Evolving Hierarchical Systems: Their Structure and Representation 9780231881890

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Evolving Hierarchical Systems

Evolving Hierarchical Systems Their Structure and Representation Stanley N. Salthe

Columbia University Press New York

1985

Columbia University Press New York Oxford Copyright © 1985 Columbia University Press All rights reserved Printed in the United States of America

Library of Congress Cataloging in Publication Data Salthe, Stanley N. Evolving hierarchical systems. Bibliography: p. Includes index. 1 Biology—Classification. Q H 8 3 S 2 6 1985 574'.012 ISBN 0-231-06016-5 ISBN 0-231-06017-3 (pbk.)

2. Evolution 85-483

I. Title.

Clothbound editions of Columbia University Press Books are Smythsewn and printed on permanent and durable acid-free paper.

Contents Preface 1 An Introduction: Structure and Representation of the World 2 The Individual Entity 3 Some Basics of Hierarchical Structure 4 Representing a Dynamic System Hierarchically: The Basic Triadic System 5. Representing a Dynamic System Hierarchically: The Nontransitivity of Effects Across Levels 6 The Explicit Elaboration of a Hierarchy of Nature 7 Organic Evolution and the Hierarchy of Nature 8. Organic Evolution: Its Origin and Hierarchical Structure

vii 1 19 39 67 115 161 185 249

Appendix

273

Glossary

279

References

311

Index

331

The mind—what is it? It is the sound of the breeze blowing through the pines in the picture.

Ikkyu

When it blows from t h e west, fallen leaves huddle in the east.

Buson

Unmoving fishes seen below the surface; the autumn wind.

Seisei

The winter gale has blown the ducks together near that s t o n e wall.

Hekigodo

When the wind falters, the snow flakes mill about above the withered reeds.

Michihiko

Washing my hoe sends ripples across the w a t e r — wild ducks in the distance.

Buson

This brushwood, cut for fuel, is beginning to sprout.

Boncho

Preface Let this work be a preface to all those that came before it, from which the new approach is growing. This is a work of metatheory of science from the perspective of a biologist concerned with evolutionary theory. The questions taken up are matters of ontology, but I am overwhelmingly mindful that no such matters can be taken up without explicit reference to the epistemological constraints making it possible to approach them in the first place. In particular this work will deal with representations of the things in the world (its "furniture"—Bunge 1977) and their relations, and with how these relations give rise to and guide the processes the things are caught up in. The paradigmatic process serving as an attractor for all the statements in this work is "the evolutionary process." The basic assumption behind this work is that the world (and therefore nature, its representation) is unlimitedly complex, as characterized in the very general metaphysics of lustus Buchler (1966). Mandelbrot (1977) has provided a mathematicopoetic picture of the material world that resonates well with Buchler's. Biology and its associate sciences (as also, for example geology and many-body physics) have become entangled in this complexity with, so far, as little ability to negotiate it as a fly a spider's web. In particular, biological nature is undercharacterized in our representations, and because of that so is the rest of nature. We must recognize complexity before we can deal with

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it. We shall find as an aspect of complexity that the world has real discontinuities and, as a consequence of the "smallest entity" necessarily appearing to be continuous at yet "smaller" scales, that there are no nonarbitrarily designated fundamental units. What is required at this juncture is a general representation of the world, one having a structure capable of dealing with transformations. While this work will concern itself primarily with biology, the representation explored here will be applicable to any science My attempt will be to display the world as a determinate machine in conformity with the attitudes of biologists in the twentieth century, but I do not believe that the world is such a machine nor will the system described herein be limited by that aim. Ultimately, we must seek extreme precision of s t a t e m e n t — a kind of propositional calculus which in the present work remains only an ideal. Precision, to be sure, distorts; but nature without it is obscure. In science it may be the case that a dozen different precise statements may be required to express a reality conveyed by the connotation of a single inflected word in a conversation or performance of s o m e verbal art. Our framework s h o u l d be one that could generate those statements if need be. Arthur Koestler in 1978 called for a "coherent philosophy of nature," and that is the general direction we must aim toward. Maritain (1951) reminds us that this will be a discipline in between science and metaphysics. Buchler can serve only as a starting point because he is too general to be applicable even to science in general. It is time to forge tools. Our attempt must be to be able to make our statements as complete as possible. It is this single requirement that leads us by way of Bertrand Russell (1903) to discover the basic structure of the system we n e e d — a hierarchy of entities at different levels of organization. N o statement referring to a given level will be complete enough, and here we invoke the shadow of Kurt Goedel (1931); every event, every statement about such an event, requires, in particular, other events at a higher level of organization, another statement referring to a higher level of organization, to make it complete or to frame i t — t o give it a context that will allow us to understand it or to judge its truth. Logicians a n d philosophers have exercised great ingenuity to avoid this

PREFACE

ÍX

"clumsy," " c u m b e r s o m e , " structure (Russell himself in 1910 with his "axiom of reducibility"), but 1 fear scientists will not be a b l e t o follow t h e m b e c a u s e they are involved with obdurate m a t t e r which d o e s not allow itself to b e "reduced" at whim—their repr e s e n t a t i o n s must b e of t h e c o n c r e t e material world. Hierarchical structure is o n e realization of Buchler's "principle of ordinality"—a particularly apt o n e for t h e s c i e n c e s . Most biologists already acknowledge at least t h e pedagogical usefulness of such a concept, but very few take it seriously in their work. This is primarily b e c a u s e no useful framework exists that would allow such application. However, such an approach would a l s o at present be found somewhat foreign t o our habits of thought because, for example, it would require a s much thought to be devoted t o control or regulation a s t o (material or efficient) causality, while we have for the most part been trained to focus on the latter only. This would further require us to give as much attention to o t h e r constraints on a process a s t o t h e laws governing it—that is, t o what we are used t o seeing a s mere contingencies. Here we may a l s o note that in t h e twentieth century hierarchical a p p r o a c h e s have often been used a s a springboard for attacks on reductionism (e.g. Morgan 1923; S m u t s 1926; Needham 1943; Koestler 1967; Polanyi 1968); and these, a s well a s episodic c o n n e c t i o n s with left-wing politics (e.g. Novikoff 1945), have conspired t o make this kind of approach s e e m t o o risky, t o o far-out for many American biologists. Reductionism in fact requires hierarchical structure in order t o make s e n s e (Bock 1979), but its preferred focus on proximate causality is a very limited way of dealing with such a rich tapestry. When faced with such even obviously complex problems as t h o s e involving e c o s y s t e m s or the mind I think we can no longer restrict our vision with this one-way attitude. (The political connection t o a large extent involves t h e o p p o s i t e p r e f e r e n c e — t h a t is, a belief that regulatory c h a n g e s in society can be m a d e that would elicit positive social r e s p o n s e s from persons regardless of t h e genetic and historical c a u s e s predisposing s o m e of them toward antisocial or asocial behavior). A more c o m p r e h e n s i v e perspective is needed. The aim of this book is directed at chapters 7 and 8. The others are preparations leading to them Without t h e rest of the book t h e s e chapters would b e o p a q u e to most biologists.

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PREFACE

Nevertheless, I believe the rest of the book makes a contribution to hierarchy theory itself, which, as I found it, was not sufficient to develop chapters 7 and 8 My own contributions here center primarily on chapters 4 and 5. Evolutionary theory is one of those complex subjects that even now requires a large framework such as that developed herein to organize and articulate its disparate parts. The idea that it is a subject requiring hierarchical representation was nicely captured by Van Valen's (1976a) maxim, "evolution is the control of development by ecology." As a further point of departure we may quote Wright (1964). "The task of science is not complete until it has followed phenomena through all levels of the hierarchy, up and down as far as possible, and after obtaining the best statistical description at each, has tied them all together." It is my pleasure to acknowledge relevant conversations or c o m m u n i c a t i o n s with the following persons: Jonathan Adler, Howard Allen, Tim Allen, Mike Conrad, Joel Cracraft, Julie Downey, Niles Eldredge, Mike Gochfeld, Marjorie Grene, Martha Herbert, Steve Himes, David Hull, Bob Kaplan. M a r i o n n e Kirk, lay Lemke, luan Carlos Letelier, Bill Livant, Paul Mankiewicz, Les Marcus, Everett Olson, Ron Pilette, R. C. Richardson, Beth Singer and Keith Thomson Rebecca Salthe proofread the manuscript, which was typed by Judy Steinberg. Lou Moriber and George Fried s u p p l i e d support and encouragement. The quotation from Eldredge and Salthe (1985) in chapter 7 is reprinted with the kind permission of Niles Eldredge. Sketches that accompany openings for chapters 1, 2, 4, 5, 7, and 8 have been drawn by me, after the sketchbooks of Leonardo.

Evolving Hierarchical Systems

Chapter 1

An Introduction: Structure and Representations of the World A. STRUCTURE

4

The Qualities of Things

5

Praxis

5

Self-Reference

6

Theoretical Constructs

7

System Structure

8

The Structure of the World

B. REPRESENTATION

9

11

Nature

11

Represenational Incompleteness

12

C o m m o n Scientific Representations Today

13

Visual Representation

14

Legitimizing Visual Representation

15

What Things Are Real?

16

Hierarchy Theory

17

I

T is important, in a book of this nature, for the author to set out his basic assumptions and to provide a background for the distinctions he will make. Hence, in this chapter I will provide an outline of the structure of thought from which my philosophical base will be discernible. Now. given that my background is biology and not philosophy, this chapter may appear awkward and naive to the philosopher of science. But that is not important as this work has not been composed as much for them as for biologists. It is more metatheory than metaphysics. It is not important that my point of view is aligned here with Whitehead, there with Aristotle, or elsewhere with Russell or Polanyi. Works by these and other philosophers will be cited for details as needed in the body of this work. Here I wish only to indicate as simply as possible from what perspective I view my work so the reader may be better oriented in attitude space. This chapter serves as context for the others just as the next six serve as context for the last two. This work points at ontology much as a compass needle points north. Ontology is the attractor of my statements, even if they ostensibly denote only epistemological matters, as most of them in fact do. The scientist usually believes in an external world independent of his observations. The theoretical scientist tries to visualize that world—even though science almost never asks ontological questions. The question typically is not what is an ecosystem, but how do we measure certain relationships between populations, how do some variables correlate with other variables, and how can we use this knowledge to extend our domain. The question is not what is the mitochondrion, but what processes tend to be restricted to certain regions of a cell. For the working scientist these need not be things at all, but processes that can be scanned by our measuring tools to discover characteristic suites of values that can be repeatedly ascertained by anyone trained to manipulate the rulers and clocks of the profession. Now, the scientist is usually not, on the other hand, a self-conscious epistemologist That would mean going beyond his area of narrow training for the purpose of questioning its point. Functioning as a scientist means functioning within the rules of a game learned during an apprenticeship in which ex-

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amination of the philosophical foundations of that game plays a characteristically tiny role. One strives to b e c o m e a member, not to potentially undermine the club by examining its structure from outside. Only when commitment to a way of life is secure is it possible for s o m e to examine its foundations with sympathy. The result is that the typical young scientist is trained to measure, assuming that what he measures exists, and he is little cognizant of how little his measurements justify that working assumption. Justification, in fact, is not required as long as the science is flourishing, contributing its share to the social context. But, when it falters, we fall upon times of foundational reexamination, a s with evolutionary biology today. The signs of that faltering may b e scorned (creationism), poo-poohed (punctuated equilibrium), or held to be scientifically unimportant, resulting from overextended misapplication (sociobiology), but when the gauntlet is thrown nothing can be done to retrieve it. Unhappily, we hear people beginning to ask. "What is the evolutionary process anyway?" I will try to approach that question in chapters 7 and 8. For now, I have been thrown all the way back to:

A. STRUCTURE

We have p r o c e s s e s and we have things. Things may b e viewed as processes; 1 am a nucleus for processes, or a nexus of process, just like a whirlpool, but 1 am also a thing, a matter of functional boundaries, and so is a whirlpool. I believe (along with Sommers 1963) that it is not simply a matter of the linguistic inheritance of primitive word-concepts that leads us to believe that things exist. We can bring to bear an enormously complex battery of measurements to demonstrate boundaries (Mandelbrot 1977). Somehow, the world is broken into parts which seem to us to behave as i/they had a u t o n o m o u s existences (Weiss 1969) A rock is a thing; so is the mountain it fell out of. A pond is a thing; so is the field it is in, and, in a different way, so is the county where the pond is found. To b e sure, the English Ian-

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5

guage is heavily focused upon things, but for present purposes that is gratefully acknowledged. Reification becomes a problem (Lumsden and W i l s o n 1981), but I know just what 1 mean when I say that a dust devil is a thing.

The Qualities of Things Now, when we approach things we find they have a variety of qualities, such as wetness and hardness, that we might call the results of contemplative interaction between us and the things. Reflection informs us that these qualities can be analyzed into combinations of more general qualities. Consider as an example how many different odors and scents there can be; and consider, too. that, the biological organism cannot have a separate detector for each. If we wish to deal with the most general kinds of things as well as the most concrete, we can work our way into a list of the least derivative qualities things could have. Whether my list is the best or most complete is not important, as its use will illumine my procedure in any case. I find that for the purposes of this work, 1 need three pairs of opposing qualities from which I can generate the relevant qualities of the entities dealt with in this work. They are change versus stability, discontinuity versus continuity, and bigger versus smaller. The things that we meet in the world tend to be relatively stable, to have boundaries, and to be rankable by scale, whatever other qualities they may have of interest in other contexts.

Praxis Now, we do not interact with these things only passively. We approach them with a certain verbiness, if I may put it that way; we classify things, we measure them, we cause them to displace or deform, we regulate the extent of their displacement or form change, we judge them in different ways, and we mingle with them in an interaction we can call "time"; that is, we remember and/or anticipate them. Here we have a sense of praxis as opposed to passive contemplation. If we are very careful about our

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usage we might wish to note that so-called passive perception is really quiet praxis (Gibson 1966) That is, however, besides our theoretical point and gets us into organism functioning rather than the logical distinctions we are trying to make, one of which is that no matter how hard we may strive to find out that a thing is wet, that wetness (or, in point of fact, the potential for it) may be taken as a property of the thing a n d is not always confined to our interaction with it. But, it is important to note our orientation in approaching things as well; what we discover will vary according to whether we are trying to cause something to move or trying to classify it.

Self-Reference Having made this distinction we are logically forced, in an attempt at more complete description, to acknowledge that we ourselves, who have thinglike properties, may be taken as things in the world that, as we have already made out, interact with other things. Indeed, we can detect others d o i n g just that. From this we derive that different observers, like ourselves, have somewhat different perspectives on the things we are all interacting w i t h — w e can recall the blind men touching the different parts of an elephant and we can note the possibility of being deaf instead of blind. We may compare a lumberman's description of a forest with that of a poet. S o m e things, therefore, are observers s o m e of the time and so we may wish to distinguish a special kind of r e l a t i o n — observer-things. Since we are ourselves both things and observers, and since some of the other things we observe are also observers, we find an expansion of the thing-observer relation, notably (thing-observer)-observer. If we wish to generalize to all observers we discover that the thing-observer relation has rules that apply to our own current observations as well (see, e.g., Locker and Coulter 1977). We then project into the role of observer-observing-itself-observing and we realize that in s o m e sense there can be a logical extension of this, as in a hall of mirrors—where our images recede, one after another, into invisibility. If we are to honestly acknowledge that our description of a situation is affected by our perspective we must note that any

STRUCTURE AND REPRESENTATIONS

7

representation of events must include (even if only cryptically) a self-reference. For example, we can consider a map to be a description. We ourselves are present in it in the treatment of scale (see also chapter 3). We must see ourselves as part of the system we are describing (von Foerster 1972). In an autobiograp h y the effect is overwhelming; in the description of an ecosystem the effect may be more subtle, even insidious, if unacknowledged. (We may note parenthetically that representation is another important way that we interact with the things in the w o r l d — w e try to represent them in various ways). In this work, then, we will carry the spirit of the Copernican Revolution into biology by insisting that our view of the world is conditioned by our privileged position in it.

Theoretical Constructs We can now quickly construct s o m e theoretical concepts out of these primary qualities of things and our modes of praxis on them. We shall wish to have a definition of e n t i t y . We may note, for example, that things are discerned by their stability, by the fact that they are b o u n d e d at a discontinuity with the rest of the world and by their scale. We could use these properties to define e n t i t y (see chapter 2). which will be our theoretical representation of 'thing in the world'. Things in the world will have many other properties than these, but these are germane to our present interest. A note about scale—if things become very small, like grains of sand, we deal with them en masse, as a beach, a new entity. If they are very large, like an ocean, we are apt to focus on parts of them like waves or plankton or schools of fish. Thus, scale c o m e s from our relation to a thing, but we can also see that s o m e other things are bigger than still other things just as we note that we too are things. Hence, whether a thing is readily viewed as an entity or not depends on its scale with respect to ourselves. In other words, I do not want my definition, which will be carefully honed in chapter 2, to go outside the interactions of things, s o m e of which are observers, to some more abstract realm. Having entities, we now note that, while on the whole they tend to be relatively stable, they do in fact change—they

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may b e displaced or d e f o r m e d or put into new relations with e a c h other. If t h e c o n c e p t s of entity and of c h a n g e and c o n tinuity are c o m b i n e d we can derive t h e c o n c e p t process. Note t h a t in t h e p r e s e n t view e n t i t i e s a r e therefore logically prior to t h e p r o c e s s e s in which they participate. When we e x a m i n e what s e e m t o b e natural e n t i t i e s and p r o c e s s e s , we b e c o m e aware t h a t they show various patterns, b o t h of form and of relationship. C o m p a r a t i v e study ( m e a s u r e m e n t , etc.) of t h e s e p a t t e r n s reveals t h a t many t e n d t o b e related. We can in fact classify t h e m into groups of p a t t e r n s which are d i s c o n t i n u o u s b e t w e e n t h e m s e l v e s . Inquiring why t h i s might be, we can (and I will) d e c i d e that they reveal s o m e t h i n g a b o u t t h e world that we c a n not directly o b s e r v e — t h a t they reveal s o m e t h i n g of its structure. How can t h i s b e justified? N o t e t h e pattern of t h e logical path in t h e procedure just outlined. We start with unexplained primitive c o n c e p t s — c h a n g e , bigger, etc. By c o m b i n a t i o n we d e d u c e from t h e s e certain t h e o r e t i c a l c o n c e p t s — e n t i t y , p r o c e s s . Using t h e s e t h e o r e t i c a l t o o l s to order our empirical o b s e r v a t i o n s we induce from t h e s e o b s e r v a t i o n s that they reveal underlying structure b e c a u s e they o c c u r in d i s c o n t i n u o u s c l a s s e s . Not every pattern t h e o r e t i c a l l y p o s s i b l e exists, only s o m e of t h e m . We t a k e this t o b e significant b e c a u s e , ultimately, t h e world we are in is just o n e such p o s s i b l e world; it t o o is a finite entity. S i n c e t h e r e c o u l d theoretically b e o t h e r worlds, t h e c h a r a c t e r i s t i c s of t h i s o n e a r e significant. Finally, we c o m p l e t e a circle by realizing t h a t study of natural e x a m p l e s of our primitive c o n c e p t s like c h a n g e ' reveals t h a t they, t o o , show structural p a t t e r n s , many of t h e s a m e o n e s exemplified by natural p r o c e s s e s and forms. Why s h o u l d this b e ? B e c a u s e we observers a r e parts of t h a t s a m e world and we should e x p e c t our i n t e r a c t i o n s with t h e rest of it t o b e patterned in ways c h a r a c t e r i s t i c of t h a t world. We may now c o n c l u d e t h a t structure' is p e r h a p s the m o s t powerful c o n c e p t we have although it is a secondary, derived, o n e .

System Structure This b o o k is a b o u t structures. They are held t o have o n t o l o g i c a l primacy. The changing forms and r e l a t i o n s h i p s of e n t i t i e s n o t

STRUCTURE AND REPRESENTATIONS

9

only reveal these structures, and even perhaps cause them to exist in measurable ways, but are also controlled by them. That is, the things in the world form a system (Forrester 1969; Bunge 1979). I will presume that no change of form or process can occur which violates the structural rules of the system of our world. Note that the concept of control or regulation has a tremend o u s importance in this structuralist (e.g. Piaget 1971) viewpoint. I will say a g o o d deal more about this concept in chapter 4, where I compare it with the concept of causality.

The Structure of the World Is there an overall, simply conceived pattern of the world? In a sense it is psychologically necessary for us that the answer be yes, converting that to a rhetorical question. The real question for us is what is the basic structure (or order) of the world? Not many have been proposed. It must be a structure that allows causal relationships to exist as well as relationships of control. It must be a structure that will generate complexity (Buchler 1966, Wimsatt 1974; Mandelbrot 1977). It must be a structure that is spontaneously stable (Simon 1969; Soodak and Iberall 1978). It must be a structure that generates things, boundaries (Simon 1969; Mandelbrot 1977; Soodak and Iberall 1978), at least in our interaction with it (Salthe 1983). Very few will do all these; o n e that will is hierarchical structure—that is, nature viewed as a hierarchy of entities existing at different discrete levels of organization (e.g., Koestler 1967, 1978; Dawkins 1976b; Bunge 1979; Allen and Starr 1982). Two diagrammatic views of such a structure are shown in figure I. Note that the major characteristic of these patterns is difference in scale or importance; s o m e things are bigger than others, some exercise greater (broader) influence than others. Figure l.A shows a compositional hierarchy of nested entities; figure I B shows a control hierarchy, which may or may not be nested. It will be the view of this work that the world is ordered in both of these ways simultaneously and that, since nesting has characteristics of both, the material aspects of the world are ordered in a nested manner. S o m e things are very big—e.g. the w o r l d — a n d others,

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STRUCTURE AND REPRESENTATIONS

Figure I. Two diagrammatic views of hierarchical structures. (A) a compositional hierarchy of nested entities; (B) a control hierarchy.

