Dynamics, Department of Communication Studies,
Oude Hoogstraat 24, 1012
11(4) (1994) 31-51
The meaning of "time"
a post-modern "chaology" differs from "time" in the Newtonian
The construction of "time" in the cosmology dates back to debates among
Huygens, Newton, and Leibniz. The deconstruction of this cosmology
an uncertainty in the time dimension. While order has been conceived as
an "harmonie préétablie," it is considered as emergent in
an evolutionary chaology. Communication systems can be considered as
in space and time: substances contain force or action, and they
communicate not only in (observable) extension, but also over time.
each communication system can be considered as a system of reference
a special theory of communication, the addition of an evolutionary
to the mathematical theory of communication opens up the possibility of
a general theory of communication.
Key words: time,
cosmology, epistemology, self-organization
Prigogine and Stengers
 have pointed to the centrality of the concepts of "time and
for the cosmology contained in Newtonian physics, but they have not
this issue beyond the domain of physics. In a chaology, however, one
fully appreciate that different systems may use different clocks .
the post-modern understanding were to assume a standard clock, it might
be caught eventually within the very cosmology which it wished to
In other (e.g., social) systems time may have to be given a
The problem of the
of time among systems (e.g., clocks) was central to Huygens' research
the differential calculus enabled Newton and Leibniz to develop the
of infinite and continuous time within the new physics. Towards the end
of the 17th century, these scholars provided natural philosophy with
mathematical and metaphysical foundations. I shall deconstruct this
and present an alternative chaology in terms of the philosophical
which have been basic to the mathematization of physics.
1. The construction
of the modern cosmology
In 1690, Christiaan
According to Descartes,
one is able to infer reflexively from the uncertainty which one finds
one's Ego ("cogito") to clarity concerning the existence of the
subject of this reflection ("ergo sum"). Consequently, the act
doubt provides us with a point of departure for further investigations.
With hindsight, Huygens' analysis clarified that Descartes had
a one-dimensional theory of knowledge, namely one in which the subject
is able to replace uncertainty with clarity by reflection. In order to
be able to distinguish between mathematical clarity and empirical
Huygens needed a two-dimensional theory of knowledge: whatever one
on a priori grounds, and however clear this may be in
terms, the inference remains an hypothesis about the physical world
yet needs to be tested empirically in order to become more certain.
What is the nature of
relation between contingent uncertainty and a priori (e.g.,
clarity if one distinguishes between the two? Let me quote Huygens
While Newtonian thought
is most versatile in terms of an idealized mathematical system in
to the contingent mechanical worldview, the Cartesian Huygens was
by philosophical problems. Huygens, however, was in the first place a
he was so deeply impressed by Newton's Principia (1687) that he
expressed the wish to pay the author a visit, which became possible
the Glorious Revolution in England (1688-1689). After his return he
in a letter to his friend Leibniz that he found Newton's hypothesis
gravitation still "absurd."[Note 4] Analogously, he had reservations
Leibniz' differential notations, since they were based on algebra and
on geometry. However, from 1690 onwards, Huygens began to use Leibniz'
notation for differentials along with ideas from Newton's physics in
own work, despite his philosophical reservations. Physics had
become one theoretical system.
the New Philosophy
The philosophical point
in the above quotations is different from the question of their
for the understanding of the history of early modern physics.
the "cogito" leaves room for other notions of the "res extensa"
than the Cartesian identification of a body with extension. What does
mean that a mathematical dimension could be added to the mechanistic
The theory of knowledge
in Cartesian philosophy was implied in the fundamental first step of
central inference which is internal to the Ego. The argument of
"Cogito ergo sum" preceded the step in which Descartes invoked
Goodness of God ("Veracitas Dei") as a warrant that our
imaginings about the (external) world correspond with a physical
(including our own corporal existence). There is nothing in contingency
itself which guarantees that this environment exists as "res extensa,"
i.e., as physical matter, and not as mere imagination. The cogito
itself clarifies only the contingency of the cogitans: a system
which is in doubt about itself is reflexively aware that it could have
been otherwise, i.e., that it is contingent. This contingency refers to
other possible states of the same system.
Additionally, if one is
uncertain, one is uncertain about something. But neither the
of the res extensa nor its dimensionality can be determined by
itself. In short, there is always self-reference to the system which is
uncertain, and at the same time there is a reference to a demarcation
something else which is thus considered as environment. But a reference
to a demarcation is not a demarcation! In the act of doubt, the
cannot determine itself substantively, since it does not in itself
knowledge about the existence or the nature of an outside world.
the contingency can only be specified self-referentially.
the reflexive cogito with a previous state, and thus with a
to finite time. Consequently, the delineation of the contingentEgo
implies a reference to a transcendent Other, infinite
or Eternity. However, the contingent Self can only be delineated
from its Transcendency. Any positive delineation of the contingency
additional information, i.e., information which does not originate
within the cogito, but from its relation with an environment.
long as there is no delineation from an external system, there can only
be contingency in relation to transcendency.[Note 5] As soon as
else is considered as different but contingent, one has to assume
between system and environment, communication in time, and
of the system's time.
