GRADIENT CORRELATION

Topology and simple physics constrain natural selection.

by Gregory B. Yates

July 7, 1996

[excerpts, with annotations in square brackets]

Copyright © 1996 by Gregory B. Yates. All Rights Reserved.

Preface

I propose a theory of evolution and call it Gradient Correlation Theory [which forms the bulk of A-Priori-Object Theory in Dragon Puzzle Story.¹] Gradient Correlation Theory is here presented as an extension to Charles Darwin's theory of evolution. [This is for simplicity: Like the Topological Theory of Autism, Gradient Correlation Theory does not formally depend on Darwin's theory.²] The theory yields technical and ethical implications, and I pursue both. A familiarity with basic scientific thought and a concern for the effects of theory will likely aid understanding of the text.

Abstract

After introducing some strengths and weaknesses of Darwinian theory, the text takes the following general course:

• The existence of objects requires correlated physical gradients.
• These gradients constrain natural selection, producing gradients of expected organism traits.
• Gradient correlation leads to the expectation of gender, food chains, and rapid speciation during life's evolution.
• Gradient correlation has shaped human evolution: Significant average trait differences are expected between genders and according to long-term population position on Earth.
• Autism and bipolar disorder may have been favored by Gradient Correlation.
• Trait overlap and complementarity are also implied, so Gradient Correlation does not justify gender- and racial prejudice or support any group's claim to global superiority.
• Religious doctrines have followed correlated gradients on Earth.

Introduction

Charles Darwin's theory of evolution by natural selection rests on three principles: An organism's traits 1) are heritable, 2) are variable and 3) differently affect the viability of an organism and its offspring. The power of Darwin's theory lies in the logical necessity with which these three principles produce an engine of evolution. Darwin's contemporary Thomas Henry Huxley agreed "...Mr. Darwin does not so much prove that natural selection does occur as that it must occur..."³ To the three Darwinian principles Gradient Correlation Theory effectively adds a fourth: An organism's traits 4) are constrained, for example by topology and simple physics.

Darwin's theory by itself suffers from three important weaknesses. First, in predictive form it verges on the tautological. The popular formulation of Darwin's theory as "survival of the fittest" is not Darwin's phrase, but captures the difficulty: In a complex world it is difficult to determine the fitness of an organism except by conducting an experiment to see what organism survives. This, however, reduces the seemingly predictive "survival of the fittest" to the tautological "survival of the survivors".

A second weakness of Darwin's theory is that the fossil record most obviously suggests not gradual but rapid evolution -- often correlated with geologically significant events like asteroid impacts -- followed by long periods of little change in the outward appearance of organisms.

A third weakness of Darwin's theory is that it lends itself to scientistic and pseudoscientific misapplication. Thus, for example, Darwin's theory has been cited to defend phrenology, Social Darwinism, and draconian racial policies. This weakness is inevitable for any theory whose broad outline is easy to grasp by those impatient with its details and limits.

Gradient Correlation Theory directly addresses the first two weaknesses of Darwin's theory: It relieves somewhat the tautology of Darwinian theory by supplying a priori statements about organism fitness, and it also leads to a general expectation of rapid speciation. However, it does not escape vulnerability to misapplication, in part because its central ideas are, like Darwin's, general and easy to grasp, and in part because its details and limits are still being worked out.

Physical Gradients

The Certainty Gradient

The headwaters of gradient correlation may be found in stories. There are many stories about life's unfolding. Some may be called scientific and others revelation, but all presume the existence of distinguishable entities -- of objects, for example. All objects (things) share an important property: A distinguishable object cannot exist with uniform certainty everywhere. Otherwise the object, existing uniformly everywhere, would be indistinguishable from anything else. An object exists with less certainty in all directions away from where it is. Thus even though it is difficult to be absolutely certain of anything it is possible to report an outwardly declining certainty of existence in objects. There is in objects a Certainty or Probability Gradient: Proceeding outward through an object the certainty of its existence eventually declines and the certainty of its nonexistence rises. In other words, [past some point] the a priori probability of an object's continued existence declines radially. An everyday object may be substantially contained in a sufficiently large sphere. The Certainty Gradient is the central gradient of gradient correlation.

Correlated Physical Gradients

Various basic physical gradients correlate with the Certainty Gradient. These include the Density, Velocity and Local Correlate Gradients.

