Chapter II


Generalization of the Structure of
Mendeleev's Periodic Table



The universe is a Systems-Hierarchy. It has evolved in a cumulative manner, each higher step in this hierarchy, after the first, consisting of lower step components plus a new entity which has emerged out of the hierarchy, mutually modified.l,2 The world is therefore at the same time "richly strange and deeply simple."

The objects represented by each of this dis-assembled cup's rings appear and are, of course, extremely different; yet they display a single background plan, the same when viewed from the "side" (side elevation) and from "above" (ground plan).

General (Abstract) System-hierarchy

The template for the assembly of
empirical systems.

"A System-hierarchy is a hierarchy such,
that each member of the hierarchy (except the first) consists of previous members of the hierarchy plus a new entity which the hierarchy has created, mutually modified."
Cassidy, Quine, Haskell, 1964.


When you observe the cumulative edifice from below you are amazed to see that the structure of all the higher rings is potential and implicit in the forms and laws of the lower ones. And conversely, when you observe the universe from its highest rings you see that they collapse into huge numbers of their lower ring components. Theologians observing this, insist that the universe is teleological; that the lower kingdoms were designed to fulfil the goal of evolving ' into the higher kingdoms. In doing so, they arouse unending controversy with, or cold estrangement from, most one-field scientists. Assembly of the sciences, however, permits us to see that the universe is teleomorphic and teleonomic3; to see that the forms and laws of the lower kingdoms are such as to result in the higher kingdoms. This insight transforms the controversy and estrangement into a neutral state, where our scientific cultures' statement does not contradict the statement of our humanistic culture. The only alternative to the humanists' hypothesis of Mind is the one-field scientists' equally improbable hypothesis of Chance. (It scarcely needs to be said that from the viewpoint of the theory of probability, the latter is all but self contradictory in the immensity of its improbability.) The basis for discussion is thus strengthened, and will be expanded systematically in the following pages, as synthesis assembles the sciences into a single discipline.

FIGURE II-1 (b) The Cup of Life.49

Consider the deep simplicity of Unified Science: the "steps" of its great natural hierarchy fit together like the broad rings of the collapsible aluminium drinking cup, shown dis-assembled in this r figure. Each broad ring represents a natural kingdom or Major Stratum. Large portions of the bottom ring, stable particles, nest into the second ring, atoms, as shown by means of the nested braces at the left of the drawing. (Stable particles--plus neutrons which are composed of stable particles--combine to form atoms.) Large portions of these two rings nest into the third ring, molecules. (Atoms combine to form molecules.) Large portions of these three nest into the fourth ring called geoid systems. (Particles, atoms, and molecules combine to form the lowest geoid systems, gas-dust clouds, and these form all the higher ones--stars, planets, moons and so forth.) And so on up to the highest known natural kingdom, human cultures.

The hierarchy of ecosystems extends, at the left of the drawing, from Alpha to Omega , the beginning and the end--of organization. Not just the end of complexity, but of what, Warren Weaver calls organized complexity.4,5

In the vicinity of , we represent the basic natural kingdom, that of atomic particles; the entities which, many cosmologists think, comprise the cores of quasi-stellar objects, usually called quasars.6 The quasar, the nucleus of an emergent galaxy, is the habitat of atomic particles, where habitat is defined as All things that an entity affects, and which affect it.7 This nucleus is the first ring in the Grand System-hierarchy.

FIGURE II-2 The Genesis of the Atom Population. Reference to cosmic genotypes and the Mendelian population of atoms (cosmic phenotypes) refers to the discovery of Mendelian ratios in the atom population, and of the mechanism which probably produces them. The Chi Square test yields just under 98% significance probability28. See fold-out chart, top of the middle column. Data from Greenstein & Schmidt8.

Out of the quasar expand its hollow spherical shells. In the first shell some atomic particles (protons and electrons) combine to form the simplest, smallest atoms; representatives of the second natural kingdom, namely atoms of hydrogen and helium, with a single electron shell. As the first quasar shell expands, some of the small atoms build up into larger atoms, with two and three nuclear and , electron-shells, while a small new quasar shell emerges inside the first. And as the large first quasar shell grows still larger, still larger atoms form, with four nuclear and electron-shells. Iron atoms have been observed in this quasar shell, indicating the existence of about a quarter of the population of chemical elements.8 The atoms, however, consist of particles, and particles move into, out of, and among these atoms. At this period of its development, this quasar shell thus constitutes an ecosystem made up of two natural kingdoms: a lower kingdom of particles and a higher kingdom of atoms, always and necessarily integrated.

This System-hierarchic integration obliges us to recognize and coin a cumulative concept; one visually represented by the nest formed by the first two braces in our side elevation (Figure 1) and geometric ground plans (Figure 7). Namely, the concept, natural empire or Major Period. A Major Period is a cumulation of natural kingdoms or Major Strata.

As in human empires, so also in natural empires, the highest Stratum confers its name upon the empire as a whole. (For instance, the Roman Empire.) The kingdom of atoms being here the controlling Major Stratum, we call the second Major Period the empire of atoms.9

At some point in the outermost quasar shell's development--quite probably an early one--some atoms combine to form molecules, beginning the third natural kingdom and thereby, the third natural empire.

Atoms and molecules now draw together into clouds of gas, mist and dust. These are the simplest entities of the fourth natural kingdom, for which we propose the name geoid systems. These clouds draw together by gravitational attraction, forming the rest of this natural empire: stars of all magnitudes, solar systems, meteors, and so forth. Geoid systems thus comprise all celestial bodies except quasars, out of which they emerged.

FIGURE II-3 A spiral galaxy like our Milky Way.

I now suggest that as these celestial bodies form, they pull the outer quasar shell apart along half of its equator, shrinking the great sheet of stars into the curving equatorial arm of a lens-shaped spiral galaxy; a galaxy like our Milky Way in whose oldest and outermost arm our Solar System is located.

Our Solar System's habitat is our galaxy; and our galaxy's habitat is the millions of other galaxies, jointly called the Universe. That may be the ultimate ecosystem, the vastest space-time system known and knowable to Man; the physical pedestal from and within which, two or three billion years ago, emerged the biosphere.l0 The fourth Major Stratum, that of geoid systems, controls the fourth Major Period represented in Figure 1 by the first four nested braces.ll

The fifth Major Stratum emerges at a particular state in the development of a particular kind of planet in a particular kind of solar system by a richly strange process called biopoesis.l2 This process, which probably is itself Periodicl3, culminates in a tiny self-replicating sun-energy using structure called a bacterium or a one-cell plant: an entity so small that it is invisible to the naked eye. This is the emergence of the kingdom of plants, the fifth Major Stratum.

Self replication being, however, an exponentially cumulative process; and being augmented by positive, self-intensifying entity-habitat retroaction, this planet's kind of surface--solid, liquid and gaseous--is modified ever more rapidly. The natural kingdom of plants herewith presently becomes the controlling Major Stratum of the fifth Major Period, the natural empire of plant ecosystems.

Let me interpose this paragraph parenthetically: At this point, which is the emergence of life, and from here on, the discussion between theologians and scientists tends to heat up or to get broken off. As you will soon see, however, the first four (non-living, abiotic or azoic) natural kingdoms are just as richly strange as the three highest kingdoms, Man's included. What fouled up the communications and parted the ways of the West's Two Cultures was not the complexity of their subject matter, nor even the scientists' shift from the authority of sacred writings to the authority of empirical data. What fouled communications most was the scientists' long failure to assemble their findings. How can you compare a coherently working system, such as each of the Great Religions is to its professors, with what William McElroy, Chairman of the National Science Foundation, calls "the assemblage of institutional and disciplinary fragments it (science) is largely today?"14 However, when the sub-assemblies have been organized in a scientifically acceptable way, as I hope they are here, comparison with the theological systems becomes possible. That is why we find ourselves in an entirely new situation; one in which science comes full circle: becomes normative, and can be compared with theology; a situation in which the Two Cultures come together.

Resuming our discussion of the Systems-hierarchy: The sixth natural kingdom, that of animal ecosystems, emerged within the plant empire. But only the highest animals (which are, from the viewpoint of systems-theory, not apes but beavers) began to exert control over their ecosystems, and thus over a natural empire.

The minimal hypothesis necessary to explain the emergence of the simplest animal requires four simultaneous, coordinated changes, the kind of coincidence at which thermodynamics boggles: At some point, O. R. Anderson believes, a one-cell plant mutated part of its photosynthesizing process into rudimentary vision.l5 (It had already mutated organs of auto-motion, possibly flagelli, like those of Euglena viridis.) It sharpened a taste organ into an organ of smell, permitting it to follow waterborn gradients of decaying particles to their plant sources. At the same time one of its absorbing organs adapted itself to ingest plant ma'terial. And the development of genetic or non-genetic organs for information storage and association permitted, besides location and choice of distant foods and congenial habitat conditions, avoidance of dangers. This was the emergence of the kingdom of animals and of the highest kind of organization, which Teilhard de Chardin has called the noösphere.16 This is the sixth Major Stratum, the highest one of Major Period 6. It emerged from the lowest Period in the Periodic Table of plant ecosystems, and only the highest animal Period in the Periodic Table of animal ecosystems, that of beaver and certain ants, achieved significant control or empire over plant ecosystems.

Beavers are true agriculturalists: Through their technology of pond and canal construction, they grow thousands of acres of plants, aquatic and terrestrial. (They regularly harvest floating algae, called pond scum.) Certain ants, on their part, are both agriculturalists and pastoralists. But they control small plants and animals by means of technogeny: elaborate genetically evolved and transmitted techniques, without which they could not live. Technology and technogeny are diverse methods by which animals achieve control over their habitats.

The seventh natural kingdom, that of human cultures, emerged from the next-to-the-highest animal ecosystem, that of the anthropoids. The first three human Periods--Lower Hunters; Higher Hunters and Lower Agriculturalists; Middle Agriculturalists and Lower Pastoralists17,18 did not equal the beavers, control-wise. But the Higher Agriculturalists--who developed irrigation, crop-rotation and fertilization--began to do so. And the Literates, Toynbee's great civilizations, far surpassed them.l9 Our Lower Industrial civilization comprizes the highest known Period of the highest known Major Stratum of the highest known Major Period of the Universe; namely, the natural empire of Man.--Einstein afflrmed that "God is a tendency in the universe."

Thus far however mankind, having developed vast technology but failed to achieve coordination of its understanding, is destroying its natural empire, which of course includes itself. Mankind is daily accelerating disintegration, the increase of entropy, the downward tendency toward Alpha, the collapse of the Cup of Life's highest ring into vast numbers of lower ring components, and of these components' arrangements into ever less organized states.

This is far easier to see than the opposite tendency, ectropy, for it not only happens faster but is immensely easier to produce: An animal can easily be killed, a forest fire made to wreck an ecosystem, H-bombs to destroy continents. All we have then is ashes and rocks; molecules, atoms, particles--only the Universe's lower staircases. "The highway to destruction is broad," say theologians, and they call this tendency God's Adversary, the Destroyer. Its theoretical limit we call Alpha . (See Figure l, the left-hand column.)

What needs to happen for any given natural empire to be transmuted into the next lower Major Period? Simply removal of its top Major Stratum. A glance at our side elevation, Figure 1, will show that if Mankind, Major Stratum 7, is removed, we have the natural empire of animals, Major Period 6. If Major Stratum 6 is removed, we have some fragments of the natural empire of plants, Major Period 5. And so on down to Major Period 00 which is the Void.

FIGURE II-4 Organization-Time Graph of the System-Hierarchy: Natural Kingdoms combined into Natural Empires.

How devolution and evolution come about, the qualitative or moral relations which produce them, whatever the natural empire, will be described two sections later on.--Summed up in a simple graph, the quantitative aspect of the Systems-Hierarchy appears as follows:

The principle of cumulative emergence, and of the cumulative-systemic thinking required to represent it and control it, permits us both to keep our lower mental systems and to generate higher ones: The first natural kingdom that emerges, particles, persists as entity to the present time; much of it does. A part of it, however, is organized into the next higher kingdom, atoms; a part of them both into the third; a part of all three into the fourth, and so on to the seventh, human cultures. Thus, while higher and higher natural empires emerge out of the lower, examples of the lower ones none the less persist. Thus does the span of the Systems-Hierarchy increase toward . And by the reverse process, that of removing any given natural empire's top Stratum, the span of the Systems-Hierarchy decreases toward .--There is a visible correspondence between the structure of this natural hierarchy and one in human thought: the Natural number system, especially as expressed in Roman numerals: I, II, III; X, XX, XXX, etc.


It follows logically from our definition of the System hierarchy that examination of any of the natural kingdoms or Major Strata should show the general structure which all of the natural kingdoms are postulated to have in common; and that all Periodic Tables should be equally good demonstration models. (This will some day, I believe, prove to be factually true.) Today, however, at this particular point in the history of science, there is one Major Stratum, that of atoms, whose Periodic Table has been worked out and verified incomparably further and better than any other. This Periodic Table, therefore, is the classification whose structure has been generalized.--First, let us consider this model in its traditional form; the form based on empirical data; then in its geometric form obtained by generalizing its structure Systems-Theoretically: the Periodic Coordinate System.

The Periodic Chart of the Chemical Elements appears on the walls of chemistry labs and class rooms around the world; and it appears in several forms. Whatever its form, it has developed from a brilliant arrangement of data about the chemical elements which early l9th century chemists and physicists had accumulated. This classification was announced in 1869 by the Russian chemist Dimitri Ivanovich Mendeleev.20 Its structure has been verified, extended and improved ever since, and currently displays the form given it by Glenn T. Seaborg, Chairman-emeritus of the U.S. Atomic Energy Commission.21 For purposes of exposition, however, I have simplified its representation i~to s form elosex' to the one originally proposed by Mendeleev.22

All of the hundred-odd sets of atoms called chemical elements fall empirically into nine Groups; the nine patterns into which the major properties of the chemical elements resolve themselves. The Groups appear as the vertical columns numbered from I to VIII, plus the right-hand column which may conveniently be called Group O. And, since there are over a hundred of these sets, these patterns are repeated Periodically. These Periods form the table's horizontal rows.

Mendeleev did not try to explain theoretically why there are nine Groups. (As a matter of fact, when he first announced his Periodic Table, it had just eight: the Group O elements, the inert gases, were all discovered later.) The reason why there are nine Groups appears to be systems-theoretic in nature. It holds good for all the Periodic Tables to which the structure of Mendeleev's table has been generalized, and is one of the principal hypotheses upon which this assembly of the sciences is based.

FIGURE II-5a The Kingdom of Atoms: Major Stratum 2. The empirical classification from which the Periodic coordinate system was derived.

FIGURE II-5b The Periodic Table of Chemical Elements mapped into the Periodic Coordinate system. Simplified: coaction cardioids omitted. (Shown in Figure 11.)

The systems-theoretic reason why there are nine Groups is as follows: Natural systems are basically made up of two coacting components, shown in the general or abstract concepts diagrammed in the central part of Figure 1a. The habitat or work component--which cyberneticians often call collectively the factors23--and its usually much smaller entity, which they call the controller. (In atoms, the controller is the small, massive nucleus; the work component is the large electron cloud.) Those properties of the system that fall into the Groups, manifest the theoretically and empirically possible sets of coactions between the work component (habitat) and the controller (entity).