1.2. "Time" in the
The question about how
time is communicated among systems and with reference to infinite time
was crucial to the new philosophy. In relation to transcendency,
contained only its own time which was negatively delineated from
time and eternity; as soon as one has inferred beyond God to the
of a contingent system other than the cogito, one can raise the
question of how the systems manage to remain synchronous over time? Can
they use their mutual communications for updates or do they have to
independently to a "standard clock"?
In philosophy the
problem is at the core of the well-known mind-body problem: how do the
body and the mind communicate when knowledge of the physical world is
and subsequently, how do they communicate in human action as an
of the free will? Descartes originally raised this question in terms of
the communication between the substances: how do the res cogitans
(thinking) and the res extensa (matter) communicate? The
of two clocks which run synchronously was introduced by the Cartesian
However, not only the metaphor, but also the formulation in terms of communication
between two systems remained central throughout the 17th century. For
when Leibniz published his system in the Journal des Savants at
the end of this century, he entitled his treatise "New systems of the
and of the communication of substances, and of the union between the
and the body" .
In the metaphor of the
synchronicity between two clocks, the one clock represents the physical
world, the other the spiritual one. How does it happen that our mental
perceptions correspond with reality? As noted, Descartes' metaphysical
answer to this problem had been that the Goodness of God implies that
would not continuously deceive us. However, in a mechanistic
one would like an answer to the question of how this mechanism works in
Huygens made this very
question central to his research programme for the new physics. The
question of the day was the problem of keeping clocks synchronous on
of ships at sea. Huygens generalized this problem to the question of
communication between oscillating bodies in a study of 1673, entitled Horologium
oscillatorum (cf. ). Note that this latter study was not a
to the practical problem, which had already been amply discussed in his
1655 study entitled Horologium, but more importantly to the
theoretical problems in the new Natural Philosophy.
While Huygens gave an
mechanistic answer to the question of how different systems communicate
time, Geulincx at Leuven had proposed that at the moment of each
God had to intervene to keep the two clocks synchronous (so-called
In a study, entitled Harmonie préétablie (1696),
elaborated a third possibility for keeping the two clocks operating
1.3. "The Time of
Lord is the Best of All Times" [Note 6]
the hypothetical character of the harmonie
which he proposed. He formulated that
The quest for an
solution became particularly urgent in 1685 when Protestantism was
vehement attack by the counter-reformation. In this year, Louis XIV
the Edict of Nantes, and in England, a catholic king (James II) had
to the throne. Protestantism was on the defensive; one might even say
the verge of a breakdown. Could it be provided with other options than
a retreat to defensive orthodoxy in its relation to the new philosophy?
How could the internal contradictions between the new religion and the
new philosophy be resolved in order to maintain both freedom of
and the explaining power of the emerging modern science? Was there any
possibility of bringing these great systems into harmony?
In the winter of
Leibniz wrote the first draft of his Discours de la
Newton completed his Principia,[Note 9] to be published in
and Huygens was ill and depressed in The Hague, since he was not
to return to the Academy in Paris of which he had been director for so
many years.[Note 10] Although there would remain differences of opinion
among these three scholars,[Note 11] in the years 1685-1689 the
system in terms of Newtonian physics, the calculus, and Protestant
was put into place. When Huygens came to visit Newton in 1689, his
brother Constantijn was the private secretary of the new King of
(William of Orange). Newtonianism could thus become the basic ideology
for the English revolution from 1689 onwards . A metaphysically,
and ideologically supported coalition could be formed between England,
Holland, and Prussia, which laid the foundation for the 18th-century
In the decades
these events, the various ingredients to resolve the tensions between
mechanistic philosophy and the Christian religion had been developed
in the relations and oppositions among Huygens, Leibniz, and Newton
e.g., ). Huygens agreed with Newton about replacing the Cartesian
with a concept of continuous and empty space; Leibniz and Newton had
the mathematical idealization of differential calculus independently of
each other; and all three of them agreed about the existence of
and infinite time (and by consequence, about eternity). The grand
however, was forced by the historical situation.
