The way that complex behavior such as masses bouncing on springs or arbitrary waves can always be broken down into sums of simpler behavior
"Always" in textbook examples. Not always in all cases: the intractable cases don;t make it into textbooks. Physiists have written against the assumption of universal reductionism.
I can't endorse everything in all these works, but they each provide insights into understanding reduction.
What else do ya'll recommend?