(1) The Flynn Effect
    (a) Have IQ scores risen linearly or exponentially (additively or multiplicatively)?
    IQ scores on the WAIS and S-B have been rising  of the order of 3 points per decade over at least the 83 years since 1918.Question: Has IQ risen additively, climbing three points per decade by 25 points over this 83-year interval (83 years X 0.3 IQ points/year) or has it risen exponentially (multiplicatively) 3 points per decade for a total of 28 points (e^0.25) over the interval? In other words, are these percentages additive or are they multiplivcative? Presumably, they're multiplicative, since IQ tests have been restandardized several times overthe 85-year period. Dr. James Flynn's most recent paper quotes a 28-point rise since 1918, consistent with the idea that the Flynn Effect increases are multiplicative. It could fairly be argued that the changes aren't entirely regular or easy to measure, and that a three-point difference is in the noise level. However, (a) the cumulative effects may readily be measured by giving present-day test subjects the 1916 Stanford Binet and the oldest versions of other IQ tests, and (b) these disparities become more significant if we extend this 0.3% per year rise in IQ back into the 19th century.

    (c) Are we talking a standard deviation of 15 or of 16 when we discuss the Flynn Effect?
    The difference is only 2 points at the 2-sigma level, but of course, it enlarges as we deviate farther from the norm.

    (b) An IQ gain of 25 points looking backward to 1916 translates into an IQ gain of 33 points looking forward from 1916.
    The average citizen in 1916 might expect to rate an IQ score of 75 on an IQ test normed in 2001. Conversely, today's average citizens (IQ = 100) should earn about 133 (100/75 X 100) on the 1916 Stanford Binet.  However, the pre-1960 IQ scores were largely ratio IQ scores, while scores today are deviation IQ scores. 25 points of deviation IQ represents 27 points of ratio IQ. Note the distinction between IQ changes viewed retrospectively, and IQ changes viewed prospectively. If a mutual fund drops in value by 33%, it will have to rise 50% from its new, lower price to return to its original price.

    (c) Is this Flynn-Effect shift in IQ a shift in deviation IQ or is it a shift in ratio IQ?
    We know something about the ratio-IQ distribution in 1918, 1921, and the 20's, and 30's from the Terman Study, from Leta Hollingworth's "Children Above 180 IQ", from the Quiz Kids in the 40's, and perhaps, from a review of the Army Alpha Test results. One of the finds is that in these relatively small populations, IQ's of 200 (based upon a standard deviation of 16, and generally measured using the 1916 or 1937 S-B) were found with a frequency of about 1 in 500,000 rather than 1 in 5,000,000,000. All other IQ's at levels more than about 2 standard deviations above the mean were found with greater frequency than a Gaussian distribution predicts. So when we get a 33-point shift in average IQ, as seen prospectively from 1918, we're looking at a significant difference between a 33-point increase in ratio IQ and a 33-point increase in deviation IQ (equivalent to a 37-point delta in ratio IQ). And if we examine the Flynn Effect upon IQ's even modestly above the mean--viz., a 2001 ratio IQ of 121 or a 2001 deviation IQ of 120--and we suppose that this will translate into a 1916 S-B ratio IQ of 158 if the Flynn Effect  has acted upon mental ages, or a deviation IQ of 153 if the Flynn Effect has acted upon deviation IQ's, these differences become quite significant. The average proletarian today presumably earns a ratio IQ of 133 on the 1916 S-B, while the individual with a deviation IQ of 120 today would register a ratio IQ of 153 or 157 on the 1916 S-B. Converting both scores to deviation IQ's yields deviation IQ's of 130 and 145, or 148, respectively. This would compress the Gaussian distribution of IQ's, pulling in its wings. On the other hand, if the Flynn Effect has acted upon deviation IQ's, raising them all by 37 points of 1918 ratio IQ or 33 points of 1918 deviation IQ (standard deviation of 16, looking forward from 1918), then the Gaussian would simply have been shifted to the right by 37? 33? points of IQ measured on a 1918 scale, or 25 points of IQ measured with today's yardstick.

