Robert Rosen’s anticipatory systems

Abstract

Robert Rosen instituted a rigorously mathematical treatise on the subject of anticipatory
systems, the theory of which provides the conceptual basis for foresight studies. This article
is an expository introduction[1]. The ubiquity of anticipatory systems in Nature is explained.
An anticipatory system’s present behavior depends upon ‘‘future states’’ or ‘‘future inputs’’
generated by an internal predictive model. This apparent violation of causality is, however,
simply an illusion. The topic of anticipatory systems in particular, and methods of relational
biology in general, provide important tools for forecasting and planning.

Full text

Robert Rosen’s anticipatory systems
A.H. Louie
Abstract
Purpose – This article aims to be an expository introduction to Robert Rosen’s anticipatory systems, the
theory of which provides the conceptual basis for foresight studies.
Design/methodology/approach – The ubiquity of anticipatory systems in nature is explained.
Findings – Causality is not violated by anticipatory systems, and teleology is an integral aspect of
science.
Practical implications – A terse exposition for a general readership, such as the present article, by
definition cannot get into too many details. For further exploration the reader is referred to the recent
book More than Life Itself by the author.
Originality/value – The topic of anticipatory systems in particular, and methods of relational biology in
general, provide important tools for foresight studies. It is the author’s hope that this brief glimpse into the
world of relational biology piques the interest of some readers to pursue the subject further.
Keywords Research, Biology, Philosophical concepts
Paper type Conceptual paper
Preview
Robert Rosen instituted a rigorously mathematical treatise on the subject of anticipatory
systems, the theory of which provides the conceptual basis for foresight studies. This article
is an expository introduction[1]. The ubiquity of anticipatory systems in Nature is explained.
An anticipatory system’s present behavior depends upon ‘‘future states’’ or ‘‘future inputs’’
generated by an internal predictive model. This apparent violation of causality is, however,
simply an illusion. The topic of anticipatory systems in particular, and methods of relational
biology in general, provide important tools for forecasting and planning.
Robert Rosen
Robert Rosen (1934-1998) was for many years one of the world’s foremost
theoretical biologists. He authored some 250 research papers and a dozen books,
concerned with both the development and the implications of the theory underlying
biological processes.
He very early began to develop the concept that biology should be based on notions of
function rather than structure, and that it was function that was of primary concern in
understanding the basis of life and of organism. He subsequently explored the possibilities
of building function-based models of biological processes. These turned out to be very
different from, and far more general than, reductionistic treatments based on structural
ideas. His teacher Nicolas Rashevsky, who initiated the first definitive study in this area, had
termed this approach ‘‘relational biology’’.
Among his many publications, these three books may be considered The Rosen Trilogy:
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A.H. Louie is a
mathematical biologist
based in Ottawa, Canada.
The author gave two sessions of
tutorial on anticipatory systems
at FuMee 1 (2008) in Rovereto,
Italy. This article is a
condensation and transcription
into prose of these sessions’
PowerPoint slides. The subject is
Robert Rosen’s Anticipatory
Systems. The author's role is
that of an expositor, so what is
new in this article is the author's
presentation and not the
scientific content itself, the
originality of which, naturally,
belongs to Rosen. Aristotle said:
“When a thing has been said
once it is hard to say it
differently.” Some repetition of
what Rosen has already written
(which is worthy of repetition in
any case) is unavoidable. Let the
acknowledgement “Robert
Rosen said it first.” be the
disclaimer. The compilation,
interpretation, and delivery
contained in these two tutorial
sessions and hence this article,
however, are the author's own.

1. Fundamentals of Measurement and Representation of Natural Systems (1978);
2. Anticipatory Systems: Philosophical, Mathematical & Methodological Foundations
(1985); and
3. Life Itself: A Comprehensive Inquiry into the Nature, Origin, and Fabrication of Life (1991).
Therein lies the comprehensive treatise of Rosen’s science. (Henceforth I shall use the
abbreviation AS when referring to the book Anticipatory Systems, and use the term spelt out
in full when referring to the object ‘‘anticipatory system’’ itself[2].)Figure 1
‘‘What should we do now?’’
