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Interview with Bob Williams (Parts One and Two)


Author(s): Bob Williams & Scott Douglas Jacobsen

Publication (Outlet/Website): Noesis: The Journal of the Mega Society

Publication Date (yyyy/mm/dd): 2021/02 (Issue #207)


Bob Williams is a Member of the Triple Nine Society, Mensa International, and the International Society for Philosophical Enquiry. He discusses: growing up; a sense of an extended self; the family background; the experience with peers and schoolmates; some professional certifications; the purpose of intelligence tests; high intelligence; the geniuses of the past; the greatest geniuses in history; a genius from a profoundly intelligent person; profound intelligence necessary for genius; job path; the more important aspects of the idea of the gifted and geniuses; thoughts on the God concept or gods idea; science; some of the tests taken and scores earned (with standard deviations); the range of the scores; worldview-encompassing philosophical system; meaning in life; intelligence in the abstract; and the mainstream and fringe theories of human intelligence on offer over time; intelligence in the public consciousness; consciousness within those who spend more time thinking about it, in professional circles; the scientific constructs; the majority opinion definition of general intelligence; other peripheral, though respected, definitions of general intelligence; most noteworthy and prominent names in psychometrics history; arguments for national intelligences; the form of data gathering on the national intelligences; age 16 as a capstone; tests measure g; scores extrapolated beyond their highest range; and the range of validity and reliability of these alternative tests.

Keywords: Bob Williams, intelligence, International Society for Philosophical Enquiry, IQ, Triple Nine Society.

Conversation with Bob Williams on Background, Genius, Theories of Intelligence, Psychometrics, and Worldview-Encompassing Philosophical System: Retired Nuclear Physicist (1)

*Please see the footnotes, bibliography, and citation style listing after the interview.*

Scott Douglas Jacobsen: When you were growing up, what were some of the prominent family stories being told over time?

Bob Williams: Family stories were about what my grandparents and parents experienced before I was born. I recall thinking that I would not see advances as dramatic as those experienced by my grandparents. They were born before electrification and before flight, yet lived to see the first humans land on the moon. It is difficult to compare my life to theirs, but I think there have been at least as many big changes as they experienced.

Jacobsen: Have these stories helped provide a sense of an extended self or a sense of the family legacy?

Williams: Stories of past lives and experiences help to put my life in perspective. There has been an enormous change in the standard of living that my family has experienced as a result of increasing amounts of education and the technology that has increased exponentially in the last two centuries.

Jacobsen: What was the family background, e.g., geography, culture, language, and religion or lack thereof?

Williams: I was born during WW2 and grew up in Virginia in the suburbs of a city that was third largest (back then) in our state. We had two groups: whites and blacks. {Today this seems strange. As a student I only met one child who was Jewish and that was in primary school. We had one Catholic church, but I only knew of one student in my school who was Catholic. There were no Hispanics, Arabs, Russians, or any of the ethnic groups that we only knew about from movies.} Everyone claimed to be Christian; that meant Protestant as Catholics were presumed to mostly live elsewhere. Crime rates were low and violent crimes almost nonexistent. There was a very strong hatred of the North that was residue from the war. My great-great-grandfathers fought for the South, as did the families of those I knew. Today, that feeling has vanished. Technology and multiple generations caused many changes, even in local demographics.

Jacobsen: How was the experience with peers and schoolmates as a child and an adolescent?

Williams: I began first grade when I was 5 (6 was the usual). I had to go to a private school for one year, then transfer to the public schools. Through every grade, I was the youngest and, fortunately, one of the tallest in every class. One curiosity I have is about what was known about me by the schools and teachers. I don’t recall what if any standardized tests were given back then. I was apparently tested by a psychologist before being allowed to start school at age 5.

Jacobsen: What have been some professional certifications, qualifications, and trainings earned by you?

Williams: I have two degrees in physics and one in business administration. I went into the nuclear reactor business and worked (core design, modeling, analysis, instrumentation, etc.) in the private sector, then in the nuclear weapons business (we were intending to build a tritium producing reactor, before the SALT treaty made it unnecessary). In that particular market, everything is either proprietary (private sector) or classified (weapons program). As a result, despite constant writing, nothing was seen “outside.” We had only advancement as a reward. I joined my private sector company as an associate physicist, but the company decided to make everyone an engineer, so my job titles went that way, from engineer, to senior engineer, to principal engineer, and to fellow engineer. During that time I also held a range of management titles. I also became the company representative (we had research labs and production plants scattered over the eastern part of the US) for joint research projects, which led me to a very enjoyable stint of high level meetings with people in the US, over much of Europe, and the Middle East.

Jacobsen: What is the purpose of intelligence tests to you?

Williams: Today we can measure intelligence reliably and with good predictive validity. The only purpose of these tests is to predict important life outcomes. If the tests don’t do that, they are worthless… but they do it quite well. More intelligence means that there is a higher probability that a desirable outcomes will happen and undesirable ones will not. More intelligent people are more likely to experience: higher income, increased longevity, greater general health, more life satisfaction, higher degree of body symmetry, higher educational achievement (grades, years completed, difficulty of major), higher SES (a product of intelligence, not a cause of it), faster speed of mental functions, better memory, faster learning rate, greater number of interests (held with competence), higher job performance, higher brain efficiency (relative to glucose uptake rate and speed of mental operations). And … they are less likely to be impacted by smoking, HIV infection, crime, incarceration, school dropout, teen pregnancy, illegitimate births, and unemployment.

At the national level, mean national IQ correlates positively with per capita GDP, economic growth, economic freedom, rule of law, democratization, adult literacy, savings, national test scores on science and math, enrollment in higher education, life expectancy, and negatively with HIV infection, employment, violent crime, poverty, % agricultural economy, corruption, fertility rate, polygyny, and religiosity.