After 1689, the
system had been brought into harmony with its surrounding culture by
order in the time dimension. The human soul has to live on earth, i.e.,
in finite time, but its immortality provides it with the possibility to
follow Christ, and to return to God's eternal time.[Note 13] The
of differential calculus serves most graciously and convincingly to
the transition between the transcendent and the contingent: the
of this contingent world should be understood as a manifestation of
time and space. The infinitesimal transition exhibits how worlds other
than the one which we perceive with our senses resound within it. One
not even be able to understand the contingent properly without drawing
upon the idealized model. More generally, understanding physical
through the mathematical model provided a mental model to reconcile the
idealistic and the mechanistic interpretations of experimental facts.
possibility of reconciliation between mathematical clarity and
uncertainty is warranted ex ante, but has to be realized
1.4. The dynamic
between (un)certainty and (un)clarity
The cosmology warrants
order within each of the substances and between them, so that what
at first to be different (i.e., the Word and the world) can be resolved
into harmonic correspondence. The harmonic solution at the cosmological
level warrants reconciliation at the metaphysical one: nature is
to us by God's grace, and therefore we are able to reconcile our
image with physical reality. While there is initially a gap between the
complexity of the contingencies and the idealization in the model
the two dimensions of mathematical clarity and empirical uncertainty
be brought to interact, and we are warranted in achieving scientific
i.e., true knowledge about the world. Such interaction, however,
a process in the time dimension.
Taking time as a
given, Newton and Huygens could then formulate the two central
on how to achieve more clarity and certainty by scientific
On the one hand, Newton tended towards the empiricist position when he
formulated his well-known "hypotheses non fingo":
2. The construction
of a chaology
As soon as there are
than two systems to synchronize, the interaction can in principle be
in more than one way, and therefore the transcendental relation may
become uncertain. If this is historically reflected in philosophy--as
has been--the issue is no longer whether one should build upon the bank
of subjective (un)clarity or on the (un)certainty in the phenomena, but
rather the question of which uncertainty or which unclarity one may
and/or be able to build on. In the absence of a single metaphysical
for preestablished harmony and cosmos, asynchronicity and chaos will
I showed above in terms
of Huygens' critique that the question of how clarity can be related to
uncertainty was raised in the 17th century, but was then answered in a
specific way in order to secure the progress of physics. I shall argue
in the second part of this study that one can nowadays specify the
under which clarity can be generated in relations among systems which
and process uncertainties.
Indeed, in the
of science, in the social sciences, and most pronouncedly in the
sociology of science (e.g., ), we have increasingly lost all notion
of truth in the transcendental sense of fundamental certainty; we have
become fundamentally uncertain. Can anything more than informed opinion
be formed in sociological theorizing? Does this imply that one can
achieve only uncertainty?
As noted above,
may substantively mean something different in various dimensions.
we need a definition which leaves room for the variance in the
meaning of uncertainty, i.e., a definition which is analytically
of any system of reference. A definition without reference to a system
has to be content-free, i.e. a mathematical definition.[Note 16]
In 1948, Shannon
us with such a definition of "uncertainty" as part of the mathematical
theory of communication . Shannon defined "information" as the
contained in a finite sequence of signals or, more generally, in a
Whether one should call this quantity "information" has been heavily
(e.g., [2, 5]). But more important than these semantic problems, was
equation of the concept with probabilistic entropy . In contrast to
thermodynamic entropy, however, the probabilistic uncertainty is
yet content-free, i.e., it is still open to substantive specification.
a measure of disorder among molecules in thermodynamics, and it can
be used to describe the direction of time in evolutionary processes
[6, 7, 49]). In the social sciences, however, one is usually not
in the non-equilibrium thermodynamics of a physico-chemical system, but
in the development of uncertainty, disorder, and complexity in social
Thus, the uncertainty refers to a different substance, and it can be
only by a different theory of communication. But how can substances
if there is no pre-established harmony and synchronicity?
interpretation of communication
of concepts like "entropy" and "communication" to the dynamics of
other than the physico-chemical one requires further reflection on the
assumptions contained in the mathematization of physics. As noted, the
concept of communication is much older than the thermodynamic concept
entropy  or its probabilistic interpretation in the mathematical
of communication . Descartes and Huygens, for example, had to
that "motion" (momentum and energy) is communicated in a collision in
to be conserved, and thus they discussed this conservation in terms of
the "laws of communication of motion."[Note 17] I showed above that
gave the Cartesian concepts a physical interpretation. I shall now use
the example of the collision in a classical system to infer the
concept of communication from this older notion of communication as a
In a system of
balls momentum and energy have to be conserved, and thus to be
upon collision. As we know nowadays, the efficiency of the
of momenta in a physical realization depends on the amount of (free)
which dissipates as thermodynamic entropy. The ideal communication of
and kinetic energies of the colliding balls is thus dampened by this
When the physical realization approximates the ideal case, the
entropy vanishes, but the redistribution of momenta and energies at the
macro-level becomes more pronounced (since there is less dissipation).
