Complexity is quantity and diversity of components and relations. Anything that increases these factors increases complexity. A situation can be very complex due to quantity, the molecules of gas in a closed jar, but rather simple in the nature of that complexity if, for instance, there is only one kind of molecule. The nature of the complexity is quite different if every component is of a different type, even if their numbers are nowhere near that of the gas in a jar. It often happens that with diversity of components there occurs a greater diversity of relations. With well developed forms of complexity, the quantity and diversity of components and relations come together to form organizational complexity, the complexity of cells, organisms, social systems, and ecosystems. The primary problem with analyzing complexity by way of simplification is that this technique looses touch with organizational complexity.

Simplification can hinder the analysis of complexity well before the analysis of its organization, in the analysis of its quantitative aspects. There are six basic quantities to the complexity of any situation. (1) How many components there are and (2) how many different kinds of components, and then (3) how many of each kind. (4) How many relations there are and (5) how many different kinds of relations, and then (6) how many of each kind. More detailed quantitative analyses of complexity are possible, such as how many relations a particular component has and how many different kinds they are, but the six basic quantities are minimal for understanding the quantitative aspects of complexity. A method that neglects any of these six is incapable of providing a realistic understanding of complexity.

Each of the six can be ascertained by observing the complex situation and counting them. Such a realistic approach can take considerable time and effort, and attempts are made to find simpler measures of complexity. Unfortunately, each of these simple approaches has some element of shying away from the intrinsic nature of complexity. One form in which this occurs is to avoid the difficulty of measuring the complexity directly by measuring some factor that is related to but not actually intrinsic to the complex situation. These factors are typically derived from the complex situation by way of some procedure each step of which takes the analysis further and further away from the nature of complexity.

In his article, What Is Complexity? Murray Gell-Mann begins by recognizing that “a variety of different measures would be required to capture all our intuitive ideas about what is meant by complexity.” The examples he gives, however, do not capture the intrinsic complexity of his sample complex situations.

His first example of a quantity that has been proposed as a measure of complexity is computational complexity. It can be used as a time measure, that is, “how long it would take, at a minimum, for a standard universal computer to perform a particular task.” But the time “needed to carry out a certain computation” is an indirect measure, a full step away from the intrinsic complexity of the computation itself. It misses whether the computer performs a particular step many times or performs an equivalent number of steps each of which is different. The time it takes to perform a computation is related to the complexity of the computation, but as a measure of that complexity, it is a simplification because it melds diversity within simple quantity, thus disguising any organizational complexity that might be a quality of the computation.

Gell-Mann next discusses information measures, which refer, “roughly speaking, to the length of the shortest message conveying certain information.” The application of this method to an entity of the real world, such as a living cell, involves a two or three step process away from the complexity intrinsic to the entity. The first step is the creation of a language description of the entity, a description of its complexity. The second step is the encoding of the description, a conversion from language into a string of bits. Then, as a possible third step, the code is processed by a computer.

How many times has it been said that a picture is worth a thousand words? In this case the picture would be the entity itself, a living cell, which can be observed like a picture. Since it takes a number of words to describe each individual feature of the entity, the description will be larger and more complex than the entity. Not only is the complexity of the description different quantitatively from that of the entity, it differs also in the nature of the relations one part to another. The molecules of a cell, for instance, interrelate in ways entirely different from the rules of grammar that relate the parts of speech such as nouns, verbs, and prepositions. With just this first step, the information measure, the length of the description, becomes more a measure of the description than of the complexity of the entity.

Encoding the description into a string of bits simply makes matters worse. What is to be measured is one more step away from what was supposed to be the object of investigation, the entity itself. The coded description exists in a form so different from the manner in which a living cell exists that what is left of what was derived from the complexity of the cell is now essentially meaningless. And worse, what pattern of complexity that has survived the transitions is ignored when the measurement, the length of the bit string, is taken. Even though the language description and then the encoded description are quantitatively greater than the complexity of the entity, the end result is still a simplification in that diversity and organizational complexity have been rendered into a single quantity, the length of a string of bits. While the bits were derived by way of the process from the entity, the end product has very little actual relation to the complexity of the entity.

The intriguing aspects of complex systems and situations are due not so much to their quantitative features as to their stages of development and organization. With complexity, the question is not really which situation is the most complex in a simplistic quantified manner, but rather which is the most complex developmentally and organizationally. While the quantifying methods discussed by Gell-Mann may perhaps be of some utility in the analysis of bit strings and such like, cryptic codes for instance, they are at best insignificant for use with non-artificial complex situations.

