2. Resource explanations

Resource explanations are, broadly speaking, a kind of mechanistic explanation. Mechanistic explanations decompose entities into parts, the coordinated activity of which explains some characteristic activity of the whole (Craver Reference Craver2007; Bechtel and Richardson Reference Bechtel and Richardson2010). When we break down a mechanism into spatiotemporal parts, however, we find that these often come in one of two different flavors. To explain how an internal combustion engine produces rotary motion, we have to talk about pistons, valves, and injectors, on one hand, and gasoline and air and oil, on the other. These play different roles within the broader explanation and need slightly different treatment. Following Klein (Reference Klein2018), I will distinguish between mechanical parts and resources. Very roughly speaking, this corresponds to an agent–patient distinction: mechanical parts do things (to other parts or to resources), whereas resources have things done to them. We can sharpen up that characterization along four different criteria.

First, mechanical parts tend to persist over the timescale of the explanation, whereas resources are often transformed. Gasoline and air are mixed and burned; the pistons and valves stay the same throughout. Note that transformation need not be dramatic or irreversible: cool oil is fed into the engine block and is warmed as it removes heat. It is later cooled, and the cycle continues. Second, mechanical parts tend to be individual, whereas resources are often aggregate. There are four pistons, and each of them needs to do the right thing at the right time. By contrast, gasoline is a mass that is broken into smaller bits, as needed. Although continuous resources are the cleanest cases, we can have discrete resources as well. A youth soccer team needs so many oranges at half time: the individual identity of the oranges is not important, only that there are enough for everybody. Third, mechanical parts are often realization indifferent, whereas resources are often realization sensitive. Spark plugs and valves are classic functionalist examples: for the purposes of explanation, nobody cares that much about what they are made of, so long as they are made of something that can do the job. Gasoline, by contrast, is not fungible: put in diesel, and the engine won’t work.

Note that the mechanical part–resource distinction—and therefore the satisfaction of the first three criteria—is often explanation relative. If I care how my car stops, brake pads are mechanical parts: persistent, individually important, and functional. If I’m managing a racing team, I may go through so many brake pads that I treat them as a consumable resource. Whole mechanisms in one context can be mere resources in another: the Jeep is a complex whole to the mechanic, matériel to the quartermaster. The point of distinguishing mechanical parts and resources is thus not to draw a firm metaphysical line in the world but to emphasize the different roles that different spatiotemporal parts of a mechanism can play within the same explanation.

Fourth and finally, mechanical parts are usually causally conservative, whereas resources are causally promiscuous. Each valve has a fixed role and interacts with a few different things in predictable ways. Indeed, an important rule of thumb in engineering is to keep systems modular, if possible, that is, to minimize the ways in which mechanical parts interact (Simon Reference Simon1996; Calcott Reference Calcott2014). By contrast, resources are often used by multiple different processes at once. In most cars, engine oil both lubricates and cools the engine. The functions can interact: if the oil gets too hot, it ceases to be a good lubricant.

Indeed, in many domains, there is a familiar possibility of resource competition with attendant resource starvation as an explanation of failures. It takes so much rangeland to support so many head of cattle. Why? Any individual animal would need much less, but the fact that they are all competing for the same grass means that starvation threatens on a smaller plot. Conversely, many engineering problems arise from the need for resource management. Electrical grids would be simple if there were one producer and one consumer. Delivering energy to many different households with different patterns of demand requires considerable infrastructure just to make sure that everyone gets what she needs.

I have written mostly of concrete resources. However, the point can easily be generalized to more abstract resources. Economics is all about the interaction between various concrete resources (pigs, whiskey, fireworks) and various abstract ones (money, futures, derivatives). A key set of abstract resources is found in computational theory. In particular, computational complexity theory studies how different algorithms require different amounts of time, memory, processor cycles, bandwidth, and so on (Aaronson Reference Aaronson, Copeland, Posy and Shagrir2015). Sometimes these resources trade off against one another: we might cache results from a computation to save time at the expense of space. They also enter into explanations that involve resource competition and resource starvation. My poor choice of a sorting algorithm means that my computer used too much memory, which explains why the operating system crashed. Both would have been fine on their own, but the fact that they were competing for the same, causally promiscuous pool of memory means that they couldn’t coexist.

3. Transition and elaboration

Return to the evolution of brains. Brains—and nervous systems more broadly—are incredible resource hogs. Raichle and Mintun (Reference Raichle and Mintun2006, 467) estimate that the human brain uses about 20 percent of a person’s total energy expenditure despite being only about 2 percent of body weight. Furthermore, the majority of that is a standing cost: it is paid wheneverone is awake, regardless of what one is doing. In Sterling and Laughlin’s (Reference Sterling and Laughlin2015) survey of overarching principles of neural design, they show that resource constraints shape even the most basic nervous systems. Some of these constraints also have important nonlinearities. Notably, both the energetic and the volumetric costs of sending information rise disproportionately as the rate increases (Sterling and Laughlin Reference Sterling and Laughlin2015, 54).

