Tuesday, December 3, 2013

Connectivity Explained

There seems to be a bit of a hullabaloo developing over the state of neural connectivity in autism. But to be honest, I fail to see what all the fuss is about — a little autism science logic can clear up the matter instantly. To wit:
  • Some studies have shown that various regions of autistic brains are under-connected relative to typical controls. This is a problem because everything associated with autism is bad.
  • Some studies have demonstrated that various regions of the autistic brain are over-connected (hyper-connected) relative to typical controls. This is a problem because everything associated with autism is bad.
  • Some studies have suggested that various regions of the autistic brain are indistinguishable from typical controls. This is a problem because everything associated with autism is bad.
There, see how easy it is to clear up these matters when you apply a little autism science logic.

Monday, September 23, 2013

Every Disney Drama Has a Cruel Villain

I'll tell you what Autism Speaks understands: the big money it garners from corporations like Disney.

And I'll tell you what Autism Speaks doesn't understand: autistic kids.

Sunday, August 11, 2013

Cohorts, Time and the Flynn Effect

Agbayani (2013) is a recently published paper on the topic of the Flynn effect and age-related IQ decline, and is a continuation of the ideas presented in Agbayani (2011) and Dickinson (2010). (Of these, only Agbayani (2011) is not paywalled, but each paper comes to roughly the same conclusion from essentially the same set of data, so reading Agbayani (2011) is enough to get the gist of the idea.) What these papers do is take the results from Wechsler IQ exams given at different time periods and for a variety of age categories and combine these with Flynn effect norming information to produce what is in essence a directly comparable grid of intelligence scores along the two dimensions of calendar year and age. It is the same technique I have employed (in idealized form) in previous posts, for instance in Intelligence as Field. As such, the empirical results of Agbayani (2013), although admittedly limited in scope, provide some corroboration for my idealized charts.

There are three temporal patterns that emerge from the Agbayani (2013) data:
  • For any given calendar year, the age-related pattern of raw intelligence scores shows a peak for test takers in early adulthood, followed by a gradual yet significant decline for test takers at increasingly older ages.
  • For any given age category, raw intelligence scores show a consistent increase across calendar years, with the rate of increase being similar for all age categories.
  • The intelligence profile for any given birth cohort (which would be obtained by reading diagonally across the grid) shows a relatively flat level of scores from early adulthood until around age 70 or so. This is consistent with most longitudinal intelligence studies applied to individuals.
An idealized chart of comparable intelligence scores roughly matching the empirical results of Dickinson (2010), Agbayani (2011) and Agbayani (2013) would look something like Chart A:

AgeChart A
Comparable Intelligence Scores by Calendar Year and Age
60 80 88 97
40 90 99 109
20 100 110 121
1960 1980 2000
Calendar Year

Note that this chart is consistent with the three temporal patterns listed, and in particular note that for the cohort born in 1940 (age 20 in 1960, age 40 in 1980, age 60 in 2000), the raw intelligence profile is relatively flat across adulthood, just as Agbayani (2013) highlights.

In Dickinson (2010), Agbayani (2011) and Agbayani (2013), these results are interpreted in the following way (I will call this the Agbayani interpretation):
  • The Flynn effect is a function of cohorts.
  • In the absence of a Flynn effect, the cross-sectional age-related declines in intelligence scores will mostly disappear.
In essence, these authors look at the flat intelligence profile for a given cohort and combine this with the assumption that the Flynn effect remains constant over the lifetime of that cohort, and conclude that the flat age-related intelligence profile that emerges is therefore the natural age-related intelligence profile. Or in other words, these authors are saying that the cross-sectional age-related declines in intelligence scores evident for any given calendar year will disappear once the cohort-induced Flynn effects are factored out.

That interpretation is almost certainly wrong.

An alternative interpretation to the Agbayani interpretation, one that I find far more natural and plausible, can be outlined as follows (I will call this the Griswold interpretation):
  • The Flynn effect is a continuous, universal function of time (not of cohorts).
  • In the absence of a Flynn effect, the age-related decline in intelligence scores will emerge in each cohort, demonstrating that such decline is in fact the natural age-related intelligence profile.
Under the Griswold interpretation, the cross-sectional age-related declines in intelligence scores at each calendar year are indicative of the actual age-related intelligence profile and are unaffected by the presence of any Flynn effect. The flat intelligence profile that is today evident in each birth cohort arises from the combination of two independent and mutually offsetting influences: one, the natural decline in intelligence that occurs as one ages, and two, the increase in intelligence that results from the continuous influence of the Flynn effect throughout one's lifetime. (It is something of a coincidence that these two opposite-direction influences are nearly equal in magnitude.)

To compare the Agbayani and Griswold interpretations and assess their consequences and resulting plausibility, we need to examine each interpretation under a scenario in which there is no Flynn effect, then follow this with a description of how each interpretation can be transitioned into a scenario in which the Flynn effect has full impact. Such an investigation will highlight the fundamental contrast between the two interpretations and will demonstrate how each necessitates a dramatically different understanding of how the Flynn effect must work.

