It couldn't have been efficient since it is patently idiotic. Just spread 34 groups of 7 stones each on the ground and count them! That's all you have to do. No algorithm at all, just symbolic logic, and you need fewer stones, and probably takes less time as well. The only way to use this algorithm to portray the mathematical prowess of native Ethiopian culture in some positive way is to argue that the Shamans purposefully used this algorithm to obfuscate the process and maintain the life style and privileges of the priestly class. I dare you to claim with a straight face that this "algorithm" is even remotely comparable to what the Greeks did, e.g. Archimedes' proving, PROVING I repeat, in a mathematically rigorous way, in the 3rd century BC, that a sphere has 2/3 the volume and surface area of its circumscribing cylinder.
I don't get why there has to be a 'positive' or 'negative' angle on the story. You're trying to compare two different cultures in terms of which is 'better', which is a completely pointless goal. Nobody is saying native Ethiopians developed abstract mathematics as complicated as those of Greek, Arab, Chinese, etc. cultures.
>This algorithm allows people to multiply two numbers if all they can do is multiply and divide by 2, and add.
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.
> 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.
I don't know. I notice that I am confused, so I know that between my existing beliefs and the details of this story, something important is fictional.
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.
You are comparing a later development of mathematics to an ancient one and then calling the ancient one stupid.It is basically like studying string theory now and then calling Galileo's speculations idiotic because he used his pulse to measure time instead of a quantum-logic clock.
No, he is comparing an ancient system (ethiopian multiplication) with an even more ancient one (just fucking counting) and calling it stupid. As far as I can tell, he's got a point.
That's a fine argument with 7 times 34, because you only need 7 holes of 34 stones.
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.