The basic question about transitions, recall, was why a change in information flow might be favored, given that the obvious benefits of such a change to the evolvability of new functions don’t arise until after the transition. Put in the language of the previous section, transitions may well allow for the evolution of new mechanical parts, but the possibility of new parts cannot be the reason why the transition occurs. An obvious place to look for the answer is instead with resource constraints. Furthermore, as I’ll argue, it is possible for a transition favored on resource grounds alone to facilitate new patterns of information flow and thus new functional parts down the line.

Here is an example, using artificial neural networks, of the sort of thing I have in mind. Consider a recurrent neural network containing s neurons and requiring t time steps to calculate some function f. A well-known result shows that this network can be “unrolled” into into a purely feed-foward network, which computes f containing t layers and st neurons.Footnote ² Assume that the timescale is comparable in each case (that is, that recurrent loops take the same amount of time as additional layers), so that the recurrent and unrolled networks also take the same amount of time to compute f.

Now, flip this picture around. Suppose an organism with purely feed-forward connectivity calculates some f by circuit N but that f could be calculated by a recurrent network N′, such that N is the unrolled version of N′. Ex hypothesi, both circuits calculate the same function in the same amount of time. However, if N has several layers, the shift to N′ might come at a substantial energetic savings, because N′ would use s(t – 1) fewer neurons.

In fact, the trade-off is a bit more complex. Artificial recurrent networks are harder to train: simple back-propagation faces a problem of vanishing or exploding error gradients.Footnote ³ Recurrence in biological systems faces an analogous problem, one assumes, because of the inherent instability of excitatory feedback loops. Long-range feedback might also mean more long-range wiring costs, which are themselves a substantial resource drain (Sterling and Laughlin Reference Sterling and Laughlin2015) and one that brains seek to minimize (Cherniak et al. Reference Cherniak, Mokhtarzada, Rodriguez-Esteban and Changizi2004). So additional steps are needed to make a recurrent network stable and trainable. Let’s assume that these costs scale with the number of neurons by some constant factor c. Then, we might expect an evolutionary transition from N to N′ to be favored, on resource grounds alone, just when st > sc.

In other words, we should not expect recurrence to evolve and stabilize when the additional costs of stabilizing a recurrent network are more than the cost of the additional layers needed by a feed-forward network. Furthermore, because these trade-offs are vague and approximate, if recurrence does occur, we should expect there to be some point where both N and N′ are live options; that is, N′ does not have an obvious advantage over N, despite added complexity.

Or, to be more precise, N′ does not have an advantage with respect to computing f. However, the transition to a recurrent network might bring benefits for computing other functions, for N′ can compute functions that take longer than t without having to add additional hardware. What N′ can do with time, N must do with space—and time is often cheaper than space. That is, if an organism has the leisure to run a function for longer, it gets the benefit of recurrence for minimal additional metabolic cost. Adding neurons and wiring, by contrast, adds a substantial fixed cost. Furthermore, the choice of whether to run an algorithm longer can be made on the fly, whereas making a bigger brain usually requires developmental changes.

For a concrete example of the sort of algorithms that benefit from more time, one might consider what Zilberstein and Russell (Reference Zilberstein and Russell1996) call anytime algorithms. These approximate a certain function and do a better job the more time they are given, and hence they “allow computation time to be traded for decision quality” (Zilberstein and Russell Reference Zilberstein and Russell1996, 181). Some algorithms of this sort, such as Newton’s method for finding roots, are well known. However, there are interruptible anytime versions of algorithms for many problems faced by real-time control, such as the traveling salesman problem (Zilberstein and Russell Reference Zilberstein and Russell1996, 190ff.).

My claim is that a network like N′ might get the benefits of these algorithms effectively for free, whereas N has no obvious way to perform additional iterations aside from adding more layers (and thereby committing more resources). That in turn opens up the possibility of real functional change by making possible algorithms that would be too costly to be useful in simple feed-forward networks.

This is all a how-possibly explanation, of course, and an abstract one at that. The point is not to make claims about an actual transition but rather to show how resource considerations alone could support a neural transition. The foregoing explanatory pattern suggests that the transition itself might be favored on pure resource competition grounds. The same function f is computed in the same amount of time before and after the transition. However, the consequence of the transition may well be the evolvability of more complex, more efficient, or more useful functions—functions that the original network may resist evolving precisely because of the added cost.