Extremely High IQ: Characteristic of Intellectual and Community Isolation
Up until 1939, virtually all IQs were reported on a 16 point ‘ratio’ scale. While the distribution was very close to normal or Gaussian within a +/- 2 sigma range, outside of that range, high IQs were over-represented compared to statistical expectation. The higher the IQ the more the over-representation. For example, people with 160 R16IQs are about 25 times more commonthan they should be based upon the ‘normal distribution.’
Beginning in 1939, IQ scores began to be rendered on the basis of a 15 point or 16 point ‘deviation’ scale. Primarily through the efforts of David Wechsler and his IQ tests, the 15 point deviation is now nearly universal. What that means is that the distribution of IQs is being forced to a normal, bell curve distribution, despite not exhibiting such in raw form. The argument is that IQ in adults is not a natural scale and that any deviation from expected distributions is more likely to be an artifact of the test than a measure of any actual differences.
On the surface, this may appear to be a relatively uninteresting ‘inside baseball’ sort of distinction. However, upon closer inspection, I would contend that it is not and that, in fact, it is of central concern to the future.
Because very high IQ scores were assigned to historical personages based upon R16IQ scores, highly intelligent people whose IQs are being reported today on a D15IQ scale seem significantly less smart than historical geniuses. For example, Cox, et al estimated Leonardo da Vinci’s IQ at 180. However, that was a R16IQ and translates to a D15IQ of 159. In other words, if you score 159 on a modern IQ test, you are about as smart as da Vinci. However, since his IQ is generally reported on a R16IQ scale, you will likely assume that he was much smarter than you.In a slightly less dramatic range, Benjamin Franklin was estimated at R16IQ 160 which translates to a D15IQ of about 147. Many may wish to argue the assignation of a 159 D15IQ to da Vinci and 147 D15IQ to Franklin is too low. However, Cox and her team actually rendered even lower IQs on a naive ‘first try’ and then adjusted the scores upward. The accuracy of IQ estimations of historical geniuses is a valid concern and the methodology, Historiometrics, is arguably insufficiently precise to be of meaningful value. I am inclined to accept the assigned IQs as relatively accurate when performed by a team, using the Delphi Method, and in the presence of sufficient biographic information. However, I’ll have that argument at a different time. The Cox study was the most comprehensive attempt to assign IQs to eminent people ever undertaken and as such is ‘best evidence.’ Also, the method has been used more recently by Dean Keith Simonton, lending a degree of credence to it.
Another interesting consideration is the relationship between IQ and brain size. In the 19th Century it was assumed that a larger head meant more brains which meant more intelligence. During the 20th Century the argument was made that other factors, biochemical and morphological, are more important and that brain size is not correlated with IQ. In the late 20th Century the conventional wisdom changed and brain size and IQ, adjusted for sex and height, is now considered to be mildly correlated.
Recently, having read that Chris Langan, a person of very rare IQ, mentioned that his head is so large that he couldn’t find a motorcycle helmet that would fit. This struck me as peculiar because an extraordinarily large brain should not be found in a 160+ D15IQ if the two metrics are only mildly correlated. It is certainly possible that they may be mildly correlated in the +/- 2 sigma range but be highly correlated at extreme deviations. A good example is height and basketball. Between +/- 2 sigma height is only mildly correlated with basketball ability. However, it is highly correlated for those with heights over 2.1 meters.
Curious about this, I found a number of estimation formulae for brain size and working with another 160+ IQ person, settled upon on equation that appeared to be the best estimator. My brain size was estimated at 2,007 cc, far above the 1,406 cc average for Caucasian men. My friend’s brain size was 1,936 cc. Garth Zeitsman, well known for scoring 185 D16IQ on the Megatest, came in at 1,986. I expanded the search modestly, adding another five data points and we discovered that people with IQs over +4 sigma usually also have brain size over +4 sigma. We only found one example in the eight where a 160 D15IQ had a relatively normal (1,497 cc) brain size.