Transforming the multi-relational nature of complexity into the linearity of bit strings, and reducing the diversity and organizational aspects of complexity to quantity are two forms of simplification that avoid dealing with the actual nature of complexity. Another approach to the study of complexity is that of the specialist, wherein complexity is defined in terms of some specialized branch of science or limited field of research, which inevitably results in a somewhat simple, limited view of complexity. In his essay, Complex Systems Theory, Stephen Wolfram wrote, “One of the disappointments in complex systems theory so far is that the approaches and content of most of the papers that appear reflect rather closely the training and background of their authors.” The same thing happened back in the heyday of general systems theory. There were no generalists. All the researchers were specialists, and specialist viewpoints and terminology often confused communication and understanding. They did identify a number of general factors, such as emergence, but their training and backgrounds did not prepare them to achieve deep structure understanding or to identify which general factors tie it all together. Nevertheless, one must always keep in mind that the work of specialists is absolutely necessary. Specialists generate the knowledge that forms the basis of more general understandings. Without specialists, generalists cannot even exist.

In the Introduction to their article, Modelling Biological Complexity: A Physical Scientist’s Perspective, Peter V. Coveney and Philip W. Fowler provide an example of defining complexity by way of a limited field of research, “Complexity is the study of the behaviour of large collections of simple, interacting units, endowed with the potential to evolve with time (Coveney & Highfield 1996).” Whether they are referring to complexity itself, “Biological Complexity,” or a field of research, “Complexity is the study of,” they severely limit their view and understanding of complexity by including only large collections of simple units that evolve. That their view and understanding is in fact limited is evident in the following sentence where they list as simple units atoms, proteins, and cells. Whatever simplicity can be attributed to atoms, the other two, proteins and cells, are not simple. Consider the development of their complexity, beginning with elementary particles. All three are based on the same set of three such particles—protons, neutrons, and electrons.

Atoms have 3 basic levels of hierarchic organization, individual elementary particles, protons and neutrons joined as the atomic nucleus, and the atomic level itself that occurs with the addition of electrons. The most complex atoms have something over 100 protons, and more or less equivalent numbers of neutrons and electrons, which gives something over 300 components. There is only one mid-level type of unit, the nucleus.

A protein has 8 obvious levels of hierarchic organization, (1) individual elementary particles, (2) atomic nuclei, (3) atoms, (4) first molecular level, atoms to atoms, such as the amino group, NH2, (5) second molecular level, molecule to molecule, such as the amino group connected to the carboxyl group, COOH, by way of the alpha-carbon atom, (6) the level of the amino acid, the primary component of a protein, (7) linear polymer of amino acids, and (8) a protein molecule when the polymer is folded. Proteins are not made out of the largest atoms. Still, they contain a fair number of elementary particles, 51,000 would be a conservative estimate for a medium sized protein. There are 5 basic atoms in a protein. There are at least 9 basic atom to atom units. There are at least 21 possible molecule to molecule combinations. There are 20 commonly occurring amino acids in proteins. And finally, an amino acid chain recombines with itself to create various subunit structures which all together make up a protein. The quantity and diversity of components and relations within an average protein is massive compared to those within even the largest of atoms.

The hierarchical organization of a living cell has not been fully mapped. Within a single atom there is but one hierarchical sequence—elementary particle, nucleus, atom. Within a protein there are many atoms, and thus many cases of the atomic hierarchy. Within a cell there are vastly more atoms, hundreds of thousands of them, with the atomic hierarchy occurring that many times. Then there are the molecular levels of hierarchy above that of the atom. There are minimally tens of thousands of molecules in a living cell, occurring in great diversity. Molecules in a cell are often components of cellular structural elements, such as organelles, forming hierarchical levels above those of molecular levels like that of a protein. There are many kinds of organelles, and thus many kinds of hierarchic structure at this level.

In a cell, hierarchic organization is there repeatedly at the atomic level, at the simple molecular level, at more complex molecular levels, at various levels of cellular structure and organelles, and as the cell as a whole. A critically important aspect of the hierarchical complexity of the cell is that these multitudes of hierarchic structures interrelate one with another both by way of the simple but multi-stepped sequence from elementary particle to the cell as a whole, but also by way of almost any level directly with any other level. It is this kind of organizational complexity that distinguishes the cell as a seriously complex system. The quantity and diversity of components and relations within an average cell is massive compared to those within even the greatest of proteins.

Proteins and cells are not simple units, their interrelations with one another, proteins with proteins and cells with cells, are not actually simple, nor are their interrelations with their environments. Techniques for the study of complexity based on the interrelations of large numbers of simple units are valid specialist approaches, but they are so only for specific types of systems or for specific types of relations between units. Relative to the nature of organizational complexity, these methods provide only limited simple results.

One last important point concerning the article by Coveney and Fowler. Even though their definition of complexity reflects rather closely the training and backgrounds of these authors as specialists, they are actually discussing ways to broaden their perspective, to incorporate multilevel analysis in their approach to complexity.

