The Deep Study Of Nature Is The Most Fruitful Source Of Knowledge
It’s warmly appropriate that Jean-Baptiste Fourier left us with the poignant quote above as a stark reminder to continuously turn to our connection with nature as a source of inspiration for knowledge. It’s appropriate because, well, Fourier’s greatest contribution, the Fourier Series, both literally & figuratively, stems from a deep study of nature.
Literally, his key contribution to the annals of math history, the sole purpose of this exposition, came from the solution to a question posed by nature — mainly, how does the temperature on a metallic plate distribute over time? How about at any given point on the plate? Figuratively, the search for the solution stemmed from a long-spanning tradition: our innate need to make sense of the world around us by describing it in terms of a circle.
Since ancient times, the circle was placed on a pedestal as the simplest shape for abstract comprehension. A simple center point & a fixed-length radius/string was all needed—every point on the perimeter perfectly equidistant from the center. The key to understanding the Fourier series (thus the Fourier transform & finally the Discrete Fourier Transform) is our ancient desire to express…