
Ethiopian Binary Math - midgetjones
http://www.uh.edu/engines/epi504.htm
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vilhelm_s
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...](https://en.wikipedia.org/wiki/Ancient_Egyptian_multiplication)

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drnooo
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.

~~~
troydj
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...](http://mitpress.mit.edu/sicp/full-text/book/book-
Z-H-11.html#footnote_Temp_68)

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MarcusBrutus
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 shaman. Reality doesn't always conform to the
PC narrative of how all civilizations are equal. Unless you are a sociology
major that is.

~~~
alanctgardner2
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. For the people who employed it, it was an efficient algorithm,
or else they wouldn't have continued to use it. Nobody is proposing you're not
as smart because you don't do math this way (although frankly, I doubt if you
would have derived this by yourself, under the same conditions).

On a side note, I strongly recommend 'Guns, Germs and Steel'. I've been
knocked for mentioning it before because it's a pop-sci book, but it explains
why cultures 'progressed' at different rates because of largely environmental
factors. This might help you overcome your ridiculously defensive bias against
African cultures.

~~~
MarcusBrutus
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 purposefully used this algorithm to obfuscate
the process and maintain the life style and privileges of the priestly class.
I dare you to claim with a straight face that this "algorithm" is even
remotely comparable to what the Greeks did, e.g. Archimedes' proving, PROVING
I repeat, in a mathematically rigorous way, in the 3rd century BC, that a
sphere has 2/3 the volume and surface area of its circumscribing cylinder.

~~~
ekm2
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.

~~~
jlgreco
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.

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anextio
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.

~~~
jlgreco
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.

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cpleppert
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](http://www.pballew.net/old_mult.htm)

This method in practice would have used objects that represent larger
numbers(1,5,10) and with those a practitioner only needs to know how to add,
subtract and multiply or divide by 2. All of which are operations which can be
performed quickly. It certainly isn't true that you would need as many stones
as the final result.

~~~
yaakov34
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.

~~~
eshvk
> 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.

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mcphilip
For a much clearer visual explanation, see this BBC video on the subject:

[http://youtu.be/Nc4yrFXw20Q](http://youtu.be/Nc4yrFXw20Q)

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

~~~
bcoates
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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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...](http://ed.ted.com/lessons/the-magic-of-vedic-math-gaurav-tekriwal)

2\. [http://www.openthemagazine.com/article/art-culture/the-
fraud...](http://www.openthemagazine.com/article/art-culture/the-fraud-of-
vedic-maths)

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eadlam
_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.

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jatin085
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.

