Read an Excerpt
CHAPTER 1
Hierarchies
Many disciplines use hierarchy theory. Herbert Simon wrote the seminal paper in 1962 with ideas stemming from organization theory in business administration and economics. Another early hierarchist is Ilya Prigogine, who addresses emergence of new levels of order in physical chemical systems. Simon and Prigogine were both Nobel Laureates. Ahl and Allen (1996) point to the central titanic figure in psychology, Jean Piaget, as an early constructivist. Constructivism supersedes both empiricism and nativism (nature versus nurture) by suggesting that learning is a process of interaction. Piaget's constructivism arose with a theory called genetic epistemology, which explicitly uses levels of observation and analysis as well as psychological hierarchies. Piaget late in life worked collaboratively with the chemist Prigogine, which indicates that hierarchical thinking is an endeavor in itself that transcends disciplines. Koestler (1967) worked on social and linguistic hierarchies. O'Neill et al. (1986) were explicit even in the title of their book, that ecosystem analysis needs a hierarchical accounting.
In all these areas of discourse, technical improvements allowed the practitioners to achieve finer grain data over wider extents. It follows from coarsening of grain and widening extent that at some point hierarchies will invite themselves into the discourse. With the gradual encroachment of ecology into larger and smaller realms (global ecology and microbial ecology) ecological insights are to be won outside commonplace human experience. There are changes of perceptual scale taking place that allow the discipline to transcend the limits imposed by the naked senses. Rich direct human sense experience is held in a fairly narrow range between large and small: we cannot literally see molecules, and we lose track of individual organisms across vast tracts of remotely sensed landscape. Technology widens our experience such that the environmental movement of the second half of the twentieth century is rooted in the first view of our whole planet in space. The width of the extent of observations increases in ways that change the sense of where we think we live. Across the wider extent of experience we have technology that lets us detect and remember remarkably fine grained detail, perhaps of individual trees across county-wide swaths of land. With that enriched set of senses, the science of ecology can perform at levels of analysis as never before.
We appear to face greater complexity with the new technology, but that is only a matter of appearances. The common assertion that complexity increases with the size of the unit is a holdover from naïve realist positions of modernism in the middle of the past century. For the realist some lower level grain is given privilege as being the real level, and it is held constant as the lower reference when the discourse expands in scope to address a larger situation. The chosen level is an observer position not a material necessity. If the extent is then widened the increased size of the unit (the extent) does appear to increase complexity because of the wider difference between grain and extent. Complexity arises from the gap between grain and extent, not extent by itself. There is no grain that exists without human decision, and referencing external reality ontologically only offers confusion. The privilege of the grain taken as a primitive in the discourse is a decision, not a reality. As a rule increase in extent demands a coarsening of grain, otherwise we exceed our memory and analytic capacity (although technology helps). As grain and extent move upscale together complicatedness might actually stay the same or even decrease.
The error in assuming increased size increases complexity is to imagine that complexity is a material issue as opposed to a matter of how the system is observed. In biology many discussions that claim to address complexity in fact speak only of complicatedness. Complexity is something normative, based on decisions about how to observe. It is a special sort of scaling issue where bigger does not mean more but rather means different. Hegel anchors his philosophy to qualitative distinctions arising out of increased quantity, and we tie complexity to it as well.
Let us justify that complexity is a normative issue, not a matter of material distinction. The brain is particularly complex if it is considered as a mass of neurons. The questions there might be about how thoughts have a basis in neurons. By contrast the brain is simple if the question is, "How did the reptilian brain become mammalian?" The answer to that question invokes a grain that distinguishes only three parts (hind-, mid-, and forebrain), and one trend of the forebrain getting bigger. That is a simple situation. There is no real grain that exists without human decision. Complexity comes from the question and is not an intrinsic material property. Complicatedness, by contrast, may reflect a material situation, but only one that is tied specifically to some announced observation protocol of a set of parts, whose identity is only asserted.