The relations between these two basic systems components are fundamentally action (or causation) and retroaction which, when it activates the controller, is called feedback, shown as a leftward arrow in Figure 1a. These cybernetic relations are jointly called coactions,24 and are obtained by considering the totality of rate-changes which each coactor can induce in the other. Not only do + and - represent rate changes (acceleration and deceleration, respectively) but 0 too is regarded as a rate-change; namely, as 0 rate-change. The theoretical and empirical totality of coaction is then obtained by cross-tabulating +,0 and - for work-component and controller, as in Figure II-6, top.


This cross-table Gestalt changes almost at once into the conventional pattern that every school child learns, the plane Cartesian coordinate system shown in the center of Figure 6. It changes into a Cartesian coordinate system on whose X axis Unified Science maps the system's work component, and on whose Y axis, the controller.

FIGURE II-6a The Coaction Cross-table.

FIGURE II-6b Newton's Cartesian Coordinate System: Zero, positive, and negative numbers. (Aberration from Descartes' system.)

FIGURE II-6c Descartes' Coordinate System: Zero and positive numbers only. Completion of this coordinate system yields the Periodic coordinate system, Figures 7, 8, 9, 10.

The Cartesian coordinate system, however, has just one point at which coaction is ( 0, 0 ), its center or origin. It follows that the rate-changes of only one kind of system at a time can be mapped into it. This means that it cannot be the framework into which the sciences are to be assembled. To unify the sciences--to map the Periodic Table of chemical elements geometrically, as in the lower part of Figure 5, and all the other Periodic tables representing the empirical Systems-hierarchy from to into a single coordinate system (below)--a drastically new coordinate system had to be invented, and a suitable method of calculation worked out for it.

To show how it came about--and how it involves a change from the traditional, mutually exclusive categories to inclusive, nested categories--this invention will be considered in the context of the history of the coordinate system:

The first quadrant of the traditional (Cartesian) coordinate system (Figure 6, center) was the first to be invented, and remains firmly in place in the Periodic coordinate system. (It was invented in Ancient Egypt and reinvented in ancient Greece.) Why only quadrant 1? Because these civilizations had only the Natural number system, which at that time started with the number 1 and has just positive integers.

This one-quadrant coordinate system was lost during Egypt's dark ages, was reinvented in Greece, and lost again in the dark ages resulting from the disintegration of the Graeco-Roman civilization. Some time after the rise of Western Christendom it was reinvented independently by Descartes and Laplace in a more advanced form, one which includes zero, as shown in the bottom part of Figure 6.

It was not a complete concept. However, two of Descartes' famous dreams of the night of March 19, 1619 in Nuremberg indicate that its completion would have to result, not in the Cartesian, but in the Periodic coordinate system: Descartes' principal dream was as follows: "I saw physics reduced to geometry and all the sciences extending out of it as a great chain".25,26 This chain seems to appear in Figure II-lb as the interlocked braces whose first four links represent the physical sciences, and out of which extend three more links representing the biological and social sciences. (These linked braces reappear much more graphically, however, in Descartes' quadrant of the Periodic coordinate system shown in Chapter V.)

The other of Descartes' obviously relevant dreams was simply "Est et non" ("Is and not"). This can be interpreted as positive numbers (est) and zero (non), and thus as implying exclusion of negative numbers. This exclusion is not trivial: it is essential to the realization of Descartes' first dream, the great chain of geometrized sciences.

To achieve this ancient objective, it is obviously necessary to start the coordinate system with the symbol which represents the very bottom of the Systems hierarchy. This symbol is Alpha which represents the point of maximum disorganization or entropy. It; lies at the origin, the center, of the Periodic coordinate system, Figure II-7.

FIGURE II-7 Periodic Coordinate System: zero and positive numbers. The Major Strata are shown, each representing a Periodic Table. Matter and Mind.

This part of unified science's coordinate system may be regarded as the plan view of the "Cup of Life," whose side elevation appears in Figure lb: the seven Major Periods are here shown in their nested position, viewed from "above."

Let us pass lightly, for the moment, over the half circle near representing half of the kingdom of stable particles. (The other half, representing the stable anti-particles, is shown in the Inverted Periodic coordinate system, near the center of Figure II-8.)

We thus come to the second Major Stratum, the kingdom of atoms, represented by what will be called a Major scalar-zero circle. This circle represents the whole geometrized Periodic Table of chemical elements shown in Figure II-5. Each of the other five nested scalar-zero circles in Figure 7 similarly represents an entire geornetrized Periodic table, though they cannot be shown in this short book.27 Each of the natural kingdoms or Major Strata is represented by a nested set of Periods, like the one representing Major Stratum 2, the kingdom of atoms (Figure 5.) Thus, each of the broad rings of the "Cup of Life," shown in Figure 1, turns out on closer inspection to be itself a "collapsible drinking cup." Whether Major Strata 3 and 4 (the kingdom of molecules and the kingdom of geoid systems) display Periods, and if so how many, remains to be determined. But the Kingdom of plants (Major Stratum 5) appears to have four Periods, the kingdom of animals appears to have five, and the kingdom of human cultures (which we will discuss in Chapter IV) seems to have six Periods, and to be in process of generating a seventh.28

The chain of interlocked braces in the Periodic coordinate system appears to be Descartes' "great chain of sciences." It is inherent in this model of unified science, and had been drawn some years before I read of Descartes' dreams. I am, however, most happy to acknowledge the priority of his two interdependent discoveries: limitation of the coordinate system to positive numbers and 0 (Est et non), and the nesting of seven Periodic coordinate systems which this makes possible, and is represented by his "great chain of sciences."29 (To interpret Descartes' l7th century dreams in this meaningful way it was, I think, necessary to have executed them previously in 20th century detail.)

This new detail, moreover, prevents us from omitting the breakdowns of higher systems into their lower system components. Since evolutions of higher systems are here represented as extending outward from along the X and Y axes, their breakdowns or devolutions have to be represented as progressing inward toward , and to be mapped along the inward-directed X and Y axes. (See Figure 7.) This mapping does not, however, imply the use of negative numbers. What it implies is subtraction from the upper limit of this coordinate system: from its largest zero circle, with radius Omega, (Est), toward its lower limit (Non). (Also subtraction within each Period, from its ( 0, 0 ) circle, as will be shown.)

Mathematicians, of course, see instantly that the method of calculation appropriate to the Cartesian coordinate system does not suffice for the Periodic coordinate system. The methods appropriate to the latter include the former, but go beyond it.--One method, developed by Harold G. Cassidy, is set forth in the Addendum to his Chapter I. Another method, which is still incomplete, was developed by Gause and Witt, following Volterra, Lotka and others.30,31 At the suggestion of G. Evelyn Hutchinson, I generalized this construct in 1947, thereby obtaining the Periodic coordinate system. However, while their equation works in quadrants 1 and 3, Cassidy and I have not succeeded in adapting it to quadrants 2 and 4. Through their method is promising, it is therefore here omitted.--Interested mathematicians are invited to take up this calculation tool and make it useable throughout the Periodic coordinate system. It can almost certainly be done.

FIGURE II-8 Inverted Periodic Coordinate System: zero and negative numbera. Anti-matter only; Major Strata.

Turning now to the part of Unified Science's Coordinate system which hardly anyone but particle physicists and habitually think about, it scarcely needs to be pointed out that for the representation of the probably immense regions of the universe inhabited by anti-matter, exclusive use of zero and negative numbers isjust as essential as exclusive use ofzero and positive numbers is for the representation of our familiar world of matter. There are socalled "black holes" in the sky: great celestial bodies through which matter apparently converts itself into anti-matter,32 presumably generating an Anti-System-hierarchy from to Anti . The Inverted Periodic coordinate system, into which anti-atoms and the rest of the Anti-System-hierarchy can be mapped, appears in Figure II-8.

Some effects of the anti-particles have been observed. What they imply has, theoretically, to be extrapolated into the construct of an anti-universe, as represented in this figure. Our understanding of the nature of anti-matter implies, however, that partially material beings such as we are cannot verify this figure's hypothesis empirically: To do so would annihilate our material parts. For this very reason however, it is important to consider the probably immense antiuniverse scientifically. And the Inverted Periodic coordinate system constitutes, it is hoped, a contribution to this study.

FIGURE II-9 Alpha Coordinate System: zero, positive, and negative numbers. (Inverted Cartesian Coordinate System, Figure 6b). Stable Particles.

In any case, it is essential to unification of the sciences. For the first natural kingdom of the anti-universe, the stable anti-particles, constitutes just under half of the single Period which comprises the Periodic Table of stable particles, Figure 9. This is the Major Period which the universe and the anti-universe have in common; and its representation is the bridge linking the Periodic and the Inverted Periodic coordinate systems to each other.

The Alpha coordinate system's structure is, on one hand, implicit in the structures of the two Major Periodic Coordinate Systems; and on the other hand, determined by the data mapped into their lower parts. The transitional coordinate system consists of the other two coordinate systems' inward-directed axes. It is thus a combination (and repetition) of the end segments of these four axes, and turns out to be the Cartesian coordinate system with axes and coordinates reversed. For obvious reasons I have called it the Alpha coordinate system.

Mapped into it is the Periodic Table of stable particles: This is obtained first by repeating the half circles near the origins of the Periodic and Inverted Periodic Coordinate Systems and then by adding the photon which, being its own anti-particle, maps into its scalar zero circle. To correspond with reality, the Periodic Tables of all the material natural kingdoms beyond particles must be confined to zero and positive numbers; those of all anti-material higher kingdoms, to zero and negative numbers, as we have seen.

Relative Plus and Minus as well as Zero

There are different kinds of pluses and minuses: absolute ones, representing pro-matter and anti-matter which annihilate each other; and relative ones representing, say, proton ( + ) and electron ( - ), whose mutual attraction is essential to the formation of It thus turns out that the symbols ( + ) and ( - ) have long represented quite different kinds of things, just as has ( 0 ).

Long ago Kelvin discovered a radically different kind of zero than Celsius' relative zero, the freezing point of water at sea level; namely cessation of translational movement, which is absolute. What we now find are fully as different kinds of + and -. The difference between protons +P and anti-protons -P, and between electrons -e and positrons +e is absolute: They literally nullify each other. But the difference between protons +P and electrons `-'e is relative: they combine to form atoms just as -P and `+'e probably combine to form anti-atoms. Only when these distinctions are mirrored in our notation is it possible to map the stable particles into a coordinate system. This mapping appears as shown in Figure II-9, where semi-quotes distinguish relative plus (`+') and relative minus (`-').

The four neutrinos fall on the four coordinate axes, each of whose coaction symbols contains a zero (Figure 6). Protons and antiprotons fall in quadrants 3 and 1, respectively. Their coaction symbols ( + , + ) and ( - , - ) nullify each other, producing ( 0 , 0 ) as the corresponding natural phenomena "annihilate" each other, producing photons ( 0 , 0 ).

Similarly, electrons (-e) and positrons (+e) fall into quadrants 2 and 4, respectively. Electrons are labeled `-'e because they and protons (+P) attract each other. They form atoms, systems higher in the hierarchy, which is the opposite of what positive and negative numbers do to each other.

It is thus clear that all minus quantities in the Periodic coordinate system (Figure 7) are relative: They represent subtraction from some relative-zero circle. It thus turns out that there need to be relative and absolute minuses and relative and absolute pluses just as there are relative and absolute zeros.

I present the Alpha Coordinate System in response to the following hope voiced by the nuclear physicist C. S. Wu: "Physicists," she wrote, "continue to study the smallest fragments of matter in the hope that careful analysis will fit quantitatively with a simple mathematical pattern that is yet to be found."34 The stable particles constitute but a small part of the kingdom of particles. Their mapping into the Alpha Coordinate System may, none the less, prove to be a step in the direction called for by Dr. Wu.

These three frames of reference-the Periodic, the Alpha, and the Inverted Periodic coordinate systems-comprise a single, logically consistent system whose components scientists can handle individually. Mathematicians can, however, visualize them as a single hyper-spatial coordinate system.35 In either case the coordinate system of unified science by-passes (or, rather, incorporates) the four-quadrant construct shown in the center of Figure 6, the Cartesian coordinate system.

This most used of all coordinate systems, was designed by Isaac Newton some decades after Descartes' famous dreams. It incorporates Descartes' one-quadrant coordinate system (bottom of Figure 6). But, by violating Descartes' dream Est et non (through inclusion of negative numbers), it precludes the realization of Descartes' dream of geometric unification of the sciences. This is the fateful rock which shattered the stream of science's development into a fan of separate disciplines, and thereby shattered the mind of Western civilization into two mutually paralyzing parts, which C. P. Snow has aptly called the Two Cultures. On one hand the great historic culture of the humanists; on the other hand the fatefully discoordinated culture of one-field scientists and technologists; and between them the confused gulf of mutual dislike and non-understanding.36

How have we by-passed the Cartesian rock of cultural division? By making it the keystone of the unified culture which Snow predicted would presently emerge in the United States. We have inverted the Cartesian coordinate system and placed its origin or center in a position corresponding to the one displayed by Nature: the mysterious solitary point located between the objective universe of pro-matter, to which we equate the subjective universe of absolute positive numbers; and the universe of anti-matter to which we equate the mental universe of absolute negative numbers.

Instead of many separate Cartesian coordinate systems, each centered on a relative-zero point which bears no relation to the other systems' origins, we now array the series of concentric, hierarchically related scalar-zero circles. The function of the Cartesian system's absolutely negative numbers which we have assigned to anti-matter is now fulfilled by the subtraction of positive numbers from these scalar-zero circles in the direction of .


There is a series of discontinuities which mark the boundaries of what Quine calls natural kinds.38 The greatest of these is the boundary between pro-matter and anti-matter, which I propose to call . The next most important boundaries separate the natural kingdoms or Major Strata, represented by the concentric circles in Figures 7 and 8. The third most important natural kinds are those of the Periods within each Major Stratum represented, for instance, by the circles in the lower part of Figure 5 (kingdom of atoms), but implicit in each of the other Major Strata as well. The third and fourth most important natural kinds are Strata (e.g. electron shells and nuclear shells) and Sub-strata (e.g. their orbitals). These too are implicit in the Periods of all the other Major Strata.

Relative ( + ) and relative ( - ) thus play just as important roles in unified science as does relative ( 0 ), which reappears in each Period and Major Stratum.

The formal quantitative aspect of unified science is summed up by putting together the three parts of unified science's coordinate system. There is a series of discontinuities which mark the boundaries of what Quine calls natural kinds.38 The greatest of these is the boundary between pro-matter and anti-matter, which I propose to call . The next most important boundaries separate the natural kingdoms or Major Strata, represented by the concentric circles in Figures 7 and 8. The third most important natural kinds are those of the Periods within each Major Stratum represented, for instance, by the circles in the lower part of Figure 5 (kingdom of atoms), but implicit in each of the other Major Strata as well. The third and fourth most important natural kinds are Strata (e.g. electron shells and nuclear shells) and Sub-strata (e.g. their orbitals). These too are implicit in the Periods of all the other Major Strata.