Where an object does not exist it cannot be dense. Thus there is in objects a radial Density Gradient: Past some point an object's density declines outward. A particular object's density may rise outward -- locally -- but it must decline outward eventually. This is so at many scales surrounding the scale of everyday objects. It is also so whether the density is of parts, events, features or stuff: An object cannot have parts, features or events where it does not exist. Even in crystals surface parts lack outer neighbors and so exist in relative sparseness. The Density Gradient is the first of many that correlate with the Certainty Gradient, ultimately shaping natural selection and giving Gradient Correlation Theory its name.

The correlated gradients apply for objects of all kinds, whether they are connected objects or not. In collective objects like populations the Density Gradient appears as an expected outward decline in population density.

The greater the net distance traveled by a part in any period of time the greater its average velocity. Thus the larger the region of an object the greater the average velocity possible within it in any period of time. This is true for both radial and rotational motion. The larger the radius, the larger the region of an object encompassed. Thus there is expected in objects a Velocity Gradient: The velocity of moving parts is expected to rise outward in an object. The Velocity Gradient can be seen in other ways. For example, if a piece of an object moves far enough in a short enough time it no longer correlates with the object: Central parts of an object may move, but parts at the threshold of correlation must move. Further, everyday objects usually arise through accretion and fall apart through the reverse: In both accretion and falling apart parts may move at the object's center but must move through its periphery.

Where an object does not exist there can be no local correlates of its existence because there is nothing there to correlate to. Thus there is in objects a Local Correlate or Causal Gradient: There is expected a priori an outward decline in local correlates or causes of an object's existence. Because the probability of existence declines outward, all causes must appear on average to favor the destruction of outward-moving parts, and the sustenance of inward-moving parts.

Where there is great certainty there is little information to be gained through further observation. The Certainty Gradient ranges from relative certainty of existence to relative certainty of non-existence. Uncertainty is at a maximum midway. Thus there is in objects an Information Gradient [or Belt]: Object-correlated information is expected to rise to a maximum midway down an object's Certainty Gradient, and to decline from there outward. Where the probability of existence is high parts tend to be stable and where low, short-lived and so newer on the whole. Thus in objects an Information [Stability] Gradient proceeds outward from stable to novel information.

Where the likelihood of a part's existence is low the fact of its actual existence is surprising and so carries information. Thus the information per part rises consistently outward [past some point.]

A-Priori Expectations and the Universe

The correlated physical gradients represent a priori expectation for all objects at a wide range of times, places and scales surrounding those of everyday objects. In other words, the gradients reflect actual average behavior of objects even in the absence of detailed observation, or of any observation at all. Gradient Correlation Theory applies most strongly at the middling scale of everyday objects -- the scale of many organisms and populations.

The certainty gradient declines outward in time as well as space. Thus the certainty of existing objects' existence has increased to the present moment, and declines into the future. The past has favored the formation of everyday objects and the future favors their destruction. The existence of everyday objects draws almost no comment, but to propose that an existing everyday object will never perish can surprise.

Detailed observation reveals many deviations from the expected gradients. This is inevitable if the universe is anything other than a great blob. Holes and hollows, for example, require local outward density rises in objects. However, such deviations must be local if they reflect the structure and behavior of actual objects.

Density, velocity, local correlate, and information gradients all correlate with the object-defining certainty gradient. Although other physical gradients correlate with the certainty gradient, these four already significantly constrain natural selection.

Physical Gradients Yield Trait Gradients

The bodies of organisms are objects, and populations are collective objects. Hence correlated physical gradients are expected of them as of any stone. Gradient correlation constrains natural selection and relieves the tautology of "survival of the fittest" by providing a priori determinants of organism fitness. For each physical gradient a gradient of organism traits is expected prior to observation, and as with the physical gradients the trait gradients and their corresponding poles are expected to correlate.

Physical constraints can influence evolution by natural selection. Whether a constraint affects natural selection is chiefly determined by the length of time the constraint is present and whether it influences organism survival and reproductive success. Gradient correlation has existed as long as there have been objects and influences organisms' survival and reproduction, as presently described.

Like any object a population of organisms exhibits a density gradient, and so in any population some organisms live in regions of sparse population and others in dense. Even in a colony of closely-packed organisms symmetry is broken: Those on the surface lack outer neighbors and so live in dramatic sparseness relative to their interior companions. An organism is fitter to survive in a sparse region when its traits allow thriving at relative distance from others of its kind, in an environment dominated less by kindred society than by things or dissimilar organisms. In other words, in sparse regions what may be called loner traits and traits conferring natural- or object-world savviness are adaptive. This is the a priori expectation for organisms of any kind -- and at any era or scale. The converse holds, too: An organism is fitter to survive in a region of dense population when its traits allow thriving near kin. Thus in dense regions social, gregarious and cooperative traits are adaptive. In sum, correlated with the density gradient in any population is expected a gradient of organism traits ranging from cooperative, gregarious, social-world savvy organisms in dense regions to loner, object- or natural-world-savvy organisms in sparse regions.

