Intelligence and the Flynn Effect, One More Time

[Edit 02/11/2017: The final version of this essay can be found here.]

Imagine an experiment that proceeds in the following fashion. There is a stage, and onto that stage researchers place boxes that are fairly nondescript other than that each has a small hole near the bottom. Each box is left on the stage for precisely an hour, during which time a small quantity of water drains from the hole and is collected and measured.

After taking a broad sampling of boxes it is discovered that there is some variation in the results — some boxes produce more water, some less. The distribution comes out nearly normal, with a mean around 500 ml collected in an hour and a standard deviation around 100 ml. To provide some visualization for these results, the researchers place just three boxes on the stage: a left box producing 400 ml in an hour, one standard deviation below the mean; a middle box producing 500 ml in an hour, right at the mean; and a right box producing 600 ml in an hour, one standard deviation above the mean.

The study of these boxes is of some importance to the researchers because the boxes serve useful purposes in the community. For instance, among other valuable features, food placed on top of a box does not spoil as quickly as it would otherwise. Furthermore, other experiments have shown that a box's usefulness tends to be directly proportional to the box's water production score, and although this correlation is not exact it is statistically significant and it emerges in all kinds of usefulness experiments. Based upon this strong correlation, the researchers define a box's usefulness as equivalent to its water production ability.

Curious about the variation in scores and wanting to learn more about the cause of water production ability, the researchers conduct experiments that focus on the physical/generational characteristics of each box. Some of these characteristics, such as surface material and factory of production, emerge as helpful candidates, because variations in these characteristics correlate with variations in water production scores. Again, the correlation is not exact but it is statistically significant and it allows the researchers to predict water production scores with a reasonable degree of accuracy given any box's overall characteristics. These results are strong enough to convince the researchers that a box's water production score and its physical/generational characteristics are tightly linked. The researchers begin to form theories about the nature of this linkage.

These experiments are frequently repeated, at least once each year, and the researchers note that the results remain extremely consistent — same variation, same distribution, same correlations. All the prior years' findings are regularly verified, no theory gets overturned.

And yet over time, there does arise one nagging problem.

Despite the fact that almost every feature of the experiment remains exactly the same — same set up, same variation in results, same distribution, same usefulness, same correlations, same everything — despite all this remarkable consistency, the water production scores keep going up. They keep going up every year, and they keep going up for all the boxes. The amount of increase is not overwhelming but it is large enough that it cannot be ignored. For instance, the collection containers that were used in the early years of the experiment eventually have to be replaced with bigger containers to prevent spillage. After ten years of these experiments, when the researchers place the three representative boxes onto the stage to help visualize the results, the left box now produces 480 ml of water in an hour, the middle box produces 600 ml, and the right box produces 720 ml. The researchers realize that an average box now has the same water production ability as did a box one standard deviation above the mean from just ten years prior.

Many explanations for this phenomenon are offered and investigated, beginning with a focus on the boxes themselves. Has there been a change in the surface materials? The researchers discover that for a small number of boxes some slight alterations have indeed been introduced. Has there been a change in the construction process? Again the researchers find that one factory has been mothballed and another remodeled, although the majority of production facilities remain as before. The researchers look for still other clues, such as changes in size or weight, and although particular instances can be found, such changes are not pervasive. Indeed, that becomes the telltale defect against all these explanations — each accounts for only a small number of cases at best, and appears inadequate in the face of the water production increase across boxes and across time.

The researchers then focus on the boxes' environment, thinking that this line of attack might uncover a more wide-ranging solution. For instance, a few stages where experiments are conducted now sit higher than they used to. Other stages are made out of metal whereas they were formerly made out of wood. And some stages have had a ventilation system installed. But here too, such circumstances account for only a limited number of cases, and furthermore, environmental explanations suffer from a still more troubling defect, namely that no one can explain how an environmental change would translate into the necessary change in physical/generational characteristics for each box. Everyone agrees — as a consequence of the experiments conducted each year — that water production scores and the physical/generational characteristics of each box are tightly linked, so that any change in water production scores corresponds to a change in the boxes' characteristics. But how does an environmental change produce such an effect? How does a higher stage, a metal stage or a ventilated stage produce the requisite change in surface material or point of origin? It seems implausible.

One researcher attempts to solve this dilemma by demonstrating how an environmental change and a physical/generational change can feed off each other with an amplifying effect. He uses terms such as multiplier and feedback loop and produces an impressive array of mathematics. “For instance a small change in surface material or production quality can generate a subtle difference in air flow around the box,” he begins. “At the point of maximum air flow differential, a powerful feedback vibration is set up inside the box. Then the vibration amplifies the rearrangement of surface material, which impacts the air flow still more the following year, which causes ….”

Another researcher, noting the large number of hypotheses generated so far and each one's inability to account for all the cases, suggests that perhaps there is not just one explanation for the rising water production scores but that the solution is to be found in a combination of explanations. This approach seems promising to the researchers, although they have to agree it is not the kind of definitive answer they originally had in mind.

Then one day a visitor shows up and mentions something to the researchers. “I don't know about you, but it seems to me that it keeps getting warmer all the time — I've been coming to your experiments for several years now, and each time I visit, it feels hotter than it did the last time. Then it occurred to me, that would make for an elegant explanation to your rising water production scores.”

“How so?” ask the researchers.

“A general rise in temperature is a perfect match to what you're looking for. It has all the essential features. For one, the increase in temperature mirrors the increase in water production scores. Also, the increase in temperature is continuous over time — just like the rise of water production scores. And finally, the increase in temperature is ubiquitous, it affects all the boxes the same.”

The researchers are not convinced.

“Here are the shortcomings in your explanation,” they say to the visitor. “In the first place, your explanation isn't germane to the problem. We are investigating water production ability, as measured by water production scores and contained in the physical/generational characteristics of these boxes. It's hard to see how ambient temperature can even be relevant to that discussion. But assuming it were somehow relevant, your explanation has an even bigger defect: you can't provide a plausible description for how a change in environmental temperature will alter the physical/generational characteristics of each box. Are you trying to suggest that a slight increase in temperature will somehow rearrange a box's surface materials in a profound way, or somehow reset a box's factory of origin. That would be ridiculous. If a change in temperature were the cause of a change in water production scores, then that change in temperature must also impact the physical/generational characteristics of each box, because those characteristics are the source of a box's water production ability.”

The visitor thinks about this for awhile, then gives a lengthy reply:

“I believe you're working under a mistaken assumption. Listen, I agree with you that variations in a box's physical/generational characteristics produce corresponding changes in a box's water production score — you have plenty of experimental evidence for that, and the results are strong and compelling. But the results are so strong and compelling that they seem to have convinced you that the inference is valid also in the other direction — that is, that every change in water production score is necessarily accompanied by a change in a box's physical/generational characteristics. But actually, you have no evidence that the inference is valid in that direction, all your evidence runs the other way. Moreover, the increase in overall water production scores across time and across all boxes suggests quite strongly that such an inference would be wrong.

“Here's how I would describe the situation. We have three different quantities in play: a box's capacity to produce water, the water production score, and the ambient temperature. Let's let letters stand for these quantities:

C = a box's CAPACITY to produce water,
S = a box's water production SCORE, and
T = the ambient TEMPERATURE.

“A box's water production score (S) is the combination of the two other factors (C and T) working independently. This can be expressed in a simple relationship:

S = C x T.

“That relationship fits the experimental results to a tee. At any given point in time, the ambient temperature (T) will be constant, so when experiments are run at that time, all the variation in S will be the direct result of the differing physical/generational characteristics of each box, because those characteristics drive a box's capacity to produce water (C).

“But over time it's the orthogonal effect that holds sway. Over time, it is C that remains constant. Your investigations have already told you this, because when you went looking for physical/generational changes across time that would explain your results, you discovered that physical/generational changes across time are minimal at best, hardly worth the notice. But if C remains essentially constant, then all the increase in S over time is explained solely by an increase in T. The rising ambient temperature causes water production scores to increase over time and does so without impacting any box's physical/generational characteristics.”