Relative ( + ) and relative ( - ) thus play just as important roles in unified science as does relative ( 0 ), which reappears in each Period and Major Stratum.

The formal quantitative aspect of unified science is summed up by putting together the three parts of unified science's coordinate system.

FIGURE II-10 The Coordinate System of Unified Science: Quantitative Aspect.

Data which would heretofore have required an indefinite number of arbitrarily arrayed Cartesian coordinate systems are hereby assembled into a single hyper-spatial construct whose center turns out to be a Cartesian plane coordinate system in reverse: the Alpha coordinate system. This rock of fateful division, by-passed in its original form, thus turns up inverted and renamed at the center of the mental organization which Leibniz predicted under the name of Universal Characteristic.37 This is the absolute point at which Relativity--both physical and ontological--begins, and from which they derive coherent existence and meaning in the mind of Man.

We turn now to the Universe's qualitative principles.


One of the surprising ways in which this assembly of special sciences, this whole, exceeds the sum of its parts is the emergence within it of the Moral Law. Gottfried von Leibniz foresaw this clearly in the seventeenth century, as will be shown. And Werner Heisenberg has restated it for the twentieth century in Physics and Beyond as follows: "The problem of values ... concerns the compass by which we must steer our ship if we are to set a true course through life. The compass itself has been given different names by various religions and philosophies: happiness, the will of God, the meaning of life--to mention just a few ... I have the clear impression that all such formulations try to express man's relations to the central order. Of course we all know that our own reality depends on the structure of our consciousness; we can objectify no more than a small part of our world. But even. when we try to probe into the subjective realm we cannot ignore the central order or look upon the forms peopling this realm as mere phantoms or accidents. ... In the final analysis, the central order, or the `one' as it used to be called and with which we commune in the language of religion, must win out. And when people search for values, they are probably searching for the kind of actions that are in harmony with the central order, and as such are free of the confusion springing from divided, partial orders. The power of the `one' may be gathered from the very fact that we think of the orderly as the good, and of the confused and chaotic as the bad."39

When the Periodic coordinate system first appeared (in 1940), I called it The Coaction Compass.40 Soon after that an article appeared in the Scientific Monthly entitled "The Religious Force of Unified Science."41 To whatever extent Unified Science is an assembly of the whole, it represents, of course, the "one"; to whatever extent this assembly meets the scientific tests of correctness, its structure must correspond to the central order; and to whatever degree this happens, it represents the Moral Law.

This conclusion is implicit in the Systems Hierarchy depicted in Figure 1, the "Cup of Life": The apex of this hierarchy, the human mind, Heisenberg's "subjective realm", consists of representations of the previous systems, plus something more which has emerged from this hierarchy (namely, Man's mind), mutually modified.42

Unification of the sciences in any human mind implies this mind's assumption of the order central to the universe. For to the extent that in this mind, accurate representations of the universe's parts (one-field sciences) are so related to each other as to yield verifiable predictions, it probably is correct. To the extent that it is correct it probably results in "the kind of actions that are in harmony with the central order ..." And that is the Moral Law.

"We think of the orderly as the good," Heisenberg says, "and of the confused and chaotic as the bad." In less traditional terms, the increase of disorder is called increase of entropy and the increase of order is called increase of ectropy:43 In 1947 Warren Weaver pointed out that the sciences should be arrayed relative to these two universal tendencies.44 This has accordingly been done: the point of maximum entropy constitutes one limit of our organizing framework; the point of maximum ectropy its other limit. The whole quantitative aspect of the universe's moral manifestation, from Omega through Alpha to Anti-Omega, is shown in Figure 10. That is to say the range of one aspect of the Moral Law; its quantitative range.

These theoretical limits of entropy and ectropy constitute boundaries for mental organization, over-all. Each increase or decrease, however, implies a zero point, relative to which it has been recognized and then perhaps estimated or measured. Unorganized science permits these zero points to be arranged in ad hoc, hap-hazard, random fashion, as they long have been. Organization of the sciences, on the other hand, requires a rational, empirically based arrangement of zero points or lines, centered at the center of existence , and extending to its upper limit .

Since the universe's major moral tendencies are called entropy and ectropy, I propose for their zero or reference-tendency, the term atropy; and, as its geometric representation, a circle.

This theoretical concept may suggest what to look for empirically. What would atropic systems be? Would they not be inert systems; systems which neither combine with others ectropically, nor disintegrate other systems entropically? In the kingdom of atoms there is a complete Group of such systems: the inert or noble gases. They constitute Group 0 of the Periodic table of chemical elements, Figure 5.

How could they be represented geometrically? The limit of entropy is the point Alpha, the point where the regress of coordinate systems stops. A point may be regarded geometrically as a circle with zero diameter. Increases of ectropy may therefore be represented by concentric relative-zero circles with ever larger diameters, as shown in Figure 7; and increases of anti-ectropy may be shown in the same way, Figure 8. Organized representation of the Major Strata can thus occur in terms of concentric circles of atropy.

In geometrizing the Periodic Table of chemical elements (Figure 5, b), we begin by relating each Period to a zero circle, defined by an inert element, classed in Group 0; an element whose characteristic coaction is atropy ( 0 , 0 ).

FIGURE II-11 One Period of the Periodic Coordinate System showing the circle of atropy and the coaction cardioid. Radius angles are measured counterclockwise from the X axis. They are called theta angles, and their symbol is . Hence the generalized Periodic Law reads, R = f ( ). Its graphic representation is the coaction cardioid. The Groups of the Periodic Table of chemical elements, should be mapped on cardioids.

Let us assemble the three major manifestations of the Moral Law: the non-living or abiotic, the living or biotic, and the human or cultural, organizing our vast warehouse of what has been called, by William Eblen, the A B C interrelationships.45 The early formulations displayed various aspects of the Moral Law. They were statements about cultural relations, Major Stratum 7; and were, moreover, made thousands of years ago in the idioms of simpler cultures. "As ye sow, so shall ye reap."46 "Do unto others as you would that they did unto you."47 It is therefore natural that to this day discussions of values are made almost exclusively in terms confined to Man; and that, even by physicists. "The problem of values ..." says Werner Heisenberg, "concerns the compass by which we must steer our ship if we are to set a true eourse through life." And that includes the whole Systems-hierarchy.

Unified Science agrees unequivocally that values constitute the most determining human relations. But it goes further: it points out than Man belongs to the category of Culture, the highest member of the Systems-hierarchy, and that by definition these self same values must occur in various forms on its lower levels. Values must have been, and must still be displayed by biotic systems (by animal and plant ecosystems); and by abiotic systems: (geoid, molecule, and atomic systems). In fact, they must be displayed even by particles: Teleonomy, it was pointed out above, appears on every level of the Systems-hierarchy. It follows, of course, that we have been seeing the Moral Law at work on each of these levels all our lives without recognizing it, as people had seen falling apples and other objects all their lives without recognizing that they display the law of gravity. When each of these laws is pointed out, stated verbally, and formulated mathematically, so that it can be clearly verified or disproved, the gate is opened to our Two Cultures' complete, organic union.

The first formulation of the complete Moral Law for a non-human natural kingdom was Dimitri I. Mendeleev's 1869 announcement of the Periodic Law: "The properties of the chemical elements are functions of their atomic weights."20

This looks no more like a statement of the Moral Law of Man than a falling apple looks like an orbiting planet. Yet what it states for atoms is that "As ye sow, so shall ye reap," where "reaping" is the properties of the chemical elements and "sowing" is (as I will show) the coaction between the atom's work component, its vast, light electron cloud, and its controller, its tiny, massive nucleus. This "reaping" is the result of the doing of the one to the other, and the other's doing unto it.

Hindsight shows that atomic weight was the first manifestation of intra-atomic coaction discovered and measured by scientists. Its next manifestation was atomic number, the number of protons in the atom's nucleus. So the Periodic Law of atoms was improved to read "The properties of the chemical elements are functions of their atomic numbers." But with the (unconscious) discovery by T. H. Langlois48 that The properties of animal societies are functions of coactions between work component and controller (the 97% of small and medium fishes in the ponds, and the 3% of the largest fishes), the Periodic Law became a black box problem.49 As these two components of animal systems did unto one another, so they reaped:

Where the Majority and Minority cooperated ( + , + ), all their societies' properties were positive: the largest percentage of the populations survived, they grew the best, had the least sickness, and formed the most cohesive societies. Where the Majority and Minority persistantly damaged each other ( - , - ) all these properties were negative: the smallest percentage of the populations survived, they grew the least, had the most sickness, and had the most disintegrated societies.

Langlois, it is true, discovered only three or four of these coactions and their resulting property configurations in animal societies; and he did this empirically, as Mendeleev had done with atoms before him. But with the Periodic Law in existence; with the knowledge that in its atomic case there are nine Groups; and with Toynbee's clear demonstration in human civilizations that the corresponding properties of Man's societies are functions of the coactions between the Majority and the Minority, the black box problem of the explanation of the Periodic Law could be formulated, and a tenable solution be obtained: If the properties of systems in general--abiotic, biotic, and cultural--were functions of coaction between work component X and controller Y then their functions should be exactly nine Groups of properties (Figure 6); for instance, the nine Groups in the Periodic table of chemical elements, Figure 5.

The start of a tenable solution was obtained in 1940 by means of the crosstable shown in Figure 6, which yielded the requisite number and kinds of Groups. This tentative numerologicai approach to a solution was confirmed theoretically in 1948 by Norbert Wiener's "Cybernetics--Or Control and Communication in the Animal and The Machine."50 This, and the broader Systems-Theoretic works of von Bertalanffy51,52 and de Latil23 back up, and articulate Mendeleev's, Langlois' and Toynbee's a, b, c discoveries theoretically, showing them to be Systems-hierarchic manifestations of one universal law: "As ye sow"--as your work component and controller "do to one another"--"so shall ye reap"--such shall be your system's properties.53

Over a number of subsequent years the Periodic coordinate system was developed to express general, abstract relationships jointly displayed by these empirical a, b, c phenomena. And the empirical Periodic table of chemical elements (Figure II-5a) proved mappable into it (Figure II-5b).

When the Systems-hierarchy was defined by us (1964), it implied what actually is a very old idea: that any fundamental Law which obtains in one Major Stratum of the General Periodic Table obtains in all. That a single Law pervades the universe.

This concept is implicit in Leibniz's l7th century theory that it would one day be discovered that all sciences have a common structure. This prediction appears to be fulfilled by the Periodic coordinate system, whose recurrent structure is displayed (for the Abiotic Major Strata) in Figure 11.

The Periodic coordinate system is Cartesian with respect only to quadrant 1; and even there, just in respect to the circle of atropy. This circle's radius is determined by the intersection of perpendiculars erected in the cartesian manner at coordinates located on the X and Y axes. This circle-of reference represents the derivative of position (zero) which is the same in all quadrants, whether the axes are Cartesian or Periodic.54

This coordinate system is so constructed that all its higher derivatives--those of rate-change (of positive and negative acceleration) and thus the path of its radius vector--obey the General Periodic Law stated below. The path of the radius vector, therefore, turns out of the circle of atropy in the positive, Omega-ward part of the plane (in Greek, out-turning is ectropy); and it turns inside the circle of atropy in the negative, Alpha-ward part of the plane (in Greek, in-turning is entropy).

By letting the vector's scalar or length component (R) represent the system's properties, and letting the vector's directional component () represent the coactions of the system's work component X and controller Y, we obtain as the radius-vector's path, the coaction cardioid or heart-shaped curve in Figure 11. This is a geometric representation of the Periodic Law in its general or universal form: the form which applies to the kingdom of atoms, as Mendeleev's law does, and to all other natural kingdoms as well. The geometric, general form of the Periodic Law thus reads as follows:

R = f ()

The length of the radius vector (R) is a function of its direction (). This says in System-theoretic language that "The properties (R) of a system are functions of (are determined by) the coactions between its work component and controller ()," our empirically verifiable hypothesis.

Such is the general or abstract form of the Periodic or Moral Law. Let us now consider some of its concrete forms: abiotic, biotic, and cultural.


To map the chemical elements into this coordinate system (bottom part of Figure 5), we begin at the Axis of Atropy which bisects quadrant 2, and proceed counter-clockwise, representing the elements' increasing atomic numbers at 45° intervals.

The first Period has only two elements, hydrogen and helium. The second and third Periods begin on the Y axis and proceed around the coordinate system at 45° intervals, omitting Group VIII, but including Group 0.

It is important to understand why Period 1 consists just of Groups VII and 0, and can thus be regarded formally as beginning on the Y axis like the other Periods. (If one does not, this geometric mapping must seem arbitrary.) It happens to be a fact that two electrons (helium's number of electrons) complete the atom's smallest electron shell, the K shell. And it is shell-completion that makes atoms inert or atropic, the salient property of Group 0. It also happens that having one electron short of a completed electron shell (and hydrogen's one electron leaves it one short) makes atoms electro-negative, acidic, and extremely grabby, the salient properties of Group VII, the halogens.

Given these facts of nature, there is no other (physical) way for Period 1 to start. We are thus faced with two alternatives: Calling the halogens Group I, the inert elements Group II, and starting all Periods after the first with Group III; or doing what Mendeleev did intuitively: calling the first Group after the first Period Group I. I personally am glad that Mendeleev was obliged by the state of knowledge in his day to do the latter. Yet there is a dilemma, which some try to resolve in other ways.--Cassidy, for instance, places H in Group IV.33 It is dilemmas such as this that make the world so fascinatingly and richly strange.

Beginning with Period 4 (the Period which has four Strata, four electron shells--K, L, M and N), another strange thing happens: The new outer shell, (N) starts to fill up. The next ten electrons, however, go into the inner (M) shell, where three of them start Group VIII, with three sub-Groups, a, b, and c. (This is shown empirically in Figure 5 top, geometrically in 5 bottom, and in Figure 11.) Then it goes on around to germanium, whose electron goes into the outer (N) shell, and so on to the double Period's completion with krypton, Group 0.--(We will discuss the Triple Group (VIII) when we come to the top Major Period, human cultures, where it concerns us most directly. Figure II-16b).--All Periods which circle the coordinate system twice in completing a new electron shell are called double Periods. They contain all nine theoretically possible Groups. The rest have either eight Groups or (the first Period) just two. It takes a big system (one belonging to a high Period) to develop and be able to survive Group VIII, the ( - , - ) Group.55To map the chemical elements into this coordinate system (bottom part of Figure 5), we begin at the Axis of Atropy which bisects quadrant 2, and proceed counter-clockwise, representing the elements' increasing atomic numbers at 45° intervals.

The first Period has only two elements, hydrogen and helium. The second and third Periods begin on the Y axis and proceed around the coordinate system at 45° intervals, omitting Group VIII, but including Group 0.

It is important to understand why Period 1 consists just of Groups VII and 0, and can thus be regarded formally as beginning on the Y axis like the other Periods. (If one does not, this geometric mapping must seem arbitrary.) It happens to be a fact that two electrons (helium's number of electrons) complete the atom's smallest electron shell, the K shell. And it is shell-completion that makes atoms inert or atropic, the salient property of Group 0. It also happens that having one electron short of a completed electron shell (and hydrogen's one electron leaves it one short) makes atoms electro-negative, acidic, and extremely grabby, the salient properties of Group VII, the halogens.

