I am interested in a number of practical goals relating to human spiritual health -- in particular, in finding the means to make it easier for people to assemble the elements of well-being, to realize their creative potential, and to experience the beauty in living. These areas used to be the province of religion, but now in the face of science, not to mention pluralistic faiths, it is often difficult to achieve them through religious practice. In fact part of the problem is that, though we don't realize it, science is itself a religion, and subtly undermines attempts to benefit from its alternatives. Some people are capable of carrying out the monumental effort of integrating and reconciling science with their chosen faith, preventing this undermining; most are not so gifted.
Regardless of our opinion of it, we are stuck with science, and need to find a way to bring its machinery to bear in the areas that are most important for human spiritual health. Psychology is the branch of science most relevant, but although there are wonderful and unique insights to be derived through qualitative, holistic approaches such as those developed by Carl Jung, Abraham Maslow, and others within this tradition, these systems are not truly scientific in that they abandon the objectivist stance. Science must find a way back to the subjective without cutting off its objectivity. For this reason, a psychology that will be truly useful to mankind must have its foundation in reductionistic, mathematically-connected "hard" science. At the same time, such a psychology must also make direct contact with the subjective; drug-based psychiatry based purely on knowledge of chemical balances in the brain is insufficient.
My research has therefore broadly focused on the problem of building a bridge between neurobiology and psychology from both sides. I describe these areas further below. To get straight to the peer-reviewed upshot so far, see the papers and abstracts available here.
At the level of neurobiology, I have worked on understanding how the cerebral cortex develops sensory representations and uses them to direct behavior. Although the hippocampus, amygdala, basal ganglia, and cerebellum play roles in manipulating representations, the bulk of the actual pattern space is maintained in the (neo)cortex. A fundamental property of the cortical architecture is that it is regular and modular: It is divided into local areas, each receiving information from and sending it to a particular subset of the other areas, and each area has approximately the same local circuit structure - whether it processes sensory input (in some modality), motor output, or more abstract information. A central unanswered question is how computational labor is divided up between within-module processing and between-module integration. Clearly information from multiple areas is combined in directing behavior, but it is not known what level of abstraction the combination occurs at. Part of the difficulty in making this determination lies in the fact that the local circuitry, although reasonably well-understood at a mesoscopic level, is not known well enough at the microscopic level to characterize the architecture of the relevant neural networks. In particular, each area receives inputs to different cell layers from different sources, but the degree and form of interaction between these layers within the area is not well specified.
In my dissertation research, I clarified this circuitry by collating anatomical data from the literature and applying constraint-satisfaction methods to fill in missing information. The resulting connectivity structure is employed in a spiking neural network model, the behavior of which is compared with simple stimulation experiments on neocortical slices. The model, thus validated and calibrated, is then simplified as much as possible while still retaining the basic dynamic properties of the original and used to investigate computational questions. In particular I have been studying the Hebbian learning of connection weights between areas in attempt to understand how features come to be represented in cortical sensory systems. What determines what features are used and which areas they are found in? Because of the structural regularity mentioned above, insight into the general nature of this process can be applied to understanding how the cortex processes information in all of the wide variety of subdomains with which it deals.
At the level of psychology, I have focused on working towards transforming a particular descriptive framework for conceptual structure - that developed within the cognitive semantics tradition of linguistics - into a theoretic and predictive one. In cognitive semantics, concepts are understood as composed of collections of simpler ones related together in particular ways, eventually grounding out in primitives derived directly from regularities in sensorimotor experience. Because different concepts share substructural components, processes like metaphor understanding and analogy construction are possible. Novel concepts themselves can be viewed as being built by a process of cognitive mapping, in which substructural parallels between previously-existing concepts and the focused domain serve as anchors to pull in subcomponents, whose combination is the new concept.
In my own work, I am characterizing the mapping process more precisely by examining its role in mathematical cognition. Mappings are at work in both the creation of mathematical structures through definitions and their guided manipulation in mathematical proofs, and they can be studied more easily here than in other domains because the mappings and the structure of concepts are both simpler and more explicit in mathematical discourse than elsewhere. Furthermore, the recorded history of mathematics offers a rich source of data.
Regarding integration of the work at the two levels, although there will likely be a wide gap for some time to come, a now-old approach - Gestalt psychology - offers some clues as to how it might be bridged. It makes use of the concept of energy minimization on structures subject to forces within a field to describe cognitive processes from the perceptual and motor to the conceptual levels. Although the characterization of this process was never developed with satisfactory precision, it can today be related in nontrivial ways both to modern theories of neural network dynamics and to the concepts of mapping and constraint satisfaction employed in cognitive semantics. These relations, vague though they are, provide at least the seeds of something to go on in an area where very little is known - or even visible...
See my papers online for more information.
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