Irrational Numbers

Walking home from the gym today, I saw a poster that started me thinking about the French system of numeration (I'll spare you the details), and that started me thinking about the English system of numeration. Specifically, how on earth did the plainly anomalous "eleven" and "twelve" come about?

Short answer: our entire system of number-names has its roots in German, and the words in question came from the predecessors to the modern German "elf" and "zwolf".

Long answer: "eleven" started life as the old German "ainlif". The first half of this word mutated into "ein", which is still the German word for "one", and which led to the English "one" (with, no doubt, a nudge from the French "un"). The second half is a suffix related to our word "leave", as in "left over". Thus, the whole word originally meant "one left over (from the decimal base)". "Zwolf" has a similar origin: the modern German word for "two" is "zwei".

"Twenty" follows a parallel path: the modern German version is "zwanzig." The zeds turned into tees (as happened with "zwei" and "zwolf"); the "-zig" suffix was thus transformed into "-tig" in Old English and then into "-ty" in Middle English times. This transformation of zeds into tees is also clear in such words as "thirteen", modern German "dreizehn", "three-ten".