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Gotthard Günther 
2000 Special

GÜNTHER - 2000

A contribution in three parts 
to the 100th aniversary of Gotthard Günther

Topic of Part 3:
"Zeit - Mehrzeitigkeit - Polyrhythmie // 
Time - Polytemporality - Polyrhythmicity"
(see also Introductions to Part 1 and Part 2)

by Eberhard von Goldammer

In the last chapter of his book "THE NATURAL PHILOSOPHY OF TIME" Whitrow shortly summarizes :[1]

"...the history of natural philosophy is characterized by the interplay of two rival philosophies of time - one aiming at its 'elimination' and the other based on the belief that it is fundamental and irreducible. The central point of dispute concerns the role of time in the relation of man to the external world."

And Whitrow continues:

"According to Kant, time (like space) pertains only to the perceiving mind and not to things in themselves. According to McTaggart, series which in themselves are non?temporal appear to us as temporal: in principle, the same set of objects are eternally (i.e. ´timelessly') there, the only change being in our consciousness from less (and more confused) to greater (and clearer) awareness. I maintain, however, that our conscious awareness of time is neither a necessary condition of our experience, in the sense intended by Kant, nor a simple sensation, as Mach believed, but an intellectual construction that depends not only on our physical surroundings but also on the particular type of culture in which we happen to live [italics from evgo]. Unlike McTaggart, most scientists believe that our perception of time is based on an objective factor that provides an external control for the timing of our physiological processes. This external factor is what we call physical time, but what is the nature of this 'universal' time?"

In the present introduction to part_3 of the Günther_2000-special we will neither discuss the philosophical question on the nature of a ´universal´ time nor the different physical concepts of time such as given by the Einsteinian relativity theory or by irreversible thermodynamics [2]. Within the present context, we only would like to point on part_1 and _2 of the Günther_2000 series, where we shortly discussed that physical processes can be described within a mono-contextural framework of logic, resulting in a so-called ´positive language´ of description. In physical sciences there is no need for a poly-contextural theory. In other words, Whitrow´s ´universal time´ results from a strict mono-contextural view of the world - a physical world without subjectivity. From a poly-contextural scientific point of view, however, the idea of an ´universal time´ is completely meaningless. As long as scientific research is founded exclusively on mono-contextural conceptions, its search for a ´universal time´ or a ´universal scientific theory´ (including living systems) will be a search of the bottom in a bottomless barrel. In a mono-contextural scientific conceptions ´live´ has to be pre-supposed as it is the case in today's so-called life sciences such as biochemistry, molecular biology, etc. On the basis of mono-contextural conceptions, time is a physical parameter in order to describe a linear sequence of events of processes that belong - in Günther´s parlance - to an intra-contextural description of a process. That means, the physical concept of time (directed or not) only has a definite meaning within one contexture and only under this condition the principle of causality can be used without anomalies, i.e., it is possible to speak from the past and the present as a linear sequence of events. It is this concept of a linear sequential time that was banished by Heinz von Foerster in "TIME AND MEMORY": [3]

"Dr. Whitrow said .. that we know little about ´memory.´ I whole-heartily agree but I would like to add that we know even less about ´time´. The cause for this deficiency I see in the superior survival value for all perceptive and cognitive living organisms if they succeed to eliminate quickly all temporal aspects in a sequence of events or, in other words, if ´time´ is abandoned as early as possible in the chain of cognitive processes..."

Within the analysis of the living present, the temporal coding in the brain, for example, addresses a pivotal issue in modern cognitive neurosciences in order to study the functionality of how ensemble oscillations and cooperative transitions represent the outer and inner world of a living system [4]. In his contribution "RECONSTRUCTION OF SUBJECTIVE TIME ON THE BASIS OF HIERARCHICALLY ORGANIZED PROCESSING SYSTEM" Pöppel (cf. ref. 4a) writes:

"... Subjective time in the psychophysical tradition has erroneously also been considered a continuous phenomenon. However, if one analyses subjective phenomena in different temporal domains, one is impressed by the great number of experimental observations on discontinuous information processing. Apparent continuity of time is a secondary phenomenon - actually an illusion - which is made possible by discrete information processing on different temporal levels..."