Given these facts of nature, there is no other (physical) way for Period 1 to start. We are thus faced with two alternatives: Calling the halogens Group I, the inert elements Group II, and starting all Periods after the first with Group III; or doing what Mendeleev did intuitively: calling the first Group after the first Period Group I. I personally am glad that Mendeleev was obliged by the state of knowledge in his day to do the latter. Yet there is a dilemma, which some try to resolve in other ways.--Cassidy, for instance, places H in Group IV.33 It is dilemmas such as this that make the world so fascinatingly and richly strange.

Beginning with Period 4 (the Period which has four Strata, four electron shells--K, L, M and N), another strange thing happens: The new outer shell, (N) starts to fill up. The next ten electrons, however, go into the inner (M) shell, where three of them start Group VIII, with three sub-Groups, a, b, and c. (This is shown empirically in Figure 5 top, geometrically in 5 bottom, and in Figure 11.) Then it goes on around to germanium, whose electron goes into the outer (N) shell, and so on to the double Period's completion with krypton, Group 0.--(We will discuss the Triple Group (VIII) when we come to the top Major Period, human cultures, where it concerns us most directly. Figure II-16b).--All Periods which circle the coordinate system twice in completing a new electron shell are called double Periods. They contain all nine theoretically possible Groups. The rest have either eight Groups or (the first Period) just two. It takes a big system (one belonging to a high Period) to develop and be able to survive Group VIII, the ( - , - ) Group.55

Moral Tendencies Displayed by Atoms

The most cosmically important properties are those which, as Heisenberg points out, we regard as bad and good. Bad, he says, is the tendency to the confused and chaotic. Good is the tendency to increasing order or ectropy. Einstein probably referred to this when he said, "God is a tendency in the universe."

The chemical Group, relative to which these opposite tendencies can best be discerned, typically displays the (0,0) coaction and is aptly numbered Group 0: the relatively inert or "noble" gases. (I would prefer to drop the latter name since, in my view, Noblesse oblige.) When mapped into the Periodic coordinate system, they fall on the circles of atropy, the 0 circle in quadrant 3. (See Figure 11 and Figure 5b.)56

The most highly cooperative, creative, and thus ectropic elements typically display the ( + , + ) coaction. They are classed in Group IV, and are naturally mapped in the ( + , + ) quadrant; namely, in quadrant 1 where Omega is located.

Carbon is the first and most famous Group IV element. "Organic molecules," says Harold G. Cassidy, "are the class of molecules that contain at least one carbon atom. There are more than a million different members of this class." And he goes on to discuss the brilliant electron-structure that makes carbon the most ectropic element.33 Carbon atoms, Cassidy shows elsewhere, played and still play the key chemical role in biopoesis, the organization of life on our planet.28

The second Group IV element, silicon, plays the key role in the formation of life's habitat, the Earth. "Silicon plays an important part in the inorganic world, similar to that played by carbon in the organic world," says Linus Pauling. "Most of the rocks that constitute the earth's crust are composed of the silicate minerals of which silicon is the most important elementary constituent ... the framework minerals (hard minerals similar in their properties to quartz), the layer minerals (such as mica), and the fibrous minerals (such as asbestos)".57

And so forth through the existing Group IV elements and beyond them to the furthest ones envisaged for future creation or discovery. The "islands of stability," the theoretical regions in which the largest atoms are considered possible belong, Glenn Seaborg says, to Group IV.21

Turning to the chemically disintegrative, entropic elements, the most dramatic example is perhaps the halogens, Group VII, whose typical coaction is amensalism ( - , 0 ). These atoms, lacking one electron for completion of the outer shell or Stratum, attack many large molecules and destroy them in filling their need. "Fluorine ... is the most reactive of all the elements," says Linus Pauling. "Substances such as wood and rubber burst into flame when held in a stream of fluorine, and even asbestos ... reacts vigorously with it and becomes incandescent."57 The next element in Group VII, chlorine, was the first poison gas of World War I. And so forth.

Some chemists question the classification of hydrogen in Group VII because of its creative (rather than destructive) role in so many life processes. The explanation, however, involves us in an Irish bull: If straight hydrogen (H) occurred abundantly in nature, nobody would ask this question for there would be no chemists. One of the things that make them and other life forms possible is the order in which the elements and molecules were formed: H atoms were the first to be formed in the expanding quasar shells, Figure 2. Their great reactivity or grabbiness made them combine into the first molecules, H2. On one hand H2 molecules behave not like halogen atoms but like Group IV elements. And on the other hand, the lightness and smallness of H atoms permits larger atoms such as carbon to transform grabber into grabbed, thus (to anticipate) changing potential amensalism ( - , 0 ) into symbiosis ( + , + ), and potential entropy into ectropy. One function of unified science is to elucidate questions whose answers transcend the boundaries of one-field disciplines.

Space limitations permit us to discuss only one chemical Group displaying each of the primary moral tendencies: atropy, ectropy and entropy. The empirical reason why there are nine (and only nine) Groups has, to my knowledge, been discovered only implicitly, and thus unconsciously: It is implicit in Willard Gibbs' law that, given enough time and energy, a system will go through all of the states of which it is capable. In the expanding quasar shells there is enough time and energy for the whole atom population to ontogenate. (It did not evolve, as species do, but ontogenated as an individual organism does).28 Gibbs' law may thus be called the Law of Ectropy, the counterpart of the second law of thermodynamics.

An explanation of Periodicity (with a capital P) is implicit in the Law of Ectropy: since there are only nine coactions, not more than nine Groups can constitute a Period. If a system continues to grow, some or all of the same Groups have to recur in each higher Period; another Stratum is thereby added to the one or more Strata already in existence, displaying the same Groups.--Whenever, on the other hand, the top Stratum's last remaining Group's entities disintegrate, the system declines to a lower Period. Grouping, Stratification and Periodicity are thus interdependent. And that, from bottom to top of the System-hierarchy.

Because of their strong and justified reaction against anthropomorphism, physical scientists have been reluctant to discuss, let alone to name the coactions displayed in the abiotic kingdoms.58

A geometrically coded vocabulary has, however, been developed for biotic systems, as shown below in Figure 12. These coaction terms may be extended thence to abiotic systems by readers who see their way clear to doing so.


Proceeding visually from the abiotic (the lifeless) systems up the Systems-hierarchy (Figures 1 and 7) to living ones, the coordinate system remains constant, while the terms mapped into it become first those of biology, and then those of political theory. Historically, however, the coactions were discovered in biotic systems (Langlois' societies of fishes mentioned above), completed theoretically as in Figure 6, and then extrapolated "downward" to abiotic, and "upward" to cultural systems. This seems to fulfill predictions made in various ways by philosophers of science such as Warren Weaver,4 and Suzanne Langer,59 that synthesis would probably start with biology somewhere near the center and extend thence in both directions.

What made these extensions possible is the apparently universal validity of the relation which Niels Bohr called the correspondence principle.59 He demonstrated wide and significant correspondences between the laws and relations which govern geoid systems (Major Period 4), stated in terms of classical or Newtonian physics, and those which govern particles and atoms (Major Periods 1 and 2), stated in the very different terms of atomic physics. Bohr was forced to adduce this principle by the insuperable difficulties presented by the disparities between the Newtonian theories for geoid systems and those of Planck, Einstein, Heisenberg, Schrodinger, Pauli, Fermi and others for particle and atom systems.--And the data, reality, permit it. Bohr was thereby foreshadowing the present scientific revolution: One paradigm of unified science is the assumption that correspondence is universal, that it extends through the entire System-hierarchy. This belongs to a system of paradigms which reverses previous assumptions. (See Chapter V.) Thus it is the hallmark of what Kuhn has defined as a scientific revolution.6l

Some major correspondences between the biotic and the atomic Groups have already been indicated. Biologists, however, have long had their own vocabulary, whose major terms are here mapped into the Periodic coordinate system.

FIGURE II-12 Biotic Coactions Mapped into the Periodic Coordinate System. Since no terms for ( - , 0 ), ( 0 , - ) and ( 0 , + ) exist in the literature, they had to be coined. They have since been discovered in nature: plant, animal, and human.

The coaction vocabulary contained in biological glossaries and dictionaries is rather indefinite, displays several kinds of signal fouling and, when mapped in this coordinate system, displays the absence of three Groups. Namely, amensalism ( - , 0 ), allopathy ( 0 , - ) and allotrophy ( 0 , + ).24 All three missing coactions have since been found in nature many times; and that, in all human Periods as well as in one plant Period and two animal Periods.

In order to present a biotic Periodic table, it is necessary, however, to show correspondence not only of the Groups, but also of Periods, Strata and Sub-Strata with those of lower Major Strata. Just as the atoms' Periods build up cumulatively, Stratum by Stratum, so also do those of the biotic and cultural Major Strata. Their relationship is diagrammed in Figure 13 by Harold G. Cassidy.

FIGURE II-13 The relationships of Sub-Strata to Strata, and of Strata to Periods in all Major Periods or Natural Empires. Abstracted by Harold G. Cassidy.

In all the natural kingdoms, the first Period has one Stratum; the second Period has two Strata; the third Period, three, and so forth. For all of them, the rule thus is that for each Period, the top Stratum's number is the number of the Period. The same holds true for the Sub-Strata: for every Stratum, the top Sub-Stratum's number is the number of the Stratum.

The Characteristic Numbers and their Assembly
into Maps of the Web of Life

When Mendeleev classified the chemical elements, their number was well under a hundred; and it is not much over 100 to this day.62 What we propose now is to classify hundreds of thousands of not just organisms, but of complex ecosystems; and to do so in a similar way.

How is this possible? It is possible if a method can be proposed, as will be done below, whereby scientists can team up to collect strategic data systematically and cumulatively, and feed them into modern computers. The computer can integrate these data periodically into a model of what ecologists call the web-of-life. It can simulate the operation of this web in such ways as to reveal the data's most strategic gaps and errors. Thereby it can direct the complex scientific effort in coherent, practically useful ways toward ever more accurate and complete models of the web of life on Earth.63

The object will, I hope, remain what it has been from the beginning of this undertaking: To help Man to gain, under God, control over his destiny. Toynbee has seen this sort of thing happen repeatedly, and calls it the Genesis of Civilization.

The first question which scientists will probably ask is this: What are the parameters, the variables, for this cumulative mapping of the web of life?

They are the variables which the Grand System-hierarchy's systems have in common; the ones in which, as Bohr would probably have put it, they correspond.60 There are at least five such parameters. And they yield, when put together, the strategic construct which Leibniz apparently had in mind when he said, "We can assign to every object its determined Characteristic Number".64

Physical scientists have long been writing parts of such numbers for atoms. It is natural therefore that it should be a chemist who proposed the pattern here adopted: Harold G. Cassidy. The preceding diagram by him displays most of the pattern: Sub-stratum, Stratum, Period.

To these three parameters we add Mendeleev's Groups; but, naturally, couched in their general, geometric notation. And thereto, finally, we add the number of the classificand's Major Stratum or Periodic table.

Assembly of these five parameters of any given natural system into a conventional pattern results in its "determined Characteristic Number." These characteristic numbers can then be assembled into working models of portions of the web-of-life; and these can in due course be assembled into a world-web model.

The web of Characteristic Numbers lies one level higher than the Periodic Tables within the Systems-hierarchy of meta-theories or, as Quine puts it, background theories: The web of characteristic numbers contains all of the Periodic tables, plus one or more additional entities which have emerged, mutually modified.

The two parameters classified in Mendeleev's table are Period and Group. In adding the other three parameters to his Periodic table--and to the other Periodic Tables constructed in its image--we develop his table and Periodic Law further, fulfilling the prediction he made in 1889 before ajoint meeting of the Royal Society and the Chemical Society: "It (the Periodic LawJ needs not only new applications but also improvements, further development, and plenty of fresh energy. All this will surely come ..."20,65

The general form proposed for all Characteristic Numbers is shown in Figure 14a; a concrete example of a web of Characteristic Numbers is then displayed in Figure 14b.

FIGURE II-14a The Characteristic Number, mapping any process (except molecules and geoid systems) into the Periodic coordinate system. Designed by H. G. Cassidy and E. F. Haskell. Term coined by Leibniz.64

FIGURE II-14b Sample of the Web of Life, mapped in terms of Characteristic Numbers and designed for eventual computer programming.

Practical implementation of Characteristic Numbers appears in the mapping of any portion of the web-of-life in any given spacetime region. These relations have not been mappable in the past because of the absence of a systematic meta-language. This meta-language has now been developed, as demonstrated in Figure 14b. By itself, however, it would be practically useless: The web's enormous complexity and rapid dynamism far exceed Man's mental capacity to grasp (diagnose), retain, and usefully modify it in real time. Modern computers, however, are capable of handling such problems. We need therefore have no anxiety as to the practical applicability of the web of characteristic numbers, no matter how complexly and rapidly it changes.--For modern Man, the impossible just takes a little longer. And this has been, and will be increasingly, an international modern undertaking.

Our little example maps a small part of a great world problem: the plant rusts.--These comprise some thousands of species of fungi, basidiomycetes, one or more of which live upon almost every species of seed plant, as well as some ferns. The rusts are probably, phylogenetically speaking, mosses which have degenerated through parasitisation of higher plants. Wherever they become dominant in a high (fourth Period) plant ecosystem, they destroy the highest plant Stratum (seed plants) and break the ecosystem down to plant Period 3; and when they become dominant in Period 3 ecosystems (whose highest Stratum is occupied by ferns), they break them down to plant Period 2, whose highest Stratum, 2, is mosses, the parasites' own highest ancestors. In whatever natural empire a lower Stratum destroys the controller and takes its place, this kind of breakdown follows cybernetically.

Our example is deliberately confined to a plant-animal ecosystem, Major Stratum 5. We are thus dealing with wild wheat. (Man, if he were included, would belong to the pre-agricultural human Period, 1.) In following this presentation, the reader is invited to refer to the framework of the animal Periodic table, Figure II-15; and to Figure I-6, diagramming plant Periods and Strata.

In the coaction-web drawn in Figure 14b, the coactions of four organisms are related to each other qualitatively as they occur at a given point in space-time. The coaction symbols + , 0 and - indicate positive, zero, and negative relationships. Numerical values can be ascertained and assigned to these symbols,28 but are here omitted both because they have not yet been ascertained, and for the sake of initial simplicity.

The fungus' Characteristic Number is linked to that of its host, the wild wheat plant, by the symbol for parasitism ( + , - ) in Figure 12. This fungus belongs to the plant kingdom (5 at the center of its Characteristic Number); is situated in a seed-plant ecosystem (plant Period 4, written at the bottom); belongs to Stratum 2 of that Period (written at the top); and is in its second ontogenetic stage (Sub-stratum 2, written at the left).

Its host is a plant (5 in the center), belongs to the top plant Period (4, bottom), to its highest Stratum, seed plants (4, top), and is at its highest ontogenetic stage (4, left). This wheat plant is linked with the Characteristic Number of the weasel by ( + , + ), the symbol for symbiosis, for reasons which will appear directly.

