Where and how could intentional programs be generated in the brain?

BioSystems 88 (2007) 101–112

Where and how could intentional programs be generated in the brain? A hypothetical model based on glial–neuronal interactions B.J. Mitterauer ∗ Forensic Neuropsychiatry and Gotthard G¨unther Archives, University of Salzburg, Ignaz-Harrer Strasse 79, A-5020 Salzburg, Austria Received 15 March 2006; received in revised form 14 April 2006; accepted 18 April 2006 This paper is dedicated to Jochen Pfalzgraf (Computer Sciences, University of Salzburg, Austria).

Abstract Based on glial–neuronal interaction a formalism (negative language) for the generation of intentional programs is proposed. An intentional program generates a specific multirelational structure in an inner or outer appropriate environment according to the principle of feasibility. After description of the glial spatio-temporal boundary-setting function in its interaction with the neuronal system, it is hypothesized that intentional programs may be generated in glial networks (syncytia) in line with the formalism of negative language. Gap junctions are interpreted as multirelational negation operators, generating cycles in a permutation system. These cycles could represent intentional programs that can either be realized or not in neuronal networks embodying a permutation system. The feasibility of these intentional programs is essentially dependent on appropriate environmental information. Since the realization of intentional programs in neuronal networks allows high degrees of freedom, the problem of free will is tackled, as well. Free will is defined as the subjective freedom to choose between the inner determination of intentional programs and the overdetermination of their feasibility in an appropriate environment. Finally, the possible implementation of the proposed brain model in robot brains is briefly discussed. © 2006 Elsevier Ireland Ltd. All rights reserved. Keywords: Glial–neuronal interaction; Intentional programs; Negative language; Glial syncytia; Free will; Robotics

1. Introduction and hypothesis Living systems are essentially based on intentional programs that strive for realization in their environment (Iberall and McCulloch, 1969). They have biological needs such as hunger that urge them for a rhythmic satisfaction within specific time scales. Human beings must not only satisfy their biological needs, but are additionally capable of generating ideas and desires in the sense of intentional programs that can be either realized or remain unfeasible desires. According to Brand (1984),

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desires clearly resemble intentions in the sense that they are realizable. The conception of intention or intentionality is closely related to the problem of free will (Gomes, 1999). Our environment is dominated by objects that embody the outcomes of intentional design (buildings, books, computers, etc). Today’s physics has nothing to say about the intentionality resulting in the existence of such objects, even though this intentionality is clearly causally effective (Ellis, 2005). There is modest progress in our understanding of voluntary decision processes (Wegner, 2004). fMRI and PET scans indicate that the anterior cingulate gyrus (ACG) is involved with intentional decision making. The ACG originates intentional action, whereas the posterior portion is

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related to the emotional aspect of action (Denton et al., 1999). Much of the work by Goldman-Rakic relating to working memory and attention involves slow periods of time (seconds to minutes) in which conscious intentional activities are ongoing. These studies involved the frontal lobes (Leung et al., 2005). Interestingly, she found that astrocytes have approximately 30% of the dopamine receptors in the frontal lobe (Khan et al., 2001). Contrary to classical interpretations, the cerebellum is active in conscious motor activities and not the prefrontal areas, which are involved in unconscious activities (Parsons et al., 2000; see Donald, 2002 for review). It seems that immediate attention and working memory cannot be separated from intentional explicit actions. However, any progress in our understanding of where and how intentional programs arise in our brain may be dependent on the underlying brain model. The brain theory proposed here is not only referring to the neuronal system, but also to the glial system and to some new interactional principles (Mitterauer, 1998, 2000, 2001; Mitterauer and Kopp, 2003). This study presents a formal elaboration of the hypothesis that intentional programs are basically generated in the glial system and become realized or not in the neuronal system. The formalism applied shows many degrees of freedom and could contribute to a better understanding of decision processes in the brain. Specifically, this hypothesis states that not only the neuronal system is selforganized as a network (Malsburg, 1995), but also the glial system embodies a self-organized network (Jung et al., 1998) termed syncytium. Between these networks a bidirectional interaction occurs. The glial syncytium consists of astrocytes, oligodendrocytes interconnected via gap junctions. It is hypothesized that gap junctions compute multirelational structures in the sense of intentional programs. These intentional programs are transferred via astrocytic and oligodendrocytic processes to the neuronal network, where an intentional program can be realized or not dependent on appropriate sensory information. The basic formalism is called negative language (Guenther, 1980) and operates on a permutation system. Supposing that the neuronal network embodies a permutation system, the intentional computations of the glial syncytium could be tested for their feasibility in the neuronal network. Before describing the glial–neuronal interaction with respect to a possible generation of intentional programs in the glial system, the conception of intention or intentionality is discussed together with an attempt to define intentional programs.