To one degree or another, this ‘‘question of ought’’ is the same question the biologist, the
economists, the political scientists, the urban planners, the futurists, and many others want
to know. However different the contexts in which these questions are posed, they are all alike
in their fundamental concern with the making of policy, and the associated notions of
forecasting the future and planning for it; in short, foresight. What is sought, in each of these
diverse areas, is in effect a technology of decision-making. But underlying any technology
there must be an underlying foundation of basic principles: a science, a theory. What is the
theory underlying a technology of policy generation? Rosen proposed that this is the theory
of anticipatory systems. Note that the concept of ‘‘anticipation’’ had not been new (see, for
example, Roberto Poli’s article in this issue), but the systemic study of anticipation was new
when Rosen wrote the book on it.
Now what is an anticipatory system? Here is Robert Rosen’s definition:
An anticipatory system is a natural system that contains an internal predictive model of itself and
of its environment, which allows it to change state at an instant in accord with the model’s
predictions pertaining to a later instant.
Note, in contrast, that a reactive system can only react, in the present, to changes that have
already occurred in the causal chain, while an anticipatory system’s present behavior
involves aspects of past, present, and future. The presence of a predictive model serves
Figure 1
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precisely to pull the future into the present; a system with a ‘‘good’’ model thus behaves in
many ways as if it can anticipate the future. Model-based behavior requires an entirely new
paradigm, an ‘‘anticipatory paradigm’’, to accommodate it. This paradigm extends – but
does not replace – the ‘‘reactive paradigm’’ which has hitherto dominated the study of
natural systems. The ‘‘anticipatory paradigm’’ allows us a glimpse of new and important
aspects of system behavior.
The idea of anticipation in science is controversial, because of ‘‘objective causality’’
pronounced in the ‘‘Zeroth Commandment’’:
Thou shalt not allow future state to affect present change of state.
Anticipation is almost always excluded from study at every level of system theory[3]. The
reasons for this rest on certain basic methodological presuppositions which have underlain
‘‘science’’ in the past few centuries:
B
the essential basis on which ‘‘genuine scientific inquiry’’ rests is the principle of causality
(which an anticipatory systems apparently violates); and
B
‘‘true objective science’’ cannot be argued from final cause (but an anticipatory system
seems to embody a form of teleology).
We shall debunk these two characterizations of science in some detail below. But let us first
consider a few examples of anticipatory systems.
Biology is replete with situations in which organisms can generate and maintain internal
predictive models of themselves and their environments, and use the predictions of these
models about the future for purpose of control in the present. Much, if not most, biological
behavior is model-based in this sense. This is true at every level, from the molecular to the
cellular to the physiological to the behavioral, and this is true in all parts of the biosphere,
from microbes to plants to animals to ecosystems. But it is not restricted to the biological
universe; anticipatory behavior at the human level can be multiplied without end, and may
seem fairly trivial: examples range from avoiding dangerous encounters, to any strategy in
sports, and even to Linus’s waiting for the Great Pumpkin in the pumpkin patch on
Halloween[4]. Model-based behavior is the essence of social, economic, and political
activity. An understanding of the characteristics of model-based behavior is thus central to
any technology we wish to develop to control such systems, or to modify their model-based
behavior in new ways.
It should be clarified that anticipation in Rosen’s usage does not refer to an ability to ‘‘see’’ or
otherwise sense the immediate or the distant future – there is no prescience or psychic
phenomena suggested here. Instead, Rosen suggests that there must be information about
self, about species, and about the evolutionary environment, encoded into the organization
of all living systems. He observes that this information, as it behaves through time, is capable
of acting causally on the organism’s present behavior, based on relations projected to be
applicable in the future. Thus, while not violating time established by external events,
organisms seem capable of constructing an internal surrogate for time as part of a model
that can indeed be manipulated to produce anticipation. In particular, this ‘‘internal
surrogate of time’’ must run faster than real time. It is in this sense that degrees of freedom in
internal models allow time its multi-scaling and reversibility to produce new information. The
predictive model in an anticipatory system must not be equivocated to any kind of
‘‘certainty’’ (even probabilistically) about the future. It is, rather, an assertion based on a
model that runs in a faster time scale. The future still has not yet happened: the organism has
a model of the future, but not definitive knowledge of future itself.