The Velocity Gradient is evident among organisms as a gradient of organism mobility and is probably most obvious in a population expanding into surrounding territory: Newly inhabited territory is necessarily first entered by moving organisms, with the fastest-moving organisms at the fore. The process here is rather like chromatography (and in the early stages of life's evolution may literally have been chromatography) in which a muddy mix of substances separates into a spectrum of species arrayed according to speed of movement, with the fastest leading. It is also like the splash of a wave on a shore (and may, too, literally have involved this). Populations flow and ebb. When the direction of chromatography is reversed or a wave recedes fast-advancing parts become fast-receding parts. The expectation of the Velocity Gradient is that whether in advance or retreat the most mobile organisms are likely to be found in a population's sparse regions -- near its external and internal frontiers.

Although the influence of the Velocity Gradient may be most obvious at the frontiers of an expanding population, the gradients exist and are correlated at a wide range of scales, including the scale of density fluctuations within a population. Thus they constrain natural selection even in a population with well-contained frontiers.

Organisms disposed to move a lot may be called mobile or restless. Muscles and wanderlust exemplify specific traits favoring restlessness. By contrast, organisms disposed to remain relatively stationary may be called sedentary or tenacious. Roots of plants exemplify a specific tenacity-favoring trait. In sum, corresponding to the Velocity Gradient in any population is expected a gradient of traits ranging from sedentary or tenacious interior organisms to mobile or restless outer organisms.

The local causes of an organism's existence include nutrients, with various forms of energy prime among them. The Local-Correlate Gradient appears significantly among organisms as a Nutrient Gradient: In any population an outward decline in the prevalence of nutrients is expected a priori. Dense population in itself supplies evidence of nutrients: No such a priori inference is possible where there is no population. The a priori expectation is that inner organisms are relatively nutrient-rich and outer organisms nutrient-hungry. Nutrients are needed to sustain population density, for example to reproduce, and energy is needed to move. The Nutrient Gradient leads to an expectation of a trait gradient extending from organisms preferentially using plentiful nutrients to reproduce, to organisms efficiently using scare nutrients to move.

When an organism receives fewer and fewer nutrients it does not simply become less and less alive: At some point it dies. Even seeds and spores perish. This Nutrient Threshold Effect (ultimately a reflection of object containability) constrains natural selection in regions of low nutrient density. Temporal environmental fluctuations like droughts and snowstorms can abruptly produce large areas of low nutrient density. Because of the Nutrient Threshold Effect such an area may contain nutrients sufficient to sustain one organism but not two. Here cooperation cannot succeed: Survival is mutually exclusive. In such a grim place the organism whose traits incline it to prevent a neighbor from eating, and to grab the available nutrients, thus killing the neighbor, is the only organism whose traits will persist there. At the low end of the Nutrient Gradient natural selection tremendously favors competition, aggression, and even violence, murder and cannibalism, which supplies nutrients as well as eliminating competition. Traits favoring murderous competition are further consistent with population sparseness for the stark reason that killing organisms reduces their population density. [Cooperation can succeed in very sparse regions only as long as supply lines tenuously render the regions more nutrient-rich, and the more remote the region the more tenuous the supply line.]

Recall that inner organisms are expected to be relatively cooperative. Inner organisms may have their competitive moments, but these in general pale beside what occurs at the grim end of a nutrient gradient. In conclusion, there is a Competition Gradient: Proceeding outward in a population there is expected a gradient from cooperation to competition extending even to extreme violence. A corresponding trait gradient is expected.

The Information [Stability] Gradient for its parts leads to the expectation of a trait gradient ranging from inner organisms adapted to store stable information to outer organisms adapted to acquire and manage novel information. The greatest storage capacity and greatest novel information rate (bandwidth) may be expected to arise respectively just inside and just outside the information maximum midway down the Certainty Gradient [i.e. in the middle of the Information Belt].

In order to survive in an environment filled with novelty an organism must be adaptable and even innovative. Outer novelty-facing organisms also face something deadly: Risk. The Certainty Gradient provides the a priori expectation that the probability of existence declines outward in a population. In other words, there is a Risk or Danger Gradient: Proceeding outward in a population there is expected a rise in life-threatening risk faced by organisms. This gradient applies to risks from all sources. The risk gradient can be sensed from the simple observation that if one proceeds in any direction on space or time one eventually encounters a region where continued existence is unlikely. The Risk Gradient itself constrains natural selection and leads to the a priori expectation of a trait gradient extending outward from danger-avoiding to danger-facing organisms. Because of the correlated Competition Gradient, in regions of low nutrient density not the least risk arises from an organism's own kind.