Our complaint about realism may have set off the reflex response of modernists that science gets closer to reality. But do notice here we have not denied a material external reality in principle. We are not so antirealist as to deny that Allen, the writer here, is in his real office typing on a real keyboard; we would hasten to add that the meaning of such a belief, for that is all it is, is far from transparent. When we object to realism, all we are saying is that realism often muddles the material and the normative in the conduct of science. When we object to realism in the conduct of science, we are not at odds with a belief that science, when it is all over or is at least at a stage for reflection, appears to approach some sort of reality or at least a biologically, culturally shared understanding of what is real. The two positions on reality address either practice, on the one hand, or the larger meaning, on the other hand. As such they operate at different levels, and so are only orthogonal not opposite. The conduct of normal science includes a narrowing of discourse, so the universe is highly contrived. In a narrow discourse we can be more confident about the reliability of what emerges with that exact protocol but will be less confident as to general application. There are fewer checks through alternatives. When colleagues agree in the light of the full study there have been many alternatives introduced, the agreement of which leads us to have confidence in generality and be less fearful of local artifact. The apparent contradiction about local and general verity is only superficial. Understanding the muddle of material and normative issues helps so we can know what comes from us as opposed to what comes from elsewhere. That distinction gives us control in problem solving, and gets us unstuck from an epistemological mire.
So complexity is significantly a matter of relative scaling. It is the aim of our contribution to deal with the scale problem in its own right. That lets us work toward tools and general models that may encourage ecology and other scientific disciplines to escape from limitations that have historically prevailed. Rosen's modeling relation indicates when scaling applies, and when something is scale independent. The modeling relation suggests that when two different material systems can be encoded and decoded into and out of a formal model, the two systems become analog models of each other. All experimentation depends on that relationship. An unspoken indication of analogs is that everything is the same except scale; that is not true, but is one of those assumptions in science that cleans things up for an orderly scientific treatment. A formal model might be the laws of aerodynamics (Figure 1.1). The power of a formal model, such as aerodynamics, is that it captures scaling relationships, such as speed and lift, through the Reynold's number, a dimensionless number involving drag. Therefore formal models are scale-relative and so are scale-independent. Experimentation uses two material systems that can fit into and be derived from a single formal model that applies across scales. Experimentation turns on analog models, which are not coded, but rather look at the compression of the two material systems into a relationship.
A Historical Perspective
Biologists and ecologists have long been aware of scale as a central issue, for example in data collection in ecology. Even so some thirty five years ago there was a ground swell of increased concern about problems of scale in ecology. This scale orientation could be viewed as just the result of the meeting of field biologists, mathematicians, and computer technologists. Perhaps that made the time right for the first edition of this book. Even so there were theorists focusing on scale in biology even a century ago. That size matters has a long history in biology. Even as early as the end of the eighteenth century, Goethe identified problems of shape and relative size in biology. Works on homology in organisms of different size were well advanced before their evolutionary significance was realized. In fact these studies on comparative form were part of the intellectual climate that spawned evolutionary concepts. Theories of evolution were essentially attempts to provide a mechanism for the unity Goethe saw across organism of different size. Evolution came from a scaling issue.
By 1917 D'Arcy Thompson had written his treatise On Growth and Form. His appreciation for quantifiable aspects of scale is still very relevant today. In a foreword to a later edition of D'Arcy Thompson, Bonner (1961) comments, "The most conspicuous attitude in the book is the analysis of biological processes from their mathematical and physical aspects." Thompson's quantification of scale problems is all the more impressive in that it antedates both the revolution in applied statistics that began only in the 1920s and the advent in World War II of computers large enough and fast enough to make a critical difference to strategies of problem solving. We see expressed in Thompson the biologists' instinct that tells them that biological systems are complex because they involve the interaction of differently scaled processes. Biologists know that their material must be considered as importantly multilevel. What is astonishing is that Thompson saw this as a quantitative problem before the tools were at hand to carry the program of analysis through. If he could see the necessity of quantification at that time, it is little wonder that inquiry into problems of scale arises more generally now that the methods and machines for numerically probing such questions are generally accessible.