Correspondingly, the message that the collision has taken place
a larger amount of information (i.e., Shannon-type uncertainty). Thus,
the two types of entropy can vary independently: the one may increase
the other vanish in the same event. The reason for this independence is
that the systems of reference for the two entropies are different:
entropy refers exclusively to the distribution of, for example, momenta
and positions among molecules, while the reference system for
entropy in this case is the system which conserves macroscopic momenta
and energy. Thermodynamic entropy is generated only in the special
where the communication has the physico-chemical system as its
definition of entropy enables us to develop a content-free definition
communication systems which operate by processing distributions. In the
example above, the macroscopic energy system communicated in terms of
kinetic energies of (billiard-type) balls, the momentum system in terms
of momenta. Social communication systems communicate in terms of means
of social communication (e.g., discourse, visualizations, money, etc.);
human bodies communicate in terms of hormones and neural potentials. In
these cases the probabilistic entropy is defined with reference to
other than the physico-chemical one.
The translation of
uncertainty into mathematical clarity by Descartes has been generalized
by Shannon to the understanding of a contingency as a probability
Like the uncertainty in the act of doubt, the mathematical awareness of
a probabilistic event cannot be given a substantive meaning internally
by this theoretical system; it needs an external reference. However,
external reference again need not be physical existence. In
other than the physical one, other quantities than "motion" may have to
be conserved, and therefore communicated.
For example, in
chemistry a mass balance for each element involved in the reaction is
In this case, the atoms of the elements are redistributed. One can
the communication of any redistributed quantities as a message which
information, and thus in terms of probabilistic entropy. The systems
subsystems)[Note 19] are different with respect to the quality of what
is being communicated, not with respect to the generation of
entropy. If the system under study generates probabilistic entropy with
respect to two communications (e.g., on the occasion of a collision
respect to energy and momentum), a probabilistic entropy is generated
each dimension of relevance. In general, the number of dimensions
the information in the message that the event happened is equal to the
number of systems of reference for the information. Each system of
reference adds another quality to the uncertainty, and therefore
dimension to the communication.
Thus we arrive at a
formulation of the problem noted by Huygens that the dimensionality of
the uncertainty has to be specified. When Huygens refered to
space and physical extension, he hypothesized two dimensions
mathematical a priori knowledge and physical uncertainty),
Descartes had hypothesized only one dimension, in which clarity
can substitute for uncertainty. If, for example, in a chemical reaction
three (qualitatively different) elements have to be balanced in terms
their respective total mass, the message of this event will analogously
contain a three-dimensional uncertainty.
Information is never
but necessarily itself processed within a contingent communication
The communication systems are delineated in terms of what they
Whatever they communicate is redistributed in the communication, and
redistribution is in itself a message which is sent to all the
systems with which this system can communicate externally. In a single
communication, i.e., by its contingent operation, the system
internally that it has reached a new state, and externally to all
systems that this contingency has happened in their environment.
the receiving systems can only receive the message by operating, and
by redistributing their own information contents. Cycles of
are thus generated. The complexity increases rapidly (i.e., with the
of the number of systems [Note 20]) unless the systems are also able to
(self-)organize the information.
What are the conditions
under which communication systems can also organize their chaos, either
among one another or internally? In other words: what are the
under which networks can retain and organize information? As noted,
systems are conservative, i.e., the number of elements which can be
is fixed. In general, the number of elements (n) which a system
contains sets a limit to the information which the system can hold. One
may also express this as the maximal entropy (viz., equal to log(n)).
As noted above, the number of elements in systems can be multiplied by
adding other systems of reference to the communication, and thus by
the number of dimensions in the information (n x m).
open systems like social communication systems can be defined only in
of the communication, and consequently these systems have uncertain
Each additional node of the network n adds (n - 1)
links. In general, when the number of elements increases more rapidly
the information content of the system, the redundancy which can be
as the complement of the information content also increases. Thus, the
addition of new dimensions or new elements can lead to a relative
of the probabilistic entropy contained within the system.[Note 21] In
words, the uncertainty can be reduced within the system either by
the internal complexity or by growth.
The maintenance of the
system is a balanced outcome of its necessary production of
entropy by operating, and this capacity to organize the uncertainty
the system. Self-organization  or autopoiesis  can only
be achieved by communication systems which are able to reflexively vary
the organization of the uncertainty along the time dimension.
systems reconstruct their histories so that they can face their future
in terms of expectations. Note that this reflexive capacity can never
observed directly, but only hypothesized as an internal mechanism of
system(s) under study.
systems develop through processing, i.e., by redistributing whatever
communicate. With respect to this processing one can distinguish
self-referentiality (the internal processing of the message that the a
priori distribution of the substance of communication was changed
the a posteriori one), and external referentiality to all
of reference. On the one side, the number of reference-systems
the dimensionality of the information content of the self-referential
On the other side, the frequency of the update sets the system's clock.
Note that this frequency can be multi-variate, and thus be a frequency
distribution, i.e., a spectrum. The clocks tick with a variety of
There is no a priori reason for harmony: communications are in
Thus, in addition to
a potentially multi-variate environment for one another, the
systems constitute each others' environments in terms of time. To the
that communication among systems is sustained, the systems also have to
communicate frequency distributions in the time dimension. However,
is not a normal variate. This further complicates the analysis.