STRUCTURE AND REPRESENTATIONS smaller, are found within them as parts. We note the very important part-whole relationship. Everything has parts (I will deal with fundamental particles later); everything is also a part of something yet bigger (I will deal with the physicist's universe later). Everything controls its parts and, as a part, is controlled by the whole it is part of. Things that are both parts and wholes simultaneously have been dubbed "holons" by Koestler (1967), and so, in our view things in the world are all holons. We may derive hierarchical structure from our array of basic qualities, primary activities, and theoretical concepts. We already have the concept of structure, and this is only a particular example. But, being so, it requires further specification to derive it. Its basic content is scale, that scale being embodied by entities, some including others as parts. I feel that a very important other ingredient in this concept, however, is aesthetic judgment, another of our ways of interacting with the world. We can take hierarchical structure to be an example of significant form, of what Gruber (1979) calls an "image of wide scope." We are fascinated by its general applicability, by the number of transformations of it that we are confronted with (for example, the tree of life or phytogeny, the chain of command, complex fugal structure in music, cascading phenomena in all realms—all topologically similar). It has power and exerts fascination. We may explain this as resonance between one part of the world (our minds) and other parts, all embodying the same basic structure. More mechanically, we derive our mental patterns via natural selection operating in a world that has this structure.

B. REPRESENTATION

Nature Let us back off and take another approach to things and their relationships. We find ourselves in a world whose structure is unknown, but we find a need to represent it (von Foerster 1972). In ceference to that legion of intellects who have written about the

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world by referring to it thus, I will call our representation of the world nature.' The scientific aspects of that representation will ultimately consist of highly explicit statements in a form something like propositional calculus, but including mathematical formulations as well. The contents will be (and are) descriptions, laws (observational regularities), theories (explanations), and some formalism (not now available) to handle constraints like initial and boundary conditions, that tend to be unique. Nature's physical existence will be in books, papers, film, computer software and the like. A part of nature will be devoted to our own self-representation It will represent that part of the world with which, given our form (and behavior), we interact via praxis. Using von Uexkiill's term (1926), we can call this part of the world our "umwelt." It is that part of the world we relate to, partly through adaptations. Again, we are part of nature as we are part of the world. But there is a curious difference here from other parts because this part is actually making the representation nature'. Hence, we must represent our representation process as well in an attempt at completeness. That is part of the world and so it must be part of our representation of it as well.

Representational Incompleteness Given that we attempt to make this representation rich enough in detail, it must forever remain incomplete if it is to be internally consistent (Goedel's incompleteness theorem—Davis 1965; Hofstadter 1979). It could be completed by placing it inside yet another logical system that will resolve undecidable questions within the original representation (Carnap 1937), but then that larger system will remain incomplete. In fact, within the realm of logical representations completeness will never be achieved. Yet in a sense things are complete, nothing is lacking in the world. We can insure completeness for our representation, nature, only by placing it too as a thing in the world generated by the praxis of respresentation (J. L. Lemke, personal communication). Hence, in our representation some symbol or suggestion of something bigger than, and outside of, nature must be provided. But that thing cannot in fact be represented

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because it is the real world, not a representation. Thus, as a very simple example, the fossil record is part of our representation of the world; it can be c o m p l e t e d (in principle) only by recourse to digging in the earth. Notice, however, that this is not really a good example because the incompleteness of our ultimate representation is not caused by simple lack of knowledge but by the structure of logic itself. N o t all questions even of logic can be decided within the system. It is at least for this reason that I do not believe the world can be represented as a deterministic machine.

Common Scientific Representations Today

Let us examine some of the characteristic representations of science as they exist today. We may take a research paper from a field not too closely related to our own. We find we cannot in fact understand all of it. But workers in that particular field have no trouble with it, and in fact it is only to t h e m that it is directed Much of it is in a kind of shorthand, referring sketchily to assumptions and techniques well known only to those in the i m m e d i a t e field. It is really a communication on research in progress within a close knit group. Their daily praxis completes for t h e m what to anyone else is a woefully incomplete statement. The communication is in fact one of the research tools of the group. Anyone who has a t t e m p t e d to learn some technique solely from the primary literature even with the vade mecum literature thrown in knows from painful experience that it is either impossible or a waste of t i m e given that the opportunity for apprenticeship presents itself. Recipes are always context dependent And, indeed, all the workers in the know learned their trade by apprenticeship, not from books. Science as an ongoing practice is taught partly by example, ostensively. O n e learns how to proceed by participating in it. It is praxis, mostly implicit, with written documents serving limited and short term purposes. As Leslie W h i t e has remarked (1949), "Science is sciencing." Now we can look over a review article. This is written for a more inclusive a u d i e n c e — t h o s e in related fields—and is intended for a longer useful life. The realities of the situation

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are kept in mind with locutions like "in so and so's hands this observation could not be repeated" or "according to X the situation is as this, but Y has evidence that . . ." Yet in many of these review articles there is a tendency for the notion of the accumulation of knowledge with time to creep in, so that a review of the state of the art at time tx tends to slide over to a review of how much we know about this aspect of the world at time tx. The connotations of the two statements are importantly different. The second has lost touch with the basic incompleteness of all representations and is, simply and obviously, incomplete. The first is completed by reference to the activities of those making the investigations. When we come to textbooks we find that touch with reality has generally been completely lost. We find "The mitochondrion is ." Presumably such works serve the purpose of orientation toward basic attitudes and some kind of pro-science propaganda and consciousness raising. What this means for education must be left to be pursued elsewhere.

Visual Representation Our representations frequently are visual in content (figure 1), and most of us feel particularly comfortable with these This no doubt reflects a primate bias toward visual experience, and is a sort of crypto-self-reference. We often attempt to "visualize" the invisible, things that are not and never have been visible to anyone or anything (e.g. Bohr's atom). In biology we often try to visualize what something would look like if we were tiny creatures who yet (magically) had eyes like ours. We can apply a hand lens to a sample of pond water—this might be what a fish fry sees. Moving further we use light microscopy. We have entered the world of heavy technology, and it is not clear that what is made visible has ever had a natural relation to being observed in this way. Restlessly we push on into electron microscopy. Now it is clear we have contrived to see the absolutely invisible (linking vision with light). Artifacts become a worrisome possibility, but we are convinced that what we are doing is legitimate. It feels legitimate. But, what can it mean to see a mitochondrion? Surely its function has no relation to being

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15

seen Ideed, seeing is surely a misplaced predicate in this context. Visual contours cannot have any actual meaning in connection with mitochondrial function, so why look at t h e m at all?

Legitimizing Visual Representation Well, we can move to justify our delight in seeing these mitochondria by a t t e m p t i n g t o get at them in other ways so as to corroborate their existence. We can perform centrifugation experiments that separate out of a region of cells that contains our visual entities and we can show that certain metabolic functions are by and large restricted to that portion of the separated cell contents that contain them. Thus, we can correlate function with our little vesicles, and it is now more convincing that we have detected by vision something functionally real. Of course, it might be objected that in vivo this function is really spread throughout the cell while after death there remains a residual function in these so-called mitochondria. What we do now is to line up three justifications for our procedure. (1) We use the principle of parsimony; our interpretation is simpler. Furthermore, we note that there is no evidence whatever for the objection, which therefore represents merely a willful desire to interfere. (2) We use the principle of robustness (Levins 1966; Wimsatt 1980b), which in fact we used to generate our centrifugation experiment. We detected the same things in two different ways and so increased our confidence in their reality. They were robust t o perceptual exploration. We can continue in this vein and look for and test metabolically mitochondrial preparations from a wide variety of different organisms. Every time we find them we corroborate again their existence. Finally, (3) we will tend to rest content with our interpretation because it is in line with the mechanistic reductionism that has characterized the field of cell biology throughout the twentieth century. So why should we look elsewhere? This may be called the strategy of confirmation as opposed to the strategy of testing associated with Karl Popper (Popper 1963). Thus, we want vision to be our guide. We get further results suggesting it is an adequate guide These results also corroborate others of our biases

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and we can bring in two principles to bolster our result—the aesthetic principle of parsimony and the epistemological principle of robustness. But, is it really so objectively? We don't really care; we have done all we can.

What Things Are Real?

Now, this line of reasoning brings out an important point: biologists truly believe that there are things in the world smaller than we ourselves are and that often they are parts of bigger things. It is part and parcel of our reductionist orientation. In order to balance our thinking we also perfunctorily acknowledge that there must also be things in the world bigger than us, and then we usually return to examine the little ones. There could be other opinions on this, perhaps more parsimonious ones. We could believe instead that only those things more or less on our scale exist as things and need to be treated as such. For the rest we could adopt an operationalism—mitochondria are what are discovered by making the following procedure. . . . Certain positions on, and movements of, dials in our rulers and clocks would be the reality of what we now take to be little things. A gas pressure would not be interpreted as the result of the movements of unseen molecules; it would simply be a gas pressure with certain uses for us. This kind of approach has in fact been rare in any science. Perhaps the best known attempt was behaviorism in psychology, where behavior was defined as responses to specific experimental probes. In such an approach man is truly the measure of all things! A world representation of this sort has not to my knowledge been proposed. What we have instead is a vaguely hierarchical world view, which has been forced on us in part by our need to make visual representations. We don't really know that there are things smaller than we can see. There are forces we can detect that we represent as the result of actions of smaller-scale phenomena. In this sense the hierarchical representation discussed above is a theory about the nature of the world. Actually it is a metatheory—a theory about theories. What it proposes in part is that theories be couched in terms of individual entities.

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Hierarchy Theory Another way to go would be to consider process to be prior to entities. The world would be a field wherein processes of different frequency interact in various complex ways. We would not treat ourselves as things but as foci for processes. In actual fact such a viewpoint would be largely translatable into a thing viewpoint and vice-versa. Tiny things would become high-frequency phenomena; long waves would become big things. The orientation we choose is in large part a metaphysical matter if we choose consistency, and instead we might switch our view as the scientific context requires. This work is thing oriented. Levandowsky and White (1977) and Allen and Starr (1982) are examples of process-oriented works, and I have no trouble mapping the s t a t e m e n t s in t h e s e works into my own. What is most important is the focus on scale and its implications. Hierarchy theory, then, is a theory about the interactions of phenomena of different scale, and it is a metatheory in the sense that it proposes that theories devoid of scale considerations are going to be deficient. The hierarchy theory embodied in this work, however, goes further and, being entity oriented, proposes in addition that boundaries must be taken into consideration if we are to make s e n s e of t h e world. Boundaries allow us to separate processes and localize them in the world, and this localization generates both behavior and events. Indeed, 1 am of the opinion that the process-oriented approach is really crypto-thing oriented but with certain constraints removed for the sake of simplicity Hence, 1 believe that the more complete hierarchy theory is one with a metaphysical commitment to individual entities as primary phenomena In order to do science this difference is largely a matter of what is more convenient given the problem. That is why this is in part a work of the metaphysics of science.

Chapter 2

The Individual Entity A. T H E E N T I T Y

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Criteria of Entification

23

1. Boundaries

23

2. Scale

24

3

25

Integration

4. Spaliotemporal

Continuity

Definition of Entity B. T H E I N D I V I D U A L Entification

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29 30 30

Individuality

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C. U N I Q U E N E S S

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Nomothetic Versus Idiographic

35

I

N this chapter I introduce and define the actors and furniture of t h e world. They are unique individual entities and depend for discrimination upon observers. Material entities are asserted to have individuality on the basis of the criteria of indivisibility and particularity, and each is unique. Entities are critical for the development of hierarchical structuralism because that sort of structure depends upon varying "intensities of interaction" (Simon 1962). In the physical world t h e s e intensities are dependent upon propinquity. An indefinite number of unique individuals can exist in a finite material world if they are nested within each other and if that world is expanding. Hierarchical structuralism will be the ideographic complement of nomothetically organized classical science. In the last decades there has been a movement away from viewing things as of primary importance in favor of process. Buchler (1966) eschews "the language of entities" as being t o o limited for his extremely general discussion of ontological complexity. Allen and Starr (1982) even suggest that traditional discussions of hierarchical systems in an ontological way have been a block to a broader a c c e p t a n c e of hierarchical viewpoints in ecology Presumably they allude to the superorganism concept (Spencer 1876-1896, Clements 1905), which has been under considerable attack in ecology (e.g. Simberloff 1980) since it tends toward incompatibility with the reductionist approach to science so lately successful in other fields of biology. As I have indicated in the introduction, I will not abandon the entitative ontological perspective in favor of the kind of operationalist phenomenalism suggested by, for example, Allen and Starr. A metaphysical commitment to things has a purpose. It is part of a strategy that encourages us to take the configurations we discover in nature seriously. First of all, we feel that we ourselves are things. In our culture things are felt to have a solid weight, to be important; this is mediated even through language. Process is by comparison viewed as fleeting. By this move toward the primacy of things we avoid the glib phenomenalism (or even the danger of solipsism) of a completely epistemological approach and it b e c o m e s easier for most of us to feel the reality of structure in the world Of course, objectively, both form and process as surface structures equally reflect the

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deep structure of the world, and my move in this direction is a local tactic By mediation of this move, however, it becomes possible to have a healthy concern about potential artifacts generated by observational style or experimental design. Indeed, in a completely operationalist approach, which immersion in process tends to engender, it is difficult to see what the word artifact' could mean. But if we believe there are things out there not immediately evident to us it makes sense to worry about whether or not the configurations we detect accurately reflect the structure of those things. Furthermore, in a formal sense thing-orientation is a richer view of the world than process-orientation, which is in some cases a useful simplification.

A. THE ENTITY We must formally relate the concepts thing', entity' and object'. Object', the richest, implies an observer, maker, or doer (subject) and a thing operated upon (object) (e.g. Reed and lones 1977; Pattee 1978a). It is fundamentally a psychological or experiential concept and has an irreducibly diadic structure— object' makes no sense without subject'. We can by analysis note that it is possible for a subject to turn from one object to another (one diad replaces, and in naturally lived experience may even be transformed into, another). Some of those various objects (material ones) have a thingness about them (to be examined shortly), and so we can for theoretical purposes simplify lived experience by analytically severing the subject-object diad into observer and thing. For purposes of further conceptual manipulation it becomes necessary to make a more formal characterization of thing', and so we define entity' as a representation of 'thing' (this usage is narrower than many philosophers prefer. For them (e.g. Hull 1978, 1980a,b) entity', may accommodate more than just things|. Formal definitions are parts of our construct, Nature; things are, on the other hand, out there, in the unknown wilds. Like most definitions entity' has the logical structure of a class; any thing can be a member of the class

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23

entity', and may be represented as "an entity ". |Some phenomena, however, may not be things—rainbows, for example (von Baeyer 1984).| Thus, objects are experienced, things are believed in, and entities are defined, but the three become interlaced in hectic experience. Yet it becomes necessary for us to define only entity'.

Criteria of Entification On the way to definition, criteria of entification must be discussed, and they are four. 1 Boundaries. Entities are to a significant degree discontinuous with the environment that contains them. The discontinuity may be perceptually as distinct and obvious as a membrane or as subtle as a perceived steepening of a gradient in the values of some measured variable (Allen and Starr 1982). To an important degree the boundary represents what the entity is not, what is excluded; it is a constraint that narrows the possible range of states the bounded system may take; it therefore decreases the entropy of the bounded portion of the world. Note, however, that the observer provides the perception of the boundary and so there is an epistemological dimension to the concept (Simon 1962). Thus, a system separate from its environment may be defined to contain those subsystems that have significant mutual interactions over some specified time period and to exclude those potential subsystems which are only unilaterally connected to those contained in the system over that period of time (Forrester 1969; Varela 1979; Salthe 1983). Boundaries defined this way imply as a consequence that the rates of processes found at different organizational levels will be different—a commonly ascribed trait of hierarchical systems (see chapter 4). The choice of a limited time period of observation is an important epistemological input into the definition of entity'. If we leave the period unspecified, then we can ultimately connect all possible subsystems in the universe via both direct and indirect interactions so that they all become mutually connected

24

T H E I N D I V I D U A L ENTITY

(see figure 2), and, as Quastler (1965) put it, black boxes would become converted to white boxes and we would have one grand single system (Salthe 1983) We might note that there could yet be found discrete subsystems in this conglomerate system, if we work at a given time scale, and that this implies that some kind of boundary still defines them. Ultimately, the least subsystems in a system will be those that appear distinct in our observational field, those that might, for example, have a visual boundary (see the work on the frog's visual perception—Ingle 1976) Quastler (1965) felt that an entity must be a black box and that if we came to know too much about its internal connections, its boundary would tend to disappear. He concluded that a certain amount of ignorance on the part of the observer was requisite for entification. It is just this epistemological boundary that will lead us to identify the least subsystems in some given field. This view of entity boundaries is so general that, even if one chooses to view the world as a field for processes of different frequency, the standing waves or diffraction patterns generated in some environments by mutual reinforcements and cancellations will serve as boundaries for some subject for whom there will then appear to be perceived objects that subsequently can be defined as entities on the belief that they are things. 2. Scale. This criterion does not yet get at the thingness of an entity, but refers to an important relation with other entities that is always present. Entities are heterogeneous with respect to size. A thing cannot be an entity unless it is perceived as bigger or smaller than something else. This point is made in a simple example of visual patterns in figure 3. All the things in both 3.A and 3.B are tetrahedral, but in 3.A they are all the same size and they fade into an overall pattern. In 3.B, however, we can much more easily find the individual tetrahedron than we can in 3.A because of its heterogeneous surroundings. Again, we can examine two lots of sand—beach sand and sharp sand such as is used in construction. Beach sand presents a uniform surface much as does water; individual grains tend to be lost, but we readily pick out small grains from the lot of sharp sand. This important distinction emphasizes that our experience determines what we take to be things, and that when we put scale

T H E INDIVIDUAL ENTITY

25

Connections discriminated ovsr short period of tims Connections discriminated over longer period of time

Connections to rest of world unspecified

Figure 2. If we leave the observation period unspecified, then we would ultimately discriminate all possible subsystems in the universe as being mutually connected. forward as a criterion of entification, we are building into our definition a further self-reference. 3. Integration. In a more direct assault on the problem of what an entity is as opposed to what it is not or to how it relates to

THE INDIVIDUAL ENTITY

26

B

A

Figure 3. A simple example of visual patterns The components of B are more easily discriminated individually.

others it has frequently been claimed (e.g. Engelberg and Boyarsky 1979, Corning 1981) that, if it is at all complex, an entity must be a well-integrated cybernetic system. That is, its subsystems will be c o n n e c t e d by information networks and feedback loops such that they are functionally integrated and more or less interdependent. Given that this system has s o m e kind of boundary making it distinct from its environment (and this is always assumed), it can a p p e a r to be a self-contained whole. We may note that it is usually referred to with a noun, not a verb. Koestler (1978) suggests t h a t such wholes ("holons" in his terminology) tend to be self-assertive. This m e a n s at least that they produce o u t p u t of s o m e kind that may have an effect on their environment. The parts of a system have functions in producing output, which may further suggest that t h e s e systems show "purpose" in t h e s e n s e discussed by Wimsatt (1972). When pres-

THE INDIVIDUAL ENTITY

27

ent, such p u r p o s e would give functional m e a n i n g t o t h e act i v i t i e s of t h e s u b s y s t e m s of a h o l o n . P u r p o s e is for t h e m o s t part a c o n s e q u e n c e o f t h e t h e o r e t i c a l v i e w p o i n t of s o m e o b s e r v e r a n d h a s t h e following synt a c t i c a l s t r u c t u r e : " t h i s s y s t e m b e h a v e s in t h e way it would if it w e r e c o n f o r m i n g t o o u r t h e o r y . " It b e h a v e s " a s if" it w e r e c o n f o r m i n g t o s o m e t h e o r y ( s e e a l s o V a r e l a 1979). T h u s , o r g a n i s m s o f t e n s e e m t o b e h a v e in w a y s t h a t c o n f o r m t o t h e t h e o r e t i c a l n e c e s s i t y of n e o - D a r w i n i s m t h a t t h e y m a x i m i z e t h e i r f i t n e s s . Their " p u r p o s e " in t h i s t h e o r y is t o m a x i m i z e t h e i r n u m b e r of successful offspring. Their parts can then b e s e e n to have t h e f u n c t i o n s t h a t f a c i l i t a t e t h e r e a l i z a t i o n of t h a t p u r p o s e . W e s h a l l b e c o n c e r n e d b e l o w with t h e q u e s t i o n of w h e t h e r all h o l o n s h a v e p u r p o s e s in t h i s s e n s e . T h e a n s w e r will pretty m u c h d e p e n d u p o n w h e t h e r o r n o t w e c a n g e n e r a t e a t h e o r y (as part of an a t t e m p t t o e x p l a i n s o m e e m p i r i c a l o b s e r v a t i o n s ) t h a t will r e q u i r e t h e e n t i t i e s in q u e s t i o n t o s h o w a c e r t a i n b e h a v i o r . It m a y well b e a n t i c i p a t e d t h a t with t h i s a p p r o a c h t o p u r p o s e entities can indeed generally b e found to have purposes. 4. Spatiotemporal continuity. If we o b s e r v e two or m o r e p a r t s of a p r e s u m e d entity, t h e y s h o w m u t u a l i n t e r a c t i o n s a t any given t i m e O b s e r v a t i o n s a t d i f f e r e n t t i m e s will, in a d d i t i o n , d e m o n s t r a t e s i g n i f i c a n t c o r r e l a t i o n s b e t w e e n t h e i r s t a t e s ; t h e y will c o vary t h r o u g h t i m e T h i s is t h e " c o m m o n f a t e " c r i t e r i o n of C a m p bell ( 1 9 5 8 ) , d i s c u s s e d by W i m s a t t in m a n y p l a c e s (e.g. 1 9 8 0 b ) . T h e p a r t s of an e n t i t y will s h a r e a c o m m o n f a t e if t h e y really a r e p a r t s o f o n e a n d t h e s a m e t h i n g . Hull (1975, 1980a, b, 1981) d i s t i n g u i s h e s b e t w e e n t w o c l a s s e s o f e n t i t i e s of i n t e r e s t in e v o l u t i o n a r y s t u d i e s . An e n t i t y in t h e narrow s e n s e is o n e t h a t h a s very l i m i t e d a b i l i t y t o c h a n g e a n d a f i n i t e p e r i o d of e x i s t e n c e . S u c h an e n t i t y c o u l d b e a unit in a s e l e c t i o n p r o c e s s ; e x a m p l e s m i g h t b e o r g a n i s m s o r s p e c i e s . T h e o t h e r sort, t h e " h i s t o r i c a l entity," h a s t h e c a p a b i l i t y of i n d e f i n i t e c h a n g e w h i l e still r e t a i n ing s p a t i o t e m p o r a l c o n t i n u i t y ; an e x a m p l e w o u l d b e a l i n e a g e . T h e t w o a r e h e l d t o b e m u t u a l l y e x c l u s i v e kinds of s p a t i o t e m porally r e s t r i c t e d e n t i t i e s . I w o u l d a r g u e t h a t t h i s d i s t i n c t i o n is t h e r e s u l t of o u r t a k i n g a ( p r a c t i c a l l y n e c e s s a r y ) l o c a l i z e d pers p e c t i v e o n t h e d u r a t i o n o f e n t i t i e s of d i f f e r e n t s c a l e ( s e e c h a p -

