Thursday, February 13, 2014

Which Celebrity Pet Are You Most Like?

You are most like Jane Seymour's cat.

Jane Seymour and Max

Now that we have that out of the way...

I've written several posts expressing disdain for "unscientific" thinking. Now, don't get me wrong - I fully understand that life is full of problems you can't solve by science alone. Science might help you with the nutritional aspects of whether to eat steak or beans, but the final decision is going to involve other concerns that science isn't going to help with.

But what bugs me is when the science is there but people refuse to use it. Today's target is economics. Many people consider economics to be a science, and people who have subordinated themselves to the advice of economists, expecting that advice to be scientific, have suffered terribly.  How scientific is it? Let's find out.

By science, I mean the exact sciences - ones that write laws in the form of mathematical equations. There are other sciences like biology that don't do much of this. But biologists only claim to explain certain interesting aspects of plants and animals. Other than that, they mostly leave you alone. Economists go around advocating rules that you personally must live by, such as paying a 25% tariff on pickup trucks.

To put economics in perspective, I have to describe some characteristics of an exact science. I'll use classical mechanics as an example. Let's consider the important equation

F = ma

What does it mean? It means that the net force on a body equals the mass of the body times its acceleration. But it contains much more than that. It contains (among others) the following definitions and assertions:

- A body is a fixed quantity of matter.
- Force and acceleration have directions, but mass doesn't
- Forces and masses are the same regardless of whether we're moving when we observe them.
- The acceleration may appear different to different observers, so there must be some restriction on the kinds of observers who will find this law to be correct.
- It makes sense to talk about the motion of a body even though there may be several points on a body that all have different motions

I could go on, but the idea is that you have to know what it is you are talking about before it makes sense to put it into an equation. If you don't know the general properties of acceleration, this equation makes no sense. If you use mass in more than one equation, it has to be exactly the same thing in all respects. Not similar, not analogous, but exactly the same. There is no way to distinguish one electron, or one water molecule, from another.

I'm not talking about metaphysical questions of what mass "really is". I'm talking about stating carefully that mass has certain logical-mathematical properties that limit how it can appear in a physical law.

Carefully collecting all the assumptions underlying a law of physics is called "axiomatization". Not many laws of physics have been completely axiomatized, but the point is to try. Sometimes in the process of axiomatization, it is found that a law is logically inconsistent with other laws we are more confident in. Then, changes have to be made.

The laws of physics have a pretty good track record of being useful for making predictions, so this business of carefully stating assumptions is probably the right thing to do.

It would seem that economics could be developed in the same way. You start out by saying we are going to study money. Before you write down any laws, you have to talk about the properties of money. Can it be created? Destroyed? Is its location important? Can you talk about the speed of money? Does money appear to act the same way to different observers?

One problem that arises right away is that while we can exchange dollars for yen or gold at a certain rate, there doesn't seem to be an underlying unit of money with fixed properties. The same is true of speed; different inertial observers see the same object traveling at different speeds. Because of this, speed can only be used in certain ways in a law of physics. If someone proposed a new law of physics saying that the force was proportional to the speed, you would know right away he was wrong, because force is a vector and speed is a scalar, and vectors can't be proportional to scalars.

It seems to me that, not having defined the properties of money (or any other thing economists talk about, like unemployment) very carefully, economists are never going to be able to write down any really useful laws. Instead, you have professional economists arguing with each other and having to stop and ask: are you talking about nominal dollars or constant dollars? It's like physics was in the 16th century, when people were still having trouble with the difference between mass and weight. All economists can come up with are rules of thumb, like the price of a good is influenced by supply and demand.

The classic rejoinder to all this is that the "real economy" is too messy to subject to such logical treatment --- which is another way of saying that economics isn't a science. Somehow, in the physical sciences we managed to come up with laws that describe the real, messy world - not exactly in every case, but pretty close. You economists can do it too, if only you try.


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