2.3. An example of
Before extending the
in the time dimension, let me illustrate this abstract
by elaborating on the simple example of a telephone conversation as a
with relevance for two qualitatively different systems, i.e., the
system and the telephone network.
First, the contingency
of a telephone conversation can be analyzed in terms of physical
through a network which can be mathematically modelled. The social
in a telephone call, however, remains external to the mathematics of
propagation of signals through the lines. Nevertheless, the social
system and the telephone system interact in this single event. By
both systems change as a consequence of the interaction. (Of course,
sending and the receiving systems are also involved.)
The social system and
telephone network, however, were not a priori in harmony. No
deity is involved, but only a couple of engineers who have done their
to make the telephone system function. As Latour (, at p. 188)
"There is no preestablished harmony, Leibniz notwithstanding, harmony
locally through tinkering." However, a user may fail to establish the
each communication system remains failure-prone in the interaction.
each of the two systems, while related to the other system in the
event of this historic phone call, does not contain nor acquire full
about the contingent boundaries of the other system through these
In general, the two systems remain virtual for one each other
interacting. They can observe one another only through the "lens" of
the two systems are not transparent for one another: it makes a
difference whether people communicate by telephone or through other
of communication, and it may make a difference for the telephone line
it transported data or voice-input (e.g., in terms of costs of the
In the interaction, the two systems "disturb" one each other, but they
do not delimit each other. Thus, they are each other's environment only
in the specific sense of having a communication window on each other.
the difference here from the concept of the relation between system and
environment in, for example, biology.[Note 22]
In summary, the two
disturb each other in the event of the historical interaction. The
is a contingent event, since it could have been otherwise. It is a
contingency, but it has a different relevance for each system of
Within each system the uncertainty in the event can be evaluated with
to the self-referential contingency within the respective system. The
of the one system is underdetermined by the other, since it is not
from it as such, but only in the interaction. Analogously, the
in the other system is also not delimited by the interaction. The
communicate in relation to one another autonomously like Leibniz'
but they are contingent! However, since they cannot fully perceive each
other's contingency, the systems are autonomous centres of control in
to one another, and only on this basis can they interact. In this
it is not clear for each system which systems interact, since each
only contains its own contingency, although each system is partially
informed about the interacting systems by the interaction.
In the reconstruction,
each system has no other source of information about the possible
interactions in the communication with other systems than the
which it can retrieve from its own history. But the system can only
knowledge internally from this uncertainty, if it is capable of storing
information about its previous states, and if it is additionally
of taking this information reflexively into memory. If so, it may
itself historically, and in relation to the multi-dimensional space of
systems of reference, and thus produce meaning in a second-order
Thus, only systems which can reflexively reconstruct, in addition to
part of a (relational) construction, can produce expectations.
reconstruction requires the capacity of the system to take the
self-referentiality of the system's history into memory. Obviously,
are (among [Note 23]) systems which can act reflexively.
As noted, Huygens
his experience within his contingent cogito differently from
However, if a cogito expects that another system is a relevant
disturbing) environment, how many negative instances does the cogito
need in order to revise this hypothesis? In other words: how frequently
does it internally update this reconstruction in relation to the
construction at the operational level? Additionally, one may raise the
question of whether social systems or theoretical knowledge systems are
not only constructed, but are also reconstructive, and whether they are
also able to update in a second-order cybernetics. However, this raises
further questions about the dynamics of distributed memory management,
since the memory function of social systems is operationally located in
human beings .
2.4. Extension to
Remember that we
in the first part of this study at the conclusion that without further
demarcation, the reflexive communication system contains only
in the time-dimension about the frequency of its self-referential
and it knows itself to be contingent. However, it can determine what it
communicates substantively only with reference to an environment; and
can only receive information from the environment insofar as the
consists of other communication systems. Thus, this notion of a system
is yet content-free: the contingency refers only to its finite
its being sequenced in time, and its being the yet unspecified
of a communication system among other communication systems.
The special character
time as a variate of a communication system was only recently made a
of methodological reflection in the social sciences. If two (or more)
communicate parts of the variance in each of them will usually have
post when compared with the situation ex ante, and the
of the respective variances will have remained the same. In other
one expects both continuity and change in the systems under study. The
continuous parts of the variances co-vary over time, and are therefore
"auto-correlated." If variances are auto-correlated, then so are their
error terms, and this violates a central assumption in regression
. Furthermore, a multi-variate system is expected to develop
from a set of non-coupled elements. Since each two or more of these
may form a system (or a subsystem within a system), the number of
expectations for future behaviour increases exponentially with the
of elements, and thus the inductive analysis rapidly becomes
24] The methodological statement that time-series data should not be
for regression analysis without correction for auto-correlation in the
data, means in qualitative terms that change in the multi-variate data
can only be assessed on the basis of an hypothesis for the delineation
of the self-referential system(s) that exhibit the observed
are right when they state that existing statistical models in the
sciences cannot cope with the complexities of social developments in
historical dimension. Social science statistics is most sophisticated
addressing problems of multi-variate analysis, but in a dynamic design
there are shortcomings with respect to the combination of the
and the time series perspective. How can an historical series of events
be assessed for its significance in relation to the range of
which might have occurred?