    (c) How much of the Flynn Effect is hollow with respect to g and how much is real?
    How precocious are children today? When do they start to speak? When do they start to read? How does today's Gesell Development Guide compare with the same guide in the 1930's? Have vocabulary, arithmetic, and general information increased since 1918? Since 1950? How much?
     (However, one confounding problem might be that many older IQ tests placed a premium upon vocabulary, arithmetic, and general information, and this has risen minmally over the past 85 years.)

    (d) How were adult IQ scores above 100 normed on older IQ tests that relied on mental age?
    It seems to me that they would either have to have been anchored to the projected IQ's of adults whose childhood IQ's were known but which were subject to regression to the mean and were not completely reliable, or they would have to have been determined on a percentile basis, but for outliers, this makes a big difference when it comes time to evaluate their scores.
    There would seem to me to be three problems with generating a mental age scale for adults above the basal mental age (which was taken in those days to be 16).
    One would be the problem of ceiling effects for raw scores above 90% correct out of the total number of questions on the test. (In many cases, based upon my own experience in administering IQ tests, it probably arises well below that 90% level when someone is very strong in a particular area such as spatial relations.) This 90% limit for many tests such as the Henmon Nelson would seem to me to reduce the valid ceiling of the test from a mental age of 24 to a mental age no greater than 20.5, corresponding to an adult ratio IQ of 128. The test-taker must answer 81 questions correctly out of 90 to earn a mental age of 20.5. So for practical purposes, the reliable ceiling on the Henmon Nelson would seem to me to be no greater than an adult IQ of 128. For the California Test of Mental Maturity, with 145 questions and a mental age ceiling of 32, the effective ceiling is 25.6 years of mental age, corresponding to an adult ratio IQ of 160.
    The second problem would have been the possible discrepencies between a Gaussian distribution and the actual distribution of adult intelligence. Up to an adult IQ of 125, we could probably assume, based upon the situation with childhood IQ's, that there is no more than a difference of the order of one-point between a normal distribution and the actual, observed upper-half distribution of IQ's. However, above that range, the discrepencies accelerate. Consequently, percentiles would have afforded a reliable ratio IQ yardstick up to about the 94th percentile (adding one point to the derived ratio IQ to allow for the ~1 point discrepency between ratio IQ's and deviation IQ's).
    The third problem would have been that childhood IQ's couldn't have been used very reliably to estimate adult mental ages because they often change by some number of points as the child matures.
    So how did the designers of those old IQ tests arrive at an adult mental age scale? One way to aproach it might have been to have established reliable mental ages for the IQ range between 75 and 125 by using percentiles and generating deviation IQ's, which, as I've argued, will probably be within about about a point of each other. I can probably add a point and assign a ratio IQ of 126 and a mental age of 20 yrs., 2 months to someone who scores at the 94th %tile (deviation IQ = 125). Then to arrive at a mental age of 24 to establish the ceiling of the test, I might be able to utilize the adult scores of test subjects who earned a mental ages approximating 20 years when they were 13 years, 4 months, for IQ scores of 150 on a test with a ceiling (for that age) of 180. This presumably gives them enough headroom to avoid ceiling effects. If I assume no decline in IQ between 13 years, 4 months, and 16 years of chronological age, then I can use these individuals to help benchmark my adult test. However, there still remains the influence of ceiling effects upon these "benchmarkers". As 16-year-olds, they probably aren't all going to make perfect scores on the Henmon Nelson test. None of them can earn scores that are greater than perfect,  and if some of them make scores that are less than perfect, they'll drag down the average mental age for the group, since 24 (corresponding to an adult IQ of 150) is the highest mental age anyone can earn.
    ???

