This is probably a stupid question.
If 2^2 is known as "Two squared" and 2^3 is "Two cubed", then why do we stop at 2^3? Why do we not call 2^4 "Two tesseracted", and so on?
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I think the word tesseract is rather recent, apparently originating with Charles Howard Hinton (1853-1907) in the 1880s. However, much older literature sometimes referred to 4th and 5th powers as "square-square" and "cube-square" (or "square-cube") I think. – Dave L. Renfro Feb 09 '21 at 21:26
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This actually makes a lot of sense, as 2^2^2 equals 2^4. – Jack Larson Feb 09 '21 at 21:28
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We could, but don't for several reasons.
- Squares and cubes calculate areas and volumes; in everyday life we never encounter the geometric generalizations.
- You can't keep inventing a new word for each dimension. There isn't one for hypercubes in dimensions greater than four. So it's not clear what your "and so on" should be.
- In higher dimensions mathematicians want the name of the calculation to tell you the dimension, so you use the dimension itself, not a made up word. So "two to the $17$th" for $2^{17}$.
- "Tesseracted" is ugly.
Ethan Bolker
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