green-eyed person.</li>
<li><em>Any of the</em> green-eyed persons attacking <em>any of the</em> blue-eyed persons is equally as likely to occur as <em>any of the</em> blue-eyed persons attacking <em>any of the</em> green-eyed persons.</li>
</ol>
<p>All four claims are correct, but claims 1 and 2 are meaningless because they are incoherent. It is clear they are incoherent because statement 1 makes the green-eyed people seem like victimizers while statement 2 makes the green-eyed people seem like victims. The claims seem to be making observations about rates of inter-ocular violence, but actually they are only making observations about the minority status of green-eyed people.</p>
<h3>Hypothetical Scenario 2: all inter-ocular violence is directed</h3>
<p>Consider a different hypothetical town with 900 blue-eyed people and 100 green-eyed people. In this town, all the blue-eyed people live on one side of a river, and all the green-eyed people live on the other side of the river. The residents only cross the river when they feel like committing an inter-ocular crime. On both sides, 1 out of every 10 people feels like committing an inter-ocular crime.</p>
<p>In Scenario 1, it did not make sense to talk about violence committed by <em>one particular</em> person against <em>any of the persons</em> of a group, because each attack was inflicted on <em>one particular</em> person randomly. In Scenario 2, it <em>does</em> make sense to talk about violence committed by <em>one particular</em> person against <em>any of the persons</em> of a group, because I have stipulated that each inter-ocular attack is inflicted on <em>any of the</em> persons of the other group.</p>
<p>In Scenario 2, as I have so far described, <em>one particular</em> green-eyed person is equally as likely to attack <em>any of the</em> blue-eyed persons as <em>one particular</em> blue-eyed person is to attack <em>any of the</em> green-eyed persons. However, if I modify it so that <em>G</em> out of 10 green-eyed people feel like committing an inter-ocular attack and <em>B</em> out of 10 blue-eyed people feel like committing an inter-ocular attack, then the correct claim becomes as follows:</p>
<ul>
<li><em>One particular</em> green-eyed person is <em>G/B</em> times as likely to attack <em>any of the</em> blue-eyed persons as <em>one particular</em> blue-eyed person is to attack <em>any of the</em> green-eyed persons.</li>
</ul>
<p>And in this scenario, the ratio of <em>G/B</em> becomes a meaningful metric to measure and ponder. If all inter-ocular crime is directed, and if the blue-eyed population is equal to the green-eyed population, then <em>G/B</em> is also the ratio of actual green-on-blue crimes committed to actual blue-on-green crimes committed.</p>
<h3>Scenario 3: Reality</h3>
<p>It is probably obvious that I'm using "blue-eyed" and "green-eyed" as an emotionally neutral mask to the real question at hand, namely race and violence, specifically between blacks and whites. In reality, there is a certain amount of interracial violence that is random and color-blind. There is also a certain amount of interracial violence that is directed, where a black guy is determined to attack the first white person he sees, or a white guy is determined to attack the first black person he sees. My contention is that the majority of interracial crime is random, that reality is closer to Hypothetical Scenario 1, but reality has some elements of Hypothetical Scenario 2.</p>
<p><a href=https://www.amren.com/videos/2022/11/latest-interracial-crime-stats>Jared Taylor makes the claim</a> that in the United States, blacks are 35 times more likely to attack whites than the other way around. The formulation of his claim is the same as the form of claim 1 in Hypothetical Scenario 1. Whether or not this claim is meaningful depends on the situation. If all or most interracial crime is directed, then the claim is coherent and meaningful. If all or most interracial crime is random, then the claim is incoherent and meaningless.</p>
<p>We can try to get to the bottom of things by exploring the following question: what would the rates of interracial violence be if the black population were equal to the white population? We can't answer this question with the NCVS <a href="#FN1" id="FL1">[1]</a>, because the NCVS data is only reported at the national-level, where the current ratio of white population to black population is fixed at about 5. But we can attempt to answer the question with the 2020 NIBRS <a href="#FN2" id="FL2">[2]</a> data, because the NIBRS reports each incident at the county level, and the counties of the United States have many different values for the ratio of white population to black population. One limitation of the NIBRS is that it does not distinguish between so-called "hispanic white" offenders and "non-hispanic white" offenders, so I'm only going to use the NIBRS to explore interracial violence between "blacks" and "whites (hispanic+non-hispanic)".</p>
