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If we want to understand the physical world deeply there's really no getting around understanding it mathematically. As Pythagoras put it, "Number is the ruler of forms and ideas, and the cause of gods and daemons." There is nothing else.If we want to understand the physical world mathematically, there's really no getting around the Fourier transform. The transform is what allows us to look at really any mathematical function (likely representing a physical phenomenon) and change it to a function that is periodic, e.g. repeats itself through time. Number is the ruler, and it has a spectrum—a wave, like light or sound. We are waves, cycles in a cyclical world."The Fourier transform decomposes a function exactly into many components," explains UCLA's Terrence Tao, "each of which has a precise frequency. In some applications it is more useful to adopt a 'fuzzier' approach, in which a function is decomposed into fewer components, and each component has a range of frequencies rather than consisting purely of a single frequency."Unfortunately, the single big waves describing you and I aren't very good descriptions of us. A better view would be if we had instead a bunch of really tiny waves each describing a different feature of us. Maybe we could just dump ourselves (our waves) through some filters, each one picking out waves with different characteristics. We are waves, but waves are just sums of other waves, smaller cycles within cycles.That's probably not very satisfying. Fortunately, the Fourier transform happens to be the subject of this week's 100 Second Science video, in which the University of Cambridge's Carola-Bibiane Schönlieb lays out Fourier much more neatly.