Commenter pumpkinhead doubts Oprah’s head is as big as I say it it, writing:

 Given this information of 1358 cc cranial capacity(for white females mind you) and 91 SD, Oprah would be 7.45 SD above average making her 1 in the tens of trillions.

I don’t want to argue about Oprah’s head size here since we’re already having that argument in the previous thread, but rather I want to make a more general point.

The problem with pumpkinhead’s argument is it assumes cranial capacity fits the Gaussian curve which is a reasonable assumption for non-pathological heads, but there’s just one problem with it.  If head circumference is normally distributed, and head circumference has a cubic relationship with cranial capacity, then extreme cranial capacity can not be normally distributed.

For example, the late J.P. Rushton suggested that at least in very young children, cranial capacity ( cm³ ) = circumfence³/118.4.  This is the formula for a volume of a hemisphere, which as Rushton acknowledged, is an oversimplification, because the cranium is not a perfect hemisphere and there is massive individual variation in head shape.

But let’s imagine a world where all crania were perfect hemispheres.  I randomly generated 60 crania and these had a mean of 54.7 cm (SD 1.28 cm which because of my small sample size, is slightly smaller than the actual U.S. female SD).  In this sample, the one in several billion level (+6.3 SD) would be reached at 62.76 cm.

Now what happens when all the circumferences are converted into cranial capacity using the hemisphere formula.  The mean becomes 1387 cm³  and the SD becomes 97.  What this means is that a head that is +6.3 SD in circumference (62.38 cm), becomes +7.2 SD in cranial capacity (2088 cm³ ).  So the cubic effect of going from circumference to volume make extreme humans seem superhuman.

Of course our crania are not perfect hemispheres, but the cubic effect still applies.

You would think that after the civil rights movement and half a century of affirmative action, that the racial income gap would be closing, but nothing could be further from the truth.

People look at billionaire media queen Oprah and President Obama and think blacks have made real progress. FALSE!  Oprah has made real progress because she was born with a freakishly large brain and she used that brain power to not only make herself a success, but to put the Obamas in the White House.

However without this rare genetic mutation that caused one person to jump from poverty to Queen of the World in record time,   there’s been little progress.

And yes I realize a genetic mutation is a “just-so story” but if other people get to tell them, why not me?  At least I have physical evidence.

They year was 1968.  Aretha Franklin (aka Queen of Soul) was getting into her limo in Milwaukee.

A young black runaway approached her sobbing. asking for money.  The generous star handed the girl $100 U.S. (that’s $724 in today’s dollar).

Little did she know that young girl would grow up to be the World’s ONLY black billionaire and the most influential woman on the planet.

In Aretha’s day, the idea that a black woman could be become such an influential billionaire was unimaginable, but thanks to the trail Aretha helped blaze, they are finally getting their R-E-S-P-E-C-T.

When I was a child, I didn’t understand that adults were more intelligent than children.  I thought adults just seemed smarter because they had more experience, but I didn’t realize there were biological changes in the brain that made them smarter.

Similarly there are some anthropologists like Sally McBrearty and Alison Brooks who argue that late stone age humans were just as smart as modern people, they just didn’t have as much time to accumulate culture, since our species was very young then.

This begs the question, since cultural evolution happens so much faster than biological evolution, how do we know when cultural progress reflects biological progress?

Most kids don’t study calculus until their later teens.  Is this because they’re not biologically ready until the brain approaches adulthood, or they simply haven’t had time to acquire the prerequisite knowledge?

Similarly representational art does not appear before the upper paleolithic?  Was this because our species wasn’t biologically ready, or not culturally ready?

Perhaps one way to tell is to look at the growth curve.  If knowledge or culture is progressing gradually in a person or our species, there’s no reason to suspect it’s anything more than cultural progress, but if the growth suddenly starts accelerating, then maybe cultural has had some help from biology.

