It turns out that many things behave very differently in high dimensional space. The below paragraph is picked from a book. I need extra help to understand. The book says,
if you pick a random point in a unit square (a $1\times 1$ square), it will have only about a $0.4\%$ chance of being located less than $0.001$ from a border( In other words, it is very unlikely that a random point will be extreme along any dimension). But in a $10,000$-dimensional unit hypercube (a $1\times 1\times 1\times 1\times 1\times 1\ldots \times 1$ cube with ten thousand 1s), this probability is greater than $99.99999\%$. Most points in a high dimensional hypercube are very close to the border.
Q) What is the author trying to convey from the above paragraph?
If you pick two points randomly in a unit square, the distance between these two points will be, on average roughly $0.52$. If you pick two points in a unit 3D cube, the average distance will be roughly $0.66$. Now If you two points picked randomly in a $1,000,000$ dimensional hypercube, the average distance will be about approx $408$?
How is it possible?