The probability of our result, given no or mild correlation, is essentially non-existent. Quite clearly, brain size and IQ is highly correlated at the extreme upper end. Furthermore, and this is the key point, the regression line of the measured population is .2brainsize – 180=IQ. This line is consistent with 16 point ratio IQs, not 15 point deviation IQ. For example, Garth Zeitsman has a cranial IQ of 217, which is much closer to the R16IQ equivlaent of 225 than the D15IQ rating of 180.
This result supports the following calculation. A 160 D15IQ equates to a 183 R16IQ. This, then, equates to a mental age of 29.28. We can then determine by the equation 29.28/16=16/x, that the 160 D15IQ person would assess the mental age of the 100 IQ person the same as the 100 IQ person would assess the mental age of an average eight year old child.
Consequently, the use of the D15IQ scale may imply less difference between normal IQs and very high IQs. As such, the intellectual gulf between people of moderately high IQ and very high IQ may be greater than it appears. I will undertake to explain this through two different lines of reasoning, the mental age construct and the range of mutual understanding construct.
In order to understand the mental age construct, we should first make a short digression into the history of IQ. IQ began as a measure of children’s intellectual maturation. In other words, an 8 year old child who scored like the average 10 year old would be given an IQ of 125 = 10/8X100. When these scores were analyzed, they were found to be more or less normally distributed with a standard deviation of 16. When tests for adults were developed, it was quite reasonable to create tests that distributed in the same way, even though ‘mental age’ no longer had much meaning. It would, at least in theory, create a continuity of scores from childhood to adulthood.
Based upon statistical expectations, the smartest child in a population of one million would be expected to score 176. However, instead of one child it was found that about 90 children would score above that IQ. It was also found that the smartest child in a million would be expected to have an IQ of 204! This means that the smartest child in a million 8 year olds would score at the adult level. Looked at the other way around, as an adult, such a person would perceive the average adult, intellectually, to be like an 8 year old child.
Let’s use a little less rare example. Suppose you have an D15IQ of 160. That is the limit of nearly all IQ tests given today. In other words, if you are at this level, you will not be given an IQ score, per se, but rather will be told that your IQ is ‘above 160.’ The score is essentially the same as what Cox, et al, estimated for da Vinci. 160+ D15IQ people have a rarity of one in 31,574, so while far from common, there are still quite a few people in this IQ range. Your R16IQ is 180, so as an adult, you have a ‘mental age’ of 16X1.8=28.8. The average D15IQ of a PhD is 123 or about a R16 IQ of 125. So, their mental age as an adult is 16X1.25=20. Because we generally baseline from ourselves, if your D15IQ is 160, the average PhD holder will appear to you as a 20/28.8X16=11.1 year old child.
This analysis, if correct, presents quite a problem for the 160 IQ person. Even very smart people will seem, from an intellectual standpoint, childlike in their analyses and arguments. That, however, is not how the average PhD holder will see it. Even if they are aware that you have an IQ of 160 and they have an IQ of 123, they are likely to minimize the significance of the difference. In other words, they will suggest that above a certain IQ the additional IQ points are more of a test artifact than a difference in real world intellectual ability. There is evidence to support this assertion, however, it would be incorrectly interpreted as such. Furthermore, since da Vinci had an IQ of 180 and you have an IQ of 160, they feel comfortable in granting da Vinci a higher level of perception than themselves while not granting it to you. In other words, even if they accept that you are smarter than they, in the final analysis, you aren’t really all that smart.
Recently, having read that Chris Langan, a person of very rare IQ, mentioned that his head is so large that he couldn’t find a motorcycle helmet that would fit. This struck me as peculiar because a extraordinarily large brain should not be found in a 160+ D15IQ if the two are only mildly correlated. It is certainly possible that they may be mildly correlated in the +/- 2 sigma range but be highly correlated at extreme deviations. A good example is height and basketball. Between +/- 2 sigma height is only mildly correlated with basketball ability. However, it is highly correlated for those with heights over 2.1 meters.