“But it has to impact those characteristics,” the researchers insist. “A box's physical/generational characteristics embody its water production ability.”

“No, that's just it,” the visitor answers. “Those physical/generational characteristics tell only half the story at best. If you want to fully understand the nature of water production ability, you have to take into full consideration the ambient temperature too. And if it's the increase in water production ability you're trying to explain, then all the focus has to go towards the ambient temperature, because that's the only factor that changes over time.”

The researchers are polite but end by saying they cannot discuss the matter any further — they have combinations of explanations and impressive mathematical formulas to attend to.



I believe the above analogy forms a nearly exact isomorphism to the current situation regarding intelligence and the Flynn effect.

IQ scores are like water production scores, and individual people (or individual brains, if you will) are like boxes. Scientists have built up a large, compelling cache of evidence that variations in IQ scores among individuals are driven by a presumed set of neuronal/genetic characteristics, the idea being that if we had good knowledge of an individual's neuronal/genetic background, we could predict with a reasonable degree of accuracy that individual's IQ score and corresponding likelihood of success within the community. The correlations are not exact but they are strong enough to be informative across both individuals and groups of people.

If that is all there were to it, then intelligence would be essentially explained. However, that is not all there is to it. In addition to the experimental evidence outlined so far, scientists have also discovered that raw IQ scores keep going up over time, a phenomenon that has been dubbed the Flynn effect. The scores keep going up every year and they keep going up across all sorts of populations.

Lots of explanations have been offered. Many of them focus on presumed improvements to a human's neuronal/genetic underpinnings — through better nutrition for instance, or assortive mating. Other explanations focus on changes in environmental features, such as increasing visual stimulation or a wider access to education. None of these explanations however can account for the widespread impact of the Flynn effect, plus the environmental explanations suffer from the further perceived difficulty that they must be translated into more or less permanent changes in a person's neuronal/genetic characteristics, because everyone agrees those characteristics are what drive intelligence. This translation often seems implausible.

Dickens and Flynn (2001) have suggested the problem can be solved by demonstrating that neuronal/genetic characteristics and environmental factors resonate off each other with amplifying effect. They have developed multipliers, feedback loops and complex mathematical formulas that show how this mechanism can be tuned to experimental results. Other researchers, perhaps frustrated over the lack of a definitive solution, have suggested that the Flynn effect can be explained by no one factor alone, but that instead a combination of factors must be involved.

My contribution to the Flynn effect discussion is simple — I seem to have noticed something that apparently no one else has. I have noticed that the amount of non-biological pattern, structure and form contained within the human environment keeps going up over time. This increase is apparent from a survey of human history, from the human great leap forward through the agricultural revolution through the ancient civilizations of Mesopotamia, Egypt and Greece through the Renaissance and finally culminating in the explosion of technologies and constructions we live within today. When humans move through their environment, they navigate an increasingly complex maze of pattern, structure and form, and they navigate this maze at a faster and faster pace. Measuring the quantity of this maze would be a challenge, but however one would measure the amount of non-biological pattern, structure and form tangibly contained within the human environment, one would have to conclude it keeps going up year after year after year.

This increasing amount of pattern, structure and form contained within the human environment makes for an ideal and elegant explanation of the Flynn effect. It has all the essential features. For one, the increase mirrors the increase in raw IQ scores. Also, the environmental increase is continuous over time – just as with the rise in test scores. Plus the environmental increase is ubiquitous, people are exposed to it literally everywhere. Furthermore, in considering the content of an IQ exam — all those questions formed out of pattern, structure and form — one recognizes that navigating an IQ exam is not all that unlike navigating the maze of the surrounding world, and thus it cannot be too surprising that ambient pattern, structure and form must have something to do with human intelligence.

Here is how I would describe the situation. There are three different quantities in play: a person's neuronal/genetic capacity for intelligence, the raw IQ score, and the amount of pattern, structure and form contained within the human environment. We can let letters stand for these quantities:

C = a person's neuronal/genetic CAPACITY for intelligence,
S = the raw IQ SCORE, and
A = the AMOUNT of pattern, structure and form contained within the human environment.

A person's IQ score (S) is the combination of the two other factors (C and A) working independently. This can be expressed in a simple relationship:

S = C x A.

That relationship fits the experimental results to a tee. At any given point in time, the ambient pattern, structure and form (A) will be constant, so when experiments are run at that time, all the variation in S will be the direct result of the differing neuronal/genetic characteristics of each person, because those characteristics drive a person's capacity to demonstrate intelligence (C).

But over time the orthogonal effect holds sway. Over time, it is C that remains constant; we have little in the way of evidence to suggest that profound neuronal/genetic changes occur over time, just as to be expected under the tenets of biology and evolution. But if C remains essentially constant, then all the increase in S over time is explained solely by an increase in A. The rising amount of pattern, structure and form contained within the human environment causes IQ scores to increase over time and does so without impacting any person's neuronal/genetic characteristics.

Scientists have a hard time considering — let alone accepting — this description of intelligence because they are working under a mistaken assumption. Their evidence is so strong and compelling that variations in neuronal/genetic characteristics lead to corresponding differences in IQ scores that the scientists have somehow become convinced that the inference is valid also in the other direction — that is, that every change in IQ score is necessarily accompanied by changes in neuronal/genetic characteristics. That unsupported assumption is what leads everyone astray. For instance, all the complexity of the Dickens-Flynn model is driven entirely by a perceived need to have environmental influences and neuronal/genetic characteristics interact. But in point of fact that interaction is not called for at all, all the evidence clearly indicates that changes in those two factors are essentially independent.

If there is one major consequence to this simple description of the Flynn effect, it is that it compels a complete reassessment of the word intelligence. Because of the perceived bi-directional linkage of IQ scores and neuronal/genetic characteristics, scientists have been restricting use of the word intelligence to the domain of that linkage alone. But neuronal/genetic characteristics tell only half the story at best. If we want to come to a complete and accurate understanding of the nature of intelligence, then we must take into account also the amount of non-biological pattern, structure and form tangibly contained within the human environment. And if it is the increase in intelligence that we are trying to explain, then all the focus must go towards the structural human surroundings, because that is the only factor that changes over time.



Dickens, W. T., & Flynn, J. R. (2001). Heritability estimates versus large environmental effects: The IQ paradox resolved. Psychological Review, 108, 346-369.

A Match Made in Hell

On her Twitter feed, Michelle Dawson picks up on the troubling circumstances autistic kids face on a daily basis:

"There is a puzzle piece missing in their brain"--one way typical children (10yrs) now describe atypical children http://t.co/1ElTk7XD8x
— Michelle Dawson (@autismcrisis) June 15, 2013

In parsing that sentence, I notice that the first half (“There is a puzzle piece”) is supplied by the advocacy of groups such as Autism Speaks, and the second half (“missing in their brain”) is harnessed from the shibboleths of neuroscience. Talk about a nasty double team.

Measures of Success

It's with split interest that I note the publication of Kuhl (2013) and the dissenting comments from two of the paper's reviewers, Jon Brock and Dorothy Bishop. As Brock and Bishop rightly note, Kuhl (2013) resorts to an after-the-fact cherry picking of data from a broad array of dubious measures, and presents those post-selected findings as significant. The dissents of Brock and Bishop are part of a slowly growing movement against such questionable techniques — a few in the scientific community have begun to recognize (perhaps with some egg on their faces) that all this post-hoc data mining might not be the best route forward in the advancement of human understanding. I applaud this growing dissent, feeble though it may be.