Feedforward
Anticipatory behavior involves the concept of feedforward[5], rather than feedback. The
distinction between feedforward and feedback is important, and is as follows.
The essence of feedback control is that it is error-actuated; in other words, the stimulus to
corrective action is the discrepancy between the system’s actual present state and the state
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the system should be in. Stated otherwise, a feedback control system must already be
departing from its nominal behavior before control begins to be exercised.
In a feedforward system, on the other hand, system behavior is preset, according to some
model relating present inputs to their predicted outcomes. The essence of a feedforward
system, then, is that the present change of state is determined by an anticipated future state,
derived in accordance with some internal model of the world.
We know from introspection that many, if not most, of our own conscious activities are
generated in a feedforward fashion. We typically decide what to do now in terms of what we
perceive will be the consequences of our action at some later time. The vehicle by which we
anticipate is in fact a model, which enables us to pull the future into the present. We change
our present course of action in accordance with our model’s prediction. The stimulus for our
action is not simply the present percepts; it is the prediction under these conditions. I
emphasize again that ‘‘prediction’’ is not prescience, but simply ‘‘output of an anticipatory
model’’. Stated otherwise, our present behavior is not just reactive; it is also anticipatory.
Model
The essential novelty in Rosen’s approach to anticipatory systems is that he considers them
as single entities, and relates their overall properties to the character of the models they
contain. There have, of course, been many approaches to planning, forecasting, and
decision-making, but these tend to concentrate on tactical aspects of model synthesis and
model deployment in specific circumstances. Rosen’s AS is not at all concerned with tactics
of this type. It deals with, instead, the behavioral correlates arising throughout a system
simply from the fact that present behavior is generated in terms of a predicted future
situation. It does not consider, for instance, the various procedures of extrapolation and
correlation that dominate much of the literature concerned with decision-making in an
uncertain or incompletely defined environment. AS is concerned rather with global
properties of model-based behavior, regardless of how the model is generated, or indeed of
whether it is a ‘‘good’’ model or not. In other words, AS looks at properties of an anticipatory
system, not how to build an anticipatory system.
A model, defined formally, is a commutative functorial[6] encoding and decoding between
two systems in a modelling relation[7]. Intuitively, we may just take the common-usage
meaning of ‘‘model’’:
B
a simplified description of a system put forward as a basis for theoretical understanding;
B
a conceptual or mental representation of a thing; or
B
an analog of different structure from the system of interest but sharing an important set of
functional properties.
Robert Rosen closed AS with these words:
The study of anticipatory systems thus involves in an essential way the subjective notions of good
and ill, as they manifest themselves in the models which shape our behavior. For in a profound
sense, the study of models is the study of man; and if we can agree about our models, we can
agree about everything else.
The crux in the formulation of a theory of anticipatory behavior is the conception of ‘‘model’’.
What is the nature of the relation between two systems that allows us to assert that one of
them is a model for the other? The essence of this property is that we may learn something
new about a system of interest by studying a different system that is its model. Roughly, the
essence of a modeling relation consists of specifying an encoding and a corresponding
decoding of particular system characteristics into corresponding characteristics of another
system, in such a way that implication in the model corresponds to causality in the system.
Thus in a precise mathematical sense a theorem about the model becomes a prediction
about the system. When these remarks are rigorously pursued, the result is a general theory
of the modeling relation. This theory has many important implications: to more general
situations of metaphor, to the way in which distinct models of a given system are related to
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each other, and to the manner in which distinct systems with a common model may be
compared.
The situation may be represented by Figure 2.
A modeling relation exists between the natural system N and the formal system F when there
is a congruence between their entailment structures. A necessary condition for congruence
involves all four arrows, and may be stated as ‘‘whether one follows path c or paths 1, i,
d
in
sequence, one reaches the same destination’’. Expressed graphically, this is:
!
¼
!
1
!
i
!
d
:
If this relation is satisfied, we say that F is a simulation of N.
If, in addition, inferential entailment i is itself entailed by the encoding 1 of causal entailment
c, i.e., if:
ð
!
c Þ
!
1 ð
!
i Þ
is also satisfied, then we say that F is a model of N, and N is a realization of F.