This statement tells us that the continuity of time has to be considered as an illusion and the question arises what then is the concept of time if living systems are the focus of scientific research? So far as this question is concerned, Varela opens his discussion at the New York Academy of Sciences with the following optimistic statement: [5]

"The question I wish to address is the following. At face value, there are two kinds of time: inner time and physical time. The first is the linear sequence of moments given by the clock we live by, and the other is what we live in. Both are valid as sources of facts and of scientific investigation. The first gives rise to well-developed physical theories; the other, to human temporality, centered on the present and manifesting as a threefold unity of the just-past and the about-to-occur. Both can be developed in precise scientific detail [italics from the author] ..."

Varela continues describing the situation in experimental psychology of time and in modern cognitive neuroscience (cf. ref. 5):

"...Instead of a long historical discussion, let me turn right away to a classic example that illustrates the situation very well. This is the chromatic phi?phenomenon, where a red light followed by a green light is shown at a specific temporal distance. The common perception is that of an ´apparent´ jumping of the lights, but interestingly the light changes color at midcourse! Unless we wish to assume a violation of the direction of causality, we are forced to conclude that perceived temporality is not simply isomorphic to linear time. Thus, this is a paradigmatic example of the needed distinction of not a single, but at least two kinds of time...."

Now we are confronted with a kind of complementary conception of time, namely the "inner (or subjective) time" and the "outer (or physical) time". This is a well known situation reflecting more or less the very old conflict of the subject-object dichotomy. For the experimentalists in life sciences, however, there are only two ways left: either the "inner time" is considered as result from the inner processualtity as a mental entity on one hand and cannot be measured - and that was it; or the inner time is considered as a physical entity and the inner processuality will be analyzed by comparison with a standard process, - a clock. Within the usual mono-contextural scientific conception no other alternatives exist. But we are still confronted by the question, what is the difference between an outer and an inner time, provided there exists something like time? In "TIME AND MEMORY" von Foerster (cf. ref. 3a) gives an interesting comment that clues to this question:

"...The conceptual construct of ´time´ is ... just a by-product of our memory, which in some instances may use ´time´ as a convenient parameter ? a tertium comparatum, so to say ? to indicate synchronism of events belonging to two or more spatially separated sequences. Of course, there is no need to refer to time in such comparison, for it is always sufficient to take one sequence as ´standard´ and to associate with standard events the events of another sequence..."

In other words, ´time´ as a by-product of our human brain represents like ´space´ a category of description. Or quoting Whitrow again, time is "an intellectual construction that depends not only on our physical surroundings but also on the particular type of culture in which we happen to live".

Von Foerster´s comment reveals some further interesting aspects. If ´time´ has to be considered as a conceptual by-product of the brain on one hand and on the other hand if it is the brain that has to describe the brain's conceptual construct of time, cognitive neuroscientists are hopelessly captured within a logical circle. This circle can be blown up apparently only if life sciences restrict their research efforts exclusively on physico-chemical processes. But then the question arises, what about mental processes, such as, for example, the development of conceptual construct of ´time´ ? In part_2 of this series we pointed to the fact that mental processes cannot be described without running into antinomies and ambiguities on the basis of a mono-contextural linguistic frame, i.e, a ´positive scientific language´ [6].

Obviously there is a principal logical problem involved - a problem which already has been pointed out by W.S. McCulloch 1945 in his study "A HETERARCHY OF VALUES DETERMINED BY THE TOPOLOGY OF NERVOUS NETS" [7]:

"Because of the dromic character of purposive activities, the closed circuits sustaining them and their interaction can be treated topologically. It is found that to the value anomaly, when A is preferred to B, B to C, but C to A, there corresponds a diadrome, or circularity in the net which is not the path of any drome and which cannot be mapped without a diallel on a surface sufficient to map the dromes. Thus the apparent inconsistency of preference is shown to indicate consistency of an order too high to permit construction of a scale of values, but submitting to finite topological analysis based on the finite number of nervous cells and their possible connections..."

