> no-one would have previously thought of using a ton of numbers to represent a song

Music has long been represented using math and math concepts. Musical notation is a cartesian plane with time on the x-axis and pitch on the y. But that's the representation, and it's not about the representation, it's the ability to manipulate at extremely high speed.

I see what you're saying, but musical notation isn't a precise representation of the audio. Given the same score, two musicians can produce very different interpretations. Perhaps I should have said 'audio' instead of 'song'. (I took classical piano exams as a kid, and at some point a group of us would perform our prepared pieces for each other as practice, and I remember always being surprised at how different everyone's pieces sounded. I'd thought mine was the One True Way!)

Claude Shannon showed that everything is just data, that's why it wasn't done previously. It seems obvious today, but wasn't always.