Instead of changing our clocks, we could just change our numbering system. Having 50 (that's 5 x 12) seconds per minute, 50 minutes per hour, and 20 hours per day seems perfectly reasonable.
There is a currency based on it (with the provably least number of coins necessary to make any kind of change), ternary logic, balanced ternary is especially cool, etc.
I've tried to explain it to people before, but we never manage to count past four without someone laughing.
(If you don't get it, think about it longer.)
