Essays for performers: Instability and Determinism in the Brain


In the theory of mind debates, I am on the side of materialist monists. I accept determinism but because of chaos/complexity,  life as I experience it is still awesomely beautiful, and unpredictable, and thoroughly consciously lived. You might ask: How is that possible? Doesn’t determinism suck all the joy and hope and agency from life, leaving speculators listless or uncomfortable in the lie of freewill they must tell themselves to survive? Well, yes it does, if you only have a naive understanding of how deterministic systems behave.  Luckily, stuff is much more intricate than suggested by the demonstrations of newtonian physics presented in science class. I won’t try to explain how exactly consciousness arrises or agency operates, but the following is a series of ideas which make space for the influence of top-down thinking on an animal’s actions. Most of the relevant ideas come from math, specifically dynamical systems.

Dynamical systems form a topic in applied mathematics which explores deterministic systems. The definition of a dynamical system is, in fact, a system (of equations usually, but really could be anything) for which there is only a single defined future given the present initial conditions. With the formalised framework of a system + time, we can explore how different initial conditions lead to different outcomes (e.g. sustained states like fixed points, oscillations, or chaos) thus defining the dynamics of the system, and with some of ideas of how the systems potential behaviour, we can also consider how parameters of the system (adjustable components of the defining equations) change these dynamics. Got that? Well here is an example which should help ground these terms.

Consider the dynamical system of a coin on a level table (Exciting, eh! I’m pretending it’s a canadian quarter.) There are three fixed points in the dynamics of the system: the coin flat on the table surface (one side or the other), and the coin balanced on its edge. If the initial conditions of the system have the coin in a fixed point, the system will stay as such. Balanced on edge is an UNSTABLE fixed point, as it will only stay balanced so long as no vibrations interfere, while flat on the table is STABLE.  If the initial conditions are anything other than the fixed points, the coin/table system will progress toward the stable fixed points of flat on the table. The dynamics of the system is then these three fixed points and all the rolling and falling which the coin will pass through on the way to eventually being flat on the table, the attractor on the system.

Coins have two faces, heads or tails. If we balance the coin on its edge, some vibration will make it fall, eventually. If you knock it with your hand, you can pretty easily control which side stays up, but if you give the table a little shake instead, the coin will roll and wind and it will be very difficulty to predict which side will be on top at the end. The winning side is determined by a myriad of tiny factors you can’t control, like the roughness of the table surface, the wear on the coin, the exact angle and force of the nudge you gave the table. If you could, to the best of your ability, repeat this balance and indirect nudge experiment, it’s likely you’d still not learn to successfully call queen or moose before the coin starts to wobble. This unpredictability is not a failure of determinism, it is just a fact that these two stable fixed points can be reached from very similar conditions. In theory, if you know everything about the coin, like where on the table it is, how it is leaning, how it is moving, and what forces are acting on it, and everything about the table, specifically all irregularities of its surface, and if you had infinite precision in your calculations of the coin’s motion,  you could correctly anticipate heads or tails. But that level of detail is unobservable, practically and scientifically, so in the case of the coin-face problem, its best you anticipate both possible outcomes of the nudge.

Sensitivity to initial conditions is a really big deal for prediction of all kinds, and it is a defining component of chaos (in math). Popular discussion of chaos usually emphasis the scaling difference of initial conditions to outcomes (Y/N butterfly flaps its wings => Y/N hurricanes in NYC , *sigh*), but the progress between is also really important. There are a lot of very simple systems, or at least systems which are simple in parts, which show crazy complicated behaviour, like the weather. On the one hand, we understand a lot about how air pressure, water molecules, temperature, radiation from the sun, and different particulates interact in the small scale. But we can’t predict the weather perfectly because our measurements of present conditions are always a little rough, and those tiny discrepancies can be the difference between rain or shine in two days time. Consider the earth;s whole atmosphere, and we have a beautifully complicated and diverse range of behaviours happening all over, many at the same time,  all out of the same basic components. The bigger the system, the more opportunity for complicated chaotic behaviour, like the sustained but ever evolving patterns of el nino and jet streams. All this to say, determinism isn’t boring, nor is it predictable.

And now we can get to living organisms. Life as we know it depends on at least two principles: sustaining the unstable state of being alive, and replicating. Near identical replication is another common (if not necessary) characteristic of chaotic systems, and it is super cool how we get wonderfully flexible organisms from relatively little information, but I’m not going there today. Staying alive, that’s the issue right now. Loosening the dynamical systems frame work a little, consider the organism a system, and the stuff outside it different conditions through which the organism may or may not be able to avoid falling into the stable state of being dead. Many adaptations allow for the maintenance of the organism’s system despite changes in the external conditions (homeostasis), while others enable greater diversity of actions out of similar states of aliveness.

One of the key tools for survival in the animal kingdom is locomotion. Consider a sea slug sitting on a rock (the aplysia are very popular for basic neuroscience, as their neurons are huge and only number around 20000). If you poke it, it will twist, or squirt ink, or shrink away, all responses considered to be little more than defensive reflexes in response to a threatening stimulus. If you just leave it there, however, it will eventually crawl off the rock all by itself. What makes the slug move without the prompting from the outside? Maybe it is hungry, or cold, or inspired to move by some random accidental firing of a neuron in the right place at the right time (i.e. noise in the system). Regardless, while it sat on the rock unperturbed, its state allowed simultaneously two possible outcomes, to move or to stay put, and the supporting conditions for those two continuations of aliveness were necessarily very close together as the difference would be internally generated and very slight. The potential to move or not is a protected instability in the slug’s nervous system, making many possible continuations accessible from a sustainable position of rest.

Now humans have way more layers of information processing on top of the basic controls of our outward behaviour, and in the piles of grey and white matter is an amazing capacity to predict what might come out of these or those external conditions, and what might result from that or the other action we could take. As the complexity of contingency plans increases, we must correspondingly increase our tolerance for ambiguity. In many situations, it is factually impossible to know what will happen, and so it is advantageous to entertain multiple possible developments. Just like our bodies (and the slug’s) are generally able to engage in different actions from very similar starting points, our minds are ready to spin out many possibilities of a present (or hypothetical) situation. Knowledge, memory, and practice are then extra tools for modelling accurately what may happen, influencing the outcomes we project on the many possibilities. From the concurrent explorations of options, some preference can form and be implemented.

All this neural activity supporting internal debate is, in the grand schema of things, really only tiny shifts of electrical potential and ion concentrations in our heads, but by virtue of the sensitivity of our organisms, these tiny changes can very well be enough to trigger different action plans. These plans will be executed through a haze of practice and circumstance, but in the moment of indecision, your body still maintains the potential to execute multiple distinct paths, waiting for resolution to fall towards any given strategy.

Obviously, this doesn’t grant us total freewill. Some would argue that referring to sensitivity in our neural system (the only way to practically consider neural instantiation of our lived experience, in my opinion) passes the burden of determinism up from neurochemistry to life lessons. And I can’t disagree with that: I do think of the human mind/body as the product of experience. but at least, given the built-in possibilities, the conscious experience of introspection and decision making need not be dismissed as superfluous. This layer of order in our minds can influence up and down the scale. This allows for memory and knowledge as well as direct stimuli (light, threat) and hormones to influence what happens to us and through us. Our skins, by separating us from the outside diversity of conditions, protects our instabilities, our potential, and allows our minds, our complicated brains, to exert delicate influence on great action.

Notes: kudos to Steve Strogatz who’s pendulum example I riffed off of for the coin/table system, and James Gleick and Mitchell Waldrop  for feeding my brain the basic components years before I got to work with the mathematical details of dynamical systems.


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