I noticed that Euler's number (or the exponential function generally), seems like it can be interpreted as configuration spaces, but I'm not sure about the first term.
The series expansion of the exponential function $e^x$ –
$$ e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!} = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + \frac{x^5}{5!} + \cdots $$
You can imagine the numerators as ordered configuration spaces, and the denominators as the respective permutation groups. Therefore each term is an unordered configuration space (UCS).
For example, the third term, $\frac{x^2}{2!}$: it's easy to see if you put it down on some axis and choose number for x. Let's say $x$ is 1 (so we're looking at Euler's number). Then you can imagine the term as the spatial measure of the UCS:
$\frac{x^2}{2!}$ term UCS for Euler's number
The entire area is the ordered configuration space, the grey shaded area is the UCS.
The 4th term, $\frac{x^3}{3!}$, comes out like this, a cube divided into six congruent tetrahedra, each of which contains every combination of coordinates within the cube:
$\frac{x^3}{3!}$ term UCS for Euler's number
But what about the first term? I don't know if $\frac{x^0}{0!}$ is a proper configuration space.