    (e) What kind of score does today's average child make on the 1916 Stanford Binet?
    The Army Alpha and Beta tests? The Thorndike CAVD? How about above-average children? What about average adults? What's the shape of the curve(s)? What studies have been run, and by whom?

    (f) Has the Flynn Effect boosted IQ's in proportion to their values?
    If someone has a ratio IQ of 200, is the Flynn Effect twice as great for them as it is for an IQ of 100? If not, then the distribution of IQ's would have to have changed since 1918. It has been mentioned that the Flynn Effect acts primarily upon those whose IQ's lie close to the mean.
          Case I: No, or minimal Flynn Effect at the upper end of the IQ spectrum
          To show what this would mean, let's suppose that the Flynn Effect has had no effect upon upon individuals with deviation IQ's of 143. (In reality, it would probably be a sharply reduced effect but it probably wouldn't be zero. But I have an explanatory motive in selecting that IQ of 143, and in setting its Flynn Effect equal to zero.) Now suppose that a group of present-day 6-year-olds with an average IQ of approximately 100 takes the 1916 Stanford-Binet. They would presumably earn an average score of ~133 on that test, corresponding to a mental age of about 8. Another group of 6-year-olds with present-day deviation IQ's clustered around 143 also takes the 1916 S-B. Since a deviation IQ of 143 corresponds to a ratio IQ of 150, and since the Flynn Effect is presumed to have had no effect on IQ's in this upper register, they would be expected to average 150 on the 1916 S-B, just as they would on the 1973 Revision of the S-B. Thus, they would have a mental age of 9, only 12.5% higher than the children with a present-day IQ of 100. In other words, the entire present-day distribution of IQ's between IQ 100 and a present-day deviation IQ of 143, or a ratio IQ of 150 on the forthcoming Fifth Revision of the Stanford Binet, would be squeezed into the range from 133 to 150 on the 1916 test. The implication would be that today's individual with a deviation IQ of 143, instead of being "50% smarter" or "43% smarter" than today's average channel surfer would only be "12.5% smarter". Our present-day tests wouldn't necessarily reveal this because they're based strictly upon percentiles. But that would mean that enormous distortions have occurred in the distribution of intelligence since 1916. It would no longer be even remotely Gaussian.
        Case 2: The same Flynn Effect for all IQ's
          Suppose that the Flynn Effect is the same 3 points per decade for all IQ's. Obviously, we have a problem at the bottom of the bell curve, where the lowest possible IQ is now 33, measured on the 1916 S-B, or 25 measured on present tests. Now let's return to our example of a cohort of today's children with an IQ averaging 100, and a cohort of today's children  with a ratio IQ averaging 150, (deviation IQ of 143). On the 1916 S-B test, today's average child would score 133, as before, and today's child with a ratio IQ of 150 would score 183.The ratio of 183 to 133 is about 1.376, or less than today's 150/100 ratio of ratio IQ's (or 143/100 for deviation IQ's). The distribution function would have become compressed and distorted, but not nearly as much as it was in Case 1.
         Case 3: A Flynn Effect that's proportional to the IQ
           In this case, the child with a present-day deviation IQ of 143 or a present-day ratio IQ of 150 would hav experienced a Flynn Effect rise since 1916 of 33 X 1.5 = 49.5 (as measured on the 1916 S-B test, and would be expected to score ~199.5 on that test. In this case, the shape of the curve is preserved as we transition from 1916 to the present time. The only sticking point arises, as it did for Dr. Flynn, when we try to reconcile someone like Carl Friedruch Gauss, who learned to read at 2 and corrected his father's arithmetic before he was 3, with the reduced IQ that we must assign to him by virtue of a Flynn Effect that wouldn't allow him a current ratio IQ greater than 150, and a current deviation IQ greater than 143!

