Calculus as a Basic Way of Seeing the World

Chen Danqing is a painter I admire. He speaks his mind, and he can be funny without trying too hard. In one interview, however, he raised a question that exposed a familiar weakness among Chinese intellectuals. The question, roughly, was this: he considered himself far more knowledgeable than people who lived in periods such as the Northern Wei, yet their work remained far better than his. He could not understand why.

Anyone who has studied calculus already has a useful answer. Imagine a person as a function. Your present value may be higher. You know more, you have seen more, and you possess tools that did not exist in an earlier age. Yet the earlier artist may still produce the greater work because the derivative of his function is larger. Across a reasonable interval of time, his trajectory outruns yours.

In less mathematical language, knowledge and ability are not the same thing. You may begin from a higher point and still be less capable of moving beyond it. The quality people keep calling “ability” is, in this analogy, the derivative.

This is why I think calculus should be taught as part of a modern person's basic understanding of the world, not merely as a technique for passing mathematics exams. Without calculus, and without the prior idea of a function, people are easily trapped by static comparisons. They mistake a current level for a capacity to change. Their explanations then become conventional, approximate and often wrong. The weakness is especially visible in Chinese literary and intellectual circles.