Another way in which a specialist approach can detrimentally simplify complexity research occurs when a powerful and exceptionally successful research tool comes to dominate the thinking of the researcher. The nature of the tool and all that can be done with it temps the user to be more involved with its use and less than realistic in its application to the intrinsic nature of the complexity of reality. Math and computers can have this effect.

Wolfram himself is a case in point. In the first paragraph of his essay, he states, “It is now a crucial problem for many areas of science to elucidate the mathematical mechanisms by which large numbers of such simple components, acting together, can produce behaviour of the great complexity observed.” In reality—not talking about theory, concepts, or constructs—in reality, components acting together do not produce behavior by way of mathematical mechanisms. Mother Nature doesn’t do math.

Everything that exists has some quantitative aspect of its existence, of its mode-of-being, of its intrinsic character. But quantity and the roles it plays in the existence, development, and organization of reality do not equate to math or mathematical mechanisms. In the larger reality of the universe for example, quantity plays its roles directly, as quantity, as itself. In math quantity is usually represented symbolically, 1, 2, 3, a, b, c, 1, 10, 11, and so on. Throughout the universe, beyond the minds and artifacts of sentient cognitive beings, the roles of quantity occur by way of the intrinsic nature of quantity, by way of what it is, by way of what is-there to play those roles. The roles are-there because what quantity is is-there. There is a direct relation between the existence and intrinsic nature of quantity and the existence and intrinsic nature of its roles. In math quantities are procedurally interrelated by way of rules. What exists and occurs within the mind of a researcher, or within a computer, doing calculations to determine the sustainable harvest of deer for the next year based on this years take, combined with certain inputs concerning the status of the habitat, is almost entirely different from what exists and occurs with the deer herd itself, out there in that habitat, that actually determines the size of the herd next fall. Consider what happens in the solution of a long division problem with pencil and paper. The various steps and relating of quantities never occur other than with sentient cognitive beings and their artifacts.

Boys often spit from high places. They watch the white dot slowly getting smaller and smaller until it disappears in the distance below. Now, calculations can be made using the quantity of spit and the factors of gravity to determine the rate of fall of the projectile. However, with the fall itself there are no calculations involved. In the actual situation, such calculations do not exist—they are not there. There are no mathematical mechanisms producing the behavior of the falling spit, or the behavior of boys for that matter.

In the reality beyond the interrelations of ideas, the existence and the intrinsic nature of what goes before bring into existence and determine the intrinsic nature of what follows. This occurs by way of the determinate consequent-existence that goes with the continuing-existence of that which exists. It occurs by way of the determinate consequent-existence that goes with self-organization, motion, emergence, cause, and through-flow situations. There are roles in each of these general factors for quantity, but no roles for math.

Wolfram chose to “study mathematical models that are as simple as possible in formulation, yet which appear to capture the essential features of complexity generation.” He hoped to find “laws” that govern those mathematical models and that would be “sufficiently general to be applicable to a wide range of actual natural systems.” Math is an effective tool that can be applied to the study of the nature of reality. But it is only a tool. “Laws” found through the study of mathematical models do not govern systems. Reality does not function through mathematical mechanisms. Mathematical models can provide only a depauperate view of complexity. To achieve understanding of complexity, the tool must be used within the context of the general factors that do create complexity.

Later in his essay, Wolfram wrote the following.

But I suspect that many of the systems for which no exact solutions are now known are in fact computationally irreducible. As a consequence, at least some aspects of their behaviour, quite possibly including many of the interesting ones, can be worked out only through explicit simulation or observation.

and,

In biology, computational irreducibility is probably even more generic than in physics, and as a result, it may be even more difficult to apply conventional theoretical methods in biology than in physics. The development of an organism from its genetic code may well be a computational irreducible process. Effectively the only way to find out the overall characteristics of the organism may be to grow it explicitly. This would make large-scale computer-aided design of biological organisms, or “biological engineering”, effectively impossible: only explicit search methods analogous to Darwinian evolution could be used.

There is another way. Everything that exists has both quantitative and qualitative aspects to its existence, organization, and development. To quantitative analysis must be added qualitative analysis. Indeed, to realistically fulfill its promise, quantitative analysis must be performed within, and conform to, qualitative analysis. Rather than simplifying diversity, relations, and organization to quantity, the task of quantitative analysis is its application to those qualities, and to do that one must first identify the diversity and the relations, and then achieve understanding of the organization.

Reality, that which exists, is developmentally and hierarchically organized. Prior stages and lower levels that play roles in the origins of later stages and higher levels very often continue to play roles in the ongoing existence of those later stages and higher levels. It is not possible to fully understand more developed situations without understanding those prior factors that play originating and sustaining roles. To understand the complexity of reality it is necessary first to achieve an understanding of the factors that play roles in its origins.