The common solution on
the qualitative side is to take the historical axis as a sort of
variable, to which all other developments are then discursively
in a narrative. This solution, however, is irreflexive with respect to
the time dimension; one should not assume that there exists one single
(i.e., historical) time. Time can only be defined with reference to a
and a clock can only be a system's clock. System clocks, however, may
according to a spectrum of different frequencies.
In general, clocks of
systems are expected to be asynchronous. There is no a priori
why the various periodicities should be the same for different systems,
i.e., why different systems should operate synchronously.
is a local event, which requires explanation. For example, it is only a
consequence of the rotation of the earth that many systems on earth
to be updated daily. In addition to whatever information may be
systems with a history must also update mutually, and occasionally must
synchronize in the time dimension.
to the problem of "auto-correlation" in the data is to reverse the
auto-correlation is not first to be corrected for on the basis of an
ideal case, but systems can only develop over time self-referentially,
i.e., with reference to themselves at a previous moment. By operating,
systems generate and redistribute variances by which they inform one
and which a reflexive analyst may be able to use as information about
interactions, and about their development. If the (reconstructive)
leads to the conclusion that the variances are not
not auto-correlated--this may indicate a special case where the systems
under study changed so importantly that a completely different system
(cf. ). Alternatively, the system may not have been correctly
in the time dimension is an event like all other communications. What
communicated is a frequency distribution (i.e., a spectrum).
to communication in other dimensions, some communication systems are
able to communicate this information, others are able to store it, and
specific ones are able to reflect upon it and give it an
Note that communications are discrete events, and that thus continuous
time is an idealization by the reconstructive system. Consequently, one
should be cautious in using differential calculus for the
because of the assumptions contained in it concerning the limit
to continuous time.[Note 25] Synchronization among systems always
3. Towards a
theory of communication
In analogy to the
interpretation of entropy, and the consequential definition of time in
terms of spectra of frequencies, one can give a probabilistic
to concepts in physics which build on the notion of entropy. However,
codified knowledge in physics is logically consistent, other concepts
modern physics can also be given a probabilistic, i.e., non-physical,
in a mathematical theory of communication.
How should one
a probabilistic interpretation of concepts and laws from physics? An
access is provided by using those concepts which, like the Boltzmann
rely heavily on the concept of entropy. From the probabilistic
of these laws and concepts one can derive content-free (mathematical)
which can subsequently be given meaning with reference to systems other
than the chemico-physical one.
In practice, computer
and cognitive scientists have already begun to investigate the
of Boltzmann equations for modelling complex network problems (e.g.,
For example, if a system tends to be in discrete states, the
of finding the system in each of these states is not different in the
than the probability of finding an electron in the various orbits which
are allowed in an atom. (In chaos-theory these discrete states are
"attractors.") Thus, we have the rich mathematical apparatus of physics
at our disposal for studying systems which can be described in terms of
Let us take the concept
of probabilistic temperature as an example. At prevailing probabilistic
temperatures one observes both the (self-)organization of systems
storage of probabilistic energy) and their generation of entropy in
(i.e., dissipation of probabilistic energy). However, if one "freezes"
the systems, one removes the factor of dissipation by bringing all
to their lowest energy states (according to the Boltzmann equation). In
chemical physics, we know this state as, for example, crystalline. The
attractors can be sorted separately, since they "peak" against one
in the observation at extremely low probabilistic temperatures. Note,
that a probabilistic temperature is not a physical temperature, but a
concept which can only be given meaning with reference to a system (or
a system of systems).
The range of
of these probabilistic simulations is fascinating: on the one hand, in
cognitive psychology attractors are constructed by training computer
e.g., for pattern recognition (so-called "Boltzmann-machines"; cf.
On the other hand, for example, Kuhn's  concept of "paradigms"
us with a mental model of the possibility of attractors in the social
the paradigm not only controls what is communicatable within it, but
shapes a social boundary between those who are "inside" and "outside"
relevant scientific community. Analogously, technological regimes can
considered as the higher-order attractors of interactions among
technological trajectories and socially distributed learning
The extension of
from physics to non-physical realms may sound at first like positivism,
but this is not positivism. First, we did not impose the model of
normatively upon the other sciences, but we used the results of modern
physics reflexively for the understanding of systems other than the
one by first giving the concepts a different (i.e., probabilistic)
Other systems are, among other things, much more complex than the
one in terms of what is being communicated. For example, in a simple
system a large number of mass balances are already involved. In
systems, people process feelings and thoughts, which are most difficult
to operationalize so that they can be externally observed. In social
people communicate by using language and symbolic media of
The nature of these communications, i.e., their operationalization, can
only be specified by theorizing at the relevant systems level. The
theory of communication guides us with respect to the modelling of the
interactions among the so specified communication systems, and provides
us with the mathematics for explaining their behaviour over time.
