show ten fingers, close both fists, show ten fingers.
(ten plus ten)
show ten fingers, close both fists, show nine fingers.
(eleven plus nine)
Anyway...there are other alternatives if you're going to attribute the origin of our numeric system to the number of fingers we have. A base 6 system would be really likely as well. One hand could represent the most significant digit, and the other could represent the least significant digit. Then you could easily count to 35 with your fingers before you finger overflow.
Or you could do a binary finger count where every finger represents a different significant digit. Then you're at 1023 before you finger overflow. This is more unlikely given the large number and the unintuitive idea that each finger represents exponentially more value than the previous one. Plus you end up with some really awkward finger positions to represent certain numbers.
But I'm just not buying the idea that base ten is most likely because we have ten fingers. I'd say the base 6 system is best for our fingers. Overflow in one hand just naturally increments the finger count in the other hand. And as with the base eleven or two systems, each finger always represents the same written glyph.
A finger is a natural 1, and 45 is 2deci, thus your hands make a natural decimal-base.
Note that when you tried to show base-(9+2), you made a mistake in counting. It looks like you treated "all fingers" as 9+2, and "all but one fingers" as 9. That's inconsistent. Unless you have 6 fingers on one hand?
"But now the number of fingers you held up doesn't equal the number of items you were counting."
That's true in either case though.
Once you finger overflow the real representation is up to interpretation of what came before and what the known base is. That's why (as stated in a previous response) I think base 6 is most appropriate for our hands. You can accurately and naturally represent numbers 0 to 35 with no weird shenannigans.
show ten fingers, close both fists, show nine fingers. (eleven plus nine)
Anyway...there are other alternatives if you're going to attribute the origin of our numeric system to the number of fingers we have. A base 6 system would be really likely as well. One hand could represent the most significant digit, and the other could represent the least significant digit. Then you could easily count to 35 with your fingers before you finger overflow.
Or you could do a binary finger count where every finger represents a different significant digit. Then you're at 1023 before you finger overflow. This is more unlikely given the large number and the unintuitive idea that each finger represents exponentially more value than the previous one. Plus you end up with some really awkward finger positions to represent certain numbers.
But I'm just not buying the idea that base ten is most likely because we have ten fingers. I'd say the base 6 system is best for our fingers. Overflow in one hand just naturally increments the finger count in the other hand. And as with the base eleven or two systems, each finger always represents the same written glyph.