Bluematter quotes Alfred Marshall:
(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.
It seems to me to be fairly good advice, but Bluematter’s not convinced that either the maths or the real world examples are useful! Let’s examine a real world example to illustrate the issue.
Suppose that we were interested in tax policy (stranger things have happened). It is quite conceivable that we might want to know the impact on peoples’ labour decisions from our tax. So how would one go about analysing it? Well, one would need to consider the impact of our tax via both income and substitution effects, and then sum those effects to see what effect it had on labour supply. If you are one who shuns maths, pause here to consider how you would describe the decomposition of the movement in labour supply. Ask yourself if you could do it more concisely and more precisely than this.
Slutsky’s equation sums up in one line what would take paragraphs of English to describe. Even in those many paragraphs it would be difficult to be as precise as Slutsky is with his single line. Maths simply gives us a language to accurately discuss complex systems. Natural languages, such as English, aren’t designed to concisely do this and provide inadequate tools for talking about such systems.
The most common criticism I hear of economics is that it would be impossible to describe human behaviour because it is too complex. I don’t want to dive into that, but if we are to attempt to describe complex things then we need a language capable of talking about them in an accurate and succinct fashion. Maths is obviously the best language for the job. That the same people who claim human behaviour is complex often also rail against the mathematisation of economics baffles me.