QOD #11
!!(No help from Alums, please.)!!
Dr. Stuart Stephens, believing that his astronomy lectures were not challenging enough for the class of SSP'95, posed the following take-home problem in the hopes of possibly preparing some of his students for the rigors of Caltech.
"We all know what 3-dimensional space is," said Dr. Stephens. "If we talk about the positions of objects, by convention we use the N-S-E-W plane and the up and down directions." He continued, "Now if we ask, 'What's a 4th dimension?', most people would simply respond with 'time.'
"What if I asked you to come up with an answer other than 'time' that also qualified as a 4th dimension? To qualify as a distinct dimension, the new dimension must be independent of other dimensions. For example, as a 3rd dimension, the up / down direction cannot be put in terms of any combinatoin pf north, south, east or west directions (i.e. the 2nd dimension.) In the spirit of yesterday's guest speaker Dr. Paul MacCready, think of as many solutions as you can to the problem of a 4th dimension, or even examples of 5th, 6th, etc....dimensions."
The students groaned as they left the lecture room for lunch break. However, they realized that once they got started, it wasn't as hard a problem as they thought it would be.
*Creative/theoretical solutions are encouraged, but real-world examples will receive bonus points. In all cases, explain why or how your answer fulfills the requirements of multi-dimensionality.
Solution and comments