2. Intention, intentionality and intentional programs The definition of mind in terms of intentionality that originated in the Scholastic doctrine of intention (Aquinas, 1988) was revived by Brentano (1995) and has become a characteristic theory of German phenomenology. Basically, intention (Lat. intention, from intendere) means to reach out for something. Intentionality is the modern equivalent of the Scholastic intention representing a property of consciousness, whereby it refers to or intends an object. The intentional object is not necessarily a real or existent thing, but is merely that which the mental act is about (Runes, 1959). Several schools of thought have formulated the concept of intentionality in modern terms. According to Searle (2004), the most common contemporary philosophical solution of the problem of intentionality is some form of functionalism. The idea is that intentionality is to be analyzed entirely in terms of causal relations. These causal relations exist between the environment and the agent and between various events going on inside the agent. In general, Searle interprets intentionality as representation of conditions of satisfaction. Here the brain and robotic oriented approach to intentionality is comparable to that of Searle, but satisfaction is only a special biological case of intentionality. Therefore, the concept of feasibility of intentional programs is introduced, since feasibility is not always accompanied by satisfaction. In the eliminativist view of intentionality, there really are no intentional states. A variant of this view is the idea that attributions of intentionality are always forms of interpretation made by some external observer. An extreme version of this view is Dennett’s conception of the intentional stance (Dennett, 1978). This conception states that we should not think of people as literally having beliefs and desires, but rather that this is a useful stance to adopt about them for the purpose of predicting their behavior. Bennett and Hacker (2003) are right in their criticism that Dennett misconstrues what modern philosophers since Brentano have called intentionality. Of course, in theoretical neurobiology intention and intentionality implicitly play a role, but these conceptions are mostly used undefined (Kelso, 2000). Especially in the chaos-theoretical approach to brain function a definition of these conceptions is as yet not possible (Werner, 2004). Here an attempt is made to define the conception of intentional programs in terms of the underlying theory of intentionality. For a review of the current neurophilosophical controversial debate about the conception of intentionality see Bennett and Hacker (2003).

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McCulloch, one of the founders of cybernetics, mentions over and over again that the most important relation is the intentional relation: “when I point do not look at my finger! Look where I point”. The relation of intention is crucial in psychology, psychiatry, law, and where ever we turn. The relations we need are triadic, not dyadic. If triadic relations can be formalized, then N-adic relations are possible (McCulloch, 1966). Most interestingly, Lawrence J. Fogel (1966) indicated already in 1966 by computer simulation that one can only build a conscious intentional mechanism if it is based on a many-valued logic as proposed by Guenther (1964). Meanwhile, the negative language represents a special formalism of a many-valued logic in the sense of a multirelational logic (Guenther, 1980; see Section 4). The present approach to the problem of intentionality is based on the conception of intentional programs, defined as follows: an intentional program generates a specific multirelational structure in an inner or outer appropriate environment based on the principle of feasibility of that program. The genetic code may be an impressive example of an intentional program. A gene embodies a program for the expression of a specific set of proteins. The term expression connotes intentionality, since the genetic program generates a product in the sense of its feasibility. The same principle may basically operate in the networks of our brain. Contrary to this approach, Lewontin (2000) rejects the interpretation of the genome as an information processing system arguing that the organism does not compute itself from the information in its genes nor even from the information in the sequence of environments, but bears a significant mark of random processes. However, it should be clearly stated that the aim of this paper is to formally describe and interpret where and how our brain generates intentional programs, and not where and when we are aware of them (Eagleman, 2004).

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system in the sense of information structuring (Mitterauer, 1998). In other words, glial cells (astrocytes, oligodendrocytes) divide the brain into spatially limited areas or compartments, on the one hand, and create functional units in various time scales with the neurons, on the other hand. There is a general consensus in neuroscience that the brain is compartmentalized (Rall, 1995). However, astrocytes and not only neurons fill these compartments as the astrocytic syncytium. They also interconnect compartments throughout the cortex. Additionally, astrocytic pallisades streaming vertically from the glia limitans isolate individual compartments or modules. Groups of dendrites are frequently associated with astrocytic capsules in the cortex as well. Fig. 1 shows a schematic diagram of two glial–neuronal compartments. The entire system is composed of the following cell structures: three receptors (R) are shown that can be occupied by appropriate stimuli (St). Axons (Ax) lead to the corresponding neurons (N). Three processes (Po) lead from an oligodendrocyte (Oc) to axons, where the axons are enveloped by myelin sheaths (Ms). Processes (Pa) lead also from an astrocyte (Ac) via a synapse (Sy) to the neurons. With respect to the neuronal system, the diagram shows three dendrites (D) leading via a synapse to the neurons. Oc and Ac are interconnected via gap junctions (g.j.). As an example, an Ac of compartment x is connected with

3. Glial–neuronal interactions As already mentioned, any neurobiological explanation of basic concepts or principles constituting human behavior is dependent on the underlying brain model. Here, the focus is set on glial–neuronal interactions. 3.1. The spatio-temporal boundary-setting function of the glial system in its interaction with the neuronal system It is hypothesized that glial cells have a boundarysetting function in their interaction with the neuronal

Fig. 1. Schematic diagram of two glial–neuronal compartments. Compartment x is composed of various neuronal and glial cell structures. The same holds true for compartment y, where only an astrocyte (Ac) is depicted. Three receptors (R) are shown that can be occupied by appropriate stimuli (St). Axons (Ax) lead to the corresponding neurons (N). Three processes (Po) lead from an oligodendrocyte (Oc) to Ax, where the Ax are enveloped by myelin sheaths (Ms). Processes also lead from an Ac (Pa) via a synapse (Sy) to N. Concerning the neuronal structure, the diagram shows three dendrites (D) leading via a Sy to the N. Two glial cells, Oc and Ac are interconnected via gap junctions (g.j.) and two Ac to each other (Ac of compartment x and Ac of compartment y).