That reality is complex is due to the roles of a variety of factors. These range from factors playing roles at the foundations of reality, with the existence of space, to factors of high intrinsic complexity that create additional factors of high intrinsic complexity, for example, evolution creating organisms, and organisms creating social systems. As is so often the case in the organization of reality, the developed forms operate by way of the combined roles of the foundational forms.

For there to be existence there must be some continuous, voluminal existential quantity. Anything that has a continuous aspect to its mode-of-being has parts. If there are parts there are relations. For complexity, this is the beginning.

It is the beginning for complexity because the foundation of reality, space, exists in just such a manner. Every part of spatial place has direction and either adjacent or distance relations with every other part of that infinite continuum. Spatial places and their extensional relations constitute a pattern of organization. The places are components with relations, and many components with many relations constitutes complexity, here existing in as simple a form as is possible. For all its immaterial simplicity, space is infinitely complex.

This is of critical importance for all other forms and cases of complexity because space is the existential context for all else that exists. The complexity intrinsic to spatial extensional relations is the existential context for any other form of complexity that could possibly exist. All materially based forms of complexity occupy and are existentially dependent on the complexity of spatial extensional relations.

Spatial places are coexistent. If there is coexistence there is relation. The relation is something more than the components. Relation is an enhancement of the situation, an enhancement of the combined existence of the components—combinatorial enhancement. Because there are minimally two extensional relations between any two spatial places, the quantity of relations increases faster than the quantity of spatial place. Combinatorial enhancement is why the whole is greater than the sum of the parts, and it is one of eleven general factors that in more than seventy roles contribute to the deep structure origins of complexity.

The basis of complexity is quantity and diversity of components and relations. Anything that enhances the quantity or diversity of components or relations contributes to the origins of complexity. The understanding of the foundational factors of complexity has a three tier organization. The first tier consists of space, matter, and motion, three primal factors of existence. The second tier is the eleven general factors which are qualities or relations of the first tier. And the third tier consists of the many individual instances of those general factors in the foundational development of reality.

The eleven general factors are (a) combinatorial enhancement, (b) sequential enhancement, (c) quantity, (d) diversity, (e) additional factor, (f) initiation, (g) self-organization, (h) emergence, (i) cause, (j) through-flow situations, and (k) coherence.

The manner in which space, matter, motion, and the general factors make their contributions to the origins of complexity can occur in two forms. One way is as a quality or aspect of the being of something that exists, such as the infinite quantity of spatial places. The other way is to actually create new factors, such as the initiation of new part of continuing-existence or the emergence of new pattern of material organization.

While space is infinitely complex, due to infinite quantity, it is yet a simple form of complexity, having basically but four factors of diversity—spatial place, and adjacent, direction, and distance relations. Each spatial place has a three-dimensionally radial pattern of direction and either adjacent or distance relations with all other spatial place. Within this situation there is a sub-pattern of extensional relations that contributes significantly to the origins of complexity. It provides the existential context for forms of complexity that have motion as a factor of their existence. This sub-pattern is coexistent-sequential-difference. Adjacent to any spatial place is another place, and beyond that one, there is another, and so on, infinitely.

Coexistent-sequential-difference not only provides the place or pathway for an ongoing motion, it has an intrinsic contribution to the origin of complexity. The further away from any particular spatial place the more spatial place there is, and therefore the more relations that place has with other spatial place. This is sequential enhancement—the more spatial extension involved, the more components in the form of locationally distinct spatial places, and the more relations. With the sequential enhancement that goes with coexistent-sequential-difference, each spatial place has extensional relations with all the places in the sequence—each place has multiple relations. Thus there are more relations in the sequence than places, and the more extension there is the number of relations increases faster than the number of places—the quantity of relations increases faster than the quantity of place.

Spatial places are coexistent and static. All the components and relations of the complex situation are there together, unchanging. Spatial extension—spatial place—contributes to the foundations of complexity by way of the qualities of its being. Infinite spatial place contributes by way of quantity. Coexistence of spatial places contributes by way of combinatorial enhancement. Extensional relations contribute through both diversity and quantity, while the sequential arrangement of spatial places, coexistent-sequential-difference, does so as sequential enhancement.

Spatial continuing-existence is an aspect of the existence of space that is distinct from the extensional aspect. It is an additional factor, with its own contribution to the origin of complexity. The parts of continuing-existence are not coexistent, and their relations one to another are of a different sort than those of the parts of the extension of spatial place. Like spatial extension, spatial continuing-existence occurs as continuous sequential-difference, but in this case it is noncoexistent-sequential-difference. Noncoexistent-sequential-difference is change.

