Math, reading, and purpose

By Matt Nolan 23/08/2013 6


Noah Smith recently smashed math in economics (specifically macroeconomics) stating:

Math can also be used as obscurantism; if every paper in a field starts with a dense thicket of formal statements and functional equations, it will be difficult for even very smart outsiders to come in and evaluate what the people in a field are doing with their time. Again, I doubt all but the most cynical macroeconomists would be intentionally obscurantist; they would just be subtly rewarded for doing things that ended up having an obscurantist result.

Paul Krugman then neatly defends maths, stating the following:

mathematical models are useful in economics: used properly, they help you think clearly, in a way that unaided words can’t.

And:

What is true is that all too many economists have lost sight of this purpose; they treat their models as The Truth, and/or judge each others’ work by how hard the math is.

This all reminds me of one of my favourite quotes, by the semi-fictional character Liang Zhuge:

“I consider the pursuit of knowledge to be about what one learns, rather than what one can recall”

But as James has often noted to me in the past, there is as much danger, if not more, from going too far down this line.  Reading books and papers, writing, math, these all have a purpose in terms of helping us try to understand problems.  Having an understanding, and creating knowledge that helps us make decisions is the purpose.

Yes, people can overquote from books, they can use books and math as excessive signals of ability, and they can use these things to obsfucate points and prevent true knowledge being gained.  But this just suggests we need to be more careful about how we use maths and quotations from authority when building arguments and discussing these issues – not that these methods for doing so are inherently bad.

As we often do with economic problems, when we are thinking about communication we should be trying to clearly define what outcome is truly of interest, we should be figuring out how what we observe is related to these outcomes of interest, and the way the “primitives” and things we can control that are involved directly influence the things we observe and are interested in.  This is of course where good old Alfred Marshall had the idea!

  1. Use mathematics as shorthand language, rather than as an engine of inquiry.
  2. Keep to them till you have done.
  3. Translate into English.
  4. Then illustrate by examples that are important in real life
  5. Burn the mathematics.
  6. If you can’t succeed in 4, burn 3. This I do often.

The way economists communicate with each other and the public, and their ability to persuade others and shift priors with the argument they are making, is part of how we can tell if what economists are doing is really “relevant”.  That is why communication is important.  Or maybe an indication that we need to help incorporate price signals into the discipline.

UpdateByran Caplan at Econlog is more cynical, and about math in Econ more generally not just Macro.

I’ve heard such claims a thousand times.  But after enduring four years of Princeton economath, and publishing two pure theory pieces (here and here), I am convinced that most economath badly fails the cost-benefit test.

I believe Paul.  But I have a slightly different interpretation: His seminar audiences needed the economath because their economic intuition was atrophied from disuse.  I can explain Paul’s models to intelligent laymen in a matter of minutes.  Since they know no economath to blind them, they don’t need economath to grasp the obvious-once-you-point-it-out.

I am far from convinced by this – the maths provides both a “burden of proof” and a “conditional” element to the argument that is important for making sure we actually understand the intuition without relying on “common sense”.  At the margin there might be overinvestment in mathematical training – but I fear this is overstating the case!

I have seen “intuitive” arguments abused (namely over reliance on partial equilibrium logic) too often to be quite this cynical about maths.  Of course, the margin I work in is considerably different – I am not an academic, and spend significantly less time trekking the hard yards involved with mathematics.  And in that case, I would note that views on the “over reliance” of maths are then dependent on where you are sitting with reference to arguments – implying that the entire argument that there is “too much” maths must be seen as a statement about a specific area, not on economic debate in general.

Update 2Krugman, Caplan, Waldmann.

Note the selection bias in blogs – bloggers will tend to be people with a comparative advantage in written forms of communication.  I am not sure “economath” will get a fair trial in such a place.  I like Ryan Decker’s tweet in this context (Note, associated post):

And still, in today’s crop of anti-math posts, we see a lot of criticisms of math that also apply to narrative/heuristic theorizing.


6 Responses to “Math, reading, and purpose”

  • Parts of your argument read—to me—as conflicting at points – or at least being a bit confusing! For example, the first of the list of steps you advocate seeks to remove maths from a means of inquiry yet your final two paragraphs in the addendum appear to advocate for the use of maths as a tool of inquiry.

    Put aside what you have written then and presenting some general thoughts:

    For communicating the gist of some work, especially if communicating to a wider non-specialist audience, by all means explain the concepts that the maths convey in place of the actual maths.

    For a scientific approach to the work itself, more than ‘common sense’ is needed. A key general point about scientific enquiry that is conveyed in Feynman’s remark that (words to this effect) that the first thing is not to fool yourself and you are the easiest person to fool. Relying on ‘common sense’ or ‘intuition’ is perhaps the fastest way to fool yourself.

    A point about using maths is that, used properly, it’ll force, or at least encourage, the worker to examine their assumptions and to derive quantitative results (that hopefully they’ll test to move them past proposal/hypothesis).

  • Hey Ross,

    I’m not really sure what you are saying – just a note though that your wikipedia link appears to be broken!

    Hey Grant,

    “Parts of your argument read—to me—as conflicting at points – or at least being a bit confusing! For example, the first of the list of steps you advocate seeks to remove maths from a means of inquiry yet your final two paragraphs in the addendum appear to advocate for the use of maths as a tool of inquiry.”

    My intention was to state that others were saying that maths can be abused as a language to think through ideas (hence why it was a series of quotes). But then to state that it was not an absolute. My apologises that this wasn’t clear – I was just quoting, rather than quoting in support.

    I completely and totally agree with you when you say:

    “A point about using maths is that, used properly, it’ll force, or at least encourage, the worker to examine their assumptions and to derive quantitative results (that hopefully they’ll test to move them past proposal/hypothesis).”

    The usefulness of maths, and clear language, is that we can make our assumptions and their purpose transparent. The old English school view of appealing strongly to common sense is flawed as you note – especially if we have no model of where common sense comes from in the first place 🙂

  • http://en.wikipedia.org/wiki/Black_Scholes

    Try that one. The original copy and paste screwed the underscore to a @

    Its staggering that a Nobel prize can be given for a way of (apparently) working out chaos in the finance system.

    Why aren’t we all winners and we all haven’t got PhDs in Maths and Physics- the filed where the “Quants” come from.

  • #$%*&

    We aren’t all winners and we all haven’t got PhDs in Maths and Physics – the field where the “Quants” come from.