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The first says that belief revisions take longer than the time horizon of the interest rate peg (interest rates stop being pegged before you fully revise your beliefs -- which doesn't seem like a very long peg); the second says you revise your beliefs to a high order before the interest rate peg ends (which actually makes more sense). The limits that Woodford takes (n dt → ∞ and T → ∞ simultaneously, in both orders) don't make any sense. [2] I've sort of come through the rabbit hole on this one. In my first forays into econ, I basically thought economists were just fine with math. I tended to defend econ from usurping physicists (here and here). 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