<p>To make a long story short, I'm going to make each county a data point, and plot "logarithm of the ratio of black-on-white violent incidents to white-on-black violent incidents in 2020" as the dependent variable, and "logarithm of the ratio of white population to black population in 2020" as the independent variable. It's important to take logarithms to transform a hyperbolic operation (taking a ratio) into a linear operation. That makes choosing a black-to-white ratio equivalent (up to a sign) to choosing a white-to-black ratio, so that the choice becomes arbitrary. I'm going to take a linear regression of this plot to estimate the ratio of interracial violence when the black population is equal to the white population. <a href="https://github.com/EAweblog/EAweblog_assets/blob/main/parse_incident_level_file.py">Here is the script to generate the plot</a>. Here are the results:</p>
<p style="text-align:center"><img src=/assets/img/black_white_county_ratios.png></p>
<p>(In this paragraph, "white" means white (hispanic+non-hispanic)). According to this regression, the expected ratio of black-on-white to white-on-black crimes is 10^0.493 = 3.11 when the black population is equal to the white population. But just taking the total of the interracial crimes in the USA gives a ratio of 2.81. This underestimates the expected ratio of black-on-white to white-on-black crimes at equal population by a factor of 3.11/2.81 = 1.11.</p>
<p>(In this paragraph, "white" just means non-hispanic white). I will presume that the total of the interracial crimes in the USA from the NCVS underestimates the expected ratio of black-on-white to white-on-black crimes at equal population by the same factor of 1.11. The ratio of black-on-white crimes to white-on-black crimes from the 2021 NCVS is 6.87. The expected ratio of black-on-white to white-on-black crimes is then 1.11*6.87 = 7.63, if the white population were equal to the black population. <b>Therefore, if the black population were equal to the white population in the United States, then it is expected that blacks would be 7.63 times as likely to attack whites as the reverse.</b></p>
<h3>Notes</h3>
<ol>
<li>
<a href="#FL1" id="FN1">^</a> The NCVS - National Crime Victimization Survey - collects information on non-fatal personal crimes from a sample of about 240,000 Americans. The NCVS is informative about interracial crime (excluding homicide) at the national level. The 2021 NCVS report is available <a href="https://bjs.ojp.gov/content/pub/pdf/cv21.pdf">here</a>. The datasets are available for full download <a href="https://www.icpsr.umich.edu/web/NACJD/series/95">here</a>.
</li>
<li>
<a href="#FL2" id="FN2">^</a> The NIBRS - National Incident-based Reporting System - captures details on single crime incidents from local law enforcement. The NIBRS is informative about interracial crime at the county level, with the limitation that hispanic white offenders are not distinguished from non-hispanic white offenders. The datasets are available for full download <a href="https://www.icpsr.umich.edu/web/NACJD/series/128">here</a>
</li>
<li>
<a href="#FL3" id="FN1">^</a> The <a href="https://www.icpsr.umich.edu/web/NACJD/search/series/">NACJD</a> - National Archive of Criminal Justice Data - is a collection of various datasets available for full download, including a few very useful ones like the National Crime Victimization Survey (NCVS), the National Incident-Based Reporting System (NIBRS), and the Uniform Crime Reports (UCR), which are cited extensively in Edwin Rubinstein's <em>The Color of Crime</em> <a href="#FN5">[5]</a> used by Jared Taylor. I'm adding a link to the NACJD to my sidebar.
</li>
<li>
<a href="#FL4" id="FN2">^</a> The <a href="https://www.icpsr.umich.edu/web/ICPSR/search/series">ICPSR</a> - Inter-university Consortium for Political and Social Research - is a superset of the NACJD including various other datasets available for full download, related to opinion-polling, education surveys, and whatever else they've thrown in. I'm adding a link to the ICPSR to my sidebar.
