But let's say it was. In saying that the shaman knows how to put two sets of 7 stones in a particular pile, it is implying that the shaman also knows how to put 34 sets of 7 stones in a particular pile. He also knows how to count them, so the problem is already solved. What he is doing is a bit more "rube goldberg" than novel. It may have parallels with some real algorithm for multiplication, but it is certainly not a very direct representation of it.
(https://en.wikipedia.org/wiki/Multiplication_algorithm#Peasa...)
This algorithm is totally pointless if you're not going to work with a positional notation for the number; I am sure it was never used in the way described, with stones. Anyone capable of understanding the problem in the first place - 34 goats, 7 pieces per goat - would count out the price - here is 7 for the first goat, 7 for the next, etc. - and tell the shaman to take a hike. This story amounts to calling Ethiopians idiots for taking an algorithm suited for positionally represented numbers - or at least numbers in some kind of a concise representation - and using it in a totally unnecessary way with numbers represented as groups of stones, and not understanding the pointlessness of all the drudgery.
It's a big difference: 1000 * 1000 would require 1000000 stones if done with the "Ehiopian algorithm", but it can be done with less than 1000 stones by using normal binary multiplication.
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.
I agree that this isn't a remarkably efficient algorithm, but it is novel (it's completely unintuitive to the average reader), and it has a sound basis in mathematics. For the people who employed it, it was an efficient algorithm, or else they wouldn't have continued to use it. Nobody is proposing you're not as smart because you don't do math this way (although frankly, I doubt if you would have derived this by yourself, under the same conditions).
On a side note, I strongly recommend 'Guns, Germs and Steel'. I've been knocked for mentioning it before because it's a pop-sci book, but it explains why cultures 'progressed' at different rates because of largely environmental factors. This might help you overcome your ridiculously defensive bias against African cultures.