Remember the digital photo from the four-megapixel camera: it’s described by 4 million numbers, one for each pixel. (And that’s before we take color into account!) So that image is a 4-million-dimensional vector; or, if you like, a point in 4-million-dimensional space. And an image that changes with time is represented by a point that’s moving around in a 4-million-dimensional space, which traces out a curve in 4-million-dimensional space, and before you know it you’re doing 4-million-dimensional calculus, and then the fun can really start.