A simulation of a process provides an alternate description of the entailed effects, whereas a
model is a special kind of simulation that additionally also provides an alternate description
of the entailment structure of the mapping representing the process itself. It is, in particular,
easier to obtain a simulation than a model of a process.
Examples are in order. For instance, Claudius Ptolemy’s Almagest (c. 150
AD) contained an
account for the apparent motion of many heavenly bodies. The Ptolemaic system of
epicycles and deferents, later with adjustments in terms of eccentricities and equant points,
provided good geometric simulations, in the sense that there were enough parameters in
defining the circles so that any planetary or stellar trajectory could be represented
reasonably accurately by these circular traces in the sky. Despite the fact that Ptolemy did
not give any physical reasons why the planets should turn about circles attached to circles in
arbitrary positions in the sky, his simulations remained the standard cosmological view for
1,400 years. Celestial mechanics has since, of course, been progressively updated with
better theories of Copernicus, Kepler, Newton, and Einstein. Each improvement explains
more of the underlying principles of motion, and not just the trajectories of motion. The
universality of the Ptolemaic epicycles is nowadays regarded as an extraneous
mathematical artifact irrelevant to the underlying physical situation, and it is for this
reason that a representation of trajectories in terms of them can only be regarded as
simulation, and not as model.
As another example, a lot of the so-called ‘‘models’’ in the social sciences are really just
sophisticated kinds of curve-fitting, i.e. simulations. These activities are akin to the assertion
that since a given curve can be approximated by a polynomial, it must be a polynomial.
Stated otherwise, curve-fitting without a theory of the shape of the curve is simulation; model
requires understanding of how and why a curve takes its shape.
Simulation describes; model explains.
Figure 2 The prototypical modeling relation
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Note that in common usage, the two words ‘‘simulation’’ and ‘‘model’’ are often synonyms.
Some, alternatively, use ‘‘model’’ to mean mathematical theory, and ‘‘simulation’’ to mean
numerical computation. What I have presented above, however, are Robert Rosen’s
definitions, in precise category-theoretic terms, of these two words.
Natural law
It can be commonly agreed that no one, whether experimenter, observer, or theorist, does
science at all without believing that nature obeys laws or rules, and that these natural
regularities can be at least partly grasped by the mind. That nature obeys laws is often
subsumed under the notion of causality. The articulation of these causal laws or relationships
means, in brief, that one can establish a correspondence between events in the world and
propositions in some appropriate language, such that the causal relations between events
are exactly reflected in implication relations between corresponding propositions.
‘‘Law of Nature’’, or Natural Law, consists of two independent parts. The first of these
comprises a belief, or faith, that what goes on in the external world is not entirely arbitrary or
whimsical. Stated in positive terms, this is a belief that successions of events in that world are
governed by definite relations, termed causality. Without such a belief, there could be no
such thing as science. Causality and general ideas of entailment guarantee a kind of
regularity that one expects in nature and in science. Roughly, we are guaranteed that the
same causes imply the same effects. Therefore, in the causal world, one sees the operation
of laws in terms of which the events themselves may be understood.
The second constituent of Natural Law is a belief that the causal relations between events
can be grasped by the mind, articulated and expressed in language. This aspect of Natural
Law posits a relation between the syntactic structure of a language and the semantic
character of its external referents. This relation is different in kind from entailment within
language or formalisms (i.e. implication or inference, which relate purely linguistic entities),
and from entailment between events (i.e. causal relations between things in the external
world). Natural Law, therefore, posits the existence of entailments between events in the
external world and linguistic expressions about those events. Stated otherwise, it posits a
kind of congruence between implication (a purely syntactic feature of languages or
formalisms) and causality (a purely semantic, extra-linguistic constituent of Natural Law).
Summarily, Natural Law makes two separate assertions about the self and its ambience:
1. The succession of events or phenomena that we perceive in the ambience is not arbitrary:
there are relations (e.g. causal relations) manifest in the world of phenomena.
2. The posited relations between phenomena are, at least in part, capable of being
perceived and grasped by the human mind; i.e. by the cognitive self.