In sum, corresponding to the Information [Stability] and Risk Gradients is expected a gradient of traits extending outward from conservative storers of stable information to risk-facing acquirers of novel information.

Because the physical gradients correlate, corresponding trait gradients are also expected to correlate. In any population of organisms the a priori expectation is that there will arise, correlated with the Certainty, Density, Velocity and other physical gradients a

Gradient of Correlated Traits

extending

FROM	TO
sedentary/tenacious	mobile/restless
cooperative	competitive/aggressive/violent
gregarious	loner
social-world savvy	object- /natural-world savvy
stable-information-storing	novel-information-acquiring/ innovative
danger-avoiding	danger-facing
fast reproducers	slow reproducers

(This is a partial list, and the terms are relative.)

This terse table has been hard-won. It is a prize, however, because it is the simple consequence of natural selection constrained by the mere fact that organisms and populations are objects, and because it thus represents a priori expectation for all populations at all scales and eras.

The Origin of Life -- a conjecture

[The paper details a scenario, implied by Gradient Correlation Theory, for the origin of life. It appears as a theory application in Dragon Puzzle Story.] The scenario suggests how genetic information, gene-driven catalysis, genetic variation, genetic recombination, in-gathering of catalytic chains and reproducing cells may all arise together as a result of simple physical processes.

Energy-Information Exchange and the Origin of Gender

Outer organisms in a population gain information about surviving novel risks. Risks can move -- indeed that is the expectation of the Velocity Gradient. Danger-shy inner organisms have much to gain from information about how to survive possibly approaching risks. The very existence of an organism at the frontiers speaks eloquently of its risk-surviving traits. Some of these traits can be of distinct value to inner organisms.

Inner organisms have much to gain from risk-related information but are rich in potential energy and other nutrients. Outer organisms are energy-hungry and rich in risk-related information. The conditions for symbiosis thus exist. Natural selection favors inner and outer organisms that exchange nutrients and novel information. Outer organisms face risk and supply information about how to survive it: Inner organisms supply energy and other nutrients while storing risk-surviving information. [Thus, Nutrient-Information Exchange, and Energy-Information Exchange in particular, are expected a priori to mark the development of organisms and brains.]

Because within a species inner organisms reproduce the traits of surviving outer organisms, as well as their own, their offspring form a spectrum of inner and outer types. Inner organisms can thus implicitly supply energy to outer organisms by relieving outer organisms of the energy cost (and motion impairment) attendant on reproduction. When inner organisms produce outer-type offspring, outer organisms -- already slow reproducers - can entirely cease to reproduce. In this way natural selection constrained by gradient correlation favors the origin of gender among organisms. Non-reproducing but information-supplying organisms are typically called male, and reproducing, information-accepting organisms female. Because male and female organisms meet to pass information, gender is a relatively local effect of gradient correlation. However, mixed groups of males and females can live in either sparse or dense regions, so topological effects also occur on a larger scale.

The Competitor Condensation Cycle

In a nutrient-rich area a small decline in nutrient level may produce a small drop in organism population. By contrast, because of the Nutrient Threshold Effect, at the nutrient-poor frontiers a small decline in nutrient level can send a large area across this threshold, rendering the area uninhabitable. The few mobile and competitive organisms living in such a wasteland are then, regardless of gender, faced with a choice: Move inward -- up the Nutrient Gradient -- or die. Obviously, under such circumstances natural selection favors those outer organisms that overcome their loner tendencies and employ their mobility to head back toward denser population. Because of trait correlation, as these ravenous frontier organisms retreat they encounter organisms progressively less competitive than they are. The competitive can be violent but it need not be: One population may decimate another simply by gathering available nutrients more rapidly. The cooperative traits of inner organisms can provide some defense, but times of severe nutrient decline favor the wave of mobile, competitive organisms retreating from the frontier. This is Competitor Condensation. In times of great nutrient increase natural selection conversely favors rapidly reproducing organisms [leading to Cooperator Expansion.] However, very rapid population growth can precipitate nutrient crisis as well as encroach on loner frontier organisms, and thus itself trigger Competitor Condensation. Nutrient levels constantly fluctuate: A cycle of alternating Cooperator Expansion and Competitor Condensation is an expected feature of organism and brain development. [Population density in these cycles is likely to have a sawtooth shape because of a fundamental Growth-Death Asymmetry: Growth takes time, but death can happen suddenly.]