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an Ac of compartment y via a gap junction. So the glial system builds a network per se, called glial syncytium. It is experimentally well established that glial cells exert an active role in modulating the efficacy of synaptic transmission (Teichberg, 1991; Mitterauer et al., 1996; Oliet et al., 2001; Haydon, 2001; Mitterauer, 2003). Since the purpose of this paper is attempting to show how glial–neuronal interactions could generate and realize intentional programs, reference is made only to two experimentally based examples of spatial and temporal glial boundary-setting functions. 3.1.1. Experimental indications for the spatial boundary-setting function of the glial system Rakic (1988) proposed an experimentally supported “radial unit hypothesis” for the development of the cerebral cortex. According to this hypothesis, the ependymal layer of the embryonic cerebral ventricle consists of proliferative units that provide a protomap of prospective cytoarchitectonic areas. The output of the proliferative units is translated via glial guides to the expanding cortex in the form of ontogenetic columns, whose final number for each area can be modified through interaction with afferent input. The radial unit model provides a framework for understanding cerebral evolution, epigenetic regulation of the parcellation of cytoarchitectonic areas. According to Rakic, the cerebral cortex develops from a glial protomap such that an isomorphism exists between the places on the protomap and the cortical columns. One can also say that radial glial cells determine the spatial distribution of neurons in the developing cerebral cortex in the sense of a spatial boundary-setting function. In other words: the radial glia determine the places where the neurons are at work. Mainly, the active role of astrocytes in information processing can be interpreted as a boundary-setting or information structuring function (Mitterauer, 2005). However, what oligodendrocytes concerns, so far it has been difficult to interpret their function as boundary-setting. Now it has been shown for the first time by McGee et al. (2005) that myelin sets boundaries in brain development and adult neural plasticity. Their findings indicate that oligodendrocytes determine via their myelin proteins (NgR, etc.) neural plasticity and posttraumatic axonal regeneration. In other words: myelin may play an important role in both brain maturation and in locking down neural circuits in the adult brain as well. 3.1.2. Experimental evidence for the glial temporal boundary-setting function An impressive example of the glial temporal boundary-setting is represented by the model of tripar-

tite synapses. According to the prevailing view, chemical synaptic transmission exclusively involves bipartite synapses consisting of presynaptic and postsynaptic components and a synaptic cleft, in which a presynaptically released neurotransmitter binds to cognate receptors in the postsynaptic cell. However, there is a new wave of information suggesting that glia, especially astrocytes, are intimately involved in the active control of neuronal activity and synaptic transmission. Smit et al. (2001) proposed a model of a cholinergic tripartite synapse that might turn out to be a milestone for our understanding of the glial–neuronal interaction. But first this type of tripartite synapse should be briefly described. These authors identified a glia-derived soluble acetylcholine-binding protein (AChBP), which is a naturally occurring analogue of the ligand-binding domains of the nicotinic acetylcholine receptors (nAChRs). Like the nAChRs, it assembles into a heptamer with ligandbinding characteristics typical of a nicotinic receptor. Presynaptic releases of acetylcholine induce the secretion of AChBP through the glial secretory pathway, and once in the synaptic cleft, it acts as a molecular decoy, binding the transmitter and reducing its availability at the synapse in the sense of a negative feedback on synaptic efficacy. This model, which focuses on the role of AChBP in neurotransmission, suggests that there is a basal level of AChBP in the synaptic cleft, maintained by continuous release from the synaptic glial cells. Under conditions of active presynaptic transmitter release, high millimolar concentrations of free ACh will probably activate both postsynaptic receptors and nAChRs on the synaptic glial cells, which would enhance the release of AChBP, thus increasing its concentration in the synaptic cleft. This may either diminish or terminate the ongoing ACh response or raise the concentration of basal AChBP to the extent that subsequent responses to ACh are decreased. Fig. 2 shows a schematic drawing of a tripartite synapse as proposed by Smit et al. (2001), but generalized for all neurotransmitters (NT). For the sake of clarity, reference is not made to other modulatory substances such as the functional significance of calcium waves (Charles and Giaume, 2002; Rose et al., 2003). A neurotransmitter is released from the presynaptic terminal ready for occupancy of glial BP and postsynaptic receptors. In parallel, glial receptors are occupied by neurotransmitters, which increase the production and secretion of soluble glial BP into the synapse. The increased levels of soluble BP in the synapse reduces that amount of free neurotransmitter that can bind to postsynaptic receptors, and neurotransmission is inactivated by this form of negative feedback. Once the NT levels have