4. Discussion and
Naturally enough the
which I discussed above lead us back to the origins of Natural
in the 17th century. The individualistic revolutions gave way to
among religious, political, scientific, and economic communications,
maintaining a unified cosmology. In science, the embeddedness of the
subject in what it wants to investigate pointed to the reconstructive
reflexive nature of human knowledge. However, in this reflection one
on the question of what specific contingency meant for the development
of the whole, which was itself specified in terms of a transcendency.
the natural sciences, for example, one could assume that one could
from the specific positions of people with reference to the natural
by using the concept of a transcendental subject.
In relation to society,
or more generally with reference to social systems, this metaphysically
warranted assumption of commonality disintegrated in the 19th century
Marx). The claim of an objective meta-position is nowadays untenable in
the social sciences, since it is, for example, irreflexive to the bias
which is necessarily brought into the analysis by initial assumptions.
Whether this bias is a class position, a male bias or a wish to
the discourse (cf. Foucault) is secondary. The primary point is that a
theoretical system reconstructs the social system from a particular
of view. The crisis of the single great story distinguishes
The mere formulation of
the objective of general theory, therefore, may seem an invitation to
for those social scientists and philosophers who deny the possibility
general theory on normative and sociological grounds. Indeed, the issue
of general theory in sociology emphatically raises the issue of the
of the individual in society, and of the theory's own historicity.
Max Weber the first complex of issues has been debated in terms of the
(voluntaristic) theory of action . However, does the historicity of
an individual act destroy a priori the possibility of
society by using a theoretical model? In my opinion, the problem of
specifies only one criterion for a theoretical model, namely that it
be able to account for historicity. Additionally, theory should be able
to cope with its own historical contingency reflexively, i.e., to
itself in terms of a reconstruction.
The crucial point is
neither the substance under study nor the scientific communication
should be considered as spatial extension only; all communication
contain contingency in four dimensions, i.e., in space and
Observable stability is the special case in which one has to assume
continual reiteration or propagation of an already presupposed effort
counter-effort" (Leibniz)[Note 27] or--as we would now say--of a
feedback. Thus, an observation can only be informative with reference
an expectation, but the theoretical expectation is embedded in a system
of expectations. One may wish to close the system at either level, but
the closure can be deconstructed.
Newton and Leibniz
that substance should be considered as force or action, but they
their theoretical apparatus by basing it on a priori
On the one hand, these scholars were able to entertain concepts like
and "acceleration", since the calculus provided them with the concept
a second derivative. Obviously, if one wishes to explain events in a
of space and time, one eventually needs to supplement the geometrical
with an algebraic understanding.
On the other hand, this
conclusion has consequences for those sciences that have hitherto
on geometrical narratives for their understanding [15, 46]. In a
the theoretical apparatus is itself reflexive on its contingency; it
itself to be a communication system among other possible communication
systems, subject to continual changes. But since both the data and
interpretation are in flux, one needs an algebraic model for the
This next-higher-order complexity in comparison to Newtonian physics
for the interpretation of results in algorithmic "computerese" as a
extension of the "natural" language that uses geometrical metaphors.
of entropy, and its extension to a general theory of communication
us with methods to account for the historicity of both the lower-level
construction and the second-order reconstruction. A general theory of
adds to Shannon's mathematical theory of communication the concept of
of reference, and the non-equilibrium perspective. With respect to the
systems of reference, one needs special theories (by definition). The
perspective enables us to model evolutionary processes such as paradigm
developments, lifecycles, etc.
The scientific model,
remains reconstructive, and therefore part of a cultural evolution. The
reflexive awareness of this methodological status is the one important
aspect in which communication theory differs from biological evolution
theory. The latter hypothesized "natural selection" by the environment
as an external principle which independently organizes a variety of
data. Evolution theory then allows us, for example, to define "missing
links" in the evolutionary data, and it guides us in searching for
evidence of these instances. Reconstructions, however, provide us with
alternative hypotheses concerning what has guided the system(s) under
The alternative hypotheses may describe various aspects of learning,
the consequent emergence of patterns of behaviour and communication,
may then begin to act as selection mechanisms.
environments do not have to develop synchronously with the systems
study. A second-order cybernetics between selection and stabilization
to be assumed (e.g., [26, 33]). Evolution theory is then the
case in which the (natural) environment is considered the single
factor for selection. Sociological data, however, exhibit a
of dynamics, and the various systems are only hypothesized systems of
("attractors") instead of a single evolution. Thus, in relation to
the socio-cultural perspective adds reflexivity to the theoretical
While in other sciences it may be fruitful to take either variation or
selection as predetermined by "Nature" as a cosmologically warranted
of reference, sociological theorizing requires a reflexive awareness of
the variance and historicity of both dimensions.