A (logical) re-interpretation of McCulloch´s study has been published in 1988/89 and is available from the internet [8]. It is amazing that McCulloch´s idea of an heterarchical structure (of mental processes !) has been completely ignored until today by the scientific mainstream of the cognitive neurosciences. From a conceptual point of view, one even can state that modern cognitive neurosciences have not yet reached the intellectual level of McCulloch´s ideas published more than fifty years ago. A very good example that confirms this statement is given by the discussion "TIME AND THE OBSERVER: THE WHERE AND WHEN OF CONSCIOUSNESS IN THE BRAIN" [9] which deals with temporal anomalies of the processuality of the neurophysiological processes in the human brain. If heterarchical structures occur within these processes - as described by McCulloch - one should expect anomalies (in the sense of a logical paradoxes) given the interpretation of the temporal structure of neural events being exclusively considered as a hierachically stuctured processuality. This problem, however, has not been discussed in "TIME AND THE OBSERVER...". There is no comment, no reference which points to McCulloch´s fundamental considerations.

But it is not only McCulloch´s "A HETERARCHY OF VALUES..." which has not yet been reflected by the mainstream of cognitive neuroscientists, it is more or less the huge amount of conceptual work developed at the BCL [10] that has been ignored. One example is the work of Gotthard Günther, mostly published in German, with the exception of some studies in English, e.g., "TIME, TIMELESS LOGIC AND SELF?REFERENTIAL SYSTEMS", published in 1967(!), which will be presented in part_3 of this series. A relatively longer German version was published in 1966 [11].

In his paper Günther does not discuss the various conceptual constructs of time instead he goes back to the sources of our Western thinking and starts with a philosophical and logical analysis of ´time´. Therefore his contribution is still up-to-date although it has been written more than thirty years ago.

Since Günther´s article has no direct link to the problem of time in cognitive neurosciences as mentioned above, we will try to bridge this gap. [12] In order to give some insight into the timing problem of the neurosciences, we will quote again to Varela´s contribution in "NATURALIZING PHENOMENOLOGY" (cf. ref. 5b):

"... Even under a cursory reduction, already provided by the reflections of Augustine and James, time in experience is quite a different from time as measured by clock. To start with, time in experience presents itself not only as a linear but also as having a complex texture ... a texture that dominates our existence to an important degree ... this texture can be described as follows: There is always a center, the now moment with a focused intentional content ... This center is bounded by a horizon or fringe that is already past ... , and it projects towards an intended next moment ... These horizons are mobile: this very moment which was present (and hence was not merely described, but lived as such) slips towards an immediately past present. Then it plunges further out of view: I do not hold it just as immediately, and I need an added depth to keep it at hand. This basic texture is the raw basis of what I will be discussing in extenso below. In its basic outline, we shall refer to it as the three-part structure of temporality. It represents one of the most remarkable results of Husserl's research as a result of phenomenological reduction ... "

This short excerpt from chapter II - entitled "LIVED TIME IS NOT PHYSICAL-COMPUTATIONAL" - Varela characterizes the time as ´complex texture´. It is obvious that it must be the underlying processuality, which is of complex structure too, resulting in a conceptual construct of time which necessarily has to be of some complexity. But what is the meaning of ´complex structured´ processes or in Varela´s words a ´complex texture´ of time? If McCulloch is right - and we are convinced that he is right - then nervous activity has to be described as an interplay of heterarchically and hierarchically structured processes which only can be described - without the usual logical circles - in a poly-contextural logical theory (for more details see ref. 8). From this point of view the concept of time cannot be considered any longer simply as a linear or sequential arrangement of events but rather as an ensemble of poly-rhythmic events that yield an inner poly-temporality (´Mehrzeitigkeit´) if considered in an inter- and intra-contexturally structured processuality. We would like to emphasize that it is only the intra-contextural time, i.e. within one contexture, which can be extracted experimentally by comparison with a standard process - a clock. In other expression, any measurement defines its own contexture, i.e. measurements can only be considered as mono-contextural events. (cf. ref. 12).

