Riemann space

[Monte Davis]

> Of the dozens of topologists/geometers that I've asked about this, I've 
> found only one who claimed he could visualize such spaces.  
> I'm pretty sure he was deluded.

That's been my experience too. Like the rest of us, they lean on
lower-dimensional analogies: Flatland/Lineland etc, or spacetime as a rubber
sheet with masses forming gravity "wells." When they're actually working,
they're manipulating symbols according to rules. 

>From an interview I did long ago with Richard Feynman: "Do physicists vary
greatly in their ability to see the qualitative consequences of an
equation?"

"Oh, yes-but nobody is very good at it. Dirac said that to understand a
physical problem means to be able to see the answer *without* solving
equations. Maybe he exaggerated: maybe solving equations is experience you
need to gain understanding. But until you do understand, you're just solving
equations."

(As a counterweight to the pop view of Feynman as intuiitive free-spirited
magician, keep in mind that he was very good -- scary good -- at "just"
solving equations.)