Aristotle’s revenge

Imagine you’re walking around a university campus. It’s a couple of weeks after the spring semester has ended, and so there aren’t many people about. You enter a building and walk into one of the rooms. It appears to be some kind of undergraduate lab, most likely either physics or engineering.

In the lab, you come across a table. On the table, someone has balanced a rectangular block on its smallest end.

You nudge the top of the block. As expected, it falls over with a muted plonk. You look around to see if you might have gotten in trouble, but nobody’s around.

You come across another table. This table has some sort of track on it. The table also has a block on it that’s almost identical to the one on the other table, except that the block has a pin in it that connects it to some sort of box that is mounted on the track.

Not being able to resist, you nudge the top of this block, and it starts to fall. Then, the little box on the track whirs to life, moving along the track in the same direction that you nudged the block in. Because of the motion of the box, the block stays upright.

The ancient philosopher Aristotle believed that there were four distinct types of causes that explained why things happened. One of these is what Aristotle called the efficient cause: “Y behaved the way it did because X acted on Y“. For example, the red billiard ball moved because it was struck by the white ball. This is the most common way we think about causality today, and it’s sometimes referred to as linear causality.

Efficient cause does a good job of explaining the behavior of the first rectangular block in the anecdote: it fell over because we nudged it with our finger. But it doesn’t do a good job of explaining the observed behavior of the second rectangular block: we nudged it, and it started to fall, but it righted itself, and ended up balanced again.

Another type of cause Aristotle talked about was what he called the final cause. This is a teleological view of cause, which explains the behavior of objects in terms of their purpose or goal.

Final cause sounds like an archaic, unscientific view of the world. And, yet, reasoning with final cause enables us to explain the behavior of the second block more effectively than efficient cause does. That’s because the second block is being controlled by a negative-feedback system that was designed to keep the block balanced. The system will act to compensate for disturbances that could lead to the block falling over (like somebody walking over and nudging it). Because the output, a sensor that reads the angle of the block, is fed back into the input of the control system, the relationship between external disturbance and system behavior isn’t linear. This is sometimes referred to as circular causality, because of the circular nature of feedback loops.

The systems that we deal with contain goals and feedback loops, just like the inverted pendulum control system that keeps the block balanced. If you try to use linear causality to understand a closed-loop system, you will be baffled by the resulting behavior. Only when you understand the goals that the system is trying to achieve, and the feedback loops that it uses to adjust its behavior to reach those goals, will the resulting behavior make sense.

Henry Yin on what the cyberneticists got wrong

I’ve been on a bit of a control systems kick lately, and, serendipitously, I happened to see this tweet, which referenced a paper by Henry Yin at Duke University titled The crisis in neuroscience.

In the paper, Yin argues that neuroscience has failed to make progress in modeling human behavior because it tries to model the brain as a linear system, where you can study it by generating inputs and observing outputs.

Input/output model of brain

Yin proposes an alternative model, that you need to view the brain as composed of a collection of hierarchical, closed-loop control systems in order to understand behavior from a neurological perspective.

Now, the cybernetics folks have long argued that you should model human brains as control systems. But Yin argues that the cyberneticists got an important thing wrong in their control models: their models were too close to engineering applications to be directly applicable to organisms.

Classical engineering model of a feedback control system

In an engineered control system, a human operator specifies the set point. For example, for a cruise control system, you’d set desired speed. In the block diagram above, this set point is provided as the input to the system.

The output of the “Plant” block diagram is the current state of the variable you’re trying to control (e.g., current speed). The controller takes as input the difference between the set point and current state, and uses that to determine how to drive the plant (e.g., input to the motor).

Here’s a block diagram of everyone’s favorite control systems example, the thermostat:

A thermostat that controls temperature

I’ve used a double-arrow to indicate signals that propagate through the environment, and single-arrows to indicate signals that propagate through wires. I’ve put a red box around where Yin claims the cyberneticists hold as their model for control in animals.

The variable under control is the temperature. A human sets the desired temperature, and a temperature sensor reads the current temperature. The controller takes as input the difference between the desired temperature and the current temperature, and uses that to determine whether or not to turn on the furnace.

The actual temperature in the house is determined both by the output of the furnace, and by other factors (e.g., temperature outside, how good the insulation is, whether someone has opened a door), which I’ve labeled disturbance.

The problem with this, Yin argues, is that the red box is not a good model for the control that happens in the brain. As an alternative, he proposes the following model:

You can think of the red box as being the stuff inside some aspect of the brain, the “plant” as being the things that this aspect controls (e.g., other parts of the brain, muscles).

The difference in Yin’s model is that the controller determines the set point. There’s no external agent specifying the desired value as an input. Instead, the controller generates its own set point, which Yin calls the reference value.

Also note that Yin’s model includes the input function inside the red box. This takes sensory input at calculates the variable that’s under control. The difference between this model and the thermostat is that, in the thermostat model, you know from the outside that temperature is the variable being controlled. In Yin’s model, you can’t see from the outside what the variable is that’s being controlled for: the variable is internal to the control system.

Despite knowing nothing about neuroscience, and only knowing a bit about control systems, I still found this paper surprisingly accessible. I recommend it. There’s a lot more here than what I’ve touched on in this post.