Sure, but the hard thing to accept intuitively, for me, is the existence of an alternative representation of a function, particularly for functions with require intricate, data-heavy descriptions to express. It's kinda crazy that you can combine sinusoids such that they look like an arbitrary function; it's only slightly more crazy that there is a way to calculate what those sinusoids are. My intuition is also violated by the fact that you can go back and forth between these representations losslessly. It would seem to me that some functions, even simple ones like a line, would require a great explosion of information to represent as sinusoids. A function requiring two numbers to describe now requires infinite numbers to describe, in the linear case!