In chapter III of Varela´s contribution the following statement can be found which not only confirms our discussion but also reveals the difficulties of any bottom-up analysis of brain functions (cf. Varela, ref. 5b):

"... From an enactive viewpoint, any mental act is characterized by the concurrent participation of several functionally distinct and topographically distributed regions of the brain and their sensori-motor embodiment. From the point of view of the neuroscientist, it is the complex task of relating and integrating these different components that is at the root of temporality. A central idea pursued here is that these various components require a frame or window of simultaneity which corresponds to the duration of lived present ...

... One of the main results of modern neuroscience is to have recognized that brain regions are indeed interconnected in a reciprocal fashion (what I like to refer to as the Law of Reciprocity). Thus, whatever the neural basis for cognitive tasks turns out to be, it necessarily engages vast and geographically separated regions of the brain. These distinct regions cannot be seen as organized in some sequential arrangement: a cognitive act emerges from the gradual convergence of various sensory modalities into association or multimodal regions and into higher frontal areas for active decision and planning of behavioral acts. The traditional sequentialistic idea is anchored in a framework in which the computer metaphor is central, with its associated idea that information flows up-stream. Here, in contrast, I emphasize a strong dominance of dynamical network properties where sequentiality is replaced by reciprocal determination and relaxation time."

In this short introduction, we will not further demonstrate and discuss the difficulties of modern cognitive neurosciences. We would, however, state that it is in principle impossible to analyze mental processes exclusively in a bottom-up fashion on the basis of experimental sciences as it is the scientific program of today´s neurosciences and its philosophical facet the neurophilosophy and/or neo-connectionism.


Part_3 offers the following contributions (as pdf files):


Gotthard Günther 
Time, Timeless Logic and Self-Referential Systems

This contribution was published in 1967 in Annals of the New York Academy of Sciences (Vol. 138, p.397-406). In 1966 a somewhat longer study entitled Logik, Zeit, Emanation und Evolution was published by Günther in ´Arbeitsgemeinschaft für Forschung des Landes Nordrhein?Westfalen, Geisteswissenschaften, Heft 136, Köln und Opladen and later Logik, Zeit, ... was reprinted in "Beiträge zur Grundlegung einer operationsfähigen Dialektik" (Band 3), Felix Meiner Verlag, Hamburg 1980.


Gotthard Günther and Heinz von Foerster 
The Logic Structure of Evolution and Emanation

This contribution again is from the Annals of the New York Academy of Sciences (Vol. 138, 1967, p. 874-891) and was presented at the panel discussion.


Heinz von Foerster 
Time and Memory

At the same panel discussion of the New York Acacemy of Sciences (Vol. 138, 1967, p. 866-873) Heinz von Foerster lectured on Time and Memory. It is not very difficult to see the connections between von Foerster´s contribution and Günther´s Time, Timeless Logic ...


Gotthard Günther 
Diskussion zu: "Logik, Zeit, Emanation und Evolution"

Die This discussion was published together with Logik, Zeit, Emanation und Evolution in 1966.


Gotthard Günther

Since volume 3 of Beiträge zur Grundlegung einer operationsfähigen Dialektik contains Logik, Zeit, Emanation und Evolution we present the introduction to volume 3 of Beiträge...


Rudolf Kaehr 
Neue Tendenzen in der KI Forschung - Metakritische Untersuchungen über den Stellenwert der Logik in der neueren Künstlichen-Intelligenz-Forschung

In part_2 we already started to present some studies by Rudolf Kaehr and we continue this with an analysis of logical systems published in 1980 in Stiftung Warentest.


