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Ethiopian Binary Math

uh.edu

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Re: Ethiopian Binary Math

#51

Post by huxley »

yaakov34 wrote: post #23
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…

It's true that Ethiopia has had large ancient Christian (and also Jewish and Muslim) populations, but it also has established Folk traditions that exists even today, there are still about 2 million animists in Ethiopia.

Re: Ethiopian Binary Math

#52

Post by fnordfnordfnord »

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

Good grief. Lienhard's "Engines of Our Ingenuity" is a series of short (<5 min) radio monologues that are played every weekday morning and afternoon on KUHF public radio in Houston, (and other places I'm told). I would imagine that Lienhard simplified the bit to get it in the allotted time, and to make it understandable and interesting to a radio audience. I've met Lienhard several times and I can tell you that he is a quite personable guy for an old engineer. It is pretty funny to imagine Lienhard, or much else of KUHF as if it were some enclave of PC progressive liberal influence. And, if you'd ever been to the UH campus, especially the College of Engineering buildings, you probably wouldn't be stricken by the grandeur of the place.

Re: Ethiopian Binary Math

#53

Post by fnordfnordfnord »

judk wrote: post #30
skunkworks wrote: post #20

Earlier quoted context omitted.

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.

Give Lienhard a break. IIRC He's a mechanical engineer; so, prior to learning of Ethiopian Multiplication, he probably used hammers to count with.

Re: Ethiopian Binary Math

#54

Post by eshvk »

yaakov34 wrote: post #23
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…

> 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.

You are flailing at windmills here. Sure the country has a long history of Christianity; however that part of the world has a long history of overlapping animistic traditions too.

Re: Ethiopian Binary Math

#55

Post by JPKab »

vilhelm_s wrote: post #2

This algorithm is also known as Ancient Egyptian multiplication, Egyptian multiplication, Ethiopian multiplication, Russian multiplication, or peasant multiplication. https://en.wikipedia.org/wiki/Ancient_Egyptian_multiplicatio...

Thanks. The OP article is awful. Have the decency to put in a graphic if you are going to describe a math algorithm involving stones in holes.

Re: Ethiopian Binary Math

#56

Post by dvanduzer »

MarcusBrutus wrote: post #48
bayesianhorse wrote: post #37

Earlier quoted context omitted.

I don't see a particular reason why one should mention "PC narrative of all civilizations being equal" in this context. This article is merely an example of how stone-age "technology" can perform a certain task. I also take issue with the automatism of accusing "political correctness". Nobody says civilizations are equal, there are numerous obvious differences. Somehow whenever I dig deeper and ask about what those p…

I wouldn't normally want to comment on that since it's not relevant to the original thread but what exactly do you mean "no birth right to it"? Like, I can't bequeath anything to my kids cause that would confer an "unfair" advantage on them? Or maybe we need a "fair" inheritance tax. Like 95% maybe? Somehow it is your political / worldview bias that's transparent in your post, not mine. I said nothing about genetic o…

Quite simply, the variation within a population is far greater than the variation between populations.

Individuals have genes that make them sublime musicians or athletes or mathematicians or painters. Cultures have different patterns which set the tone of that music and sports and math and art.

Since you're hedging with "peoples are genetically different" instead of "people are genetically different" I wonder if you've had some kind of formal rhetorical training.

Re: Ethiopian Binary Math

#57

Post by DanBC »

nhebb wrote: post #29
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…

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.

> 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.

Sure. Me laying in bed listening to radio 4 is not ingenious, even though there's some ingenuity in creating radio (and the industrial infrastructure to get a radio to me).

Of course, no-one is yelling about ZOMG PC CONSPIRACY when I say how amazing it is that I can buy a radio for a few dollars.

Re: Ethiopian Binary Math

#58

Post by [deleted] »

JPKab wrote: post #55
vilhelm_s wrote: post #2

This algorithm is also known as Ancient Egyptian multiplication, Egyptian multiplication, Ethiopian multiplication, Russian multiplication, or peasant multiplication. https://en.wikipedia.org/wiki/Ancient_Egyptian_multiplicatio...

Thanks. The OP article is awful. Have the decency to put in a graphic if you are going to describe a math algorithm involving stones in holes.

[deleted]

Re: Ethiopian Binary Math

#59

Post by DanBC »

mistercow wrote: post #25
DanBC wrote: post #9

Earlier quoted context omitted.

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.

> 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.

So why didn't they?

Re: Ethiopian Binary Math

#60

Post by DanBC »

mistercow wrote: post #26
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…

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?

try it for 57 * 48
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