Curious about this, I found a number of estimation formulae for brain size and working with another 160+ IQ person, settled upon on equation that appeared to be the best estimator. My brain size was estimated at 2,007 cc, far above the 1,406 cc average for Caucasian men. My friend’s brain size was 1,936 cc. Garth Zeitsman, well known for scoring 185 D16IQ on the Megatest, came in at 1,986. I expanded the search modestly, adding another five data points and we discovered that people with IQs over +4 sigma usually also have brain size over +4 sigma. The probability of our result, given no or mild correlation, is non-existent. Quite clearly, brain size and IQ is highly correlated at the extreme upper end.
The least squares solution for IQ and CC (cranial capacity) is IQ=.2CC-180. This line is far more consistent with the R16IQ scale that the D15IQ scale. For example, Garth Zeitsman has an estimated CCIQ of 217, not far from his R16IQ of 225 but substantially higher than his D15IQ of 180. Consequently, the use of the D15IQ scale may be implying far less difference between normal IQs and very high IQs than actually exists. As such, the intellectual gulf between people of moderately high IQ and very high IQ may also be greater than it appears. This may have very profound ramifications for both the very high IQ person and for society as a whole.
In the 1930’s and 1940’s Leta Hollingworth studied children with R16IQs over 180 or, in modern terms, D15IQs over 158. She concluded the following, “… generally speaking, a leadership pattern will not form–or it will break up–when a discrepancy of more than about 30 points of IQ comes to exist between leader and led” Children Above 180 IQ Stanford Binet: Origin and Development (1942 p. 287) What she was saying was that a child with a R16IQ of 180 will simply not be understood by a child with a R16IQ of 150. This has been corroborated in adults by Dean Keith Simonton, “Even if the exceptionally bright individuals are able to target their use of language to the needs of their audience, the complexity of their ideas may be less accessible to listeners with IQs more than one standard deviation lower than their own” (Simonton, 1985; 1999a)
D.K. Simonton found a ‘persuasive sweet spot’ at about 1.2 sigma. This has been corroborated by Gibb (1947) who found that military officer candidates had IQs 1.2 to 1.5 sigma above the group they were to lead. Ghiselli (1963) found that success of middle managers was optimized when the manager’s IQ was 1.2 to 1.5 sigma above their staff. So, we have an IQ range of mutual understanding that absolutely is limited by 30 R16IQ points and is optimal for leadership at about 18 to 22 IQ points. D.K. Simonton worked primarily with the +/- 2 sigma range and as such the differences between D15IQ and R16IQ distributions was not significant.
At the core of the problem is the tendency for adolescents to challenge authority. The 160+ D15IQ child has the intellectual tools to win the debates against their teachers and other adults around them, but rarely has the emotional maturity to do so carefully. As a person matures to adulthood, they will learn ways to avoid such situations, but, by then, the damage is usually already done.
This all leads to another unsettling thought, based upon the work of Leta Hollingworth or what I will call the mutual understanding construct. She studied children with IQs over 180. Since, in her time, she, like nearly everyone else, used ratio IQs, she was studying children that today would be assigned IQs over 160.
The 180 R16IQ child has a D15IQ of 159. The 150 R16IQ child has a D15IQ of 140. What that means is the range of comprehensibility may become compressed at the higher end. After Simonton, the 180 R16IQ person, would be most persuasive to the 164 R16IQ person. However, when these are converted to D15IQs, the optimal differential is not 15 points but rather 9 points. 180 R16 IQ = 160 D15IQ and 180-16=164 R16IQ=151 D15IQ!
The range of absolute comprehensibility is also compressed. 180 R16IQ-30=150 R16IQ. 150 R16IQ = 140 D15IQ. 160D15IQ – 140 D15IQ = 20 points Essentially, this means that the practice of compressing the high end of the IQ scale to conform to a normal distribution may be masking the degree to which people with D15IQs over 160 are intellectually isolated from their social and professional surroundings. If correct, it suggests that the 160 D15IQ person will be most persuasive to people with D15IQs of 151 and will be virtually incomprehensible to people with D15IQs below 140. Converted to frequencies, they can be understood by one in 261 and those most persuaded will only be one in 2,968
Matters only get worse as IQ climbs above 160 and it does so quickly. A D15IQ of 165 leads to a optimal of 156 D15IQ and an absolute floor of comprehensibility of 147 D15IQ. This means optimal is one in 10,584 and comprehensibility is limited to one in 1,157.