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duce glutamate as a transmitter by which they negatively feedback on the presynaptic element of the synapse. In other words: in tripartite synapses glia have a temporal boundary-setting function in temporarily turning off synaptic information transmission. In addition, neuronal synchrony is mediated by astrocytic glutamate through activation of extrasynaptic Nmethyl-d-asparate receptors (Fellin et al., 2004). This is an experimental verification of the “neuro-glial synchronization hypothesis” (Mitterauer et al., 1996) in the sense that glia may actively determine temporal processes in neuronal networks. Fig. 2. Model of a tripartite synapse. Depending on the type of synapse, a pertinent neurotransmitter (NT) is released from the presynapse ready for occupancy of glial binding protein (gl.BP) and postsynaptic receptors (ps.R). In parallel, glial receptors (gl.R) are occupied by NT, activating the production of additional gl.BP. After occupancy of gl.BP and ps.R, glia negatively feed back to the presynaptic terminal inactivating the neurotransmission. Now the synaptic information processing can start again.

returned to baseline, the BP levels will drop because the glial cells are no longer being stimulated to produce BP; the synapse will return to its initial state, and synaptic information processing can start again. Admittedly, AChBP has only been found in several species of mollusks, and database searches in the genomes of humans and other species have not yielded orthologs of this binding protein (Sixma and Smit, 2003). But it is very probable that gl.BPs will eventually be identified in vertebrates, including humans. This is usually the case. For instance, much of what we know about memory is based on the biochemistry of Aplysia, the California sea slug. Most of the neurotransmitters originally identified in these animals were later shown to be equivalent, with minor exceptions, to those of vertebrates, including man. But presently we can only speak of putative human glial binding proteins. In particular, the role of the glutamatergic tripartite synapse has been documented over the last years (Auld and Robitaille, 2003). The astrocytes which play a role in these synapses do not make use of a BP, but pro-

4. Generation of intentional programs within the glial syncytium First of all, if one speaks of intentional programs, one has to define the formalism on which these programs are based. 4.1. The formalism of negative language According to Guenther (1980), a negative language can be formalized in an n-valent permutation system. Generally, a permutation of n things is defined as an ordered arrangement of all the members of the set taken all at a time according to the formula n! (! means factorial). Table 1 shows a quadrivalent permutation system in a lexicographic order. It consists of the integers 1–4. The number of permutations is 24 (4! = 1 × 2 × 3 × 4 = 24). The permutations of the elements 1 2

to

3 4

4 3 2 1

can be generated with three different NOT operators N1 –N3 , that exchange two adjacent (neighbored) integers (values) by the following scheme: 1 ↔ 2; (N1 )

2 ↔ 3; (N2 )

3↔4 (N3 )

Table 1 Quadrivalent (n = 4) permutation system arranged in a lexicographic order

This permutation system consists of 24 permutations (1 × 2 × 3 × 4,. . .,4 × 3 × 2 × 1) according to the formula n = 4! (factorial) = 1 × 2× 3× 4 = 24. The 24 permutations are lexicographically arranged.

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Table 2 Example of a Hamilton loop generated by a sequence of negation operators (Guenther, 1980)

The first permutation (P = 1 × 2 × 3 × 4) is permutated via a sequence of negation operators (N1 × 2 × 3,. . .,2 × 1 × 2 ) generating all the permutations once until the loop is closed (1234) in the sense of a Hamilton loop.

Generally, the number of negation operators (NOT) is dependent on the valuedness of the permutation system minus 1. For example, in a pentavalent permutation system four negation operators (N1 –N4 ) (n = 5 − 1 = 4) are at work. It is possible to form loops, each of which passes through all permutations of the permutation system once (Hamilton loop). In a quadrivalent system they are computable (44 Hamilton loops), but in higher valent systems they are not computable. Table 2 shows an example of a Hamilton loop (Guenther, 1980). The first permutation (P = 1234) is permutated via a sequence of negation operators (N1×2×3,. . .,2×1×2 ) generating all the permutations once until the loop is closed. Such permutation systems can be mathematically formalized as negation networks, called permutographs (Thomas, 1982). Fig. 3 shows a quadrivalent permutograph. The individual NOT or negation functions N1 –N3 are represented between the permutations (1,. . .,24). The various Hamilton loops differ in NOT or negation opera-

Fig. 3. Example of a Hamilton loop in a quadrivalent permutograph. The numbers in circles represent the permutations (1,. . .,24) interconnected by negation operators (N1 –N3 ) of a closed permutation system called permutograph (Thomas, 1982). A Hamilton loop or negation sequence is indicated by a dashed line.

