One of the dangers of having an IQ way off in the stratosphere is that the average American is literally mentally retarded compared to you, and because they can’t understand how you made all your money, they assume you must be some kind of evil witch, out to do them harm.

If Bill Gates’s IQ is anywhere near as high as the SAT measured it (IQ 170), then Bill Gates is to the U.S. population as the average American is to the Downs Syndrome population.

If the average American woke up to find the rest of the country had Downs Syndrome, they would understand what it’s like to be Bill Gates. They would easily become the richest person without even trying, but they would soon encounter jealousy and resentment (as Bill Gates faced when the justice department attacked Microsoft in the 1990s) and if they tried to help the masses, it might backfire spectacularly.

The New York Times writes:

Mr. Gates, 64, the Microsoft co-founder turned philanthropist, has now become the star of an explosion of conspiracy theories about the coronavirus outbreak. In posts on YouTube, Facebook and Twitter, he is being falsely portrayed as the creator of Covid-19, as a profiteer from a virus vaccine, and as part of a dastardly plot to use the illness to cull or surveil the global population…

…Misinformation about Mr. Gates is now the most widespread of all coronavirus falsehoods tracked by Zignal Labs, a media analysis company. The misinformation includes more than 16,000 posts on Facebook this year about Mr. Gates and the virus that were liked and commented on nearly 900,000 times, according to a New York Times analysis. On YouTube, the 10 most popular videos spreading lies about Mr. Gates posted in March and April were viewed almost five million times.

…Mr. Gates, who is worth more than $100 billion, has effectively assumed the role occupied by George Soros, the billionaire financier and Democratic donor who has been a villain for the right. That makes Mr. Gates the latest individual — along with Dr. Anthony Fauci, the leading U.S. infectious disease expert — to be ensnared in the flow of right-wing punditry that has denigrated those who appear at odds with Mr. Trump on the virus…

…His disdain for Mr. Trump, whom he has met several times, has also become public. In 2018, footage surfaced of Mr. Gates recounting how Mr. Trump needed help distinguishing H.I.V., which refers to the human immunodeficiency virus and causes AIDS, from HPV, which is the human papillomavirus, a sexually transmitted infection.

“Both times he wanted to know if there was a difference between H.I.V. and HPV, so I was able to explain that those are rarely confused with each other,” Mr. Gates said to laughter in comments to his foundation.

Commenter Billy was kind enough to share with us the raw scores he obtained on the WAIS-IV and I have converted these into scaled scores and composite scores. I apologize to the other people who have also asked me to do this for them, but Billy just happened to ask when I had more free time and his demographics make him a unique case study.

Billy is a young American black man born to an upper-class immigrant family. Despite spending his early childhood in sub-Saharan Africa and not learning English until coming to the U.S. at around age eight, Billy obtained one of his highest scores on the culturally loaded Vocabulary subtest.

Below are Billy’s scores. Note that the subtests are scored on a scale from 1 to 19, where 10 is the U.S. mean for one’s age and 3 is the standard deviation. This is comparable to the distribution of male U.S. height, where in the peak age group, the mean is about 10 inches (above five feet) and the standard deviation is about 3 inches.

Presumably Billy took the WAIS-IV circa 2020 (14 years after it was normed). Because older tests tend to give inflated results, in the far right column I have adjusted all of the scores for the Flynn effect. The unadjusted scores are probably too high but the adjusted scores are probably too low because the Flynn effect might not be as large as folks think and may have plateaued or even reversed since 2006 (we’ll know better when the WAIS-V comes out).

Normally the WAIS-IV includes the subtests Information (general knowledge) and Block Design (spatial analysis) but for whatever reason, Billy’s examiner decided to use optional subtests (Comprehension and Figure Weights) respectively. Such substitutions are allowed as long as the examiner makes them a priori, and not to help or hurt a particular subject’s scores.

Billy wrote the following in the comment section:

Like I said, it’s unofficial, so I was tested out of convenience; not from a professional. Though my personal reason outside of knowing my IQ is knowing where I’m deficient – or my cognitive profile. Based on my Mensa scores, a wonderlic at 75th percentile while a passing RAIT score just doesn’t hint at a stable profile for me. I seem to have a hard time concentrating on tasks, so I figured it’s probably a working memory and or processing speed issue. I’ve never been tested for a mental illness.

Billy’s profile shows Verbal Comprehension > Perceptual Reasoning > Working Memory > Processing Speed.

Unfortunately the WAIS-IV lumps Visual Abstraction (Matrix Reasoning and Figure Weights) into the same category as Spatial Reasoning (Visual Puzzles) creating a meaningless hybrid known as “Perceptual Reasoning index”. However if we untangle these two abilities, we see that Billy’s Visual Abstraction is almost as high as his Verbal Comprehension (both domains are highly g loaded) and that his Spatial Reasoning is somewhat lower than his Working Memory.

He’s comfortably above average in all domains, but his weak point is Processing Speed, probably because this is the least g loaded domain. It might also imply a weakness in Executive Function, but we’d need neurological testing to infer that. His very superior score in Comprehension implies high social intelligence; on the other hand Comprehension was lower than his other Verbal Comprehension scores. Had the WAIS-IV not foolishly removed the Picture Arrangement subtest, we’d have a fuller look at his social cognition.

Billy’s relatively low scores on Processing Speed and Arithmetic probably explain why he underperformed on the Wonderlic, a speed based test with a lot of number crunching.