    (g) Does a lifetime of intellectual exercise in an increasingly complex world lead to Flynn Effect boosts for the elderly? Are we keeping up with the times? There is evidence that indicates that part of the age-related cognitive decline that we've attributed to the elderly is a manifestation of the Flynn Effect. IQ tests have gotten tougher, but one's IQ seems to be frozen at the level of one's youth, particularly on tests of fluid g. One way to examine age related cognitive decline might be through the age corrections for WAIS scores.
    Using the coefficients in the table, I've calculated below the maximum WAIS IQ score for the various age ranges. What's shocking about this is the age-related cognitive decline as we go from 25-29 to 75-79. We might expect a Flynn-Effect decline over the 50-year period of 15 points of iQ, but instead, we find a 45-point decline in absolute scores, which I'll take as a proxy for IQ. The average 75+-year-old will score only 60.5% as well, in terms of absolute scores, as the average 25-29-year-old. Only the top 2% of 75+-year-olds will match the average 25-29-year-old on an absolute basis. Someone with a 160 IQ at 25-29 will have fallen back to a 125 IQ measured without age correction by age 75+.

Age 16-17: Mean 103.7 SD 23.61   = 161.18
Age 18-19: Mean 106.74 SD 25.16 = 155.6
Age 20-24: Mean 110.10 SD 25.69 = 152.49
Age 25-29: Mean 113.55 SD 24.98 = 151.91
Age 30-34: Mean 107.09 SD 24.30 = 157.35
Age 35-39: Mean 108.77 SD 25.06 = 154.65
Age 40-44: Mean 103.17 SD 24.04 = 160.42
Age 45-49: Mean 101.53 SD 27.04 = 154,62
Age 50-54: Mean 95.99 SD 24.73   = 163,31
Age 55-59: Mean 92.83 SD 26.27   = 161.19
Age 60-64: Mean 90.21 SD 24.15   = 168.19
Age 65-69: Mean 88.13 SD 22.92   = 172.21
Age 70-74: Mean 77.19 SD 21.42   = 186
Age 75+:    Mean 68.71 SD 21.56      = 191.34

    Equally intriguing are the changes going from age 16 to age 25-29. On older IQ tests, it was assumed that the IQ didn't change beyond the age of 16. This table shows that it increases almost 10%, peaking at age 25-29. If we subtract 3 points going from 16-17 to 26-27 to correct for the Flynn Effect, then it differs by about 13%.

    This second table attempts to show how the IQ varies with age after correcting for the Flynn Effect (assuming the usual three-points-per-decade rate of change for the Flynn Effect). Obviously, there's a lot more going on than the Flynn Effect.

Age 16-17: Mean 100.7 SD 23.61
Age 18-19: Mean 103.74 SD 25.16
Age 20-24: Mean 111.60 SD 25.69
Age 25-29: Mean 113.55 SD 24.98
Age 30-34: Mean 108.59 SD 24.30
Age 35-39: Mean 111.77 SD 25.06
Age 40-44: Mean 107.67 SD 24.04
Age 45-49: Mean 107.53 SD 27.04
Age 50-54: Mean 103.49 SD 24.73
Age 55-59: Mean 101.83 SD 26.27
Age 60-64: Mean 100.71 SD 24.15
Age 65-69: Mean 100.13 SD 22.92
Age 70-74: Mean   90.59 SD 21.42
Age 75+:    Mean   83.71 SD 21.56
 

(2) How do various capabilities scale with IQ? With mental age? (I'm looking for absolute measures of intelligence.)
    Why are IQ's measured only on relative scales? Why aren't they measured in absolute terms? Saying that someone is brighter than than 99% of the population is no more meaningful than saying that someone is taller than 99% of the population.

• How does backward memory span for digits,random  letters, sentences, images, etc., vary with mental age? Who has researched this topic?
• How does totalrecognition vocabulary scale with IQ? Who has investigated this topic?
• Has general information ever been assigned levels of difficulty? (I'm thinking in terms of common information such as, "What state lies north/east/south/west of Utah?", "What is the atmospheric pressure at sea level?", "Who wrote the Preamble to the Constitution of the United States?" or "Who said,, 'If I had a long-enough lever and a place to stand, I could move the Earth'?")
• How does rote learning scale with IQ?
• Can we quantify conceptual learning? What studies have been performed, and what were their overall quantitaive results and conclusions?
• Are there other absolute measures of intelligence? How do they relate to IQ? The times to solve a various problems would be an acceptable kind of metric.

