Pythagoras and his followers at first thought that irrational numbers didn't even exist, though the story that they drowned a guy for proving by contradiction t

Pythagoras and his followers at first thought that irrational numbers didn't even exist, though the story that they drowned a guy for proving by contradiction that sqrt(2) is irrational is probably not right. Rather, strings with length ratios made of small integers, like 2/3 or 3/4, sound good (harmonize) when played together. So the started with the ratios, because that's what made sense. Not to use ratios was considered, well, irrational. :-)