We begin with a brief resume of quantum mechanics. Quantum mechanical objects are described by complex numbers known as amplitudes. The probability of a process is the square of the magnitude of the amplitude. The most fundamental principle in the theory is that of superposition: To compute the total amplitude for a process add the amplitudes of its component processes. Quantum mechanics presents a view of reality which is a radical departure from the previous mechanistic viewpoint. Quantum mechanical objects do not have an objective existence before measurement.

In the path integral formulation of quantum mechanics, one needs to compute the sum of an infinite number of paths at each step.  Although Schrodinger's equation is linear, the reduction of the wave packet, upon observation, is a nonlinear phenomenon. Ob­servation is thus tantamount to making a choice. From another perspective, there is an asymmetry in the preparation of a state in a quantum system and that of its measurement, because the measurement can only be done in terms of its observables. In a classical system also there is intervention at the beginning and the end of the physical process that defines the computation. Time-reversible equations of physics cannot, in themselves, explain communi­cation of information. Creation of information requires reduction in entropy. Owing to the fact that these models must carry the input along, reversible models can become extremely slow, so as to become unable to solve the problem in any reasonable period of time. Since measurement in a quantum system is a time-asymmetric process, one can speak of information transfer in a quantum observation. Such a process in the so-called von Neumann chain. According to Wigner (1961), the reduction should be ascribed to the observer's mind or consciousness. According to the orthodox view, namely the Copenhagen interpretation, the workings of the measuring instruments must be accounted for in purely classical terms. This means that a quantum mechanical representation of the measuring apparatus in not correct. In other words, a measurement is contingent on localization. In such a view the slogan that "computation is physics" loses its generality. It is not surprising that certain types of computations are taken to indicate the participation of conscious agents.  Thus if we were to receive the digits of in transmissions from outer space, we will take that as indication of life in some remote planet. The same will be true of other arithmetic computations. In brief, signals or computations that simulate the world using models much less complex than the real world indicate intelligence. Quantum mechanics may be viewed as a theory dealing with basic symmetries. The wavefunction can only be symmetric or antisymmetric, defining bosons and fermions, re­spectively. In a two-dimensionally constrained world there are other possibilities that have been named anyons (Wilczek 1990) but that need not concern us.

Quantum knowledge

Quantum theory defines knowledge in a relative sense. It is meaningless to talk of an abjective reality. When we talk, for example, that electric fields exist in a field, this implies that such measurements can be made. Knowledge is a collection of the observations on the reductions of the wavefunction tp, brought about by measurements using different kinds of instrumentations. The indeterminacy of quantum theory does not reside in the microworld alone. For example, Schrodinger's cat paradox shows how a microscopic uncertainty transforms into a microscopic uncertainty. Brain processes are not described completely by the neuron firings; one must, additionally, consider their higher order bindings, such as thoughts and abstract concepts, because they, in turn, have an influence on the neuron firings. A wavefunction describing the brain would then include variables for the higher order processes, such as abstract concepts as well. But such a definition will leave a certain indeterminacy in our description.

The fallacy of knowing the parts from the whole

If we knew the parts completely, one can construct a wavefunction for the whole. But as is well known (Schrodinger 1980; originally in 1935): "Maximal knowledge of a total system does not necessarily include total knowledge of all its parts, not even when these are fully separated from each other and at the moment are not influencing each other at all." In other words, a system may be in a definite state but its parts are not precisely defined. To recapitulate, we claim that without going into the question of how the state function associated with the brain is to be written down there is a fundamental indeterminacy asso­ciated with the description of its component parts. This is over and above the reasons of complexity that one cannot discover the details of the workings of a brain. Now, in a suitable configuration space, where the state function is described in the maximal sense, quantum uncertainty will apply. Since the results of the interactions between the environment and the brain are in terms of the self-organization of the latter, clearly the structure, chosen out of the innumerably many possibilities, represents one of the quantum variables.

Structure

We must first distinguish between the structures of nonliving and living systems. By the structure of a nonliving system we mean a stable organization of the system. The notion of the stability may be understood from the perspective of energy of the system. Each stable state is an energy minimum. But the structure in a living system is not so easily fixed. We may sketch the following sequence of events: As the environment (the internal and the external) changes, the living system reorganizes itself. This choice, by the nervous system, of one out of a very large number of possibilities, represents the behavioral or cognitive response. We might view this neural hardware as the classical instrumentation that represents the cognitive act. This might also be viewed as a cognitive agent. Further processing might be carried out by this instrumentation. We may consider the cognitive categories to have a reality in a suitable space. A living organism must have entropy in its structure equal to the entropy of its environ­ment. If it did not, it will not be able to adapt (respond) to the changing environment. Principle: The position of the organism in its ecological environment is determined by the entropy of its information processing system. This defines a hierarchy. According to this view the universe for an organism shows a complexity and richness corresponding to the complexity of the nervous system. This idea should be contrasted from the anthropic principle where the nature of the universe is explained by the argument that if it was different there would not have been man to observe it. According to our view, the universe might come to reveal new patterns if we had the capacity to process such information. Computer assisted processing will then reveal new patterns. It is characteristic of neurophysiology that activity in specific brain structures in given a primary explanatory role. But any determination of the brain structure is impossible. If the brain has 10¹¹ neurons and 10¹⁴ synapses, then even ignoring the gradations in the synaptic behavior, the total number of structures that could, in principle, be chosen exceeds 2¹⁰ , which is greater than current estimates of all elementary particles in the universe. Assume a system that can exist in only two states. Such a system will find its place where the environment is characterized by just two states. So we can speak of an information theoretic approach to the universe. Any structure may be represented by a graph as in Figure 4, which may, in turn, be represented by a number, or a binary sequence. Thus in a one dimension, the sequences 00111001,10001101010,11000001111

represent three binary-coded structures.Assume that a neural structure has been represented by a sequence. Since this repre­sentation can be done in a variety of ways, the question of a unique representation becomes relevant.