•     For study purposes, how is "black" defined? The majority of U. S. blacks are probably racially mixed.  So when setting up a comparative study of blacks versus whites, how does one discriminate which blacks are blacks, and which are mulattos, quadroons, and octaroons? (I'm sure these factors must have been taken into account in setting up such studies.)
•     What is the SD for blacks? 12.75 (85/100 X 15)? If so, the 5 SD level would come at IQ 149 and the 4.75 SD level (one in a million) would be IQ 145.56. (Again, I'm sure all of this is available; I just don't know where to find it or whom to ask.)
•     How does the distribution look? Is it normal? Is it log-normal or Pearson Type IV--i.e., "abnormal"?
•     One of the difficult problems with adult IQ tests is that, on most of them, ceiling effects begin to occur above the two-sigma level. This is particularly true for those whose gifts are lopsidedly distributed. The WAIS-III has a ceiling slightly above the three-sigma level. But discrepencies between ratio IQ's and deviation IQ's only begin to become significant above the two-sigma level. However, assuming for blacks a mean IQ of 85 and a standard deviation of 12.75,  a Caucasian IQ of 130 (SD = 2,) corresponds to a black IQ of 152.94 (SD = 3.53). And by the time we've reached 3.53 standard deviations from the mean, the difference between a ratio IQ and a deviation IQ become quite significant (10 points at 3.75 SD). In other words, an IQ test like the WAIS-III should have a ceiling of 5.75 SD for blacks, and should afford reliable measurements up to, perhaps, 4 SD for blacks. In other words, blacks should be ideal for studying the differences between adult ratio IQ's and adult deviation IQ's. Why? Because ceiling effects plague other groups before deviations from a Gaussian distribution become significant, but for blacks the ceilings are high enough (in standard deviations) that significant differences ought to be apparent and measurable..
•     How has the Flynn Effect acted upon the black IQ distribution?

(4) Miscellaneous Questions

•     It has been argued that the deviations from a normal curve that occur among children are simply a function of varying rates of mental maturation, and that the distribution of adult ratio IQ's is Gaussian. (Yeah, I know. It's hard to define an adult mental age above the norm, and it's probably hard to confidently measure adult ratio IQ's.) Is that true? I have some reason to doubt it, based upon distributions such as the distribution of adult AGCT-derived IQ scores in the table below. They show a frequency of occurrence that agrees closely with all the childhood ratio-IQ distributions I've seen, and suggest that log-normal aproximations fit adult IQ distributions tolerably closely. Why am I so interested in the relationship between ratio IQ's and deviation IQ's? Because deviation IQ's have no absolute meaning. Ratio IQ's may not mean all that much, either, but my own very limited experiments have suggested that, for instance, changes in ratio IQ's may be the proper yardstick for measuring the Flynn Effect, particularly when we get to IQ values that are removed even moderately from the mean. (Actually, I'd like to see some kinds of absolute fiduciary standards, such as nerve conduction speeds, decision speeds, comprehension speeds, and problem-solving speeds, and that gets back to the idea of absolute measures of intelligence.) But the question is: do very high adult ratio IQ's appear with greater-than-Gaussian frequency just as they do with children?
•     If the answer to this question is "yes", then what does it portend for regression to the mean as children grow to adulthood? If specific individuals tend to regress toward the mean as they mature but the overall distribution remains the same as it is for children, then there must be "late-bloomers" who rise to take their places in order to keep the upper ranges of the distribution populated.

