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Ethiopian Binary Math

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Re: Ethiopian Binary Math

#11

Post by DanBC »

shawnz wrote: post #10
alanctgardner2 wrote: post #4

Earlier quoted context omitted.

Correction: to run the algorithm you're required to have at least as many stones as the end result. That's like saying because MAX_INT is set, math on computers is pointless. Any physical process will have a finite upper bound on the size of the result. 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…

Okay, first and foremost, the algorithm obviously was never actually used in the way this story describes, because it is totally ridiculous and that is not even the point of the article. 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 the…

Does it help if you don't call them "stones" but call them "bits"?

(https://en.wikipedia.org/wiki/Multiplication_algorithm#Peasa...)

Re: Ethiopian Binary Math

#12

Post by cpleppert »

MarcusBrutus wrote: post #3

I fail to see the ingenuity, or even any common sense in this. If to "run" the algorithm you are required to have as many stones as the end result (actually quite more if you count those spent on "evil" holes), you might as well spread out on the ground 34 groups of stones with 7 stones in each group and just count them. Or create a 34X7 rectangle and count the stones. So I dare say we differ a lot from the Ethiopian…

It is simply a way of performing multiplication without requiring a positional notation system. If you don't have that this allows you to do multiplication of very large numbers assuming you can divide and multiply by 2. You could do this on paper but usually you would have objects that would represent number units used in the culture such as 50,10,5,1 etc. So your objection that you might as well count them out is simply not true, this method is faster than what you suggested.

>>Reality doesn't always conform to the PC narrative of how all civilizations are equal. Unless you are a sociology major that is.

I'm not sure what your point is. True positional numerals have a long cultural history that doesn't lend itself easily to an analysis of which culture performed math better.

Re: Ethiopian Binary Math

#13

Post by mchouza »

DanBC wrote: post #11
shawnz wrote: post #10

Earlier quoted context omitted.

Okay, first and foremost, the algorithm obviously was never actually used in the way this story describes, because it is totally ridiculous and that is not even the point of the article. 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 the…

Does it help if you don't call them "stones" but call them "bits"? ( https://en.wikipedia.org/wiki/Multiplication_algorithm#Peasa... )

No, the algorithm as described is very different from binary multiplication. It requires a number of stones proportional to the result, while the number of bits required when doing binary multiplication is polylogarithmic.

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.

Re: Ethiopian Binary Math

#14

Post by cpleppert »

shawnz wrote: post #10
alanctgardner2 wrote: post #4

Earlier quoted context omitted.

Correction: to run the algorithm you're required to have at least as many stones as the end result. That's like saying because MAX_INT is set, math on computers is pointless. Any physical process will have a finite upper bound on the size of the result. 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…

Okay, first and foremost, the algorithm obviously was never actually used in the way this story describes, because it is totally ridiculous and that is not even the point of the article. 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 the…

We know that the algorithm was used because it was specifically described in ancient Egyptian texts. The calculator would use either symbols on paper or objects representing successively larger numbers (1,5,10 etc) to perform the algorithm. He obviously wouldn't use only a single stone to count out each number.

Re: Ethiopian Binary Math

#15

Post by vacri »

DanBC wrote: post #5
MarcusBrutus wrote: post #3

I fail to see the ingenuity, or even any common sense in this. If to "run" the algorithm you are required to have as many stones as the end result (actually quite more if you count those spent on "evil" holes), you might as well spread out on the ground 34 groups of stones with 7 stones in each group and just count them. Or create a 34X7 rectangle and count the stones. So I dare say we differ a lot from the Ethiopian…

> Unless you are a sociology major that is. John H. Lienhard is Professor Emeritus of Mechanical Engineering and History, getting his PhD from UC Berkeley. > I fail to see the ingenuity, You can't see something ingenious with probably illiterate people using a different base to multiply numbers? As per the Wikipedia link posted by vilhem_s "The method as interpreted by conversion to binary is therefore still in wide…

You can't see something ingenious with probably illiterate people using a different base to multiply numbers?

While it's a nice trick, it's a circuitous route to get to the answer, and requires considerably more stones than the number you're trying to count to. Simply laying out X stones per Y items and counting them uses no methods that the shaman's system doesn't already use, requires less stones, and doesn't require any 'good' or 'evil' silliness.

Besides, if a trick works, but it isn't understood why it works, then the users of it lose the 'ingenious' tag, methinks.

Re: Ethiopian Binary Math

#17

Post by yaakov34 »

DanBC wrote: post #11
shawnz wrote: post #10

Earlier quoted context omitted.

Okay, first and foremost, the algorithm obviously was never actually used in the way this story describes, because it is totally ridiculous and that is not even the point of the article. 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 the…

Does it help if you don't call them "stones" but call them "bits"? ( https://en.wikipedia.org/wiki/Multiplication_algorithm#Peasa... )

No, it absolutely does not help. In the algorithm you are citing, the numbers never leave their binary representation; there is no counting of the units that make up the number. The step of multiplying by 2 is done by shifting the binary representation of the number, which is not the way that this supposed "Ethiopian algorithm" works. The long multiplication algorithm (in binary or not) has complexity O(log(NM)), where N and M are the numbers to be multiplied, while this algorithm has complexity O(NM), and also gets there in a roundabout way.

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.

Re: Ethiopian Binary Math

#18

Post by cpleppert »

How to multiply isn't necessarily self evident, especially if you don't have a positional notation system. Even after the introduction of arabic numerals into Europe there were many different algorithms for performing multiplication, some of which are only moderately recognizable as our long multiplication system: http://www.pballew.net/old_mult.htm

This method in practice would have used objects that represent larger numbers(1,5,10) and with those a practitioner only needs to know how to add, subtract and multiply or divide by 2. All of which are operations which can be performed quickly. It certainly isn't true that you would need as many stones as the final result.

Re: Ethiopian Binary Math

#19

Post by alanctgardner2 »

MarcusBrutus wrote: post #7
alanctgardner2 wrote: post #4

Earlier quoted context omitted.

Correction: to run the algorithm you're required to have at least as many stones as the end result. That's like saying because MAX_INT is set, math on computers is pointless. Any physical process will have a finite upper bound on the size of the result. 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…

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 purpos…

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.

Re: Ethiopian Binary Math

#20

Post by skunkworks »

MarcusBrutus wrote: post #8
DanBC wrote: post #5

Earlier quoted context omitted.

> Unless you are a sociology major that is. John H. Lienhard is Professor Emeritus of Mechanical Engineering and History, getting his PhD from UC Berkeley. > I fail to see the ingenuity, You can't see something ingenious with probably illiterate people using a different base to multiply numbers? As per the Wikipedia link posted by vilhem_s "The method as interpreted by conversion to binary is therefore still in wide…

> John H. Lienhard is Professor Emeritus of Mechanical Engineering and History, getting his PhD from UC Berkeley. Close enough for me. Frankly I doubt that he honestly believed every word he wrote. People in high places have to routinely perform public worship of the PC god, "all cultures are equal", etc. Regarding the "ingenuity" see me reply above: https://news.ycombinator.com/item?id=6502665

You're taking a cute fictional story and running wild with it to somehow fit your weird anti-PC agenda. No one here, including the original article's author, is claiming that this is evidence of cultural equality. Way to waste your energy.
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