Conundrum: our hands give us eleven symbols: various fingers and thumbs for 1 to 9, everything out for ten, and closed fists for zero.
While the sociologists are off figuring out why this gave us a base ten number system instead of base eleven, the computer scientists are showing off how they can count to a thousand instead.
(And also get thrown out of every bar where they order four of something.)
You can actually conveniently count to 12 with one hand. Use the tip of the finger, the first and second finger joints * 4 fingers = 12. Then use the thumb as the pointer to keep track.
A base-12 number system would be advantageous because 12 is a "superior highly composite number". However, needless to say, despite the number theoretical advantages changing from our current base-10 system is essentially impossible.
Note that other cultures started numbering the individual finger bones using their thumb, ending up with a base 12 or 24 system (or so the "just so" story goes).
Regardless of its origin, base 12 is still a major part of our lives (24 hours to a day, 60 minutes to an hour, even 60 minutes to a grade in angles).
Just use each finger as a binary digit, open or cloned, and you can get to 1023. If you're really struggling to count you might add your eyes, elbows or and knees and get to 2^16 - 1. That should be enough for anyone.
While the sociologists are off figuring out why this gave us a base ten number system instead of base eleven, the computer scientists are showing off how they can count to a thousand instead.
(And also get thrown out of every bar where they order four of something.)