But there's also a bitter irony to be found here. As noted in my previous post, it is Dorothy Bishop herself who has pronounced, without the slightest hint of disingenuousness, the recipe for success in today's science: “If you want to make your way in the scientific world, there are two important things you have to do: get grant funding and publish papers.” Well, let's compare Kuhl (2013) against those criteria, shall we? Let's see, the paper was supported by grants from the National Institute of Mental Health and the National Institute of Child Health and Human Development. So get grant funding, check. And of course we're all discussing this paper precisely because it has appeared in the highly regarded PloS ONE journal. So publish papers, check. Heck, with the aid of a tacked-on co-author, Kuhl (2013) has even managed to score some media exposure, which will no doubt lead to further grant funding and more publications. So, bonus check check. By Dorothy Bishop's criteria for modern scientific success, Kuhl (2013) could only be described as a stunning achievement!

Listen, I know that Kuhl, Brock, Bishop and all their scientific colleagues mean well, but I'm one of those old-fashioned folks who tends to judge people on what they do, not on what they mean or say. And the one thing I can say Kuhl, Brock, Bishop and all their scientific colleagues manage to do in common is stand firmly behind, indeed even form, the machinery of modern science (grant funding, formal publication, peer review, academic credentialing, co-authorships, etc.). So I'm having a hard time seeing how any of them have earned the right to complain about the costs of that machinery. Because make no mistake about it, one of the costs of that machinery is the massive proliferation of papers such as Kuhl (2013). It's as inevitable as 2 following 1.

I'm impressed when the dissenters are willing to speak out against the problem, but I'll be even more impressed when the dissenters quit justifying and forming the conditions of the problem.




Kuhl PK, Coffey-Corina S, Padden D, Munson J, Estes A, et al. (2013) Brain Responses to Words in 2-Year-Olds with Autism Predict Developmental Outcomes at Age 6. PLoS ONE 8(5): e64967. doi:10.1371/journal.pone.0064967

You Reap What You Sow

Here is a revealing statement from Dorothy Bishop, someone who has made her way in the current scientific world:

If you want to make your way in the scientific world, there are two important things you have to do: get grant funding and publish papers.

I wonder if Newton, Darwin or Einstein ever subscribed to that view. At any rate, I'm beginning to think my criticism of modern scientists is misconceived — perhaps I should pity them.

Perception, Mathematics and Autism

[Edit 02/11/2017: The final version of this essay can be found here.]

Perception, including human perception, has not always been a well-defined concept, but these days I believe general agreement can be reached somewhere along the following lines. Animals receive, through their nervous system, an assortment and range of sensory experience from which is distilled an awareness of the animal's environment, as well as a reaction back into that environment. It is the distillation part of this process that stands at the core of what we would typically call perception. Perception is necessary because the entirety of sensory information would be too much. Unfiltered and undifferentiated sensory experience would lead only to a chaotic awareness of the animal's environment and would make the enactment of targeted and productive reaction problematic at best. Perception extracts signal from sensory noise, perception distinguishes figure from sensory ground. The foregrounded elements of sensory experience are precisely those elements that an animal perceives.

As such, particular types of perception can be described in large measure by highlighting the characteristics of what tends to foreground within that perception and also juxtaposing these against the characteristics of what tends to remain ignored (unperceived). Applying this technique across the entire animal kingdom is instructive, for it reveals a broadly consistent and unifying theme. As any regular observer of television nature shows could easily attest, the experiences and attentive focus of untamed animals are both predictable and mostly unvaried across the many species, and can be classified, almost entirely, under just a small set of headings: food, water, danger, shelter, family, sexual targets, sexual rivals, predators, prey, conspecifics. There is of course nothing random or surprising in that list; each of its constituents is an essential component in the drive for survival and procreation, and this type of perception is one that efficiently serves the biological process. Nonetheless, while noting these characteristics of what tends to foreground within animal perception, it is worthwhile also to consider those sensory elements that go undiscerned. The wind rustling in the grass and leaves, wisps of cloud overhead, an arrangement of bushes along the distant horizon — unless such elements and characteristics happen to play a direct role in an animal's quest for survival and procreation, they will go almost entirely unnoticed. And this will be true for a very large portion of an animal's sensory experience, it will simply fade unobserved into the sensory background.

I would like to give a name to this universal tendency to foreground primarily (perhaps exclusively) those sensory features that are essential to survival and procreation. I will call this tendency biological perception. And on the other side of the coin, I would like also to give a categorizing name to the sensory features themselves — that is, those features that tend to foreground within biological perception (food, water, danger, etc.). Since I am unaware of any such name in common use I will invent one, darwinamatics, an awkward term to be sure but one chosen because it corresponds nicely to its ready-made counterpart, a counterpart we will consider shortly.

Human perception is intriguing because it is both animal perception and it is not. Human perception adheres to biological perception's rule of universality and yet it also provides the only known exception to biological perception's rule of exclusivity. That human perception is a form of biological perception can be seen readily enough from two different considerations. First, there is mankind's long anthropological history, which reveals that for an extremely large portion of time after the evolutionary split from the other apes, man's existence — and along with it, his perception — must have remained as animal-like as all the other beasts. From Australopithecus down through the later genus Homo, there is little in the way of evidence to suggest that mankind's foregrounded focus and endeavor ever deviated far from the constraints of survival and procreation. Some might even argue that this perceptual state remained constant until as recently as fifty thousand years ago, but at whatever point one places the timing of mankind's perceptual turn, it seems certain that our species' perceptual characteristics must have comprised little more than biological perception for an extremely long period of time.

The second consideration that demonstrates human perception is a form of biological perception can be observed directly today. For although modern human perception can no longer be defined in terms of just biological perception alone, modern human perception still retains the vast majority of its former biological traits. When we observe what tends to foreground within modern human awareness, we discover that food, sex, danger and all the rest continue to play a prominent role — darwinamatics still constitutes much of the locus of human attention and endeavor. Indeed, a healthy dose of biological perception is considered to be critical for both development and everyday functioning, with those judged to be inadequately attuned to such things as family, rivalries and conspecifics judged also to be the bearers of various psychological or developmental disorders. Foregrounded elements of survival and procreation no longer play the crucial role they once did on the prehistoric savanna, and yet they still motivate and drive much of the action in a modern human society.

Thus biological perception is not the characteristic that distinguishes human perception from animal perception, since that form of perception is still shared in common. What distinguishes human perception from animal perception is that human perception, and apparently it alone, has acquired a significant addendum. When we observe what foregrounds within modern human awareness, in addition to those still influential components of survival and procreation, we find also a host of distinguished sights, sounds and other sensory features that no wild animal would ever naturally perceive. An iterated list of such features would be lengthy, and it would include not only the symbols of language, the architectural traits of buildings, the rhythms of music and the intoxications of perfume, but also the wind rustling in the grass and leaves, wisps of cloud overhead, and the arrangement of bushes along the distant horizon. Man now foregrounds a vast range of sensory features not directly connected to the immediate urges of survival and procreation; man has acquired a second type of perception.

In addition to their mostly non-biological nature, the foregrounded elements in this second type of perception can be seen, upon closer inspection, to carry a consistent and unifying theme. At their core (perhaps tautologically) these elements would appear to emerge in perception precisely because they carry the properties that inherently defy chaos and sensory background, and as was the case with biological perception, these unifying properties can be listed under just a small set of headings: symmetry, pattern, mapping, order, object, structure, form. When we examine the attention-grabbing, ever-expanding innovations of the modern human world we find everywhere an underlying cornucopia of number, shape, order, rule. The distinctiveness of the present age is a constructed distinctiveness, in fierce defiance of nature and its biologically limiting constraints. The foregrounded elements of man's second type of perception are characterized by the fact they are drawn from just a small set of structural, mostly non-biological features, ones that now emerge persistently and prominently from a modern human's sensory background.