The weasel is an animal (6 in the center); belongs to the fourth animal-ecosystem Period (4 at the bottom). (The Periodic Table of animal ecosystems is shown as Figure II-15.} The weasel belongs to its highest Stratum (4 at the top); and, while able to hunt, is not yet fully grown (3 at the left). Its Number is linked to that of the rabbit by the symbol for predation ( - , + ). (This is a standard symbol, Figure 12. Its form is correlated to its position in the coordinate system.)

The rabbit is an animal (6 at the center), in the fourth animalecosystem Period (4 at the bottom), the fourth Stratum (4 at the top); and is just old enough to get about (2 at the left).

The wheat-rabbit coaction is shown as predation ( - , + ), but could have been shown as parasitism ( + , - ) almost equally well. The essential relation is, that the wheat is damaged by rabbit ( - ), which is benefited by wheat ( + ) and this can be shown either way.6s Since the weasel checks a damager of wheat, and since the wheat benefits the weasel's prey, the weasel-wheat coaction is ( + , + ).

Conversely, since fungus and rabbit damage each other's food (wheat), their coaction is synnecrosis ( - , - ). Finally, the fungusweasel coaction is estimated to be parasitism ( +, - ), since the weasel protects the wheat (the fungus' food), but the fungus damages the food of the weasel's prey, the rabbit.

This example shows the following: Characteristic Numbers represent, not empirical species but ecological roles. (This is the great advantage of the Periodic Table of chemical elements, whose entries consist of partial Characteristic Numbers.) This is what made it possible for Mendeleev and Seaborg to predict the discovery or invention of missing elements.

The greatest difference between atoms and organisms lies in the vastly greater number and variety of organismic species that can play any given ecological role, and in the changes of ecological roles which species can display. This makes it necessary to add the organism's traditional name to its Characteristic Number; and frequently to include additional information besides. For instance, while the rabbit-wease? coaction is predation ( - , + ) in the short run (synchronically), in the long run (diachronically), their coaction is symbiosis ( + , + ): rabbit-weasel population-explosions are reciprocally prevented. (The phased cyclic oscillation of prey-predator populations are typically cybernetic in character.)

The cardinal feature of this, and most other ecosystems, however, is the fact that each one has a controller (the wheat in this case) and a work component (the other organisms here represented). This system's relations are all determined by, and defined relative to, the wheat. In ecological terms, it is the ecosystem's dominant organism.--The clear distinction between controller and work component is basic to the diagnosis of an ecosystem's condition, and to the prognosis of its development. Should one of the lower organisms, say wheat rust, become dominant (become the controller), the ecosystem would break down to its lower Period. Conversely, where a high organism comes to dominate (control) a low ecosystem, the system transmutes up to the controller's Period.-In Chapter IV, this cybernetic principle will reappear in human cultures, resolving otherwise quite unresolvable political coniusion, and consequent disputes.

Anyone familiar with computers can see at once how accurately this meta-language, when developed, should permit computer mapping and simulation of the web-of-life. This is a contribution obtained by geometrization of coaction vocabulary.

Students in inter-disciplinary courses which use this metalanguage become quite expert at writing and interpreting the Characteristic Numbers of particles, atoms, plants, animals and men. They learn herewith to locate any of these natural systems, including particular persons at various points in their life-runs, within their own Periodic tables, and these within the Periodic co-ordinate system as a whole.

All parts of the Characteristic Number written in Arabic numerals belong to the left-hand part of the General Periodic Law, R = f (). They belong to the properties of natural systems R which are functions of coaction (). Stated another way, the Arabic numerals comprise the scalar aspect of the radius vector, the Roman numerals (or their geometric counterparts) represent the coactions of which these properties are functions.

FIGURE II-15 Framework of the Periodic Table of Animal Ecosystems, Major Stratum 6, in terms of Characteristic Numbers.


The Periodic Table of Animal Ecosystems

We turn now to the first step in the cumulative assembly of Characteristic Numbers into the framework of, for instance, a biotic Periodic table. In Figure II-15, an entire biotic Periodic table is displayed in token fashion: the Periodic table of animal ecosystems. (The framework of the Periodic table of human ecosystems will be shown in Chapter IV.) These frameworks consist essentially of arrays of what biologists call type specimens, and Quine calls paradigm cases. In all these frameworks, however, the specimens are systems; and usually ecosystems. For it is never the organism alone that evolves; it is always, and only, the ecosystem: the habitat-organism system. Collecting these specimens will require appropriate equipment and techniques; and storing the data will involve pictures, films and tapes, besides paper-filing cabinets. The framework of the Periodic table of animal ecosystems is seen opposite.

Across the top right half of this framework, the nine Groups are listed and numbered with Roman numerals in their traditional order; and the Periods proceed upward at the left from the bottom to the top.

Each Period has a four-part description, ordered in four columns: The column at the far left lists the Periods' numbers. Next to it is listed the name of the animal Phylum which occupies the top Stratum of the Period in question. In the third column is listed in each case the new, emerged process which these animals display, and which distinguishes them from the previous Period's highest animals. And in the right-hand column, are stated the four scalar (Arabic-numeral) parts of the Characteristic Number of the particular organism in question. This summarizes the first three columns.

Period 1 is thus labeled Proto, Meta, Para-zoan ecosystem; its characteristic process is Auto-motion; and the scalar part of its characteristic number, in the fourth column, is
1 6
Its nine possible Groups then follow across the right-hand side of the table, each to be labeled with the reference to a list of the animals, plants and men which typically display the coaction in question with the organism of reference.

Each higher Period, as we proceed up the table, contains the preceding Periods (usually in modified forms) as its lower Strata. Among these modifications are each lower Period's mutated forms, thousands of which are represented in token or framework fashion by the dashed slanting arrows in the fourth column. (The extinguished lines-of descent do not appear.) Leftward-slanting dashed arrows represent degenerative (entropic) evolution; rightward dashed arrows represent creative, ectropic evolution; and solid vertical arrows indicate atropy: zero or negligible evolution.

All characteristic numbers in this table (except the upper right-hand one in each Period after the first) denotate zygotes, the lowest Sub-stratum marked 1 at the left. The upper right-hand one, however, represents the mature adult. (The Sub-stratum attained is here equal to the Stratum ceiling, the number at the top.) Where necessary, as in the case of the stages of insect metamorphosis, Sub-strata can and should not only be entered numerically, but should be keyed to their traditional scientific names as well.

Since this ecological classification is based upon, and includes, all organisms listed in the taxonomic series, it makes use of all the achievements of genetics and evolution theory. (It thus includes all of what is traditionally called Natural Law.) Yet it decreases the penalties incurred by the taxonomic series' omission of habitats and of the moral or tropic tendencies.67

The Periodic tables of plant and animal ecosystems include all of pathology and immunology related to parasitism (Group II), all of predation and the defenses against it (Group VI), all of co-operation, mutual help and synergism subsumed under symbiosis (Group IV); and so forth through the nine theoretically possible and empirically recognized coactions and their ranges of gradations. It thus includes a considerable portion of what is traditionally called the Moral Law, and states it in scientific terms. In consequence, these tables can be made to present part of a framework for the coherent, systematic study of the web-of-life's moral or tropic tendencies relative to the highest member of its System-hierarchy, human cultures. (See the Appendix at end of book.)


We turn now to what Mendeleev called "the relations of mansocial and political," which he predicted could be included in "the general reign of order in nature, and in the entire universe as a whole."20

A few years before Langlois discovered that the properties of bass societies are functions of the coactions between the Majority and the Minority, Arnold Toynbee had, also unconsciously, discovered a similar version of the Periodic Law in more than twenty human civilizations.l9 He had found that during the periods when these two components had been symbiotic and helped each other, ( + , + ), their societies' major properties were these: high productivity, cohesiveness, and good health, especially mental health. He called these periods the genesis of civilization, and their Minorities creative. But when predation developed ( - , +), so that the Minority benefited greatly at the expense of the Majority, these properties sharply changed: mental health declined (schizm of the soul), social cohesiveness went into its opposite (schizm of the body politic), and productivity plummeted: on one hand a large part of it became armaments; and on the other, real goods were destroyed by these armaments. These periods he called the breakdowm of civilization, and their Minorities dominant. At this point each of these twenty-odd civilizations went into what Toynbee called the rhythm of disintegration: it oscillated back and forth between predation ( - , + ) and parasitism ( + , - ), finally reaching the climax of committing suicide by mutual destruction, synnecrosis ( - , - ). Toynbee called this disintegration of civilization and showed that it regularly results in the transmutation of the civilization's breakdown-products into what we now call a lower human Period.

Toynbee discovered these opposite tendencies in Literate societies, which comprise human Period 5, as will be shown in Chapter IV. They have also been observed in a Lower Agricultural society (Period 2) by Gregory Bateson, and in Industrial societies, (Period 6) by many social scientists.

In his book on the Iatmul of New Guinea,68 Bateson showed that primitive societies split or fission in two opposite ways which he calls horizontal schizmogenesis and vertical schizmogenesis: When they split horizontally, between the Majority or lower Strata and the Minority or controlling Strata (which usually involves negative coactions between the two), the society disintegrates. But when they split vertically, so that a large part of the Majority and Minority together leave the village (which usually involves positive coactions), both the old and the new village remain viable societies. (This peaceful, vertical schizmogenesis occurs routinely in many high animal societies such as those of bees. So also in Literate human societies such as the one which formed Australia, New Zealand, and Britain's American Colonies.)

A notable case of vertical splitting which has been reported for an Industrial society (Period 6) occurred in modern Switzerland.69 A tiny group of commercial, industrial, political and social leaders (part of the Minority), together with a sufficiently large group of the broad public, the Majority, formed a Federation of Cooperatives (Migros), a political party (the Landring of the Independents), and an educational and research institute (the Gottlieb Duttweiler Institute). In a series of brilliant, tenacious campaigns that began in 1925 and continue today as strongly as ever, they have forced Switzerland's Dominant or Caste Minority to lower monopolistic prices, thus changing predation ( - , + ) symbiosis ( + , + ); forced truth about monopoly prices, profits, wage demands, strikes, lockouts, and so forth into the press (often excluded in the name of freedom of the press); forced discussions of the same into Parliament (often excluded in the name of free speech); and turned repressive law suits into public forums. (Migros now has the largest press in Switzerland. Persistence of the vertical front in that country is therefore very probable.)

The best study, for the United States, of Bateson's classical concept "vertical and horizontal schizmogenesis" is Baltzell's famous book, "The Protestant Establishment--Aristocracy and Caste in America."70 But perhaps the most famous cases of the prevalence of the vertical over the horizontal front in the English speaking world are the Magna Carta and Cromwell's Protectorate. In neither case was the Dominant Minority destroyed or liquidated. Instead, it was forced by a Creative Minority to change its predation ( - , + ) into a considerable degree of cooperation ( + , +). This strategic and creative maneuver resulted both times in a Genesis of Civilization.

The most famous cases of the prevalence or "victory" of the horizontal front, on the other hand, are the French and Russian revolutions. In both cases, a Dominant Minority was destroyed. The society was thereby decapitated to such a degree that it has not recovered. It resulted, in the case of France, in perpetual oscillation between republics and empires; in that of Russia, in perpetual and spreading dictatorship and terror.71 It thus appears that human cultures, emerging at the apex of the System-hierarchy, obey the General Periodic Law as clearly as do their preceding and accompanying biotic and abiotic systems.

Historical forces and accidents, however, have resulted in systematic though unconscious errors of theory which transform what would otherwise be intellectual schools of political science and sociology, comparable to those in physical and biological sciences, into emotional ideologies. On one hand the tradition of the vertical front occurred as the growth of folk custom in the tradition, say, of British and American Common Law. On the other hand the tradition of the horizontal front developed as a theoretical system in the tradition, say, of French rationalism and German philosophies. These two political traditions are thus not only emotionally and temperamentally diverse; they are, in addition, couched in the two diverse and here-to-fore incompatible modes of thought: The first is carried on by way of what James Conant calls the inductive empirical mode of thought; the second by way of the deductive theoretical mode.72 (See Figure V-I.) Both of these temperaments and modes of thought, moreover, occur not only in every industrial nation, but in each Stratum, and Sub-Stratum or age-grade of each industrial and even most sub-industrial nations.

Formulation of the strategic problem of the psycho-socio-political sciences, and resolution of their ever growing crisis and impasse, can occur only in terms of a discipline which defines and distinguishes these cultural categories, beginning with their simpler counterparts in the abiotic and biotic sciences; of a science, moreover, which has developed a method for cleansing these sciences' vocabularies of communication fouling: namely, the geometric definition of concepts and terms in Unified Science. The coaction compass can be boxed in the languages of the anthropo-socio-political as well as in those of other sciences.

The basically diverse historic meanings of the paradigmatic framework of political thought, Left and Right, were clearly displayed by the seating arrangements of the British House of Commons on one hand and of the French Etats Généraux in the year 1789 on the other. In the House of Commons (as in the U.S. Congress) the seating did not display social stratification; but it did in the Etats Généraux. What it displayed in the British case was (and remains) the following: on the Right, adherence to the Government at the time in question; on the Left, the Government's Loyal Opposition. Since all social Strata are represented on both sides ofthe Speaker and the aisle perpendicular to him, this aisle represents and demarcates a case of the vertical front: that Left and Right remain predominantly class-cooperative is guaranteed by the institution of universal suffrage by secret ballot. Members of Parliament ipso facto belong to the Minority. But they are elected freely by, and represent, the Majority. They cannot otherwise sit either on the Left or Right.

The composition of the Etats Généraux of 1789 was basically different: There l'aristocracie, the nation's Minority or controller , sat in splendor at the Right (of the rostrum), the Jacquerie (or Proletariat) in squalor on its Left, and the bourgeoisie between them, in the Center. The latter two Strata together represented the system's Majority or work component, with the much smaller Bourgeoisie ready to seize the control.

The coaction was different too: These basic components of the culture, Majority and Minority, had long been alienated from each other: L'aristocracie was a Dominant Minority, the Jacquerie and bourgeoisie an alienated proletariat in Toynbee's meaning of being in, but not of, the society. At this point in history they became enraged at each other. Their negative coaction approached the limit of ferocity. And that negative coaction was fixated as the paradigm of political theory, and became the dominant value premise of large regions of the world.73 The King and all aristocrats who could be found were imprisoned and executed by savage mobs and tribunals. Any profession of loyal opposition became grounds for arrest. All possibility of a vertical, class-cooperative front was consciously destroyed, and the Proletariat rampaged destructively through the streets.

