Nathan Matthews
Not being an economist, I cannot really evaluate Batten’s claims about traditional economics. But regardless of what academic economists believe, it seems that business and our economy have always embraced the idea of positive feedback. The idea is not that complicated—a change in the world makes a following change, of similar character but greater magnitude, more likely. The 19th century boosters Batten describes seem to have embraced unrefined versions of this concept. The capitalist idea of growth, expanding markets, and never-ending progress is itself an idea of positive feedback. I would think nearly all Americans have been exposed to the idea that economic growth fuels further growth. Surely, the economists have heard of the idea.
Admittedly, the popular conception of positive feedback is limited and flawed. Positive feedback is not necessarily “positive”. It does not always describe growth or progress, and similarly growth and progress will not always be positively reinforcing. Confusion around this point occurred in our class discussion of traffic and congestion. In a quickly moving freeway, when congestion begins to slow traffic, the downward spiral to a traffic jam is, as it begins, an example of positive feedback, even though traffic is slowed and ultimately brought to a deep basin of an attractor. Every act that slows down traffic—slamming on the brakes, rubbernecking to see an accident, whatever—produces more of the same acts. Even though the flow of traffic is decreasing, the feedback is positive. What happens once the traffic is jammed? If it is jammed, and is going to stay that way, there is no more change, and hence no positive feedback. In a jam, acts that could produce change (a clearing in the traffic) tend to be dampened, rather than amplified, as everyone rushes to exploit them and thereby nullifies them. The system has transitioned to negative feedback.
Positive and negative feedback are not conceptually difficult, but the transition between the two is (as measured by the objective standard of my understanding). Batten’s thoughts on this may not be groundbreaking but they are clarifying. He describes a model of a dynamic world skipping between punctuated equilibria. These equilibria are attractors or steady states—wells that a convulsing system, such as one accelerated by positive feedback, can sink into. In a simple model of traffic, one equilibrium is a state of swiftly flowing traffic, and another is a stop-and-go traffic jam. Negative feedback causes a traffic flow in either of these states to remain in it, although we can imagine that the effect of negative feedback is stronger in a traffic jam (that state is a stronger attractor). Traffic transitions from one state to the other when some event overcomes the effect of negative feedback. Positive feedback (may) then augment the disturbance, sending the system further away from the equilibrium. If the system approaches the other attractor, the effect of negative feedback can catch it and keep it there until the process repeats.
This story is easy to tell with traffic jams, but as Batten tells it for cities, it becomes more elaborate. He incorporates more forces into his models, but the tricky part is that the attractor is not a single city size, but a place in the larger country’s distribution of sizes. As Batten describes the amazing convergence of forces accounting for Chicago’s boom, explicitly claiming another source of positive feedback every other paragraph, one wonders why Chicago would ever stop growing. The power-law distribution of cities explains why we should have expected some city to boom—the distribution of cities in the US was bottom-heavy, we should have expected city composition to return to the power-law distribution. However, it also explains how big we should have expected the boom city, wherever it happened to be, to become. Unfortunately, Batten has not fully explained why this distribution is such a basin, and a description of the negative feedback that halts a city’s growth would be a restatement of that explanation.
As a final clarifying point about feedback: positive and negative feedback should be described as effects, rather than forces. The combination of forces present in a system at any point in time can sum to produce a positively or negatively reinforcement of any change. By thinking of feedback as an effect, rather than a force, we can better understand the transition from one type of feedback to another. As a system approaches a steady state, there is not an overarching force of positive feedback that must be overcome. Thus, when traffic slows to a jam, we needn’t look around and wonder what happened to the positive feedback that was driving the change. The positive feedback was an effect of the cars slowing down: once the cars have stopped, we’re not going to observe this effect anymore.