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xkcd #2904: Physics vs. Magic
(imgs.xkcd.com)
Alt text:
'At the stroke of midnight, your brother will be hurtling sideways at an altitude of 150 meters' is a regular physics prediction about your nonmagical trebuchet, whereas 'you are cursed to build a brother-launching trebuchet' falls out of the Lagrangian.
Or why you'd want to use them.
I had to do a semester of learning how to deal with Fourier Transforms, with vague mentions of sine waves and slopes, before seeing Technology Connections' video on CDs and finally understanding what all that math was actually for.