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ter 7. under "gene"). Thus, a lineage persists as the species in it replace each other just as an organism persists as the molecules in it replace each other Since we do not know whether a lineage has the kind of seemingly preprogrammed termination that an organism does, and since we can observe organisms, but not lineages, being replaced as such in a succession of them, the distinction may be a useful one. For the present I will note that entity' as here defined both changes and endures for some period of t i m e and so all members of this class are historical entities in a general sense. There may, however, arise problems in this context concerning some of the entities we will be concerned with below. Do all parts of an entity have to co-vary? If not, what p r o p o r t i o n or which ones? Are some parts dispensible or may we allow for significant transformation of some of them and still have the same entity? Given an historical entity, some parts must be changing through time—at least as a consequence of thermodynamic considerations In that particular context we can at least stipulate what sorts of general changes will be allowable w i t h i n a given system because they are predicted from theory. Spatiotemporal continuity is our stability criterion. Some entities may well be unchangeable in time, but most will become altered. Yet the latter may show stabilities of one kind or another. Thus, entities that are open systems will of necessity show certain characteristic trajectories of change as they proceed from immature to mature stages of development (Margalef 1968; Zotin 1972; Wesley 1974). They will come to acquire more stored information, they will acquire this information at a slower and slower rate, and they will change from one moment to another at a slower and slower pace, or, they will come to be more internally stable. The acquisition of increased internal stability (a kind of measure of negentropy) will mean that constitutive changes in the system will slow down On the other hand the stability of these systems to environmental perturbations (May 1973) will become less and less as they become more mature (they senesce). Now, given that we can predict these directions of change, any spatiotemporally connected system that shows them may be held to be stable. It is in this broad sense (of Lyapunov stability) that entities are stable—either

THE INDIVIDUAL ENTITY

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they do not change at all or they change in prescribed (constitutive change) or predicted ways.

Definition of Entity Hence, we can arrive at a definition of "entity" useful for the material world. An entity is something of a given size distinct from its surroundings which, if more or less complicated, is a cybernetic system some parts of which, if it seems to us to have detectable duration, co-vary in time. The definition carries with it, as do all definitions, various problems, some of which (how much and what patterns of internal change may be allowed) have already been alluded to. Another problem is that of artifactual reification (Lumsden and Wilson 1981). Particularly in those cases without clear boundaries obvious to our senses (e.g. subspecies), how do we know we have detected a real entity by means of the steepening of gradients in some measured variables? Essentially we are driven here to a single defense of our discovery—we must show that when we measure yet other variables, or when we manipulate the data using other values for parameters in our system, we come up with discontinuities that map to essentially the same region of (geographic or phase) space. This is Wimsatt's principle of robustness (Levins 1966; Wimsatt 1980b) discussed in the introduction. Another problem arises in the context of scale. Since the definition refers to complexity and to duration in time, will it not be the case that at some small scale we might no longer be able to carry out the requisite observations, and will not that lead us, as it did Bunge (1979), to postulate the existence of fundamental particles? Or, for that matter, as things keep getting bigger do we not ultimately come upon (in thought experiments) the total universe? Later in this work 1 will argue against these concepts, which might, on the face of this definition, seem to be not unreasonable. The possibility of reaching these concepts from this definition leaves me unsatisfied with it. I would not like to restrict the entity concept to only those things so near us in scale that we can make empirical observations on them.

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Let us note finally that, using this definition, we could find entities using the techniques of those who prefer not to use "the language of entities" like Allen and Starr (1982) or Levandowsky and White (1977). Thus, for example, waves come in different sizes; wave fronts are boundaries; waves have a dynamic cohesiveness such that it would not be out of place to consider them systems, perhaps cybernetic; and the different parts of waves certainly covary in time. Using the above definition, I would assay to include at least some wave patterns, field and frequency phenomena in the class entity'.

B. THE INDIVIDUAL

How do boundaries arise? Given some entification process, may it not continue to operate in such a way that boundaries might shift somewhat so that different subsystems may move over time from one supersystem to another? Wherever such a process is significant, the individuality of the entities becomes compromised. This hinges on the definition of "individual," which will be taken up now.

Entification

A boundary is a fact, not a datum (Kvale, 1976), that is, it is a product of the interaction of an observer with the world and cannot be held to unconditionally exist. So, as pointed out by Russell (1903), Wimsatt (1974) and Allen and Starr (1982), a whole may be divided up in many different ways depending upon the observational context alone. If this epistemological constraint were the whole story we might (Russell) or might not (Allen & Starr) worry about the consequences. But, if the entification process per se may continue to shift boundaries regardless of observational perspectives, we have before us a genuine physical problem in the traditional sense. We know for example that eddies in the North Atlantic (Kerr 1981) may come

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to be captured by the Gulf Stream, where they are d u b b e d "cold core rings" (The R i n g G r o u p 1981), a n d are now parts of a different supersystem. C h r o m o s o m a l entities may c o m e to reside in different s u p e r s y s t e m s by way of sexual recombination. Cellular slime m o l d a m o e b a e live a l o n e for a time a n d then join others a n d s u b s e q u e n t l y differentiate a s parts of a larger system ( B o n ner 1952, 1974). M e m b e r s (really parts) of a c o m m u n i t y of birds breeding in Baffinland will migrate to different wintering g r o u n d s where they will b e c o m e parts of quite different c o m m u nities. In all these c a s e s we discern several entities with parts, but the individuality of these entities s e e m s uncertain.

Individuality The individuality of an entity resides in two q u a l i t i e s — i t s indivisibility (or continuity) (Quastler 1965; Buchler 1966) a n d its separate identity (or particularity) (Hull 1975). In the examples just given, the Baffinland c o m m u n i t i e s a n d the g e n o m e s of sexual o r g a n i s m s , while easily qualifying as entities with separate identities (they could, for example, be given proper names), appear o d d from the point of view of the continuity criterion. They c o m e apart; their s u b u n i t s d i s b a n d a n d reform elsewhere with other s u c h units that hail from other places. The cellular slime m o l d a m o e b a e a n d the oceanic eddies, while being entities that display g o o d e n o u g h continuity, seem o d d because they tend to lose their separate identities a n d to become lost a m o n g others of similar kind by b e i n g s u b m e r g e d into a larger clearly identifiable entity, which in o n e case itself bears a proper name. They are not then s o easily told apart as they were before; one c o u l d more easily c o n f u s e t h e m with other entities. Let me try to make this distinction between entity' a n d 'individual' with another example: H o k u s a i ' s well-known image "The Great Wave Off Kanagawa" s t a n d s out as an individual entity of a nonmaterial kind in our collective c o n s c i o u s n e s s or mind. Each p e r s o n ' s recollection of it a n d their a s s o c i a t e d e m o t i o n a l reactions to it are probably slightly different, but it retains its typical individuality throughout these transformations. Now, let u s examine two se-

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ries of copies of this print, one series being actual woodblock prints made in nineteenth-century lapan, and the other a series of modern four-color prints run off in one day in a particular printing establishment and subjected to subsequent quality control The modern prints are all exceedingly alike and it would be difficult to tell them apart. Each is an entity and could enter into a separate historical career, but they lack the particularity of form of individuals. On the other hand, each of the woodblock prints are distinct. Each one has its own separate identity, and could even come to be known by a proper name They were the products of blocks cut by different persons at different times and they have all the irregularity of any "hand-made" item even when taken from the same blocks. These are individual tokens of an individual type, something like the performance of a play, each of which is always to some degree individual. From this discussion we derive that not all entities are individuals. But if, as I have indicated above, I am taking all entities to be historical entities (Hull 1975)—that is, I have narrowed the definition of entity—then this conclusion is in fact not warranted Each of the almost identical four-color prints of the Great Wave may have a distinct subsequent historical career, which may well mark it in some way. A clearer example here would be used postage stamps, each identical, but each cancelled in a different way; these, too, may even come to be given individual proper names. I am in fact proposing that for our purposes material entities are all to be taken as historical entities. But, does this mean they are endowed with physical indivisibility? If they may come to an end, yes. Thus, the breeding bird communities reconstituted in Baffinland each summer are each separate, new, individual entities They are entities that last for rather short periods of time, and so are the individual genomes of successful gametes. Hence, for the purposes of a theory of material evolution, I propose that all relevant entities are historical entities and individuals. This means that, as Hull (1975) noted, a single atom of gold could theoretically be treated as an individual entity. Anything bearing the four criteria of entification that I have proposed above (boundaries, scale, integration, and spatiotemporal continuity) will also show the two criteria of individuality

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(indivisibility and particularity) This is a consequence of the entification criteria themselves, as given. Given boundaries and integration, indivisibility appears when we bring in the concept of the proper name. Given spatiotemporal continuity, the proper name becomes a reasonable concept. Notice that, although it has tended to become lost in a crowd of similar entities, the individual cellular slime mold amoeba can be followed as an individual entity if one makes an effort to do so, by marking it before the aggregation phase. Subunits (subsystems, compartments, components, parts) are still individuals—individual holons. They are themselves composed of further subsystems and, furthermore, the supersystem they are part of is part of yet larger individuals. Of course, the particular individuality of given waves, electrons, liver cells, and others of this sort is in most contexts a dormant possibility. These can be taken to be individuals as the problem requires; that is all we need to have established here.

C. UNIQUENESS

An individual (even an event for that matter) may be taken to be a unique configuration if there is reason to believe that its development could occur only once in the history of the world. The word development' here subsumes, e.g., the ontogeny of an organism, the (possibly perturbed) trajectory of an historical entity or event, the changing relationships between members of a culture and some planet (Morning Star, Evening Star, Venus), or even a sequence emitted by a Markov source if it is "ergodic" in the sense of Gatlin (1972). The phrase "occur only once" subsumes low-probability events as well as absolute impossibility Now, in the strong sense we can never know whether or not an individual is unique because the answer to that question depends on whether the world (or the applicable universe) is infinite or not. If it is, then no individual can be unique because all configurations will occur infinitely many times, as will an infinite number of variations on each configuration. If we are

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discussing the material world, on today's cosmogony (e.g. Silk 1980) the universe is finite. In a finite world containing a finite number of things the probability of uniqueness increases with the evident complexity of the phenomenon. Electrons may be individuals but we certainly do not think of them as unique because we suppose that they are less complex than, say an ecosystem. Reasoning this way, Smuts (1926) suggested that ecosystems might have more individuality than would electrons while Koestler (1978) suggested they would be more flexible, with more degrees of freedom. As I will develop hierarchical theory below, this would be a false conclusion in part because it reifies the properties of limited observers. No observer can (1) range over unlimited numbers of levels so as to objectively compare the complexity of different scaled things, and (2) remember more than a limited amount of information or acquire more than a limited number of different kinds of information (Landsberg 1972; Watanabe 1972). Here, I will follow Buchler (1966), who postulates that no natural complex (anything discriminated in any way) can be more complex than any other in and of itself. Applied to the material world the import of this is that even quarks must be taken to be as complex as ecosystems (see Salam 1980; Harari 1983) Assuming then, that small-scale phenomena are as complex as large-scale ones (in the present context this implies an indefinite number of things in the world), there is a high probability that all individual phenomena are each in some way unique. An indefinite number of things can exist in a finite world if the things are nested within each other and the world is expanding. Hence, we may take the individual entities dealt with in this work to be unique. In Buchler (1966) the "contour" of a natural complex is unique. This is the totality of all relations (including being observed) that a complex can and does enter into. We should not, however, overlook the evident fact that we do distinguish different degrees of complexity in the world of practical affairs. The least apparently complex things are gathered into classes (natural kinds)—electrons, gold, etc. Somewhat more complex as they appear to us are species of living things We easily distinguish lions from tigers from jaguars, and so forth; but, without intensive training, every tiger is

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pretty much like the rest. In contrast, individual dogs and other organisms that live intimately with man b e c o m e familiar enough to a s s u m e separate identities. Individual people, of course, readily a s s u m e the quality of persons, and are felt to have a self, more so if they are m e m b e r s of our own social group. S o there is a whole gradation of uniqueness, beginning at persons and diminishing to a grain of salt. This will b e seen in this work to b e a c o n s e q u e n c e of t h e fact that we exist at a specific location in a natural hierarchy of entities—thus natural kinds are a kind of homocentric artifact. While I postulate that all physical entities at all scalar levels are essentially the same kinds of things, the fact that they do not s e e m to b e so to us must be incorporated into our work. When we look in the other direction, at entities of larger scale than ourselves, we have usually treated them as places transitively located inside each other—there is a pond in New York, that pond is in North America, and it is in the "New World," and it is on Earth. This t o o will be found to be artifactual on our finite locatedness, and yet will have to be taken account of.

Nomothetic Versus Idiographic We have arrived at a view of the world as being composed of arrangements of an endless series of unique individual entities of different degrees of evanescence associated with their size or scale. We must now reflect on how this picture jibes with the traditional scientific view of nature as a field for the activity of natural laws (the nomothetic viewpoint). Now, laws are simply observational regularities discovered by comparing measurements taken in the world (Campbell 1921). Obviously, such measurements cannot b e taken from unique properties or they would not show regularities. As we examine the things in the world we find that we are more impressed by the similarities they have than by their differences. No matter how unique they are, they occur in clusters of similarity and in clusters of clusters, making possible taxonomic classifications. We can gather individual entities into c l a s s e s of greater or lesser scope. The definitions of t h e s e classes refer to t h o s e characteristics (char-

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acters, t r a i t s ) t h a t a r e n o t u n i q u e a m o n g t h e i n d i v i d u a l

mem-

bers. W e m a y p a u s e t o n o t e t h a t m y d e f i n i t i o n of e n t i t y ' g i v e n a b o v e r e f e r s t o a c l a s s — t h e c l a s s of all m a t e r i a l c o n f i g u r a t i o n s ( t h i n g s ) of i n t e r e s t t o d i a c h r o n i c s c i e n c e . O n e of t h e characteristics of t h e m e m b e r s of t h i s c l a s s that I h a v e c l a i m e d is that in s o m e w a y o r o t h e r e a c h is s o m e w h a t d i f f e r e n t f r o m all t h e o t h ers, o r h a s u n i q u e p r o p e r t i e s ; a n d t h e r e f o r e this c l a s s is n o t c a p a b l e of e x t e n s i o n a l d e f i n i t i o n ( R u s s e l l 1 9 0 3 ) — t h a t is, o n e c o u l d n o t n a m e t h e m e m b e r s o n e b y o n e a n d t h u s b u i l d up t h e class; it is a p u r e l y i n t e n s i o n a l l y d e f i n e d class. A r e p r e s e n t a t i o n of e v e r y t h i n g in t h e w o r l d b e l o n g s in t h i s class, but n o t t h e c l a s s itself (it is n o t a m e m b e r of i t s e l f ) b e c a u s e a c l a s s is n o t a thing. N o w , f r o m t h i s c l a s s w e m a y t a k e s u b s e t s — a l l a p p l e s , all r a b b i t s of p o p u l a t i o n X in l o c a l i t y Y, all s p e c i e s of t r i l o b i t e s — a n d m a k i n g t h o s e d e s c r i p t i o n s o f t h e s u b s e t s f i x e s s o m e traits that are h e l d in c o m m o n , a n d w h i c h , t h e r e f o r e , can b e m e a s u r e d and c o m p a r e d . T h e u n i q u e a s p e c t s o f e a c h m e m b e r a r e i g n o r e d in t h i s t r e a t m e n t ; o n l y w h a t t h e y s h a r e in c o m m o n is t r e a t e d t o o b s e r v a t i o n f o r t h e p u r p o s e s of c o n s t r u c t i n g ( o r

discovering)

s c i e n t i f i c laws. T h e s c i e n c e of c l a d i s t i c s ( N e l s o n a n d Platnick 1981), s t a r t i n g w i t h a r o u g h l y d e f i n e d s e t of t h i n g s (e.g. all s p e c i e s of t r i l o b i t e s ) u s e s e x p l i c i t t e c h n i q u e s f o r t e a s i n g it apart i n t o s u b s e t s such t h a t t h e s m a l l e s t s u b s e t s a r e d e f i n e d by s o m e u n i q u e c o n f i g u r a t i o n of traits. A s i d e f r o m this, s c i e n c e is chara c t e r i s t i c a l l y u n c o n c e r n e d w i t h u n i q u e n e s s . Thus, if w e are m e a suring r a b b i t s ' ears, w e d e f i n e s o m e v a r i a b l e (e.g. l e n g t h ) which it is p o s s i b l e t o f i n d o n e v e r y ear, t a k e t h e m e a s u r e m e n t s , a n d i g n o r e t h e p r o b a b l e f a c t t h a t e a c h e a r is in s o m e w a y unique. Now, scientific laws are thus described on groups while s t u d i o u s l y i g n o r i n g u n i q u e n e s s , y e t t h e hierarchy of n a t u r e is a r e p r e s e n t a t i o n of a w o r l d of u n i q u e i n d i v i d u a l t h i n g s (it is an idiographic i m a g e ) . T h e s e u n i q u e properties, and o t h e r essentially u n i q u e c o n f i g u r a t i o n s of e v e n t s , h a v e an i m p o r t a n t r o l e t o p l a y in s c i e n c e , a n d that is t o s u p p l y t h e c o n s t r a i n t s within which t h e l a w s of n a t u r e m u s t o p e r a t e ( W i g n e r 1964; P a t t e e 1977). M u c h of t h e p o i n t o f t h i s c h a p t e r f i n d s f o c u s in this statement. W e n e e d a f o r m a l i s m , or e v e n a science, t o discover the rules, of constraint. I a m p r o p o s i n g that the hierarchy of nature

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may serve as a theoretical framework for the idiographic viewpoint which, in the past, has not had any at all and has been presented more or less as one damn thing after another, one ad hoc objection after another, one fact after another brought up to crush some theory. Hierarchical structuralism will be a theory of differences not of similarities; it will be fundamentally qualitative, not quantitative. And its role will be to complement the nomothetic perspective (for example by enhancing our ability to detect classes of historical events) in ways that will become clear below.

Some Basics of Hierarchical Structure A. COMPLEXITY B. S C A L E A N D POLARITY

41 47

Scale

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Truncation

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Asymmetry

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Polarity and R e c u r s i o n

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C. L E V E L S A N D RANK

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Self Similarity The O r i g i n of D i s c o n t i n u i t i e s Between Levels

D. N E S T I N G — W H O L E S A N D PARTS Branching Hierarchies

58 58

61 61

W

E will see that physical complexity has been defined as characterizing a situation where contiguous entities cannot interact dynamically and are restricted to constraint transactions with each other. This is then found to be the case when entities of different scale impinge upon each other. Thus, the qualitative difference between constraint and dynamic interaction is a result of quantitative differences. However, the presence of scalar differences is seen to follow from the qualitative fact of the fixed position of an observer (or any process) at a given scale. We will further find that a hierarchy of entities of different scale has polar structure so that all transactions between differently scaled individuals will be asymmetrical—this will be seen to interdict recursive transactions between levels. Such a hierarchy can be represented as a row of ranked organizational levels. It is widely held today that hierarchical structure (see figure 1 for some simple visual images) is a consequence of the "complexity" of a system. This being held to be so, we should examine this idea of complexity.