Science depends in equal parts on these two separate prongs of Natural Law. Part 1, that
causal order exists, is what permits science to exist in the abstract, and part 2, that this
causal order can be imaged by implicative order, is what allows scientists to exist. Both are
required.
In short, the logic, order, and regularity of the universe are intelligible.
Causality
The concept of anticipation has been rejected out of hand in formal approaches to system
theory, because they appear to violate causality. We have always been taught that we must
not allow present changes of state to depend on future states; the future cannot affect the
present. We now show that this restriction is simply an artifact of the Newtonian reactive
paradigm.
However much the languages that we use to construct system models of whatever kind may
differ, in detail and emphasis, they all represent paraphrases of the language of Newtonian
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mechanics. Two separate ingredients are necessary for the process of system description;
they are:
1. a specification of what the system is like at any particular instant of time, with the
associated concept of the instantaneous state of the system; and
2. a specification of how the system changes state, as a function of present or past states
and of the forces imposed on the system, i.e. the dynamics.
The characterization of the instantaneous state involves the specification of an appropriate
set of state variables, while the characterization of how the system changes state involves a
specification of the equations of motion of the system. Another name of this Newtonian
reactive system is ‘‘dynamical system’’.
Succinctly, the assumptions of the Newtonian paradigm are:
1. A physical system is defined by its constitutive parameters, and is manifested as a
sequence of events in space and time. A system behavior is some property of such a
sequence.
2. The universe of events can be effectively partitioned into two distinct domains.
3. The first domain is characterized by regularity and order – the province of natural law.
4. In the second domain no perceptible regularity is discernible – the realm of initial
conditions.
5. Physics ¼ system laws þ initial conditions.
In this context, causality is ‘‘past implies present, and present implies future’’.
As long as we restrict ourselves to Newtonian dynamical equations under these
assumptions, which inextricably involve traditional view of causality, anticipatory systems
are clearly excluded from discussion. However, when we proceed to consider systems in
terms of relations between input-output pairs of mappings of time, we find that causality
needs only dictate natural regularities relating causes and effects, without necessarily
including a built-in forward-temporal restraint. Thus anticipatory behavior not only is
possible, but, because general input-output relations contain Newtonian dynamics as
special cases, it is actually less restrictive and therefore in some sense generic.
Teleology
We now consider the assertion that anticipatory systems involve teleology or final causes in
an essential way, and thus must be excluded from science. Feedforward behavior seems
telic, or goal-directed. The goal is in fact built in as part of the model that connects predicted
future states and present changes of state. But the very suggestion that a behavior is
goal-directed is repellent to many scientists, who regard it as a violation of the Newtonian
paradigm.
The formulation of this ‘‘teleophobic’’ assertion goes back to Aristotle’s conception of
causality, in which four distinct kinds of ‘‘causes’’ for any physical event are recognized.
Adapting this Aristotelian parlance to the above discussion, if we regard the current value of
an observable at an instant as such an event, and if we allow only Newtonian dynamical laws
to express relations between events, then we may say that:
B
the initial conditions are the material cause of the event;
B
the constitutive parameters of the system are its efficient cause; and
B
the system laws are its formal cause.
This assignment of three of the causes exhausts all the quantities and relations in the
Newtonian expression; hence the event can have no room for the fourth, final cause. This
observation is essentially the entire basis for asserting that scientific explanation (which is
posited in advance to be exclusively embodied in reactive relations) cannot involve final
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causes. Moreover, since final causes presuppose future states and/or future inputs, we must
according to this argument a fortiori exclude anticipatory systems.
However, already in physics we find numerous situations in which present events appear to
be determined by subsequent ones. Of course, such situations are not directly governed by
reactive laws. An obvious example is any system which obeys an ‘‘optimality principle’’,
such as Fermat’s principle in optics or Hamilton’s principle in mechanics; here the actual
path described by a physical process is as much determined by its terminal state as by its
initial one. A similar teleological aspect can be seen in Le Chatelier’s principle in physical
chemistry and in Lenz’s law of electricity. These principles express that in case of
disturbance, the system develops forces that counteract the disturbance and restore a state
of equilibrium; they are derivations from the principle of minimum effect. Further, the
transition of a system to a state of ‘‘minimal free energy’’, ‘‘maximum entropy’’, etc., involves
a tacit characterization of such a state as the final cause of motion toward it. Precisely the
same situation is encountered in probability theory, where the family of convergence
arguments, collectively called the law of large numbers, asserts that limiting probabilities
exert an apparent attractive force on the successive steps of a random process, even
though those steps are independent. In sum, even though dynamical laws in physics
express conventional views regarding causality, they are mathematically equivalent to
principles in which a future state acts retroactively on a present change of state.