The manner in which order was restored reinforced the paradigm of class-conflict: It was not the introduction of a better (less predatory, more symbiotic) coaction, as in Switzerland, but artillery turned on the mob by a young offlcer, Napoleon Bonaparte. He represented, and restored control to, the Dominant Minority in another form, the Bourgeoisie; a form which presently evolved with equal savagery into what Talmon calls Totalitarian Democracy,74 controlled by what Milovan Djilas calls The New Class.75,76

Had the vertical front of class cooperation been generalized into a theory about "all of recorded history," it would have been incorrect, for no one coaction ever has excluded all the others. Yet it is positive coactions that predominate on our planet. They have predominated in all natural Kingdoms for billions of years, as shown by the fact that evolution has been mainly upward. And all the great religions unite in afflrming it. The largely class-cooperative British and Americans however, as Conant has pointed out, tend to be weak in the deductive-theoretical mode of thought.72 Their Creative Minority therefore failed to produce a coherent, let alone a compelling, socio-political theory demonstrating the value of positive coactions. Baltzell shows this most clearly in his chapter on "The Intellectual Counterattack on Caste: The Social Gospel, Reform and the New Social Science."70

The English-speaking Dominant Minority, it is true, developed no more coherent or compelling theory of horizontal splitting, as Baltzell shows in his chapter on "The Ideological Defense of Caste."70 But their angry colleagues in Continental Europe, being traditionally prone to the deductive-theoretical mode of thought,72 picked out and exalted local experiences of horizontal, conflictive schizmogenesis into what they consider to be a universal axiom: "All af recorded history is the history of class conflict".77,78

This paradigm they reinforced in both theory and practice: They deduced theoretically that the only way to end exploitation ( - , + ) is to destroy the controller, the Minority, which they have done throughout over a third of the world. And they deduced that the only way to generate symbiosis ( + , + ) is to develop a "controlless" ("class-less") society. This goal being objectively impossible--and they themselves having, of course, assumed control, as Djilas has shown in The Nerw Class75--this Dominant Minority enacted its goal subjectively: it called itself "The Vanguard of the Proletariat," where "proletariat" is defined as the first three social strata. Being convinced that the only class relation possible to Mankind is conflict (and being involved in it themselves), they fear and punish their identification as a class, and declare their misinterpretation of history to be "irrevisible."

Forced by their clearly incorrect theory on one hand to imprison or execute those who show its inconsistencies, and on the other hand to substitute in place of objective reality and intellectual force a vast apparatus of radios, jammers and agitation, the horizontal front has filled the upholders of vertical fronts around the world--which may well be the silent majority-with deep anxiety. Being unable to defend itself theoretically for the reason just given, it tries to do so militarily, involving itself too in contradiction. Both fronts are thus involved in ever more fearfully dangerous, protracted and self intensifying politico-military conflicts.79 And today, in the Seventies, they are as clearly bringing on World War III as in the Thirties they were bringing on World War II. But World War III would probably fulfill the old and persistent predictions of Apocalypse: It would destroy the Earth's System-hierarchy all the way down to radioactive, lifeless rocks and oil-slicked water which looks not altogether unlike what these ancient predictions have described as "dead men's blood".80

This is, of course, a total contradiction of the appealing course of events predicted by the horizontal front's glib theoreticians. But these conflict-prone Left and Right theoreticians are as helpless to change their course as are the less articulate upholders of vertical front; its "silent Majority" and equally silent Minority. For what is true of scientists applies even more strongly to ideologists: "What scientists never do when confronted by even severe and prolonged anomalies", says Thomas Kuhn, "[is to] renounce the paradigm that has led them into crisis ... Once it has achieved the status of paradigm, a scientific theory is declared invalid only if an alternative candidate is available to take its place."61

As chairman of a 1936 delegation observing fascism, communism and democracy in ten countries, I was forced to realize that the conflict-dominated theories of the Extreme Left and Extreme Right-of Communists and fascists-were bringing on World War II. And it was perfectly clear that no matter who won that war, these theories would, in the absence of a compelling alternative, bring on World War III, as they are clearly doing now. It was this conviction which determined me to undertake unification of the sciences. For that is the only effective alternative to ideologies I could envisage.

I had no conscious idea that the cardioid of values would emerge in this sum of zero-valued parts. But the value-cardioid proves to inhere in Unified Science's very corner stone, the Periodic Law. Herewith it challenges both the zero value-premise of the one-field scientists and the negative value-premise of the ideologist; and it supports the positive value-premise of what Toynbee has called the seven great religions. Herefrom it follows, as the day the night, that the great schizm caused by the rise of the sciences has come full circle, and that the mental and spiritual crisis of industrial civilization is finally capable of coming to an end.

The schizm began, as Authur Koestler shows, when the empirical scientists and theoretical theologians agreed to go separate ways: the scientists agreed to confine themselves to res extensa, the theologians to res cogitans, splitting the West into the Two Cultures.81 This crisis developed into chaos as the sciences on one side grew apart from each other, and the ideologies and religions on the other side parted from each other too.

The scientists rationalized their separations by assuming that abiotic, biotic and cultural processes differ basically from each other. And humanists supported this assumption by declaring that Moral Law and values are confined to Man, and are not shared by animals, plants, and non-living entities. The groundless axiom of each of these sub-cultures supported that of the other in forcing industrial civilization's breakdown, and preparing conditions for the rise of the negatively biased ideologies.82

Unified Science's paradigm is opposite to those of both of our traditional sub-cultures: The structures of all systems--abiotic, biotic, and cultural--are assumed to be isomorphic unless proved otherwise, which has certainly not been done. The laws of the simplest systems, those belonging to Major Stratum 1 and 2, are assumed to be teleonomic; to be so structured that their telos or goal-which is the highest Major Stratum, human culture-is implicit in their Systemhierarchic combinations. The Periodic Law of chemical elements is shown to be a special case of a general law which rules throughout; namely, the Moral Law.

In 1889 Dimitri I. Mendeleev foreshadowed all the paradigms of Uunified Science in his above mentioned address before the Royal Society of London: "There are in the world two things which never cease to call for the admiration and reverence of man," he said, quoting Kant: "the moral law within ourselves, and the stellar sky above us. ... But we must add a third subject, the nature of the elementary individuals which we discover everywhere around us. ... In the atoms we see ... the submission of their seeming freedom to the general harmony of nature."20

This law--extending from Man through the hierarchic sky down to the atoms--affirms that the properties of systems are functions of their coactions; that "As ye sow, so shall ye reap." This contradicts the paradigm of the Cultural Relativists who affirm that cultures with diametrically opposite value-premises are equally valid.83 In the same way it contradicts the Existentialists' paradigm that there are no objective values; that it is therefore indifferent what values the individual may choose to follow.84

When I say that the world has come full circle I mean that we have come to recognize that Moral and Natural Law are the same thing. A person is free to defy them both subjectively. Objectively, however, he is free to select the degree of grace with which he submits to the general harmony of nature. No lower member of the Systems-hierarchy has such freedom.


The so-called political spectrum has served for nearly two centuries as political science's frame of reference. Yet it is flagrantly incorrect.

FIGURE II-16a The Political Spectrum; l8th century construct which timc has shown to be radically misleading.

Its criticism and correction will be carried out in two complementary ways, theoretical and empirical.

The deductive-theoretical mode of thought permits short and decisive treatment. The situation can be formulated geometrically, thus: The traditional political parties represent the principal resultants of two variables, X and Y. These cannot be deployed correctly on a straight line because the limiting resultants (at the ends of the line) are actually adjacent. Their correct deployment requires the line to be curved so that its ends adjoin.

FIGURE II-16b The Coordinate System of Political Science: obtained by mapping the Political Spectrum into the Periodic coordinate system7l.

*The locus of the Sub-Group VIII b ( - = - ), whose political name is Nihilism.90

The concept, political spectrum, resulted from a false analogy between the array of political coactions and the physicists' color spectrum. The color spectrum deploys a single variable, wave length. This extends from very short at one end of the straight line to very long at the other. This deployment is correct: Where the variable is arrayed perpendicularly to the straight line, the interval between shortest and longest variable corresponds to the interval between the straight line's ends, whatever its length.

Because this false analogy does not conflict with the system of incorrect paradigms underlying the array of fragmented sciences (see Chapter V), the analogy was accepted in the face of dramatic empirical contradictions to be set forth next.--We turn now to the inductive-empirical mode of thought.

Empirical Criticism and Correction of the
So-called Political "Spectrum"

For thousands of years, Toynbee has shown, the seven great religions have displayed positive value-biases. That is to say, they have advocated and stressed mutual help and class cooperation in various ways, degrees, and idioms.85 With the rise of modern science since the l5th century (studying, as it had to, parts of systems), values were subjectively confined to the humanistic and literary sub-culture. However, what the rising scientific sub-culture actually (objectively) adopted was a value-bias. Namely, the zero value-bias. It claimed, subjectively, to have nothing to do with values. And since its various specialists dealt largely in isolated parts of systems--e.g. in habitat-less plants, animals, and people, in which the Periodic Law is not discernible (and since it did not recognize the moral nature of that law in atoms, where it is discernible, as Mendeleev intuited)--it confused its zero value-bias with no values, and banned discussions of morals from its leading societies.

Then, in the l8th and l9th centuries, emerged the negatively biased misinterpretations of history, advocating class conflict on the Far and Extreme Left, race and national conflict on the Far and Extreme Right.

Traditional scientists (who study just system-components), having renounced values, are helpless to interfere with ideologists in any effective way. Traditional men of religion--speaking, as Bishop Robinson affirms, in the no longer effective language of pre-industrial civilizations--have been engaged in mere rearguard actions for over a century.86,87 And so, as the conflict-spreading propaganda apparatus penetrates the world's mass media--its films, television, radio, and press--the traditional spokesmen and their followers, the great majority, fall silent. For in a culture whose dominant value-premise is becoming negative, as it is now in ours, the people with positive value biases become deviant; and deviants tend to become silent, even when they are the majority.

What Unified Science now asks mainly of scientists (who are the best equipped to get the thrust of this question) is the following: Can we accept a frame-of-reference--a coordinate system such as, for instance, the so-called political spectrum--without considering the way it has been formed?

Consider the case of physical scientists before Einstein's theory of Relativity emerged and corrected their only locally correct Newtonian frame of reference. Would it be realistic to consider social scientists immune to similarly incorrect micro-centric points of view? I quote from a paper I presented at the Second International Congress for the Philosophy of Science:

Einstein has shown that in physics, ideas of local physical phenomena are generalized into theories of the universe. (A perpetually rotating room or free-falling elevator, he shows, would give rise in its inhabitants to specially biased kinds of physics.) Similarly, autocratic and predatory cultures on the one hand, democratic and symbiotic cultures on the other, have given rise in their inhabitants to specially biased kinds of political philosophy. These intellectual biases we call logo-centrisms ...

The same principle has been shown ... to operate on feelings and emotions. Societies with emotional "climates" of overwhelming fear and hate produce, in their inhabitants, philosophies of universal conflict and danger; societies with "climates" of friendly cooperation produce in their inhabitants equally biased philosophies of universal friendship. These emotional biases we call pathocentrism.

The opponents within each political system share the same logo- and patho-centrism. Hence the relative ease with which they exchange roles, and the difficulty with which they change systems ... The bearers of each of the patho- and logo-centrisms tend to attribute their own views and motives to the bearers of the other ... in spite of contrary empirical evidence ... This illusion is systematically utilised by the ideologists, to prepare their prospective victims for involvement in mental infection and physical conquest.

The greater the proportion of conflict and falsehood in a political philosophy, the greater the isolation necessary for its continuation. As, in Einstein's hypothetical falling elevator or rotating room, opaque walls are essential to the maintenance of the inhabitants' special kinds of physics, so in the Two-Ideology system an "Iron Curtain" is necessary to maintain the inhabitants' mis-interpretation of the world and of history. The "Curtain" exists in fact.

It follows that, with the development of geometric definition, mutual confrontation of the . . . systems-or their basic natures, structures, origins, functioning, and consequences-must tend to counteract falsehood and other negative relationships ... Geometrization will therefore help the creative individuals among the inhabitants of these local habitats ... to evaluate them realistically, and hence to transform them ...71


Gilbert Allardyce has compiled descriptions of a single political phenomenon, fascism, as seen from three frames-of reference: the communist Left, the humanist-socialist Center, the conservative Right. (See "Fascism as the End of Liberal Society" both as treated by him in his preface and by the authors in the text of his book The Place of Fascism in European History.88) Several other interpretations of fascism are included in his book, most of which fall into various categories of Unified Science. (But they necessitate more detailed analysis than can be included in the present volume.)

The point which needs to be made here is that Unified Science uses the same method to reconcile the discrepancies due to diverse frames of reference which relativity physics has used so successfully: systematic transformations made possible by the emergence of an invariant background-theory and its geometric background language. (See Harold Cassidy's assessment of Unified Science in the opening chapter, made from the viewpoint of a physical scientist.)

The profound and pernicious incorrectness of the one-dimensional "political spectrum", Figure II-16a, has been sensed by political scientists for nearly fifty years: "Some scholars," says Allardyce, "had already connected fascism and bolshevism in the 1920s, almost from the moment that the Blackshirts appeared on the Italian scene. Being for the most part men of liberal and democratic opinion, they associated Mussolini and the Bolsheviks with a common assault upon free institutions and open societies. It appeared to some of them that the terms `Left' and `Right'-descriptions which had never been very satisfactory anyway-no longer defined political reality, but rather seemed to obscure it." p. 13.88

This was the clear recognition of profound anomaly which typically characterizes the outbreak of crisis in any science. And here as in other sciences, it is a coherent scientific theory, based upon an incompatible paradigm, which resolves the basic anomaly and solves a number of troublesome subsidiary problems, which marks the outbreak of a scientific revolution.61 Such is the case at present, as I will now try to demonstrate:

What obscures political reality is not the terms Left and Right, which correspond to fundamental cultural structures, but the failure of that l8th century frame-of reference to group together the symbiotic (Center) Left and Right, to group together the synnecrotic (Extreme) Left and Right, and to separate these fundamentally diverse pairs of phenomena from each other. This greatest of all moral distinctions, and the intermediate distinctions between these limits, appear when the traditional simplistic, amoral l8th century political frame-of-reference, Figure II-16a, is mapped into the Periodic coordinate system, the frame-of-reference of the Moral Law, as shown in Figures II-16a and b.

The political scientists' schools array themselves just as neatly as schools formed during the crises of other sciences: Those ideologies which Digby Baltzell groups under "The Ideological Defense of Caste" fall on the Right of Center; those which he classes under "The Intellectual Counterattack on Caste" fall on the Left of Center. The Right Center schools stress evidence connecting social status to genetically determined, hereditary traits, and minimize evidence connecting social status to environmentally determined factors. The Left Center schools, on the contrary, minimize evidence connecting abilities and social position to genetically determined, hereditary traits; and emphasize evidence relating environmental factors to social position, low and high. Those Leftist ideologies holding positions up to and including the Moderate Left are egalitarian and culturally relativistic (that is, anthropologically egalitarian); those up to and including the Moderate Right believe in what Thomas Jefferson called Natural Aristocracy; namely, that people born with outstanding talent and virtue (like himself) should, and usually do, occupy controlling social positions.89


Egalitarianism and environmentalism subjectively raise lower Strata and lower Periods relative to higher Strata and Periods, grinding their incumbents' axe, and making Left theorists their spokesmen and leaders. On the other hand, minimization of environmental effects, and exaggeration of hereditary factors increase the self assurance (subjective power) of those occupying controlling positions, and decrease that of those occupying lower Strata. This grinds the top Strata's axe and makes Right theorists their spokesmen and intellectual leaders.70

What these schools share, however, is far more important than that which separates them. Namely, the positive value-bias summed up in the commandment, Do unto others as you would have them do unto you.47 All the political schools of the Center listen to each other's view and evidence respectfully (though sometimes reluctantly), credit each other's sincerity, and trust each others' loyalty to the principles of free speech, press, assembly and the ballot. Symbiotic freedom is the expression of love, of positive coaction. That makes inequality, which is fundamental throughout the universe, creative. Hence the term Creative Center. At the Center, Left and Right are convinced of their common positive value-bias and thus of their Ioyalty to each other in opposition. These are the criteria of the most important political system.