A. COMPLEXITY Complexity certainly involves the notion of many things jumbled together or strung out in time. But if the things, no matter how many, are all alike somehow complexity tends to be lost (see figure 3) The Markov source becomes a source only of boredom if it continually emits the same signal at unvarying intervals. This much is intuitively clear. Buchler (1966) has made the most general discussion of complexity available (or perhaps even possible). For Buchler, complexity is a result of multiple relatedness among phenomena. This entails, for example, Wimsatt's (1974) "descriptive complexity" (which results from observers with different perspectives decomposing a system into subsystems differently) and also his "interactional complexity" (which is the case when the resulting parts are seen to interact directly with, say, parts

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of parts of parts as well as with other parts). As an example of descriptive complexity we can recall Neils Bohr's discussions of light as being capable of being viewed as a wave phenomenon in the context of one experimental design and as a particulate phenomenon under other experimental setups. Buchler's concept of complexity includes, importantly, possibilities as well as actualities. Not everything is possible given the structure of a situation or system, but many things and events that do not occur (or occur very infrequently) nevertheless might occur in any given situation and must be included among the traits of what Buchler calls a "natural complex." |. L. Lemke (personal communication) has suggested that such possibilities be viewed as constituting a "metasystem" which is necessarily associated with any material "supersystem." The world inclusive of possibilities is conceptually larger than, and so beyond (meta), the mere actual physical world, which can be designated a supersystem because all known entities are subsystems of it. Since all phenomena, and all possible phenomena, have multiple possible relations, including those with different observers, the world is ontologically densely, or indefinitely, complex—in fact so much so that Buchler provides a problematical base ("complexes of complexes") for scientific work without introducing constraints capable of simplifying the field somewhat (focusing upon particular material orders) so as to give us room for praxis But we should note the important contributions of Buchler's thinking about complexity that must serve as starting points: (1) Complexity is a concept concerning relationships. 1 will restrict consideration to relationships between physical things (some of which make observations) that are larger or smaller than, or dominant or subordinate to, or of the same or different scale as, other material things. (2) The notion of possibility is absolutely essential in dealing with systems that will provide output, that will produce events in the material world. 1 will try to relate an observer to the system to be described, thereby both defining and restricting the possibilities. Pattee le g. 1970, 1972, 1973, 1977, 1978b, 1979; see also Teggart 1925 and Wright 1964, as interesting forerunners) has developed a compatible but more materially restricted view,

BASICS OF HIERARCHICAL STRUCTURE

43

such that complexity is viewed a s a result of interactions between physical and symbolic s y s t e m s (i.e. between qualitatively different kinds of p h e n o m e n a ) . A physical s y s t e m is o n e characterized a s being d e p e n d e n t upon t h e rates at which p r o c e s s e s occur. Its rules (natural laws) are often of t h e form dY/dt. Symbolic systems, on t h e o t h e r hand, are r a t e - i n d e p e n d e n t and frequently serve a s c o n s t r a i n t s within which physical s y s t e m s operate (parameters with c o n s t a n t or o t h e r values; Pattee 1977). Indeed, symbolic s y s t e m s are characteristically a m o n g the products of t h e activity of physical s y s t e m s ( P a t t e e 1973; s e e c h a p t e r 4) An example will make t h e s e ideas clearer. Consider a living cell and its g e n o m e . The cell is a physical system operating within o t h e r physical s y s t e m s (say, a pond). The g e n o m e (the symbolic system) is part of this cellular physical system but its p r e s e n c e serves t o constrain that system t o certain characteristic a v e n u e s of o n t o g e n e t i c and h o m e o s t a t i c behavior such t h a t t h e c e l l ' s form is a l s o c o n s t r a i n e d . This it can do b e c a u s e it c o n t a i n s s t o r e d information toward which t h e cell behaves in a way c o n s t r u a b l e "as if" t h e cell regards it as m e a n ingful. Information is p o s s i b l e in t h e g e n o m e b e c a u s e it is c o m posed of a long linear array of a limited n u m b e r of kinds of units whose s e q u e n c e c a n n o t b e regulated or d e t e r m i n e d by any physical p r o c e s s a s such (Gatlin 1972). It can therefore physically exist (or b e s t a b l e ) in a large n u m b e r of different forms (permutations, in fact) in any given environment; that is, it has a large entropy value | = information carrying capacity if each (or many) of the configurations were t o b e taken a s having a different meaning for s o m e system]. S i n c e t h e n u m b e r of strands of such units that can fit into any o n e cell are quite limited, only a few versions of t h e string of units can b e present at any t i m e and therefore each cell can c o m e t o contain different information. Given that a particular idiosyncratic s e q u e n c e is characteristic of a cell, that s e q u e n c e would have t o b e stipulated in any description of that cell. The n u m b e r of sufficient s t a t e m e n t s it takes t o d e s c r i b e a system is a rough m e a s u r e of the a m o u n t of its stored information. Each cell, then, not only has (potentially) a large information-carrying capacity t o t h e d e g r e e that e a c h unit in its g e n o m e might have been replaced by o t h e r s of a different kind, but it

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also has (actually) a large amount of stored information because at any given moment it contains only one (or a few) of the large number of possible genome sequences and phenotypic forms reflecting these sequence. Now, if the sequence carries meaning for the cell, it can serve as a constraint on that cell's behavior. In order for meaning to be extracted from the genomic string the cell must have a particular form so that its processes (metabolic and synthetic) can be receptive to guidance by the messages in the genomic sequence (Commoner 1968; Weiss 1969, 1971, 1973; Atlan 1981; Hubbard 1982; Campbell 1982). The cell's form is partly a result of prior guidance of its ancestors' processes by similar information, and partly a result of regulation by the larger environment (the pond). The requirements of this regulation have to some extent become incorporated (by natural selection) into the information in the genome as well because, in the past, some sequences that would have produced perfectly adequate cells in some environment could not in fact do so in the particular ponds that were the ancestral environments. This means that the genome can be interpreted as a representation of the requirements of the cell in a given environment (Pattee 1972, 1977) or, even as a representation of the environment itself inside the cell (Dawkins 1982). In this way of looking at things a part of a physical system can be seen to work as a representation of other parts for a still further, third, part. That is, a portion of a physical system, particularly if it has certain properties like a large informational entropy potential, can function symbolically for some other portion (Roitblat 1982) When that is possible in a physical system, the system can be described as being complex in the sense of that concept commonly associated with hierarchical structure. This notion of complexity is consistent with the principles to be derived from Buchler's work; it concerns relations between (qualitatively different kinds of) entities, and some of the possibilities of the system take the form of informational entropy. The idea of an observer is built into the complex system because that portion of the system which contains a representation of any portion of the system functions as an observer in a generalized sense.

BASICS OF HIERARCHICAL STRUCTURE

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Pattee developed this view of complexity in the context of considering hierarchical systems. It is therefore not surprising that, even though it is probably more widely applicable, it can be developed further in the context of the concept of scale. Note that, if a portion of a system (scale has already been introduced) has an internal representation of a portion of the system, we already have entities at three levels nested one within the other. A physical system is making its way as a part within a larger physical system using a smaller physical system (one of its parts) as a guide through, or map of, some portion(s) of the larger system (Roitblat 1982). The genome is the cell's guide through the pond. A molecular system is being used by a cellular system to negotiate an ecosystem. The molecular system has the requisite informational entropy from the point of view of the cell so that it can store information about the environment-cell interaction. Viewed by an outside observer (the scientist) this situation can be made explicit as three levels, each of which has an "alternative description" (Pattee 1970, 1972). The molecular level can be taken as a field of collisional energy-transferring activity of the molecules themselves or it can be alternatively described in terms of the kinds of effects aggregated molecular activity has on the cellular level as if it were being felt by the cell as a flow of foodstuffs, deformations of its liquid crystalline compartments, changes in pH, accumulation of waste products, and so on. Cellular activity in the pond can be described either in terms of escape from crowding, seeking mates, etc. or as changes in the density of cells or their products in various portions of the pond. These alternative descriptions are alternative representations for us observers in either a microsystemic style at the level in focus or in a macrosystemic style from the next higher level, the one being appropriate for some purposes, the other for others. The summed aggregate activity of the cells in the pond could function as information in some process in which the pond is participating, but in which the cells themselves, as individuals, would not be involved. We have arrived at what Pattee (1970) calls a "descriptive hierarchy," and we see that it is characterized by Wimsatt's (1974) "descriptive complexity" (see above). We

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will be concerned later with questions which rather obviously follow—such as, is the activity of individual cells in some way used" by the population as a representation of the pond? Is there some sense in which that is a reasonable question? (See chapter 8). Is Pattee's formulation generalizable across levels or was it simply a good metaphor based on familiar events at certain specific levels? In any case, Pattee's work is one way of deriving a connection between the illimitable general complexity of Buchler and the current notion that somehow hierarchical sytems are necessarily connected to a concept of physical complexity. Are kinds of complex systems other than hierarchical ones possible? Simon (1962) has suggested that in the actual world there could not be: "Among possible complex forms hierarchies are the ones that have time to evolve." In other words, only hierarchically organized systems have the property of being stable because they can be built up by stages which are themselves stable (see also Levandowsky and White 1977) Thus, "two watchmakers assemble fine watches, each containing ten thousand parts. Each watchmaker is interrupted frequently to answer the phone. The first has organized his total assembly operation into a sequence of subassemblies; each subassembly is a stable arrangement of 100 elements, and each watch, a stable arrangement of 100 subassemblies. The second watchmaker has developed no such organization. The average interval between phone interruptions is a time long enough to assemble abut 150 elements. An interruption causes any set of elements that does not yet form a stable system to fall apart completely By the time he has answered about eleven phone calls, the first watchmaker will usually have finished assembling a watch. The second watchmaker will almost never succeed in assembling o n e — h e will suffer the fate of Sysyphus. as he rolls the rock up the hill, it will roll down again" (Simon 1973). Quoting Dawkins (1976b), "hierarchical organization provides a way of making complexity manageable". Hence, the connection between complexity (the contiguity of entities of different scale) and hierarchies, which, if sound, allows many other possible definitions of physical complexity. For example one that will become clearer in chapter 4: a system is complex if there can be entities located in the same place that nevertheless do not dynamically directly interact.

BASICS OF HIERARCHICAL STRUCTURE

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B. SCALE AND POLARITY

Scale We have seen that current interpretations of complexity tend to lead into matters of scale. Scale alone will be considered here as the fundamental determinant of hierarchical structure. Scale differences in a dynamical system give rise to complexity because processes at different levels will not be able to interact dynamically and will be restricted to the mutual provision of informational constraints (see chapter 4). But bald quantity is not here giving rise by itself to quality; note that the utilization of informational constraint requires a process (possibly observation) that remains fixed in scale. Following Mandelbrot (1977) we might get into the idea of scale by considering maps. Maps can be drawn to different scales, arbitrarily chosen. A large-scale map might show all of North America. If we look at the contours on the map and devise some way of measuring the density of embayments and peninsulas, or the changes in direction of the line, on the basis of some per unit area of the map, we will derive a number representing the complicatedness of the line. If we now decrease the scale of the map, so that we have only the New England coastline showing on a map of the same size, we can again measure the complicatedness of the shoreline, and we will find it to be roughly the same. Narrowing in on Massachusetts, we find its coastline just as complicated on the same per unit area of the map surface. The same for Cape Cod. If we actually walk some length of beach and map its shoreline in detail, that too will show the same complicatedness of line if it were projected onto a map of the same size. If we focus down on a few inches (we might need to make a statistical sample here) we will get the same result as our pencil traces grains of sand and lumps of shell. We could keep going with magnifying glasses and microscopes and find that outlines remain about as complicated as they were at first given that our window is a map drawn on a sheet of paper of the same size in each case. Complexity does not seem to change as we change scale. Things do not get simpler just because they are bigger or smaller. However, note that

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in this example we imposed an epistemological c o n s t r a i n t — t o use, as our unit of measurement, the s a m e area of m a p paper on a m a p of t h e s a m e size. If instead we were to c h o o s e as our unit to m e a s u r e line complication s o m e area such a s 50 miles square as it relates separately t o the scale of each map. then t h e coastline of North America would a p p e a r very simple while a length of beach that we m a p p e d would be much more complicated. In this case we are locating ourselves at a particular scale and not changing our scale a s we examine different scaled m a p s of t h e s a m e size. In t h e first case what we were doing was changing our own observational scale each time we changed t h e scale of the map. This can be done, of course, only in theory, which is all right since maps are theoretical kinds of things. So are levels of organization. As we discuss levels here in purely theoretical ways, we will d o t h e equivalent of changing our scale as we c h a n g e the scale of t h e observed level (we will b e c o m e omnipresent observers) but we will always try to keep in mind t h a t this is what we are doing, and at certain points, we will switch to the other mode, mimicking our actual physical constraints, b e c a u s e it is in this m o d e that we actually engage in process, d o experim e n t s and make empirical observations—processes t h a t Maritain (1951) has declared to be the proper subject matter of natural philosophy. In this m a p example we could have m a d e a m a p at any arbitrarily chosen scale and so, in the first, omnipresent, mode, we could conclude that there do not a p p e a r t o be natural discontinuities in t h e complexity of the world. That is, for an omnipresent observer not only is t h e complexity of t h e world the s a m e at all scales (a local exemplification of Buchler's principle of ontological parity—Singer 1976), but scale can be changed in continual gradations without ever meeting discontinuities. This is not t h e case with an observer of fixed scale. A commonly discussed example (see Mandelbrot 1977) is the physical observation that as t h e size of the observational field increases the average density of matter (taken as measured at a fixed scale) gets less and less. Thus, on t h e earth we get a certain value. As we include t h e whole solar system, the value diminishes. As we include t h e whole galaxy, it drops again. Note that t h e scale of what is taken to be "matter" d o e s not change with t h e scale here,

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while more and more of what we perceive to be space is added to the observation field. Of importance for the present context, there are drastic discontinuities in these values of the average density of matter as we jump from smaller to larger clusters of bodies. These discontinuities depend upon the measurement remaining at a fixed scale—that is, they are dependent upon the perspective of the observer. These discontinuities are crucial for the ontology of entities (see chapter 2) yet they are the result of epistemologica! constraint. But this constraint appears precisely because, as entities, we are finitely located and bounded. It takes an entity to find one.

Truncation

Formally, the increase or diminution of scale may continue endlessly. At least that is the most parsimonious way of dealing with the question of limits. And that is the way perhaps most workers who have dealt with this problem have viewed it (Needham 1936; Gerard 1958; Bateson I960; implication in Buchler 1966) Hence, no new principle need be brought forth to truncate the hierarchy, as attempted, for example, by Bunge (1979). 1 will take the truncation of the natural hierarchy to be a practical consequence of our finite locatedness at a given scalar level We cannot penetrate with our probes much beyond "fundamental particles" or the physicist's "universe"; and our conception of entities at the more remote levels that we can barely attain is probably distorted in the extreme from what would be the point of view of an observer that could change its scale, if there could be such a thing.

Asymmetry

Piaget (1971) and Wilden (1972) pointed out that hierarchies of scale referring to the physical world that one meets with in the literature are of two kinds—hierarchies of composition such as we have been concerned with so far, and hierarchies of logical type (Russell 1903). The latter are concerned with the generality

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or scope of the statements one can make at the different levels of reference Thus, statements of physics referring to the properties of matter, since they continue to be true whether one is discussing biological or sociological phenomena, are of the greatest generality and are therefore found at a higher level than are biological statements, while the latter are more general than sociological statements (given that social entities are also organisms) and are consequently located at a higher level than are sociological statements. The reason for bringing this up here is that this hierarchy of generality of statements has the opposite directionality than does the compositional hierarchy of parts and wholes. What is at a higher level in the one system is at a lower level in the other, and this tension between the two emphasizes the crucial asymmetry of hierarchical phenomena In chapter 6 these considerations will be taken up again and transformed.

Polarity and Recursion Given that each succeeding level encompasses the one below it in a hierarchical structure, any system s o structured (e.g. the physical or material world)) will have an irreducible polarity (Conrad, 1972; Bunge, 1979). For an observer located somewhere within the structure, phenomena existing at higher levels than himself will appear to be radically different in kind from those existing at lower levels. To make this observation more formal (though less dramatic), s u p p o s e we have a mathematical description of some portion of such a system, y = ax. If the parameter a derives from lower level phenomena, it will be a statistical summary such as a mean value. If, on the contrary, it derives from higher level phenomena, it will be represented by a true constant (Pattee 1973; Patten 1975; Levandowsky and White 1977; Allen and Starr 1982; Muir 1982). To be sure, its effect on the solution of the equation will be the same in either case (it is simply a stable valued parameter) but the meaning of the equation is radically different in the two cases, as will be its derivation. The interesting case of more complex equations, with

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parameters from both upper and lower levels, will be taken up in chapter 4. The polarity of the hierarchical system is such that recursion of effects across more than one level is formally forbidden. Nowhere does the structure fold back on itself so that a higher level entity finds itself within a lower level entity (Dawkins 1976b; see Hofstadter 1979 for a good discussion of what this means). This circumstance will be discussed at length in chapter 5 Here I will simply point out that in the practical world of noisily fluctuating phenomena this pristinely beautiful interdiction is frequently, though episodically violated. This fact may have interesting permanent results of the kind discussed by Prigogine (1980), but one must be aware that these represent only historical accidents (like the origin of life, say) even though they may be of some consequence to us. The fact of such fluctuations must be kept in proper theoretical perspective. It frequently is not. For example, Lumsden and Wilson (1981), in their discussion of the molecular, cellular, organismic, and population levels, have effects moving up through the levels (in good reductionist style) and then, finally, have the population level giving a direct effect back down to the molecular. This is not stated as an occasional but interesting fluctuation; it is given as the basic structure of the system. Preparing the reader for this move, they claim that natural systems are not hierarchies but "heterarchies" (the "mixed hierarchies" of Woodger 1929), by which they signify that anything goes in terms of transactions between levels, the condition labeled "interactional complexity" by Wimsatt (1974). My point here is that interactional complexity, no matter what the practical importance to us of its occasional occurrence, must be something that is treated gingerly in a hierarchical context because the result of its unbridled occurrence is to destroy the hierarchical structure itself (Wimsatt 1974) It simply cannot be the rule if the world is hierarchically structured as it appears to be and as I will assume in this work that it is. Thus, there can be no consistent direct effect of the population of organisms on the genes of its members (really parts), or of the genes on the population of the organisms within which they exist Most treatments of these relationships

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a r e m e t a p h o r i c a l in t h e e x t r e m e , for e x a m p l e , a s in p o p u l a t i o n g e n e t i c s . We m u s t try t o s e e exactly how t h a t m e t a p h o r is c o n s t r u c t e d in a l a t e r c h a p t e r . A r e l a t e d p r o b l e m is r a i s e d by B u c h l e r ' s ( 1 9 6 6 ) e x a m p l e of t h e citizen. B u c h l e r h a s an a l m o s t t o t a l l y u n r e s t r a i n e d view of r e l a t i o n s h i p s t h a t b o r d e r s on c h a o s . Any n a t u r a l c o m p l e x is viewed a s having " t r a i t s , " which may b e parts, a t t r i b u t e s , c o n s e q u e n c e s , p o s s i b i l i t i e s , e t c . Thus, a s a c i t i z e n a p e r s o n m a y b e a trait (in t h e s e n s e of p a r t ) of a s o c i e t y . But, it is c l a i m e d , o n e of t h e t r a i t s of t h i s p e r s o n is c i t i z e n s h i p , in t h e s e n s e of t h i s b e i n g o n e of his o p p o r t u n i t i e s or duties, o r part o f h i s s t a t u s in t h e society, which m a k e s t h e s o c i e t y o n e of h i s t r a i t s e v e n a s h e is o n e of t h e s o c i e t y ' s . T h e d i s c u s s i o n i m p l i e s t o my m i n d a s e n s e of s y m m e t r y b e t w e e n t h e s e r e l a t i o n s h i p s ; b o t h a r e " t r a i t s " of e q u a l c o m p l e x i t y . In t h e c o n t e x t of t h e p r e s e n t work d i s t i n c t i o n s would h a v e t o b e m a d e t h a t may b e of n o i n t e r e s t in B u c h l e r ' s very g e n e r a l t r e a t m e n t . It is n o t difficult t o find r e l e v a n t d i s t i n c t i o n s here. A citizen is an o r g a n or part of a s o c i e t y His s t a t u s p l a c e s him in t h e r e l e v a n t p o s i t i o n in s t a t e s p a c e , s o t o speak. That s t a t u s r e g u l a t e s h i s b e h a v i o r a n d m a y e v e n a t t i m e s affect his physiology. His o p p o r t u n i t i e s o r d u t i e s a r e p a r t s of t h a t r e g u l a t i o n , n o t p a r t s of his p e r s o n . T h e i n t e r a c t i o n m u s t b e analyzed i n t o m a n a g e a b l e c o m p o n e n t s with an orderly struct u r e a c c u r a t e l y reflecting, in part, t h e a s y m m e t r y of interlevel t r a n s a c t i o n s . In o u r c o n t e x t , o n e n e e d s a r o o t e d d e s c r i p t i o n of a m o r e r e s t r i c t e d s c o p e t h a n B u c h l e r ' s u n i v e r s e of d i s c o u r s e . This e x a m p l e h a s further i n t e r e s t for b i o l o g i s t s . A c i t i z e n ' s s t a t u s may b e t a k e n t o r e s i d e within him in o n e s e n s e — t h a t h e has a c o n c e p t of it in his m i n d . This r e p r e s e n t a t i o n is a n a l o g o u s t o t h e r e p r e s e n t a t i o n of an o r g a n i s m ' s e c o l o g i c a l n i c h e p o s s i b i l i t i e s ( t h e f u n d a m e n t a l n i c h e ) l o c a t e d in its g e n e s ( P a t t e e 1970, 1972, 1977; Plotkin a n d O d l i n g - S m e e 1981). B u t r e p r e s e n t a tion is a very s p e c i a l kind of relation, referring t o a very different o r d e r of n a t u r e t h a n t h e p a r t s a n d w h o l e s of p h y s i c a l b o d i e s we a r e usually d i s c u s s i n g in s c i e n c e ( P a t t e e 1978a, b). A r e p r e s e n t a tion of s o m e t h i n g m o r e e n c o m p a s s i n g t h a n t h e o b s e r v e r may e x i s t within t h e o b s e r v e r a n d t h e r e f o r e b e e n c o m p a s s e d in a physical s e n s e . W h e t h e r or n o t a r e p r e s e n t a t i o n s h o u l d always b e taken t o b e l o c a t e d within t h e o b s e r v e r is an i n t e r e s t i n g

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point. Superficially, of course, we see that it is not so—not even in self-representation. If we decide that it must be internal, then we must be prepared to discover some unfamiliar entities. We need not pursue the question here. The asymmetry of relations moving upward in a hierarchy compared with relations moving downward will be strongly emphasized here—especially in the next two chapters—perhaps more so than in any previous work on this topic.