We can begin with the Agbayani interpretation. Assuming a scenario in which there is no Flynn effect and given the Agbayani assumption that there will be little age-related decline in intelligence scores in the absence of a Flynn effect, the resulting two-dimensional grid of raw intelligence scores would now have to look something like Chart B:

AgeChart B
Agbayani interpretation, no Flynn effect
60 97 97 97
40 99 99 99
20 100 100 100
1960 1980 2000
Calendar Year

Chart B meets the requirements of the Agbayani interpretation. Note that there is practically no age-related decline either at any calendar year or for any cohort, and of course there is also no telltale sign of a Flynn effect. From this base, the trick now is to figure out how to introduce a Flynn effect — that is, transition from Chart B to Chart A — and do it in a way that is consistent with the Agbayani interpretation.

When I first contemplated the Agbayani interpretation, I could see no reasonable way to make that transition work, but upon further reflection I recognize I was being too hasty. In truth, there is a way to make the math work out. What needs to be done is to add something to each birth cohort — call it a Flynn effect boost (FEB) — and in order to account for the fact that the Flynn effect is evident across all age groups (including child age groups), it is necessary to add this boost right from the very beginning (at birth, if you will) and then have its influence remain constant over the cohort's lifetime. Mathematically, the technique looks something like Chart C:

AgeChart C
Agbayani interpretation, Flynn effect transition
60 97 x (1 - 2 x FEB) 97 x (1 - 1 x FEB) 97 x (1 + 0 x FEB)
40 99 x (1 - 1 x FEB) 99 x (1 + 0 x FEB) 99 x (1 + 1 x FEB)
20 100 x (1 + 0 x FEB) 100 x (1 + 1 x FEB) 100 x (1 + 2 x FEB)
1960 1980 2000
Calendar Year

Chart C starts from the no Flynn effect base of Chart B, then each successive cohort is given a Flynn effect boost that is larger than the boost provided to the previous cohort. Furthermore, each cohort is given the entirety of its Flynn effect boost right from the beginning, with the influence of the boost remaining constant thereafter over the cohort's existence. Reading diagonally across Chart C and observing how the Flynn effect is introduced and maintained in each cohort, we see that this technique is exactly what is required in order to remain consistent with the Agbayani assumption that the Flynn effect is purely a function of cohorts.

If we plug in an FEB value of approximately 0.1, then Chart B transitions quite smoothly into Chart A, thereby demonstrating that the suggested technique provides a plausible mechanism for how the Flynn effect must work under the Agbayani interpretation. I leave open the possibility that I have overlooked something, but as far as I can tell, this technique is the only one mathematically plausible under the conditions of the Agbayani interpretation.

By contrast, the scenarios and transitions look quite different under the Griswold interpretation. We begin once again by considering the scenario in which there is no Flynn effect, along with the Griswold assumption that the age-related intelligence decline will continue to be evident under such a scenario. This means that the two-dimensional grid of raw intelligence scores must now look something like Chart D:

AgeChart D
Griswold interpretation, no Flynn effect
60 80 80 80
40 90 90 90
20 100 100 100
1960 1980 2000
Calendar Year

Chart D meets the requirements of the Griswold interpretation. Note that the age-related decline is still evident for all calendar years, and furthermore the age-related decline is now evident also for each cohort. Plus there is no hint of a Flynn effect anywhere in these numbers. As before, the next step is to introduce a Flynn effect — that is, transition from Chart D to Chart A — and do it in a way that is consistent with the Griswold interpretation.

Here, the math is fairly straightforward and practically suggests itself. Consistent with the Griswold assumption that the Flynn effect produces a continuous and universal impact over time, the transition is produced simply by introducing a Flynn effect boost (FEB) at each calendar year and across all age groups. Mathematically, the technique looks something like Chart E:

AgeChart E
Griswold interpretation, Flynn effect transition
60 80 x (1 + 0 x FEB) 80 x (1 + 1 x FEB) 80 x (1 + 2 x FEB)
40 90 x (1 + 0 x FEB) 90 x (1 + 1 x FEB) 90 x (1 + 2 x FEB)
20 100 x (1 + 0 x FEB) 100 x (1 + 1 x FEB) 100 x (1 + 2 x FEB)
1960 1980 2000
Calendar Year

Chart E starts from the no Flynn effect base of Chart D, then a Flynn effect boost is introduced continuously and universally over time, impacting all age groups and all cohorts the same, exactly as required under the assumptions of the Griswold interpretation. If we plug in an FEB value of approximately 0.1, then Chart D transitions quite smoothly into Chart A, demonstrating that the suggested technique provides a plausible mechanism for how the Flynn effect must work under the Griswold interpretation.

Since each interpretation appears to be mathematically plausible, we need to search further for evidence to rule out either (or both). The ideal approach to this task would be to examine an adult population for which there is no Flynn effect: if the cross-sectional age-related intelligence scores are flat over such a population, the Griswold interpretation could be ruled out, and if the cross-sectional age-related intelligence scores are in decline over that population, the Agbayani interpretation could be ruled out. Unfortunately, it is unclear whether any extant human population can be characterized as untouched by the Flynn effect (the Flynn effect's relentless ubiquitousness being one of its more tantalizing features), and thus the ideal approach appears to be unavailable.