With continuing-existence there is continuous initiation of new part of the ongoing existence of space. New part, as an additional factor, is an enhancement of the situation. The occurrence of a series of these newly existing additional factors is noncoexistent-sequential-difference, and another case of sequential enhancement.

One other aspect of spatial continuing-existence that plays a role in the creation of complexity is the foundational development-of-origin of self-organization. The creation of new part of spatial continuing-existence is a direct consequence of the existence of space, without a role for anything else that exists. The creation of the sequential relations of the parts of continuing-existence, their organization one to another, is due entirely to factors intrinsic to the situation. This foundational case of self-organization provides the existential context for all other forms and cases of self-organization and for their roles in the origins of complexity.

Because the existence and nature of what is new is determined by the existence and nature of what has gone before, the sequential relations of parts of changing situations are significant. With its after and before relations, and with the sequential relations of new part with prior parts, the noncoexistent-sequential-difference of spatial continuing-existence provides an existential context for the sequential relations of processes that play roles in the creation of complexity. It also provides the existential context for forms of complexity that have change as an aspect of their nature, such as biological evolution, ecological succession, and ontogeny.

Foundationally, spatial continuing-existence is time and it provides the temporal existential context for all temporal aspects of all forms and cases of complexity.

In addition to space, there is matter. As in the case with space, matter contributes to the foundations of complexity both by way of what it is and by way of its continuing-existence. With matter something is there that is not immaterial. Matter comes in the form of extensionally limited units of substantiality. There are a lot of them, and matter contributes by way of quantity. Scientists have found a variety of elementary particles, which enhance complexity through diversity.

Two cases of combinatorial enhancement occur with the addition of matter. First there is the coexistence of matter with space. Here there is an occupation relation, with any particular unit of matter occupying, at a specific instant of its existence, a particular spatial place, and sharing with that place all its extensional relations with the rest of spatial place. Second, there is the coexistence of the units of matter. Here the units, by sharing the extensional relations of the places they occupy, have extensional relations between one another. This constitutes pattern of material organization. It is also another contribution to complexity by way of quantity in the form of all the extensional relations of all the units.

The next additional factor is material continuing-existence. Again complexity is enhanced through the initiation of new factors, new additional part of the continuing-existence of matter. This occurs individually with each and every unit of matter. The continuous initiation of more part of material continuing-existence occurs as noncoexistent-sequential-difference, one more case of sequential enhancement. Similar to the case with spatial continuing-existence, there is a contribution by way of quantity from all the prior part of material continuing-existence that has occurred. Further, each new part has after relations with all prior part, this also contributing with quantity to the origin of complexity. With only one type of component, part of continuing-existence, and two sequential relations, after and before, material continuing-existence provides only minor diversity.

Another additional factor is motion. Motion exists as a form of noncoexistent-sequential-difference. It is a form of ongoing change and involves initiation of new part of ongoing motion. New part of sequential change is a further additional factor. Continuous motion is a form of sequential enhancement, and is also a form of self-organization because once a motion is originally initiated, no other factor outside the intrinsic nature of the motion itself is required to keep it going. The order of initiation of the sequential parts of a motion is a consequence of the nature of motion. As noncoexistent-sequential-difference, motion contributes to quantity in two distinct ways, the prior quantity of motion that has taken place and the after relations of following part with all prior part, the two together being the history leading to the current state of the motion. And then there are the two kinds of basic sequential relations, after and before, through which all forms of noncoexistent-sequential-difference enhance complexity.

The next additional factor is motion continuing-existence. As with all cases of continuing-existence there is initiation of new factors, new additional parts of continuing-existence, and the occurrence of both noncoexistent-sequential-difference and the associated sequential enhancement. Once again, with this fourth case of change, there are the contributions by way of quantity both from prior part and from the relations of the parts that come after with all the parts that have gone before. There are here also the two relations, after and before, as contributions to diversity.

So far there has been a series of additional factors—matter, motion, and three cases of continuing existence. Each of these enhances the foundational origins of complexity either by what it is or by initiation of new factors. All this comes together in a relation that makes possible all further developments of complexity. This relation is a development-of-origin for change in self-identity. The change in self-identity that occurs here makes possible the changes in self-identity of situations, the observable changes in objects, systems, and the universe in general. These situation changes are those by which highly developed complex systems, such as complex adaptive systems, come into existence and by which they operate. The critical relation is that between motion and continuing-existence, and the change in self-identity occurs with motion.

Because all space exists as an infinite whole, with all parts coexistent, there is no change in the self-identity of space during the ongoing change of its continuing-existence. Motion, however, with its noncoexistent parts, exists only as the current part. Each part, as it occurs, has unique self-identity. To exist as a form of noncoexistent-sequential-difference involves a continuous change in what it is that exists. Self-identity is derived from existence. A change in what exists involves a change in self-identity. A sequential difference of self-identity occurs with ongoing motion.

