It seems that every new function is just a function that asks something of the one before it, for example: First we have addition. That is the starting point. Now, multiplication, which asks "How many times to we add this number to itself." Then we went to exponents, which asks "How many times do we multiply this number to itself."
Why did we not create something that asks "how many times do we exponentiate this number to itself?"
Seems like the next step to me. We could even keep going forever and ever. How do we represent this in mathematics?