03 Feb Mapping a Thought
What is truly going on in a network of billions of cells with trillions of connections? Can we even begin to figure it out – is mapping a thought possible? When I was in the midst of my studies in which I initially wrote this, MRIs and CAT scans were the best of our ability to capture a composite picture of brain activity at any given moment. At best, these techniques could only deliver low resolution pictures of brain activity. Things have improved dramatically, yet we are still unable to map a thought or feeling to a specific set of neurons or even clusters of neurons. We are also unable to trace the brain activity that lead to the thought. One of the foldouts in the February 2014 issue of National Geographic shows a “Mind Machine” designed to track thoughts.
It’s amazing how much more we know now than we knew 100 years ago, but there’s much more that is unknown than what is known. (Mind Machine from National Geographic Article) Consider this analogy. There are hundreds of millions of addresses in the United States of America. That is orders of magnitude fewer than the number of neurons in the brain. Still, if MRI and other imaging techniques could be applied to U.S. addresses, they could only tell us that a piece of that thought lives in Cincinnati, another piece lives in Little Rock, and another in Salinas. The actual addresses would remain unknown.
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It would be nice to be able to watch cognition at the neuron level. Even if that were possible, however, the connectionist view of the microstructure of thought suggests that we may not learn anything important, no matter what level of detail we could capture. Fortunately, there is hope: “Although trillions of connections made by billions of neurons in the brain may seem to constitute a hopelessly complex web of relations, very systematic patterns of interaction exist between neurons in various brain areas.” (LeDoux, 1996, p. 140)
The Wire Metaphor
Neurons of different types in the cerebrum and the cerebellum occupy different positions and perform different roles (Post on Cerebellum). This is analogous to electronic circuits where different components in different places perform specialized roles. That comparison leads us to the wire metaphor. 
The conductance properties of the axoplasm are very important in the circuitry of the brain. The processes underlying electrical signaling in the brain can best be understood if we begin by picturing the relevant structural components of the nerve fiber which carries the signals. Kuffler, et al., suggest we think of the fiber as “a tube filled with a watery solution of salts and proteins (axoplasm) separated from a similar extracellular solution by a membrane…the axoplasm is analogous to a copper wire and the membrane to a layer of insulation around a wire” (1984, p. 100). 
Of course circuits are quantitatively different since the density of charge-carrying ions in the axoplasm is so sparse that the conductance is not remotely comparable to wires. At these low levels of conductance, components in the axoplasm that can influence conductance may be critical. In this diagram of a circuit, the wires on this side of the board are green and the components (chips and transistors) are other colors. Both the components and the wires are built into neurons. The question we must consider is this: how complex is neuron circuitry?
Thought to Action
There is a continuum of duration from the beginning of a nerve impulse (seed of a thought) to its realization in action (the fruit of the thought). Here are some rough estimates: The computer I originally typed this on was processing keystrokes at 200 mHz (a fraction of current speeds), so a register changed two hundred million times a second. The speed of thought is relatively slow compared to the speed of computation (see my post on timing), yet human ability to think up really complex and inventive things is unparalleled by any machine. So although speeding up computers is bound to help us build smarter machines by reducing performance barriers, we will need to do more. We need to design machines that act more like the brain. To do this, we may need to design systems that are modeled after the brain.
Nerve Membranes and Pathways Within Cells
How reasonable is it to compare axons and dendrites to wires in the circuitry of the brain? It has been shown that the membranes of squid neurons, independent of internal fluids or components, can conduct all the electrical potential applied to them within the range of their normal processing capabilities (Hodgkin 1964). So which represents the wire? The membrane or axoplasm? Well-informed opinions take both sides of the issue, but little real evidence supports either position. If axoplasm is indeed “the wire,” there is a strong possibility of cytoskeletal participation in transductance. The graphic depictions of neurons appearing in this work and throughout the literature suggest that the smooth, slender appendages of neurons look like wires. These images, however, belie the actual morphology of nerve fibers (see Signal Transduction in Neurons).
Reconstructive work done at the University of Toronto (Stevens, Trogadis & Jacobs, 1988; Harris & Stevens, 1988) has shown that the actual morphology of some or all nerve processes more closely resembles streams of wax dripping from a burning candle than strands of wire. We know that the soma primarily serves as the biological support center of the cell. If there is any complex circuitry in neurons, it must be in the fibers. The amount of potential transduced by cell membrane is a critical question in this exploration. If the axoplasm within the membrane and/or intracellular structures conduct a significant portion of the potential, then their roles in the cybernetic functions of neurons become much more important. The most critical parameter this affects is the influence of individual inputs on the aggregate response.
As indicated earlier, IF and MT have the capability of transducing electrical potential. Before we can be confident in our assumptions about the nature of both local and action potential flow in and between neurons, we need to produce more accurate descriptions of the ratio of potential flow in neural membrane, axoplasm, and cytoskeletal components. In the illustration at right, the green lines represent intermediate filaments, and the red and blue lines represent microtubules. These IF and MT may serve to selectively direct and control the level of potential flow from specific inputs and to specific outputs. This complex functionality is not modeled in most existing artificial neural networks.
Perceptual Dimensions
If achieving threshold action potential is the most significant cybernetic event occurring in neurons, then neural modeling should be possible strictly with digital hardware. In other words, given a predefined structure and a set of formulae for adapting to certain situations (input patterns), it should be possible to simulate functions of the brain with a model primarily based on neuromorphic hardware with a few simple functions to propagate activation. Even if simple gates exist within a neuron – say in the cytoskeleton – modeling should be straightforward.
For perceptual processes that differentiate or extract components from input stimuli, hardware-oriented models have proven very useful, accurate, and surprisingly robust. Perhaps this is because input stimuli for perceptual systems (stereo images, sounds, tastes, smells, and tactile sensations) can be represented in two-dimensional space. Images can be projected on two two-dimensional grids. Other senses exhibit similar regularity and predictability. Rules that govern perception are generally two dimensional, so they can be easily modeled using probabilistic techniques. PC-based simulations of neural networks consist of spreadsheet-like structures in memory where each cell represents a node. Hardware networks also exist – in neural chips and massively parallel computers, for example. All these possibilities will be discussed further as we proceed along the pathways of mapping thoughts to computers.
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