[fnbr]

Hmmm. I would disagree with you. It is impossible to visualize the equations as that isn't possible to do in 3 dimensions, but it is possible to develop an intuition. After taking functional analysis, for instance, I began to develop an intuition for how function spaces work, and was able to visualize that to a certain extent (for a given definition of "visualize").

[adamnemecek]

You get it. Few people understand what's happening in every dimension at every point, but getting a feel is doable.

[posterboy]

The whole argument is that its not doable without the right tools and that visualizations are a very good tool for this.