We should note that hidden teleology by itself is not sufficient to define an anticipatory
system. An optimality- or otherwise determined future still constitutes a reactive system. An
anticipatory system needs to use the information from its predictive model to change the
present, so that a possibly different future from one that is originally predicted may result.
Anticipatory system
Having analyzed and dispensed with those formal arguments adduced to justify excluding
anticipatory systems from system theory, let us now be positive, and construct (necessarily
informally in this introductory exposition) a sample anticipatory system with some synthetic
arguments.
Let us suppose that we are given a system S that is of interest. S may be an individual
organism, or an ecosystem, or a social or economic system. For simplicity we shall suppose
that S is an ordinary (i.e. non-anticipatory) dynamical system. As we have seen, this fact
allows us to make predictions about the future states of S, from a knowledge of an initial state
and of the system input. Indeed, the dynamical law itself already expresses a predictive
model of S.
But let us embody a predictive model of S explicitly in another physical system M. We require
that if the trajectories of S are parameterized by real time, then the corresponding
trajectories of M are parameterized by a time variable that goes faster than real time. Thus,
any observable on M serves as a predictor for the behavior of some corresponding
observable of S at that later instant.
We shall now allow M and S to be coupled; i.e. allow them to interact in specific ways. For the
simplest model, we may simply allow the output of an observable on M to be an input to the
system S. This then creates a situation in which a future state of S is controlling the present
state transition in S. But this is precisely what we have characterized above as anticipatory
behavior. It is clear that the above construction does not violate causality; indeed, we have
invoked causality in an essential way in the concept of a predictive model, and hence in the
characterization of the system M. Although the composite system (M þ S) is completely
causal, it nevertheless will behave in an anticipatory fashion.
Similarly, we may construct a system M with outputs that embody predictions regarding the
inputs to the system S. In that case, the present change of state of S will depend upon
information pertaining to future inputs to S. Here again, although causality is in no sense
violated, our system will exhibit anticipatory behavior.
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From the above remarks, we see that anticipatory behavior will be generated in any system
that:
B
contains an internal predictive model of itself and/or of its environment; and
B
is such that its dynamical law uses the predictions of its internal model in an essential way.
From this point of view, anticipatory systems can be viewed as a special class of adaptive
control systems.
There are many another modes of coupling, discussed in AS, which will allow S to affect M,
and which will amount to updating or improving the model system M on the basis of the
activity of S. We shall for the present example suppose simply that the system M is equipped
with a set E of effectors that operate either on S itself or on the environmental inputs to S,in
such a way as to change the dynamical properties of S. We thus have a situation of the type
shown in Figure 3, formulated as an input-output system.
An anticipatory system S entails the following:
B
S possesses a model subsystem M;
B
there is an orthogonality between the model M and the collection of observables of
S , M;
B
the rate of change (the adaptation) of observables of S , M depends on M;
B
the effect of the model M creates a discrepancy – S would have behaved differently if M
were absent; and
B
M is a predictive model – by looking at a present state of M, one obtains information
pertaining to a future state of S.
Errors
A natural system is almost always more than any model of it. In other words, a model is, by
definition, incomplete. As a consequence, under appropriate circumstances, the behavior
predicted by a model will diverge from that actually exhibited by the system. This provides
the basis for a theory of error and system failure on the one hand, and for an understanding
of emergence on the other. It is crucial to understand this aspect in any comprehensive
theory of control based on predictive models.
Anticipation can fail in its purpose. A study of how planning can go wrong is illustrative;
indeed the updating of models from lessons learned is the essence of an anticipatory
system. The causes of errors in anticipation may be categorized into:
B
bad models;
B
bad effectors; and
B
side effects.
