[useerup]

Actually, many western number systems have traces from base 20. Just consider how you have names for numbers up until 20.

In Danish, the way we name numbers are heavily inspired by French, which also exhibit traces from base 20.

The name in Danish for 60 and 80 in modern Danish are "tre(d)s" and "firs", respectively. These are shortened forms of "tredsindstyvende" and "firsindstyvende" used historically, literally meaning "3 times 20" and "4 times 20", respectively. The number for 50 is "halvtreds" - derived from "half way to treds (60)" - meaning half way (when the "way" is 20 long) between 40 and 60.

In french 80 is quatre-vingt (4-20).

If anything, arguably our common system in which we have named numbers up until 20 (i.e. base-20) and then shift to base-10 for numbers above 20 is illogical.

[jessekv]

Ha! Although you could also argue that the transition is from twelve to thirteen ("three-ten").

On the other hand, in english, there is "score" for 20.