C. LEVELS AND RANK

Having discussed complexity, scale, and polarity, we are now in a position to broach the topic of levels of organization. Entities, events, or processes of different scale will be held to be found at different organizational levels. In a move to define this concept we shall run through some recent attempts to do so. Wimsatt (1976a) took a realist view of levels superimposed upon a view that changes in scale are more or less continuous and in spite of his belief that interactional complexity characterizes relationships between processes at different levels (interactional complexity, of course, would destroy neatly organized levels structures). He nevertheless felt that in our interaction with the world it does appear to us that there are phenomena of clearly different scales. He suggested that we might view levels as "local maxima of predictability and regularity.'' In other words, we might detect phenomena at any scale at all in a gradation of them, but more would be repeatably found at some scales than at others, or, observation by us of phenomena located at some scales was more certain or vivid or more repeatable and dependable. He reasoned that these levels were those that our lineage had mostly related to during an evolutionary process that produced our powers of observation. Levels are therefore part of our umwelt. On the one hand there is a large epistemological component in this definition, but at the same time those levels we best relate to are in fact ontologically just as real as all the others we don't relate to as much, and are

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more real for us. In this definition organizational levels are taken to be real phenomena in their own right It is interesting to compare this with a somewhat similar but nominalist view taken by Allen and Starr (1982). According to Allen and Starr, two levels would be distinct if the "ratio of time constants" of processes going on at them "is large." This against a background assumption that there could be a gradual change of scale in the world and in the context of repeated statements that they do not wish to comment on the question of whether levels really exist in the world or not. Hence, levels are phenomena to be discovered by transformations and other manipulations of data. And it literally does not matter whether or not they are taken to be ontologically real. Notice that the necessity of discovering certain levels that is implied by Wimsatt's approach is not part of this concept at all. The levels to be discovered are completely arbitrary and restricted to the local study which led to their elucidation. This, of course, is not my view, but we must note that if there were levels in nature in the Wimsatt sense we would indeed be able to discover them using Allen and Starr's proposed technique. Ratios of the rates of phenomena occurring at different real local maxima of predictability and regularity would be large, and hence we may take these two approaches to be concordant. In a much more formal approach, Bunge (1979) defines levels as sets of concrete things in a family of such sets such that members of some sets are composed of members of other sets. "One level precedes another if all the things in the latter are composed of things in (some or all of) the former. A thing belongs to a given level if it is composed of things in (some or all of) the preceding levels." Note that this is based on an approach to things similar to that of the present work, although it could be rephrased to a more general sense by replacing "thing" with "phenomenon." This approach explicitly brings in the concept of rank. We are told how to decide which phenomena are in higher and lower ranking levels in a compositional hierarchy. That can be generalized as well so that, for example, a process could be found to belong to a given level if it entrains processes assigned to some or all preceding levels in a control hierarchy. We may note that Allen and Starr's approach also implicitly

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refers to rank in that ratios can be made with either set of data in the denominator. Hence, if the ratio is large the level from which data in the numerator were taken is the higher level; if it were small the reverse situation would be found. The most important difference between Bunge and Wimsatt is that Bunge's levels are not taken to be real phenomena in themselves. They are sets or classes—human cognitive structures, representations. Nevertheless, the things that are members of these levels are real things. Members of higher levels are composed of members of lower levels in part-whole relationships. The two approaches can be made concordant by reworking Wimsatt's statement to read: "levels are ways of representing the fact that the scales of most phenomena we encounter are such that scale changes appear to occur nonuniformly in local maxima of predictability and regularity." It is in fact most important to note that levels are abstractions with intensional definitions If this were not the case it would really be impossible to make general idiographic statements about the phenomena of the world. It would therefore be impossible to erect a general ideographic (constraint) theory about the world to complement the nomothetic theories in use in science today. Thus, things are members of levels that do not include levels as members. Things that are parts of other things are not members of the same level as the things they are parts of. Things exist as wholes with parts. Levels are classes of such wholes or parts. Things are ordered by composition according to scale; levels are ordered by seriation according to rank. The rank of levels is assigned according to the scale of the things which are their members (see figure 4). Some important consequences of this viewpoint will be drawn in chapter 5. For now I will only note that theories about sets and the relationships among them can be directly related to theories about symbolic systems, and so we begin to see that set theory (e.g. Petrich 1973) may provide a basis for representing the symbolic aspects of the world as discussed by Pattee (see above) or hierarchy theory in general in contrast to the scientific theories common today in dealing with the economic-dynamic aspects of the world. Having established that one can construe the world to be structured in such a way that it can be represented as existing at

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LEVELS

I

• • ••

A

A

A

O O O

Figure 4. The ranks of levels are assigned according to the scale of the things which are their members. different levels, it seems to have been irresistible to next examine what characteristics all levels might have in common. That is, what kinds of statements might be used in an intensional definition of some level? This leads one to consider what features are isomorphic across levels because the statements must touch on these as a consistent means of comparison (Miller 1978). This momentum has historically led to a fairly consistent search for commonalities among levels well exemplified by re-

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cent studies dealing with the organic evolutionary process. Without exception these are concerned only with comparisons between selective processes at different levels (e.g. more recently, Alexander and Borgia 1978; Hull 1980, Wimsatt 1980a; Campbell 1981; Cloak 1981; Gould 1981; Plotkin and Odling-Smee 1981; Skinner 1981; Arnold and Fristrup 1982). I hope to move radically away from this—especially in chapter 5, but it is the case that there must be something common between levels so that we can see that they are members of the same "family of sets" (Bunge 1979). Obviously all levels have as members entities of similar scale. Some statement concerning scale would be required to identify a level. This might include statements about subsystems and supersystems. It might also refer to the scale of some process which is isomorphic across levels—thus, species selection, group selection, etc. In this connection it is interesting that many laws of nature are exemplified at (seemingly) all scales. For example, since it requires only that a particular configuration of complex phenomena might have been otherwise arranged to establish the possibility of some kind of selective process, it seems clear that selection can occur at any level. It is a process that only requires a few primitive particulars (Hull 1980a, b) to become activated or realized. Indeed, it may profitably be speculated that all basic laws of nature are isomorphic across levels of organization (von Bertalanffy 1968). Certainly that proposition should not be startling in view of the fact that levels are not a nomological perspective but an idiographic one, that hierarchy theory is a theory of difference not of similarity. Consider the laws of thermodynamics. Consider growth laws. All of these are exemplified at whatever level we choose to find them. In any case, at least some of the basic laws of nature are isomorphic across levels, and one might describe a level by referring to the scale of the particular realization of such a law. Other commonalities across levels would be the basic structure of transactions between entities found at different levels, to be examined in the next chapter. However, it is not clear from my understanding of these relationships that they change in any way with scale (a rather interesting possibility), and so it might not be possible to locate a level by reference to the local surface realization of this structure.

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58 Self Similarity

The problem of similarity between levels can be brought into somewhat sharper focus using the geometrical concept of selfsimilarity explored at s o m e length in Mandelbrot (1977). Levels, we have determined, are sets, the member entities of which are all at the s a m e scale. These sets make up a family of sets (Bunge 1979). That family of sets is actually a larger set, L, whose members are sets. Like the integers, L is an unbounded, serially ordered set with non-overlapping membership (there is only one set of each rank or scale in the membership). R a n d o m sampling in the vicinity of a focal rank, F, gives rise to subsets that are formally similar to the larger set with respect to F and a ratio, r, which indicates the average ratio between the scale of one s a m p l e d set a n d the next (Mandelbrot 1977) If we sample without replacement, the u n i o n of the sampled sets is also formally similar to the original a n d to any of the sampled sets. The original set is by this criterion self similar. (For a more visual impact of self similarity which can give rise to a gut feeling about its meaning, see figure 5, which demonstrates it geometrically). With a self similar set of an infinite number of levels, the formal relationships between levels are everywhere the same, regardless of the scale of the focus, F. Thus, certain aspects of the hierarchy of nature can potentially be modeled by set theory (for those who might wish to pursue t h i s — s e e Petrich 1973). 1 will now try to use this approach to model the origin of o b v i o u s discontinuities between levels, which is not necessarily the case with set L, where levels of minutely different scale may succeed each other in rank, the analogy then being, not the integers, but the real numbers. This approach is concordant with that of Wimsatt (1976).

The Origin of Discontinuities Between Levels S u p p o s e we have a set of levels with arbitrarily minute difference in scale between adjacent ranks (as in the real numbers). For s o m e reason a s a m p l i n g process is started at a given focus, F. A subset is constructed by taking a large number of samples without replacement; the s a m p l i n g process is characterized by

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Figure 5. A geometric demonstration of self similarity. From The Practical Geometry of Nature, by Benoit B. Mandelbrot. W. H. Freeman and Company Copyright © 1983 by Benoit B. Mandelbrot. All rights reserved the variance of the ratio, r. Now, according to Mandelbrot (1977), should we increase the variance around r, the ranks of the sampled levels will spontaneously begin to cluster when ordered, and the clusters will in turn cluster, and the clustering process becomes more pronounced as we increase the variance around r. If the original set of levels was self similar, this new set with clustered levels will be formally similar to it as w e l l — similarity referring to relationships between the members of the ordered, newly constructed set, (e.g. the focus is the same; a level that was between two others in L will be between them in the ordered subset if all three are sampled, etc.). If we assign integers to each cluster of levels in the subset, the analogy to discontinuity appears.

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Now. s u p p o s e t h a t t h e world may actually b e c h a r a c t e r ized by an infinite n u m b e r of p o s s i b l e levels minutely different in s c a l e (as, e.g. in W i m s a t t 1976a, or in Allen and Starr 1982). Our s e n s e of s t r o n g discontinuity between t h e s c a l e s of levels can b e viewed a s t h e result of s o m e kind of historical s a m p l i n g p r o c e s s s u c h t h a t o u r umwelt c a m e gradually t o take on a d i s c o n t i n u o u s nature. What is t h e p o s s i b l e n a t u r e of t h i s s a m p l i n g p r o c e s s ? It c o u l d b e viewed from many p e r s p e c t i v e s . Being evolutionary b i o l o g i s t s , let's take it t o be a result of s e l e c t i o n proc e s s e s (an e q u i v a l e n t a r g u m e n t could b e c o n s t r u c t e d using drift theory) Let t h e r e b e s e l e c t i o n p r o c e s s e s occurring a m o n g ent i t i e s found at all levels (all that is required h e r e is t h a t c o m p l e x c o n f i g u r a t i o n s might have b e e n otherwise and still conform with t h e r e q u i r e m e n t s of natural laws). Focusing on our own level, we look for r e s u l t s of t h o s e many s e l e c t i v e p r o c e s s e s t h a t may have had a s t r o n g m e a n i n g for us (or, m o r e simply, that affected us in m a j o r ways). Not all t h e s e p r o c e s s e s going on at a large n u m b e r of levels would continually have effects of import a n c e t o us but, h e r e and there, a result will have had such an effect If t h e i m p o r t a n t results have effects t h a t b e c o m e built by heredity into our p e r c e p t u a l structure, we will gradually s t o r e up a record of t h e s e e v e n t s in a way a n a l o g o u s t o building a set a s a b o v e . If many i m p o r t a n t s e l e c t i v e e v e n t s t e n d t o have c l u s t e r e d a r o u n d what we call t h e population level, we will have b e c o m e ever m o r e a t t u n e d t o d e t e c t population-level p h e n o m e n a In general, s e l e c t i v e p r e s s u r e s from more d i s t a n t levels, even though they t o o will lead t o differentiation, will have fewer important i m p a c t s upon us and fewer o p p o r t u n i t i e s t o act a s s e l e c t i v e p r e s s u r e s , a n d c o n s e q u e n t l y t h e s e levels will a p p e a r t o us t o b e l e s s d i s t i n c t b e c a u s e we have n o t b e e n tuned t o vibrate in s y m p a t h y with t h e m s o much a s with levels c l o s e r t o o u r s in rank. The levels we a r e familiar with a r e t h e n t h e result of historical a c c i d e n t from a strictly s e l e c t i o n i s t point of view. However, we might wonder, s i n c e we know t h a t t h e direction of s e l e c t i o n r e s p o n d s t o environmental s e l e c t i v e forces, just what configuration of e n v i r o n m e n t s (events at higher ranking levels) were involved in producing our b i a s e s and w h e t h e r or not they might easily have b e e n different. Alas, it is n o t p o s s i b l e to rec o n s t r u c t p r o c e s s e s and/or initial and boundary c o n d i t i o n s from t h e r e s u l t s t h e y gave rise t o b e c a u s e t h e s e are many—>one

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t r a n s f o r m a t i o n s . In any case, d i s c o n t i n u i t i e s in n a t u r e , b a s i c t o t h e o n t o l o g y of t h i n g s , c o u l d b e in large part t h e result of an e v o l u t i o n a r y s h a p i n g of r e l a t i o n s h i p s b e t w e e n t h e world a n d an observer.

D. NESTING—WHOLES AND PARTS

W h a t we have d i s c u s s e d s o far in t h i s c h a p t e r w o u l d b e a p p l i c a b l e t o e i t h e r a n e s t e d or n o n - n e s t e d hierarchy of e n t i t i e s . In t h i s work, however, we will b e c o n c e r n e d with t h e c a s e w h e r e m a t e rial e n t i t i e s of d i f f e r e n t s c a l e (the " h o l o n s " of Koestler 1967) c o n t a i n o t h e r m a t e r i a l e n t i t i e s of s m a l l e r s c a l e within t h e m a s p a r t s — t h e c a s e of t h e n e s t e d s t r u c t u r a l hierarchy of material e n t i t i e s . Such a hierarchy may b e ideally r e p r e s e n t e d by t h e Fournier universe d i s c u s s e d by M a n d e l b r o t (1977)—see figure 6. Note that strong forces would be unable to span more than a b o u t o n e level, s o t h a t we would n o t e x p e c t i m p o r t a n t direct i n t e r a c t i o n b e t w e e n any r a n d o m l y c h o s e n e n t i t i e s of d i f f e r e n t scale. W i m s a t t ' s (1976a) "interactional simplicity" w o u l d b e t h e rule, with significant c o m m u n i c a t i o n m o v i n g regularly a c r o s s a g a p of only o n e level, giving, in t h e c a s e of figure 6, a " s p a n " (Simon 1962) of five s u b s y s t e m s directly u n d e r t h e i n f l u e n c e of each of t h e 156 h o l o n s figured t h e r e . S p a n ' we t a k e t o m e a n t h e n u m b e r of s u b s y s t e m s directly i n f l u e n c e d f r o m a b o v e by s o m e s y s t e m — t h a t is, t h e n u m b e r of its p a r t s t h a t it directly c o n t r o l s . N o t e a l s o t h a t in figure 6 t h e c o n c e r t e d e f f e c t s of exactly five s u b s y s t e m s will i n f l u e n c e any of t h e figured h o l o n s in such a way a s t o p r e d i s p o s e it t o b e h a v e in s o m e way. We m i g h t call t h i s hierarchy a "perfect hierarchy" ( W o o d g e r 1929), a n d we can b e s t i m a g i n e it if we a p p l y it t o c l u s t e r s within c l u s t e r s of t h e a s t r o n o m i c a l universe, a s did Fournier d'Albe a n d o t h e r s .

Branching Hierarchies Now, however, c o n s i d e r t h a t each entity s h o w n in figure 6 is n o t a s i m p l e bald s p h e r e with only "gravitational" e f f e c t s on t h e

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Figure 6. A flat Fournier universe. From The Practical Geometry of Nature, by Benoit B. Mandelbrot. W. H. Freeman and Company. Copyright © 1983 by Benoit B. Mandelbrot. All rights reserved.

others, but a very complicated mass of different kinds of things radiating various sorts of energies, like visible light or sound waves. Thus, even if it receives input only from its sister entities of the same scale, from the concerted activity of its parts, and from the holon it is a part of (that is, from no more than one level away—interactional simplicity), it might well be the case that more than one kind of signal could impinge simultaneously

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upon any given entity at any moment (Wimsatt 1976a). Being finite, our entity could accept only a small part of the impinging signals at any given moment (Bunge 1979). converting the rest to noise. Yet in the next moment it might be able to respond to another class of signal and. indeed, it might become structured by an evolutionary process to respond to different kinds of signals separately, perhaps sequentially, or in some other orderly fashion, thereby gaining some degree of nonconfusion in negotiating its environment. In this case it could be said that the entity in question has to some degree separated its environment into several different ones. This could be the case even with the various signals coming only from the higher level supersystem of which it is a part—its environment proper. Now, suppose this supersystem sends light signals and also radio signals Suppose its parts respond to these separately by engaging in different behaviors for each kind of signal. Or it might be that one subset of them responds to light, another, perhaps overlapping one, to radio waves. As the environments provided by the supersystem vary so do the behaviors of the subsystems. When that is the case it becomes possible, if enough different upper-level signal types become synchronized, that the lowerlevel subsystems will reify these batteries cf signal mixes into different categories which could be felt to be simultaneously established at the higher level. They would be functioning as if the next upper level were divided into separate supersystems of the same scale. That level would have become differentiated into more than one entity (some number less than the total number of signal types by which it communicates with its parts). Formally, we could say that the hierarchy of nature here branches (Bunge 1979—or "overlaps"—Dawkins 1976b), and our set L might come to have more than one member set at each scale A recent, much discussed example would be where at the organism level one finds human beings relating simultaneously and/or sequentially to a higher level biological population and also to a higher level society (Plotkin and Odling-Smee 1981; Lumsden and Wilson 1981). This structure poses no problems for the non-nested case, but we must consider carefully just what is the situation here in the nested case. If a natural hierarchy branches in this

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manner, a lower-level entity may come to form part of and function in several parallel hierarchies even though the physical structures remain as they were in figure 6. Now, this raises some evolutionary matters that will not be discussed until a later chapter. But, we may look at it as follows: consider three planets of similar kind. One is barren of living things, one has living systems of a simple sort, say single cells, the last has more complex organisms with social behavior. In one sense these are all the same kind of thing—three planets; and they presumably would each function satisfactorily in that capacity in some star system. They are entities at the same level of organization, having the same scale. Their surfaces are differentially complicated, perhaps as a function of time alone. In the simplest one we find dissipative structures (Prigogine 1980) like dust storms, whirlpools, Benard cells and the like at a level above the molecular. In the next, living structures, cells, join those abiotic ones at the same scalar level, while populations of these join higher-scale complexes of turbulence like local weather patterns. Finally, on the third planet, characteristic behavior patterns of the living organisms give rise to further complicatedness at the upper level, where we find only the population and turbulent physical systems on the second planet and only turbulence systems on the first. Thus, through time a given level of organization might become increasingly differentiated into more entities and appear to us to be acquiring new dimensions without changing its scale or rank in the hierarchy of nature. This is a point that has caused so much confusion that essentially nothing has been ventured on it by scientists. Wright (1964) did appreciate it. A few philosophers, like Charles S. Peirce, have said some things, to be noted later. The above furnishes a basic image of the organizational levels as developed in this work—these levels are characterizable by scale alone, increasing scale implying for a fixed observer an increasing scope for complication. Wimsatt (1967a) implies that after branching, a hierarchy may come together again. Thus, in our example above, both a society and a biological population of humans exist in one and the same ecosystem and will separately receive input from that ecosystem. In other words, the differentiation of entities at one level of organization does not seem to require pro rata

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differentiation at either the next higher or lower levels. It may or it may not. If there are any rules on this we are in any case ignorant of them at the moment. What is implied here, however, is that what has appeared to many of us as radically new inventions in evolution, say, social living, were in fact immanent in the less differentiated systems of an earlier time (Whitehead 1929; Wright 1953; Burgers 1975). When and if they reach stable realization they do not necessarily embody new levels of organization in the sense that that phrase is used in this work. The reason is that the fundamental basis of levels is scale, not complicatedness. Scale implies complexity, but that concept as used here does not entail mere elaboration. Physical complexity is present at any degree of complicatedness if and only if some of the complicatedness is due to the simultaneous presence of entities at scalar levels so different that they cannot dynamically interact, and so can affect each other by way of constraint only.