The parts of motion are noncoexistent. To be so they must occur at different parts of motion continuing-existence. This is a basic relation between change in self-identity and continuing-existence. For there to be the one, there must be the other. The noncoexistent-sequential-difference of motion occurs in concert, and necessarily so, with the noncoexistent-sequential-difference of the motion’s continuing-existence. For there to be change in self-identity, there must be the change that is continuing-existence.

With motion there are two forms of noncoexistent-sequential-difference, that which is motion itself and that which is motion continuing-existence. Together they make it possible for there to be change in self-identity. They are both required for there to be that kind of change. It is a form of combinatorial enhancement. Two cases of noncoexistent-sequential-difference in concert making it possible for there to be change in self-identity. As such it is the first of three stages of development involving combinatorial enhancement that enable progressive stages of change of self-identity.

The next contribution to the foundations of complexity comes with the coexistence of space, matter, and motion. With the coexistence of these three distinct modes-of-being, there is the coexistence of their three cases of continuing-existence. The continuing-existence of the motion is simultaneous in a one on one relation of parts with the continuing-existence of the matter that is moving. And both that of the motion and that of the matter are simultaneous in a one on one relation with the continuing-existence of the space through which they are passing.

Just as the noncoexistent aspect of the continuing-existence of motion makes it possible for there to be change in the self-identity of motion, the noncoexistent aspect of the combined cases of continuing-existence make it possible for there to be change in the self-identity of the overall situation of space, matter, and motion. This is the second stage involving combinatorial enhancement that enables change in self-identity that contributes to the complexity of reality. The critical relation here is the role the combined cases of continuing-existence play in the relation between the moving unit and spatial extension.

It is continuing-existence that makes other forms of change possible. Different parts of other forms of change can occur at different parts of continuing-existence. With continuing-existence there can be changes in the nature of what it is that is continuing to exist, such as the change from part to part of an ongoing motion.

In coexistence situations, continuing-existence makes it possible for there to be change in relations. Differences in the nature of a relation between components of a situation can occur at different parts of the continuing-existence of that situation. The change that is motion takes place in relation both to its own continuing existence and to the other continuing-existences. There is a one on one simultaneity of the sequential parts of motion and the sequential parts of the continuing-existence of the moving matter and of space. This relation makes it possible for there to be differences in the relation of motion to spatial place. A moving unit can be at one part of spatial place at one part of the continuing-existence of space and at a different part at a different part of spatial continuing-existence.

There is here the coexistence and simultaneity of four cases of noncoexistent-sequential-difference—motion and three cases of continuing-existence. Space however exists as coexistent-sequential-difference. Motion is matter passing through space, and occurs in relation to both the noncoexistent-sequential-difference of continuing-existence and the coexistent-sequential-difference of space. Motion relates, in a one on one relation, the noncoexistent parts of continuing-existence to the coexistent parts of spatial extension. This is the foundation for the differences that occur with ongoing processes, including complex processes, as they change over time. It is one of the primary steps in the deep structure organization of reality that make processes possible, and thus is critical to the origins of complexity.

Matter occupies spatial place and shares with the place occupied all its extensional relations with the rest of spatial place. When a moving unit of matter is at one place at one part of continuing-existence and at a different place at a different part of continuing-existence, that unit has a different set of extensional relations at each place. It is motion that changes the location of the unit and initiates these differences in extensional relations.

Creation of new extensional relations between the moving unit and spatial place is a process that enhances the quantity and diversity of components and relations. Each new extensional relation is an additional factor. As matter moves there is a continuous creation of new extensional relations. This results in a sequence of different noncoexistent relations, a case of noncoexistent-sequential-difference, and just as in the previous cases, continuing-existence and motion itself, with the continuous creation of more there is a sequential enhancement of the situation. Continuous creation of new relations between the moving unit and spatial place increases the number of such relations that have occurred during the motion, and is a contribution to complexity by way of quantity. And all the different extensional relations that occur during the motion sequence are a contribution by way of diversity.

When there is a change in what exists, here individual extensional relations and the overall pattern of relations between the moving unit and spatial place, there is a change in the self-identity of the situation. This change is due to the coexistence of space, matter, and motion, a case of combinatorial enhancement providing a change in self-identity. This is the second of the series of three.

So far this description of the foundational development of the complexity of reality has dealt only with the relation of one unit of matter with space. The next additional factor is another unit of matter, and the contribution to complexity is due to the coexistence of the two units and to the motion of one of them relative to the other. Because the units share the extensional relations of the places they occupy, they have direction and distance relations with one another—simple combinatorial enhancement.