This effect does not have a known ceiling. The Study of Mathematically Precocious Youth is a longitudinal study started by Julian Stanley and maintained today by Camilla Benbow and David Lubinski. Part of the study evaluated cohorts in the top 1% of intelligence. It showed that there are large differences between those in the bottom quarter of this range and those in the top quarter of the top 1%. These differences, favoring the more intelligent top quarter have been found in number of doctorates, number of STEM publications, number of patents awarded, income and literary publications.

Jacobsen: When was high intelligence discovered for you?

Williams: Apparently it was well before I was aware of it. Even in primary school, I was selected for special treatment (a summer camp), a place on the varsity high school debate team when most participants were 4 years older, etc. By age 15, I began to win awards in science fairs

that led to half a dozen trips to various parts of the nation; two trips to the International Science and Engineering Fair (one was part of the World’s Fair in Seattle); lots of prizes, a summer job, and ultimately scholarships that paid for much of my college education. Upon entering my university I was given a chemistry test, which let to my being put in an advanced chemistry class that destroyed 2/3 of the students who were placed in it (I was up to it). Then there was a surprise trip by the Air Force (I was at Virginia Tech, which was compulsory military for two years, but I stayed in the Corps of Cadets for all four.) to send me to visit an airbase. It was years later that they told me I had made the second highest score on the Air Force Officer’s Qualification Test. The only thing I knew was that I did well on tests; it took years for me to connect various events to testing.

Jacobsen: When you think of the ways in which the geniuses of the past have either been mocked, vilified, and condemned if not killed, or praised, flattered, platformed, and revered, what seems like the reason for the extreme reactions to and treatment of geniuses? Many alive today seem camera shy – many, not all.

Williams: It is amusing to see how interested people are in genius (the real thing, not simply high IQ), yet bright people who are successful seem to be frequently looked down on. Genius is such a complex thing that it is extraordinarily rare. It happens when a constellation of necessary, but not sufficient traits exist at maximum expression. Hans Eysenck believed that both traits Neurosis and Psychoticism had to be elevated in true genius. Obviously if either trait is overly expressed, the individual would be hobbled and not achieve enormous feats of creative genius. When N and P are somewhat elevated they positively impact success, while likely creating an unpleasant personality. For example, P may cause a person to be seen as aggressive, cold, egocentric, impersonal, impulsive, antisocial, unempathic, tough-minded, and creative. Arthur Jensen believed that genius is the product of high ability x high productivity x high creativity.

ability = g = efficiency of information processing

productivity = endogenous cortical stimulation

creativity = trait psychoticism

The result of genius traits is not pretty, nor is it consistent in how it is displayed in geniuses. We have all read about the lives of various composers, artists, and scientists who were sufficiently “unusual” as to be unable to fit into normal life patterns. I think the common reactions that you mention are not restricted to genius. We see other people rejected when they have personality, or even physical, differences. Curiously, I see this same rejection and bullying among the Canada geese that live in my yard. Lame geese and even normal geese without a group are rejected and sometimes attacked.

Jacobsen: Who seem like the greatest geniuses in history to you?

Williams: As a scientist, I am going to surprise you. It is the great artists, because they give us things that only they can produce. The major scientific discoveries would all be made, even if the people who discovered them had not existed. Of the greats, I think Beethoven is the most important person in all of history. His work was so profound, moving, and complex that nothing compares. Of course, the other composers (Bach, Mozart and many others) have made contributions that are treasures. In the arts, Michelangelo and Picasso lead the list of greats.

I have never seen a credible list of the IQs of any real geniuses. My guess is that those in the arts may be reasonably bright, but that it is their creativity and skill that sets them apart. In science, things are different. The scientists are brighter and higher on traits Agreeableness and Consciousness.

Jacobsen: What differentiates a genius from a profoundly intelligent person?

Williams: Personality and creativity. I have already discussed how personality can make a genius seem unlikable and unreachable. The thing that I find to be interesting is that the biological factors that are associated with bright brains are sometimes opposite from those associated with creative brains. We know from prodigy studies that prodigies have IQs that range from 100 to about 147 (those actually studied). Prodigies are found in rule based disciplines: chess, art, music, and mathematics. The highest IQs are those of the math prodigies.

One of the significant factors in the creative brain is an inhibitory function that is weak. This condition lowers the filtering system that rejects stimuli that are not needed for the task at hand. We experience this selective attention when we are in a noisy environment. Our brains usually tune out the noise, for example people talking in a social gathering, and focus on the sensory input that is needed (understanding the person we are talking to). When this selective attention is low, the person may find unrelated stimuli arriving in his brain simultaneously. This promotes new combinations of ideas that would normally be prevented by the inhibitory function. But this is exactly opposite of what we need for intelligence. A mathematician, scientist, or engineer must stay on task, not be distracted, and remain focused. An example of lowered inhibition is seen with alcohol and other drugs. Imagine trying to take a calculus test while you are inebriated!

There is a similar consideration in brain networks. The brain with poor connectivity (long mean path lengths and fewer connections to hubs) causes a single thought process to follow an inefficient path around the brain before it reaches its intended destination. During this long route, it can access information that leads to creative combinations of previously unrelated ideas. Again, this is opposite of what one needs for complex problem solving. There are other examples, but the point here is that creativity taps a set of brain conditions that are often opposite of those that are required for deep scientific reasoning.

Jacobsen: Is profound intelligence necessary for genius?

Williams: “Yes,” for STEM fields, “no” for the arts. This is not to say that artistic geniuses are not bright, but rather that they do not require “profound intelligence” of the sort we see in great scientists.

Jacobsen: What have been some work experiences and jobs held by you?