tor sequence. An example of a Hamilton loop is indicated in this permutograph by a dash-dotted line. It is defined by the following negation operator sequence: N 1 –N 2 –N 3 –N 2 –N 3 –N 2 –N 1 –N 2 –N 1 –N 2 –N 3 –N 2 – N 3 –N 2 –N 1 –N 2 –N 1 –N 2 –N 3 –N 2 –N 3 –N 2 –N 1 –N 2 Already in the 1980s it was shown that the negative language may represent an appropriate formal model for a description of intentional programs generated in neuronal networks of biological brains. Based on this formalism, computer systems for robot brains have also been proposed (Mitterauer, 1988; Thomas and Mitterauer, 1989). Here, it is attempted to further elaborate on this possible intentional programming in our brains, focusing on glial–neuronal interaction. 4.2. Glial gap junctions could embody negation operators In situ, morphological studies have shown that astrocyte gap junctions are localized between cell bodies, between processes and cell bodies, and between astrocytic end-feet that surround brain blood vessels. In vitro, junctional coupling between astrocytes has also been observed. Moreover, astrocyte-to-oligodendrocyte gap junctions have been identified between cell bodies, cell bodies and processes, and between astrocyte processes and the outer myelin sheath. Thus, the astrocytic syncytium extends to oligodendrocytes, allowing glial cells to form a generalized glial syncytium, also called “panglial syncytium”, a large glial network that extends radially from the spinal cord and brain ventricles, across gray and white matter regions, to the glia limitans and to the capillary epithelium. Ependymal cells are also part of the panglial syncytium. Additionally, activated microglia may also be interconnected with astrocytes via gap junctions. However, the astrocyte is the linchpin of the panglial syncytium. It is the only cell that interconnects to all other glia. Furthermore, it is the only one with perisynaptic processes.

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Gap junctions are channels that link the cytoplasm of adjacent cells and permit the intercellular exchange of small molecules with a molecular mass < 1–1.4 kDa, including ions, metabolites, and second messengers. IP3 is the most important since this initiates the calcium wave in the attached cell after it transverses the gap junction channel (Giaume and Venance, 1998). In addition to homologous coupling between cells of the same general class, heterologous coupling has been observed between astrocytes and oligodendrocytes. Newman (2002) has demonstrated that gap junctions interconnect Muller cell to Muller cell and Muller cell to regular astrocytes in the retina. Homologous and heterologous coupling could serve to synchronize the activities of neighboring cells that serve the same functions. Such coupling could extend the size of a functional compartment from a single cell to a multicellular syncytium, acting as a functional network. Gap junctions are now recognized as a diverse group of channels that vary in their permeability, voltage sensitivities, and potential for modulation by intracellular factors; thus, heterotypic coupling may also serve to coordinate the activities of the coupled cells by providing a pathway for the selective exchange of molecules below a certain size. In addition, some gap junctions are chemically rectifying, favoring the transfer of certain molecules in one direction versus the opposite direction. The main gap junction protein of astrocytes is connexin (Cx) 43, whereas Cx32 is expressed in oligodendrocytes in the CNS as well as another type of connexin, Cx45. Heterelogous astro-oligodendrocyte gap junctions may be composed of Cx43/Cx32, if these connexins form functional junctions (Baumann and Pham-Dinh, 2001). Recent experimental results suggest roles of glial gap junction-mediated anchoring of signalling molecules in a wide variety of glial homeostatic processes (Penes et al., 2005). Gap junctions are showing properties that differ significantly from chemical synapses (Zoidl and Dermietzel, 2002; Nagy et al., 2004; Rouach et al., 2004). The following enumeration of gap junctional properties in glial syncytia may support the hypothesis that gap junctions could embody negation operators in the sense of a generation of negative language in glial syncytia: First, gap junctions communicate through ion currents in a bi-directional manner, comparable to negation operators defined as exchange relations. Bidirectional information occurs between astrocytes and neurons at the synapse. This is primarily chemical and based on neurotransmitters. It is not certain that all glial gap junction communications are bidirectional due to rec-

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tification. This is a poorly understood area because of extremely severe technical difficulties, especially in vivo (Perea and Araque, 2005). Second, differential levels of connexin expression reflect region-to-region differences in functional requirements for different astrocytic gap junctional coupling states. The presence of several connexins enables different permeabilities to ions and molecules and different conductance regulation. Such differences of gap junctional functions could correspond to the different types of negation operators. Third, neuronal gap junctions do not form syncytia and are generally restricted to one synapse. Fourth, processing within a syncytium is driven by neuronal input and depends on normal neuronal functioning. The two systems are indivisible. It is important to emphasize that neuronal activity-dependent gap junctional communication in the astrocytic syncytium is long-term potentiated. This is indicative of a memory system as proposed in neuronal synaptic activity by Hebb over five decades ago (1949). Fifth, the diversity of astrocytic gap junctions results in complex forms of intercellular communication because of the complex rectification between such numerous combinatorial possibilities. Sixth, the astrocytic system may normally function to induce precise efferent (e.g. behaviorally intentional or appropriate motor) neuronal responses. Admittedly, the testing of this conjecture is also faced with experimental difficulties. Now, let us tie gap junctional functions and negative language together. Negation operators represent exchange relations between adjacent values or numbers. So they operate like gap junctions bi-directionally. Dependent on the number of values (n) that constitute a permutation system, the operation of different negation operators (n − 1) is necessary for the generation of a negative language. With concern to gap junctions, they also show functional differences basically influenced by the connexins. Therefore, different types of gap junctions could embody different types of negation operators. Furthermore, a permutation system represents – like the glial syncytium – a closed network generating a negative language. So we have a biomimetic interpretation of the negative language. But what makes that language so intentional? 5. Glial generation of cyclic pathways in neuronal networks Now we are confronted with the question what part of the permutation system proposed could be embodied by the neuronal network. It is hypothesized that the neuronal network could embody the permutations of a permutographic system. For example, a quadri-