The Hybrid Engine

Both Energy-Information Exchange and Competitor Condensation have the effect of bringing inner and outer organisms into contact, where offspring with a mix of inner and outer traits are formed. (The condensation by novel-information-bearing frontier organisms can thus itself be seen as a form of energy-information exchange.) These offspring then scatter in general according to their mix of traits, including any serendipitous synergies. The constraint of natural selection by gradient correlation thus results not only in a gradient of traits, but also in a great engine producing hybrid organisms. Emerging hybrids immediately encounter correlated gradients and so the hybrid engine keeps turning. This helps account for the stability of the phenomenon of gender in spite of hybridization. Hybrids arise predominantly near the information maximum of the parent population.

Rapid Speciation

From the Information Gradient it is expected that proceeding from one object to another nearby there is little gain in novel information: Novel information tends to be more remote. In other words, neighboring objects tend to be more similar than widely separated ones. The Information Gradient is thus also a Similarity Gradient: Proceeding outward through any object there is expected a decline in the similarity of its parts as compared to central parts. This gradient [is obvious for rocks and rivers, and it] is obvious for most organism populations: Because of the nearness of parents and offspring organisms tend to live relatively near relatives. Organisms sufficiently dissimilar cannot jointly produce viable offspring.

From the preceding, the outer part of a population is expected to be a forge of novel, even radically innovative traits. This novelty can arise through such mechanisms as stress-induced mutation, fragile chromosomes, ostracism of mutants, rapid recombination, and inbreeding. Novel, even bizarre, organisms retreating from the frontier during Competitor Condensation encounter others not only less competitive than they are: Because of the Information Gradient the encounter organisms less and less similar to them. During a severe nutrient crisis, such as likely occurs during geologically significant events, a catastrophic instability results: The wave of condensing competitors crashing back from the frontier destroys the outer layer of still rather-competitive cousins and then easily cuts a swath of destruction inward through progressively less competitive and less similar organisms. By the time the wave stops the retreating frontier organisms may find themselves in contact with cousins so dissimilar that they can no longer jointly produce viable offspring. Speciation has occurred. The constraint of natural selection by gradient correlation thus leads to an expectation of rapid speciation with extinction of intermediate forms, as is commonly observed in the fossil record.

Catastrophic condensation can also occur when two arms of a parent population meet and one of the arms is more competitive at its frontier: Then there is no wall of competitive cousins to overcome and one arm can condense through the other. If the two arms have become separated from the parent population then they are essentially tribes and their collision produces what is, effectively, war.

If the condensing frontier organisms are initially so competitive as to be somewhat cannibalistic, then competitor condensation becomes Predator Condensation and a food chain is the result: The modern division of plant and animal kingdoms may be the echo of an ancient Predator Condensation.

Gradient Correlation Theory resolves some weaknesses of Darwinian theory and appears to account for some gross features of life's evolution on Earth. Although there are necessarily countless local deviations from the expectations of gradient correlation, if observation suggests that the basic physical gradients have been correlated on a large scale in a population then the trait effects of gradient correlation may be anticipated. These circumstances arise in the evolution of Man, and give rise to profound ethical questions.

Human Evolution

Human Gender

The basic correlated gradients have been inevitable in human and hominid life. Population density has declined outward in families and tribes, with the most restless members tending to the population frontiers and the more sedentary to the center. Food has been gathered toward tribes and families, resulting in outwardly declining nutrient gradients, and so on. A parallel gradient of correlated traits has also been evident -- most obviously in the phenomenon of gender.

It is a remarkable fact that human societies are not homogeneous, but are formed of two distinct types -- female and male. It is remarkable because one can easily imagine that it might have been otherwise. As discussed earlier, gender reflects gradient correlation. Some of the gradient correlation effects on gender are grossly physical and therefore obvious. For example, it is obvious that women reproduce and men do not: Men provide genetic information but only women produce offspring. It is also obvious that child-bearing women have been at a distinct mobility disadvantage relative to longer-legged, more muscular and womb-less men, so that a mobility gradient has existed on average between the genders. However, the trait effects of gradient correlation are expected to extend well beyond the grossly physical and to include an entire gradient of correlated traits [including traits of behavior and brain.] Thus, for example, the actively reproducing humans (women) are expected from gradient correlation not only to be less mobile in general, but also to be relatively gregarious, socially adept, cooperative, risk-avoiding and stable-information-storing. The longer-legged, muscular and non-reproducing humans (men) are expected to be on average relatively restless, competitive, isolated, innovative -- particularly in the world of objects, and inclined to face danger. They are also expected to be on average more violent.

