Nowhere else is the challenge of embracing complex systems greater than when confronting the problem of *causation*. “What causes what” is *the* central problem in science, at the very core of the scientific enterprise.

One of the missions of neuroscience is to uncover the nature of signals in different parts of the brain, and ultimately what causes them. A type of reasoning that is prevalent is what I’ve called the *billiard ball* model of causation[1]. In this Newtonian scheme, force applied to a ball leads to its movement on the table until it hits the target ball. The reason the target ball moves is obvious; the first ball hits it, and via the force applied to it, it moves. Translated into neural jargon, we can rephrase it as follows: a signal external to a brain region excites neurons, which excite or inhibit neurons in another brain region via anatomical pathways connecting them. But this way of thinking, which has been very productive in the history of science, is too impoverished when complex systems – the brain for one – are considered.

We can highlight two properties of the brain that immediately pose problems for standard, Newtonian causation[2]. First, anatomical connections are frequently bidirectional, so physiological influences go both ways, from A to B and back. If one element causally influences another while the second simultaneously causally influences the first, the basic concept breaks down. Situations like this have prompted philosophers to invoke the idea of “mutual causality”[3]. For example, consider two boards arranged in a Λ shape so that their tops are leaning against each other; so, each board is holding the other one up. Second, *convergence* of anatomical projections implies that multiple regions concurrently influence a single receiving node, making the attribution of unitary causal influences problematic.

If the two properties above already present problems, what are we to make of the extensive cortical-subcortical anatomical connectional systems and, indeed, the massive combinatorial anatomical connectivity discussed in Chapter 9? If, as proposed, the brain basis of behavior involves distributed, large-scale cortical-subcortical networks, new ways of thinking about causation are called for. The upshot is that Newtonian causality provides an extremely poor candidate for explanation in *non-isolable* systems like the brain.

What are other ways of thinking about systems? To move away from individual entities (like billiard balls), we can consider the temporal evolution of “multi-particle systems”, such as the motion of celestial bodies in a gravitational field. Physicists and mathematicians have studied this problem for centuries, which was central in Newtonian physics. For example, what types of trajectories do two bodies, such as the earth and the sun, exhibit? This so-called two-body problem was solved by Johann Bernoulli in 1734. But what if we’re interested in three bodies, say we add the moon to the mix? The answer will be surprising to readers who think the problem “should be easy”. On the contrary, this problem has vexed mathematicians for centuries, and in fact cannot be solved! At least not in the sense that the two-body, because it doesn’t admit to a general mathematical solution.

So, what can be done? Instead of analytically solving the problem, one can employ the laws of motion based on gravity and use computer *simulations* to determine future paths[4]. For example, if we know the position of three planets at a given time, we can try to determine their positions in the near future by applying equations that explicitly calculate all intermediate positions. In the case of the brain, where we don’t have comparable equations, we can’t do the same. But we can extract a useful lesson, and think of the joint state of multiple parts of the brain at a given time. How does this state, which can be summarized by the activity level of brain regions, change with time?

Before describing some of these ideas further, I’ll propose one more reason thinking in terms of dynamics is useful. For that, we need to go back in time a little.

[1] Pessoa (2017, 2018). 2017: Motivation Science; 2018: CONB.

[2] Mannino and Bressler (2015).

[3] Hausman (1984); Frankel (1986).

[4] Computational investigations in the past years have revealed a large number of families of periodic orbits (Šuvakov and Dmitrašinović, 2013).

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