Coexistent units of matter have simultaneous continuing-existence, and because of that there can be differences in their relations from one part of their continuing-existence to the next. It is motion that initiates these differences, and the coexistence of the two units and motion constitutes the third case of combinatorial enhancement that results in a change of self-identity. In this case it is change in self-identity of the pattern of material organization that is-there due to the coexistence of the units. This, then, is foundational to all changes in self-identity of more advanced stages and higher levels of the development of material organization.

In the basic development of complexity, there is a series of stages each of which is existentially dependent on the developmentally prior stages, and foundational to the developmentally following stages. Prior stages are still there in following stages, still playing their roles. Stages which are more developed are constituted or made of prior stages. A full understanding of a developed stage is not possible without a concurrent understanding of the prior stages of which it is composed. This is of critical importance in the analysis of highly complex systems such as volcanoes and organisms. Such systems are hierarchically organized, with lower levels still there, still playing their roles. Highly developed complex structures and behaviors are completely dependent on the intrinsic natures of their subsystems and the manner in which those subsystems interrelate. These systems exist and operate both as an overall level of organization, at which they exist as a whole, and as a hierarchic organization, from elementary particles on up through the various levels to the whole system. The understanding of them should be organized in the same manner.

The change in self-identity of the pattern of organization of the units is based on changes in the extensional relations between them. There is here the beginning development of material hierarchic organization, and two levels of enhancement occur, that of individual extensional relations and that of the pattern of units and relations. In the previous stage, motion initiates changes in the extensional relations between a unit and spatial place, while at this stage motion initiates changes in extensional relations between the units of matter. This is a development from spatial organization to material organization. Again the situation is enhanced by the addition of newly created extensional relations. This time, however, something more happens. When the extensional relations between units change, the pattern of organization changes. New pattern of material organization comes into existence—new pattern emerges. This is the development-of-origin for the process of emergence, and is the beginning of the role of emergence in the origins of complexity. New pattern is additional pattern, and as such is an enhancement.

There are, then, two levels of contribution by way of sequential enhancement. There is the sequential change of extensional relations between the units, and also the sequential change of pattern of material organization. In this situation, the contributions to the development of complexity of both quantity and diversity have this double nature. Quantitatively there is all the prior part of the sequence of changing extensional relations, and there is all the prior part of the sequence of changing pattern of material organization. Diversity contributes with all the different extensional relations and all the different patterns of organization that occur during the sequence of ongoing change.

The foundational development of complexity follows the foundational development of reality. The next major stage is a collision situation in which motion brings two units of matter into adjacent relation, wherein there is no spatial place between the two. The prior roles of motion initiate organizational changes in the relations of units, changes in extensional relations either of a unit to spatial place or to another unit. The roles of matter in these stages are the occupation of spatial place, that which moves, and differentiation of material pattern of organization. These stages, however, can be characterized primarily by the role of motion and its effect on organization. Even though motion continues to play a role, the collision stage, and its four sub-stages, are characterized by matter, by its substantiality. This is so because matter here plays roles in the emergence of supra-organizational factors.

Because there is something there that is not immaterial, when two units come together in an adjacent relation the contact relation comes into existence, it emerges. This is emergence by way of motion leading into combinatorial enhancement. The adjacent relation is organizational in nature, but contact is something more, a consequence not of the organization of matter, but of its substantiality. Contact is a supra-organizational factor, and is significant to the origins of complexity in that it makes possible direct interaction of matter one part with another. Contact, an additional factor and the first of the four sub-stages of collision, vastly increases the quantity and diversity of possible material relations. It does so through the roles of blocking, cause (simply push at this stage), effect (simply transfer of motion at this stage), developed interaction (e.g. deflection), coherence, and the organizational consequence of coherence, structure.

To most clearly follow the deep structure events in collision, it is best to analyze the simplest case, that with one moving unit and one stationary unit. The second sub-stage, which involves the emergence of a second supra-organizational factor, is that where the stationary unit blocks the onward motion of the other unit. Again there are organizational factors, the path of the moving unit and the location of the stationary unit, but it is the substantiality of the stationary unit that plays the critical role in the emergence of the supra-organizational factor, blocking. The importance of blocking is that it sets the situation for the emergence of the next supra-organizational factor, one which again plays a major role in the origin of complexity.

Space is immaterial and cannot influence the motion of matter. Motion will continue on as long as no other matter interferes. Motion is substantiality passing through space. When the moving unit encounters the stationary unit it presses against that blocking unit—it pushes against it. This is a development-of-origin for cause. Cause, in simple form, is push.

