That is not the same. A complex set of equations are not required to calculate how to make an object to throw at people, nor is it required to make a glove or to figure out where to place your hands to catch the ball, but generating resonance at a given volume and frequency is a very hard thing to do. Stradivari may not have been a great mathematician, but he still had to carefully measure, and set to very exacting specifications each one of his instruments. He had to follow the calculations even if he did not know those calculations. In the time of ancient Greece, before those calculations were completed, it did require a mathematician to devise a musical instrument more complex than a drum. This is why many cultures never got past the stage of drums and horns before the more complex instruments were imported from Europe. These equations can be used by those unfamiliar with them, but they can’t be created without someone learning those equations in the first place in the same sense that computer software cannot be created without engineering.
That is not the same. A complex set of equations are not required to calculate how to make an object to throw at people, nor is it required to make a glove or to figure out where to place your hands to catch the ball, but generating resonance at a given volume and frequency is a very hard thing to do. Stradivari may not have been a great mathematician, but he still had to carefully measure, and set to very exacting specifications each one of his instruments. He had to follow the calculations even if he did not know those calculations. In the time of ancient Greece, before those calculations were completed, it did require a mathematician to devise a musical instrument more complex than a drum. This is why many cultures never got past the stage of drums and horns before the more complex instruments were imported from Europe. These equations can be used by those unfamiliar with them, but they can’t be created without someone learning those equations in the first place in the same sense that computer software cannot be created without engineering.