From Krugman’s blog today, via Deane Yang’s FB feed:
Math is a friend of mine. There have been a number of occasions in my life when doing the math on an economic model has led me to conclusions very different from my preconceptions.
But I have always been able, after the fact, to find a way to express in plain English what the math is telling me. If you resort to math to justify what looks like a very foolish claim, and you can’t find a plausible way to express that justification in plain English, something is wrong.
I disagree. The reason we use mathematical formalism is exactly because it expresses things that can’t be said precisely in English, or any other natural language.
We can, should, and do utter English sentences that paraphrase mathematical assertions; but that’s not the same thing.
Possibly useful analogy: “Music is a friend of mine. There have been a number of occasions in my life when a piece of music has conveyed to me a powerful emotion or sensation. But I have always been able, after the fact, to express in plain English the way the music sounded and the way it made me feel.”
If someone told you this, you would say “NUH UH,” and I think the same response is due Krugman here.