Chapter 4

Representing a Dynamic System Hierarchically: The Basic Triadic System A. PRELIMINARY MATTERS "The Dialectic Between Form a n d P r o c e s s " ( B a t e s o n 1979 )

69 69

Rate Differences Between Levels

72

Time

74

B. THE BASIC TRIADIC STRUCTURE

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Lower-Level C o n s t r a i n t s

77

Upper-Level C o n s t r a i n t s

82

Experimental Science a n d R e d u c t i o n i s m

85

Aristotelian C a u s a l i t y — a Reinterpretation

86

The Basic Triad Itself

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1 Initiating Conditions

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2 Boundary Conditions

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3

97

Historicity

4 Determinism 5

Emergence

6

Formal Analysis of Equations

7 A Simple Concrete Example 8 Summary

Self Reproduction

98 100 103 108 111 112

T

he major burden of this chapter is to provide hierarchical structuralism with a transformational mechanism. To accomplish this, I introduce what 1 term the basic triadic system. In it the dynamics of upper and lower levels produce output that can influence the dynamics of the focal level. Lower-level constraints, dubbed initiating conditions, will be seen to give rise autonomously to focal level dynamics which exemplify some law(s) of nature, while higher-level constraints, which I propose should be referred to as boundary conditions, regulate the results of focal level dynamics. The system obviously raises questions about causality, and simple models of this concept must be eschewed. I also examine Aristotelian causal notions. I have, after having given them modern interpretations, found them to be more or less adequate to the task of describing causality in a hierarchical system of differently scaled dynamics.

A.

PRELIMINARY MATTERS

The Dialectic Between Form and Process" (Bateson 1979) Chapter 3 dealt only with synchronic structural matters. If, however, we wish to represent the world as a dynamic system that transforms input to output, further considerations and limitations must come into play. We need to represent the world as a diachronic, transformational structure, and that means we must further elaborate our hierarchical structure. Entities at different levels must affect each other in some way, a point raised as a problem by Valentine (1973). Patten et al. (1976) noted that the interplay of state dynamics and input-output dynamics in systems is "conceptually difficult." The explanation of some phenomenon may involve reference to events at levels other than that at which the phenomenon is located (Conrad 1972, 1976, 1979a; Arnold and Fristrup 1982; Allen and Starr 1982). How, in fact, do entities at different levels interact? The general answer is: by mutual constraint. And what is constraint? Well, "limiting

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is not like physical causation" (Buchler 1966). A constraint defines "what cannot happen" (Allen and Starr 1982) In our context constraints arise from the material conditions (in which 1 would sometimes include relations like Hooke's Law or the Reynolds number) out of which a process emerges and within which it occurs. These are particular configurations of material events and relational constraints which serve as a stage for the play of natural laws, and without which no actual results would emerge from lawful processes. Events are specified, not by natural laws per se, but by those laws together with the "initial conditions" obtaining during the time the lawful processes occur (Wigner 1964). These initial conditions are derived from the results of lawful processes not examined during the focal study in which they are acting as constraints—in fact, as will become clear below, largely from processes at other levels of organization. Thus, the properties of atomic structures set limits to what kinds of things can occur at the molecular level, as do also the temperature, viscosity, and pressure regimes of the environments of the chemical reactions; but neither of these sorts of constraints derive from these molecular processes as such, and are not reducible to them (Polanyi 1968). The temperature and pressure, for example, may be arranged by the observer in an experimental situation, and result in general from the specific spatiotemporal location of the molecular process on some planet (e.g. during daylight hours at the surface of an ocean on a large planet at a given stage in its evolution). In both of these cases temperature and pressure are constraints that derive from levels higher than focal level. Pattee, in a series of papers (1970, 1972, 1973, 1977, 1978a, 1978b, 1979) has pursued this question of the nature of constraint. Events emerge from the interaction of "holonomic (lawful) constraints" and "non-holonomic constraints." These latter are what we are considering here as, simply, constraints. These constraints have the nature of information. Abstractly, a process could be imagined to occur in the absence of a context It could not produce anything. But non-holonomic constaints will inform the process, as it were, what particular games it is involved in so that an actual result can ensue. A possible model would be

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a dynamic equation with one or more constant parameters. Until these are specified the equation produces nothing. The specific values of these parameters derive from the particular context under consideration. Typically, these are not (or not all) recursive functions of the equation in hand itself, which only describes the structure of the relevant holonomic constraint. While this seems pretty clearly to be Pattee's basic model, his argument is elaborated into a rich tapestry of physical application of great beauty, some of which was discussed in chapter 3. Constraints always carry information which has meaning for the entities involved in natural processes. This information is not dynamically involved in the processes occurring in time and cannot be directly altered by them, but has instead a timeless quality. Furthermore, it is not altered by the rate at which some entity interprets it. That interpretation, however, is subject to rate-dependent processes, so that the perceived message may alter depending upon the rate at which it is read. Thus, the mass of an object will increase as it approaches the speed of light; the fitness of certain phenotypes will alter as the rate of growth of a population slows down. Mass or fitness, like temperature and pressure, may appear as constant parameters in an equation describing some process which does not have, respectively, speed or population growth as variable descriptors. The actual values of these parameters are set by "environmental conditions," and therefore carry (actual or "stored") information from higher levels. An example would be the information a sailboat obtains about its environment by way of force vectors on its rudder, keel and sails. J In Pattee's work information typically comes only from more intrinsic factors (see chapter 3), and I will be making a deliberate extension of the sources of information herein as part of the hierarchical description ! The meaning of the information is finally derived from the results of the operation of the process described by the equation. We can discover this meaning in our world of representations by solving the equation with the specified constant parameters. The value or meaning of the information in some constraint might change from moment to moment and be a function of something— perhaps a random function—or be relatively stable and change

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only slowly as a constant Whichever is the case is irrelevant to the argument that this parameter is rate-independent in connection with those processes for which it acts as a constraint. Allen a n d Starr (1982) g o so far as to suggest that order itself derives from constraint In our context of material bodies this may be interpreted as referring to the fact that without definite values for constant parametric magnitudes no definite results can ensue from the processes they are involved with. Nature would be, as it were, unformed. But, given the wide interpretation Buchler (1966) gives to order' (a concept we have not explicitly d i s c u s s e d herein), orders of s o m e kind would appear even in the case of such a tentatively swirling m a s s and they might be described statistically.

Rate Differences Between Levels Allen and Starr (1982) declare that differences in the rates of processes in nature are the fundamental source of hierarchical structure. This, of course, is concordant with their non-entityoriented approach, but it s e e m s clear that scale can be found in nondynamic systems as well as in dynamic ones (see chapter 3). In dynamic systems, however, it is clear that processes occurring at different levels continue, or cycle, or go to completion at very different average rates when viewed from a fixed scale. A s a general rule, the higher one goes from level to level, the smaller are the average rate c o n s t a n t s — t h a t is, the longer it takes for chacteristic processes to occur. This has been c o m m o n l y appreciated by biological workers in very different subdisciplines (Simon 1962; von Bertalanffy 1964; Valentine 1968; Iberall and McCulloch 1969; Conrad 1972; Salthe 1975; Allen 1977; Gutierrez and Fey 1980; Miller a n d Miller 1981), a n d has been incorporated into a multiscale model of nonlinear stability by Pismen (1983). This circumstance is what effectively prevents processes at one level from directly interacting with those at another level. Thus, if entities at one level interact in such a way as to produce a result that could influence the course of a process going on at a higher level (the entities are, therefore, within another one which is at that higher level) the result of that influence could

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not in fact have a recursive impact on the course of that instance of the lower-level process, which would have been completed before "feedback" from the upper-level result could arrive. Here we see how entities with non-reciprocal relations over some cogent period of time will have communication between them lagged so as to give rise to significantly different dynamic rates. For example, if a mutant gene changes the behavior of an organism wherein it is found in such a way as to influence its subsequent reproductive success, no feedback from the organism to that gene will influence its transcriptional or replicative behavior in time to alter it in some favorable direction. However, later instances of this allele in the population could be thrown together with other combinations of alleles at many genetic loci by recombination from successful prior systems containing them. Gene products from some of these other loci might very well influence the behavior of the gene product of the allele we are observing in such a way as to improve the phenotype of the organism. This example shows why processes at one level cannot participate in processes at another level as such. The rates of the processes are crucially different. It is partly for this reason that different disciplines and different subdisciplines of some fields can be pursued independently. The objects of their study are not physically entangled with each other. Levels are, as Simon (1962) has put it, "nearly decomposable." They are not entirely decomposable because that would be the case only if no influence whatever could bridge the gap between levels. Hence, e.g., the process of natural selection does not participate in the processes of digestion or reproduction going on in the organisms involved in intraspecific competition, but it may have given rise to the rates at which these processes occur through selective elimination of organisms with certain other characteristic rates in the past. Again, the unit of the rate of progress of natural selection (minimally a generation) is such that it could not possibly intermingle with instances of digestion or mating measured in minutes or hours. Note that processes at different levels, because they occur at such widely different rates, give rise to the rate-independent informational constraints of Pattee (see above). A process at a higher level goes so slowly with respect to focal-level pro-

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cesses that it provides an essentially constant context for them In t h e s a m e way. processes at lower levels proceed so rapidly in comparison that input from them is essentially averaged over many instances or cycles of t h e lower-level process, producing again a perceived more or less slowly changing mean input. In this way both provide relatively stable nonrecursive constant parameters for descriptions of focal-level processes. Allen and Starr note that in order for constraint to be effective, t h e ratio of the rate differences between levels must be nicely adjusted. If the rates are too different, feedback between the processes would be lagged so long as to effectively sever communication between them. As we will find, processes with such different rates are characteristic of levels widely separated from each other by other intervening levels, and therefore connection between them becomes very indirect indeed (chapter 5). On t h e other hand, if the rates of two processes are very similar, they will intermingle dynamically instead of merely influencing each other via constraint if they are located in the s a m e spatiotemporal locality. We should note that this point effectively negates the possibility of constraints on a process arising from the s a m e level in the same entity at which the process occurs. More precisely, from other processes at the s a m e level. Same-level constraints, as we will see, could only arise from non-dynamic structure (form). More on this below.

Time

As I have described the constraint relationships here, factors in place at a higher level long before an observed instance of a lower level process begins might have an important influence on that process (see also, Allen and Starr 1982). This is a consequence of t h e very much slower mean rates of higher-level processes. This requires more comment. First, we must realize that when we describe "rates" t h e s e are in terms of conventional units in use by us, and therefore appropriate to our fixed scale. Yet we may describe processes going on at s o m e higher level in terms of t h e s e units by cumulating their value as multiples of units with meaning for us. Thus, a light-year is fathomed by us

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as 6 x 1012 miles. Yet, surely, for any entity for which processes take place in terms of light-years/time unit, a mile will have no more tangible meaning than a millimicron has for us. At both levels there is presumably a c o g e n t " m o m e n t . " A physiological m o m e n t for us is perhaps the t i m e it takes for us t o shift our e y e — a n augenblick. The second' is a m o r e precise and "objective" version of that unit of time. But m o m e n t s at different levels of organization in the hierarchy of nature clearly will not be the same. We may translate many of these into our own " m o m e n t s , " into seconds or multiples of them. The effort t o translate m o ments of higher-level processes like organic evolution into multiples of our own t i m e units would, all on its own, g i v e rise t o a concept of time. T i m e in science is cumulated moments. Diachronism is really our perspective on larger-scaled phenomena Iconversely, synchronism (or structuralism) tends t o be a projection of the kinds of relationships known t o us at our scale o n t o (typically) larger-scale p h e n o m e n a ] . T o say that a process occupies a long period of time, or g o e s on at a slow rate, is equivalent t o saying that it occurs at a c o g e n t rate in a system whose m o m e n t s are larger than ours. For an omnipresent observer (see chapter 3) there would b e no t i m e at all beyond the memory-now-anticipation model of neurophysiology applied indiscriminately t o any level whatever.

B.

THE BASIC TRIADIC STRUCTURE

In the face of a potentially overwhelming complexity of transactions between entities at different levels we must seek t o discover what might be the basic minimal set of relationships that would satisfactorily frame most (or the most important) relationships. A reading of s o m e of the literature on systems reveals for us what that structure is. The smallest cluster of levels required to represent fundamental interactive relationships is a triad of contiguous levels, so that w e can simultaneously examine s o m e process (or the events it produces), the context of these events, and their causes Quoting Bateson

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(1979), we w o u l d look for t h e "relations b e t w e e n t w o levels of s t r u c t u r e m e d i a t e d by a n i n t e r v e n i n g d e s c r i p t i o n of process." N o t e how t h i s s u g g e s t s t h a t t h e focal level ( t h e m i d d l e level) is p r o d u c e d by i n t e r a c t i o n of its t w o f r a m i n g levels. But t h e a s y m metry of t h e s e r e l a t i o n s h i p s is b e t t e r c a p t u r e d by n o t i n g t h e s a m e t h r e e levels a s p u t forward by P a t t e n (1975): " t h e level of i n t e r e s t ( t h e s y s t e m ) , t h e level w i t h o u t ( t h e e n v i r o n m e n t ) , a n d t h e level within ( t h e c o m p o n e n t s ) , " or by B u n g e (1979): t h e " c o m p o s i t i o n " of t h e s y s t e m , its " e n v i r o n m e n t " a n d its "structure." And h e i n s i s t s o n t h e o r d e r of p r e s e n t a t i o n t h e r e a s b e i n g its "logical order," t h e r e b y a g r e e i n g with B a t e s o n . Peirce (Buchler 1955; W i e n e r 1958) a n t i c i p a t e d t h e s e f o r m u l a t i o n s t o s o m e e x t e n t with his " f i r s t n e s s " ( s t a t e of t h e entity), " s e c o n d n e s s " ( c o n s t r a i n t s g e n e r a t e d u p o n t h e i n t e r a c t i o n of entities), a n d "thirdness" ( t h e p r o c e s s t h a t r e s u l t s f r o m t h e interaction). To enrich t h e flavor of t h i s idea w e can n o t e in p a s s i n g s o m e o t h e r e q u i v a l e n t f o r m u l a t i o n s . In 1971 Piaget w r o t e of behavior arising f r o m o r g a n i s m i c s t r u c t u r e a n d s u b j e c t t o e n v i r o n m e n t a l control. Earlier, Q u a s t l e r (1965) s t i p u l a t e d t h a t "tactical elem e n t s " (in f o c u s ) w e r e "motivated" a c c o r d i n g t o t h e i r s t r u c t u r e a n d s u b j e c t e d t o " d e c i s i o n criteria" f r o m a larger system. Koestler (1978) h a s h i s " h o l o n s " s u b j e c t t o c o n t r o l by t h e i r envir o n m e n t (of which t h e y a r e a part) a n d driven by "a c a n o n of fixed rules" a r i s i n g within t h e m . For me, t h e p a r a d i g m a t i c example is a p o p u l a t i o n of o r g a n i s m s s u b j e c t e d t o n a t u r a l s e l e c t i o n The g e n e s of t h e o r g a n i s m s d e t e r m i n e t h e i r p o t e n t i a l traits or c h a r a c t e r s . Given t h e s e , t h e o r g a n i s m s will i n t e r a c t c o m petitively in c e r t a i n p o s s i b l e ways. The e n v i r o n m e n t will govern t h e rules of t h e p a r t i c u l a r g a m e in which t h e y a r e c o m p e t i n g This s a m e f o r m u l a t i o n h a s b e e n recently e x p r e s s e d by o t h e r b i o l o g i s t s a s well (Slatkin a n d M a y n a r d S m i t h 1979; Webster a n d G o o d w i n 1982; Arnold a n d F r i s t r u p 1982). Thus, t h r e e a d j a c e n t levels s h o u l d p r o v i d e for a minimal d e s c r i p t i o n of a n y c o m p l e x d i a c h r o n i c s y s t e m I w o u l d like t o e m p h a s i z e t h a t n o t only is t h i s t r i a d i c s t r u c t u r e sufficient for t h e job, it is a l s o n e c e s s a r y ; a n d a n y f o r m u l a t i o n or d e s c r i p t i o n s h o r t of t h i s will b e i n a d e q u a t e a n d of n o i n t e r e s t t o t h o s e p u r s u i n g c o m p l e x p h e n o m e n a . In t h i s c o n t e x t , we m i g h t n o t e t h a t m a n y earlier s t u d i e s (e.g. t h o s e of P a t t e e ) w e r e f r a m e d on a

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two-level model, and this may cause confusion in attempts to translate across studies (Marjorie Grene, Beth Singer, personal communications).

Lower-Level Constraints What are lower-level constraints in the triadic system? They are realized potentialities. A s such they carry some of Buchler's (1966) "possibilities." They make possible the events that may happen at the focal level. Not everything is possible given the structure of a system or situation. S o m e events or things are impossible, or have such a low probability of occurring that they are for most intents and purposes impossible. Note that here I distinguish only those phenomena that are generated at levels lower than that in focus—they are intrinsic, internal, endogenous; Varela (1979) uses the term "autonomous." In the present interpretation these make up some of Pattee's nonholonomic constraints because they are informational in nature. If we are looking at an organism, I mean by lower-level constraints various molecular configurations (including the genetic apparatus) which will make possible the next behavioral, homeostatic, or developmental p h e n o m e n o n to be realized given the environment in which the organism is located. True, mating will not occur out of season, nor will drinking occur shortly after the organism has quenched its thirst—but gastrulation will not commence until cleavage is finished, nor will fighting be engaged in unless there is a proper hormonal mix in the bloodstream. I do not refer to higher-level constraints also as potentialities (they would be included in Buchler's "possibilities") because of the formally negative or strictly permissive role they assume in the system. This comes essentially from the relatively slow frequencies by which they replace each other, so that an observer at the focal level would never think of wagering on their changes, although at the limit of the faster of these rates that might be possible. In the present system only lower-level constraints have the quality of being "creative." The possibilities that may occur at the focal level are created (generated) at the

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lower level (the internal state of the system) and only some of them will emerge or be realized upon confrontation with the wider world. Thus, from the point of view of the organism, mutations and internal behavioral impulses would be creative, while the "necessity" (of, say, Monod 1971), or necessary configurations of the outer world, winnow these impulses through the exigencies of the actual situation, thereby diminishing their numbers to a "realistic" few. Further insight into lower-level constraints may be obtained by noting the phrases and terms used by other workers for this concept, and which refer to what these constraints represent. Lloyd Morgan (1923) held that they were "involved" in producing phenomena, and suggested the rather odd term "involution" to describe their relation with phenomena at the focal level. Quastler (1965) refers to "motivations" as a reasonable analogy Koestler (1978) calls them a "canon of fixed rules" The implication here is that entities at the focal level have internal structure which generates possible relationships according to some knowable rules. Thus, within a given organism, the genes are fixed, or will be modified according to some procedure (as in the production of immunoglobulins). Patten et al. (1976) refer to "coefficients." These are values that might be entered in a matrix as those referring to the potentialities of the system, whose behavior will be actualized via selection or shuffling at a higher level. I think that none of these formulations are general enough (except metaphorically) to be applied to all situations. What do lower-level constraints do? They make possible the phenomena that do occur, they determine them; in fact, they cause them. Thus, "organisms determine their environments" (Levins 1979); the organism "imposes" its structure on the situation (Piaget 1971) Obviously I am making a special use of the word "cause" here. We can see exactly what use by referring to Mill's concept of "total cause" (Putnam 1982). The total cause at time (t0) of some events e at a point x at a later time, (t,) is well put by Putnam as "the entire distribution of values of the dynamical variables at time (t0) (inside a sphere S whose center is * and whose radius is sufficiently large so that events outside the sphere S could not influence events at x occurring at (t,)

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without having to send a signal to x faster than light)." I would make this definition even richer by explicitly referring to the nonvariable parameters as well—the initial and boundary conditions of physics, for example. These too are parts of Mill's total cause. Well, we must pick apart this impossibly dense skein of relationships, looking for what Wright (1973) called "critical variables" ( parameters' would have been better), factors that directly limit the rate of production of selected phenomena at the focal level, and not those that merely "control" the environment of the process and so influence it indirectly. We will allow into our set of "causes" at this point only members of the intersection of three sets: (a) Wright's "critical variables," (b) Aristotle's "material causes" (Montalenti 1974; Patten, et al. 1976, see below) and (c) factors intrinsic or endogenous to the entities engaging in the process under observation at the focal level. Hence, lower-level constraints that—given some definite, upper-level, environment—will determine what will occur (that is, will determine the values of nonvariable parameters representing lower-level constraints) will be referred to here simply as "causes." These particular restrictions on the word "cause" as used here are obviously in deference to the reductionist style of most of biology and much of natural science. New distinctions must be made; but why not try to retain as much of our past habits when we make them as is possible? Where do lower-level constraints come from? Since they are the properties of lower-level entities, they arise from interactions between the parts of the entities that happen to be engaged in the focal-level process under observation. These innate lower-level processes cannot directly participate in those at the focal level, but their results make the latter possible. Now, it is obvious that confusingly many things are occurring at a given level at any particular instant. In fact we do not ever try to observe them all, but only certain selected ones germane to our interests. To explain the relevant predispositions giving rise to those processes we observe, not all the parts of the interacting entities are required—only some of them. These are the strongly relevant compartments, the true subsystems of the observed system Woodger (1929), following Peirce or Lewes, has referred to these as the "components" of the entities in the

