Ethiopian Binary Math • Hacker News Board

Re: Ethiopian Binary Math

#61

Post by gucc1 » Sun, Oct 06, 2013, 3:50 PM UTC

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.

Oh. the OP ''article'' is AWFUL? have the DECENCY?

First of all it isn't an article it's a transcription. If you can't picture simple math operations with stones and holes then something might be wrong with you.

Re: Ethiopian Binary Math

#62

Post by piqufoh » Sun, Oct 06, 2013, 4:10 PM UTC

gucc1 wrote: post #61

JPKab wrote: post #55

Earlier quoted context omitted.

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.

Oh. the OP ''article'' is AWFUL? have the DECENCY? First of all it isn't an article it's a transcription. If you can't picture simple math operations with stones and holes then something might be wrong with you.

It's not apparent from OP's web-page that the content is taken from a series of radio monologues, and it's true that sometimes adding a small infographic can help perception and understanding many fold.

Maybe try to keep personal invective out of the discussion, it's not nice.

Re: Ethiopian Binary Math

#63

Post by gucc1 » Sun, Oct 06, 2013, 4:19 PM UTC

piqufoh wrote: post #62

gucc1 wrote: post #61

Earlier quoted context omitted.

Oh. the OP ''article'' is AWFUL? have the DECENCY? First of all it isn't an article it's a transcription. If you can't picture simple math operations with stones and holes then something might be wrong with you.

It's not apparent from OP's web-page that the content is taken from a series of radio monologues, and it's true that sometimes adding a small infographic can help perception and understanding many fold. Maybe try to keep personal invective out of the discussion, it's not nice.

yea sorry. the way he addressed to OP seemed a bit too harsh to me. did he expect OP to modify the University of Houston webpage to add a graphic? Come on.

Also ''No. 504''. Sounds like a series of something? by John H. Lienhard Click here for audio of Episode 504.

That definitely gives away the fact that it's a radio program.

Re: Ethiopian Binary Math

#64

Post by eadlam » Sun, Oct 06, 2013, 4:27 PM UTC

So how do we and that Ethiopian shaman differ?

Paper! Seriously, this was 1960? Even ancient Sumerians were using paper to do math. I don't understand why in 1960 anyone would seriously still be doing math with holes and rocks.

Re: Ethiopian Binary Math

#65

Post by mistercow » Sun, Oct 06, 2013, 6:14 PM UTC

DanBC wrote: post #60

mistercow wrote: post #26

Earlier quoted context omitted.

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

How is that an answer? In the end you're still going to be counting out 2736 stones either way. In the shaman's algorithm, you'll end up doing so twice and some change, in a much more complicated and easily screwed up algorithm.

Re: Ethiopian Binary Math

#66

Post by mistercow » Sun, Oct 06, 2013, 6:20 PM UTC

DanBC wrote: post #59

mistercow wrote: post #25

Earlier quoted context omitted.

>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?

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.

Re: Ethiopian Binary Math

#67

Post by DanBC » Sun, Oct 06, 2013, 6:36 PM UTC

mistercow wrote: post #65

DanBC wrote: post #60

Earlier quoted context omitted.

try it for 57 * 48

How is that an answer? In the end you're still going to be counting out 2736 stones either way. In the shaman's algorithm, you'll end up doing so twice and some change, in a much more complicated and easily screwed up algorithm.

Does anextio's reply here help? (https://news.ycombinator.com/item?id=6503669)

Re: Ethiopian Binary Math

#68

Post by jlgreco » Sun, Oct 06, 2013, 9:37 PM UTC

anextio wrote: post #41

jlgreco wrote: post #35

Earlier quoted context omitted.

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…

I'm not sure how you think "counting" works...

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.

Re: Ethiopian Binary Math

#69

Post by troydj » Mon, Oct 07, 2013, 12:18 AM UTC

drnooo wrote: post #43

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...

This has made it to HN at least a few times. Maybe it should be part of math curriculum in schools so we wouldn't keep having this conversation.

There is also a reference to this method on page 61 of SICP (footnote 40 of exercise 1.18).

http://mitpress.mit.edu/sicp/full-text/book/book-Z-H-11.html...

Re: Ethiopian Binary Math

#70

Post by jatin085 » Mon, Oct 07, 2013, 10:42 AM UTC

Wouldn't it be more quick by filling the hole with 7 stones for 34 times? They could use 34 extra stones (or goats) to keep the count. That could be done by any farmer.