Figure 3 Anticipatory system
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A bad model can result from technical, paradigmatical, or state-correspondence errors, all
due to improper functorial imaging of mappings. In short, faulty encodings lead to faulty
models. A proper choice of the internal predictive model M and the fine tuning of its updating
processes are evidently crucial to an anticipatory system’s success.
An effector E is defective when it is incapable of steering S, when it cannot appropriately
manipulate the state variables, or simply when it fails to accordingly react to the information
from M. Thus the careful construction of an anticipatory system also depends on the
selection, design, and programming of the effector system E, as well as on the partitioning of
the ‘‘desirable’’ and ‘‘undesirable’’ regions of response.
Side effects arise because, essentially, structures have multiple functions and functions may
be carried out by multiple structures. Combined with the fact of incomplete models, the
consequence is that, in general, an effector E will have additional effects on S to those
planned, and the planned modes of interaction between E and S will be modified by these
extraneous effects.
The diagnosis and treatment of erroneous anticipatory systems are frequently analogous to
the procedures used in neurology and psychology.
We may further ask, how does a system generate predictive models? On this point we may
invoke some general ontogenic principles, by means of natural selection, to achieve some
understanding. And finally, given a system that employs a predictive model to determine its
present behavior, how should we observe the system so as to determine the nature of the
model it employs?
Lessons from biology
The conscious generation and deployment of predictive models for the purpose of control
are some of the basic intuitive characteristics of intelligence. However, precisely the same
type of model-based behavior appears constantly at lower levels of biological organization
as well. For instance, many simple organisms are negatively phototropic; they tend to move
away from light. Now darkness in itself is physiologically neutral; it has no intrinsic biological
significance (at least for non-photosynthetic organisms). However, darkness tends to be
correlated with other characteristics that are not physiologically neutral, such as moisture
and the absence of sighted predators. The tropism can be regarded biologically as an
exploitation of this correlation, which is in effect a predictive model about the environment.
Likewise, the autumnal shedding of leaves and other physiological changes in plants, which
are clearly an adaptation to winter conditions, are not cued by ambient temperature, but
rather by day length. There is an obvious correlation between the shortening day, which
again is physiologically neutral in itself, and the subsequent appearance of winter
conditions, which again constitutes a predictive model exploited for purposes of adaptive
control. Innumerable other examples of such anticipatory preadaptation can be found in the
biosphere, ranging from the simplest of tropisms to the most complex hormonal regulation
mechanisms in physiology.
Since feedforward or anticipatory control is as ubiquitous as it seems to be, a number of
fundamental new questions are posed to us. Among them are the following. Can we truly say
we understand the behavior of such a system if we do not know the model employed by the
system? How is it possible to determine the character of that model, in terms of measurements
or observations performed on the system? More generally, under what circumstances is it
possible for a system to contain an internal model of its world? What relations must exist
between a set of indicators (environmental signals) and system effectors that will allow an
effective feedforward control model to be constructed? How can the behaviors of different
systems, perceiving the same set of circumstances but equipped with different models, be
integrated? (This last is essentially the problem of conflict and conflict resolution.)
The questions just raised bear directly on the present search for forecasting and planning
technologies to guide our behavior in the political, social and economic realms. Tacit in this
search is the perception that our society and its institutions can no longer function effectively in
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a cybernetic or reactive mode; it must somehow be transformed into a predictive or
anticipatory mode. That is, it must become more like an organism, and less like a machine[8].
In dealing with various challenges in our world, properties of biological systems will provide
crucial insights. Robert Rosen was fond of saying ‘‘the first lesson to be learned from biology
is that there are lessons to be learned from biology’’. Indeed, considered in an evolutionary
context, biology represents a vast encyclopedia of how to solve complex problems
effectively; and also of how not to solve them. Biology provides us with existence proofs, and
specific examples, of cooperative rather than competitive activities on the part of large and
diverse populations. Biology is the science of the commonality of relations, and relationships
contain the essential meaning of life. These insights represent natural resources to be
harvested, resources perhaps even more important to our ultimate survival than the more
tangible biological resources of food and energy. But to reap such a harvest, we need to
fabricate proper tools. It is my belief that the conceptions of nature arising from relational
biology will help us learn how to make it so.