1. Huygens , Vol.
at p. 541. See also: , at p. 37.
2. Huygens speaks of
own method as consisting of experientia ac ratione, that is,
with experience and reason.
3. Huygens , Vol.
at p. 325. See also: , at p. 131.
4. Letter of November
1690. (, Vol. IX, at p. 538.)
5. Note here the
notion of God: before delineation, i.e., in its self-referential
the contingency is exclusively defined in relation to its
i.e., in relation to God. Since the definition is internal to the
this implies a self-referential relation to a personal God, who is
in the reflection. In this sense, the Cartesian Ego reflects
6. Praise in the
choir of Bach's cantata Actus Tragicus (1707).
7. ; translated
the German edition: , at p. 269.
8. "Christian (...)
en l'estat où il se trouve, dans lequel il devroit comme
de pres l'immortabilité, il s'amuse à la controverter
une question problematique pour et contre." Letter of 22 May 1670 by
Lodewijk Huygens to the father, Constantijn Sr. (, Vol VII, at p.
9. The preface to the
edition gives May 8, 1686 as the date.
10. Huygens had
the Dutch Republic when French armies had attacked and almost destroyed
it in 1672. Notably, he had dedicated his Horologium Oscillatorum
in 1673 with the following opening sentence: "We are especially
to France, Oh Great King, for the rebirth and restoration of geometry
this century." For his glorious role in Paris, see for example: .
11. "I have been amazed
that Huyghens and Newton assume the existence of empty space. However,
this can be explained from the fact that they have persisted to discuss
in geometrical terms. More astonishing is it still for me that Newton
assumed an attraction which does not work by mechanical means. When he
states with respect to this issue that the bodies attract one another
terms of gravitation, then should this not be discarded--at least, with
respect to the observable interactions among the large bodies in our
system--although it seems that Huyghens also does not completely agree
with this." (Leibniz in a letter to Bernouilli, 1698; translated from
German edition , at p. 371.)
12. The Kurfürst
Prussia, Friedrich I, who was later to be crowned as king Fredericus
Rex, was a nephew of king William of Orange. His mother Louise
was a daughter of Frederik Henderik, Prince of Orange, who had relied
on the services of Huygens' father Constantijn Sr. The princess was two
years older than Christiaan Huygens, and as children they were raised
the same circles in The Hague. Note also that Friedrich's wife, the
Queen Sophie Charlotte, was herself a philosopher. She was a patroness
of Leibniz (who lived in Hannover), and founded the Akademie der
in Berlin upon his instigation in 1700.
13. Leibniz (1695)
that otherwise "the souls (would) remain without purpose in a chaos of
inextricable matter" (, at p. 262).
14. , Bk. I, at pp.
9-10. See: , at p. 38.
15. Whether this is
the case for quantumphysics is a separate issue. For this discussion,
for example .
16. Since mathematics
also be one of the systems of reference, one may also wish to call this
a meta-mathematical definition (cf. ).
17. "Within the
of the Cartesian program, laws of motion ought to be laws of
of motion expressed in measurable quantities." (, at p. 73.)
relation shows that in this case only a very small part of the
entropy (S) is probabilistic entropy (H). See also: ,
at p. 60.
19. At this level of
one is not able to distinguish among systems and subsystems.
20. When complexity
not with the power of n (i.e., nk), but with
exponent of n (i.e., exp(ßn)), the problem can be
complete, and therefore, becomes uncomputable in practice. See, for
21. The number of
states of the network increases with the exponent of the number of its
22. However, the
of self-organization, and its implications for the relations between
and environments, is often discussed also in relation to (biological)
theory. See, among others: [23, 25].
23. Since the systems
their operations were yet defined as content-free, the human being is
a specification (cf. ). Additionally, one has to specify what is
in the reflection (e.g., thought, feelings, etc.) and in terms of what
it is reflected.
are no auto-regressive (AREG and ARIMA) models for multi-variate data
but only for uni-variate trendlines. If one wishes to predict the
of a system of variables, one has to define a systems variable at the
level, but then one risks losing perspective on how the variances
the system change. See also: .
25. Although the
may wish to use them for pragmatic reasons, the application of
formulas to continuous distributions is theoretically more problematic
than their application to discrete ones. See also: , at p. 74.
26. In a study of the
of natural resources, Allen  found two attractors in the parallel
of the hyperbolic curve of fish against fishing boats. In formal terms,
this curve is similar to a traditional production function with capital
and labour along the axes (cf. [10, 36, 43]).
27. Quoted from
Dynamicum by , at p. 251. See also: .
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