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system b e i n g observed as d i s t i n g u i s h e d f r o m o t h e r c o n s t i t u e n t s that are merely " c o n s t i t u e n t s " of these i n t e r a c t i n g entities. These weakly relevant c o n s t i t u e n t s are entirely invisible t o o u r studies at t h e focal level, even t h o u g h they m i g h t have some sort of indirect c o n s t r a i n t - o n - t h e - c o n s t r a i n t s role t o play. The t r u e c o m p o n e n t s of t h e system are " c o n n e c t e d " as per Bunge (1979), c o n n e c t e d in ways discussed by Salthe (1983), w h i c h may be direct or indirect, t h e r e s t r i c t i o n b e i n g that they m u s t be m u t u a l l y c o n n e c t e d over s o m e (to us) f i n i t e p e r i o d of t i m e . If we are a l l o w i n g i n d i r e c t c o n n e c t i o n s t o c o u n t as relevant (and Patten 1982 has d e m o n s t r a t e d t h e necessity of t h i s approach), t h e n t h e t i m e r e s t r i c t i o n is necessary t o prevent all parts f r o m b e i n g viewed as inextricably c o n n e c t e d c o m p o n e n t s in a giant black box. Parts of t h e same e n t i t y t h a t are only unilaterally c o n n e c t e d t o t h e c o m p o n e n t s are other, weakly relevant c o n s t i t u e n t s (see figure 7, where o n l y parts 1-5 of A are its c o m p o n e n t s relative t o t h e process represented by t h e arrows crossing between A, B, a n d C. Parts 6 a n d 7 are mere c o n s t i t u ents, discovered t o be parts in yet o t h e r studies not represented here). So, in s t u d i e s of m a t i n g behavior, t h e sexual organs w o u l d be c o m p o n e n t s of t h e e n t i t i e s involved w h i l e t h e i r kidneys w o u l d o n l y be c o n s t i t u e n t s . This d i s t i n c t i o n is i m p l i c i t in Buchler (1966), w h o holds t h a t some n a t u r a l c o m p l e x e s are "strongly relevant" t o others w h i l e some are o n l y "weakly relevant." Any complexes that are related w o u l d affect o n e another. Complexes that are strongly relevant t o each o t h e r affect each others' " i n t e g r i t y " — t h e particular c o m b i n a t i o n of t r a i t s t h a t d i s t i n g u i s h e s it as t h a t complex (Singer 1982), w h i l e t h o s e t h a t are weakly relevant o n l y affect each other's " s c o p e " — t h e i r comprehensiveness or range of efficacy (in t h e present context, w h a t S i m o n (1962) calls their "span"). Relevance relates in part t o h u m a n observation, but goes beyond it t o any kind of " d i s c r i m i n a t i o n " (active or cognitive) by any agency. If we are o b s e r v i n g mating, we can discern w h i c h complexes are strongly relevant w i t h i n t h a t "order." If we observe feeding, t h a t is a n o t h e r order and still other natural complexes may be strongly relevant w i t h i n that. Thus, t h e integrity of a natural c o m p l e x is its i n t e g r i t y w i t h i n a given order. Its perceived integrity is its integrity in a perspective. The overall

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Connections per time unit — "

Figure 7. Parts 1-5 of A are its components relative to the process represented by arrows crossing between A, B, and C. Parts 6 and 7 are mere constituents. integrity of a physical entity is its "contour" in space-time. This contour of an entity is not its shape but its integrity insofar as it belongs to many orders. The "identity" of a complex is the continuous relation that obtains between the contour of that complex and any of its integrities. Thus, an entity like an organism, since its identity is complex, may be either weakly or strongly relevant within a given order (say, the amount of energy available to a population in an ecosystem—the order being energetic relationships) on the one hand, and yet either weakly or

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strongly relevant in still other orders (say, the density of the p o p u l a t i o n — t h e order then b e i n g reproductive relationships within it). W h i c h s u b s y s t e m s are f o u n d to be strongly relevant to a given c o m p l e x will differ a c c o r d i n g to which order it is being observed in Thus, the o r g a n i s m may. in two different contexts, be seen a s having n o c o m p o n e n t s in c o m m o n a n d yet be the s a m e o r g a n i s m b e c a u s e it h a s a c o n t i n u i n g contour in spatiotemporal terms that allows u s to see its identity in the two contexts. This a p p r o a c h is interesting i n a s m u c h a s it allows broaching of the q u e s t i o n of w h e n an entity is the s a m e entity in the face of s u c h extensive c h a n g e that its relevances and related c o m p o n e n t s are entirely overhauled, as w h e n a tadpole metam o r p h o s e s into a frog or a lineage persists after its species have been entirely replaced by speciation a n d extinction. E n o u g h h a s n o w been s a i d s o that we can define lowerlevel constraints, which may be d u b b e d initiating conditions. Initiating c o n d i t i o n s are constraints that arise from interaction of strongly relevant c o m p o n e n t s within entities that are interacting in an o b s e r v e d p r o c e s s at the focal level. A s s u c h they will be perceived as intrinsic properties or innate traits of those entities. They will make p o s s i b l e what might occur as the results of the focal level p r o c e s s e s and, in fact, they initiate or generate (cause, in the s e n s e b e i n g u s e d here) t h o s e processes as well (Polanyi 1968). P r o c e s s e s emerge from the very being of the lower-level entities that interact within the entities mediating them, a n d are not i m p o s e d by extrinsic or e x o g e n o u s s o u r c e s — they are possibilities generated by way of the internal states of the interacting systems. It is clear from this that the reductionist research p r o g r a m — t h e search for lower-level causal mechan i s m s — m a k e s a g o o d deal of sense, limited as it is withall.

Upper-Level Constraints We must now e x a m i n e what in the present interpretation make up the other half of Pattee's n o n - h o l o n o m i c constraints. Like lower-level constraints, they inform a n d influence focal-level processes without participating in t h e m dynamically. Where d o

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they come from? In general, from the environment of a process. This environment is the "composition of the next supersystem" (Bunge 1979). This environment itself emerges in part from the results of many simultaneous or parallel focal-level processes as influenced by even more remote environmental features— that is, the environment itself will be seen (especially by an omnipresent observer) to be factorable into levels. Features of the immediate environment are enclosed in entities of yet larger scale, and so on. As Patten (1982) has pointed out, this means that the environment of a system includes historical factors as well as immediately cogent ones—at least as seen by focal-level entities. Patten noted that many workers (e.g., Mason and Langenheim 1957) demur at such a concept of "infinite regress" in environmental influence. He himself shortcircuited that objection by strictly limiting the time duration of any proposed focal-level processes (see Salthe 1983). This problem will be taken up again in detail in chapter 5; suffice it for now to claim that the regress in any real process never actually proceeds very far. In other words, the problem is rarely if ever a practical one. What are higher level constraints ontologically? They are environmental referents—"every system is constrained by its environment" (Bunge 1979). More specifically, in Buchler's terminology, they are strongly relevant features of the environment of a process. They would be included in Wright's (1973) critical parameter set, but they would specifically be factors that issue from levels higher than the observed focal-level process. Examples, as given by Levandowsky and White (1977), might include spatial inhomogenieties, or standing wave patterns generated by the interaction of (higher-level) phenomena of different periodicities, or those periodicities themselves as relevant temporal patterns. Looked at physically they would appear as the "global characteristics of macroscopic systems" (Prigogine 1980). (In this terminology a "microscopic system" is one where global characteristics—e.g., the shape of the reaction vessel—have no important effects at the focal level.) In large systems (especially as studied in laboratories) the effects of global characteristics are normally damped out. but at bifurcation points initiated by important fluctuations (more common where experimental de-

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sign has failed to control) these global characteristics may make themselves felt. Outside the laboratory such fluctuations probably are the rule, showing us why physics is in principle such an experimental science. In this work we are more concerned with non-experimental situations—mostly as if they were being viewed by an omnipresent observer. Cybernetically. higher-level constraints appear as "all direct inputs to a holon arriving simultaneously" (Patten and Auble 1981). Of course, all "input" in the classical sense would be from higher levels outside the black box focal-level system itself. Hence any "input" to a system may be taken as germane here; it is this input that is controlled in the world of experimental science; the fluctuation becomes the experimental probe, arriving at the black box according to the observer's will. Quastler (1965) applied the term "decision criteria" to what are in effect higher-level constraints. Philosophically, Grene (1972, 1974) held that the upper-level constraints are what make the system at the focal level the kind of system it is. They are "epistemologically and ontologically prior to it" as form is prior to matter in Aristotle. What do higher-level constraints d o ? Lloyd Morgan (1923) suggested that what w e are here terming initiating conditions have the relation of "dependence" upon higher-level constraints. Depending upon the degree of organization of the triadic system, higher levels contextualize, inform (Muir 1982), select from a m o n g possible behaviors, dominate (Ashby 1956), coordinate (Weiss 1969), govern, regulate, or control (Grene 1966; Piaget 1971; Wilden 1972; Alexander and Borgia 1978; Koestler 1978; Bunge 1979), guide, harness (Polanyi 1968), organize (Grene 1966) or anticipate (Burgers 1975) the results of focal-level processes. Etymologically hierarchy' derives from the concept of control by higher levels (Simon 1962). Notice the gradient in shades of meaning in this list from philosophically neutral to more a n d more loaded connotations, passing through standard cybernetic parlance on the way. By the time we have arrived at the end of the list we have radically departed from viewpoints consistent with standard reductionism—and from experimental science where higher-level constraints are deliberately controlled by the experimenter s o as to neutralize them and focus attention upon the structure of the focal process and the causality represented by its initiating conditions.

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Experimental Science and Reductionism Contextual matters are traditionally treated only in the "Material and Methods" sections of the primary experimental literature. They are not the matter sought for inclusion in textbooks, and are felt to be almost a physical embarrassment or even an impediment to the knowledge we seek for addition to the compendium. These higher-level factors are secondarily handled only in special vade mecum texts for intermediate-level students (Fleck 1935), by the study of which students acquire standardized matters of routine performance. The higher-level factors are thus rendered transparent and we see focal-level processes through them more clearly, just as we unconsciously use a language to render our meanings transparent to others. But having done this, we lose sight of our own praxis as vital context for our knowledge and, indeed, of the fact that "in nature" there are higher-than-focal-level forces other than ourselves continually circumscribing the natural laws we have discovered at the various focal levels we have worked at. For some diverse concrete examples: in vitro synthesis of sugars and amino acids results in a mixture of racemates while in vivo synthesis results only in dextro sugars and levo amino acids (Anderson 1972); sex determination in some turtles depends upon environmental temperature (Bull 1980); the particular stages a fluid system goes through on its way to turbulence depends upon the width, etc., of the observation chamber (Robinson 1982). The actual result for a species of tree attacked by the fall cankerworm depends upon the particular mix of tree species in the ecosystem (Futuyma and Wasserman 1980). From the present viewpoint it is not sufficient to take existing environments as "given" and therefore of little interest. We must be keenly aware that different environments may well have given rise to different results, leading us to again appreciate Henderson's (1913) concept of the "fitness of the environment" (see also Lovelock 1979). Experimental science is the paradigm of reductionism and its successful use blinds us to the complexity of the world precisely by relegating higher-level constraints to our own praxis, which is, of course, not what we are usually studying. Having gotten through this, we can easily see that with our-

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selves a s part of the higher context of s o m e lawful process in an experimental setup, we can certainly "anticipate" (predict) the results or, with us as the builders of machines, we can certainly "harness" the results of lawful p r o c e s s e s (Polanyi 1968). It bec o m e s important for us to generalize from this by removing ourselves conceptually from t h e experimental setup and then by conceptually removing the experimental setup itself. Then we will find ourselves "in nature," our own devices and purposes removed and replaced by t h o s e of other contextual situations. We discover t h e "complementarity of holism and reductionism" (Weiss 1969). Historically, there have been several attacks on the hegemony of reductionism based on its blindness to the principles of regulation (e.g. Morgan 1923; Smuts 1926; Needham 1943; Koestler 1967; Polanyi 1968; Burgers 1975—the members of this list have little e l s e in c o m m o n ) and I advance their argument o n c e again within the context of this work.

Aristotelian Causality—a Reinterpretation Piaget (1971) referred to the principle of regulation in systems as "the modern finalism." This can serve as a touchstone for a discussion of t h e Aristotelian classification of causality alluded to in the section on lower-level constraints. The basic triadic system is itself both an analysis of causality and a tool for such analysis and we can use it to make a modern extension of Aristotelian causality. Lower-level contraints are certainly among the material c a u s e s of events, but it s e e m s that s o m e material causes might be considered to c o m e from what 1 am here calling higher levels as well—e.g., rainfall being an automatic consequence of higher-level meteorological arrangements in the s e n s e that, given t h e s e material arrangements, rainfall is a necessary c o n s e q u e n c e (Montalenti 1974)—"Zeus does not send rain for the purpose of growing wheat, but by necessity, because the vapors must get cold, and hence b e c o m e water and fall down": Physics 2. 198b. In previous interpretations of material cause (e.g. Polanyi, 1968, or Marjorie Grene's usage, 1967) material c a u s e s are always only lower level in that passive, inchoate matter is informed by configurational constraints (plans, princi-

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pies of design, strategies, definitions, essences—summed up under formal causes). In the present treatment the material world itself has a levels structure without considering formal, psychological, sociological, or even biological systems, which are on some planets interpolated into or intercalated between (and indeed arise from) physical entities of variable complication existing at different levels of matter in motion. Thus, if we examine the higher-level constraints impinging upon a system we will find some of them—global weather patterns, etc.—to be "mere" matter in motion which contains by its relation to the system being observed informational properties to which the latter must respond appropriately. I think we have no alternative but to take it that material causes can affect a system from both higher and lower levels. On this score Patten et al. (1976) conclude that material causes come always from the higher level! This they come to because they see matter as being part of the input to a system. They too are ignoring the fact that the system is itself primarily a material one and they are focusing only on the new material being shipped into it. Patten et al. (1976) identify formal cause with the state of a system. It is clear that they mean the state of the aggregate system, thereby involving both state variables and system variables. Conrad (1972) treats the state of the system as composed only of state variables but, inasmuch as the system is complex in the sense of breaking into different levels, both molar and molecular variables must be involved in the phrase "state of the system," which is what it is to be that system, its essence. Furthermore, the same arguments given above apply to formal cause, which in the Aristotelian system is intimately and indissolubly paired with material cause as the continuing synchronic being of material entities. Thus, formal causes may occur at both higher and lower levels However, we would most usually be looking at a system in an environment, and the properties of that environment will not be among the formal causes of the system (in contrast to its output), and so as a practical matter formal cause will mostly be lower level and innate. Efficient causes are the proximate, obvious, overt triggers of events. Events that would happen anyway without them need not be seen to be caused by any given efficient cause. Material

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and formal causes would suffice. This would be the case with events that are predicted by reasoning from natural laws But when something unusual (or even specific) happens, a specific cause, some unusual input, is required to explain it. Inputs, stimuli, excitation, perturbations would all be efficient causes In the present system perturbations that send the system (perhaps only temporarily) into a different trajectory or shock it into (new) activity would be acting as efficient causes. These perturbations, because they are individually powerful or cogent (they are not averages of large numbers of events, which would change only slowly), must of necessity come from higher, not lower, levels (Teggart 1925; Prigogine 1980). Such occurrences were labeled "events" by Teggart (1925), as distinct from historical processes by which the consequences of previous events were worked out by way of material causes. Indeed, it is easy to see higher-level constraints, to the extent that they appear to be episodic, functioning as efficient causes of the particular results of natural processes at any given time. They would be the "fluctuations" of Prigogine (1980) which drive a system away from the equilibrium conditions implied by the formal and material causes into possibly new pathways In these nonequilibrium conditions "external" or "global" conditions determine the forms of dissipative structures and "fluctuations drive the average" away. Bunge (1979) refers to such fluctuations or perturbations as "the active elements in change" as opposed to the routine, predictable, or lawful elements that we have located in material and formal causes. From the point of view of nature (or the omnipresent observer), we must locate experimental setups as efficient causes as well. Final causes are the most intriguing category as concerns their connection to science. Patten et al. (1976) locate final causes in systems as their output. This would be opaque did we not further know that Patten sees output as an interactive process such that any given environment (the "output component" of that environment) calls for certain kinds of output and rejects others. In other words, input (from the "input environment")is not automatically linked to a given output (Patten 1982). The environment has two separate influences on the output; first by way of input, but then also (and this is the reason for dividing the environment into input and output sections) by way of its

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preparedness to receive output That predisposition on the part of the environment may be taken as the fundamental basis of final cause In a system, when some portion "calls for" another it specifies it to some extent. That specification is where Patten et al locate final causes. In the system being developed here, "output" is represented by the results of the lawful process being observed at the level in focus. We can now understand what Lloyd Morgan (1923) meant when he said that lower-level processes "depend from" higher-level constraints. We have now encompassed the idea that Weiss (1969) called "macrodeterminability" and that Campbell (1974) called "downward causation." In systems designed by people as machines, final causes can be associated with the purposes for which the machine was built. Thus, if we design a robot to handle radioactive materials in an accelerator, the motions of the robot are tailored to the form of the room in which it will be working such that its purpose can be read (into it) as "go first to table one; pick up flask; go now to table two; etc." In this way the accelerator as the environment of the robot is tailored to receive its activity as part of the overall purpose of the accelerator just as the robot is so tailored as to function in that environment as part of the realization of this overall purpose. In the present work this idea is generalized so that any environment of any system can be viewed as having purpose, whether we are capable of understanding it or not—as when we ourselves are within that environment. If we cannot, it remains immaterial to our interests and we proceed as if there were no purposes at those levels, reserving the notion (it may be) for ourselves alone. In other words, the generalization of purpose proposed here is based on locating our own activities at some level, analyzing their structure, finding that our purposes are of the nature of constraints imposed by us upon susceptible systems, and then proposing that that structure applies to constraints at other levels in the hierarchy of nature as well (see also Wimsatt 1972). Patten, in his idea of "output environment" has laid the systems foundation for this application, although there is no indication that he would espouse this use of his insight. Summing up, in a hierarchical framework both formal and material causes may be located both above and below focal level. They initiate and provide environments for processes that

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exemplify the laws of nature. Efficient causes impinge episodically upon a focal level from higher levels and act as perturbations, causing fluctuations in the output (or switching) of focal-level processes. Final causes are "built into" the structure of the system, eliciting preferred output and hence relating to any focal level largely from higher levels. It is possible that efficient perturbations could be viewed as the tools of final causes. Lower-level constraints—essentially intrinsic dispositions—are generative and propose possible results, while higher-level constraints are regulatory and dispose As Wright (1973) put it, changes of input to, or output elicited from, an enzyme system are much more effective in changing its rates of activity than any alteration of individual rates within that system. As noted by Bateson (1979—but not in his words), both efficient and final causality (the latter perhaps working through efficient causes) prevent the overconnectedness that would result if the system were determined solely by lawful processes set in motion by material and formal determinants. The latter kind of system would be characterized by transitive relationships across levels, and results at lower levels would more or less directly determine upper-level results. Higher-level constraints are the causes of real boundaries between levels because to a fixed observer they are level-specific as opposed to the more general nature of lower-level causes and of lawful processes. This topic will be handled in detail in chapter 5. Upper-level constraints (especially the efficient and final causes) "dominate" the activities and productivity of focal-level processes (Ashby 1956; see also Bunge 1979). This means not only relations of the kind given in the above list (regulate, harness, etc.), but also carries the meaning that individual upperlevel perturbations are powerful in the sense that they simultaneously and globally affect all subsystems within the one where the perturbation originated. In contrast, the activities of these lower-level entities are weak because no one of them can have that kind of cogent, global influence upon the supersystem within which they exist (unless that supersystem is so constructed as to be specially receptive to one of them so that it particularly calls for its input). Some examples: the effects of ocean currents and eddies on the distribution of diatoms as

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opposed to the swimming efforts of these organisms themselves (Levandowsky and White 1977); the effect of environmental temperature on sex determination of some turtles as opposed to their genetic predispositions (Bull 1980); the effect of the tilt of the earth on the formation of glaciers as opposed to the heat capacity of, and moisture from, the polar seas (Sergin 1980; Ruddiman and Mclntyre 1981); the effect of "positional information" on the differentiation of embryonic cells as opposed to their own competences (Wolpert 1971; Bryant 1982); the "interpretation" given to symbols in a formal system is more important in determining the internal consistency of that system than are the rules of interaction of those symbols (Polanyi 1968; Hofstadter 1979). These point again to a fundamental asymmetry of relations between levels in the hierarchy of nature. Another important point about upper-level constraints is that they complete focal-level processes. Note that without a specific context no particular result could be elicited from focallevel processes. At best these would be behaving as Markov sources. Here we can also apply Patten's "output environment" and note that it calls for particular results, at least by narrowing the variance of the probability distribution functions describing that output. What I mean to relate this to here is the movement in analytic philosophy and mathematical metatheory from Russell's "doctrine of logical types" (Russell 1903) to Goedel's proof (Goedel 1931) to the effect that no logical system of meaningful complexity can be both internally consistent and complete. If it is made internally consistent, a system can be completed by statements (interpretations) in a higher-level "metalanguage" (Carnap 1937). This metalanguage must in turn be completed by statements in a yet more encompassing language, and so on. For example, in computing, first-order languages cannot express GAP problems unless boundary conditions like "closure operators" are included in the program. These problems can be expressed in second-order languages (N. Immerman 1983, symposium paper). This movement has provided the logical framework for the eventual conversion of the body of scientific knowledge into a system of propositional calculus, if that aim can indeed be realized (see Introduction). It is

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furthermore a logical framework that we must make use of in dealing with complex systems now. Weiss (1969) realized this when he claimed that collective statements that could be made about the parts of a system would have to be supplemented by further statements about the behavior of the whole. Attention to this material will prevent us from formulating theories and laws that are fatally flawed by making errors of logical typing, leading ultimately to paradoxical theoretical conclusions. Classical "macroevolution" is such a flawed concept inasmuch as it takes transformations of organismic ontogenetic processes over long periods of time to actually be a macroevolutionary process rather than an organismically based record (or representation) of such processes (Salthe 1975) The flaw is immediately seen when we realize that organisms do not last for evolutionarily long periods of time and so no process that must be realized over such a span (whatever macroevolution actually turns out to be) can in fact directly involve organisms. Some discussion of this viewpoint is to be found in Ghiselin (1981a) and in Salthe (1981), and we take up this matter more than once again below Finally, we should define upper-level constraints formally, and I will propose that we use the term "boundary conditions" to refer to them. Now, this is a term in common use in physics, and that is a drawback; but it so perfectly describes most upper-level constraints that 1 think we should appropriate it. Furthermore, my usage of it here will not in fact conflict with its usage in physics, where the term refers to non-holonomic constraints on lawful processes which are not specifically arranged by the experimenter (those that are so arranged are "initial conditions," except where that term is used by analogy for conditions at the original singularity). Hence, boundary conditions are constraints, including initial conditions, if any, that arise from the results of processes at higher than focal level. Polanyi (1968), Wimsatt (1976b, 1980b), and Atlan (1981) use this term in a very similar manner. They will be perceived as the immediate environment of focal-level processes, and as such are to them extrinsic or exogenous forces. They will guide those processes to results within a narrow range of possibilities, or they will narrow the range of possible results of focal-level processes. Formally, they would be the intersection of the following

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sets of factors strongly relevant to the observed focal-level process: (a) critical parameters (Wright 1973); (b) higher than focal level—that is. extrinsic—phenomena; and (c) Aristotle's efficient and final causes, but with room left for material causes as well.