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Fig. 4. Example of a pentavalent (n = 5) permutograph arranged in layers. For n = 5, i.e. for a pentavalent logic, a schematic circuit diagram of a permutation system (permutograph) is shown. The 120 permutations (according to the formula n! = 5! = 1 × 2 × 3 × 4 × 5 = 120) are shown as circles. The individual permutations are numbered consecutively from 1 to 120, each number representing one of the 120 permutations. They are interconnected by (n − 1) negation operators (N1 –N4 ). For example, permutation (1) stated in the upper layer 1 should be read “1 2 3 4 5”. This permutation may be converted into permutation (7) corresponding to “1 3 2 4 5” by applying the negator N2 , i.e. by exchanging the values 2 and 3. The negation operators, i.e. exchange operations of successive numerical values within permutations, are shown in this figure by the smaller numerical values (Thomas and Mitterauer, 1989).

valent permutation system may be interpreted as a neuronal network. In Table 1 only the 24 permutations (1 × 2 × 3 × 4,. . .,4 × 3 × 2 × 1) are shown. Each permutation formalizes a neuron with a specific computational quality. In parallel, the permutations determine how neurons can be interconnected according to the rule of manyvalent negation operators (N1 –N3 ) building a neuronal network that embodies a permutation system. Fig. 4 shows an example of a pentavalent permutograph (Thomas and Mitterauer, 1989). The numbers in circles designate the permutations (n = 5! = 120). The interconnecting lines represent negation operators (1–4). As already supposed, the glial syncytium could compute various sequences of negation operators in order to test their feasibility in the neuronal permutographic network. This is similar to a kind of intentional pathfinding in neuronal networks. From a biocybernetic point of view, living systems are self-referring systems (Maturana, 1975). On the highest level they are capable of self-reflection or self-observation. Formally speaking, our brain is permanently generating such reflection cycles. A cycle is not hierarchically ordered, but follows the rule of heterarchy (A–B–C–D–A; McCulloch, 1945). Therefore, the pathfinding of glial intentional programs

in neuronal networks is only successful if it results in a closed pathway in form of a cycle. In the case of a cycle that passes all neurons once in the network, we speak of a Hamilton loop. Such loops may occur in the neuronal system associated with gap junctions of the glial syncytium. With concern to the realization of glial intentional programs, there are several possibilities. First, a sequence of negation operators is erroneous, since it is unable to find a cycle. Second, a successful finding of a cycle is not reinforced by appropriate sensory information, so that the intentional program is unfeasible with regard to the environment. Third, a cycle generated by a glial intentional program corresponds to a neuronal network that is activated by sensory information. Fourth, humans are able to reject a feasible intentional program, since another program has priority for a period of time. Here one can see a parallel to Edelman’s ‘Neural Darwinism’ (Edelman, 1987). He proposed a multi-draft hypothesis where several intentional possibilities are generated, but only the one with the best response is actually generated. Fifth, the possible cyclic pathways in superastronomic complex neuronal networks offer glial intentional programs the chance to find new cyclic pathways in the

