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Ethiopian Binary Math

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Re: Ethiopian Binary Math

#41

Post by anextio »

jlgreco wrote: post #35
ekm2 wrote: post #34

Earlier quoted context omitted.

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.

Re: Ethiopian Binary Math

#42

Post by phaemon »

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?

Erm, no. Ethiopia has the kind of shamanic spiritual healers/wise men that are quite common within the various cultures that exist in that country.

Re: Ethiopian Binary Math

#43

Post by drnooo »

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.

Re: Ethiopian Binary Math

#44

Post by drnooo »

wyager wrote: post #39
ekm2 wrote: post #32

Earlier quoted context omitted.

Besides, if a trick works, but it isn't understood why it works, then the users of it lose the 'ingenious' tag, methinks. The fact that we think it is just a trick does not mean the Ethiopians did not understand it.

Given that they speak of "evil numbers", I think it is reasonable to assume that the Shamans did not understand how the algorithm works. The inventor may have, but it seems likely that the users did not.

Wolfram has a definition of "evil numbers" here: http://mathworld.wolfram.com/EvilNumber.html which include "beastly evil numbers".

Also there are "apocalypse numbers" http://mathworld.wolfram.com/ApocalypseNumber.html , "beast numbers" http://mathworld.wolfram.com/BeastNumber.html , "leviathan numbers" http://mathworld.wolfram.com/LeviathanNumber.html , and "legion's numbers" http://mathworld.wolfram.com/LegionsNumbers.html among others.

Re: Ethiopian Binary Math

#45

Post by halflings »

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.

One of my professors (I'm a French comp. sci student) taught us this as an intro on how we could build an Arithmetic Logic Unit (as part of a hardware architecture course).

Re: Ethiopian Binary Math

#46

Post by VLM »

pacala wrote: post #28
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 i…

I have an algorithm that only takes 7 holes compared to your 12 which is seven bucks per sheep means make seven holes and shove 34 sheep into each money hole then count the total.

Its an interesting Sunday morning to rack my brain trying to figure out which algorithm "wins" when parallel processed.

Obviously 34 shamans working together could each count out seven dollars/rocks, but someone needs to count up all those rocks.

There's an obvious token passing algorithm involving three shamans and I believe 7+34=41 rocks and 4 holes where one does a long count of the total and count++ every time upstream hands him a rock, then upstreams upstream does the same. So one dude counts to 34 using 34 rocks one time, the next dude counts to 7 (and does it 34 times) using 7 rocks, and the last dude counts every time dude 2 hands him a rock and never resets to zero (at least until done) giving him a total.

You can tell scientists invented the original algorithm not engineers just by a simple observation of actually implementing the algo... "Yo shaman come over and mult 7 by 34 for me" "OK but how many rocks will I need to multiply this... do me a favor and whip out your iphone and google 7 asterisk 34 so I know a lower bound of how many rocks to bring to implement this algo.."

The worst part of the whole discussion is it reads like a really extraordinarily bad stereotypical tech interview question. "So, I see you've got extensive experience on the job with Scala and Mysql and play framework, thats all very nice, but a major problem we often have here at BigCorp is sometimes we want to measure precisely 4 oz of rum but we only have a 3 oz and 5 oz cup and we were wondering what you thought of that ..." You know some kind of space alien anthropologist is going to hear this is how those ancient "humans" used to select their programmers and the space aliens who hear pop sci stories about human programmer interviews are going to think 1) We were insane/stupid 2) They're superior. Theres not much other reason for the whole story.

Re: Ethiopian Binary Math

#47

Post by anextio »

VLM wrote: post #46
pacala wrote: post #28

Earlier quoted context omitted.

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 i…

I have an algorithm that only takes 7 holes compared to your 12 which is seven bucks per sheep means make seven holes and shove 34 sheep into each money hole then count the total. Its an interesting Sunday morning to rack my brain trying to figure out which algorithm "wins" when parallel processed. Obviously 34 shamans working together could each count out seven dollars/rocks, but someone needs to count up all those…

> I have an algorithm that only takes 7 holes compared to your 12 which is seven bucks per sheep means make seven holes and shove 34 sheep into each money hole then count the total.

Good thing for the shaman's job security that there are more numbers that can be multiplied than 7 and 34, then. Try multiplying 34x34.

For large multiplications, using the method described uses a logarithmically smaller working space in a society where positional numbers didn't exist and paper was rare, expensive, or nonexistent.

Re: Ethiopian Binary Math

#48

Post by MarcusBrutus »

bayesianhorse wrote: post #37
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…

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 overall superiority although it is plainly evident to anyone not blinded by PC that some peoples are genetically more likely to produce sublime music or advanced mathematical frameworks / complex works of art or advanced technology just like other peoples are genetically more likely to be stronger, better jumpers, runners, sturdier and so on. Environment certainly played a role but after many hundreds or even thousands of generations the genetic makeup of a people changes as well (as an aggregate statistical entity).

I've no doubt these genetic differences were non-existent when we were all together in the primordial soup but we've moved past that phase and these differences now exist. I am saying nothing about overall superiority and certainly nothing about rights of individuals.

If you make the extraordinary claim that the genetic makeup of a people played no role in the difference of achievements between cultures the onus is on you to prove a negative. Explain why we take it for granted that people of Samoan heritage are huge but it's somehow racist to argue that hey, that DNA thing may be affecting brain cells as well and not just bones / muscle tissue.

Re: Ethiopian Binary Math

#49

Post by ekm2 »

jlgreco wrote: post #35
ekm2 wrote: post #34

Earlier quoted context omitted.

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.

The last time I checked Combinatorics was all "just fucking counting" and I am sure you will agree that it is not stupid.

Re: Ethiopian Binary Math

#50

Post by fnordfnordfnord »

wyager wrote: post #39
ekm2 wrote: post #32

Earlier quoted context omitted.

Besides, if a trick works, but it isn't understood why it works, then the users of it lose the 'ingenious' tag, methinks. The fact that we think it is just a trick does not mean the Ethiopians did not understand it.

Given that they speak of "evil numbers", I think it is reasonable to assume that the Shamans did not understand how the algorithm works. The inventor may have, but it seems likely that the users did not.

>Given that they speak of "evil numbers", I think it is reasonable to assume that the Shamans did not understand how the algorithm works.

Or maybe that the language translation is imprecise.

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