</li>
<li>
<a href="#FL5" id="FN5">^</a> <em>The Color of Crime</em> (<a href="https://archive.colorofcrime.com/2016/03/the-color-of-crime-2016-revised-edition/">2016 edition available here</a>) is a report on racial crime statistics from several national and sub-national sources. It is written by Edwin S Rubinstein and published by the New Century Foundation, and used by Jared Taylor in his presentations.
</li>
</ol>
</body>Contra Paul Graham: What Fraction of Talent Lives in the USA?2022-08-02T00:00:00+00:002022-08-02T00:00:00+00:00https://eternalanglo.com/usa-talent<!DOCTYPE html>
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<p>
The question in this post's title is motivated by the following tweet by Paul Graham (<a href="https://archive.ph/r3gwK">archived here</a>):
</p>
<blockquote class="twitter-tweet"><p lang="en" dir="ltr">The US has only 5% of the world's population. So if talent is equally distributed, 95% of the most talented people are born outside the US. That's why any kind of work in which ability is at a premium tends to have lots of immigrants. And tech is that kind of work.</p>— Paul Graham (@paulg) <a href="https://twitter.com/paulg/status/1552354595820539904?ref_src=twsrc%5Etfw">July 27, 2022</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script>
<p>
When Paul Graham says talent, or "ability" to perform tech work, he means cognitive ability. Cognitive ability is what is pertinent to sitting at a computer solving coding problems and engineering problems. We don't need to act totally naive to the question at the title of this post. It's not like we must say "There is no information on the distrubution of talent. We can only guess that it is evenly distributed." We actually do have a pretty good idea of the distribution of cognitively gifted people in the world because we have good estimates for the mean IQ of populations by nation. Not only is it plausible to ask "What fraction of talent is lives in the USA", it is also straightforward to propose answer(s) to the question, depending on what your threshold for "talent" is.
</p>
<p>
(There is a parallel question begged by Paul Graham's tweet: what fraction of talent is <b>born in</b> the USA? I won't attempt to answer that question in this post because it's too unspecified. Born in the last 12 months? The last 10 years? Most immigrants entering the USA at this moment were born between 1970 and 2000, so that's probably the most relevant interval.)
</p>
<p>
Going forward in this post I'm just going to assume that the national estimates for mean IQ currated by <a href="https://viewoniq.org/">David Becker</a> are accurate <a href='#FN1' id="FL1">[1]</a>, and I'm going to add one more bold assumption that, within every nation, IQ scores are normally distributed with a standard deviation of 15 points.
</p>
<p>
For any possible IQ score, we can use the cummulative distribution function for the normal distribution to estimate the fraction of people in the USA who have that IQ score or higher. We can multiply that fraction by the total population of the USA to get the total number of people in the USA who have that IQ score or higher. We can then repeat this process individually for every nation, and sum the results to get the total number of people in the world who have that IQ score or higher.
</p>
<p>
I'm going to highlight two cognitive thresholds: one is the IQ-104 threshold, which is the top 20% of IQ scores globally and is a <a href="https://www.unz.com/anepigone/average-iq-of-college-undergrads-and-graduate-degree-holders-by-decade/">Good estimate</a> for the current average IQ of graduate degree holders <a href='#FN2' id="FL2">[2]</a>. The other is the IQ-119 threshold, which is the top 5% of IQ scores globally and probably includes virtually all people who make inventive progress in tech. I think "top 5% of IQ scores globally" is a good working definition of "the most talented people".
</p>
<p>
The whole process is so straightforward that a single <a href="https://github.com/EAweblog/EAweblog_assets/blob/main/USA_IQ_threshold.py">Python script</a> can download the data, process the data, and visualize the results:
</p>
<p style="text-align:center"><img src=/assets/img/USA_IQ_threshold_graph.png></p>
<p>
So among the population of the USA, which is 4.5% of the global population, there lives 7.6% of the global population with an IQ over 104. More to the point of this post, among the USA population, there lives 6.7% of the global population with an IQ over 119, or in other words, 6.7% of "the most talented people", globally, live in the USA.