Notes
1. A terse exposition for a general readership, such as the present article, by definition cannot get into
too many details. It is the author’s hope that this brief glimpse into the world of relational biology
piques the interest of some readers to pursue the subject further. For further exploration the reader
is referred to the recent book More Than Life Itself by the author (Louie, 2009).
2. Rosen wrote AS in the first six months of 1979. I became his PhD student just as he finished the first
draft. I was one of the first to read it, so I have been associated with the subject right from the
beginning. For a variety of external reasons, the book was not published until 1985. The Pergamon
Press book is long out of print, although one may be able to find copies in university libraries (or from
a resourceful used-book dealer).
3. Note the singular form system in ‘‘system theory’’: not ‘‘systems theory’’. This last usage is an error
that became accepted when it had been repeated often enough, a very example of ‘‘accumulated
wrongs become right’’. Just think of ‘‘set theory’’, ‘‘group theory’’, ‘‘number theory’’, ‘‘category
theory’’, etc. Of course one studies more than one object in each subject! Indeed, one would say in
the possessive ‘‘theory of sets’’, ‘‘theory of groups’’, ‘‘theory of numbers’’, ‘‘theory of categories’’,
. . .; one says ‘‘theory of systems’’ for that matter. But the point is that when the noun of a
mathematical object (or indeed any noun) is used as adjective, one does not use the plural form.
4. Just in case some readers may not be aware of the reference: Linus is a character from Charles
M. Schulz’s Peanuts (q United Feature Syndicate, Inc.), the most popular comic strip in the world for
50 years. Linus gets one holiday ahead of himself, and anticipates the arrival of the Great Pumpkin
on Halloween: ‘‘On Halloween night, the Great Pumpkin rises out of the pumpkin patch, and flies
through the air with his bag of toys for all the good children in the world!’’. This is an example of an
anticipatory system in which the predictive model is somewhat faulty, and the faster time line goes a
little too fast. For a quick review one may seek out a video of the 1966 television special ‘‘It’s the
Great Pumpkin, Charlie Brown!’’.
5. A more proper contrastive word of ‘‘feedback’’ should have been ‘‘feedforth’’, but ‘‘feedforward’’ is,
alas, ingrained terminology in control system theory.
6. For the readers not acquainted with the word ‘‘functorial’’ (it being a concept from the mathematical
theory of categories), they may simply take it to mean ‘‘pertaining to a mapping that takes into
account the processes involved in addition to inputs and outputs’’.
7. The topic of my second tutorial session at FuMee 1 was the modeling relation. There is only room in
the present article, however, for a small fraction of that particular exposition. The reader is referred to
AS (if a copy can be found), Rosen (1991), and Louie (2009) for a detailed treatment of the subject,
which is considered by Rosen to be the point of departure of science.
8. As the British geneticist and evolutionary biologist J.B.S. Haldane once said, there are four stages in
the development of people’s reaction to a new scientific idea: (1) This is arrant nonsense. (2) This is
interesting but controversial. (3) This is true, but trivial. (4) I always said so. With regards to Rosen’s
science, when I was his graduate student 30 years ago, the world was definitely in stage 1; I think it
has now progressed to somewhere in stage 2.
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References
Louie, A.H. (2009), More than Life Itself: A Synthetic Continuation in Relational Biology, Ontos Verlag,
Frankfurt.
Rosen, R. (1991), Life Itself: A Comprehensive Inquiry into the Nature, Origin, and Fabrication of Life,
Columbia University Press, New York, NY.
Further reading
Rosen, R. (1978), Fundamentals of Measurement and Representation of Natural Systems,
North-Holland, New York, NY.
Rosen, R. (1985), Anticipatory Systems: Philosophical, Mathematical & Methodological Foundations,
Pergamon Press, Oxford.
About the author
A.H. Louie is a mathematical biologist. His premier interest is in pure mathematical biology:
conception and abstract formulations. This area of research is called relational biology, the
school of Nicholas Rashevsky and Robert Rosen. Dr Louie has just finished writing a book on
the subject. More than Life Itself: A Synthetic Continuation in Relational Biology was
published in 2009 by Ontos Verlag.
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