Why don't we extend the naming of powers into higher dimensions?

Question

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?

Answer 1

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.