A 170 D15IQ leads to an optimal differential of 162 D15IQ or one in 55,937 and an absolute floor of 154 D15IQ or one in 6,285.
Though completely lacking in experimental evidence, these analyses suggest that the prevailing use of 15 point deviation IQs may be masking just how isolated people with high IQs really are. As the 140’s are hard on professional success, the 160’s may be very hard on social success and the ability to form a sense of community. The problem is compounded by the incisive observation by Dr. Simonton that the extremely high IQ person may learn to tailor their use of the language to fit the audience, but the SIGNIFICANCE of the concepts will still escape them. In other words, a person with an D15IQ of 160 may learn to use only language accessible to people with D15IQ in the 120’s to 140’s but, while the words are understood, the conceptual significance is missed.
The 160+ D15IQ person may often feel that they have made a compelling case, yet the listener is not convinced. This may cause frustration in the the 160+ D15IQ person that may be perceived as different expressions to the audience, such as arrogance, condescension, etc.
In conclusion, we may have vastly underestimated the importance of creating intellectually sophisticated environments for the extraordinarily intelligent. It would appear that there is a population characterized by D15IQ’s between 140 and 160 who experience progressively greater isolation from even intellectually sophisticated environments such as Academia and a group of those with D15IQs over 160 who are completely isolated. Consequently, much of the benefit that they could provide to society is remaining unrealized.Addendum (Jan 19, 2013)Recently, as a followup to the increasing evidence that IQ and height adjusted brain size are correlated, I asked some of my 160+ D15IQ contacts to measure their heads. With the assistance of Eduardo Costa we reviewed the literature and found the best equation to rationalize all available data. What I found was that 160+ IQ people have large to huge brains. The data points are 2007cc, 1986cc, 1936cc, 1858cc, 1700cc. This compares to the average male brain size of 1,406. There are several important inferences that can be made. First, it suggests that the 16 point ratio IQ is probably the more accurate measure of absolute difference in intelligence. The regression line is .2V-181. The 1986cc data point requires no height adjustment and implies an IQ of 216. His D15IQ was measured on the Mega Test at 180 which equates to a R16IQ of 225. Clearly, the R16IQ is a better fit. The addition of the other data points makes the fit between cranial volume and R16IQ even better.
It also suggests that the right side fat tail may be the result of a secondary population with a mean R16IQ of 155. The implied mean cranial volume for the population is 1,686cc. This may be evidence of sympatric speciation caused by assortive mating with regard to intelligence. A slight increase in mean cranial volume to 1,781 will result in a cranial difference between the H. megacephalus and H. sapiens that is identical to the difference between H. sapiens and H. erectus. In other words, the next evolutionary step may already be emerging.
There is an actual meaning to the ratio IQ among children. A 150IQ eight year old child will score as a 100IQ twelve year old child. The scale is absolute. It has been argued that there is no reason to suppose that the ‘fat tail’ of the adult test results are anything more than an artifact of the test. This has been used to promulgate a D15IQ scale which now is nearly universally used. Now, we see that the ratio scale is mirrored by adult brain size, suggesting that the childhood differences are properly extended into adulthood. Consequently, from now on I will be converting all IQ scores to R16 rather than vice versa, with the designation of R16IQ.
Lastly, this evidence tends to support the evaluation of social and intellectual isolation based upon the 16 point ratio scale. For me and other 180+ R16IQ people, this is very bad news. It means that we actually can never be ‘mainstreamed’. Something like 99.6% or more of the population cannot comprehend us on a fundamental level. It suggests that organizations for such people needs to be more than ego-gratifying social clubs. We face unavoidable life challenges that can only be effectively addressed collectively.