After an initial misunderstanding of his definition of mathiness, I think passed Romer's reading comprehension quiz. Romer answers "False" to each of these questions ...
1. T/F: Romer thinks that economists should not try to use the mathematics of Debreu/Bourbaki and should instead use math in the less formal way that physicists and engineers use it.
I think this (and Mark Buchanan approving thinks Romer would answer true), but Romer answers false.
2. T/F: Romer thinks that abstract mathematical models that could turn out to be of no use in understanding data and evidence are examples of mathiness.
This captures my initial misunderstanding (I linked the original, and here is the corrective from the next day). Overall, Romer should have left off the word empirical when he said: "Like mathematical theory, mathiness uses a mixture of words and symbols, but instead of making tight links, it leaves ample room for slippage between statements in natural versus formal language
and between statements with theoretical as opposed to empirical content." (I crossed out the offending clause -- Romer's idea of mathiness is completely independent of data, so I'm not sure why he mentioned it.)
3. T/F: Romer thinks that errors in mathematical arguments are examples of mathiness.
As I said, it's lack of rigor (or "tight links" as Romer phrases it). A lack of rigor can be associated with errors, but are not identical to them.
4. T/F: Romer says that the economists he has accused of mathiness are using it to promote a right-wing political agenda designed to influence national politics.
The academic politics seems to line up with national politics, but as I mention here (in the PS) it's mostly about tribes of graduate students revolving around big names.
5. T/F: Romer thinks that economists should use less math.
I personally think economics should use less formal math, but I never attributed this to Romer.
6. T/F: Romer is angry.
I think the emotional states I attributed to Romer were being "upset", "zeal" and being "weird". I insinuated Lucas and Moll might be a bit annoyed with Romer.
The first point remains me of a book I came across when I was still in college, titled "Quantum Field Theory: A Tourist Guide for Mathematicians" by Gerald Folland. It is full of interesting tidbits about the difference between physicists and mathematicians in their work methods. For instance, here's a paragraph from the book which seems to illustrate the first of the points above:ReplyDelete
"This is a good place to bring up an intriguing difference in the way physicists and mathematicians regard mathematical objects. Mathematicians are trained to think that all mathematical objects should be realized in some specific way as sets. When we do calculus on the real line we may not wish to think of real numbers as Dedekind cuts or equivalence classes of Cauchy sequences of rationals, but it reassures us to know that we can do so. Physicists' thought processes, on the other hand, are anchored in the physical world rather than in set theory, and they see no need to tie themselves down to specific set-theoretic models. A physicist may speak of the state space H of a quantum system Q; if a mathematician asks "What Hilbert space is H?", the response is "I just told you, it's the state space of Q."
That's great -- I have to see if I can get my hands on a copy. I found a link which included this review:Delete
"The style of the present monograph is clear and the author is honest about possible mathematical shortcomings of quantum field theory."
I nearly died laughing. QFT is the most successful physical theory framework ever created by humans -- but it may have mathematical shortcomings. Maybe we should abandon it** ...
** By it, logically, I mean math. I think Romer would want to keep the math and abandon the physics ...