2. Mental Oscillations

• Phase Transitions and Psychopathology by James Brody, 2/18/98
  
  

It's late. An idea can come in a stray moment and all others shift. As if a key domino in a long chain were nudged, a static column falls. Boundaries open between separate concepts. My wonder at this effect watches for its own shadow, afraid that some of its insights are dreams, the artifact of an over rev'd mind. Sleep deprivation increases mental racing for many of us; the same ones of us who are apt to be up late with our web crawlers and or pulling our mail are apt to ride cognitive missiles, many of which erupt under us. Furious and dramatic thoughts to each of us; strange, preoccupied, and disconnected to an outsider. So be it tonight, dawn and later rest will bring circumspection.

I sat in a classroom earlier today, on one of those little chairs we use for 3rd graders and for teacher conferences with psychologists representing 3rd graders. Chuck has been tearful and puts his head on his desk if a problem is not solved easily. These things occur in computer class, where he is gifted, as well as in reading, writing, and arithmetic. The shifts correlate with a small reduction in his Prozac made about 10 days earlier. He was grandiose and unresponsive to parental direction at home. Now he listens better at home but cries in school and, at home, had a substantial panic attack last night.

My puzzlement is not his fear, it ties well to the obsessive crying that predated his medication. Neither is the interaction between his environment and his behavior, that a medicine perhaps just right for one setting is insufficient in another. My problem is his rapid shifts with changes in dose. Increase his Prozac just a bit and he's blase; drop it a hair and he's a mess. His teacher didn't understand and I pressed for a model. "It's as if he has a narrower 'maybe' range. We all have a gray area, between joy and gloom, between certainty and confusion. We have a Maybe world where we are not sure of a conclusion or a feeling. Where we have to get information and process things a bit before making a commitment." She smiled and changed the subject; she likely sleeps, I'm still thinking about the model and its relation to Stu Kauffman's theory.

Kauffman (1995) manipulates the notions of chaos, stasis, and phase transitions. Chaos refers to the absence of predictable outcomes from single or multiple events. A tiny variation in one trait cascades into every larger, ever wider changes. Stasis refers to prolonged intervals of no change whether in species or rocks. Phase transition applies to disproportionate changes from one state to another with relatively small input. The action of light switches is one example. Press the switch lever a tenth inch upwards, the bulb remains dark. It stays dark with each tenth inch the lever travels until the midpoint of the lever's range. Travel that middle tenth and the bulb lights completely.

Water supplies another, and more suitable example of phase transitions. Water has three phases, ice, liquid, and gas. Changes in ice are not obvious as we slowly raise its temperature. Liquid appears as we cross the relatively narrow boundary that surrounds 0 degrees C. There are no obvious further changes in water until we approach the range of temperatures near 100 degrees C. Indeed, the relatively abrupt and reliable nature of these transitions allowed us to define points on a thermometer and use them as an anchor for other observations. (3)

Kauffman posits that too little chaos (ice) leads to static forms, no evolution, no changes. Too much chaos (unconfined steam) precludes natural selection because there is no repetition of a living form and, therefore, no competition between entities for nature to select. He breaks out of this tautology when he poetically, but with numbers and examples, describes evolution and life as operating in that narrow "maybe" range, in that tiny interval between chaos and stasis, between too much and too little repetition of events.

One of his examples helps. Imagine 100 bulbs, all disconnected. Randomly choose any 2 and connect them to each other with a single wire. Then, complete the circuit for these bulbs by hooking them, in series, to a source of power. Two bulbs of the 100 is the largest number you can light. Continue choosing bulbs randomly, 2 at a time, and joining them. The maximum number that will light remains approximately 2 for about your first 20 choices. Between your 40th and 60th choices, the number that will light climbs dramatically to about 90%. That percentage slowly climbs again as we hook in the remaining bulbs. The interval between 2 and 40 represents stasis as does the range from 60 to 100. Not much happens in these intervals. Fifty-five through 65 is a phase transition.

The example needs to be a little more complicated in order to describe how our minds work. Again imagine 100, or 100,000, lights, each of them on or off. They are connected in such a way that a bulb lights as a function of whether other bulbs in its circuit are also lit. However, it is no longer true that all bulbs in any circuit light at the same time; intead there are different patterns of blinking that occur. Fewer than three connections beween bulbs routinely gives us short intervals before a stable response. Four or more interconnections require billions of years before a pattern is repeated.

Notice that the time required for a repetitive pattern of blinking to emerge is somewhat influenced, but not much, by the total number of bulbs. Bigger networks, like bigger brains, take longer, but only slightly longer, to stabilize than do small networks. Most of the bulbs are quickly on or off. Changing the number of interconnections between bulbs, however, changes this interval in a powerful manner that resembles psychological events.

Thus, the critical variable is the number of connections to each bulb. One or two connections is consistent with stasis. Four connections brings chaos. The important interval, the range of useful creativity, is that area between 2 and 4 connections wherein there is a reasonably short time to reach stability but there may sometimes be longer intervals, depending on the precise input and the logical connections between lights. Changes in the length of time it takes the blinking to repeat itself, to reenact the same pattern, is another demonstration of a phase transition. Likewise, changing the number of interconnections between neurons ought to move our brains from inertia through creativity to confusion, from coma, into the range of thought, and then to seizure as most of the neurons do not fire, react in finely defined patterns, or all fire simultaneously.

Kauffman and his people are clever and use math that I don't grasp and computer simulations that I cannot challenge. If they have been scrupulous and accurate, the implications are staggering whether for our personal "Grand Theory of Everything" or for our notions of psychopathology.

Substitute neurons for bulbs and axons for wires. Picture a child's mind or your own. The units don't even have to be in the same head, the principles are the same. Kauffman's model requires that some disorders will have similar features when there is a reduction in number of interconnections between cells. Impulsive decisions, greater rigidity, more spastic thoughts as well as movements, and more apparent ambivalence, all may arise from small shifts in input that gain the power to elicit dramatic swings in decisions.

We have long used "go/no go" models, or their logical equivalents such as on/off devices, or switches, but with all with an empty box for "analysis" or "decision." Kauffman allows us to fill the box, in a simple manner, and to understand but in a different way, two classes of event: first, the existence of impulsive acts and feelings in average people, second, any clinical disorder that is associated with rapid oscillations in behavior will depend on events that reduce the number of active connections between neurons.

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