Visualizing Abstract Things

I’ve heard variants of this joke for a long time, and despite being vague, it’s still kind of funny. And also completely true.

A mathematician and his best friend, an engineer, attend a public lecture on geometry in thirteen-dimensional space.
“How did you like it?” the mathematician wants to know after the talk.
“My head’s spinning”, the engineer confesses. “How can you develop any intuition for thirteen-dimensional space?”

“Well, it’s not even difficult. All I do is visualize the situation in arbitrary N-dimensional space and then set N = 13.”

(Volker Runde)

Of course, one wonders why the public lecture is on thirteen-dimensional space in the first place if a generalization to N dimensions already exists. Details!

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