I roughly understand what the article says about dimensional space (Reading higher mathematics books on the way to my meagre college course way back when, helps me a little, even if it is all half-remembered and a bit wrong -- this understanding is sufficient enough to satisfy me), however the poster above me doesn't, and clearly asked for a definition a 5 year old layman could understand.
The comment I am replying to, your comment in the tree, and the one next to you, does not seem to match that request in any sense.
Now, simplified definitions are an art, but Feynman managed it with Quantum Electrodynamics -- so it is not impossible to do it for complex subjects. And it seems to me the less you understand a subject, the less simple and more confusing your explanation will be, such as the explanations given by the other posters here. (fyi: I do not understand enough to properly convey my understanding clearly -- which is why I have not attempted to do so)
This isn't a matter of having an incomplete understanding, thanks for the offhanded aspersion though. The fundamental problem is that the concept of manifolds in state space isn't really something that has a non-tortured real world analogy, which is a prerequisite for a five year old to understand. It's probably possible to express more simply with a video demonstrating the covariance structure of a data set visually, then showing how that results from a small set of vectors, but I've read enough textbooks to be confident that a simple, concise explanation eludes words.