Computers and notions of hierarchy have a reciprocal relationship. Computing machines are at once child of and parent to the development of hierarchy theory. On the one hand evolution of computer technology has certainly incorporated hierarchical form into the construction of both hardware and software. On the other hand the development of a general theory about hierarchies has in turn been facilitated by computer-assisted summary and modeling. For example, fast machine logic has liberated for general use the powerful techniques of Fisher and Hotelling of the 1930s, and these methods of data reduction have allowed the display of hierarchical structure in ecological and other data. Using such multivariate methods, masses of fine-grain data may be summarized so as to reveal large-scale structure. Data transformation takes a matrix of datum values and treats them all consistently, often with a relativization. The binary transformation leaves all the zero entries alone, and converts all other entries to one. With judicious use of data transformation before analysis, we can change the level of organization that is apparent, achieving summary to greater or lesser degrees. Without the assistance of human value judgments, using only simple, objective, numerical criteria, the computer is able to display structures at various levels in the hierarchies associated with given data sets. Since the objective criteria can apply broadly and since a large number of data sets based on very different phenomena have yielded hierarchical structure, indications are that a hierarchical approach has general utility.
Since the first edition of this book, computational power has exploded. Around the time of the first edition the new science of complexity was emerging but was not sufficiently generally known for it to have received our full attention back then. Over the past forty years complexity and emergence have become hot topics. A general treatment of fractals (patterns that are robust across scales) had to wait until the computer power of the 1970s. Chaos theory, a related body of knowledge, emerged in ecology (May 1974) and elsewhere (Lorenz 1968) for those same reasons of sufficient numerical capacity. In the intervening decades, chaos theory became part of the mainstream culture, enough to turn up in the movie Jurassic Park (not very well explained by a know-it-all character therein), to the same extent as relativity theory is known widely although not properly understood by the lay public.
Hierarchies invoked as change in level of analysis are now everywhere. Even so we do not mean to imply that reality, independent of our cognizance, is in its nature hierarchical; in fact we are not sure what that could mean let alone what it does mean. What we are trying to say is that somewhere between the world behind our observations and human understanding, hierarchies enter into the scheme of things. The perception of hierarchy is something like a Kantian a priori or the human propensity for a dualistic thinking. Simon (1962) makes a point that echoes the issues of medium number systems:
If there are important systems in the world that are complex without being hierarchic, they may to a considerable extent escape our observation and our understanding. Analysis of their behavior would involve such detailed knowledge and calculation of the interactions of their elementary parts that it would be beyond our capacities of memory or computation.
The medium number issue in that quotation is that "important systems" refer to important enough to demand attention to its complexity. "Complex" for Simon means that the implied question cannot ignore the individuality of the parts. So many parts cannot be averaged and they then can be expected to overwhelm "our capacities of memory or computation." Hierarchical treatment, Simon's central contribution, gets us out of a medium number specification, although Weinberg did not raise the issue of medium number until later. Simon could be interpreted as suggesting that hierarchical structure is a consequence of human observations. Even if this is seen as limiting the significance of hierarchical conceptions (we take an opposite view), hierarchical approaches are of at least heuristic value.
The classic notion of hierarchy involves discrete levels. Ecology often focuses on the discrete, as when island biogeography works on discrete islands so as to allow invasion and extinction to be cast in self-evident universes. Although they may be both conceptually and pedagogically helpful, the implicit discontinuities between levels that appear singularly real and discrete are significantly arbitrary. The underlying problem in island biogeography is that on the mainland invasion and extinction are continuous situations, in contrast to islands.
Discrete levels need to be recognized as convenience, not truth. Even so, some arbitrary levels of organization are of more general application than others. For example, the level of organization that defines the whole human individual is a helpful level for many models throughout the social sciences. Humans less a bit or with some more to them are generally less useful. Philosophers are careful to identify whether an argument pertains to existence in terms of objective external reality — that is to say, whether an argument is an ontological discussion. The alternative argument is concerned with experience and is restricted to that which is knowable, an epistemological discourse. We use just the latter arguments. Throughout this book we do not much address questions of ontological reality for given levels but prefer to take an epistemological stance in a utilitarian philosophy. We ask, how do we know what we know, leaving metaphysics for the most part out of it. Hierarchies are rich enough a concern without efforts to link them to external reality. The muddle that is almost ubiquitous in ecology often arises from invoking an undefined reality in an arena where only dealing with what we know is hard enough.
(Continues…)
Excerpted from "Hierarchy"
by .
Copyright © 2017 The University of Chicago.
Excerpted by permission of The University of Chicago Press.
All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
Excerpts are provided by Dial-A-Book Inc. solely for the personal use of visitors to this web site.
