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Algebraic/topological descriptions of living processes are indispensable to the understanding of both biological and cognitive functions. This paper presents a fundamental algebraic description of living/cognitive processes and exposes its inherent ambiguity. Since ambiguity is forbidden to computation, no computational description can lend insight to inherently ambiguous processes. The impredicativity of these models is not a flaw, but is, rather, their strength. It enables us to reason with ambiguous mathematical representations of ambiguous natural processes. The noncomputability of these structures means computerized simulacra of them are uninformative of their key properties. This leads to the question of how we should reason about them. That question is answered in this paper by presenting an example of such reasoning, the demonstration of a topological strategy for understanding how the fundamental structure can form itself from within itself.

Everything in Rosen's work flows from the principle of 'closure to efficient cause', the necessary and sufficient distinguishing feature of complexity, and a necessary distinguishing feature of an organism. Some students of Rosen find considerable confusion over the meaning of 'closure to efficient cause'. Such confusion is unnecessary. The matter is entirely cleared up by the (M,R)-system, a set of three algebraic maps. Each map must include one of the others in its co-domain, and is itself in the co-domain of the remaining map. Structurally, the three maps form a circular hierarchy of containment. This peculiar structure is Rosen's closure. Since each map represents an efficient cause, they reveal the character of efficient cause. The efficient cause of a process is represented as its 'dynamical law', and is a constraint that arises from the intersection of the morphology of the process and the inherent constraints in reality represented by the 'laws of Nature'. A critical, observable property (evidently unnoticed by Rosen), entailed by the closure, is its inherent ambiguity. From a foundation of ambiguity, the bizarre properties of complexity (e.g., non-computability, non-fractionability, undecidability, and incompleteness) follow in a straightforward manner, often with proofs simpler than those that Rosen discovered.

Bach-y-Rita's clinical results in restoring lost sensory function are based on several phenomena not widely appreciated in cognitive science. First, there is volume transmission. Extensive laboratory observation has shown that the brain is much more than a network of synaptically connected neurons. Bach-y-Rita has found that a key implication of volume transmission is that it is a functional component in adult brain plasticity, also widely observed experimentally. Plasticity has led him to conclude that the structure of brain dynamics is beyond the scope of algorithmic computation. If the brain is not a computer, this insight would have a significant impact on the development of new technologies based on brain function. Bach-y-Rita's work is being extended from restoration of lost senses to the creation of new senses. This in turn could lead to a new technology of "wiring a human-in-the-loop" that would be utterly unlike any computationally based technology. Instead of mere interaction with a machine, the human "becomes one" with it.

Synaptic communication, nonsynaptic diffusion neurotransmission and glial activity each update the morphology of the other two. These interactions lead to an endogenous structure of causal entailment. It has internal ambiguities rendering it incomputable. The entailed effects are bizarre. These include abduction of novelty in response to conflicting cues, a resolution of the seeming conflict between freewill and determinism, and anticipatory behavior. Such inherent ambiguity of the causal entailment structure does not preclude the implementation of brain-like activities artificially. Although an algorithm is incapable of neuromimetically reproducing self-referential character of the brain, there is a currently-feasible strategy for wiring a "human in the loop" to use the cognitive powers of anticipation and unconscious integration to provide dramatic improvement in the operation of large engineered systems.

DISCLAIMERThis report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference hereto to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. ABSTRACTWe describe a wavelet-based technique for identifying aircraft from acoustic emissions during take-off and landing. Tests show that the sensor can be a single, inexpensive hearing-aid microphone placed close to the ground. The paper describes data collection, analysis by various techniques, methods of event classification, and extraction of certain physical parameters from wavelet subspace projections. The primary goal of this paper is to show that wavelet analysis can be used as a divide-andconquer first step in signal processing, providing both simplification and noise filtering. The idea is to project the original signal onto the orthogonal wavelet subspaces, both details and approximations. Subsequent analysis, such as system identification, nonlinear systems analysis, and feature extraction, is then carried out on the various signal subspaces.

Sensory systems are associated with motor systems for perception. In the absence of motor control over the orientation of the sensory input, a person may have no idea from where the information is coming, and thus no ability to locate it in space. Sensory substitution studies have demonstrated that the sensory part of a sensory-motor loop can be provided by artificial receptors leading to a brain-machine interface (BMI). We now propose that the motor component of the sensory-motor coupling can be replaced by a "virtual" movement. We suggest that it is possible to progress to the point where predictable movement, not observed except for some sign of its initiation, could be imagined and by that means the mental image of movement could substitute for the motor component of the loop. We further suggest that, due to the much faster information transmission of the skin than the eye, innovative information presentation, such as fast sequencing and time division multiplexing can be used to partially compensate for the relatively small number of tactile stimulus points in the BMI. With such a system, incorporating humans-inthe-loop for industrial applications could result in increased efficiency and humanization of tasks that presently are highly stressful.

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