Definition 1 Let the shortest binary program that generates the sequence representing the structure be called p. The idea of the shortest program gives us a measure for the structure that is independent of the coding scheme used for the representation. The length of this program may be taken to be a measure of the information to be associated with the organization of the system. If the external environment is a eigenstate of the system, then the system organization will not change; otherwise, it will.

One may pose the following questions:

• Are all living systems characterized by the same value of k?

• Can one devise stable self-organizing systems that are characterized by a different value of k? Would artificial life have a value of k different from that of natural life?

• What is the minimum energy required to change the value of p by one unit?

• Does a Schrodinger type equation define the evolution of structure? It appears that in the original configuration space this indeed is true. But how might such an evolution be represented in terms of structure alone? It is also clear that before a measurement is made, one cannot speak of a definite state of the machine, nor of a definite state of the environment. Clearly, we can only talk in terms of generalities at this stage. In order to make further advance in our understanding it is essential to consider the notion of structure as a classical variable first. This we do by speaking of signals that might be exclusively dedicated to altering the organization of the system. These signals may be taken to be the dual to the neuron firings that constitute the better studied response of brains. Pribram (1971) suggests a state composed of the "local junctional and dendritic (pre- and postsynaptic) potentials." Pribram also considered holographic models of memory which also require dual signaling of a certain kind. But the motivation here was more from the point of view of capacity to store information rather than self-organization. A specific type of 40 Hz oscillation as a dual signal has been proposed to explain binding. But this model is too vague at this point to provide a satisfactory resolution to the problem of self-organization. Living systems are characterized by continual adaptive organization at various levels. The reorganization is a response to the complex of signal flows within the larger system. For example, the societies of ants or bees may be viewed as single superorganisms. Hormones and other chemical exchanges among the members of the colony determine the ontogenies of the individuals within the colony. But more pronounced than this global exchange is the activity amongst the individuals in cliques or groups. Paralleling trophallaxis is the exchange of neurotransmitters or electrical impulses within a neural network at one level, and the integration of sensory data, language, and ideas at other levels. An illustration of this is the adaptation of somatosensory cortex to differential inputs. The cortex enlarges its representation of particular fingers when they are stimulated, and it reduces its representation when the inputs are diminished, such as by limb deafferentation. Adaptive organization may be a general feature of neural networks and of the neocortex in particular. Biological memory and learning within the cortex may be organized adaptively. While there are many ways of achieving this, we posit that nesting among neural networks within the cortex is a key principle in self-organization and adaptation. Nested distributed networks provide a means of orchestrating bottom-up and top-down regulation of complex neural processes operating within and between many levels of structure. There may be at least two modes of signaling that are important within a nested arrange­ment of distributed networks. A fast system manifests itself as spatiotemporal patterns of activation among modules of neurons. These patterns flicker and encode correlations that are the signals of the networks within the cortex. They are analogous to the hormones and chemical exchanges of the ant or bee colonies in the example mentioned above. In the brain, the slow mode is mediated by such processes as protein phosphorylation and synaptic plas­ticity. They are the counterparts of individual ontogenies in the ant or bee colonies. The slow mode is intimately linked to learning and development (i.e., ontogeny), and experience with and adaptation to the environment affect both learning and memory. By considering the question of adaptive organization in the cortex, our approach is in accordance with the ideas of Gibson who has long argued that biological pro­cessing must be seen as an active process. We make the case that nesting among cortical structures provides a framework in which active reorganization can be efficiently and easily carried out. The processes are manifest by at least two different kinds of signaling, with the consequence that the cortex is viewed as a dynamic system at many levels, including the level of brain regions. Consequently, functional anatomy, including the realization of the homunculus in the motor and sensory regions, is also dynamic. The homunculus is an evolving, and not a static representation, in this view. From a mathematical perspective, nesting topologies contain broken symmetry. A mono­lithic network represents a symmetric structure, whereas a modular network has preferential structures. The development of new clusters or modules also represents an evolutionary response, and a dual mode signaling may provide a means to define context. It may also lead to unusual resiliences and vulnerabilities in the face of perturbations. We propose that these properties may have relevance to how nested networks are affected by the physiological process of aging and the pathological events characterizing some neurobiological disorders. Reorganization explains the immeasurable variety of the response of brains. This reor­ganization may be seen as a characteristic which persists at all levels in a biological system. Such reorganization appears to be the basis of biological intelligence. It was a mistaken emphasis on the characterization of life in terms of reproducibility by John von Neumann that led the AI community astray for decades.