If emergence of this type does happen in the brain, it will be very difficult to figure out how processes depend on functional circuits. In reality, of course there is no oracle, so what can be done? Empirically, neuroscience can move, and is moving, towards measuring signals across many brain regions simultaneously. The goal here is not to figure out what each region is doing, but how they do something collectively.
Neuroscientists agree that particular mental processes rely on multiple brain regions. That much is not debated. A more contentious viewpoint is as follows: many individual brain regions are engaged in a single mental process. This mental process might be relatively simple, such as face perception, or syntactical aspects of language/speech. We can say that brain regions have well defined functions f:  region 1 has function f1, region 2 has function f2, and so on. So to understand how a mental process is implemented in the brain we can think of it as a function F of multiple regions: F(R1, R2, …, Rn). What is this function F? The good news is that in an interactionally simple system, we can figure out how F works by considering f1, f2, …, fn. There may be some intricacies and challenges in understanding F from f1, f2, …, fn but it’s tractable.
Another way of saying this is that the goal is to study functional circuits by understanding collective computation, namely the collective properties of multiple brain areas engaged in solving a behavioral problem or supporting a specific mental state.
How should we study an interactionally simple system? We should study its parts, characterize them experimentally until we have a good idea of what the parts do—what their functions are. In the brain, this should be feasible because, presumably, we have a pretty good idea of what the parts are: they are cortical or noncortical areas.

One reason seems clear. It’s fair to say that neuroscience follows what could be called Herbert Simon’s dictum: we’re interested and indeed comfortable in taking on research problems and domains that involve near-decomposable systems. These are cases where intra-system interactions are much stronger than extra-system ones. Engineered systems work this way, and much research in neuroscience—lesion work in neuropsychology, systems neuroscience, functional MRI research, and so on— proceeds from this vantage point. Such systems are interactionally simple, with parts interacting weakly with anything considered beyond the system’s boundaries, under a given reasonable decomposition.

How about emergence? One way to consider emergence in a pragmatic fashion— forgoing here all the philosophical nuances and challenges—is to consider situations in which the function F of a circuit is not well approximated by considering functions fi. What does this mean? Suppose that an oracle tells us that some mental process is closely associated with a functional circuit centered on regions R1., …, Rn. Let’s say that function is “fear extinction”; briefly, unlearning that a conditioned stimulus is linked to an aversive outcome because it is no longer followed by it (e.g., a light that was previously paired with foot shock, is not longer followed by the shock). What this means is that if neuroscientists studied regions R1, …, Rn in isolation they would not have concluded or derived F. In the present case: even though they studied all of the essential regions that in reality are responsible for fear extinction, they would not have figured this out from studying the individual regions.

Emergence might be incontrovertible to physicists or mathematicians, but not in neuroscience. Why is it so controversial?

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