Williams: I spent a long time in the commercial nuclear reactor world. I began in reactor core physics, where I did modeling, burnup analysis, isotopic balances, and calculated a variety of physics parameters that are used by other physicists/engineers. A good part of that time involved work on fast breeder reactors, which was enjoyable because I could design and analyze multiple configurations so that the best one could be identified. It turned out to be a flat cylinder that got the name “pancake.” That design worked well because it allowed a lot of axial neutron leakage which fed the breeding of U-235 to Pu-239. Then I spent years doing transient analysis. This meant calculating the outcome of accidents, such as an ejected control rod, or a broken pipe. I recall doing the loss of feedwater accident for Three Mile Island-II. That was the accident initiated a sequence of events that destroyed the plant, but it was not because of a miscalculation, it was because we didn’t consider that an operator would turn off the emergency core cooling system! I ultimately became the only person who really understood the Reactor Protection System (RPS). It was satisfying to be the resident expert, but it made it difficult for me to move to something I wanted to do in a different division. I developed the methods for determining RPS setpoints and personally determined these for every large power reactor we built. I also did the work that resulted in the licensing of the first digital RPS approved by the Nuclear Regulatory Commission.

After training several people to do my job, I managed to move to the Contract Research Division, which was the most memorable and enjoyable part of my career. I mentioned some of that in an earlier question. All in all, I had great experiences doing things that most people could not even know about. My last 6 years (before retirement) were spent in the nuclear weapons program. I ended up working in Washington, DC for most of that time, as a Senior Technical Advisor to the Department of Energy. On one trip, I went to Mound, Ohio. The old part of this site was built very deep underground and designed to withstand a direct nuclear blast. It was amazing to see that something like that even existed. I was with a small group and we went on to Fernald. During the trip, someone wanted to visit a vault where weapons grade materials were kept. We went through 3 or 4 checkpoints where we had to go though various presentations of security clearances, etc. and then ended up in a round concrete room. The walls were decorated with machine gun ports and the guys behind them were actually holding the machine guns. I understood the old quip about “shooting fish in a barrel,” from the perspective of the fish. After they finally let us out of what amounted to a cage, we saw the vault, which was a major letdown, then we had to repeat each step in reverse. This sort of thing does not appeal to me at all. I was never happy working with security that involved man traps, armed guards, magnetometers, sniffers, x-ray, and endless security checks.

One thing that I enjoyed was teaching/lecturing. For whatever reason, I became the go to person for delivering lectures to our reactor customers, federal regulatory agencies (including one from Italy), and prospective customers. My lectures were always well received, but we were getting feedback that our Loss of Coolant lectures were not well received. This is an area that is focused on heat transfer and hydraulics. I had not worked in the area, but agreed to take over the lectures, if the engineers there would give me some time, explaining their modeling. I figured it out, designed, and delivered lectures that generated accolades from our customers.

Jacobsen: Why pursue this particular job path?

Williams: From childhood, I knew I wanted to go into science, but had no specific area of interest. By high school, I was more focused on chemistry and won awards on the studies I did with fuel cells that I designed and built, then with my studies of gas chromatography, using a system that I designed, built, then altered into various configurations. [These led to multiple awards, up to and including a first and second at the International Science and Engineering Fairs.] When I had to pick a major, I only considered the math load. I selected physics because I figured it was more math heavy than anything else. I was right at the academic level, but by the time I entered the nuclear business, we had mainframe computers and did most of our work using numerical methods (beating the answers out, by iteration). At that time reactors were the big deal for electric utilities and they paid off big for those who bought them. Ultimately, interveners found a way to stop the industry by endless (pointless) law suits that had no merit, but they delayed construction. At that time we were in the highest inflation period of modern times, so the utilities simply couldn’t pay the cost of their loans. It was a case of the interveners losing every battle, but winning the war.

Jacobsen: What are some of the more important aspects of the idea of the gifted and geniuses? Those myths that pervade the cultures of the world. What are those myths? What truths dispel them?

Williams: Very bright people have the ability to understand and deal with multiple complex disciplines and to solve problems that are beyond even bright people. The spectrum of intelligence is defined by the structures and properties of the brain and can only be degraded by environmental encounters. That means we have not found a way to increase intelligence. The brain is built from our genetic instructions and is intelligent to the extent that its components are efficient and suffer few flaws. For example, we know that tissue integrity in both gray and white matter influences intelligence, as do the multiple factors that relate to mental speed (white matter tracts, hub connections, myelination, nerve conduction velocity, etc.). Ultimately, any brain feature that has a range of efficiency between individuals is going to favor the more efficient brain.

Studies of large populations and high end intelligence have shown that extreme intelligence is not associated with one or a few genes. It is simply part of the normal distribution of the huge number of factors that each contribute to phenotypic intelligence. We are at one of the big new directions of discovery in cognitive science: genetics. Within the past few years Genome Wide Association Studies (GWAS) have been done with large sample sizes. With over 1.2 million people represented, researchers have found more than 1,200 single nucleotide polymorphisms that are associated with intelligence. Despite this number, the effect size is only around 10%. Despite the small effect size, polygenic scores (PGS) have been derived from the GWAS and used to predict intelligence, even in embryos. These PGS have produced almost perfect (greater than correlations of 0.90) predictions of mean intelligence differences between breeding groups.

As the brain matures, the heritability of g (the sine qua non of intelligence) increases from around 40% in early childhood to about 85% in adults. This increase in the genotype is found in other traits as well. Despite the lower heritability found in young children, measurements done for ages 6 to 12 months are predictive of adult IQ and educational achievements. [Adult IQ, r = 0.59; Adult academic achievement, r = 0.53 (both corrected for unreliability)]

In the case of genius, as I previously noted, intelligence, creativity, and personality all have to be at optimum levels. This is an extremely rare event. Geniuses are typically born to families that have not shown outstanding performance in academics, invention, creativity, etc. Relatively few geniuses have children and many do not marry. Those who do have children rarely produce another genius (there are a few possible exceptions that we might find over the past several centuries).