Warren S. McCulloch 
A Heterarchy of Values Determined by the Topology of Nervous Nets

Since McCulloch´s fundamental contribution from 1945 (Bulletin of Mathematical Biophysics, 7, 1945, 89-93) has been ignored by the neurosciences we offer this paper for discussion.




[1] G.J.Whitrow, "The Natural Philosphy of Time", Clarendon Press, Oxford, 1980 (2nd ed.) back to text


[2] Prigogine and L.Antoniou, "Laws of Nature and Time Symmetry Breaking", Annales of the New York Academy of Sciences, 879 (1999) 8-28. back to text


[3] _a) H. von Foerster, "Time and Memory", Annales of the New York Academy of Sciences, 138(2) (1967) 866-873; and
_b)  H. von Foerster, "Molecular Ethology: An Imodest Proposal for Semantic Clarification", in: Molecular Mechanisms in Memory and Learning, (G. Unger, ed.) Spartan Books, N.Y., (1970) 213-248. back to text


[4] See for example:
_a) "Time, Internal Clocks and Movement", (M.A. Pastor, J. Artieda, eds.), in: Advances in Psychology, Vol. 115, Elsevier Publ., 1996; and
_b) "Temporal Coding in the Brain", (G. Buzsáki, R. Llinás, W. Singer, A. Berthoz, Y. Christen, eds.), Springer Verlag, 1994; and
_c) "Naturalizing Phenomenology", (J. Petitot, F.J. Varela, B. Pachoud, J.-M. Roy, eds.), Stanford University Press, 1999. back to text


[5] _a) F.J. Varela, "A Dimly Perceived Horizon: The Complex Meeting Ground between Physical and Inner Time", Annales of the New York Academy of Sciences, 879 (1999) 8-28. and
_b) F.J. Varela, "The Specious Present: A Neurophenomenology of Time Consciousness", in: Naturalizing Phenomenology, (J. Petito, F.J. Varela, B. Pachoud, J.-M. Roy, eds.) back to text


[6] A ´positive language´ is the result of a mono-contextural linguistic frame of science. back to text


[7] W.S. McCulloch, "A Heterarchy of Values determined by the Topology of Nervous Nets", Bulletin of Mathematical Biophysics, 7 (1945) 89-93 - re-printed in: W.S. McCulloch, "Embodiments of Mind", M.I.T. Press, (1988) 40-44. back to text


[8] _a) R. Kaehr, E. von Goldammer, "Again Computers and the Brain", Journal of Molecular Electronics, 4 (1988) S31-S37. and
_b) R. Kaehr, E. von Goldammer, " Poly-Contextural Modeling of Heterarchies in Brain Functions", in: Models of Brain Functions (R.M.J. Cotterill, ed.), Cambridge University Press, (1989) 483-497. back to text


[9] D.C. Dennett, M.Kinsbourne, "Time and the observer: The where and when of consciounsness in the brain", Behavioral and Brain Sciences, 15 (1992) 183-247. back to text


[10] BCL - Biological Computer Laboratory

BCL left behind a rich legacy. In its day, it was one of the few education institutions teaching cybernetics. Between 1958 and 1975, operating under 25 grants, the laboratory produced 256 articles and books, 14 master's these, and 28 doctoral dissertations. The topics covered epistemology, logic, neurophysiology, theory of computation, electronic music, and automated instruction.
http://www.ece.uiuc.edu/pubs/centhist/six/bcl.htm back to text


[11] G. Günther, "Time, Timeless Logic and Self-Referential Systems", Ann. N.Y.Acad.Sci. 138 (1967) 397-406 and
G. Günther, "Logik, Zeit, Emanation und Evolution" re-printed in: Beiträge zur Grundlegung einer operationsfähigen Dialektik, Band 3 (Felix Meiner Verlag, Hamburg, 1980 - ISBN 3-7873-0485-1) back to text


[12] For more details we refer to a forthcoming somewhat longer discussion that is in preparation. back to text