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Ethiopian Binary Math

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Re: Ethiopian Binary Math

#31

Post by ekm2 »

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…

So I dare say we differ a lot from the Ethiopian shaman. Reality doesn't always conform to the PC narrative of how all civilizations are equal

How did you generalize from an Ethiopian shaman's unique method of calculation to the superiority of civilizations?

Re: Ethiopian Binary Math

#32

Post by ekm2 »

vacri wrote: post #15
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…

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 requi…

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.

Re: Ethiopian Binary Math

#33

Post by ekm2 »

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.

There is probably a 'why' only that it may have been lost with the times.

Re: Ethiopian Binary Math

#34

Post by ekm2 »

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…

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.

Re: Ethiopian Binary Math

#35

Post by jlgreco »

ekm2 wrote: post #34
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 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.

Re: Ethiopian Binary Math

#36

Post by mistercow »

ekm2 wrote: post #34
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 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.

There's simply no way that multiplication by iterated addition is a newer development than the shamanistic stones and holes ritual.

Re: Ethiopian Binary Math

#37

Post by bayesianhorse »

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 people think, I get to hear/read profound racist undertones. The "PC" curse is really most common as a defense to accusations of racism.

The actual problem arises when people go on to make value-judgements along ethnical boundaries (racism). And then they go even further, using these not necessarily well founded judgements to pose "scientific facts" about how one ethnicity is genetically superior (because they believe all differences between two sets of humans have to come down to genetics/evolution)and thus are somehow entitled to more wealth than another ethnicity.

Their is no right to wealth and no birth right to it. That does not however imply a redistribution of wealth in the slightest way.

There are strong factors which contributed to the economic rise of Europe "first" and which have nothing to do with human genetics. Agriculture benefits from certain climates and soil conditions (ask the mayans about their collapse...). It also benefits a lot from domesticateable animals, and most animals are not nearly as well suited as for example horses and cows. Then the coastlines and rivers in Europe have shown to be much more conducive to commerce (before industrialization) than in Africa or America.

Systems are complex. Don't simplify them to justify judgements.

Re: Ethiopian Binary Math

#38

Post by bayesianhorse »

alanctgardner2 wrote: post #19
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…

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.

It's not pointless if your goal was to justify racism and discrimination. Then the argument makes perfect sense while still being wrong.

Re: Ethiopian Binary Math

#39

Post by wyager »

ekm2 wrote: post #32
vacri wrote: post #15

Earlier quoted context omitted.

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 requi…

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.

Re: Ethiopian Binary Math

#40

Post by bcoates »

pbiggar wrote: post #24

Looking at https://en.wikipedia.org/wiki/Multiplication_algorithm#Peasa... , isn't this exactly the same as decimal long multiplication, except using binary?

The long multiplication algorithm has two nested inner loops, each reducing one of the inputs to digits (dividing and multiplying by fixed values), multiplying them with a lookup table, then performing add-with-carry against inner and outer accumulators.

The Russian Peasant Algorithm optimizes this for the binary case by noticing that the inner multiply is always by 0 or 1 so it's trivial and never carries, removing the inner loop entirely and allowing you to use only one accumulator.

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