If instead the vibrating string is 2/3 of its original length, the note it makes goes up by a fifth (the interval from do to sol think of the first two notes of the Star Wars theme). The vibrating part of the string is now half as long as it used to be-a ratio of 1 to 2-and it sounds precisely an octave higher than the original note (the musical distance from one do to the next in the do-re-mi-fa-sol-la-ti-do scale). Now put your finger on a fret exactly halfway up the string and pluck it again. As the string vibrates, it emits a certain note. For instance, imagine plucking a guitar string. According to legend, Pythagoras felt it around 550 BCE when he and his disciples discovered that music was governed by the ratios of whole numbers. “This sense of awe goes way back in the history of mathematics. “But why should the universe respect the workings of any kind of logic, let alone the kind of logic that we puny humans can muster? This is what Einstein marvelled at when he wrote, ‘The eternal mystery of the world is its comprehensibility.’ That’s what makes it such a powerful tool for science and technology. In this way, calculus lets us peer into the future and predict the unknown. Start with something that is empirically true and symbolically formulated (as Maxwell did with the laws of electricity and magnetism), apply the right logical manipulations, and out comes another empirical truth, possibly a new one, a fact about the universe that nobody knew before (like the existence of electromagnetic waves). Yet somehow, if the translation from reality into symbols is done artfully enough, the logic of calculus can use one real-world truth to generate another. Calculus is an imaginary realm of symbols and logic nature is an actual realm of forces and phenomena. “It’s eerie that calculus can mimic nature so well, given how different the two domains are. That is why we cannot recommend Infinite Powers by Steven Strogatz enough. And that if read right, it reads like a thriller. We, however, believe this is a beautiful theme taught badly. It’s the start of the academic year and a common refrain we hear from children and their parents is, how tough calculus is.
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