This sounds analogous to the argument that mathematicians used to have: whether abstraction trumps intuition, especially in geometry. For instance, you can't r

This sounds analogous to the argument that mathematicians used to have: whether abstraction trumps intuition, especially in geometry. For instance, you can't really plot a 25-dimensional object, but the same object is trivial to manipulate with equations. It's clear to most people that both approaches have their place. In geometry, the visual component is very important to develop important intuitions about how objects behave in low dimensional space. On the other hand, if one were to insist on the visual, one would be stuck with purely intuitionist ideas and never be able to move into more complicated realms where you cannot visualize objects graphically (e.g. high-dimensional space). The Bourbaki group was a group of mathematician who aimed to put mathematics on a rigorous foundation by developing the abstractions that shaped modern math, and by moving mathematics past its intuitionist foundations. Some argue that this caused modern "geometers" to lose their feel for geometry because everything became about symbols. But without this development, a lot of modern discoveries might not have been possible.