•     It has been claimed that scores on highly g-loaded tests such as the RAPM and the Cattell Culture-Fair Test are truly normally distributed even at their upper extremes. Is that true? If so, then scores on tests of primarily crystallized intelligence, such as (perhaps?) the Slossen Test, might be expected to deviate more than a middle-of-the-road test such as the WISC and the S-B.
•    Height isn't normally distributed at heights significantly removed from the mean. It has been cited as an example of a genetically influenced trait that, like IQ, isn't really Gaussian. How is height distributed? Does it have the same distribution curve as ratio IQ's? In the case of height, we don't have to worry about ceiling effects. We can measure the guy outside.

5. The Very Brightest and Their Relationships with the World

•     I've gotten the impression that there has been relatively little research devoted to the profoundly gifted, and that what attention has been given hasn't been aimed at the question: how do we make the best use of these precious people? During my years with NASA and Georgia Tech, I casually wondered now and then why there didn't seem to be a national registry of the very brightest, with attention to their needs and their encouragement. When, two years ago, I discovered  the ragged state of affairs vis-a-vis our brightest, I was shocked. As IQ's rise from 75 to 125, there are the most dramatic changes in life outcomes and socioeconomic statuses, but that once the IQ exceeds about 120, there seems to be little correlation between IQ and success in even the most demanding intellectual pursuits. But I haven't heard of much happening in terms of investigating this mystery. Why is this so? What are we doing wrong?
•     In working with some of the profoundly gifted, I've gradually gotten some hints regarding what might possibly too-often derail their extraordinary potentialties. There seem to be major problems with extreme giftedness in a society that isn't geared to them, like the plight of an eight-footer writ large. What about this? How much has been done to attempt to ferret out and groom our brightest not only academically, but also emotionally and socially?
•     Ruth Duskin Feldman was one of four Quiz Kids who scored IQ 200 or above on the Stanford Binet Test. She writes in, "What Ever Happened to the Quiz Kids?" that she didn't continue on to graduate school because, like Buridan's Ass, she couldn't decide what single subject to select. Richard Williams had trouble deciding what he wanted to do, and ended up a second- or third-tier diplomat in the State Department (with its old-boy network). Joel Kupperman, the math whiz, became a philosophy professor at the University of Connecticut. Lonnie Lunde played piano at an upscale Chicago nightclub. It may be argued that they didn't have the drive, but I would suggest that the "drive" may be programmable, particularly if what we offered were excitement and the thrill of discovery.
•     Generally, I've gotten the idea that the utterly brilliant are left to sink or swim. I've also gotten the impression that the teenage years are crucial to future success. Four of the leading physicists and one of the leading mathematicians of the twentieth century, John von Neumann, Edward Teller, Eugene Wigner, Leo Szilard, and Paul Erdos, came from the Lutheran High School in Budapest, inspired by a science teacher by the name of Laszlo Ratz. A similar situation seems to have arisen in the physics department at the University of Rome, where the leading Italian physicists of the 20th century cut their teeth, including Enrico Fermi, Bruno Pontecorvo, Bruono Rossi, and Emilio Segre. Interestingly, Edna Fermi wrote in her account of those early days that the brightest graduate student among them didn't make it. This seems to be a common occurrence.
•     I've been asking people I know their impressions of the smartest people they've known, and I've encountered common themes. One is that of social ineptitude. Another is lack of common sense. One interesting observation is that a significant fraction of our 4+ sigmas, like Bill Gates, Nathan Myrvald (sp?), Paul Allen, and presumably, Steve Ballmer are multibillionaires. A sizable fraction of the 4+ sigmas I know are multimillionaires. I have the impression that when the rare hyper-gifted turn their hands toward making money, they succeed in spades. But what a waste! We need cures for cancer. We need better ways to relate to each other. We need cures for Alzheimer's and Parkinson's Diseases. We need a marriage between general relativity and quantum mechanics. We need works of genius. I think that "we" (society) have a vested interest in utilizing the talents of these potential geniuses.
•     I'm not aware of efforts to understand what's going wrong. Is there much work in this area?