Neither the general public nor those who teach at any level have even a modest understanding of intelligence. Russell Warne has been uncovering the details of just how little people understand. This year he did a survey of teachers asking them to rate a number of statements about intelligence on a Likert scale. Sadly, the results were not surprising. In recent years, he has surveyed US universities and found that most didn’t offer courses on intelligence and the psychology courses they taught used textbooks that primarily discussed discredited models (Gardner’s multiple intelligences) and often did not even mention g. He has written a book on the subject of myths about intelligence: In the Know: 35 Myths About Human Intelligence.


I will offer a few comments on just 3 of the many myths that are commonly accepted as facts.

Group differences

The single most damaging failure to understand is that there are large intelligence differences between breeding groups. These are differences in g and these are overwhelmingly genetic. The differences explain many of the conflicts we see between nations, within national groups, and between individuals. They explain differences in academic achievement, in job performance, in crime rates, wealth, income, health, and longevity. These differences have been known for 150 years and are forcefully denied by the proponents of political correctness. Sex differences also cause some people to get upset and deny the differences. The reality is that, around age 16 males show a higher mean intelligence and a higher variability. These combine to cause a rapidly increasing male to female ratio in the right tail. There is controversy over the difference at the mean, but my conclusion is that it has turned up in a large number of independent studies and seems to be real. The difference we see most often is around 4 points, but a few studies have shown up to 6 points.


Those who want to argue that all humans are born with identical abilities deny the very high heritability of g. We can and have measured this heritability using diverse methods that show essentially the same result. Those methods are as follows:

The correlation between MZA twins–This correlation is used directly—not squared.

Falconer’s Formula–This method was developed by Falconer and MacKay. It computed heritability by doubling the difference between the correlations of same-sex MZT and

DZT twins. Numbers are typically r = 0.88 and 0.51 respectively. After correction for reliability the numbers become .98 and .56, respectively. The difference is 0.42, so the computed heritability is 0.84.

Richard Lynn also reported two studies of heritability in India, both using Falconer’s Formula. One study yielded heritability of 0.81 and the other 0.90. After correction for reliability, these become 0.90 and 1.00, respectively.

1.0 Minus the Environmental Component–Adoption studies (and others) have shown that the environmental component is about 15% in adults (see papers by Posthuma, Haier, Lynn, and various others). This method produces the typically cited level of heritability in adults of 85%.

Path Analysis–This technique was invented in the 1920s by Sewall Wright. The method incorporates multiple linear regression to apportion the contributions of each of the multiple causal variables to the variance in the single outcome. The assumed links between the causal variables can be tested and rejected if they do not fit the assumed causation. This is not a test of causation, but provides a means of determining magnitude and of establishing the existence or nonexistence of the assumed causality link. The method is general and has been used to study diseases, occupations, etc. One study that used this method was based on the Texas Adoption Project (300 adoptees). The analysis used the IQs of mother, father, their natural children, and their adopted children (after about 17 years of adoption). The heritability derived from this study was 0.78 before correction for reliability. With correction it is about 0.86.

Brain Imaging–Within the past decade papers have appeared with heritability estimates based on brain imaging of MZT and DZT twins. Imaging by Paul Thompson showed that the brain structure was heritable at the level predicted by other methods (listed above). PGS (previously mentioned) predict between group differences with strong correlation coefficients, as already discussed.

Environmental factors–People want to believe that intelligence is molded by parental interactions, socioeconomic status, school quality, etc. No, it’s genes. Stephen Pinker wrote a whole book on this topic (The Blank Slate).

Multiple intelligences–Howard Gardner invented a model that has strong appeal to the public, but which is not supported by data and does not withstand scrutiny. He showed that it is profitable to tell people what they want to hear, even if it is incorrect.

Flynn Effect and g

Another case of people wanting to accept pop-science explanations, without understanding the details. In this case, the public believes that intelligence is increasing and some believe that it is increasing in a way that will eliminate between group differences. IQ scores have been unstable for a long time and have mostly increased. The effect is different in different nations and is different as a function of time in most nations. We now have a reversal in a good many European nations. The problem is that these score changes have been shown to be artifacts and are not due to changes in g. For example, some of the instability is due to increased guessing (the Brand Effect) and some are due to the method of scoring the test, which has nothing to do with intelligence. Meanwhile there is considerable evidence that g is declining, at least in Western nations and China.

Jacobsen: Any thoughts on the God concept or gods idea and philosophy, theology, and religion?

Williams: Over 20 years ago, I attended a presentation by Jay Glass, author of The Animal Within Us. He described exactly what I had concluded several years earlier, based on the same source material (the study of chimps). He concluded that humans are significantly like our nearest relatives in that we are genetically predisposed to organize in a dynamic hierarchical structure. Chimps and humans have this social structure (other animals as well). I think we are so drawn to this need to have a hierarchy that we don’t stop with the chief, king, or satrap, but go on to spontaneously invent gods with magical powers and elaborate stories of their adventures, including the creation of the universe and man.

In cognitive science, religion has been studied extensively. In every case (national and individual studies) the finding has been a negative correlation between measures of religiosity and intelligence. Some researchers have approached the topic by studying the degree of dogmatism in individual religious beliefs. The more dogmatic (fundamentalist) the beliefs, the lower the IQ. I can recall that, as a child, I noticed that the religious denominations in my immediate surroundings were clearly stratified by SES. I didn’t know why at that time, but today it is obviously a case of grouping by wealth and education, both of which are products of intelligence. Scientists typically show low percentages who hold religious beliefs.

Jacobsen: How much does science play into the worldview for you?

Williams: It plays to my interest. There are things that are difficult or impossible to understand from a purely scientific perspective. Ethics is one example. Yet most of the things we see are subject to scientific study and understanding. This applies even to relatively etherial things, such as emotions.

Jacobsen: What have been some of the tests taken and scores earned (with standard deviations) for you?