If the Flynn effect were to come to a halt, then that would also provide a means for assessing the two interpretations, because the halting would produce distinctly different signatures under each interpretation. Under the Griswold interpretation, a stop in the Flynn effect would immediately impact all age groups and all cohorts, something like Chart F:

AgeChart F
Griswold interpretation, halt of the Flynn effect at year 2000
60 80 88 97 97 97 97
40 90 99 109 109 109 109
20 100 110 121 121 121 121
1960 1980 2000 2020 2040 2060
Calendar Year

Under the Agbayani interpretation, a halt to the Flynn effect would produce a more complex pattern, because the halt would impact only future cohorts and not any existing cohorts. This would produce something like Chart G:

AgeChart G
Agbayani interpretation, halt of the Flynn effect at year 2000
60 80 88 97 107 118 128
40 90 99 109 120 130 130
20 100 110 121 131 131 131
1960 1980 2000 2020 2040 2060
Calendar Year

Under the Agbayani interpretation, for a period of time after the halt of the Flynn effect, intelligence scores would continue to increase in the older age categories but would begin to level off at the younger age categories (including childhood ages). Such a signature would be strong evidence against the Griswold interpretation and in favor of the Agbayani interpretation. Unfortunately, it is again unclear whether in the real world a halt to the Flynn effect is imminent or whether it could be quickly and easily recognized; and thus this technique, while theoretically interesting, would appear to be pragmatically out of reach.

Despite these obstacles, I do believe some strong arguments can be made against the Agbayani interpretation. The first difficulty is with the assumption that raw intelligence abilities would remain relatively level across the adult years in the absence of a Flynn effect. Although this is certainly possible, it runs counter to many other known biological abilities, such as athleticism and sexual vitality, and it would seem that a pattern of peak during early adulthood followed by gradual decline in later years would be the preferred assumption. To assume otherwise should require some evidentiary explanation, and of course Agbayani (2013) does not provide that explanation — it is only the Agbayani interpretation that supports the assumption of a flat level of intelligence across adulthood, and we have seen that there is at least one alternative interpretation that runs exactly counter to such an assumption.

More problematic still is the need for a Flynn effect boost to be provided to each cohort quite early in its existence, a need driven by the assumption that the Flynn effect is a function of cohorts. Although such a mechanism is theoretically possible, it runs counter to almost everything that is commonly understood about intelligence and the Flynn effect. For instance, you cannot say something like better education might produce the Flynn effect, because under the Agbayani interpretation a cohort's Flynn effect boost has to be fully in place before even the first day of school. Many similar intelligence explanations are ruled out for the exact same reason. By making the Flynn effect a function of cohorts, one removes the element of time, and much of what we understand about the acquisition of intelligence depends upon the passage of time, not upon the introduction of cohorts. Under the Agbayani interpretation, it would appear we must look only for Flynn effect causal candidates that are materially different across cohorts, present in nearly every member of each cohort, and present essentially right from birth. The list of plausible such candidates would seem to be conspicuously small. Although it is extremely common and popular to assume that the Flynn effect must be a cohort-driven phenomenon (see for instance the first sentence here), I think the proponents of that assumption fail to appreciate the difficult-to-explain consequences that must inevitably arise.

Admitting freely to my bias, it seems to me that the Griswold interpretation suffers from far less strain. In the first place it adopts the more physically natural assumption that unaided by a Flynn effect, human intelligence would peak in early adulthood then gradually decline towards old age — mirroring similar abilities in athleticism, health maintenance and sexual vitality. More importantly, by describing the Flynn effect as a universal, continuous, incremental function of time (not of cohorts), the Griswold interpretation opens the door to a straightforward, environmental explanation for the Flynn effect. Any consistently changing phenomenon that is essentially present for all people in all places at all times becomes a viable candidate as a causal explanation for the Flynn effect, and such candidates are quite conceivable. I have described elsewhere that I believe it is the increasing amount of non-biological pattern, structure and form tangibly contained within the human environment that serves as the most likely driver for the Flynn effect, and although here is not the place to argue the merits of that explanation, it is permissible for me to note it is entirely consistent with the Griswold interpretation. I am unaware of any competing Flynn effect explanation that is entirely consistent with the Agbayani interpretation.

Agbayani, K.A. & Hiscock, M. (2013). Age-related change in Wechsler IQ norms after adjustment for the Flynn effect: Estimates from three computational models. Journal of Clinical and Experimental Neuropsychology, 35(6), 642-654.

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.

Saturday, June 22, 2013

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.

Saturday, June 15, 2013

A Match Made in Hell

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

Sunday, June 2, 2013

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

Thursday, May 9, 2013

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.

Thursday, April 18, 2013

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, Gรถdel, 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.

Saturday, March 2, 2013

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.

Sunday, February 10, 2013

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.

Tuesday, January 15, 2013

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):


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.


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.


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.


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.