As we proceed toward the Left and Right extremes of this frame of reference, however, we note ever increasing vehemence and violence, ever decreasing interest in and respect for evidence, and ever decreasing mutual respect and trust. (See, for example, R. Palme Dutt's chapter in Gilbert Allardyce's book, just mentioned.)

And a certain point, called "loss of legality", a quantum change occurs, sudden and immense: suddenly the man, whether of Left or Right, finds himself not with just a vested interest, but with his very freedom and survival themselves, or those of his enemy, (Lenin's "Who-whom", dependent upon his own political control. Under these circumstances, the life, liberty and happiness of both the Left Extremist and the Right Extremist leaders depend upon the other controller's destruction, and upon the incorporation of his opponents' followers (their work components) into his own system.

This is, as Americans characteristically put it, an entirely different ball game: the Extreme Left and Extreme Right are playing for keeps, with no holds barred. They understand each other, and they fear and respect each others' ruthlessness and cunning. They are, of course, utterly contemptuous of the trustfulness, tolerance, and relative truthfulness of all Center parties. (They call them "naive, sentimental, vacillating, reformist, hypocritical," and so forth.) They enter transient "united front" alliances with Center parties against each other. They also enter temporary alliances with each other against Center parties, each closely watching for the opportunity to stab his well understood, highly perfidious "ally" in the back.

The almost certain outcome is that of the Two Ideology system's most famous case, the Stalin-Hitler pact: mutual devastation or, as biologists put it, synnecrosis ( - , - ). In a great historians terms, this is called disintegration of civilization.l9,90 Conversely, the probable outcome of continuous symbiosis of the Creative Center--of their vertical front as developed, for instance, in Switzerland69 or in Benjamin Franklin's Pennsylvania9l--is dynamic peace, prosperity, and genesis of civilization.

When the one dimensional political frame of reference is mapped into the Periodic coordinate system, as in Figure 16b, the similarities and differences which have long bewildered so many political scientists, and fouled up their communication, are fully and decisively cleared up.

This mapping shows that the difference between the Creative Center and the Two-Ideology system is very much greater than the difference between Extreme Left and Extreme Right. (The one-dimensional "spectrum" indicates precisely the opposite, seriously confusing political thought.) According to Allardyce,

To interpret the fascists as a right-wing phenomenon, to seat them beside the monarchists and reactionaries [of the CenterJ in parliaments, and to consider them a radical extension of die-hard conservatism [rather than as qualitatively different from it] was to be blind to the remarkable similarities between Mussolini and his communist `enemies.' [The semi-quotes symptomatize the anomaly in these thinkers' concept.] With the rise of fascism, it appeared, the heat and passion of both ends of the political spectrum [Figure 16a] had resulted in a fusion of political extremes-the ends had met, completing the circle of political beliefs [Figure 16b] ...

From these beginnings an inquiry has gone forward into the underlying unity of the radical movements. The result has been a continuing literature on the connections between the two political poles, with social scientists seeking the common roots of left and right extremism, and psychologists particularly involved in working out theoretical models of what has been called the `authoritarian personality'.92 But it was the dual experience of Hitler and Stalin, much more than the earlier confrontation between fascism and communism in Italy, which gave these studies their real impetus and significance. Indeed the sight of the dictatorships in Berlin [today, East Berlin] and Moscow evolving side by side has stimulated some of the most original political thought of our time. It has provided our mental imagery of the modern political state and revealed the existing possibilities for total power over men.93 The two regimes opened our vision into the world of 1984, and returned the concepts of mystery and evil to political theory88 pp. 13-14.

That, however, is but a preliminary approach to the full circle. Full circle itself is reached when the Moral Law's concepts of good as well as of evil, its new intermediate concept of atropy between them and, more particularly, its concepts of the nine Groups and their many quantitative variations-when these are ordered geometrically in the same terms as those of the physical and biological sciences, Figure 16b. Being part of a scientific revolution, it has the power to change the course of history away from the formerly probable goal described as 1984 and toward genesis of the Higher Industrial Period.91

If, now, you will look once again at the so-called "political spectrum," Figure 16a, its anomalies will be unmistakable: Using a ruler or a compass, compare the distance between Right Center and Extreme Right, or Left Center and Extreme Left, with the distance between Extreme Right and Extreme Left. The latter is more than twice as great as the former distances, when precisely the opposite is the case in reality. Is it not clear that any science-abiotic, biotic, or cultural-must be in crisis to the degree in which its frameof reference contradicts and misrepresents its data, and that the crisis of political theory and political practice has, in fact, been profound and desperate to just that vast degree?

Until the rise of Unified Science, the one-field sciences' background theory, it has been impossible for all but the most astute and imaginative Centrists and Extremists to understand each other or credit each other's actual existence: each had developed strong logo-centrism and patho-centrism, and there was no concept-system in terms of which to grasp and evaluate this self blinding fact. The Extremists, communist and fascist, could not conceive that class cooperation, race cooperation and overriding respect for evidence exist in reality rather than as mere propaganda. The Centrists--Republicans or Conservatives, and Democrats or Laborites--could not, for the same reason, conceive of the genuine contempt, treachery and cynicism with which they are viewed and treated, as a matter of course and of policy, by almost all Extremists, Left and Right. Only personal, often-repeated field-experience inside both political cultures--such as I encountered in ten countries in the mid-Thirties--can, in the absence of Unified Science, make logo-centrism and patho-centrism a visible, observable, and formulable phenomenon.7l,91 Unless you are an Einstein, you have to have lived in the free-falling elevator, rotating room, and on the solid ground--and to have moved back and forth several times from one to the other--to acquire and codify the coordinate systems of people who have spent their whole lives in only one of these windowless systems.95

Such is the new coordinate system of political science, and its resolution of the long festering crisis in political thought. When implemented in political practice, it will give the democratic shipsof state a political compass by which to set their course more safely.

"If this mixture of pragmatism and positivism does involve an ethical doctrine--" Heisenberg remarked to Pauli, "and you are certainly correct that it does and that we see it at work in America and England--by what compass does it set its course? You have claimed that in the final analysis our compass must be our relationship with the central order, but where can you find such a relationship in pragmatism?" p. 217.39 My answer is, nowhere in pragmatism, but in Unified Science it is called the coaction compass40 and is shown in Figures 11, 12 and 16.

In Chapter IV, separately studied genetic and psychological data will be related to their sociological, anthropological and political-scientific counterparts. Together, they will be assembled into a single discipline coherent with, and relevant to, the biotic and abiotic sciences.


The Unified Science Chart at the end of this book sums up this chapter's basic concepts and relates its basic figures to each other. It also relates them to a representative array of historic scientific concepts, listed in the left-hand column, which it completes, generalizes, assembles andjor maps into the single discipline, Unified Science. Experience shows that this fold-out chart, mounted on the wall, can serve the reader in coordinating his study of the rest of this volume, as perhaps also in other of his professional pursuits.96

It was Leibniz who predicted (fifth entry from the top, counting Mendeleev) that one day it would be discovered that the many scientists who had believed that they were working in separate disciplines had, unknown to themselves, actually been working on a single discipline. He predicted that this will happen when the characteristics which their data have in common are abstracted and represented geometrically, as the Universal Characteristic. And he foresaw that into this Universal Characteristic would be mapped, besides the traditional sciences, the following: jurisprudence, medicine, and metaphysics.64 Does this not close the dangerously broken Circle?

The chart before you opens the way to the fulfilment of Leibniz's prediction by assembling the constructs for closing the Circle in the Twentieth Century's Two Modes of Thought.72

In The Breaking of the Circle, Marjorie Hope Nicolson describes what the Circle of our thought was like in the sixteenth century, before it broke. Does she not, in so doing, come close to describing how it has now been closed in the 20th a "Man was in little all the sphere," she says. "As he grew and flourished, so did his world; as he decayed and died, so too his world. God's `pattern' was eternally repeated in macrocosm, geocosm, microcosm. Man's head was a `copy' of God and the universe, not only in its shape, but in its being the seat of Reason. Man, the epitome of God and the world, was rational; so were the world and the universe, into which God had imparted some of His own rationality. Each of the `three worlds' had its individuality, yet each was involved with the others, and all partook of God. Only since the seventeenth century has the poet felt the necessity of bringing together what the shears of scientific philosophy cut apart." pp. 106-797

The constructs listed in our chart's left-hand column are but a minute sample of the immense array of data and theories cut apart by the shears of l7th, l8th, and l9th century scientific philosophy; constructs which can, and will shortly be, mapped into the Periodic coordinate system. Is it not perfectly clear that we have been working on a single discipline?

The web-of-life, a tiny part of which is shown in Figure 14b, is keyed to the Biotic region of the Periodic coordinate system, shown at the center of the Chart. These will permit the conservationists' computers to talk turkey, as American slang puts it, with our fellow citizen's blind, deaf and dumb technology, and set a rational, mutually acceptable course of action.

Keyed to the Cultural region of our coordinate system, at the bottom of the Chart, we are now drawing several sets of psycho-political coaction webs: one of objective coactions, the others of subjective coactions. One of these is a web of the subjective political-economic coactions of Left-Center Liberals; one of Right-Center Conservatives; a third of Communist, and a fourth of fascist extremists.

The objective is to move our discussions from the barricade to the blackboard, to exchange our machine guns and bombers for chalk and erasers Or, in the milder terms of the Creative Center, the goal is to meet the need, as L. J. Livesey puts it, "Of institutions that seek to establish an innovative image while at the same time yearning for traditional respectability; and the never-ending process of deciding how much freedom one must yield as the price for community and government support ..."98

Fulfilment of these objectives is inherent in our execution of Leibniz's project for, as he predicted would happen once his Universal Characteristic had been created: "If someone disagreed with me [on any subject, abiotic, biotic, or cultural] I should say to him, `Sir, let us calculate!' And by taking to paper and ink we would settle the question."64 Why is this possible? Because we have now come Full Circle: The natural law and moral law are recognized once more, and have been proved in the new 20th century terms to be identical.