As was done with biological perception, I would like to give a name to this exclusively human tendency to foreground sensory elements that possess structural and mostly non-biological characteristics. I will call this type of perception logical perception. And again, as was done in the case of darwinamatics, I would like to give a characterizing name to the sensory features themselves — that is, those features that tend to foreground within logical perception (symmetry, pattern, mapping, etc.). This time, however, there is no need to invent a term, for there is one already in widespread and common use. That term is mathematics. The study of symmetry, pattern, mapping, etc. is none other than the study of mathematics.

Thus we have theorized so far that human perception consists fundamentally of two different types of perception. The first type of perception foregrounds those sensory elements directly connected with survival and procreation, and we have labeled this type of perception biological perception and have categorized the foregrounded sensory features themselves as darwinamatics. We recognize that man shares this type of perception with all the other animals, has inherited it from out of man's animal past, and continues to experience its influence in the modern age. The second type of perception, unique to humans and acquired quite recently in man's long anthropological history, foregrounds those sensory features that possess pattern, structure and form, and we have labeled this second type of perception as logical perception and have recognized its foregrounded sensory elements as precisely those elements commonly studied under the heading of mathematics.

Mathematics has always been something of a philosophical puzzle. Intimately connected with space and time, and the underpinning behind almost every facet of rational thought, mathematics appears to be at the foundation of all non-biological conception, and so it has been more than a little bit tantalizing to determine the foundation of mathematics itself. The ancient Greeks already were arguing the matter fiercely, including Plato and his idealized forms, and in more recent times such esteemed thinkers as Leibniz and Kant have made widely influential contributions. The twentieth century saw the rise and battle of three competing schools of thought — the logicist, formalist and intuitionist points of view — and at various times and in various ways, the ultimate source of mathematics has been attributed in turn to God, human intuition, the objective world and the neuronal mechanisms inside the human skull (the latter being the most mythical suggestion of them all). And yet despite these many arguments and assorted proposals, the philosophical puzzle remains as puzzling as ever.

Recognizing mathematics to be the equivalent of the foregrounded elements in man's second type of perception opens the door to a less mythical, more directly observable explanation for the origin and foundation of mathematics. The similarities between logical perception and biological perception already begin to point the way, for there has not been the same philosophical qualms about darwinamatics — such features have typically been regarded as simply open to inspection. And the placement of logical perception's rise within the time frame of man's long anthropological history provides still more reason to take mathematics as something other than mystical, more akin to a biological/anthropological event. Of course if that is all there were to it, one might reasonably complain that we have done little more than change the aspect of the problem, have made out of logical perception the same philosophical puzzle we have made of mathematics itself. What is the source and foundation of logical perception? Is it a gift from the gods? a synthetic, irreducible intuition? or an evolutionary explosion of synaptic computational miracle? Here in the early twenty-first century, we are slowly uncovering a patch of human knowledge that makes it clear the source and foundation of logical perception is in fact none of the above. Instead, logical perception is directly attributable — and in a directly observable way — to the presence and influence of an atypical group of people.

At its root, autism is a condition defined by perception. In fact in many ways, the distinction between autism and non-autism — taken in their purest form — is the same distinction as that between logical perception and biological perception. What unifies autistic experience, classified today under a broad assortment of behavioral, sensory and developmental characteristics, is a diminished bias towards biological perception, and in particular a diminished foregrounding of conspecifics. Autistic individuals do not easily or naturally attune to the particular features of the human world: they do not readily foreground human voices, they do not focus energetically on human faces, they do not enthrall to many of the most popular human concerns. This diminished awareness towards mankind and its sensory attachments is apparent from the earliest ages and remains extremely consistent — to the point of being defining — across the entirety of the autistic population. It is compensated for only slowly and with great effort throughout an elongated developmental process, and it continues to produce many subtle social anomalies well into advanced age. The natural animal experience is to foreground first and foremost those sensory features concerned with a species' survival and procreation, but autistic individuals serve as the most obvious counterexample to this nearly universal tendency. And thus autistic individuals are the least animal-like of Earth's many biological creatures, for they are the least determined by the constraints of biological perception.

A diminished facility towards biological perception means that autistic individuals are initially hindered in gaining sensory footing. Little emerges as signal, there is no figure against the sensory ground. If this condition were to hold, autistic individuals would be in the most dire of straits, with almost no sensory traction to aid in developmental progress or even in the most essential requirements of survival itself. Fortunately — both for autistic individuals and for the human world at large — this condition does not hold. In the absence of a stronger type of perception — that is, in the absence of biological perception — an alternative, perhaps we should say a default, type of perception swiftly assumes its place. It might be no more than tautological to say that the sensory elements displaying symmetry, pattern, mapping, etc. are the sensory elements that most naturally foreground from sensory chaos, but be that as it may, these features do naturally foreground, as is readily observable from the inclinations and behaviors of the youngest autistic individuals. Lining up toys, a fascination with spinning objects, flapping hands, extreme repetition in video and song, precocious dexterity with letters and numbers — these behaviors betray the deepest attention and focus on those sensory features that have emerged the most prominently. Instead of the common bias towards other humans and their species-driven endeavors, autistic individuals are drawn first and foremost to number, shape, order, rule. Instead of ease with the material of darwinamatics, autistic individuals gravitate more naturally to the material of mathematics.

(All this is observable. It is to the great shame of modern science that in its insistence on medicalizing autism and in its pursuit of so many mercenary distractions — including an endless, self-serving touting of treatment, intervention and cure — modern science has failed to make these simple observations itself. It remains unclear to me when science can begin to make its own perceptual turn, but for the moment I remain highly pessimistic.)

The history of mathematics provides still more evidence of a direct autistic connection. Although biographical details are not always complete, and although nearly every famed mathematician lived well before the recognition of autism, even a glance at the lives of Archimedes, Gauss, Newton, Euler, Riemann, Lagrange, Cantor, Fermat, Gödel, Turing makes it clear autism must have been lingering somewhere near at hand. There is not one social butterfly among these men, not one glad-handing denizen of the weekly cocktail party, and we can assume it must have been so even at the very beginning, when shape and number were first espied. Mathematics is a lonely pursuit, a calling more tantalizing to those unattached to the immediate concerns of everyday society and more compelled by the patterned arrangements of the external world. There is nothing coincidental about this. Those who are biased towards biological perception tend to become salesmen, managers and politicians; those who are biased towards logical perception become mathematicians, physicists, programmers, engineers. Everyone is drawn to the path he most clearly perceives.

A reasonable conjecture would say that logical perception first began to make its appearance on this planet around fifty thousand years or so ago, when autistic individuals would have first begun to achieve significant presence and influence within the human population (rising to the one to two percent prevalence we can measure today). Employing their structure-grounded perception to reconstruct aspects of their environment — and thereby introducing language, art and number into the human surroundings — autistic individuals would have paved the way to logical perception for all, since of course most humans are naturally inclined to do what other humans do. In turn, the non-autistic population would have maintained the connection to the biological concerns of species, helping bring both populations forward in an expansive, explosive conquest of survival and procreation. In today's prodigiously human world, each individual enjoys the benefits of the dual effect, with pure forms of either biological perception or logical perception, as well as the correspondingly pure forms of autism and non-autism, now exceptionally rare (and most often with challenging consequence). Each individual learns to employ a blended form of both logical perception and biological perception, with each individual continuing to display the outward behavioral signs of his more natural inclination.

To this point, we have recognized mathematics as the general term for the foregrounded sensory features arising from logical perception, and now we have traced the origin of logical perception itself to the atypical perceptual characteristics of the autistic population. This discovery casts the subject of mathematics into clearer, more natural light, for we can say with more confidence that mathematics is not the mind of God, it is not the fruit of human intuition, it is not a characteristic of the objective world (and it is most certainly not a neural module inside the human head). Mathematics is simply the natural consequence of the presence and influence of autistic individuals within the human population, the natural consequence of their readily observable, albeit unusual, form of perception. We have thus grounded mathematics as a biological/anthropological fact.

