Well in mathematics there is a somewhat similar phenomenon concerning the growth of finitely generated groups. If you have a finitely generated group, pick a generating set as an alphabet and a natural n, then ask how many elements of the group you can build by using only words of length at most n. This is the growth function, whose growth does not change if you pick another generating set.
See [1] the Tits alternative which implies that if your group is linear (huh) then the growth function is either polynomial or exponential. Then there is a result by Gromov [2] which says that if the growth is polynomial then the group is virtually nilpotent. There was a long standing question if there exist finitely generated groups with an intermediate growth and the first example was found [3].
So it's not interesting until it becomes interesting due to a newly discovered fact.
See [1] the Tits alternative which implies that if your group is linear (huh) then the growth function is either polynomial or exponential. Then there is a result by Gromov [2] which says that if the growth is polynomial then the group is virtually nilpotent. There was a long standing question if there exist finitely generated groups with an intermediate growth and the first example was found [3].
So it's not interesting until it becomes interesting due to a newly discovered fact.
[1] https://en.wikipedia.org/wiki/Tits_alternative
[2] https://en.wikipedia.org/wiki/Gromov%27s_theorem_on_groups_o...
[3] https://en.wikipedia.org/wiki/Grigorchuk_group