1. The original form of this concept was formulated jointly by W. V. Q,uine, H. G. Cassidy and E. F. Haskell in 1964, and has been developed by us to the present state. For a rich discussion and bibliography on related concepts of hierarchy, see Donna Wilson2 (below).
2. Wilson, Donna, "Forms of Hierarchy; A selected Bibliography" General Systems Vol. XIV, 1969 (pp. 3-15) Yearbook of the Society for General Systems Research 2100 Pennsylvania Ave., N.W., Roorn 818 Washington D.C. 20006.
3. Mayr, Ernst, "Discussion Footnotes on the Philosophy of Biology".
4. Weaver, Warren, "Science and Complexity," in The Scientists Speak (W. Weaver, editor). Boni and Gaer, New York, 1947.
5. "I am the Alpha and the Omega, the beginning and the end." (The Bible, Revelation 21:6.) This sentence is herewith completed in a scientifically meaningful way which was not possible, when it was written, for Man to understand. It is also in accord with the other two references: "I am the Alpha and the Omega, the first and the last, the beginning and the end." (Revelation 22: 13.) And "I am the Alpha and the Omega, saith the Lord God, who is and who was, and who is to come, the Almighty." (Revelation 1:8.) As the two limits of the Periodic coordinate system, and thus of Unified Science, this concept agrees with, and completes Teilhard de Chardin's scientific concept of Omega.l6
6. A still more fundamental entity, the parton, has just been discovered. If verified, it will be classed in Major Period 0.
7. Haskell, Edward F., "Mathematical Systematization of `Environment' `Organism' and `Habitat'" Ecology, Vol. 21, No. 1 Jan. 1940.
8. Greenstein, J. and M. Schmidt "The Absorption Fine Redshifts in Parkes 0237-23," Astro physical Journal (Correspondence) Vol 148, April 1967.
9. The term Major Period is a conceptual extension of the term Period in Mendeleev's Periodic Table. Similarly, the term Major Stratum is an extension of the general term Stratum, coined to include the atoms' nuclear and electron shells and their analogues in the other sciences. The Major Periodic table appears below in a simple geometric form. The term, Major Period, was coined by my research assistant, Paul Mankiewicz. (I had been using a poor term, Macro Period.) A natural kingdom is a Major Stratum; a natural empire is a Major Period. (See Figure 2-4.)
10. The Biosphere, The Scientific American, September issue, 1970.
11. Periodic tables of molecules and geoid systems have not been constructed. But Stratification, Periodicity and Grouping are postulated for them, and the construction of corresponding Periodic tables is predicted.
12. Pirie, Norman W. "The Origins of Life," Nature 180, 886-888, 1957.
13. Cassidy, Harold G., "The Kingdom of Biopoetic Systems-Phylogeny of the Cell." A chapter in Unified Science--Assembly of the Sciences Into a Single Discipline, Edward Haskell. Offset-printed in 50 copies by the National Institute of Health 1968, Xeroxed in 50 copies by the IBM Systems Research Institute, 1969.
14. Reinhold, Robert, "Scientists in Varied Fields Join in Attacking National Problems." New York Times, Oct. 6, 1970, page 1 ff.
15. Anderson, O. Roger, "An Interdiciplinary Theory of Behavior," Jour. of Research in Science Teaching Vol. 6, No. 3, 1969, pp 265-272.
16. Chardin, P. Teilhard de, The Phenomenon of Man, (transl. B. Wall) Harper, New York 1959.
17. Murdock, G. P., "Ethnographic Atlas", Ethnology, Jan. 1962-to date.
18. Hobhouse, L. C.; G. C. Wheeler, M. Ginsburg, The Material Cultures and Social Institutions of the Simpler Peoples; an Essay in Correlation. Chapman, London, 1915.
19. Toynbee, Arnold J., A Study of History (Somervell Abridgement of Vols. I-VI) Oxford Univ. Press, New York 1947.
20. Posin, Daniel Q., Mendeleyev, The Story of a Great Scientist, McGraw-Hill, New York, 1948.
21. Seaborg, Glenn T., From Mendeleev to Mendelevium--and Beyond Monograph presented at the Robert A. Welch Foundation Conference on Transuranium Elements-the Mendeleev Centennial, Houston, Texas, released by the U.S. Atomic Energy Commission, Washington D.C., Nov. 17, 1969.
22. From Science Restated--Physics and Chemistry for the Non-Scientist (page 300) by Harold G. Cassidy, Freeman-Cooper, San Francisco, 1970. Reprinted by permission of the publisher: I have shifted the position of hydrogen (H) from Group IV to Group VII for reasons to be set forth, and have reversed the order of the Periods: We start at the bottom and count upward.
23. Latil, Pierre de, Thinking by Machine--A study of Cybernetics Houghton Mifflin, Boston, 1957. Originally, La Pensée Artificelle Gaillard, Paris, 1956; Sidgwick and Jackson, London, 1968.
24. Haskell, Edward F., "A Clarification of Social Science," Main Currents in Modern Thought, 7, 45, 1949.
25. Adam, Charles Ernest, Descartes; sa vie et son oeuvre, Boivin, Paris 1937.
26. For a description of the role played by dreams in the development of mathematics and scientific theories, see Jacques Hadamard, An Essay on the Psychology of Invention in the Mathematical Field, Dover Publ., New York, 1945.
27. They appear in Unified Science--Assembly of the Sciences Into a Single Discipline; offset-printed by the National Institute of Health, 1968 and xeroxed by the IBM Systems Research Institute, 1969. (Three volumes, when completed.)
28. Haskell, Edward F., with preface and a chapter by Harold G. Cassidy, "Unified Science--Assembly of the Sciences Into a Single Discipline" Vol. I, Scientia Generalis. Offset-printed by the National Institute of Health 1968, xeroxed by the IBM Systems Research Institute, 1969.
29. This corresponds to the Great Chain of Being the medieval precursor of the System-hierarchy.
30. Gause, G. F., The Struggle for Existence, Williams and Wilkins, Baltimore, 1934, Hafner, New York, 1964.
31. Gause, G. F. and A. A. Witt, "Behavior of Mixed Populations and the Problem of Natural Selection", American Naturalist 69, 725, 1935.
32. Wheeler, J. A., "Our Universe: The Known and The Unknown." American Scholar, Phi Beta Kappa Society, Spring, 1968..
33. Cassidy, Harold G., Science Restated--Physics and Chemistry for the Non-Scientist, Freeman, Cooper, San Francisco, 1970.
34. Wu, C. S., "Subtleties and Surprises-A Brief History of the Theory of Beta Decay." Columbia University Forum 9, 1 (1966).
35. It has to be hyper-spatial because it corresponds structurally to mutually exclusive phenomena. The Periodic and Inverted-Periodic coordinate systems can no more be superimposed (occupy the same space) than can pro-particles and anti-particles. Their corresponding axes are oppositely directed. Whether their radius angles should be directed oppositely, as shown, or similarly directed I do not know. I have decided it arbitrarily, pending more knowledge.
36. Snow, C. P., The Two Cultures--and the Sczentific Revolution Cambridge Univ. Press, New York, 1959.
37. Couturat, Louis: La Logique de Leibnitz, Olms, Verlagsbuchhandlung, Hildesheim.
38. Quine, Willard V., Ontological Relativity and other essays. Columbia Univ. Press, New York, 1969.
39. Heisenberg, Werner, Physics and Beyond--Encounters and Conversations. Harper and Row, New York, 1971.
40. Haskell, Edward F., The Coaction Compass--A general Conceptual Scheme Based Upon the Independent Systematizations of Coaction Among Plants by Gause, Animals by Haskell, and Men by Moreno, Lundberg, Horney and Others.--Mimeographed, 1948. (Mentioned in Science, Sep. 3, 1948 (p. 264).
41. Haskell, Edward F., "The Religious Force of Unified Science," Scientific Monthly 54, 545, 1942.
42. In his review of Physics and Beyond, Elting Morrison remarked that "Events in the physical world take place the way a man thinks"99. And one of the great questions of philosophy has been how this could have come about. Unified science explains it by extending Bohr's principle of complementarity up from geoid systems (to which Newtonean physics applies) through the kingdoms of plant and animal ecosystems to that of human cultures. This explains why Man "thinks the way things happen in the physical world."
43. This term was suggested by W. V. Quine in discussions following this symposium: Entropy, he pointed out, is Greek for turning in; the opposite term, should therefore be the Greek for turning out, namely ectropy. Since the coaction cardioid literally turns in and out of the circle of reference, his short, elegant term has been adopted and used throughout.
44. Weaver, Warren, "Science and Complexity," American Scientist 36, 537-44, 1948.
45. Eblen, William R., Total Education in the Total Environment, SPRED, Norwalk Conn., 18, 1971.
46. The Bible, Paul's Epistle to the Galatians 6: 7 "For whatsoever a man sows that he will also reap." RSV. 2.
47. The Bible, Matthew 7:12 "As you wish that men would do to you, do so to them; for this is the law and the prophets." Luke 6:31 "And as ye would that men should do to you, do ye also to them likewise."
48. Langlois, T. H., A Study of Small-Mouth Bass, Micropterus Dolomieu (Lacepede) in Rearing Ponds in Ohio. Ohio State Univ. Studies, Oct. 1936.
49. Langlois, T. H., Haskell, Edward, "Assembly of the Sciences into a Single Discipline," The Science Teacher Vol. 37, No. 9, Dec. 1970, Supplement.
50. Wiener, Norbert., Cybernetics--Or Control and Communication in the Animal and the Machine, Wiley, New York 1948, Hermann, Paris 1948.
51. Bertalanffy, Ludwig von, General Systems Theory--Foundations, Development, Applications, Braziller, New York, 1968.
52. Bertalanffy, Ludwig von, "General Systems Theory--A Critical Review", a chapter in Modern Systems Research for the Behanioral Sciences, Walter Buckley, ed., Aldine, Chicago, 1968.
53. The paper in which these concepts were first expounded was called The Coaction Compass (see Note 40, above). Heisenberg's statement that "The problem of values...concerns the compass by which we must steer our ship if we are to set a true course through life" appears to infer this sort of thing. (See Note 39, above).
54. Coordinates of position begin at the origin and extend outward just as in the Cartesian system. But in the Periodic system, negative coordinates are subtracted from the zero circle. Example: Let the zero circle's radius be 15 units long. The coordinate X-5 is obtained by subtracting 5 units inward from the circle, and is thus a positive number: 10. This is the meaning of relative minus. The method of calculation was put forward by Gause30 and Gause and Witt,31 and was then generalized.28 For another method of calculation, see the Addendum to Chapter 1.
55. Discussion of the lanthanide and actinide elementat is here omitted, as they themselves are in Figure 5.
56. Location of Group 0 in quadrant 3 is neither geometrically nccessary nor significant, since the 0 circle falls in all the quadrants equally. It is, however, empirically convenient, since Group VIII does fall in the ( - , - ) quadrant, and Group 0 elements alternate with those of Group VIII in all the double Periods.

Techniques have recently been invented by which inert elements can be induced to combine with others, something they never do in nature; that is, spontaneously. This shows that Period 6 Man need not resign himself to acceptance of apparently immutable natural conditions, which lower Period peoples could not even dream of questioning. We shall return to this crucial fact in later chapters.

57. Pauling, Linus, College Chemistry, An Introductory Textbook of General Chemistry. W. H. Freeman, San Francisco, 1951 (Chapter 31).
58. Simple peoples, and the half-conscious and sub-conscious parts of our own modern selves, tend to explain azoic phenomena by only partially or symbolically correct zoic and human analogies called myths and symbols. One-field specialists tend to react so strongly to avoid this error, that they also avoid correct analogies or veiled truths, and thus resist synthesis. This has resulted in the Two Cultures and widespread loss of self determination through-out the West--Unification of the sciences should overcome this paralysis and help us gain some control over our destiny. (See Jung, Carl Man and His Symbols, W. H. Allen, London, 1964).
59. Langer, Suzanne, Philosophy in a New Key--A study in tht symbolism of reason, rite and art. Harvard Univ. Press, Cambridge, Mass, 1957.
60. Bohr, Niels H. D., Atomic Physics and Human Knowledge, Wiley, New York 1958.
61. Kuhn, Thomas S., The Structure of Scientific Revolutions, Univ. of Chicago Press, 1962, Chapter VIII.
62. There are, however, hundreds of isotopes which also map into the Periodic table.
63. The most famous approach to date has resulted in the models described in The Limits to Growth, produced under the auspices of the Club of Rome. Universe Books, N.Y., 1972.
64. Leibniz-Selections, Ed. P. P. Wiener, Scribners, N.Y. 1951.
65. These "improvements and further developments" of the Periodic Law appear to consist in the substitution of coaction for atomic weight or atomic number, and in the substitution of the general geometric form in place of its originally concrete empirical form.
66. The decision as to which of these coactions obtains depends upon which organism is at the time the work component (x), and which the controller (y). These relations are complex, and are described and defined in more detail elsewhere.28
67. Subsuming by this and all other scientific classifications is W. V. Quine's deductively formulated theory of natural kinds.38 His construct is therefore related to this work in the concluding chapter.Subsuming by this and all other scientific classifications is W. V. Quine's deductively formulated theory of natural kinds.38 His construct is therefore related to this work in the concluding chapter.
68. Bateson, Gregory, Naven, A Survey of the Problems Suggested by a Composite Picture of the Culture of a New Guinea Tribe, Drawn from Three Points of View. Cambridge Univ. Press, Cambridge, 1936.Bateson, Gregory, Naven, A Survey of the Problems Suggested by a Composite Picture of the Culture of a New Guinea Tribe, Drawn from Three Points of View. Cambridge Univ. Press, Cambridge, 1936.
69. Haskell, Edward F. Switzerland's Vertical Front--The Migros Federation of Cooperatives in the Light of Systematic Social Science. A chapter in Gottlieb Duttweiler by 65 authors. Speer Verlag. Zurich, 1948.Haskell, Edward F. Switzerland's Vertical Front--The Migros Federation of Cooperatives in the Light of Systematic Social Science. A chapter in Gottlieb Duttweiler by 65 authors. Speer Verlag. Zurich, 1948.
70. Baltzell, E. Digby, The Protestant Establishment--Aristocracy and Caste in America, Random House, N.Y. 1964.
71. Haskell, Edward F., "Geometric Coding of Political Philosophies." Proceedings of the Second International Congress for the Philosophy of Science, Vol. IV, Zurich 1954, Editions du Griffon, Neuchtâel, Switz., 1955.
72. Conant, James B., Two Modes of Thought, Trident, New York, 1964.
73. "Power grows out of the muzzle of a gun." Mao Tse Tung. "All of (recorded) history is the history of class conflict." Marx, Engels. (Analysed geometrically in Chapter V.)
74. Talmon, J. L., The Origins of Totalitarian Democracy, Praeger, New York 1952.Talmon, J. L., The Origins of Totalitarian Democracy, Praeger, New York 1952.
75. Djilas, Milovan, The New Class--An Analysis of the Communist System, Praeger, New York, 1957.
76. Oliver Cromwell, it has been pointed out to me, had his king beheaded, too. The crucial difference, however, is that Cromwell did this not gladly but reluctantly; that he steadfastly refused the crown; that he did not destroy the Minority; and that, when he bowed from the stage of history, he had markedly restored and improved his nation's over-all condition, which has maintained its form ever since.
77. Marx, Karl, and Friedrich Engels, The Communist Manifesto, London, 1848.
78. Until the sciences' theories are unified, strength in either of these modes of thought requires and produces weakness in the other: The parts of the universe are interlocked and display coherent structure. Until this is grasped, suitable concepts to describe it are formulated, and inter-disciplinary language-fouling is reduced, accurate empirical descriptions of its various parts necessarily result in an array of incoherent theories. Conversely, as long as the sciences remain discrete, coherent theory can be formulated only in non-empirical terms, and its content must contradict or ignore many empirical data and relationships. To the extent that unified science is empirically correct and logically consistent, it reconciles these here-to-fore mutually exclusive modes of thought. See Chapter V.
79. Strausz-Hupé, Robert; W. R. Kintner, J. E. Daugherty; A. J. Cottrall; Protracted Conflict--A Challenging Study of Communist Strategy. Harper & Bro's New York, 1959.
80. Philberth, Bernhard, Christliche Prophetie und Nuklearenergie, R. Brockhaus Verlag, Wuppertal W. Germany 1964.
81. Koestler, Arthur, The Sleep Walkers, A History of Man's Changing View of the Universe. MacMillan, New York 1959.
82. It is no accident that the Extremist ideologists so strongly and consistently oppose all religions, and vice versa: Their dominant value-premises are diametrically opposite: the ideologists prize class or race conflict, the people of religion prize cooperation.
83. Benedict, Ruth, Patterns of Culture, Houghton MifHin, Boston, 1934.
84. Sartre, Jean Paul, The Philosophy of Jean-Paul Sartre, (selections), R. D. Cumming, ed., Modern Library, New York, 1966.
85. Toynbee, Arnold J., An Historian's Approach to Religion, Oxford Univ. Press, London, New York, Toronto, 1956.
87. This insight has been extended in Divine Principle and its Applications by Young Oon Kim, The Holy Spirit Association for the Unification of World Christianity, 1611 Upshur St. N.W., Washington, D.C. 20011, 1968.
88. Allardyce, Gilbert, The Place of Fascism in European History, Prentice-Hall, Englewood ClifFs, New Jersey, 1971.
89. Allardyce, Gilbert, The Place of Fascism in European History, Prentice-Hall, Englewood ClifFs, New Jersey, 1971.
90. Geometrically, this coaction falls in quadrant 3, where the coaction cardioid displays two lobes and an apex. These geometric features correspond to the three sub-Groups in chemistry's Group VIII (Figures 5 and 11 ) . The cardioid's negative apex ( - = - ) is the geometric locus of the Sub-Group whose political expression is Nihilism. (Sometimes it is misnamed Anarchism.) This coaction is so destructive that its exponents frequently destroy themselves. See Zero by Robert Payne, John Day, New York, 1950. The "political spectrum" cannot map this phenomenon because it falls next to, yet between, its limits.
91. Haskell, Edward F. and Harold G. Cassidy, "Plain Truth--and Redirection of the Cold War," (136 pages) Privately printed and distributed, 1961.
92. Adorno, T. W. et al, "The Authoritarian Personality," Harper, New York 1950.
93. Communist and fascist regimes have the following six concrete traits in common: an ideology; a single party, typically led by one man; a terroristic police; a communications monopoly; a weapons monopoly; and a centrally directed economy. See Carl J. Friedrich and Zbigniew K. Brzezinski, "Fascism as Totalitarianism: Men and Technology." To these, Hannah Arendt adds a seventh common trait: "a foreign policy...directed toward world domination".88
94. Haskell, Edward F., "Lance--A Novel About Multi-cultural Men." John Day, 1941.
95. I have, however, expressed these two and several other centrisms--logo, patho, ego, ethno, and trato- centrisms--in fiction: "Lance--A Novel about Multi-cultural Men"94. Fiction permits the depiction of emotions which science strives to cancel out by means of invariants. Neither of the Two Cultures can be supplanted by the other. A would-be C. P. Snow must be both scientist and novelist.
96. A less complete version of this chart about four meters high formed the visual background of the 1969 Boston symposium, whose papers (two of them in expanded form) are assembled in the present volume.
97. Nicolson, Marjorie Hope, "The Breaking of the Circle--Studies in the Effect of the `New Science' upon Seventeenth Century Poetry." Northwestern Univ. Press, Evanston, Ill., 1950.
98. Livesey, L. J., Tomorrow's Education, Program of the World Future Society's First General Assembly, Washington, D.C., May 1971.
99. Morrison, Elting G.; review of "Physics and beyond--Encounters and Conversations," New York Times Book Review, Sunday Jan. 11, 1971.


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