Recognizing mathematics as a biological/anthropological fact — a fact of perception — has consequences for the practice of mathematics. Throughout its development, mathematics has frequently become entangled in controversies of legitimacy, spawned by questions not of calculation or deduction but concerns of whether certain offered concepts are genuinely mathematical. Here too the ancient Greeks already were well engaged, wrestling with the status of irrational numbers and the allowability of actual (completed) infinities. In more recent years, disputes have arisen regarding infinitesimals, the cardinal number of sets, and existence proofs that rely upon the law of excluded middle. These matters are not easily resolved: opposing camps form, debates run on and on. The trouble here is that if mathematics itself is not well grounded, then there are no practical means for settling questions of legitimacy; when the ultimate arbiter is God, intuition or a magical neuron, anyone is free to shift the foundation to fit his case.

But if mathematics itself can be grounded, there arises pragmatic means for assessing legitimacy. It is my contention that nearly every mathematical legitimacy concern comes down ultimately to a question of perception, and in particular a question of foregrounding within perception. At precisely the moment of dispute, at precisely the point of crossover from general agreement to widespread debate, we find ourselves face-to-face with a mathematical concept struggling to achieve its perceptual grounds.

Take the case of an actual (completed) infinity. By and large, modern humans have little difficulty or disagreement about foregrounding a finite sequence (one, two, three, four); they sense the distinctness of this perception just as surely as they trust their ability to construct the numbers within their physical environment. Furthermore, in addition to the constructed sequence itself, humans foreground quite easily each step of the iterative sequential process (take something, add one to get its successor, take the successor, add one to get the successor of the successor, and so on). This recipe is sharply defined and open to the senses, and no dispute or uncertainty ever arises about its nature.

But with an infinite sequence, something becomes different — perceptually different. The iterative sequential process remains fine, each step still as prominent and surveyable as all the previous steps, with the fact that the steps have no end inconsequential to their perceptual foregrounding. But the completed sequence is another matter. A fully realized infinite set is precisely the thing that does not foreground within human perception, and it remains dubious whether finite words such as “actual infinity” or “infinite set” — or axioms attached to such words — are adequate to alleviate the uncertainty. Many humans are not satisfied that the symbol or axiom itself perceptually foregrounds, not when what that symbol or axiom represents remains hidden as noise within the perceptual field. The ancient Greeks, as well as more recent mathematicians such as Gauss, have dismissed the notion of an actual infinity, while many other mathematicians have firmly disagreed.

As another example, the irrational numbers have long produced a sense of queasiness among mathematicians, with the technique of the Dedekind cut introduced to place the irrationals' mathematical existence on much firmer ground. And yet when it comes to the firmer ground based upon the notion of logical human perception, the queasiness remains. Dedekind cuts define all real numbers via unique divisions of the rationals into two order-based sets, for instance a Left set of rationals that are less than or equal to the given number and a Right set of rationals that are greater than the given number. Adherents to this technique will then provide many examples showing how this cut distinctly determines particular irrational numbers — the square root of 2, the arctangent of 3, the natural logarithm of 5. Although doubts may linger about the use of completed infinities to form the two sets, for anyone who has followed the mechanics of an actual Dedekind cut, it is hard not to be impressed by the vividness of the technique. In the examples typically offered, the process of the Dedekind cut would appear, by and large, to perceptually foreground.

Unfortunately, perceptually speaking, the examples typically offered are not the instances most in question. Long before a Dedekind cut was ever considered, various mathematical techniques had already been developed to foreground particular irrational numbers — including for instance, the square root of 2, the arctangent of 3, and the natural logarithm of 5. Indeed in many cases it is precisely the existence of such techniques that makes an actualized Dedekind cut conceivable in the usual sense. And so for those humans who are are convinced only by the evidence of their own perception, the Dedekind cut arrives as something of a white elephant: in the cases of irrational numbers that can already be perceptually foregrounded through an alternative technique, the Dedekind cut appears to be ostentatiously superfluous, and in the instances of irrational numbers that would possess no conceivable foregrounding technique, the Dedekind cut comes across as little better than useless. Of course there are many mathematicians who would argue otherwise.

Finally, we might consider the circumstances surrounding the concept of negation and the arguments reductio ad absurdum based upon negation. The potential controversy can be outlined with just a rough sketch:

In this image, there is a square region that foregrounds perceptually and two clearly demarcated regions within that square (A and B). Outside the square is an unbounded region labeled C that is meant to depict everything else (and I do mean everything else, whatever that happens to mean). Negation within the context of the square is unproblematic, because everything foregrounds. For instance, within the context of the square, the negation of A is the region B and neither A nor B is perceptually troubling. But note that negation in the wider picture is perceptually more ambiguous. For instance, the negation of the square itself (the negation of A union B) comes across differently than the former case: the square itself still foregrounds quite easily, but the negation of the square does not — in fact, the region C might not be anything more than the background chaos. When mathematicians treat these two instances of negation as similar or equivalent, disputes quickly follow, and I believe that behind almost every instance of an argument over an existence proof relying upon the law of excluded middle, one can find a similar region of perceptual ambiguity, a piece of mathematical landscape struggling to be clearly seen.

It is not exactly my intention to adjudicate these matters. The purpose behind these examples is to demonstrate that mathematical legitimacy disputes are still common and go generally unresolved, and this is because mathematics itself has remained ungrounded in any observable anthropological fact. Armed however with an understanding of the history of logical/autistic perception, and recognizing that issues of foregrounding lurk behind nearly every known dispute, we can begin to approach these matters from an entirely different direction, one more on par with our approaches to biological perception and darwinamatics. Some may have noticed that the insights suggested by reference to logical perception are similar in many respects to those principles held by the intuitionist school of thought. But one must also notice the significant distinction. The intuitionists' banishment of many of the techniques of classical mathematics is a banishment that is itself not entirely well grounded, other than that is (as their moniker would suggest) an appeal to intuition. It is past time for mathematical appeals to divinity and intuition. We are better served by grounding mathematics in our biology, our anthropology, our history. We can begin to resolve the questions of mathematical legitimacy when we place our mathematical concepts on the same perceptual footing as a sexual encounter, a live birth or a tasty meal.

In summary, we have taken a fresh journey through the world of mathematics. It began with perception, and with the discovery that in addition to the animal-inherited characteristics of biological perception, man has recently in his anthropological history acquired a second type of perception — logical perception — in which the foregrounded sensory elements are precisely those elements recognized as belonging to mathematics. We then employed the observable behaviors and inclinations of autistic individuals to conclude that logical perception must have arisen directly from autistic perception, and that it has been the presence and influence of the autistic population that has served as the catalyst for bringing logical perception and mathematics into the human world. Finally, we ventured that the establishment of mathematics as a biological/anthropological fact provides means for reassessing many mathematical disputes, means that are much more practical than either myth, intuition or unexplained neural magic.

Crappier than Twenty-First Century Phrenology?

I'm always amazed at Michelle Dawson's unerringly accurate ability to recognize the absurdity in typical psychoanalytic descriptions of autism, and yet her inability to recognize the exact same thing in typical neuroscientific descriptions of autism. What an apt phrase: “why is this crap still being published?” It's exactly what I think after nearly every neuroscience paper I read.

Psychology and neuroscience may be distinct disciplines, but they share much in common—namely an appalling lack of coherency and logic.

The Law of Unintended Consequences

The autism diagnosis changes being introduced in the upcoming DSM-V have spawned a loud lament over potential loss of services, the fear being that under the new criteria many children will be deprived of essential treatments they would have qualified for under the old criteria.

But here's my question: how does anyone know this is a bad thing? Let's face it, we have yet to see the first piece of meaningful, significant evidence that these so-called “essential treatments” are actually helpful for autistic children (or adults, for that matter). My suspicion is that many of these so-called “essential treatments” (drugs and ABA at the head of the list) are actually harmful in most instances. Suspicions aside (mine or anyone else's), even a cursory glance at the autism research literature reveals that our current knowledge about autism treatments and interventions is chaotic at best. In point of fact, we haven't the first clue whether we're doing harm or good.