</p>
<p>
There begins to be a horseshoe theory at play around the IQ-140 mark (the top 0.2% of IQ scores globally), where Paul Graham begins to be correct, that USA has only (4.5%) of these IQ scorers and (4.5%) of the global population. On the other hand, every nation on earth will have a similar drop in its corresponding graph for high enough IQ-threshold, except the single nation with the highest mean IQ (namely, Taiwan with mean IQ 106.49).
</p>
<p>
So 6.7% of "the most talented people" is a lot less then I expected for the USA. When I first read Paul Graham's tweet, I did a really crude back-of-the-envelope calculation and came up with this tweet (<a href="https://archive.ph/wip/em1KM">archived here</a>):
</p>
<p>
<blockquote class="twitter-tweet"><p lang="en" dir="ltr">Depends on your threshold for talent.<br>If "talent" is "IQ over 115" then 16% of talent is born in the USA+Canada.<br>My definition is "talent" is "IQ over 130" implying 29% of "talent" is born in USA+Canada. <a href="https://t.co/ZviwqjYPej">https://t.co/ZviwqjYPej</a></p>— Eternal Anglo ☮️ (@EAweblog) <a href="https://twitter.com/EAweblog/status/1553018346010034178?ref_src=twsrc%5Etfw">July 29, 2022</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script>
</p>
<p>
Which I immediately regretted after thinking about it for 5 minutes. If Europe plus North America plus China is over 2 billion people, and the USA is 1/6 of that, how could the USA possibly be over 1/6 (16.7%) of any IQ threshold? Frankly, embarassing. In my defense I had just woken up and wrote that tweet in my pajamas. For the amount of thought that Paul Graham put in his tweet, he probably wrote it in his pajamas too. Nothing against Paul Graham, he is admirable and brilliant and his tweet provoked an interesting question.
</p>
<p>
And the main reason the USA's fraction of "the most talented people" is a mediocre 6.7%, despite having a mean IQ of 97, much higher than the global mean IQ of 87 points, is because China's mean IQ is so damn high at 104 points. We have good reason to believe that, despite being 18% of the global population, Chinese nationals account for the majority of "the most talented people" (they are probably 58% of the global top 5% of IQ scores). This does not come as a surprise to anyone who has thought to Google Image search <a href="https://www.google.com/search?q=usa+imo+team&hl=en&tbm=isch">"USA IMO team"</a>.
</p>
<p style="text-align:center"><img src=/assets/img/China_IQ_threshold_graph.png></p>
<h3>Notes</h3>
<ol>
<li>
<a href='#FL1' id="FN1">^</a> David Becker's dataset at <a href="https://viewoniq.org/">https://viewoniq.org/</a> is now the standard dataset for national mean IQ scores, accumulating decades worth of tabulation led by Richard Lynn. An older version of the dataset was used by John Walker in 2004 to create an <a href="https://www.fourmilab.ch/documents/IQ/1950-2050/">infographic</a> about a possible future for global average IQ.
</br>I seem to remember that Jelte Wicherts had a competing dataset of national IQ scores with higher scores in African countries, but I have no idea where to find Wicherts' data.
</li>
<li>
<a href='#FL2' id="FN2">^</a> via <a href="https://www.unz.com/anepigone/average-iq-of-college-undergrads-and-graduate-degree-holders-by-decade/">Audacious Epigone</a>. GSS wordsum scores are a lossy substitute for IQ scores, so 104 should be considered a lower bound to the average IQ of graduate degree holders.
