A remark by the late William P. Thurston—
Please note: I'm not advocating that
we turn mathematics into a touchy-feely subject.
Noted. But see this passage—
|
The Mathematical Experience , by Philip J. Davis and Reuben Hersh (1981), updated study edition, Springer, 2011— From the section titled "Four-Dimensional Intuition," pages 445-446: "At Brown University Thomas Banchoff, a mathematician, and Charles Strauss, a computer scientist, have made computer-generated motion pictures of a hypercube…. … at the Brown University Computing Center, Strauss gave me a demonstration of the interactive graphic system which made it possible to produce such a film…. … Strauss showed me how all these controls could be used to get various views of three-dimensional projections of a hypercube. I watched, and tried my best to grasp what I was looking at. Then he stood up, and offered me the chair at the control. I tried turning the hypercube around, moving it away, bringing it up close, turning it around another way. Suddenly I could feel it!. The hypercube had leaped into palpable reality, as I learned how to manipulate it, feeling in my fingertips the power to change what I saw and change it back again. The active control at the computer console created a union of kinesthetics and visual thinking which brought the hypercube up to the level of intuitive understanding." |
Thanks to the Web, a version of this experience created by Harry J. Smith
has been available to non-academics for some time.
