VISITING RESEARCH FELLOW, HOKKAIDO UNIVERSITY, SAPPORO, JANUARY - MARCH 2005

(Ich bitte zu entschuldigen, dass derzeit nur ein Englischer Text zu dieser Seite vorliegt)

"Dynamic neural activity, chaotic itinerancy and hermeneutics"

From January 21 - March 29, 2005, I suspended my commitments at the ZKM for a short-term exchange in Japan where I worked with Ichiro Tsuda. The following is a summary of Ichiro Tsuda's ideas on dynamic neural activity:

Dynamic memory

The approach by Tsuda to brain theory is crucially based on the assumption that information representation in the brain is realized both by the state of neurons and by the dynamic relation among states. Those dynamic modalities have been observed and frequently described in the literature. The second crucial point is the brain's interpretative function. Tsuda adopted the framework of chaotic dynamical systems that interpret the functions of dynamic neural activity emerging in the brain, which can be regarded as a hermeneutic device that can act in a hermeneutic process. More specific, the dynamic approach is based on the assumption that memories do not emerge entirely from stored information. Rather, the nature of that which emerges is influenced at each instant by "traces" of information resulting from perception and cognition.

In order to describe a system that consists of 10⁵ to 10¹⁰ interacting neurons in a practical way, one usually describes the low frequency collective mode in a macroscopic deterministic way decoupled from the high frequency residuals that are viewed as noise. One should, however, not disregard the noise but rather include it in the model since the dynamic association of memory is sensitive to the presence of noise. Tsuda's model, therefore, consists of both a deterministic and a noise component, whereby the latter accounts for the presence of two kinds of noise.

The deterministic part consists of a multi-Milnor-attractor system whose stability is critical. Hence, without noise, its asymptotic solution is that of a multi-stable state system, in the sense that one of the Milnor attractors is eventually selected. A Milnor attractor is a generalized attractor that may be neutrally stable, as it can posses unstable directions.

The noise component includes dentritic and synaptic noise. The dentritic noise is represented by a small additive noise term whereas the synaptic noise is a type of stochastic renewal of dynamics.

Chaotic Itinerancy

A basic feature of Tsuda's model is chaotic itinerancy, which is a universal dynamical concept in high-dimensional dynamical systems. Usually, in a multi-stable system of high dimension, an attractor is separated from others by separatrices, forming a basin of attraction. The asymptotic behavior then corresponds to one such attractor, depending on the initial condition. After a strong destabilization the system moves towards a turbulent state, i.e., a noisy macroscopic state. If the instability is weak, an intermediate state between order and disorder can appear. The dynamics of such a state may be regarded as those of an itinerant process. A destabilized attractor is called attractor ruin, and the corresponding overall behavior is called chaotic itinerancy.

Attractor ruins are closely related with Milnor attractors which are limiting sets in which unstable directions are allowed. Dynamical orbits can escape from it due to small perturbations. In the case of lacking both noise terms and dynamical interactions among variables, the orbits approach a Milnor attractor. Instability due to dynamics interactions or noise is thus necessary for chaotic itinerancy.

A transition through chaotic itinerancy is topologically different from a transition resulting from noise in multi-attractor systems. Chaotic itinerancy is characterized by a decomposition of the entire state space into several subspaces which are stable within themselves. There exists, however, a direction normal to each subspace in which the system is unstable characterized by a positive Lyapunov exponent.

Among many advantages of modeling neural activity by means of chaotic itinerancy the most remarkable ones are

• simulataneous performance of learning and recall,
• memory is represented by a process,
• judgement of whether any input is close to one of the memories,
• effective search of memory,
• memory and information processing are indistinguishable.

This dynamic mechanisms and indistinguishability of memory and cognitive processes seem to characterize the human cognitive process.

Hermeneutics

The main characteristic of Ichiro Tsuda's brain theory is its interpretive practice. His approach to a hermeneutic brain theory is based on his approach to chaos theory. He considers chaos as an aspect of "Dasein" inasmuch chaos does not manifest ifself in a finite universe and would change its figure if one tries to articulate it. In Tsuda's view, chaos includes an internal observer and is therefore predestined to reconcile a philosophical and a system theoretical approach to the brain.

Chaos is non-classical in the sense that this concept explicitely accounts for the observer's ignorance. Insofar it is comparable with statistics. However, in statistics one usually invokes a "Laplacean demon" to refer to a non-observer-dependent, objective micro physics, although a demon cannot be really constructed and is rather a metaphor for this believe in objectivity. Chaos is not a statistical but a deterministic theory. If one adopts the statistical reasoning in a gedankenexperiment and reduces the macroscopic ignorance to micro particles, then each of the participating particles may behave chaotic which is not reducable to a further "non-chaotic" "femto" physics.

Brain theory is confronted with a double structure comparable to historical and social sciences, and archeology, for example. Physiological signals are interpreted to understand the interpretation process of the brain. Tsuda regards chaos as a gadget assuring a process of interpretation of the brain and to maintain above double structure. The brain interprets both the external and internal dynamics. Internal observation is an important concept in understanding how the brain understands itself. Since chaos includes an internal observer, according to Tsuda, it is a canditate for reconciling hermeneutics and system theoretical approaches to the brain.

Remarks

Although there is an enormous experimental support for the existence of chaos in the brain, Tsuda adds "that what we actually observe as chaotic behavior is dependent on our point of view". The model exhibiting chaotic intinerancy is an interpretation of how the brain interprets. The evidence, however, is overwhelming. The chaotic aspects of the brain change the conventional interpretation of brain functions. Thus, I would like to add - with a sense of humour - that Tsuda's model should prove to exhibit the doctrinaire behavior of scientists to be accepted by them with a higher probability.

Literature

Kunihiko Kaneko & Ichiro Tsuda: Chaotic Itinerany. Chaos 13, Focus Issue, 926-1164, 2003.

Peter Erdi & Ichiro Tsuda: Hermeneutic approach to the brain: process versus device? Theoria et Historia Scientiarum VI, 307-321, 2002.

Kunihiko Kaneko & Ichiro Tsuda: Complex Systems: Chaos and Beyond. Springer, Berlin, 2001.

Ichiro Tsuda: Toward an interpretation of dynamic neural activity in terms of chaotic systems. Behavioral and Brain Sciences 24, 793-847, 2001.

John S. Nicolis & Ichiro Tsuda: Mathematical description of brain dynamics in perception and action. J. Consci. Studies 6, 215-228, 1999.

Peter Erdi: The brain as a hermeneutic device. BioSystems 38, 179-189, 1996.

Ichiro Tsuda: Chaotic hermeneutics for understanding the brain. In: George Kampis and Peter Weibel: Endophysics: The world from within. Aerial, Santa Cruz, pp219-234, 1993.

Ichiro Tsuda: Die Chaotische Hermeneutik zum Verstehen des Gehirns, In: Karl Gerbel and Peter Weibel: Die Welt von Innen - ENDO & NANO, Ars Electronica 1992, PVS Verlag, Linz, p69ff, 1992.

Tetsuro Konishi & Kunihiko Kaneko: Clustered motion in symplectic coupled map systems. J. Phys. A: Math. Gen. 25, 6283-6296, 1992.

Ichiro Tsuda: Chaotic itinerancy as a dynamical basis of hermeneutics of brain and mind. World Futures 32, 167-185, 1991.

Ichiro Tsuda: A hermeneutic process of the brain. Prog. Theor. Phys. Suppl. 79, 241-259, 1984.


Sapporo 2005