I’m not able to post this on Stephen Williamson’s New Monetarist Economics blog. So I’ll post it here.

“If it’s a good economic idea, and correct, you have to be able to do the math.”

Here’s my challenge.

Give me the “math” of genuine uncertainty, Stephen.

Give me the “math” of evolving human judgment and genuine human learning in the context of novel and changing local conditions, changing profits and losses, and changing relative prices.

And a parallel case: give me the “math” Stephen for the advance of science — or for the discovery process of invention.

As Nobel Prize winner after Nobel Prize winner in Economics has explained, economists are as liable to be blinded and misled and confused by their mathematical constructs as they are to discover anything true about the world.

Everyone knows the virtues of math — everything is a “given” knowable to one mind, and everything is mathematically tractable.

Any working scientist can explain to you that not all phenomena are mathematically tractable, and yet for all that the phenomena continue to exist.

And needless to say, the whole problem of economic coordination exists just because the problem of economic coordination isn’t characterized by a set of “givens” knowable to one mind — and the coordination solution to that problem is NOT a tractable mathematical equilibrium construct — it involves groping in trades outside of equilibrium guided by human judgments of the potential future significance of changing profits and losses, relative prices of all sorts, and changing local conditions.

There is a very large chance that an economist is precisely and objectively blind to the nature of the phenomena at hand if they are so confused to think there is a math construct “model” of what I describe in the paragraph above, which is given to one mind as a tautological, formal equilibrium construct.

Well said. I couldn’t agree more. I might be able to boil it down to two words. Sh*t Happens!

Mathematics is just a language, and a very precise one. You might as well say that the English language inhibits our ability to do economics. Mathematicians and Statisticians gave us some wonderful gifts, and we should use them. Would you like to pass a law prohibiting the use of math and statistics in economic science, or what?

Advancing understanding by achieving a precise understanding of what math formulas _CAN_ and can’t do in economics implies essentially the opposite of what you suggest, i.e. to “pass a law prohibiting the use of math and statistics” in economics.

As I’ve stated on your blog, there are important roles for math and statistics in economics — e.g. they help us identify the patterns of global order / coordination and disorder / discoordination that demand causal explanation.

It’s a very flimsy straw man to suggest that the choice is between either believing (a) that math formulas and statistics can capture the _whole_ of what is of significance in an economic explanation; or (b) math formulas and statistics have no place in economics.

It’s an absurd false choice, not at all implied by the claim that there are a number of centrally significant things that cannot be put into a math formula which play a central explanatory role in economic science. Just as Godel’s proof that there are limits to what can be proved in some formal systems did not imply that logical proof should be “outlawed”, the proof of Knight, Hayek, etc. that there are limits to what math formulas can capture does not imply that equilibrium constructs, statistics, etc. have no explanatory or problem identification role to play in economic science.

As I say, it’s an extremely weak, unmotivated, and even bizarre straw man to suggest this poverty of alternatives, which has in no way been suggested by anyone.

Totally agree with Steve.

Greg, do not think all mathematicians are so stupid!

Lio, Steve’s remarks on this issue are that … unhelpful … They show genuine ignorance of the literature, of the issues at hand, and of great domains of Nobel Prize winning economics.

It’s as simple as that.

In any case, I’m not talking about mathematicians, I’m talking about Stephen Williamson.

Over the years its been common for academic mathematicians and others who know to call economists 3rd rate mathematicians. Things have changed over the years, but research on this topic shows that economists are typically people who drop serious mathematics for something easier.

Greg,

I do not know enough about Steve but I generally agree with this : “Mathematics is just a language, and a very precise one. You might as well say that the English language inhibits our ability to do economics. Mathematicians and Statisticians gave us some wonderful gifts, and we should use them. Would you like to pass a law prohibiting the use of math and statistics in economic science, or what?”

No matter how expressed reasoning, the important thing is that it is accurate. Mathematics is of no use if the reasoning is wrong. Same for the English language. The debate should not focus on the use of mathematics or not in economics but on the quality of reasoning.

Lio — the issue has a context. See the work of Frydman & Golberg referenced on this site. Or the work of Hayek or Mises.

And the debate is not an “either or” debate, as Williamson erroneously characterizes it.

It’s not about whether to “use mathematical or not in economics”.

I’ve been more than clear about that.

Lio writes,

“The debate should not focus on the use of mathematics or not in economics but on the quality of reasoning.”