Williams: Virtually all of the tests I have taken were quite a long time ago, before I had an interest in cognition. I previously mentioned two tests I took in college. I think there were various others during high school. About 30 years ago, I took two tests administered by Mensa. I have no idea what they were and what the scores were, but I used them to join Mensa, the International Society for Philosophical Enquiry, and the Triple Nine Society. The latter two admit at the 99.9th percentile. I have not had any interest in hobby tests and have written about my concerns for their validity on numerous occasions. My last effort will presumably appear in the journal Noesis (Mega Society – not a member) in February.

Jacobsen: What is the range of the scores for you? The scores earned on alternative intelligence tests tend to produce a wide smattering of data points rather than clusters, typically.

Williams: I have no idea. When I have taken tests that had consequences, I managed to do well enough. I have not engaged in the “test taking as entertainment” practice.

Jacobsen: What ethical philosophy makes some sense, even the most workable sense to you? What social philosophy makes some sense, even the most workable sense to you? What economic philosophy makes some sense, even the most workable sense to you? What political philosophy makes some sense, even the most workable sense to you? What worldview-encompassing philosophical system makes some sense, even the most workable sense to you?

Williams: I will combine the philosophy questions into one reply. Let me start with an observation by geneticist Robert Plomin. He was being honored with the Distinguished Career Interview at an ISIR (International Society for Intelligence Research) conference. As he discussed his career path, he mentioned that he began his university studies in philosophy. At some point, he realized that things that can be measured are not part of philosophy and changed majors. This reflects my view of philosophy. My interests lie in science, so that is what I read. My formal education did not include any courses on philosophy, so I don’t think in terms of Kant or Nietzsche. The one philosopher who has attracted my interest is Bertrand Russell; I found his essays about religion interesting. My belief about ethics is that, as usual with this sort of topic, there are different perspectives that can be argued endlessly. The thing I am most bothered by is another party attempting to impose an ethical standard on me. We see a lot of this as ethics is blended with politics and I believe it has become a social cancer. This relates to my previous comments about how the huge between group gaps in intelligence have serious consequences.

My view of economics is that of von Mises and Friedman. I think we have valid predictive models of economic behaviors and that we should follow those in government and fiscal policies. I consider myself to be a libertarian at heart. Unfortunately, I don’t see a path from the present political divide in the US towards a more harmonious and prosperous society. We have reached the point mentioned by Alexander Fraser Tytler at which people will vote benefits for themselves from the treasury at the expense of destroying the economic stability of the nation. This is an outcome that returns to the intelligence issue and, in particular, the decline in intellectual capital due to the negative correlation between intelligence and fertility rate.

As a matter of understanding why I see so many things as ultimately being matters relating to cognitive abilities, I think Douglas Detterman explained the gravity of it well: “From very early, I was convinced that intelligence was the most important thing of all to understand, more important than the origin of the universe, more important than climate change, more important than curing cancer, more important than anything else. That is because human intelligence is our major adaptive function and only by optimizing it will we be able to save ourselves and other living things from ultimate destruction. It is as simple as that.” [Detterman is the founder of ISIR and of its journal, Intelligence.]

While I am being pessimistic, I will share my conclusion about group conflicts. Despite all of the idealistic things that some people believe and others would like to believe, world history should have taught us all that humans are truly aggressive and will repeatedly commit atrocities and engage in wars. I see no end to it and think it is a part of our species behavior. In my lifetime we have had a world war, countless smaller wars, multiple instances of genocide, and see that these are not restricted to small, backward nations, but are done on a grand scale by the same nations that have given us artistic beauty and scientific understanding.

Jacobsen: What provides meaning in life for you?

Williams: The things that are meaningful to me are those that many people hold dear: family, liberty, and nature. I have had the opportunity to live comfortably and to enjoy a great deal of autonomy. I have surrounded myself with a zoo-like population of animals, forest, and a beautiful place to enjoy nature. I have gotten to know my Canada geese as individuals and spent hours watching the other creatures that live here with me.

Jacobsen: To set the stage for the further conversation, what comprises intelligence in the abstract?

Williams: I think g is the best match to “abstract.” It is a latent trait, so it can only be known by statistical manipulation of measurements. We have Arthur Jensen to thank for convincing skeptical researchers that the essence of intelligence is this single factor that Charles Spearman discovered in 1904. Jensen had the persistence to meet every argument with data and analysis. Today intelligence research is g research.

Jacobsen: What are the mainstream and fringe theories of human intelligence on offer over time?

Williams: Today g theory is accepted as the best representation of intelligence, defining its structure via factor analysis and linking the biology of intelligence to the outward measurements that relate to it. As I have already noted Gardner’s model is very popular among laymen. It is the sort of thing that drives researchers crazy. Gardner did not derive his model from data, did not use an inductive process to construct it, and has been unable to show that it can be demonstrated as correct from real world measurements. The thing multiple intelligences implies is that if someone has a low academic ability, they have something else to make up for it in a zero sum sense. It sounds nice, but it is nonsense. The real world is not so fair. What we have is the positive manifold, which is the way Spearman described his discovery that people who test at a given level on one category of cognitive tasks will test at a similar level on virtually all cognitive tasks. Of course it’s unfair… it means that bright people are likely to excel at almost every kind of task, while dull people will find most such tasks difficult or impossible. It is from the positive manifold that Spearman was able to reveal the general factor g (Spearman’s g) using factor analysis, which he invented.

Robert Sternberg also invented a model that he calls Triarchic theory. It consists of dividing intelligence into practical, creative, and analytical. As is the case with multiple intelligence, it sounds good to people who want to believe that g is not the answer. Some years ago, Linda Gottfredson did a detailed dissection (published in Intelligence) of his “theory,” showing that it does not withstand scrutiny.