Autism and Bipolar Disorder

It is apparent from gradient correlation that average distance to neighbor has been one of the single most influential factors in evolution. Traits inclining an individual to survive almost without companions have been favored in areas of low population density. Perhaps the most noticeable feature of autism is an ineptitude in social relationships and a tendency to self-contained existence. It is possible, therefore, that traits expressed in autism are in part a result of gradient correlation. [This is the theme of A Topological Theory of Autism, which is therefore an application of Gradient Correlation Theory.] The incidence of autism is several time greater among males than females, as expected if autism is a gradient correlation effect.

The variation between loner and gregarious behavior apparent in some forms of bipolar disorder (manic depression) may reflect an energy-information exchange mechanism in human populations: Occasionally-gregarious loners are more likely to reproduce their traits than are pure loners, and occasionally-solitary gregarious people are relatively likely to acquire adaptive novel information. Cyclic variations in average distance to neighbor are favored by gradient correlation and can probably be found in many species, as well as at milder amplitudes among humans.

Some traits change rapidly under natural selection and others vary slowly. The gender-producing effects of gradient correlation have existed for so long and at so many levels that it is very likely that gender-related traits include many that can vary only slowly. Even though the hybrid engine has produced in humans a brain of remarkable adaptability, it seems unlikely that the social and technical innovations of a few thousand years can erase the gradient effects of millions. Just as gradient correlation has shaped bodies it has also shaped brains and behavior. It is here that ethical problems arise.

Ethical Consequences of Gradient Correlation

Ethical consequences of gradient correlation's effect on human evolution include the expectation that some policies presuming the average behavioral equivalence of men and women may founder. Too, economies that reward competition and daring innovation, particularly with objects, may favor men, and those that reward social aptitude and a status quo, women.

The Hybrid Engine constantly stirs the boundary between male and female, producing what might be termed yang females and yin males -- women who possess traits more common in men and men who possess traits more common in women. These people are a natural and expected part of the human population.

The ethical consequences of topological effects on human gender are great, but gradient correlation has had other effects of perhaps even greater ethical significance.

Human Race

The Sun fuels almost all life on Earth, and the Earth is a spinning ball illuminated most intensely at its equator by the Sun. A great nutrient gradient thus extends on Earth from equator to pole. [Equatorial deserts and ocean currents complicate this gradient, but in general, and particularly on land, it holds.] Resulting gradient correlation effects are expected on a global scale for all terrestrial species.

Most current evidence suggests an African origin for the human species. Correlated gradients extending outward from Africa are thus expected for humans. Africa lies to the South and West of adjoining continents. Combining this geographical fact with the solar-nutrient and African-origin gradient yields this: For the human species basic correlated gradients, and a corresponding gradient of traits, are expected to extend north and east from Africa. The ethical implications of this conjecture -- that human behavioral traits vary on average with latitude of ancestral homeland -- are so serious as to demand corroborating evidence. Archeological evidence of large-scale human Competitor Condensation from the North and East would constitute such evidence. Here is one account of the relevant history:

But then came the great change -- a change so great, indeed, that nothing else we know of in all of human cultural evolution is comparable in magnitude.

Peripheral Invaders

At first it was like the proverbial Biblical cloud "no bigger than a man's hand" -- the activities of seemingly insignificant nomadic bands roaming the less desirable fringe areas of our globe seeking grass for their herds. Over millennia they were apparently out there in the harsh, unwanted, colder, sparser territories on the edges of the earth, while the first great agricultural civilizations spread out along the lakes and rivers in the fertile heartlands...

Notice the almost classic description of frontier traits as nomadic and roaming harsh, sparse, fringe areas (relative to the fertile heartlands implicitly at the fatter end of a nutrient gradient. The account continues:

We have nothing to go by but speculation on how these nomadic bands grew in numbers and in ferocity and over what span of time. But by...about seven thousand years ago, we begin to find...a pattern of disruption of the old Neolithic cultures in the Near East. ... There is evidence of invasions, natural catastrophes, and sometimes both, causing large-scale destruction and dislocation. ... In Old Europe the...disruption of Neolithic societies...also seems to begin in the fifth millennium B.C.E., with...Kurgan Wave Number One. ... The Kurgans were of what scholars call Indo-European or Aryan language-speaking stork, a type that was to be idealized by Nietzche and the Hitler as the only pure European race. In fact, they were not the original Europeans, as they swarmed down on that continent from the Asiatic and European northeast. ...[T]he term Indo-European...characterizes a long line of invasions from the Asiatic and European north by nomadic peoples. (emphasis added)⁴

It is possible that natural catastrophes or population growth allowed by the end of the most recent ice age precipitated the invasions. In any case, the invaders were brutally competitive and arrived repeatedly from the northeast.