Overall Billy is a man of incredibly high intelligence who should succeed at almost anything he sets his mind to. The results may even understimate his IQ, especially in the verbal comprehension sphere, because of his delayed exposure to English and U.S. culture.

On the other hand, the fact that Billy’s English vocabulary is so high despite such delayed exposure to English is consistent with research showing the impotence of early childhood intervention. For a more extreme example, see The Case of Isabelle.

James Flynn writes:

…Current environment is surprisingly self-contained: it influences one’s current cognitive abilities with very little interference from past environments. Most of us assume that your early family environment leaves some sort of indelible mark on your intelligence throughout life. But the literature shows that this is simply not so.

From page 6 of Does Your Family Make You Smarter? by James Flynn.

Imagine a pushy mother really wants her average 9.5-year-old son to get into a gifted class. Because IQ tests are normed for age and her son looks young for his age, she decides to tell the psychologist he’s only 6.5, so that he will get a much higher score.

Now assuming the boy is average for a 9.5-year-old in all cognitive domains he should score an age-ratio IQ of 146 in all domains, if the psychologist believes he’s 6.5 (because 9.5 is 146% of 6.5), however modern IQ tests use the deviation scale, where scores are assigned not by how many years advanced a kid is, but by one’s rank, relative to other American kids in one’s own age group. Being in the top 99% gives one an IQ of 65, being in the top 90% gives one an IQ of 80, being in the top 50% gives one an IQ of 100, being in the top 10% gives one an IQ of 120, and being in the top 1% gives one an IQ of 135, and being in the top 0.1% gives one an IQ of 146 etc.

Now obviously the average 9.5-year-old pretending to be a 6.5-year-old will get a high IQ in every domain, but his margin of superiority varies dramatically depending on the test. If he taken the WISC-R for example (before the norms expired), here’s how he’d have scored (for the readers convenience, I converted subtest scores, normally scaled from 1 to 19 into IQ equivalents):

Now after adjusting for test reliability, our gifted 6.5-year-old (who is secretly an average 9.5-year-old) had deviation IQs ranging from 117 (object assembly) to 145 (Arithmetic).

Why such a huge discrepancy? The most obvious answer is that 9.5-year-olds have two cognitive advantages over 6.5-year-olds. Not only are their brains bigger and more developed, but they’ve also have three extra years of life experience. On tests that require novel problem solving, their advantage will be modest because it only reflects their neurological superiority. It can not reflect their life experience advantage because by definition, novel problems are things we’ve had little experience with.

By contrast, on tests that required acquired knowledge they have two advantages. Not only does the 9.5-year-old have more neurological ability to reason arithmetically, learn and remember facts, and infer the meaning of words, but he’s also had three extra years to acquire number concepts, general knowledge, and vocabulary. Because “crystallized” tests require both neurolgical ability and experience, they show a much steeper age progression than fluid tests (and a much steeper decline in old age, though this is confounded with the Flynn effect), which require only neurological ability (beyond some basic experience threshold that virtually all Americans reach by age 5 or so). Indeed looking at the age progression is a good way to quantify crystalized vs fluid.

Notice also that the tests that show the biggest age effects also tend to be the ones that show the biggest family effects per James Flynn’s method. Because both reflect experience.

Now let’s imagine when the pseudo-gifted boy turned 16.83 and he wanted to get into Mensa, and they were unwilling to accept scores from the past. He is still exactly average in all domains for his true age, but still looking young he tells the psychologist he is only 10.5. She doesn’t buy it, but she’s not about to turn down $800 for a few hours work so she plays along.

Here are his results:

Once again, his years of extra life experience (relative to the age group he’s pretending to be) gave him a huge advantage on knowledge based tests like Vocabulary and Information. And once again, novel tasks like Block Design, Picture Arrangement, Mazes and Digit Span showed less advantage.

But what happened to Arithmetic? His advanced age gave him a huge advantage when he was a 9.5-year-old pretending to be 6.5, but now that he is 16.83 pretending to be 10.5, this subtest is even less age dependent than Block Design. The likely explanation is that once kids acquire basic number concepts in school (addition, subtraction, multiplication, and division) arithmetic depends less on experience and more on neurology.

This is why one can never say, categorically, that a given test measures fluid or crystallized ability. It depends on the population taking it. For example the Raven progressive matrices might be a fluid test within generations but a crystallized test between generations. Even something as seemingly crystallized as the math SAT might measure fluid ability in 17-year-olds with at least four years of advanced math. Among all 17-year-olds, it will still correlate with (but not so much be directly caused by) fluid ability because those with more fluid ability are likely to take advanced math in the first place.

Another interesting case is Similarities, which requires one to infer the link between common things (how are chess and scrabble alike?). This showed small age effects in early childhood, but large age effects in later childhood. At the lower end this test is just about the ability to see associations, but at the higher end, it becomes increasingly dependent on diction and sometimes esoteric concepts, making it more experience dependent.

One question is why, if crystallized tests are more culture dependent, do they often load more on psychometic g (the general factor of IQ tests believed to be a property of the physical brain). Perhaps as some have suggested, once you control for age, in countries where everyone has opportunity for schooling, knowledge tests measure both the ability to learn over an entire lifetime and the ability to store and retrieve a lifetime of learning. By contrast fluid tests only measure the ability to learn in the testing room, and not the ability to store and retrieve it years later. One theory is the more parts of the brain a test samples, the more g loaded it is, which would make sense if g is just overall cognition.