Aside from the models presented by Gardner and Sternberg, there have been various other proposed models that have been abandoned. For example, Joy Paul Gilford offered a “structure of intellect” model. This complex model was designed with 150 cells, each of which represented an ability (Gardner magnified). There are a variety of other models that have been assembled, but the only one that is significant is Cattell’s model which was basically an argument against g. Instead of one top factor, he used two: fluid intelligence and crystallized intelligence. We still use these as stratum II factors, but they are grouped with other broad abilities. The structural model that won out was the Cattell-Horn-Carroll model that serves as the basis for both the Wechsler tests and the Woodcock-Johnson. Carroll tweaked the model that Cattell and Horn were using, so that g was extracted as the single stratum III factor. This model is g theory in practice. [Despite its popularity and usefulness, the CHC model is somewhat arbitrary and is not the true structure of intelligence. That honor goes to the VPR model (verbal, perceptual, and rotational) developed by Wendy Johnson and Thomas Bouchard.]

Jacobsen: Let’s talk about the abstraction of concept “Intelligence” first, what, fundamentally, is meant by intelligence in the public consciousness?

Williams: People inherently understand that some people who are able to do complicated tasks that are beyond the abilities of average people and they are certainly aware of dullness. While the benefits of intelligence are strong as it increases, the consequences of low intelligence are much more serious. Most states have legal definitions of the threshold of retardation–usually IQ 70. Each 5 points or so in the down direction adds limitations to learning ability, learning speed, and the ability to manage personal affairs. One of the most convincing sources of information about what can and cannot be done by the population as a whole, is the National Adult Literacy Survey (NALS). The test is done for the federal government by Educational Testing Service. About 92 million adults (out of 191 million) were functioning in levels 1 or 2, meaning that they could perform only basic and elementary tasks. Most of this reflects low intellectual ability or age related decline.

I think the public understands that bright people do better in school and that they are needed in cognitively demanding careers. The thing they don’t seem to get is that intelligence is not evenly distributed between groups nor within groups. They also grossly overestimate the role of the environment in determining intelligence.

Jacobsen: What is meant by consciousness within those who spend more time thinking about it, in professional circles?

Williams: Intelligence researchers do not study consciousness. I have not encountered any casual discussions of it. Scientists (including social sciences) like to measure things, analyze measurements, and construct models that are able to predict other things. Consciousness doesn’t lend itself to such treatment, so it falls into the abstract world of philosophy. Most people seem to regard consciousness as sentience or as self-awareness. A few animal studies have reported various experiments that may test some aspects of self-awareness, such as the mirror test. So far, such tests are yes/no outcomes with little that can be modeled or analyzed.

Jacobsen: Now, to the scientific constructs, e.g., general intelligence, what is meant by general intelligence?

Williams: General intelligence, g, is the common resource that is involved in all cognitive tasks. Jensen described g as a distillate, in the sense that it is the thing that remains when the less essential factors are eliminated. At the psychometric level, g is unitary; at the neurological level, it is not. Charles Spearman found that when he tested people on unrelated tasks, the people who did well on one task were likely to do well on all tasks and vice versa. He called this finding the positive manifold. In the process of devising ways to analyze data, he invented factor analysis and from that, he was able to discover g in 1904.

The public is generally unaware of g and its central importance to the understanding of intelligence. Unfortunately, g is not the kind of thing that people study. It, as with everything we know about intelligence, is a statistical parameter and is a latent trait. We can determine g for a group of people by using a hierarchical factor analysis or other methods (bifactor analysis or principal components analysis). Each method has its advantages in certain applications, but the differences in results are insignificant.

Jacobsen: What is the majority opinion definition of general intelligence?

Williams: Within cognitive science, I think virtually everyone has accepted that intelligence is well represented by g. Today essentially all intelligence research is related to g. The easy way out of definitions is to skip “intelligence” entirely and simply discuss g. If we get into the definition of intelligence, we have many definitions from psychologists over the past century. I will give you two of them. My favorite is from Carl Bereiter: “Intelligence is what you use when you don’t know what to do.” This is a surprisingly accurate, concise, and elegant definition. The second definition is the one used by Linda Gottfredson: “Intelligence is a very general mental capability that, among other things, involves the ability to reason, plan, solve problems, think abstractly, comprehend complex ideas, learn quickly and learn from experience. It is not merely book learning, a narrow academic skill, or test-taking smarts. Rather, it reflects a broader and deeper capability for comprehending our surroundings–‘catching on,’ ‘making sense’ of things, or ‘figuring out’ what to do.” [Linda Gottfredson – Mainstream Science on Intelligence; The Wall Street Journal; December 13, 1994] This definition is the one most often cited since 1994.

{My answer (above) is based on what I think you were asking. It turns out that “general intelligence” is commonly used in reference to g, which we have discussed in various ways.}

Jacobsen: What are some other peripheral, though respected, definitions of general intelligence?

Williams: Most of the definitions that are credible are similar, as one would expect. If they are respected by cognitive scientists, they must address the things we all see and understand in connection with the word. Here are a few, that are worthwhile:

“Individuals differ from one another in their ability to understand complex ideas, to adapt effectively to the environment, to learn from experience, to engage in various forms of reasoning, to overcome obstacles by taking thought.” American Psychological Association

“. . . that facet of mind underlying our capacity to think, to solve novel problems, to reason and to have knowledge of the world.” M. Anderson

“. . . the resultant of the process of acquiring, storing in memory, retrieving, combining, comparing, and using in new contexts information and conceptual skills.” Humphreys

“The ability to carry on abstract thinking.” L. M. Terman

Jacobsen: Who are the most noteworthy and prominent names in psychometrics history who

studied general intelligence as a career?

Williams: Given the long history of the study of intelligence, we could name many people who have contributed to our present day understanding. Progress and activity level in cognitive science has followed a curve that increased slowly at first, then turned upward as rapid advances came from brain imaging and genetics (all made possible by advanced computer technology). I will list a few of the early names, then those whom I know personally who have made major contributions.