</li>
</ol>
</body>Mormon Fertility: 6 indicators2021-03-19T00:00:00+00:002021-03-19T00:00:00+00:00https://eternalanglo.com/mormon-fertility-indicators<style>
h1, h2, h3, h4, h5, h6 {
margin-bottom: 10px;
margin-top: 15px;
}
</style>
<p>I discovered that the CDC keeps a record of <a href=https://www.cdc.gov/nchs/data_access/vitalstatsonline.htm>every birth certificate in America</a> going back to 1968 (at least the metadata). You can actually download all the metadata yourself, but the version they let you download redacts all the geographic (county) data. Which makes it kind of useless. BUT you can query the data for certain statistics through <a href=https://wonder.cdc.gov/>wonder.cdc.gov</a>.</p>
<p>There are a few things I've been "wondering" about Mormons and their famously-high fertility since I saw <a href=https://www.cdc.gov/nchs/data/nvsr/nvsr68/nvsr68_01-508.pdf>this report</a> which said the white fertility in Utah fell below replacement-level in 2017. So I queried the data for 3 representative geographies: the first obvious one being Utah (the Mormon Mothership) but Utah is pretty multicultural these days so you can't get an accurate picture of what's happening with the Mormons just by looking at Utah. Two much better geographies are Utah County, Utah (home of Brigham Young University) and Bonneville County, Idaho (neighbor of Brigham Young University - Idaho). These two yuge 99% Mormon universities make both of these counties nearly Mormon-monocultural so they should be great indicators of the current fertility rate in the Mormon community. Here are the results:</p>
Edit 10:30PM MST: Thank you <a href=https://twitter.com/PoisonAero>@PoisonAero</a> for correcting the calculations! Now they are actually the Total Fertility Rate, and not the Crude Fertility Rate.<br>
Edit 29 Oct 2021, 8:00PM MST: Updated charts adding 2020 Natality data<br>
Edit 3 Dec 2022, 10:30AM MST: Updated charts adding 2021 Natality data
<p style="text-align:center"><img src=/assets/img/mormon-fertility-6-indicators.png></p>
The fertilty rate of Utah County fell 25.0% from 3.04 in 2005 to 2.28 in 2021. The White (Non-Hispanic white) fertility rate of Utah County fell 25.8% from 2.98 in 2005 to 2.21 in 2021.
<h3>Sources:</h3>
Every value in the "Fertility Rate per 1,000" column of the following tables is an average annual fertility of women over a 5-year age range. To convert to Total Fertility Rate (TFR), sum the cohort-fertility rates together, multiply by 5, and divide by 1000.
<h4>Everyone:</h4>
2003-2006 <a href=https://wonder.cdc.gov/controller/saved/D27/D315F685>https://wonder.cdc.gov/controller/saved/D27/D315F685</a><br>
2007-2015 <a href=https://wonder.cdc.gov/controller/saved/D66/D315F693>https://wonder.cdc.gov/controller/saved/D66/D315F693</a><br>
2016-2021 <a href=https://wonder.cdc.gov/controller/saved/D149/D315F694>https://wonder.cdc.gov/controller/saved/D149/D315F694</a><br>
<h4>Non-Hispanic Whites:</h4>
2003-2006 <a href=https://wonder.cdc.gov/controller/saved/D27/D315F695>https://wonder.cdc.gov/controller/saved/D27/D315F695</a><br>
2007-2015 <a href=https://wonder.cdc.gov/controller/saved/D66/D315F690>https://wonder.cdc.gov/controller/saved/D66/D315F690</a><br>
2016-2021 <a href=https://wonder.cdc.gov/controller/saved/D66/D315F691>https://wonder.cdc.gov/controller/saved/D66/D315F691</a><br>
<h3>Addendum</h3>
<p>Due to expressed interest, I have created a chart that shows the fertility rate of every county in Utah with available data (there were only 6 available counties). I have updated the source links as well; they now link to tables that include all available counties in Utah and Idaho.</p>
