If The Only Tool You Have ...

"If the only tool you have is a hammer, everything looks like a nail".

Most people shy away from simple math. In fact, publishers demand that no equations, however simply don't appear in popular books.

From this perspective, the simple graphs and equations that appear in introductory textbooks appear sophisticated. In particular, these tools have a hard time presenting anything but a super simple, static picture of the world.

If you approach the same situation with different tools, a very different picture emerges. Even simple computer simulations can show complex behavior that can't be reduced to equations of any sort.

I played around with this idea a bit but abandoned it because it would have involved an unrealistic effort to implement it. However, even while simply drawing up a specification, you can see the kind of things a model could address. Most important is the question of stability or even a stable pattern of oscillation. Model specifications seem to raise the possibility of chaos or ultimate collapse.

This is interesting because:

• The myth of the invisible hand is a static view. Any change will ultimately involve the system settling down to a new, stable state. An "optimum" state.  In a computer model, this is not assumed. You need to run the model. But the model specifications show a system that is likely to show chaotic (unpredictable) behavior.
• Any realistic model includes "environmental services", which are routinely left out of the conventional analysis. Even in a simple model, the inclusion of the environment raises the question of collapse either by exhaustion of finite resources or by exploitation of resources faster than they can be replaced. Any model that includes human population will assume that human population until limits of "environmental services" collapse.

If you are a thinker, eventually you need to come up with some idea of thinking itself. For me, "Surfaces and Essences" provides a "Royal Road" to the way our minds work. While the book has a focus on analogies in language, the final chapters shift to visual analogies and the role analogies play in scientific theory. What is the world "really like". The idea of "essences" in the title is that some analogies are better than others. The best ones provide a two-way isomorphism, where properties in one system can be deduced from (mapped on to) properties in another. Analogies are rarely this good.

A persistent problem with public discussion is that naive analogy underly the way we use language to describe an issue. Here is an explicit visualization that supposedly "explains" the business "cycle":

If you look up "business cycle", it is remarkable how smooth and neat the "waves" are. The same mental image seems to be in the mind of "climate change deniers". The assumption is "what goes up will come down".

The problem with this analogy is that it is far from "essential". It doesn't really tell us anything about the phenomenon of interest.

Real economic data looks much "rougher". It was Mandelbrot who discovered the real "shape" of curves like this - fractal.

Real Economy - The Stock Market

Fractals turn up frequently in nature. They exhibit a special kind of "randomness" that looks the same at every scale. In practice, even serious investors in the stock market are unfamiliar with this fact. In effect, the "wave" idea and the "trend" concept are forced into the data (usually in retrospect). These methods are famously unable to predict large changes, such as the 2008 crash. The easiest way to see this is that the wavey graphs are not an "essential" analog to the real economy. Climate change deniers are not familiar with any other way to see this kind of thing, yet the IPCC reports are full of graphs like this. In fact, under the surface, the IPCC models are massively complex. They don't depend on "wave" models, but on the way physical factors are known to interact. Weather is one of the first systems discovered to be ruled by chaos. We can expect nothing different from weather over the long term - climate.

The most trivial kind of graph is "marching bars", showing some quantity in a series of bars over time. Using a line instead of bars is a simple improvement, but still relies on the assumption that graphing X over time reveals the "essence" of the system under consideration. Those who have seen nothing else, and were perhaps confused by the examples they did see have a hard time visualizing an alternative. See if this graph makes sense to you:

How the quantity of sorghum produced depends on the Price

"Time" doesn't appear in this graph. In fact, the graph is a visualization of a few simple equations that supposedly illustrate certain "price points" and how they relate independent of time. This is an improvement over "marching bars", but the underlying "math" is trivial. Like all graphical methods, all data and factors that may be of interest are necessarily ignored for the sake of simplicity. Economics textbooks are full of this kind of graph, giving them an undeserved impression of sophistication.

A computer simulation is not limited to a few simplistic assumptions. Predictably, the outcome, depicted graphically, is not as neat as marching bars or waves.

An Output from "Symphony" Simulator

Compared to practical simulations such as those used to simulate climate, Symphony is a toy that makes little effort to map its model into real, objective facts or the relationships between them. What many would see in the above graph as "waves" I see as instability. Think of it this way, if your car wobbles from left to right on the highway, you will assume that there is something seriously wrong - not that it's designed to do that. You will suspect that quite soon, your car will wobble into the ditch. Historically, this is what modern economies actually do: they "wave around" for a cycle or two, then unexpectedly boom or crash.

We can be quite sure that there is not even a toy simulation behind most of the economic "stimulus" packages flogged to the voters. Especially when coming from the conservative politician, such policy seems to be based on (a) the invisible hand and (b) the idea that the economy is inherently stable and (c) at any given time, we are someplace on the "business cycle". One may assume that, behind the scenes, there are thousands of nerds playing with economic simulations. Unlike the IPCC, they don't release their methods, data or assumptions for public debate.

By the way, the IOUTopia model would have been at least as complex as "Symphony" with the additional complexity of finding a way to simulate the goals of thousands of individuals over generations. A glance behind the scenes at what the programmer sees when creating a Symphony model should give a hint at why I abandoned the IOUTopia model. I still hope somebody else does it.

The Symphony "sausage factory"

Rolesia is another economic simulator apparently similar in power, scope, and applicability to Symphony. They resemble IOUTopia only in showing the amount of effort that would go into making something like this. As far as I know, there is nothing out there that has the granularity envisioned in IOUTopia. These simulators appear to be tools for professionals who want to put a modicum of objectivity into their economic forecasts, using assumptions that are applicable to today's economy. IOUTopia was a tool to investigate the basics of what an economy is.