This algorithm allows people to multiply two numbers if all they can do is multiply and divide by 2, and add.
> It couldn't have been efficient since it is patently idiotic.
And yet is it so efficient it is how computers multiply.
Yes, and the algorithm of making N groups of M and then counting allows people to multiply if all they can do is count. And they will do it far faster than the shaman every time.
>And yet is it so efficient it is how computers multiply.
No, it isn't.
So why didn't they?
My strongest guess is that it's the stones. In any base > 1 the algorithm is efficient. In unary (counting stones), it inefficient to the point of being nonsensical.
So my guess is that this was not used by counting stones, but with some form of positional number system, and that in the retelling, stones have been added as a way to make it sound more "tribal".
Edit: Alternatively, it may be the idea that they're doing this exactly. If the doubling side is done by rough estimation (eyeballing the size of the piles), it might be faster.
But it breaks down when multiplying much larger numbers, because the number of holes you need increases by N. With this addition system, you only need log(N) holes.
The system exists to remove cumbersome aspects of multiplying large numbers by counting. Consider 34x34. While one fellow is out digging 34 holes, making sure not to make a mistake, or finding a piece of wood that has 34 holes marked in it, the other guy never needs more than 10 holes if his numbers are less than 1024. This keeps his working area small, and he can see all of it at the same time. It's less cumbersome this way.
As described, the Ethiopian Method would take far more stones and far more time. The larger the numbers you are working with, the larger the discrepancy.