<p>If you compare to the <a href=https://www.sltrib.com/religion/2018/12/09/salt-lake-county-is-now/>SLTRIB chart</a> that shows percent LDS for each county in Utah, you will see there is an almost 1-to-1 ordering between "percent LDS" and TFR.</p>
<p style="text-align:center"><img src=/assets/img/fertility-Utah-and-available-counties.png></p>
<h3>Cohort fertility in Utah County</h3>
<p>Utah County serves as a useful case study to see what is happening to fertility by age group. There have been large declines in cohort-fertility rate for 20-29 year olds while the cohort-fertility rate of 30-39 year olds has remained stable.</p>
<p style="text-align:center"><img src=/assets/img/cohort-fertility-utah-county.png></p>
<p>I added a horizontal dashed line to the graph at the 105 births per 1000 population mark. There are 6 female cohorts plotted in the graph but only 4 of the cohorts contribute to the total fertility rate in a non-negligible way (20-24 years, 25-29 years, 30-34 years, and 35-39 years). The dashed line represents the average fertility these 4 cohorts must reach by themselves to push the total fertility rate above replacement.</p>I discovered that the CDC keeps a record of every birth certificate in America going back to 1968 (at least the metadata). You can actually download all the metadata yourself, but the version they let you download redacts all the geographic (county) data. Which makes it kind of useless. BUT you can query the data for certain statistics through wonder.cdc.gov. There are a few things I've been "wondering" about Mormons and their famously-high fertility since I saw this report which said the white fertility in Utah fell below replacement-level in 2017. So I queried the data for 3 representative geographies: the first obvious one being Utah (the Mormon Mothership) but Utah is pretty multicultural these days so you can't get an accurate picture of what's happening with the Mormons just by looking at Utah. Two much better geographies are Utah County, Utah (home of Brigham Young University) and Bonneville County, Idaho (neighbor of Brigham Young University - Idaho). These two yuge 99% Mormon universities make both of these counties nearly Mormon-monocultural so they should be great indicators of the current fertility rate in the Mormon community. Here are the results: Edit 10:30PM MST: Thank you @PoisonAero for correcting the calculations! Now they are actually the Total Fertility Rate, and not the Crude Fertility Rate. Edit 29 Oct 2021, 8:00PM MST: Updated charts adding 2020 Natality data Edit 3 Dec 2022, 10:30AM MST: Updated charts adding 2021 Natality dataFertility by Race by Region, New Zealand2020-05-13T00:00:00+00:002020-05-13T00:00:00+00:00https://eternalanglo.com/map-nz<!DOCTYPE html>
<html>
<head>
<meta charset = 'utf-8'>
<link rel="stylesheet" type="text/css" href="/_css/choropleth.css">
</head>
<body><div>
<h2>Fertility Project</h2>
<ul>
<li><a href="/fertility-map-united-states">United States</a></li>
<li><a href="/fertility-map-canada">Canada</a></li>
<li><a href="/fertility-map-british-isles">British Isles</a></li>
<li><a href="/fertility-map-australia">Australia</a></li>
<li><a href="/fertility-map-new-zealand">New Zealand</a></li>
<li><a href="/fertility-appendix">Appendix</a></li>
</ul>
</div>
<div>
<h1>Instructions:</h1>
<noscript>Requires javascript enabled.</noscript>
<p> Hover mouse over geographic area to see the
<a href="/fertility-appendix#Computed_Variables" style="text-decoration: underline;">CRR</a/> and the
<a href="/fertility-appendix#Computed_Variables" style="text-decoration: underline;">ACE</a> for the given
<a href="/fertility-appendix#Racial_Designations" style="text-decoration: underline;">racial group</a> in that area.
<br>Scroll to zoom. Click and drag to move. Use widget below to switch between year, region, racial group, and color scheme.