For example, after 150,000 long  years of being confined to Africa, and being just one of several homo species on Earth, anatomically modern humans suddenly colonized six other continents,  created representational art, and replaced all other Homo species, in just 40,000 years.  This was such a massive change in our trajectory that scientists like Richard Klein think it must have been a biological leap in evolution, stating:

What happened 40,000 or 50,000 years ago was the last major change in the genotype. At least the last major biological change. Evolution continues, but the evolution that’s involved in making us capable of wielding this vast variety of cultures–that probably stopped around 40,000 or 50,000 years ago and there’s been no essential change since.

Mitchell Leslie writes:

Forget about the construction of the first cities or the introduction of the internal combustion engine. The revolution that made the biggest difference occurred on the savanna of East Africa roughly 45,000 years ago, Klein and others maintain.

Stephen Jay Gould agreed with Klein, famously stating:

There has been no biological change in humans in 40,000 or 50,000 years. Everything we call culture and civilization we’ve built with the same body and brain

However is the Upper Paleolithic Revolution really that much more dramatic than other revolutions that have since followed it?  Since cultural change is hard to judge, perhaps the most objective measure of humanity’s progress is population size.

It took us 200,000 years to reach a population size of 1 billion people,  and yet in just the last few centuries we’ve hit 7 billion!  That seems like a much bigger revolution than the Upper Paleolithic.  The Upper Paleolithic may have been when modern humans left Africa, but the industrial revolution is when humans left the Earth!

So why do people like Richard Klein invoke a massive brain mutation to explain the Upper Paleolithic, but feel no genetic explanation is needed for the industrial revolution?  Is this just political correctness or was the Upper Paleolithic genuinely in a class of its own?

I’m skeptical that a genetic mutation caused either, but just as biological evolution happens in sudden growth spurts (punctuated equilibrium model), perhaps cultural evolution does the same.

Here’s Klein discussing his views:

For many human traits, it’s perfectly obvious what it means to have twice as much.  A six-foot tall man is twice as tall as a three foot tall man.  Someone who can lift 300 lbs is twice as strong as someone who can lift 150 lbs.  Someone who can run 100 meters in 10 seconds is twice as fast as someone who can run it in 20 seconds.

It becomes more difficult to apply the same logic to IQ.  Although we can say a 2000 cubic centimeter brain is twice as big as a 1000 cubic centimeter brain, we can’t necessarily say it’s twice as smart (on average) because we don’t know if the relationship between intelligence and brain size is linear.

I do think the relationship between brain size and IQ is linear (excluding pathological cases) but that’s because brain size is normally distributed and IQ is largely forced to fit a normal curve, however that doesn’t mean intelligence itself is normally distributed.

On the contrary, a member of Prometheus society once claimed that because the human mind works in parallel, complex learning and problem solving speed doubles every 10 IQ points (he later revised to every 5).

To test this fascinating this hypothesis, I imagined people taking the WAIS-R IQ test.  Because several subtests (Arithmetic, Block Design and Object Assembly) awarded bonus points for super fast performance, it was possible to imagine a person perfectly  solving all the items within the time limit, but using 100% of the allotted time.

Such a person would have an Arithmetic IQ of 105,  a Block Design IQ of 100, and an Object Assembly IQ of 90.

Then I asked what would happen if the same person had only used 50% of the allotted time:  Arithmetic IQ 105, Block Design IQ of 105, and Object Assembly IQ of 90.

25% of the allotted time:  Arithmetic IQ 110, Block Design IQ 120, Object Assembly IQ 100.

12.5% of the allotted time: Arithmetic IQ 135, Block Design IQ 145, Object Assembly IQ 125.

6.25% of the allotted time:  This speed takes you beyond the ceiling of all subtests except Object Assembly for which you would score an Object Assembly IQ of 140

It’s hard to draw strong conclusions because David Wechsler arbitrarily decided how much speed was needed for a bonus point, but on balance it looks like a doubling of speed on a particular subtest, equates to a jump of 10 or 15 IQ points (on that subtest)

But how do we reconcile such an explosive distribution with the popular notion of a bell shaped IQ curve, which Jensen assumed IQ likely had given the fact that linear regression predicts IQs of one’s relatives and biological correlates of IQ like brain size enjoy a bell curve.