So I'll ask the question again: if more children are being denied treatments and interventions under the new diagnostic guidelines, how do we know for sure this is a bad thing? It's the law of unintended consequences. And the reason the consequences are unintended is that when it comes to autism knowledge and understanding, we remain almost totally in the dark.

A Simple Theory

There is so much absurd autism science floating around these days I hesitate to point out a particular piece of it that might actually be useful. It would have to be a fluke, right?

The piece of autism science I'm referring to is highlighted in the following abstract from Decreased Spontaneous Attention to Social Scenes in 6-Month-Old Infants Later Diagnosed with Autism Spectrum Disorders (Chawarska, Macari, Shic 2013):

BACKGROUND:

The ability to spontaneously attend to the social overtures and activities of others is essential for the development of social cognition and communication. This ability is critically impaired in toddlers with autism spectrum disorders (ASD); however, it is not clear if prodromal symptoms in this area are already present in the first year of life of those affected by the disorder.

METHODS:

To examine whether 6-month-old infants later diagnosed with ASD exhibit atypical spontaneous social monitoring skills, visual responses of 67 infants at high-risk and 50 at low-risk for ASD were studied using an eye-tracking task. Based on their clinical presentation in the third year, infants were divided into those with ASD, those exhibiting atypical development, and those developing typically.

RESULTS:

Compared with the control groups, 6-month-old infants later diagnosed with ASD attended less to the social scene, and when they did look at the scene, they spent less time monitoring the actress in general and her face in particular. Limited attention to the actress and her activities was not accompanied by enhanced attention to objects.

CONCLUSIONS:

Prodromal symptoms of ASD at 6 months include a diminished ability to attend spontaneously to people and their activities. A limited attentional bias toward people early in development is likely to have a detrimental impact on the specialization of social brain networks and the emergence of social interaction patterns. Further investigation into its underlying mechanisms and role in psychopathology of ASD in the first year is warranted.

These results are in line with similar eye-tracking studies from this research group, most of which have described controls (non-autistic infants and toddlers) as attending more frequently to other people than do autistic children. All the suggested causes for this distinction remain highly speculative, but the observed behaviors do tend to be remarkably consistent. At the same time, these researchers have had difficulty in figuring out what it is that autistic children tend to focus on in lieu of other people, other than to note it doesn't seem to be inanimate objects (which is what the researchers apparently expected).

I like these results. They should be taken with a grain of salt of course, but I see them as direct evidence for a simple theory I have that describes the essence of autism. In straightforward words: most individuals (non-autistic individuals) naturally focus upon the other members of the species, and thus humans and their activities form perceptual foreground for non-autistic individuals. By contrast, autistic individuals, to a significant degree, are not as perceptually drawn to other humans (as though there is a species ambiguity at work). Without other humans serving as perceptual foreground and in need of perceptual material to create sensory and cognitive orientation, autistic individuals gravitate instead to those environmental features that inherently stand out, features we describe with such properties as symmetry, pattern, repetition, structure and form. (Indeed, it is pattern and structure that autistic individuals are perceptually attracted to, not objects per se).

It's a simple theory really, but one that has gone entirely overlooked by autism scientists. Yet it remains the only theory I've ever seen that fundamentally addresses what autistic individuals, and non-autistic individuals, actually do.

Unnatural Evolution

The Mottron research team has a new paper available, Veridical mapping in the development of exceptional autistic abilities. Although it covers similar ground to many previous Mottron team papers, it does provide a bit more detail on many of the team's excellent ideas and is certainly worth a read.

I want to highlight one sentence from the paper:

The materials involved in domain specific savant abilities often involve human codes such as arithmetical structures, written codes, calendars, music scales, 3-D regularities, and natural taxonomies that all feature structural redundancy.

That's an accurate statement of present fact, but it also raises a fascinating historical question: Were there any savants/autistics in existence say ten thousand years ago, and if so, what were those savants/autistics perceptually attuned to? It sure as hell wasn't arithmetical structures, written codes, calendars, music scales, 3-D regularities, or natural taxonomies.

That might seem like a tangent observation at first, but it actually goes straight to the heart of the matter and should make one think. It should especially make one think when one is trying to justify a bunch of neuroscience gobbledygook.

Race to the Bottom

On her Twitter feed, Michelle Dawson quite rightly notes the approaching horror of a book called “The Philosophy of Autism,” which will no doubt be dreadful in almost every respect. In fact the only thing I can think of that would be more dreadful would be a book entitled “The Science of Autism.”

Flynn Effect Cohort Comparisons

I'm going to follow up a little further to my previous two posts and talk about making cohort comparisons under a Flynn effect.

It's quite common for researchers to talk about the Flynn effect advantage (or disadvantage) of one population cohort compared to another. For instance, in Dickinson & Hiscock (2010) and Agbayani (2011), this type of statement is frequent. Unfortunately for these researchers, a Flynn effect cohort comparison is not technically correct. In the best of circumstances it can be ambiguous, and as it is typically done, it's wrong.

The best way to see this is to understand first that the Flynn effect works across time, not across cohorts. Nearly every empirical study involving the Flynn effect shows that raw intelligence scores tend to increase universally and uniformly over time, no matter the age group, no matter the population. Whoever you are, wherever you are, no matter how old you are, what the Flynn effect cares about is how much time has passed. If you make a comparison across ten years of time, then you'll get ten years worth of Flynn effect. If you make a comparison across fifty years of time, you'll get fifty years worth of Flynn effect. If you make a comparison across zero years of time, then you'll get zero years worth of Flynn effect (which is to say, no Flynn effect at all).

So what does this mean for a cohort comparison? Let me return to the idealized chart of data I used in Intelligence as Field, and let's examine the raw intelligence history of two cohorts within it, the population born at time 100 and the population born at time 140.

Age	Raw Intelligence Scores by Age and Year
	95	40.8	41.6	42.5	43.3	44.2	45.1	46.0	46.9	47.9	48.8	49.8
	85	45.6	46.5	47.5	48.4	49.4	50.4	51.4	52.4	53.5	54.6	55.7
	75	50.4	51.4	52.5	53.5	54.6	55.7	56.8	58.0	59.1	60.3	61.5
	65	54.0	55.1	56.2	57.3	58.5	59.7	60.9	62.1	63.4	64.6	65.9
	55	55.8	56.9	58.1	59.2	60.4	61.7	62.9	64.2	65.5	66.8	68.1
	45	57.6	58.8	59.9	61.2	62.4	63.7	64.9	66.2	67.6	68.9	70.3
	35	58.8	60.0	61.2	62.4	63.7	65.0	66.3	67.6	69.0	70.4	71.8
	25	60.0	61.2	62.4	63.7	65.0	66.3	67.6	69.0	70.4	71.8	73.3
	15	51.0	52.0	53.1	54.2	55.2	56.4	57.5	58.7	59.8	61.0	62.3
	5	15.0	15.3	15.6	15.9	16.2	16.6	16.9	17.3	17.6	18.0	18.3
		105	115	125	135	145	155	165	175	185	195	205
	Year

The assumption that gets blindly made by researchers is that the birth year 140 cohort (BY140) is more intelligent than the birth year 100 cohort (BY100), due to the Flynn effect. But that's technically incorrect, or at the very least, it's technically ambiguous. The result of the comparison is going to very much depend on how the comparison gets made.

If the comparison is across time, then yes, BY140 will always emerge as more intelligent than BY100. For instance, if we are comparing the 25 year-olds of BY140 to the 25 year-olds of BY100, then there is forty years of time span between those comparison points, and thus forty years worth of Flynn effect. The same result happens if we compare the 65 year-olds of BY140 to the 65 year-olds of BY100. Cohort comparisons that span across time will always reveal the specific impact of a Flynn effect.

