By searching in google images for ordinal or ordinal omega and restricting the search to this site you can find how people in some posts on this site try to give some kind of visualization of ordinal numbers. (Or at least some small ones.)
The same search restricted to MO seems to bring less pictures attempting something like this: ordinal and ordinal omega.
I find this picture of the ordinal numbers up to $\omega^\omega$ rather hard to grasp:
I wonder if the following might be a more compelling way to visualize ordinal numbers up to $\omega^\omega$:
My questions are:
(Where) has this way of visualization been suggested before?
How fa...
The ordinal number $\omega^2$ can be visualized as $\omega$-many copies of $\omega$. Likewise, the ordinal number $\omega^3$ can be visualized as $\omega^2$-many copies of $\omega$, arranged as appropriately (= lexicographically) ordered rows in the cube $\omega^3$ (rows being sequences of cells ...