</p>
</div>
<div id="widget-nz">
<svg class="choropleth" id="choropleth-nz" viewBox="0 0 960 600"> </svg>
</div>
<div id="tooltip"></div>
</body><script src="https://d3js.org/d3.v4.min.js"></script>
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<script src="https://unpkg.com/d3-simple-slider"></script>
<script src="/_js/fertility-choropleth.js"></script>
<script src="/_js/fertility-choropleth-nz.js"></script>
</html>Fertility by Race by Region, Australia2020-05-12T00:00:00+00:002020-05-12T00:00:00+00:00https://eternalanglo.com/map-australia<!DOCTYPE html>
<html>
<head>
<meta charset = 'utf-8'>
<link rel="stylesheet" type="text/css" href="/_css/choropleth.css">
</head>
<body><div>
<h2>Fertility Project</h2>
<ul>
<li><a href="/fertility-map-united-states">United States</a></li>
<li><a href="/fertility-map-canada">Canada</a></li>
<li><a href="/fertility-map-british-isles">British Isles</a></li>
<li><a href="/fertility-map-australia">Australia</a></li>
<li><a href="/fertility-map-new-zealand">New Zealand</a></li>
<li><a href="/fertility-appendix">Appendix</a></li>
</ul>
</div>
<div>
<h1>Instructions:</h1>
<noscript>Requires javascript enabled.</noscript>
<p> Hover mouse over geographic area to see the
<a href="/fertility-appendix#Computed_Variables" style="text-decoration: underline;">CRR</a/> and the
<a href="/fertility-appendix#Computed_Variables" style="text-decoration: underline;">ACE</a> for the given
<a href="/fertility-appendix#Racial_Designations" style="text-decoration: underline;">racial group</a> in that area.
<br>Scroll to zoom. Click and drag to move. Use widget below to switch between year, region, racial group, and color scheme.
</p>
</div>
<div id="widget-australia">
<svg class="choropleth" id="choropleth-australia" viewBox="0 0 960 600"> </svg>
</div>
<div id="tooltip"></div>
</body><script src="https://d3js.org/d3.v4.min.js"></script>
<script src="https://d3js.org/d3-scale-chromatic.v1.min.js"></script>
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<script src="https://d3js.org/topojson.v2.min.js"></script>
<script src="https://unpkg.com/d3-simple-slider"></script>
<script src="/_js/fertility-choropleth.js"></script>
<script src="/_js/fertility-choropleth-australia.js"></script>
</html>Fertility by Race by Region, British Isles2020-05-11T00:00:00+00:002020-05-11T00:00:00+00:00https://eternalanglo.com/map-british<!DOCTYPE html>
<html>
<head>
<meta charset = 'utf-8'>
<link rel="stylesheet" type="text/css" href="/_css/choropleth.css">
</head>
<body><div>
<h2>Fertility Project</h2>
<ul>
<li><a href="/fertility-map-united-states">United States</a></li>
<li><a href="/fertility-map-canada">Canada</a></li>
<li><a href="/fertility-map-british-isles">British Isles</a></li>
<li><a href="/fertility-map-australia">Australia</a></li>
<li><a href="/fertility-map-new-zealand">New Zealand</a></li>
<li><a href="/fertility-appendix">Appendix</a></li>
</ul>
</div>
<div>
<h1>Instructions:</h1>
<noscript>Requires javascript enabled.</noscript>
<p> Hover mouse over geographic area to see the
<a href="/fertility-appendix#Computed_Variables" style="text-decoration: underline;">CRR</a/> and the
<a href="/fertility-appendix#Computed_Variables" style="text-decoration: underline;">ACE</a> for the given
<a href="/fertility-appendix#Racial_Designations" style="text-decoration: underline;">racial group</a> in that area.
<br>Scroll to zoom. Click and drag to move. Use widget below to switch between year, region, racial group, and color scheme.
