We are so locked into the comfortable, into the things we have been taught. And of course we need them. That is to say, we need a ground upon which to stand. And if we stand firmly enough, we can break out of it, whatever 'it' may be. Some great ones have paid a heavy price for breaking out, but I don't believe they had a choice. Some things you just have to do.
We have to come to accept the 4th dimension
Thanks to Albert, we have come to accept a 4th dimension, but the 3 familiar and the additional 4th are whole numbers. What to think of this guy Hausdorff *), who comes along with broken dimensions. Sounds to us like burning ice or dry water. Still it is a valid description of a very interesting way to describe non-euclidian forms (forms that are not circles, rectangles, etc.). We could not describe things in nature without this new kind of geometry, fractal geometry, or in short fractals.
The photo above is a representation of Broken Dimensions. It's corn in a field and has a high degree of self similarity, which is also one of the aspects of Jackson Pollock's work.