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The linear, mechanistic view of the world which pervades orthodox economics is simply not capable of capturing the richness and complexity of the rhythms and fluctuations of developed economies.
Baseball players or cricketers do not need to be able to solve explicitly the non-linear differential equations which govern the flight of the ball. They just catch it.
The temptation to use mathematics is irresistible for economists. It appears to convey the appropriate air of scientific authority and precision to economists' musings.