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sense of creativity. In other words: the neuronal system is interpreting the intentional possibilities generated in the astrocytic syncytium. Sixth, supposing that the glial syncytium also has a memory function similar to the neuronal system (Robertson, 2002), it could “self-imprint” already successful intentional programs in the syncytium, which implies a form of learning. This has been experimentally verified by Pasti et al. (1997) who showed that calcium waves in the glial syncytium undergo a form of long-term potentiation based on neuronal activation. Experimentally verified knowledge of glial–neuronal interaction may – at least partly – support this hypothetical model of intentional glial–neuronal interaction. First of all, the communication between astrocytes and neurons occurs bi-directionally (Zonta and Carmignoto, 2002). Additionally, a bi-directional feedback between astrocytes and neurons at each synapse results in the coding and integration of calcium waves, as they travel through the glial syncytium. Therefore, each perisynaptic astrocytic filopodal process (several may be present at each synapse) is a member of the syncytium. This gives a huge global distribution form of information processing throughout the brain (Perea and Araque, 2005). Most important to the proposed model of glial– neuronal interaction are experimental findings concerning synaptic activation of astrocytes evoking feedback neuronal synchronization (Fellin et al., 2004). These researchers observed in hippocampal slices how two or more slow inward currents recorded in the same neuron can have strikingly different kinetics suggesting the presence of multiple release sites from either one or many astrocytes impinging onto an individual neuron. By cooperating with the excitatory synaptic inputs to recruit specific subsets of neurons in the neuronal network, the activation of extrasynaptic NMDA receptors by astrocytic glutamate may represent a flexible mechanism that favors the formation of dynamically associated assemblies of neurons. In fact, glial intentional programs could operate in neuronal networks based on such mechanisms. In other words, successful glial pathfindings in neuronal networks could be interpreted as the formation of dynamically associated assemblies of neurons. Additionally, the glial syncytium is self-organized (Jung et al., 1998). Most importantly, one astrocyte can establish through its filopodal processes contact with approximately 145,000 synapses, each of which acts as a subcellular microdomain for information processing via calcium signalling and bidirectional feedback (Chao et al., 2002). Additionally, each microdomain independently responds to various combinations of neurotransmitter signals. This occurs at low neuronal activation. Intracellular calcium signals with associated intercellu-

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lar syncytial transfer of information occur with increasing neuronal synaptic activation (Nett and McCarthy, 2002). But the possible memory based learning effect in glial syncytia is extremely difficult to study. However, the role of gap junctions in memory formation can be interpreted as follows: gap junctions could register already generated cyclic pathways in the syncytium (formalized as a sequence of negation operators). Depending on a positive feedback from the neuronal network to the glial syncytium based on feasible intentions in regard to environmental information, gap junctions could strengthen their structure embodying a memory mechanism. If that would be the case, then we have a double memory function of gap junctions: a local embodiment of memories, on the one hand, and a pathwaymemory determined by gap junctions, on the other hand. This has already been experimentally verified (Jones and Greenough, 2002). At this point one could argue that neuronal mechanisms per se may compute intentional behavior, so that it is not necessary to refer to the glial syncytium. For example, mirror neurons are premotor neurons that fire when the subject performs an object-directed action, and they also fire when the subject observes someone else performing the same class of actions. Because action implies a goal, it has been proposed that mirror neurons provide a neural mechanism for understanding the intentions of others (Iacoboni et al., 2005). However, here we deal with the neural computation of intentions of others, and not how intentions may be generated in the brain per se. Note that only the latter problem is the topic of the present paper which hypothesizes that the glial syncytium may play a decisive role. 6. Some implications for the problem of free will As introductory mentioned, a biological discussion of the question if we are free in our decisions or absolutely determined by our brain functions, is dependent on the underlying brain model. The brain model proposed in this paper could contribute some arguments that our brain has both functional and decisional degrees of freedom at its disposal. However, it should be the topic of another study to refer to the current discussion of the problem of free will in detail. Here, only some arguments from the brain model are inferred, in the sense that we may be basically free in our decisions. To begin with the formalism of negative language according to Guenther, the intentional generation of cyclic pathways in neuronal networks permits high degrees of freedom. If a cyclic pathway works, then the function of the neuronal network is constrained by

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it. One could also say that the glial intentional generation of cyclic pathways in neuronal networks embodies an inner determination of brain functions. However, the feasibility of such inner determination is dependent on appropriate sensory information from the environment. Hence, intentional programs are selected by an appropriate environmental information or situation, generated by the perception systems (Mitterauer, 2001). Thinking is the highest level of intention. Although specific cognitive activities may be engendered by environmental stimulation, this may not always be the case. Original ideas or thoughts may suddenly come “out of the blue” without any obvious external or internal perception. Such novel and original ideas may originate in the astrocytic syncytium, since it can influence neuronal activity independently. The neuronal system is well suited for rapid and involuntary responses. Nevertheless, we are free to choose between the inner intentional determination and the environmental determination. There are following possibilities: basically, the brain is capable of producing various intentional programs continuously in the sense of testing hypotheses on their feasibility in a specific environment. In case the intentional program is not feasible, we can select another feasible program from the repertoire of various intentional programs available in the brain for a period of time. But it is also possible to hold on to an unfeasible intentional program and actively change the environment, searching for a new environmental situation that provides appropriate information. Most important may be the fact that undisturbed human brains are able to reject an intentional program despite its feasibility. The brain model proposed provides an explanation for the human capacity of rejection. The mechanism of rejection already operates on the level of cyclic pathway generation in neuronal networks. According to the rules of negative language a neuron is only interconnected with another one if the intended negation operator is finding a neuron with a realizable exchange relation. If this is not the case, this neuron cannot be referred to which means it has to be rejected. Here we deal with an information structuring function, since not all neurons can be involved in information processing during a specific period of time. This consideration may account for experimental findings showing that a synapse can be quiescent at times. If we suppose that the generation of cyclic pathways in neuronal networks embodies basic reflection mechanisms, then our brain is principally capable of reflecting intentions and their feasibility on the highest level of reflection in the sense of a deliberating selfconsciousness (Mitterauer, 1998). It follows that the