The first person who studied intelligence, made measurements, and wrote about his findings was Sir Francis Galton. He is clearly the father of cognitive science. People naturally think of Alfred Binet and Lewis Terman as important figures because of their contributions to the development of testing. Terman also famously conducted a longitudinal study of high IQ cohorts (called Termites).

Charles Spearman was one of the most important and possibly THE most important of all intelligence researchers. He invented statistical methods that were needed to study intelligence (now used widely in other fields), discovered g, invented the first matrix test (developed and carried to the market by his student John C. Raven), and produced a range of insightful observations which remain accurate today.

William Stern deserves mention because he was the originator of the ratio method of determining IQ. The method left us with a test name (IQ) and showed that intelligence could be graded as a function of age and performance.

David Wechsler rescued us from the limited usefulness of the ratio method by introducing the deviation quotient that is now the standard for IQ measurement. He is also known for the Wechsler set of IQ tests, which remain as the most important of all cognitive tests.

Arthur Jensen was clearly the most important researcher in the second half of the 20th century. He convinced his peers that g theory was the only correct basis for understanding intelligence; today that reality permeates intelligence research. Jensen was centrally involved in the study of chronometrics for measuring and studying intelligence. He was a prolific writer of books and papers (totaling approximately 400), many of them remaining as the standards of understanding specific topics today. Two were of particular importance: Bias in mental testing (1980) and The g Factor (1998). I am grateful that I had the opportunity to meet him and have numerous conversations with him at ISIR conferences. The first time I met him was in 2004. He asked me about my interests and I told him that I was particularly interested in the biological foundations of intelligence. He said he had some papers that would interest me and asked that I write my address. Within a week, I received a large envelope stuffed with these papers.

Thomas Bouchard was the founder of the Minnesota Twins Study, which was a huge breakthrough in the understanding of the high heritability of intelligence. He was particularly patient with me when I asked endless questions at the conferences. His graduate students are central figures in cognitive science today.

Richard Lynn led the way in understanding the evolution of intelligence and (later) its slow decline. He displayed the strength of Jensen and a handful of others who dared to study race differences and sex differences. He was the first to study national level intelligence and demonstrated that it was responsible for the wealth of nations (except where there is natural resource wealth, such as oil). This work led to many researchers vastly expanding the amount of national level data collected and who showed the extensive number of parameters that are influenced by it.

Brain imaging was started by Richard Haier, when he first applied positron emission tomography to study glucose uptake rates as a function of intelligence. This led to the brain efficiency hypothesis which has been repeatedly confirmed by various other forms of measurement. Haier and Rex Jung simultaneously discovered the intelligence centers of the brain, then joined forces to produce the P-FIT model that is the standard (so far) neurological model. Jung also investigated creativity with brain imaging and revealed important brain characteristics that relate to it.

Jacobsen: How does this construct g, more precisely, map onto arguments for national intelligences?

Williams: As mentioned above, Richard Lynn opened the door to national intelligence studies. His book IQ and the Wealth of Nations showed a strong correlation between mean national IQ and national wealth and productivity. In this case, the difference between IQ and g doesn’t really matter because only the most powerful predictor (g) is active, even when the discussions use IQ, because the non-g factors are lost via cancellation when very large populations are studied. Now that we have national and regional level data pouring in in from all over the world, we can see that the geographic effects exist within nations. McDaniel an others have shown that US states show the same relationships between IQ and wealth as do nations. Today we have detailed IQ data on a regional basis for many nations, including the US, China, Japan, Italy, India, Vietnam, etc. With the exception of India, IQ generally increases from south to north within nations in the northern hemisphere. These nations also show the regional relation to IQ and per capita income.

The g construct is usually thought of as the three stratum model with g at stratum III, broad abilities at stratum II, and narrow abilities at stratum I. If you look at stratum II, you can divide the broad abilities into g and non-g parts. The g parts define stratum I and the non-g parts are residuals that have little predictive validity (except possibly in the right tail). In national level studies the residuals are lost or minimized due to their randomness. We can, however, see high spatial abilities in East Asians, accompanied by low verbal abilities. These differences are large enough to have consequences.

Jacobsen: What is the form of data gathering on the national intelligences to make them more legitimate or less legitimate depending on the form of interpretation of the analysis?

Williams: It is important to convert all test data to a single standard before attempting to compare them. Richard Lynn developed the means to do this with the Greenwich IQ Standard. It basically uses white British as the standard, so all tests scores are compared as if they were normed against the same group.

One of the early criticisms of Lynn’s work was that (at that time) there were relatively few studies and many of them were convenience studies that were random and were reported by many researchers. The criticisms may have seemed sound to those making them, but now that we have a large amount of data, the results have not changed much, other than to show strong consistency. Another criticism was that Lynn estimated the IQs of some nations by using measured IQs of neighboring nations. Some critics were very critical of this estimation. After data was collected, the estimates turned out to be surprisingly accurate.

Jacobsen: With age 16 as a capstone, what is the degree of difference in the variability between males and females at that age? Is this played out differentially in terms of self-identification in sociocultural constructs of the self seen in gender, often confused with biological and genetic sex differentiation?

Williams: I haven’t seen data showing differences in variability as a function of age, but with respect to intelligence, males appear to reach their advantage at the mean (4-6 points) around age 16. The difference in standard deviation between the sexes is 5 to 15% (males higher). In real world outcomes (the things we use as measures of external validity) males dominate a grossly disproportionate number of cognitive arenas. In Charles Murray’s book Human Accomplishment: The Pursuit of Excellence in the Arts and Sciences 800 B.C. to 1950, he was largely measuring eminence. Of the 4,002 people he reported over that time frame, only 2% were women. Of course, much of that can be attributed to limited opportunity for women, so resolution of the cause is difficult. Side story… At the ISIR conference in 2006, we discussed sex differences in intelligence in an open session. Jensen believed that there was no difference, but his friend Helmuth Nyborg had been trying to show him the reality of it for some time. Anyway, Jensen made the observation that on any credible list of the top 100 composers, there would not be a single woman listed. He often commented on music in relation to various topics, as he considered becoming a professional musician (clarinet).

