Philosophical, Mathematical and Methodological Foundations
by Robert Rosen
- (1985) Pergamon Press; ISBN 008031158X [out-of-print: search used]
From the Publisher
“The first detailed study of this most important class of systems which contain internal predictive models of themselves and/or of their environments and whose predictions are utilized for purposes of present control. This book develops the basic concept of a predictive model, and shows how it can be embedded into a system of feedforward control. Includes many examples and stresses analogies between wired-in anticipatory control and processes of learning and adaption, at both individual and social levels. Shows how the basic theory of such systems throws a new light both on analytic problems (understanding what is going on in an organism or a social system) and synthetic ones (developing forecasting methods for making individual or collective decisions).“ [top]
From the Foreword
“Strictly speaking, an anticipatory system is one in which present change of state depends upon future circumstances, rather than merely on the present or past. As such, anticipation has routinely been excluded from any kind of systematic study, on the grounds that it violates the causal foundation on which all of theoretical science must rest, and on the grounds that it introduces a telic element which is scientifically unacceptable. Nevertheless, biology is replete with situations in which organisms can generate and maintain internal predictive models of themselves and their environments, and utilize the predictions of these models about the future for purpose of control in the present. Many of the unique properties of organisms can really be understood only if these internal models are taken into account. Thus, the concept of a system with an internal predictive model seemed to offer a way to study anticipatory systems in a scientifically rigorous way.
This book is about what one is force to believe if one grants that certain kinds of systems can behave in an anticipatory fashion.”
Chapter 1: Preliminaries
“Indeed, it is clear that if we are confronted with a system which contains a predictive model, and which uses the predictions of that model to generate its behavior, we cannot claim to understand the behavior unless the model itself is taken into account. Moreover, if we wish to construct such a system, we cannot do so entirely within the framework appropriate to the synthesis of purely reactive systems.
On these grounds, I was thus led to the conclusion that an entirely new approach was needed, in which the capability for anticipatory behavior was present from the outset. Such an approach would necessarily include, as its most important component, a comprehensive theory of models and of modelling. The purpose of the present volume in fact, is to develop the principles of such an approach, and to describe its relation to other realms of mathematical and scientific investigation.”
Chapter 2: Natural and Formal Systems
“Furthermore, as we shall see, the world of mathematics really consists of two quite separate worlds, which are related to each other in very much the same way as the world of percepts is related to the external world. One of these mathematical worlds is populated by the familiar objects of mathematics: sets, groups, topological spaces, dynamical systems and the like; together with the mapping between them and the relations which they satisfy. The other world is populated with symbols and arrays of symbols. The fundamental relation between these two worlds is established by utilizing the symbols of the latter as names or labels for the entities in the former, and for regarding arrays of symbols in the latter as expressing propositions about the former. In this sense, the world of symbols becomes analogous to our previous world of percepts; while the world of mathematical objects becomes analogous to an external world which elicits percepts. The primary difference between the two situations (and it is an essential one) is that the mathematical worlds are entirely constructed by the creative faculty of the mind.”
Chapter 3: The Modelling Relation
“Thus, if we had an encoding of each of these systems [two natural systems] into formal systems, or models, we would have captured all of the relevant interactive capabilities of both systems. Even though we are as always dealing with abstractions, the abstractions in this case have only neglected interactive capabilities irrelevant for the interaction in which we are interested. Consequently, any predictions we make regarding this interaction will be verified (at least to the extent that our encodings are faithful). The conclusion to be drawn from this argument is simply this: to say that any encoding is necessarily an abstraction is not in itself a reproach; indeed, we have seen that we can deal with nothing but abstractions. What we must do is see to it that the qualities retained in our abstraction are precisely the relevant qualities actually manifested in an interaction in which we are interested. The diagnostic for this is, as mentioned above, that we could replace each of the interacting systems by the subsystem we actually encoded, with no effect on the interaction itself.”
Chapter 4: The Encoding of Time
“It has long been felt that this aspect of time reversibility in conservative mechanical systems is at variance with our own intuitive perception of the flow of time. Indeed, very few dynamical phenomena in our experience are actually symmetric to the flow of time; we perceive the sharpest possible asymmetry between past and future. And yet, to the extent that the mechanics of conservative systems is itself a formalization of physical experience, and to the extent that any system can be regarded as composed of particles moving in potential fields, time reversibility appears as an inherent feature of the world. This situation has correctly been perceived as paradoxical. One immediate conclusion we can draw, which is nonetheless important, is the following: the encoding of time in conservative mechanics is not the only encoding possible. In particular, it fails to capture the basic quality we perceive in the distinction between past and future. Just from these simple remarks, we see that time is complex, in the sense that it allows (and indeed, requires) more than one encoding. Different encodings of time may then be compared with each other, just as different encodings of a natural system may be. Indeed, the characterization of such different encodings, and the relations which exist between them, is the main purpose of the present section. We may go so far as to say that many (though not all) of the problems traditionally associated with time arise from a failure to recognize that time is in fact complex, and that its different qualities require more than one kind of encoding.”
Chapter 5: Open Systems and the Modelling Relation
“This fact of experience can be stated in another way. Until bifurcation occurs, a complex system may be replaced by a simpler system (the model) with no visible consequences, at least with respect to a particular encoding. During this period, for as long as the stability of the modelling relation persists, the complex system is in fact behaving as if it were a simple system. This means that as far as the modelled behavior is concerned, only a few degrees of freedom, or interactive capabilities, of the complex system are actually involved in that behavior. We may in fact elevate this assertion to a general principle governing the interaction of complex natural systems; namely, given any specific interaction between such systems, there is a definite time interval in which this interaction involves only a few degrees of freedom of the interacting systems. This means precisely that during such a time interval, the complex system may be replaced by simpler (abstract) subsystems, or by models, without visible effect on that interaction.
The principle we have enunciated is perhaps the reason that science is possible at all.”
Chapter 6: Anticipatory Systems
“These conditions may be succinctly summed up as follows: An anticipatory system S2 is one which contains a model of a system S1 with which it interacts. This model is a predictive model; its present states provide information about future states of S1. Further, the present state of the model causes a change of state in other subsystems of S2; these subsystems are (a) involved in the interaction of S2 with S1, and (b) they do not affect (i.e., are unlinked to) the model of S1. In general, we can regard the change of state in S2 arising from the model as an adaptation, or pre-adaptation, of S2 relative to its interaction with S1. The conditions we have enunciated above establish precisely these properties.”
Chapter 7: Appendix
“Thus, the class of mathematical images of natural systems, or the class of mathematical structures which could be images of natural systems, is tacitly assumed to be some kind of category of general dynamical system. What I assert in the Appendix to follow, and what is the main revolutionary content of the Appendix, is that this class of mathematical images is too small; it is not enough to do physics in, let alone biology.
I try to make it plausible that this category of general dynamical systems, in which all science has hitherto been done, is only able to represent what I call simple systems or mechanisms. Natural systems which have mathematical images lying outside of this category and which accordingly do not admit a once-and-for-all partition into states plus dynamical laws, are thus not simple systems; they are complex. “