human brain can set priorities concerning the realization of intentional programs. A simple example can illustrate this. A woman has the urgent intention to satisfy her hunger. Food is on the table, but she rejects to eat anything, since she is presently on a weight-watching program intending to loose a significant amount of body weight. This intentional program has priority, so she is capable of rejecting the feasible intention to eat. The human capacity to reject feasible intentions represents the main argument that we are free to choose between various intentional programs during a period of time. Contrary to the example above, a hungry chimpanzee would eat a banana in any case. One could also say that the capability of rejection is an index of human subjectivity or individuality (Guenther, 1962). In accordance with the present argumentation, rejection is an implicit mechanism concerning both the generation of intentional programs and their realization, as well. It enables us to generate a subjective space of freedom to choose between the inner determination of intentional programs and the determination of their feasibility in an appropriate environment. Many philosophers today accept some version of compatibilism, which means that the thesis of free will is actually compatible with the thesis of determinism. According to this view, determinism and free will are both true (Searle, 2004). However, the problem of free will may not be compatibilistic in a strong sense, since it is not based on determinism and indeterminism, but on intentional (inner) determinism and environmental (external) determinism. 7. Future prospects Admittedly, this paper presents an interpretation of glial–neuronal interactions that is mainly hypothetical, so that experimentally oriented biologists may call it speculative. Of course, this is an area where very little is known because of big technical obstacles of studying such systems in vitro or particularly in vivo. As already argued in other studies, robotics may be a real alternative to test brain theories (Mitterauer and Kopp, 2003). If we should be able to implement the principles proposed in a robot brain, then the behavior of the agent could teach us according to which principles our brain really works and where we are wrong (Pfalzgraf and Mitterauer, 2005). Mathematically, the Hamilton circuit problem is a problem of type NP, which stands for non-deterministic polynomial time. Cook (1971) was able to provide a means of demonstrating that certain NP-type problems are highly unlikely to be solvable by an efficient, polynomial time algorithm. Specifically, what Cook did was to

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prove that a particular problem of type NP was what he called NP-complete. What this means is that if this particular problem (e.g. the Hamilton circuit problem) could be solved by a polynomial time algorithm, so could every other problem of type NP, too. However, by making one or more correct (or optimal) guesses, it is possible for a non-deterministic Turing machine to solve the problem in polynomial time (Delvin, 1988). What the implementation of the biomimetic model of intentional programs in a robot brain concerns, we can expect promising biotechnical developments. For example, Rambidi and Yakovenchuk (2001) have been using a Belousov-Zhabotinsky (B–Z) reaction computer for finding the shortest paths in a labyrinth. Such biological computation methods could also be applied to compute Hamilton loops that embody self-reference of an agent in the sense of a “touch of subjectivity”. Acknowledgements I am very grateful to James Robertson (Irvine, CA, USA) for his valuable comments on glial–neuronal interactions. I also thank Birgitta Kofler-Westergren for preparing the final version of the paper. References Aquinas, T.St., 1988. In: Martin, C. (Ed.), The Philosophy of Thomas Aquinas: Introductory Readings. Routledge, New York, pp. 38–49. Auld, D.S., Robitaille, R., 2003. Glial cells and neurotransmission: an inclusive view of synaptic function. Neuron 40, 389–400. Baumann, N., Pham-Dinh, D., 2001. Biology of oligodendrocyte and myelin in the mammalian central nervous system. Phys. Rev. 81, 871–927. Bennett, M.R., Hacker, P.M.S., 2003. Philosophical Foundations of Neuroscience. Blackwell Publishing, Malden. Brand, M., 1984. Intending and Acting: Toward a Naturalized Action Theory. The MIT Press, Cambridge. Brentano, F., 1995. Psychology From an Empirical Standpoint. Routledge, London. Chao, T.I., Rickmann, M., Wolff, J.R., 2002. The synapse-astrocyte boundary: an anatomical basis for an integrative role of glia in synaptic transmission. In: Volterra, A., Magistretti, P.J., Haydon, P.G. (Eds.), The Tripartite Synapse. Glia in Synaptic Transmission. Oxford University Press, Oxford, pp. 3–23. Charles, A., Giaume, C., 2002. Intercellular calcium waves in astrocytes: underlying mechanisms and functional significance. In: Volterra, A., Magistretti, P.J., Haydon, P.G. (Eds.), The Tripartite Synapse: Glia in Synaptic Transmission. Oxford University Press, Oxford, UK, pp. 110–126. Cook, S.A., 1971. The complexity of theorem-proving procedures. In: Proceedings of Third Annual ACM Symposium on Theory of Computing. ACM, New York, pp. 151–158. Delvin, K., 1988. Mathematics: The New Golden Age. Penguin Books, London. Dennett, D., 1978. The Intentional Stance. Little, Brown, Cambridge, MA.

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