Quantum Leaps

Words cannot really replace mathematics—but on a subject like this, mathematics cannot really replace words.

— Jeremy Bernstein on the cultural transformation of quantum theory, in Quantum Leaps

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Starbaby had a fair understanding of mathematics, apparently having studied differential equations and some number theory, enough anyway to cure me of my previous misconception that mathematics is the universal language. His argument went like this: Mathematics is a way of thinking, an approach to reality, not a language. When you look at a mathematical formula, the first thing you do is translate its symbolic shorthand into verbal language, such that "2 + 2 = 4" immediately becomes "two plus two equals four." In fact, the only way to accurately express pi is to use words: the ratio of the circumference of a circle to its diameter. As soon as you try to represent it numerically, you resort to some approximation; it might as well be Greek. Besides, if mathematics is a universal language, how is it that so few people understand it? Talking about the language of mathematics is akin to talking about the language of love: both are ways of thinking, both are valid approaches to reality, and both require verbal expression to convey that reality to another being. But I digress.

— Mark Shermin on the hybrid mind of Chris "Starbaby" Hayden, in The Life and Teachings of Starbaby