And indeed some psychometric tasks really do enjoy a true curve (without test takers having to force one).  The number of digits you can repeat from memory, or the number of abstract symbols you can copy in 90 seconds or even in the number of words in your vocabulary (when randomly selected from a dictionary) all increase in a linear way with IQ, which means all must form the same bell curve.

So my guess is that the building blocks of intelligence (brain size, memory, raw neural speed) are all normally distributed yet actual complex problem solving and real world adaptive behavior show huge inequality, perhaps because a few extra units of data can double the number of interrelations between them, so the amount of information we can process is normally distributed, but the output of that data is explosively distributed.

So what does it mean to be twice as smart?  Well, if you define intelligence as the cognitive capacity for problem solving or goal directed adaptive behavior, then being twice as smart means either the ability to solve twice as many problems or the ability to solve the same amount of problems twice as well.

If we assume most problems in the universe are complex problems, then I’d say an extra 13 math IQ points makes you twice as smart mathematically, an extra 13 spatial IQ points makes you twice as smart spatially etc.

But since different cognitive abilities are imperfectly correlated,  I’d say it takes 19 overall IQ points to be twice as smart overall (all domains averaged together).

So assuming mature apes have an IQ of 14, we can very tentatively conclude the following (for young adults):

IQ 14:  1 times smarter than an ape

IQ 33:  2 times smarter than ape

IQ 52:  4 times smarter than an ape

IQ 71: 8 times smarter than an ape

IQ 90: 16 times smarter than an ape

IQ 109: 32 times smarter than an ape

IQ 128: 64 times smarter than an ape

IQ 147: 128 times smarter than an ape

IQ 166: 256 times smarter than an ape

IQ 185: 512 times smarter than an ape

IQ 204: 1,024 times smarter than an ape

So instead of asking people their IQ, you can ask them their MiQ pronounced My Cue (monkey intelligence quotient).  A MiQ of 16 to 32 (16 to 32 times smarter than an anthropoid monkey) implies average intelligence for young adults in developed countries.  A MiQ below 8 implies impairment in a young adult but would mean gifted in a toddler.

So even though the average human brain is roughly 4 times bigger than the average ape’s, the human mind is roughly 20 times bigger.

[Please post off-topic comments here and not in the main thread]

There’s a fascinating article in The Ringer about how Tom Cruise jumping on Oprah’s couch was one of the most important pop-culture events of the 21st century, and transformed the nature of media and celebrity in America.  It goes down in history as the moment celebrities lost control of the narrative and the internet took over.

As I recall, Cruise was there to promote the movie War of the Wolds but the interview got side tracked because Cruise was so “in love” with Katie Holmes that he could hardly concentrate on Oprah’s questions and instead just jumped on her couch like a lovesick schoolboy.

I found the show entertaining, but when I checked the internet after, a storm was brewing.  Many gay men were swarming gossip sites to say “TOM YOU ARE GAY!” and were furious that he went on Oprah acting fanatically hetero.

Many gay men are attracted to Tom Cruise and thus want to believe he is gay, and don’t like it when their most iconic “gays” deny their “gayness”.

We see a similar phenomenon in the black community.  When Tiger Woods told Oprah he was “Cablinasian” (Caucasian + Black + Indian + Asian) many blacks stormed the media screaming “TIGER YOU ARE BLACK!!!”

Commenter Mug of Pee was mentioning professor James Lee, who was recently interviewed by Spencer Wells and Razib Khan.

The interview describes a study where a genomic formula predicted 11-13% of the variance  in educational attainment (highest degree or diploma obtained).