The Basic Triad Itself We have now arrived at the heart of this work. We must seek the interactions of the initiating and boundary conditions as together they produce focal-level results by means of natural laws. This image was fleetingly anticipated by Polanyi in 1968, when he referred to genes as boundary conditions harnessing the laws of nature in the service of physiology, and is directly related to Varela's (1979) formulation of a system's "identity, its performance in its interactions with what it is not, and how we relate these to distinct domains." We need to review each of these kinds of constraints again but this time with an eye to how they interlock to form reality in their relationship of "ordinal complementarity" (Grene 1972. 1974). Weiss (1979) spoke of the complementarity of holism and reductionism. 1. Initiating Conditions. Recall that these may be selected from the intersection of: Barbara Wright's "critical variables," Aristotle's "material and formal causes," and factors instrinsic to focallevel entities. And what do they do? They generate the possible results of the system at the focal-level. These possibilities may fruitfully be compared with Buchler's (1966) "possibilities." The latter are "doubly related"—to the conditions that make them possible, and to the conditions that actualize them. In the present system the conditions that actualize them are the boundary conditions operating at the focal level, /. The conditions that make them possible are boundary conditions at (-1 which have guided the system to the results at the level which now functions as the initiating conditions at I (see figure 10 below). Possibilities for a given system may arise and prevail, and they may or may not be actualized If they actually appear after regulatory sifting by the boundary conditions they come to prevail as actu-

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alities. The actualization of a possibility will introduce new possibilities and preclude others. Prevalent possibilities and actualities are interdependent (Singer 1975, 1983); in fact they together form a structural metasystem', to use the term suggested by lay Lemke. This represents some of the deep structure of the system. In a simplified formal system a portion of the metasystem could be represented as permutations of a list of primitive, independent possibilities (or internal predispositions) of focal-level black boxes. The probability of each permutation is not necessarily identical with that of the others. If we increase the numbers of these simple possibilities we increase the number of complex ones that emerge as permutations of them. Not all of these permutations need be thought of as prevalent in the system as it is, in part because combinations of boundary conditions would also need to be represented in the metasystem as having different probabilities of occurrence. 2. Boundary Conditions. These are drawn from the intersection of Barbara Wright's "critical variables," Aristotle's material, efficient and final causes, and factors extrinsic to the focal-level entities. And what do they do? They remove or cull initiating conditions generated by processes within the focal-level entities. Thus, Buchler (1966) has it that prevalent possibilities may come to prevail as actualities. As I see it, possibilities are actualized with the exclusion of all conditions not associated with the prevalence of those possibilities. Lewontin (1981) has it that higher-level constraints "destroy" lower-level ones, while Pattee (1979) points out that the quantity of information we have about constraints decreases the possibilities in the system output and that this represents negentropy or (stored) information. Formally, then, as the number of in-place strongly relevant boundary conditions increases, the number of possible events, phenomena, or things that can be produced by focal-level processes decreases. The exact pattern whereby boundary conditions may do this probably will vary from situation to situation. Some simple models are that the number of possible results will diminish with increased numbers of boundary conditions as if the latter were acting multiplicatively (figure 8,a) or, as if the boundary conditions were operating additively (figure 8,b,c).

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UJ

CONDITIONS Figure 8. Some simple models of how the number of possible results will diminish with increased numbers of boundary conditions as if the latter were acting multiplicatively (A) or additively (B,C).

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When boundary conditions increase, the uncertainty of behavior of the focal system decreases (its entropy decreases) while its predictability or its Lyapunov stability increases. Looking again at the experimental situation, as the experimenter imposes more and more "controls" (boundary conditions), the system is increasingly constrained to a narrower and narrower choice of possible responses so that initiating conditions sought by the experimenter become increasingly visible Experimental design is often the art of finding only what one is looking for (that is why it is often associated with the strategy of confirmation rather than that of falsification). Notice that this view affords another way of laying to rest Laplace's demon, who could predict everything (at all levels) in the world knowing only, as it were, the positions and momenta of every particle at t^,. The proposed situation is one where all boundary conditions have been removed, and thus nothing is constrained to occur at all, and what does occur will emerge only from the a priori probabilities implicit in the "molecular" initiating conditions. His prediction would therefore have to be based on a prohibitively large number of trials and, in any case, as soon as one thing occurs it would impose boundary conditions that are outside the demon's original knowledge. Notice also the relationship of this discussion to statistics. If we say "take an average," we mean to remove boundary conditions associated with individual events, gradually arriving at only those few relevant to all the events in question (the class of events subject to the kind of measure we are using). We are eschewing knowledge that, because highly particular, is difficult to manipulate in favor of knowledge that is more general. Of course, when dealing with events at lower levels distantly removed from ours this is the only kind of knowledge (molar) to which we can attain, "molecular knowledge" of the individual motions of particular events being out of reach When we take deliberate averages at our own scale we do so in order to try to construct knowledge that is as general as the knowledge we are forced to have of atoms and molecules. Interesting suggestions concerning ecology that are germane here have been made by Patten and Auble (1981). They suggested (in my language) that the proximate cause of the

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termination of a secondary successional sere is that all available initiating conditions giving rise to yet further processes become neutralized by developing boundary conditions as the system comes to be increasingly complex as its stored information accumulates. A g a i n we see boundary conditions related to stored information They also suggested that it is increasingly difficult for a population to invade a complicated ecosystem as its complicatedness increases because niche space becomes saturated. Niche space relates to initiating conditions in the present way of looking at this. The suggestion then becomes the interesting one that, given the in-place boundary conditions, only a certain number of processes are possible, yet the addition of initiating conditions would tend to increase them, and that this is an i m p o s s i b l e situation resolvable only by the invading populations d i s l o d g i n g some preoccupied niches, which is, of course, more difficult to do than simply moving into empty potential niche space. 3 Historicity. A difficult point about boundary conditions must be made here. Actual in place boundary conditions have a capricious (Lewontin 1967) character. They represent a very small sample of possible configurations of boundary conditions and there is no way to tell how far any given cluster of them lies from the average that an omnipresent observer might know. This is always the position of focal-level entities. To them, boundary conditions are particular and not general; indeed they are unique, or totally capricious with respect to s o m e unknown probability distribution function. This gives them their ideographic or historical character. Boundary conditions on the level in focus are in principle unpredictable by focal-level observers. F. |. Teggart (1925) had a g o o d appreciation of this idea when he distinguished historical "events" from historical process. These events he saw as descending from higher levels of organization u p o n focal-level processes and perturbing them in such a way that the output of focal events fluctuated in a manner no more predictable than the intruding results of higherlevel events themselves were. Thus, "interesting" focal-level results are characteristically produced in episodic bursts (as from a kind of Markov source) with intervening lull (or dull) periods

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even though the initiated focal processes are humming along continuously, perhaps producing uninteresting, or non-salient phenomena. I have stated that in a simple formal system the metasystem would include some representation of the a priori probabilities of boundary conditions as well as those of initiating conditions. But in the real world this would not be possible because actual collections of boundary conditions would have what would appear to be unique configurations for focal-level processes. And this uniqueness functions just as much as do the referents that a group of such collections might have in common. This is so because boundary conditions linger for focal-level time periods that are so long relative to focal-level process that many (even minor) aspects of many of them will be felt as strongly relevant to any focal-level process. An omnipresent observer could certainly construct a class of boundary condition configurations based on what they have in common, but each member would also have unique properties that would be strongly relevant to focal-level processes. Hence, even an omnipresent observer could never know all the boundary conditions in place at any given time, and we must continue to live with this. 4. Determinism. We now have a suitable framework for discussing freedom and creativity. In the model being developed here, there is a fundamental stochasticity that lies in the a priori probabilities associated with possible initiating conditions and permutations of them. We can get at this by once again asking "What will happen if no boundary conditions are in place?" Well, something must happen, and the possibilities will be narrowed by these a priori probabilities. Finally, even so, an event will issue forth "at random." That is, initiating conditions by themselves, even in simple formal systems, can never fully determine events. Because the degrees of freedom have not been used up, a "decision" must occur concerning what will happen. It is that decision to which Whitehead refers in his opposition to determinism, and he allows that it can be made at all levels in the hierarchy of nature but neither he nor anyone else could say "who" or "what" makes this decision. It is this to

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which we will apply the term "creative," and in the structure of the present system it would be a possibility at any level of organization since it is a feature of the basic triadic system. We may'note in passing that in scientific models creativity is invariably represented by a probability density function, and we are doing very little better except that we note that from initiating conditions alone all degrees of freedom in the possibilities can never be eliminated. But of course, in reality some boundary conditions are usually in place. Events will always have been t o some extent determined by initiating conditions, but boundary conditions will now further constrain the possibilities t o . . . ? The answer in simple formal systems is easy; boundary conditions will now uniquely evoke a single, deterministic, response. In the world, however, we never can know all the in-place boundary conditions and so in practice there are degrees of freedom left over even after known boundary conditions have exerted their control; Wimsatt (1976b, 1980b) refers to these leftover degrees of freedom as being contained in an "indeterminate expansion clause, Ceteris Paribus, into which go factors that are irrelevant, relevant but usually negligible in their effects, and "random" or "accidental" factors which are relevant, substantial in their effects, but infrequent and unpredictable." All of these, and even more, issue from unknown boundary conditions which are always in place beside the known ones for focal-level entities. Now, how should we handle this matter if we were omnipresent observers? If we could know all boundary conditions actually in place in the real world at some level of organization at a given moment, would we witness the disappearance of all degrees of freedom? The question is moot, but I will assume that even then a larger or smaller residuum of unused degrees of freedom will remain. I will refer to this as "the humane assumption." It is the assumption denied by Monod's (1971) "necessity," when he made an equally "metaphysical" assumption. At our scale, of course, w i t h humans interacting in the boundary conditions, we may say, if we choose, that our decisions singly contribute to evoking or inducing events at the next lower level of organization, and together help to determine events at the next higher level.

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An instructive example for evolutionary biologists to examine at this point is the supposed "creativity" of natural selection (Simpson 1947; Mayr 1963), widely subscribed to by humanistic evolutionists. The argument was made in opposition to the idea that selection is a purely negative force, weeding out the unfit. Without the framework developed in this work it is a difficult argument to fathom, but it seems to turn on the fact that at any given moment the phenotype and the ontogenetic system of a given species is not infinitely malleable, there being in effect what today we would call "developmental constraints," and that as these latter are the products of selection, a kind of controlling effect was exerted by selection over what transformations may potentially occur. The present framework allows us to see immediately that the process of selection is here being conflated with its (previous) results—with things These results we can see here as functioning as initiating conditions at the population level and as boundary conditions at the organismal level. The process of natural selection occurs at the population level. Formally it merely winnows possibilities presented to it by population-level initiating conditions on the basis of environmental boundary conditions. The process is in fact purely a negative, sifting one—as Wald (1964) put it, "we are the products of editing rather than of authorship" (that is so if we see ourselves as the products of processes only, which is the usual connotation). With respect to natural selection as a process, we may find creativity in the initiating conditions (which is where Simpson and Mayr in fact found them—in idiosyncratic predispositions), which, as well as constraining possibilities to perhaps a few kinds, also leave open some unused degrees of freedom, some of which are still left open even after environmental constraints have operated. A further relevant creativity, at another level, is of course the mutation process, which proposes what the organism might dispose. It was, correctly in part, to this process that the earlier proponents of a purely negative selective force looked for creativity in the evolutionary process. 5. Emergence. Beginning with George Henry Lewes' "Problems of Life and Mind" (1874-75), many early-twentieth-century works were devoted to deriving "mind" from lower-level processes (Al-

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exander 1920; Morgan 1923; Smuts 1926) Much of the early work on levels of organization, like these, was developed in connection with this problem of the seeming appearance of something entirely new out of interactions of phenomena different in kind from them, and mental phenomena were more often than not the explicanda ("emergents") in question. Reaching more generally for principles, Lewes initiated the famous example of water, the properties of water could not be predicted by someone (like Laplace's demon) who knew only the properties of hydrogen and oxygen. Hence, as the world evolves, truly new properties would emerge (or, Lloyd Morgan, "supervene") from the interactions of prior, simpler, phenomena. The origin of life on the earth as studied today is, 1 think, a good example of a modern research program organized on the principle of emergence. Whitehead (e.g. 1929, 1933) took instead the view that these emergents were in fact immanent in even the simplest systems, thereby depriving them of their special quality of surprising uniqueness and, by implication, of their connotation of being the products of creativity, which force he was nevertheless at pains to preserve in the production of events, as discussed above (evolutionary biologists might like to examine Sewall Wright's papers of 1953 and 1964 on this score). Hierarchical structuralists have taken positions on both sides, so we might just run this question through the present triadic system. What "emerges" we can take to be the product of some focal-level process(es). It therefore had to be among the possibilities engendered by permutations of possible initiating conditions established at the next lower level. Of course, permutations may generate immense numbers of possibilities, with some of them having very low a priori probabilities. What actually will emerge will be guided by combinations of boundary conditions imposed by the next higher level. These will have been the results of higher-level processes, some of which may have themselves been surprising to an omnipresent observer because they were associated with low probabilities. The relevant boundary conditions would have a unique configuration, being historical in nature. Thus, the actual properties of water as we know them depended in part on the actual conditions on the earth (in the solar sytem, in the galaxy, in the . . . ), and are

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not the only possible properties H 2 0 might have (see Stillinger 1980, for a discussion of how these properties change with temperature). The picture is not complete: the properties of water, as we know them (cold, wet, sweet, etc.), depend t o a very large extent on the nature of specifically located observers—ourselves. That nature was itself produced by triadically organized systems with many "historical accidents" along the way. It seems that both Lewes and Whitehead were right. The actual properties of water as we know them were immanent in molecular and atomic initiating conditions, but the actual historical sequence of strongly relevant boundary conditions at the level of, e.g., dust devils, organisms, and above, might have been so idiosyncratic that no omnipresent observer could have conceived of them let alone predict them. (This depends in part on whether we believe the world to be an equilibrium system or not.) Hence we may use the word emerge' in more or less the way it has been used by holists. There are interesting modern examples: superconductivity in plasmas was not predicted by physicists and was a wholly new phenomenon depending from wholly new (to science) boundary conditions (Anderson 1972); the effects of running familiar chemical reactions in systems without solvent were drastically different from those chemists knew before (Mclver 1980). Yet Whitehead is not wrong; he merely exaggerates perhaps the magnitudes of the a priori probabilities that were involved in the production of actual phenomena Even the views of extreme holists like Lloyd Morgan (1923) or Polanyi (1968) can be incorporated into the present model. They emphasized the upper-level regulatory possibilities of the system. Given some very high-level "purpose," boundary conditions might be controlled in sequence down through the levels so as to make phenomena like the properties of water "immanent" in what then become higher-level predispositions (note Maritain 1951). Examples of short chains of downward causation are: the presence of hemoglobin S in sufficient frequency t o produce enough cases of sickle cell anemia so that we could learn about its etiology depended proximately from a differential fitness of heterozygotes, which depended in turn from the presence of mosquitoes and malarial sporozoans in an

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ecosystem together with humans; in insects the environment controls the population density, which in turn controls the hormonal physiology of the organisms (de Wilde 1981). My point is that the system being developed here is adequate as a metatheoretical or even philosophical machine whose behavior is capable of expressing clearly the (sometimes quite subtle) views of the most divergent natural philosophers In a truly robust, vigorous, and progressive science, the image of fundamental units will be replaced by that of the basic triadic system. 6 Formal Analysis of Equations. It can be instructive at this juncture to make an analysis of the basic triadic system by means of equations. I will for this purpose use a few actual equations from biology in order to make the analysis concrete as well as precise. Suppose we observe a developing system (say, a portion of an organism) and we discover that its growth can be represented by a Gompertz equation: Y = Y,AB' where Y is the size at time t and Yf is the final size of the organ (Baranowitz et al. 1977). Thus, Y is a function of time, constrained by the constant parameters A and B. Baranowitz et al. found that in one such system (limb regeneration in the lizard Anolis) A refers to factors internal to the developing system, while B represents environmental factors of experimental design. We thus have both lower- and upper-level constraints in this example. Pursuing the lower level first, we will need to find equations of the form: N

A=

SA/N

giving us A as the result of many lower-level events cumulated over space and time. Recall that no single lower-level event, unless in exceptional circumstances, can have a direct effect by itself at the next upper level. Suppose we discover, as did Baranowitz, et al. that A is distributed in the population in such a way that it could reasonably be taken to be an acquired or inherited predisposition, perhaps proximately expressed as the concentration of some chemical substrate. Then in any given

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organism its concentration can be taken as its organism-level c u m u l a t e d effect We therefore interpret A as a concentration and it, like Y itself, can then be seen to be a function of time. Not infrequently that function will be governed by a M i c h a e l i s equation: A = V, -

K ^ - ^ )

(Dixon and Webb 1964). Now, any parameter that can be discovered to be a function of t i m e at the same scale as the variables in an e q u a t i o n will be acquiring its value at the same level of organization as are those variables (Conrad 1979b). If we substitute in the equations we convert one of the erstwhile constants of the Gompertz (in this case A) into another variable at the same level, but the equation has not incorporated anything explicit from the next lower level We have simply incorporated into the Gompertz s o m e focal-level concentrations (averages of lower-level events)—i.e., Km,s0, and A' and a macroscopic velocity, V, in exchange for A. Thus, precisely, the M i c h a e l i s e q u a t i o n is an organism-level representation of molecular events and can be substituted into any macroscopic equation which can then be rearranged to a more c o m p l i c a t e d form. Notice, then, that true lower-level events are not incorporated into the focal-level equation. A n d yet we know (it is interesting to inquire what this means here) that these velocities and concentrations are in s o m e sense representations of lower-level events. In the case before us we can in fact demonstrate that A measures s o m e t h i n g internal to the developing o r g a n i s m s — some p r e d i s p o s i t i o n (Baranowitz et al. 1977). Turning now to the upper-level influence, B, suppose we discover it to be a function of the food presented to the develo p i n g system, which as in Baranowitz et al. might be a regenerating limb in an organism. If Z is caloric intake, then B is some a s s i m i l a t e d p r o p o r t i o n of this Taking Z to be a rate will ensure that it, too, is a finite function of time and therefore an adequate focal-level representation. (It must surely be the case that our conceptual ability to c u m u l a t e and divide time limitlessly has c o n t r i b u t e d measurably to the success of the reduc-

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tionist research program ) In the case before us we can control Z and force it to be a true constant. Again, whatever the form of the function relating B and Z, it will not contain any explicit representation of higher-level events—for example, events having to do with the availability of food in the markets. These may fluctuate and force us to make more complex statistical analyses of the final regeneration data, but this would not achieve representation in the complicated Gompertz formula we now have. Summing up, information from other levels comes to focal-level equations only in the form of constants (true or statistical). If those constants are converted to variables in these equations, they are replaced by others that now carry the information from other levels (e.g., s0 or K m in the above Michaelis equation—the latter subject, for example, to temperature or pH) In other words, once again, processes at different levels of organization do not directly interact. This will be the major subject of our next chapter. These equations can be used to make a useful point about the downward causation exercised by upper-level constraints. Suppose we next discover that the size of the developing organ we are observing is related to total body size, also growing, by the "allometric" relationship: Y = sX* with X being the body size. We see that Y may be construed as a function of X as well as of t, with s and k providing upper-level input. Huxley (1932) has shown that k is a function of two factors, p/a, derived from: dY/dt =

(JYG

dx/dt

=

aXG

Now, if over some time span Y is a Gompertz function of t, it can only be so because the relationship between it and X, governed by the higher-level constant, k, happens to be a certain way, giving k a certain value. The reason for this is not to be found in either of these equations or in the combined one; it lies elsewhere, in the environment. Suppose we nonetheless try to search for the explanation and in doing so discover that dY/dt

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is related also as in the Lotka-Volterra equations! Giving dY/dt its Gompertz form: dY/dt =

Y / Y / ( ( - 6 )

(a and b relate t o A and B; Barononwitz et al. 1977), we can modify it by removing all environmental input except the "predator-prey" interaction: dY/dt = Y (-ea

- ^^ -Ch-L v-Q.--;

1 1

I I I I