While push is certainly organizational in its relations, one unit to the other, it is nevertheless existentially dependent on the nature of substantiality. It is a third emergent supra-organizational factor, an additional factor. Push—cause—makes things happen. It plays a driving role in making complexity come into existence, and thereby complexity is again vastly increased.

When a unit of matter occupies a spatial place, as in the case of the stationary unit, there is nothing holding it there, nothing maintaining the unit in that place. As the moving unit pushes against it, the stationary unit gives way. It begins to move. This effect, this emergent motion, is an additional factor.

When a moving unit encounters a blocking stationary unit, the moving unit cannot continue on in the same manner. As it pushes up against the other unit it slows down, it loses motion. The stationary unit begins to move, it gains motion. The cause and effect situation is a case of noncoexistent-sequential-difference. This transference of motion from one unit to the other by way of push is sequential enhancement.

This is a new form of sequential enhancement. It is not just more of something as in the coexistent-sequential-difference of spatial extension. It is not the creation of new part as with the noncoexistent-sequential-difference of continuing-existence, or ongoing motion. Nor is it the creation of new organizational relations, as with the newly occurring extensional relations of a moving unit with spatial place, or new pattern of material organization between a moving unit and a stationary unit. It is also something more than the emergence of supra-organizational factors such as contact, blocking, and cause.

The cause and effect relation is a development-of-origin of through-flow. It is emergence by way of sequential enhancement based on motion, contact, and cause. As a consequence of the interrelations of these factors, something—motion, momentum, impetus, energy—is transferred from unit to unit, passed on through the relation. Throughout the development of through-flow, the manner of the transference varies, but is in general characterized by an energetic flow that occurs interrelationally with some pattern of material organization through which it passes. Typically the energetic flow reorganizes the matter and the matter alters or redirects the flow.

By way of the determinate consequent-existence of the continuing-existence of self-identity, the existence and intrinsic nature of what goes before initiates and determines the existence and intrinsic nature of what follows. The determinate aspect of reality occurs in this manner because what goes before is what is-there to play the role of determining what follows. This is the core nature of what occurs with the emergence of contact, blocking, cause, and effect, and is thus the core nature of the operation of through-flow. With variation in the nature of what goes before there will be variation in the nature of what follows.

If the collision is between two spheres, the amount of slowing of the initiating sphere, the amount of transferred motion, and the directionality of those two motions will be different if the collision is directly head-on or if the initiating sphere strikes the blocking sphere an off-center glancing blow. If the collision is between a sphere and a blocking object that has a flat side, what follows will be different if the flat side is at right angles to the path of the approaching sphere or if that surface is at an angle of 45 degrees. If the speed of the initiating unit is different from collision to collision, the consequences will be different. It makes a difference, also, if the existential quantity of the two units is not the same. The greater the existential quantity of the initiating unit relative to the blocking unit, the less will be the change occurring with that initiating unit, and the greater will be the change occurring with the blocking unit. When the blocking unit is the greater in existential-quantity, the consequent changes will be the reverse. And so it goes for whatever variations there are in what goes before.

Once more, this is a stage of development of the origins of complexity that is crucial in making more developed stages possible, being of particular significance in the origin and operational aspects of such complex systems as organisms and ecosystems. It is foundational to the role of energy flow in the origin of biological organization.

Coherence is the last of the eleven general factors that contribute to the deep structure origins of complexity. Matter sticks to matter. It coheres one part to another. This coherence comes in many forms. Sometimes it is merely clumping together as with gravity keeping loose objects against the surface of a planet. Then there are the forces, the strong, the weak, and electromagnetism involved with the togetherness of protons and neutrons in the nucleus of an atom, the togetherness of electrons with an atomic nucleus, and the togetherness of atoms in molecules, and molecules with molecules. Sometimes the coherence is structural, as when the curved spines on a bur catch in the fur of a passing animal. There can even be behavioral coherence, as when Fire Ants in the southern United States cling together in masses of thousands of individuals enabling the colony to float when the countryside is flooded, thus saving the colony from dispersal or drowning.

When units of matter stick together there is combinatorial enhancement with multiunit structure as a consequence. Coherence is an emergent supra-organizational factor that contributes to the foundations of complexity by way of its organizational consequences. Emergent with coherence are (a) coherent pattern of material organization, (b) structural hierarchic organization, and (c) persistent material pattern. Coherence and these three factors result in a virtually limitless diversity of shapes of units of matter.

Through-flow is characterized by an energetic flow that occurs interrelationally with some pattern of material organization through which it passes. The flow reorganizes the matter, and the matter alters the flow. The greater the diversity of material organization, such as provided by coherence, the greater the diversity of through-flow situations there can be. The greater the complexity of coherent structure, the greater can be the complexity of through-flow processes, living cells and organisms being the preeminent examples.