</p>
</div>
<div id="widget-british">
<svg class="choropleth" id="choropleth-british" viewBox="0 0 960 600"> </svg>
</div>
<div id="tooltip"></div>
</body><script src="https://d3js.org/d3.v4.min.js"></script>
<script src="https://d3js.org/d3-scale-chromatic.v1.min.js"></script>
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<script src="https://d3js.org/topojson.v2.min.js"></script>
<script src="https://unpkg.com/d3-simple-slider"></script>
<script src="/_js/fertility-choropleth.js"></script>
<script src="/_js/fertility-choropleth-british.js"></script>
</html>Fertility by Race by Region, Canada2020-05-10T00:00:00+00:002020-05-10T00:00:00+00:00https://eternalanglo.com/map-canada<!DOCTYPE html>
<html>
<head>
<meta charset = 'utf-8'>
<link rel="stylesheet" type="text/css" href="/_css/choropleth.css">
</head>
<body><div>
<h2>Fertility Project</h2>
<ul>
<li><a href="/fertility-map-united-states">United States</a></li>
<li><a href="/fertility-map-canada">Canada</a></li>
<li><a href="/fertility-map-british-isles">British Isles</a></li>
<li><a href="/fertility-map-australia">Australia</a></li>
<li><a href="/fertility-map-new-zealand">New Zealand</a></li>
<li><a href="/fertility-appendix">Appendix</a></li>
</ul>
</div>
<div>
<h1>Instructions:</h1>
<noscript>Requires javascript enabled.</noscript>
<p> Hover mouse over geographic area to see the
<a href="/fertility-appendix#Computed_Variables" style="text-decoration: underline;">CRR</a/> and the
<a href="/fertility-appendix#Computed_Variables" style="text-decoration: underline;">ACE</a> for the given
<a href="/fertility-appendix#Racial_Designations" style="text-decoration: underline;">racial group</a> in that area.
<br>Scroll to zoom. Click and drag to move. Use widget below to switch between year, region, racial group, and color scheme.
</p>
</div>
<p>"Rural" (Province) means all the area of (Province) that is not part of a Census Metropolitan Area or Census Agglomeration.</p>
<div id="widget-canada">
<svg class="choropleth" id="choropleth-canada" viewBox="0 0 960 600"> </svg>
</div>
<div id="tooltip"></div>
</body><script src="https://d3js.org/d3.v4.min.js"></script>
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<script src="https://d3js.org/topojson.v2.min.js"></script>
<script src="https://unpkg.com/d3-simple-slider"></script>
<script src="/_js/fertility-choropleth.js"></script>
<script src="/_js/fertility-choropleth-canada.js"></script>
</html>Fertility by Race by Region, United States of America2020-05-07T00:00:00+00:002020-05-07T00:00:00+00:00https://eternalanglo.com/map-usa<!DOCTYPE html>
<html>
<head>
<meta charset = 'utf-8'>
<link rel="stylesheet" type="text/css" href="/_css/choropleth.css">
</head>
<body><div>
<h2>Fertility Project</h2>
<ul>
<li><a href="/fertility-map-united-states">United States</a></li>
<li><a href="/fertility-map-canada">Canada</a></li>
<li><a href="/fertility-map-british-isles">British Isles</a></li>
<li><a href="/fertility-map-australia">Australia</a></li>
<li><a href="/fertility-map-new-zealand">New Zealand</a></li>
<li><a href="/fertility-appendix">Appendix</a></li>
</ul>
</div>
<div>
<h1>Instructions:</h1>
<noscript>Requires javascript enabled.</noscript>
<p> Hover mouse over geographic area to see the
<a href="/fertility-appendix#Computed_Variables" style="text-decoration: underline;">CRR</a/> and the
<a href="/fertility-appendix#Computed_Variables" style="text-decoration: underline;">ACE</a> for the given
<a href="/fertility-appendix#Racial_Designations" style="text-decoration: underline;">racial group</a> in that area.
<br>Scroll to zoom. Click and drag to move. Use widget below to switch between year, region, racial group, and color scheme.
</p>
</div>
<p>CBSA = Core-Based statistical area</p>
<p>PSA = Primary statistical area</p>
<p>MSA = Metropolitan or Micropolitan statistical area</p>
<p>CSA = Combined statistical area</p>
<div id="widget-usa">
<svg class="choropleth" id="choropleth-usa" viewBox="0 0 1060 500"> </svg>
</div>
<div id="tooltip"></div>
</body><script src="https://d3js.org/d3.v4.min.js"></script>
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<script src="https://unpkg.com/d3-simple-slider"></script>
<script src="/_js/fertility-choropleth.js"></script>
<script src="/_js/fertility-choropleth-usa.js"></script>
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