But that's not how researchers typically do it.

Researchers typically make their comparison at a particular point in time. For instance, researchers will say something like, while comparing BY100 to BY140 at time 165, a Flynn effect adjustment must be made to account for the Flynn effect disadvantage BY100 has relative to BY140. Or it might be put this way: the relative scores of BY100 and BY140 at time 165 are distorted due to the Flynn effect.

Such statements are pure nonsense.

In any comparison made at a particular point in time, the Flynn effect disappears. To repeat: the Flynn effect works across time, not across cohorts. If the cohort comparison being made involves no span of time, then there can be no Flynn effect distinction. Period.

As I mentioned in Intelligence as Field, there seems to be an odd sense floating about within the research community that one's Flynn effect is established once and for all at one's birth. It is this odd sense that must be leading people to assume that the Flynn effect works across cohorts and not across time. But the empirical data does not support that assumption. The empirical data shows that the Flynn effect continues to work equally at all places and at all times—it works throughout a person's entire lifetime, it is not established once and for all at one's birth. Therefore, the Flynn effect is not a function of birth or of cohorts, it is purely a function of time.

The mistakes I'm pointing out here are extremely common within the intelligence research community, and truth be told it's a shame. These mistakes mask the true nature of the Flynn effect, a phenomenon which has very much to tell us about the nature of human intelligence. But the Flynn effect is only going to speak to us if we don't first go out of our way to misunderstand it.

References

Agbayani, K. A. (2011). Patterns of age-related IQ changes from the WAIS to WAIS-III after adjusting for the Flynn effect. Retrieved online from http://repositories.tdl.org/uh-ir/handle/10657/236.

Dickinson, M. D. & Hiscock, M. (2010). Age-related IQ decline is reduced markedly after adjustment for the Flynn effect. Journal of Clinical and Experimental Neuropsychology, 32(8), 865-870.

Dickinson, Hiscock and Agbayani

[Note: as with the previous post, if the data charts below are difficult to read, try reading the analysis at this alternative location. ]

As a follow up to my previous post, Intelligence as Field, I would like to talk about two papers that essentially cover much of the same ground: Dickinson & Hiscock (2010) and Agbayani (2011). Unfortunately, I can't find a non-paywalled version of Dickinson & Hiscock (2010), and therefore I can't link to its full text, nor have I been able to read more than its title and abstract. [This is where I would normally begin a long rant about the ridiculously closed nature of science these days, but that's a worn-out subject, so let's move on.] To the rescue, Agbayani (2011) is available online and it provides all the essential information regarding the results and methods of Dickinson & Hiscock (2010). Agbayani is apparently a student of Hiscock, and Agbayani (2011) is a thesis paper that both outlines the approach of Dickinson & Hiscock (2010) and extends the range of its data and analysis.

The approach these authors take can be outlined as follows:

• They use data from WAIS, WAIS-R, and WAIS-III to compare intelligence scores across age groups and across time.
• They use a reverse norming methodology to place all scores on an equal footing, so that they can be directly compared as though they were raw scores from the same exam.
• They adjust these raw scores for the Flynn effect, adding an empirically reasonable amount to the older age group scores to account for the generational difference between the older age groups and the younger age groups.
• These adjusted raw scores are labeled as true aging effect scores and are shown to be similar to the pattern of scores that show up for individuals under longitudinal studies.

This approach of Dickinson, Hiscock and Agbayani is essentially equivalent to the approach I took with my idealized chart of data in Intelligence as Field. To see this, you can consider one of the charts of data with which that essay began and one of the comparative data sets that arises from it:

Age	Raw Intelligence Scores by Age and Year
	95	40.8	41.6	42.0	42.5	43.3	44.2	45.1	46.0	46.9	47.9	48.8	49.8
	85	45.6	46.5	47.0	47.5	48.4	49.4	50.4	51.4	52.4	53.5	54.6	55.7
	75	50.4	51.4	51.9	52.5	53.5	54.6	55.7	56.8	58.0	59.1	60.3	61.5
	65	54.0	55.1	55.6	56.2	57.3	58.5	59.7	60.9	62.1	63.4	64.6	65.9
	55	55.8	56.9	57.5	58.1	59.2	60.4	61.7	62.9	64.2	65.5	66.8	68.1
	45	57.6	58.8	59.3	59.9	61.2	62.4	63.7	64.9	66.2	67.6	68.9	70.3
	35	58.8	60.0	60.6	61.2	62.4	63.7	65.0	66.3	67.6	69.0	70.4	71.8
	25	60.0	61.2	61.8	62.4	63.7	65.0	66.3	67.6	69.0	70.4	71.8	73.3
	15	51.0	52.0	52.5	53.1	54.2	55.2	56.4	57.5	58.7	59.8	61.0	62.3
	5	15.0	15.3	15.4	15.6	15.9	16.2	16.6	16.9	17.3	17.6	18.0	18.3
		105	115	120	125	135	145	155	165	175	185	195	205
	Year

Age	Without     Flynn Effect	With     Flynn Effect	Difference
85	47.0	55.7	8.7
75	51.9	60.3	8.4
65	55.6	63.4	7.8
55	57.5	64.2	6.7
45	59.3	64.9	5.6
35	60.6	65.0	4.4
25	61.8	65.0	3.2
15	52.5	54.2	1.7
5	15.4	15.6	0.2

If you were to apply the approach of Dickinson, Hiscock and Agbayani to the original chart of data, you would arrive at exactly the same comparative data set, only with a different set of labels:

Age	Scores that      Reflect AGD	Scores that      Reflect TAE	FED
85	47.0	55.7	8.7
75	51.9	60.3	8.4
65	55.6	63.4	7.8
55	57.5	64.2	6.7
45	59.3	64.9	5.6
35	60.6	65.0	4.4
25	61.8	65.0	3.2
15	52.5	54.2	1.7
5	15.4	15.6	0.2

In the terminology of Dickinson, Hiscock and Agbayani, AGD stands for age group difference, reflecting the type of pattern that emerges from cross-sectional studies (that is, from reading up the chart at any given time). TAE stands for true aging effect and reflects the type of pattern that emerges from longitudinal studies (that is, from reading diagonally across the chart for any population cohort). FED is the Flynn effect difference.

In a certain sense, I'm quite pleased that Dickinson & Hiscock (2010) and Agbayani (2011) exist. They are the nearest thing I can find to a real-world analysis similar to what I outlined in Intelligence as Field, and of course it is gratifying to know that the real-world outcome turns out to be essentially the same as my idealized approach.

On the other hand, there is a major problem. Although it appears to me that Dickinson, Hiscock and Agbayani have done a creditable job in the gathering of their data, they have also managed to utterly mangle its interpretation.

In reading the conclusions these authors draw from their analysis (indeed, in reading through their entire approach to the problem), one quickly realizes that they are (mistakenly) saying the following:

• The age-based differences that show up in cross-sectional studies (reading up the chart at any given time) are distorted because of the Flynn effect.
• By adjusting for the influence of the Flynn effect, one arrives at a longitudinal set of values (reading diagonally across the chart) that represents the true age-based difference in individuals—that is, the age-based difference that would show up in the absence of a Flynn effect.

That logic is completely backwards.

The only way to make logical sense of the data is to state it the other way. The cross-sectional studies (reading up the chart at any given time) are the true age-based differences—that is, the age-based differences that would show up in the absence of a Flynn effect. The longitudinal values (reading diagonally across the chart) represent the combination of age-based differences and the Flynn effect. The reason that the longitudinal raw scores remain fairly constant across adulthood is that the two competing influences (age-based decline and Flynn effect increase) are in rough equilibrium.