Gradient correlation affects human culture as well as human genes. The chief determinants of whether a constraint becomes reflected in the genome are whether the constraint is strong and whether it has existed over sufficient time. [cf. adaptive inertia in A Topological Theory of Autism.] The Competitor Condensation by northeastern nomads was the expression at a large scale of gradients that have existed throughout human and prior history. The constraints have been strong and there has been plenty of time for them to affect the genome.

Even if all human genetic evolution had ended abruptly a hundred thousand years ago a genetic trait gradient would have extended outward from the species origin by virtue of simple passive chromatography: People genetically but unchangingly inclined to be restless competitive loners would have continued to predominate at the vanguard of the outwardly expanding population. [That is, chromatography alone would have yielded a gradient of behavioral traits extending from equator to polar ice on Earth: Genetic change and adaptation amplify this expected chromatographic gradient.]

Human ancestors not only moved toward polar ice: Polar ice moved toward the ancestors in the form of ice ages. There is evidence that ice ages sometimes descended in the span of a few human generations. It is probably hard to overestimate the brutal effect of wave after wave of polar ice descending on creatures of equatorial origin. It seems unlikely that the combined effect of ice ages and northward human expansion left no effect on human genes. Many human behavioral traits that correlate with latitude and distance from species origin are probably too slowly-varying to be described as purely cultural.

Heart and Intellect

Theories of human genetic difference have been used to rationalize some of the most brutal programs of genocide in human history. They helped produce the gas chambers of Auschwitz and Birkenau.

It is customary to exclude from technical discussion mention of heart. This custom arose understandably from experience that passions can blind. Unfortunately the custom can foster the illusion that heart and intellect are unconnected. Some conclusions of this paper intrude so sharply into matters of heart that I shall now set custom aside and speak directly of heart.

Gradient Correlation Theory arose from the study of how brains are built -- from the search for written form-constraining principles applying at many scales around the scale of brains and text. The conclusions regarding gender and race were an unanticipated byproduct of this work. The possibility that the ideas of Gradient Correlation Theory might be bent to the service of future butchery immediately horrified me. After contemplating the theory for years I concluded that the best and safest thing to do was simply to introduce the theory with care.

Most theories of human genetic behavioral differences have been attempts of one group to rationalize violence to another. What disturbed me about Gradient Correlation Theory is that so many of its terms and conclusions rest on observations people can make regardless of their passions. People can pour sand all day and all day observe that it forms a density gradient, with the fastest-moving grains moving to the margins. People can observe, too, that a faster-moving organism tends to move farther, away from the crowd, and through relatively novel and risky territory. The average speed and distance to neighbors can be observed for humans (and twins) as for sand. The fraction of energy spent in moving or reproduction, and the fraction of time spent in social activity like touch or conversation can likewise be observed. I saw that, as with many ideas in science, if Gradient Correlation Theory did not arise in one place it would arise in another, perhaps someplace carelessly stated and more easily bent to harm. I sensed a responsibility to present the theory as harmlessly as possible. Fortunately two facts brought me some peace of mind.

Trait Overlap and Complementarity

Gradient Correlation Theory does not justify the violence of one group to another. It does lead to the expectation of slowly-varying average differences between groups, and that the groups may differ genetically on average in some abilities. It is difficult to discuss genetic differences in ability without seeming to slight one group or another. However, our species now faces notable problems, not the least of which is learning to exist peacefully -- and to celebrate -- differences.

Some human abilities are expected through gradient correlation to vary on average with gender and race: However, large overlap and complementarity of abilities are as surely expected, so racial and gender prejudice are not supported and no group short of all humans can claim greatest human ability. Men and people with more polar ancestors are expected to be on average relatively daring, innovative -- particularly with objects -- and competitive. Women and people with more equatorial ancestors are expected to be relatively cautious, favoring the proven -- and cooperative. However, the workings of the Hybrid Engine essentially guarantee large overlap of abilities between genders and throughout the spectrum of races. [There are no distinct races, but there is a multidimensional spectrum of races, as there is of colors in a chromaticity chart.] Men and women meet to reproduce. This and human mobility have made it essentially impossible to sustain the isolation necessary to produce a sharp split in abilities within the human species. A spectrum has been inevitable while a split has been impossible. Individuals of any race or gender may easily possess or surpass abilities more common in another race or gender.

