In "Introduction to Statistical Learning", for maximal margin classifiers, they say:
"Although the maximal margin classifier is often successful, it can also lead to overfitting when $p$ (the number of dimensions) is large," (p. 341)
also in "Elements of Statistical Learning":
"Again one can enlarge the space using basis transformations, but this can lead to artificial separation through over-fitting" (p. 135)
I don't seem to understand this. Could someone please explain why a large dimension can cause the separating hyperplane to overfit? How does increasing the dimension makes separation possible? (even if it's just artificial)?