Taking the square root, it implies that known common genetic variants correlate 0.35 with education, however Lee cautions that population stratification can inflate these numbers.  He cites the cliché  that chopstick use would seem highly genetic if the sample were a mix of Chinese and non-Chinese people, but the heritability would be misleading because it’s not that many genomic variants are causing chopstick use, but rather they’re signaling Chinese ancestry, which in-turn causes chopstick use.

To avoid the problem of population stratification in the study Lee co-authored, they looked at within family data (I guess because siblings all belong to the same sub-population) but found that the effect size of their predictors were 40% smaller.  I guess that means instead of common SNPs correlating 0.35 with education, they correlated 0.21, now explaining only 4% of the variance?

I wonder if these numbers are distorted by range restriction because families have less variance than the general population and that’s known to depress correlations.

The following chart shows height and IQ as a function of race and gender (note: these are average differences and genius IQs and giant heights exist in all races and genders):

Table I

IQ stats were estimated here. Height stats for men and women were taken from tables 12 and 10 of this document respectively (Americans aged 20-39 in 2011-2014).  Although height standard deviations were not reported, they can be calculated by multiplying the standard errors by the sample size.

In the below chart I estimate the average IQ of each race, sex, height combination.

Average IQ by height for 6 U.S. demographics (excluding pathological conditions causing extreme height)

The chart assumed a 0.244 correlation between IQ and height within sex and race, based on a massive study of   of 76,111 young Danish men.  IQs for each height were estimated by assuming that for every 1 standard deviation increase in height (within each race-sex demographic), IQ would increase by 0.244 SDs on average (each demographic’s SD were estimated in table I).

The chart suggests that on average a  black man needs to be nearly two feet taller than an Asian woman in order to have a higher IQ, and that when black men and Asian women are the same height, the IQ gap approaches two standard deviations.

Sadly, this suggests black men will have an incredibly difficult time dating taller Asian women  because the Asian woman will not only feel smarter and if she’s a racist, more evolved, but she’ll be disgusted that in the one area where the black man is supposed to be better (physicality), she surpasses him too, so her level of disrespect will be off the charts.  If the shorter black man is well built, this might help him compensate, or it will make the problem worse given the extra IQ penalty of big muscles and because women may expect even more height from muscular men.

Previously I displayed a table showing sex differences in IQ in a general British sample where the mean and standard deviation (SD) of the sex-combined population was set at 100 and 15 respectively:

If we look at 16-year-olds in table 2, what we see is that with respect to the sex-combined distribution,  males have an IQ Z score of +0.05 with an SD of 1.04, and females have a Z score of -0.05 with an SD of 0.95.

In a previous article I noted that the sex-combined distributions for U.S. whites, blacks and Asians were 100 (SD = 15), 83 (SD = 15.4) and 103 (SD 16.6) respectively (white norms).

If we assume that within each ethnic group, men and women have the same Z scores with respect to the group’s sex-combined distribution, we get the following stats:

Asian American males: 104 (SD 17.3)

Asian American females: 102 (SD 15.8)

White American males: 101 (SD 15.6)

White American females: 99 (SD 14.3)

African American males: 84 (SD 16)

African American females: 82 (SD 14.6)

Here’s some data from the WAIS-IV IQ tests about U.S. ethnic differences in IQ

Contrary to popular stereotypes, Asian Americans are not lopsided intellects who only outscore whites in mathematical or spatial ability, but actually outscore them in every index, including verbal.  Of course Asian Americans are not a representative sample of all Asians.

And contrary to the stereotype that whites are the most cognitively variable ethnic group, their full-scale IQs in this data-set actually show the smallest standard deviation of any U.S. ethnic group, though this could be be because Asian Americans are not a single race.

The scores above use U.S. norms, meaning 100 and 15 are scaled to be the mean and standard deviation for all Americans.  If we instead use white norms, (i.e. set the white mean and SD at 100 and 15 respectively), we find that  African Americans have a full-scale IQ of 83 (SD = 15.4), Hispanics score 87 (SD = 15.5), and Asian Americans average 103 (SD = 16.6).