Unfortunately, I cannot comment on self-identification, as it is something that is studied and debated in different circles. There has, however, been excellent work on outlooks and preferences as a function of sex. The best of this is from the Longitudinal Study of Mathematically Precocious Youth. The limitation of this study is that it applies to very bright cohorts in the 99th percentile, although some of the findings have been reported for less restricted range data sets. Among the things they found were that women showed a marked preference for jobs involving fewer hours of work per week; and they placed a significantly higher value on family, social involvement, community service, friendships, and giving back to the community.

Besides life preferences, there are differences in brain structures, brain activity, and connectivity that differ by sex to such an extent that when correlations are computed for activity involving specific volumes of the brain, the correlation coefficients sometimes have opposite signs for male and female. One interesting comparison that was made involved male and female subjects solving the same math problem. The male and female participants were matched for IQ. Males used the frontal and parietal lobes for solving the problem and females used only the frontal lobe.

These are just examples of the rather large number of sex differences that brain imaging has shown.

Jacobsen: What tests measure g the best? What are the ranges of those tests with standard deviations?

Williams: The most heavily g loaded tests are clearly the best, since the whole reason we can use IQ tests is that they are sufficiently g saturated that they can be used as proxies for g. In recent years, researchers have been urging the use of comprehensive tests, such as the WAIS or Woodcock-Johnson, because they do a better job. It also happens that these two tests can report g at the individual level.

Gilles Gignac and Timothy Bates did a study on the correlation between brain volume and test quality. They showed that the correlation increases as test quality increases. [see Intelligence 64 (2017) 18–29] This is expected because g reflects the biology (structure and global properties) of the brain. From their paper, here are the things they identified as determining test quality (examples of “excellent” given on the right):

number of subtests 9+

dimensions 3+ (e.g., fluid intelligence, crystallised intelligence, processing speed)

testing time 40+ minutes

correlation with g $ 0.95

In the past, researchers were often inclined to accept Spearman’s indifference of the indicator in situations that would draw criticism today. Spearman was (as usual) right, but only in a general sense. It is certainly true that a single dimension test, such as the Raven’s Progressive Matrices can give a good measure of intelligence, but even that popular test has received some criticism for having a lower g loading than the comprehensive tests (and lower than some prior claims) and for the presence of factors (as can be found in a factor analysis) that are not reported. At one time, researchers sometimes took the RPM score as a g score.

[The indifference of the indicator is based on the fact that every correlation with g is with the same g. So a vocabulary test can be used to estimate (quite well) g as can a test of analogies. Both of these give us a good estimate of the same g. There is, however, a greater fidelity when multiple measures are used, particularly in an omnibus test.]

The reason for emphasis on comprehensive tests is that they examine more of the relatively few stratum II factors. Examining more broad abilities gives a more complete picture. You can imagine trying to make out the image in a puzzle; it is better defined when more pieces are in place than with fewer.

Jacobsen: How are these scores extrapolated beyond their highest range for some individuals who claim more than 4-sigma scores on these mainstream intelligence tests?

Williams: Of professional IQ tests, I don’t know the procedures used, but I can tell you the claimed ceilings of a few. The WISC-V added extended range in 2019 and claims a ceiling of 210. The DAS claims 175. I assume that the extrapolations are simply extensions of the norming data above the range where there are no data points. Naturally, this means an increased measurement error and requires an assumption that the distribution remains Gaussian in that range (I think that an argument can be made that this is has not been demonstrated).

Hobby tests have claimed very high ceilings, but they have not established a valid support for the claimed ranges. I have read a few of the arguments used to explain their norming and have not seen anything I believe would withstand close scrutiny. There are so many deficiencies associated with hobby test designs, in addition to norming, that I think they should be considered as for entertainment only. I know there are some people who will disagree, but they have not come forth with sound support for the tests. If the tests are not used by clinical psychologists or intelligence researchers (as shown by their use in scholarly journal papers) I fail to see how they can be considered as meaningful measurement instruments.

Jacobsen: What is the range of validity and reliability of these alternative tests compared to the aforementioned mainstream intelligence tests?

Williams: For alternate tests, the disclosures vary from no mention to numbers that reflect an attempt to make some measurements, but which do not result in a full presentation of the things a real test must demonstrate: a high reliability coefficient; norming data (including group size and selection criteria) and method that is appropriate to the claimed ceiling; a predictive validity that is supported by meaningful external measurements; a demonstration of construct validity; a clear standard deviation of 15, or a proper conversion to 15 in the reporting of the score; measurement of at least three broad abilities; identification of a properly determined g loading for the test, where that loading is near or above 0.80; demonstrated invariance by population group, age, and sex (or exclusion of groups where invariance has not been shown); age corrected scoring; citations in the peer reviewed scholarly literature; and demonstrated use by professionals.

Of these, the demonstration of external (predictive) validity is the most important. If the scores do not predict differences in real life outcomes, they are meaningless. Take a hypothetical score of 160 and one of 190 by the same test. This huge, 2 standard deviation difference should produce large differences in external measures, such as the probability of earning a PhD, income, wealth, number of scholarly papers published, number of books published, probabilities of receiving world class honors (for example, those received by Richard Feynman: Putnam Fellow · Nobel Prize in a science · Albert Einstein Award · Oersted Medal · National Medal of Science for Physical Science · Foreign Member of the Royal Society), patents awarded, corporations founded, major accomplishments (think of Musk, Gates, and Zuckerberg), etc. If there is not a difference in such external measures, there is no reason to believe that the test scores have meaning.


In-Sight Publishing by Scott Douglas Jacobsen is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. Based on a work at


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