As far as I can tell, there is no reasonable way to make sense out of the Dickinson/Hiscock/Agbayani interpretation. To see this, consider what must happen to the data under and not under the influence of a Flynn effect. Let me use a version of my idealized chart of data, and let's assume there is no Flynn effect for the first fifty years. Under these conditions and under my interpretation, the chart of data would look something like this:

Age	Raw Intelligence Scores by Age and Year
	95	40.8	40.8	40.8	40.8	40.8	40.8
	85	45.6	45.6	45.6	45.6	45.6	45.6
	75	50.4	50.4	50.4	50.4	50.4	50.4
	65	54.0	54.0	54.0	54.0	54.0	54.0
	55	55.8	55.8	55.8	55.8	55.8	55.8
	45	57.6	57.6	57.6	57.6	57.6	57.6
	35	58.8	58.8	58.8	58.8	58.8	58.8
	25	60.0	60.0	60.0	60.0	60.0	60.0
	15	51.0	51.0	51.0	51.0	51.0	51.0
	5	15.0	15.0	15.0	15.0	15.0	15.0
		105	115	125	135	145	155	165	175	185	195	205
	Year

But by the account of Dickinson, Hiscock, and Agbayani, the chart would need to look much different. Since they are saying that the true aging effect scores reflect age-based differences sans a Flynn effect, then their chart of data (under no Flynn effect) would need to look more like this:

Age	Raw Intelligence Scores by Age and Year
	95	48.0	48.0	48.0	48.0	48.0	48.0
	85	53.6	53.6	53.6	53.6	53.6	53.6
	75	58.0	58.0	58.0	58.0	58.0	58.0
	65	61.0	61.0	61.0	61.0	61.0	61.0
	55	61.7	61.7	61.7	61.7	61.7	61.7
	45	62.4	62.4	62.4	62.4	62.4	62.4
	35	62.5	62.5	62.5	62.5	62.5	62.5
	25	62.5	62.5	62.5	62.5	62.5	62.5
	15	52.1	52.1	52.1	52.1	52.1	52.1
	5	15.0	15.0	15.0	15.0	15.0	15.0
		105	115	125	135	145	155	165	175	185	195	205
	Year

Now consider what would happen if a Flynn effect kicked in beginning at time 155.

In my chart and under my interpretation, the progression is quite natural. Raw scores begin to go up by say 2% every ten years for all age groups, and what results is a chart of data for years 165 to 205 that has all the same patterns we currently see in the empirical data for humans. Note that the pattern of age-based differences remains invariant under the changing Flynn effect assumptions:

Age	Raw Intelligence Scores by Age and Year
	95	40.8	40.8	40.8	40.8	40.8	40.8	41.6	42.5	43.3	44.2	45.1
	85	45.6	45.6	45.6	45.6	45.6	45.6	46.5	47.5	48.4	49.4	50.4
	75	50.4	50.4	50.4	50.4	50.4	50.4	51.4	52.5	53.5	54.6	55.7
	65	54.0	54.0	54.0	54.0	54.0	54.0	55.1	56.2	57.3	58.5	59.7
	55	55.8	55.8	55.8	55.8	55.8	55.8	56.9	58.1	59.2	60.4	61.7
	45	57.6	57.6	57.6	57.6	57.6	57.6	58.8	59.9	61.2	62.4	63.7
	35	58.8	58.8	58.8	58.8	58.8	58.8	60.0	61.2	62.4	63.7	65.0
	25	60.0	60.0	60.0	60.0	60.0	60.0	61.2	62.4	63.7	65.0	66.3
	15	51.0	51.0	51.0	51.0	51.0	51.0	52.0	53.1	54.2	55.2	56.4
	5	15.0	15.0	15.0	15.0	15.0	15.0	15.3	15.6	15.9	16.2	16.6
		105	115	125	135	145	155	165	175	185	195	205
	Year

But what are Dickinson, Hiscock and Agbayani going to do? How can they reasonably introduce a Flynn effect at time 155 and still remain true to the empirical data? For instance, they can't just begin to boost scores across all age groups, because then their chart would end up looking like this:

Age	Raw Intelligence Scores by Age and Year
	95	48.0	48.0	48.0	48.0	48.0	48.0	49.0	50.0	51.0	52.0	53.0
	85	53.6	53.6	53.6	53.6	53.6	53.6	54.6	55.7	56.9	58.0	59.2
	75	58.0	58.0	58.0	58.0	58.0	58.0	59.2	60.3	61.6	62.8	64.1
	65	61.0	61.0	61.0	61.0	61.0	61.0	62.2	63.4	64.7	66.0	67.4
	55	61.7	61.7	61.7	61.7	61.7	61.7	63.0	64.2	65.5	66.9	68.2
	45	62.4	62.4	62.4	62.4	62.4	62.4	63.7	64.9	66.3	67.6	69.0
	35	62.5	62.5	62.5	62.5	62.5	62.5	63.8	65.0	66.4	67.7	69.1
	25	62.5	62.5	62.5	62.5	62.5	62.5	63.8	65.0	66.4	67.7	69.1
	15	52.1	52.1	52.1	52.1	52.1	52.1	53.2	54.2	55.3	56.5	57.6
	5	15.0	15.0	15.0	15.0	15.0	15.0	15.3	15.6	15.9	16.2	16.6
		105	115	125	135	145	155	165	175	185	195	205
	Year

For years 165 and beyond, that chart does not match the current empirical data for humans, it is the chart of a completely different kind of population. So instead, let's let Dickinson, Hiscock and Agbayani try another approach, forcing a match to the empirical data. Then their chart might end up looking something like this:

Age	Raw Intelligence Scores by Age and Year
	95	48.0	48.0	48.0	48.0	48.0	48.0	41.6	42.5	43.3	44.2	45.1
	85	53.6	53.6	53.6	53.6	53.6	53.6	46.5	47.5	48.4	49.4	50.4
	75	58.0	58.0	58.0	58.0	58.0	58.0	51.4	52.5	53.5	54.6	55.7
	65	61.0	61.0	61.0	61.0	61.0	61.0	55.1	56.2	57.3	58.5	59.7
	55	61.7	61.7	61.7	61.7	61.7	61.7	56.9	58.1	59.2	60.4	61.7
	45	62.4	62.4	62.4	62.4	62.4	62.4	58.8	59.9	61.2	62.4	63.7
	35	62.5	62.5	62.5	62.5	62.5	62.5	60.0	61.2	62.4	63.7	65.0
	25	62.5	62.5	62.5	62.5	62.5	62.5	61.2	62.4	63.7	65.0	66.3
	15	52.1	52.1	52.1	52.1	52.1	52.1	52.0	53.1	54.2	55.2	56.4
	5	15.0	15.0	15.0	15.0	15.0	15.0	15.3	15.6	15.9	16.2	16.6
		105	115	125	135	145	155	165	175	185	195	205
	Year

That would be better if it weren't for the jarring discontinuity between the years 155 and 165. Why would the introduction of a Flynn effect cause such an immediate and ragged discontinuity across age groups and time? The answer of course is that it wouldn't.

There is only one logically correct interpretation:

• Cross-sectional studies (reading up the chart) do show a true age-related difference, most likely due to the biological impacts of aging.
• Cross-time studies (reading straight across the chart) show a Flynn effect, applicable with roughly equal magnitude to every age group.
• Longitudinal studies (reading diagonally across the chart) show the combination of age-based differences and the Flynn effect.

As a consequence, the title of Dickinson & Hickson (2010) suggests a gross misinterpretation.

References

Agbayani, K. A. (2011). Patterns of age-related IQ changes from the WAIS to WAIS-III after adjusting for the Flynn effect. Retrieved online from http://repositories.tdl.org/uh-ir/handle/10657/236.

Dickinson, M. D. & Hiscock, M. (2010). Age-related IQ decline is reduced markedly after adjustment for the Flynn effect. Journal of Clinical and Experimental Neuropsychology, 32(8), 865-870.