While gradient correlation does suggest that one group may be on average and in a narrow area more able than another, it does not conclude that any particular narrow ability is better than another. On the contrary, a complementarity of abilities is expected, with each narrow strength in one group correlated with its disability relative to a different strength predominant in another group. The requirements of symbiosis giving rise to gender, for example, essentially demand that the different average abilities of the genders are of equal and complementary value to the species. Complementarity is also found in abilities varying on average with race. A group that is on average relatively competitive, innovative and restless is less likely on average to cooperate, to consolidate wisdom and to celebrate life as it is. Both poles of ability are important to the species.

Neither inner nor outer pole of ability can claim moral superiority to the other because there is good and evil at both extremes. The outer extreme produces life-enhancing innovation and moving acts of personal responsibility, but also arrogant domination and cunning murder. The inner extreme produces selfless cooperation and peaceful celebration, but also stifling sameness and the lack of responsibility see in mob behavior and in the tolerance of innovation-preventable misery and death. Hybrid evils are familiar, too, as when an arrogant few take the helm of a mob.

Population and Technology

Population and technology are to some degree linked by gradient correlation. The two have reflected a form of energy-information exchange on Earth: Rapid (energy-intensive) reproduction has fueled the innovative (information-intensive) use of objects and the innovative use of objects has enabled rapid reproduction.

We live at an unprecedented point in the history of the human species: Population and technology have altered the scale of gradients as they existed for eons. Ancient frontiers -- the haven of loner traits -- have vanished under crowds, and with machines people now cross in an hour areas that once held all the descendants of a tribe for a thousand years.

Estimates that human population can greatly increase may overlook the fact that average distance to neighbor has been one of the most influential factors in evolution. The population explosion of the past few thousand years has occurred in a flash compared to the preceding millions during which tiny human [and hominid] tribes expanded into huge unpopulated areas. As a result the human genome is still overwhelmingly tribal and is also studded with loner traits. Our population growth may be limited soonest not by inadequate technology or resources, but by genes that virtually cry out when neighboring tribes press close, and when deep solitude becomes difficult. In the past competitor condensation, as war, was a common result of explosive population growth. However, technology has now made it difficult to distinguish global war and global suicide. We have also witnessed [for example in the Holocaust of World War II] the terrible result when one group attempts to annihilate another through tidy technical means. Our genes may still clamor for war, but our spears have curved strangely and we find their points at our own hearts.

It is tempting to blame technology for current woes but, as mentioned, technology and human life exist in a kind of symbiosis. Surviving future microbial plagues itself will need advancing technology. While to allow technology to develop without care is to kill people, to radically curtail technology is to kill people just a surely. A lively balance should be possible.

[The paper continues with observations about the relevance of gradient correlation to brain structure, artificial intelligence, cosmology, and extraterrestrial life.]

[Religions]

It is hard not to notice that religions have followed correlated gradients on Earth: Religions arising in "outer" regions -- in snow and desert far from human origins, for example -- have tended to emphasize sacrifice, radical transformation, noble achievement, and hierarchy -- often with a male at the summit. Religions arising in "inner" regions -- in populated fertile areas, for example -- have tended to emphasize selfless equality, acceptance, sacred rhythms and cycles, and the divinity of nurturing. Both poles are important, and hybrids of the two flourish.

[The paper suggests nondogmatic practices to help Gradient Correlation Theory develop harmlessly.]

Conclusion

I have never encountered a theory as firm in its implications and yet as difficult to apply as is Gradient Correlation Theory. Local deviations from expected gradients seize the attention [as deviations from the expected often do.] The theory began in stories and may well end in them -- in endless confabulation and lip-flapping. Every theory needs ability and experience to apply. If a conclusion sounds either vague or smugly certain, if it promises easy reward or derides anyone, it is not likely a valid inference of Gradient Correlation Theory. Smug certainty is an almost universal human tendency and can occur equally in the overzealous application of a theory and in the denial of a theory's merit.

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¹ Yates, G., Dragon Puzzle Story: Self-building brain theory and its link to spiritual practice, DragonPuzzle.net, 2004, Chap. 3

² Yates, G., A Topological Theory of Autism, Autismtheory.org, 2000, The Persistence of Autism

³ Weiner, J., The Beak of the Finch, Alfred A. Knopf, New York, 1994, pg. 7

⁴ Eisler, R., The Chalice and the Blade, HarperSanFrancisco, 1988, pg. 43-44