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Ethiopian Binary Math

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Re: Ethiopian Binary Math

#21

Post by [deleted] »

cpleppert wrote: post #12
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 s…

[deleted]

Re: Ethiopian Binary Math

#22

Post by alphakappa »

It's probably appropriate to also mention the (supposedly ancient) form of mathematics taught in India as Vedic Mathematics [1] that provides computational shortcuts. (The origin of this is in question though [2])

1. http://ed.ted.com/lessons/the-magic-of-vedic-math-gaurav-tek...

2. http://www.openthemagazine.com/article/art-culture/the-fraud...

Re: Ethiopian Binary Math

#23

Post by yaakov34 »

cpleppert wrote: post #18

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 large…

If you used objects to represent 5, 10, 100 stones, etc., and were capable of e.g. saying that 7 and 7 stones equal one 10-stone and 4 stones, you would have a compact representation of your number, and that would be the proper use of this algorithm.

But note that this is different from what John H. Lienhard explicitly says: "the hole contains 224 stones". His version is completely pointless. None of us are objecting to the algorithm itself - yes, it is equivalent to long multiplication in binary, it has been known since ancient times, and there is nothing wrong with it. However, Lienhart has a) apparently misunderstood the point of the algorithm, and b) ascribed it to Ethiopian village "shamans", which gives one the mental image of Ethiopians standing around and watching a shaman manipulate hundreds of stones, instead of simply counting out the price - 7 for the first goat, 7 for the second, etc. This probably never happened, and would be stupid if it did; and yet people are coming here to defend this as an example of "Ethiopian ingenuity".

What kind of "shamans" is Ethiopia supposed to have, anyway? Aren't they a Siberian thing? Ethiopia has one of the most ancient Christian traditions in the world, you know. I agree with some other posters that this whole thing is some kind of a politically correct cringe which somehow tries to compliment Ethiopians for something they have nothing to do with, and only ends up insulting them. And every reader's intelligence, to boot.

Re: Ethiopian Binary Math

#25

Post by mistercow »

DanBC wrote: post #9
MarcusBrutus wrote: post #7

Earlier quoted context omitted.

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…

You're getting a bit hung up on the stones. 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.

>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.

No, it isn't.

Re: Ethiopian Binary Math

#26

Post by mistercow »

cpleppert wrote: post #12
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 s…

How is this method faster than counting them out, when the end result is 238 stones that you have to count in order to know the answer?

Re: Ethiopian Binary Math

#27

Post by yaakov34 »

[deleted] wrote: post #21
cpleppert wrote: post #12

Earlier quoted context omitted.

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 s…

[deleted]

The algorithm actually does make sense for positional systems (or compact notations in general). Think of long multiplication: it assumes you can multiply by a one-digit number, and lets you get from there to multiplying by a many-digit number. This is the same thing, but it only assumes you can multiply by two, instead of by any one-digit number. So this is a variant of long multiplication, and equivalent to performing long multiplication in binary. But it only makes sense if you have a compact representation of your numbers, since otherwise you may indeed just perform the multiplication directly by counting out 7 stones for the first goat, 7 for the next, and so on.

It is the version described by Lienhard - which involves counting out the whole number anyway, which you could just as easily do without any special algorithm - that is pointless.

Re: Ethiopian Binary Math

#28

Post by pacala »

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…

The algorithm only requires 12 holes, and scales the number of holes logarithmically. As opposed to make one group per unit, which scales the number of groups linearly. Less holes, less work, win.

If you squint your eyes a bit, you can even imagine where this comes from. To avoid creating too many holes, you start with a group of 7 stones, then double them, then again, until you "double" them 34 times. Obviously 34 is not a power of two, so you need some extra machinery to make it work for non powers of two.

Re: Ethiopian Binary Math

#29

Post by nhebb »

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…

I see ingenuity in the creation of the technique, but if it was handed down over generations without the understanding of why it works, then that isn't a display of ingenuity. Contrast that to a typical student in who is given the same task of multiplying 7 x 34. They can get the same result and are also taught why multiplication works.

Re: Ethiopian Binary Math

#30

Post by judk »

skunkworks wrote: post #20
MarcusBrutus wrote: post #8

Earlier quoted context omitted.

> 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.

The article:

> So how do we and that Ethiopian shaman differ? Very little, I reckon. > Very little indeed. Of course, I wouldn't be surprised if he makes fewer mistakes than we do.

The article clearly dumbs down (or misunderstands)the algortihm, insulting the audience's intelligence to make a feel-good claim about the arithmetic talent of "uncivilized" Ethiopians, and is accidentally racist in the process.

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