Ethiopian Shaman knew binary math back in 1940

Because of its straightforward implementation in digital electronic circuitry using logic gates, binary math is used internally by almost all modern computers and computer-based devices such as mobile phones. In the West, the modern binary number system was discovered by Gottfried Leibniz in 1679. However, Professor John Lienhard at the University of Houston tells the story from 1940 of an Ethiopian Shaman that used binary math when bargaining to sell livestock.

He postulates:

Where did his method come from? How long have his forbears carried this rote tradition?
An anonymous genius lurks somewhere in the haze of his history.

Here is the full story:

The scene is a remote Ethiopian village in 1940. A Farmer offers his herd of 34 goats for sale. One goat is worth, say $7. The villagers don't know how to multiply, so they call in a shaman. They ask him to set a fair price for the whole herd.

The shaman digs two rows of small holes in the hard dry earth. He reaches into his sack of pebbles and goes to work. He puts 34 stones in the first hole on the left -- one for each goat. He puts half that, or 17, in the next -- half 17, or 8, in the next -- and so on. He keeps dividing by two and dropping the remainder, until the sixth hole has only one stone in it.

Now he goes to the other row. He puts 7 stones -- the value of one goat -- in the first hole. He puts twice that, or 14 stones in the next hole, and so on. Now his deliberations begin.

He goes down the left-hand side, seeing whether the holes are good or evil. An even number of stones makes the hole evil. An odd number makes it good. Two holes are good. The holes next to them, in the right row, contain 14 stones and 224 stones. He adds those numbers together. The result is the fair market value of the herd. It's $238.

You and I know about multiplication. So we multiply the number of sheep, by the value of a sheep -- 7 times 34. When we do that, we get $238. But that's just what the shaman got! So what in the world was all the business with the holes? And would he get the right answer with different numbers?

We try it with other numbers. It works every time. So we turn to a mathematician. He says it's not at all obvious. He puzzles for a long time. Finally he sees it. This Ethiopian shaman has created a remarkable algorithm.

All that business with the holes identifies the numbers in their binary form. That lets the shaman reduce multiplication to simple addition. He's multiplied just the way a digital computer does. Where did his method come from? How long have his forbears carried this rote tradition?

An anonymous genius lurks somewhere in the haze of his history. So we look at our own multiplication and realize that we too use ritual to find what 7 times 34 is. It makes no more sense to most people who use it than the shaman's holes. Our multiplication algorithm was also given us by an anonymous genius. He is also lost in rote tradition.

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.

Source: ETHIOPIAN BINARY MATH

Some ancient knowledge not lost after all? Amazing stuff.

-MM

reply to post by MerkabaMeditation


Why can't they feed themselves?

I mean if they can do advanced math why can't they plant corn or build computers like the rest of the world?

Nice Interesting stuff.I have never got a right answer on history yet.I would think any stick in the mud would be binary.SF

justreleased
reply to post by MerkabaMeditation

 

Why can't they feed themselves?

I mean if they can do advanced math why can't they plant corn or build computers like the rest of the world?

It's not advanced math. It's an odd way of doing multiplication, similar to the binary system of computers. A person using this system would take quite a bit of time though. It's interesting, not advanced.

justreleased
reply to post by MerkabaMeditation

 

Why can't they feed themselves?

I mean if they can do advanced math why can't they plant corn or build computers like the rest of the world?

Wait....Ethiopeans can't plant vegetables? I thought the reason they were "poor" was more due to socioeconomic issues, am I wrong?

reply to post by supermarket2012


And drought...

To the OP, fascinating stuff. Thanks for posting.

reply to post by supermarket2012


Lack of natural resources. If the United States was there in Africa, it too would lack a lot of natural resources, and have inhospitable weather. There are some things man has no control of.

Base 2 math. Neat.
Here's base 5 math combined with base 2. From long before 1940.
www.tommcmahon.net...

reply to post by justreleased


Learn a bit of history to know you answer, check out the impact of Italy (and other external powers) in the region...

Ethiopian Empire @ wikipedia

The Ethiopian Empire also known as Abyssinia, covered a geographical area that the present-day northern half of Ethiopia covers. It existed from approximately 1137 (beginning of Zagwe Dynasty) until 1975 when the monarchy was overthrown in a coup d'etat. Following the British occupation of Egypt in 1882, it and Liberia were the only two African nations to remain independent during the Scramble for Africa by the European imperial powers in the late 19th century.

First Italo-Ethiopian War @ wikipedia

The First Italo-Ethiopian War was fought between Italy and Ethiopia from 1895 to 1896. Ethiopia was supported primarily by Russia as well as France, that provided weapons, military officers, and medical supplies, that assisted Ethiopian forces during the war

Second Italo-Ethiopian War @ wikipedia

The Second Italo–Ethiopian War, also referred to as the Second Italo–Abyssinian War, was a colonial war that started in October 1935 and ended in May 1936. The war was fought between the armed forces of the Kingdom of Italy (Regno d'Italia) and the armed forces of the Ethiopian Empire (also known at the time as Abyssinia). The war resulted in the military occupation of Ethiopia.

Politically, the war is best remembered for exposing the inherent weakness of the League of Nations. Like the Mukden Incident in 1931 (the Japanese annexation of three Chinese provinces), the Abyssinia Crisis in 1935 is often seen as a clear demonstration of the ineffectiveness of the League. Both Italy and Ethiopia were member nations and yet the League was unable to control Italy or to protect Ethiopia when Italy clearly violated the League's own Article X.

This is interesting today as it echoes in the concept of US exceptionalism and disregard for international laws.

Italians of Ethiopia @ wikipedia

Italians of Ethiopia are the colonists from Italy who moved to colonize Ethiopia in the 20th century, and their descendants. Failing to colonize Ethiopia, the Italians instead mounted a military occupation lasting six years. In 1941, with British help, Ethiopians defeated the would-be colonists and restored Emperor Haile Selassie's rule.

Haile Selassie I @ wikipedia

Haile Selassie I (23 July 1892 – 27 August 1975), born Tafari Makonnen Woldemikael, was Ethiopia's regent from 1916 to 1930 and Emperor of Ethiopia from 1930 to 1974. He was the heir to a dynasty that traced its origins by tradition from King Solomon and Queen Makeda, Empress of Axum, known in the Abrahamic tradition as the Queen of Sheba. Haile Selassie is a defining figure in both Ethiopian and African history.

Today, Haile Selassie is worshipped as God incarnate among followers of the Rastafari movement (taken from Haile Selassie's pre-imperial name Ras – meaning Head – a title equivalent to Duke – Tafari Makonnen), which emerged in Jamaica during the 1930s under the influence of Marcus Garvey's "Pan Africanism" movemenT.

APPEAL TO THE LEAGUE OF NATIONS Haile Selassie June 1936

Those that forget or dismiss history are doomed to forever repeat the errors of the past...

Broom
reply to post by supermarket2012

 

Lack of natural resources. If the United States was there in Africa, it too would lack a lot of natural resources, and have inhospitable weather. There are some things man has no control of.

Africa HAS resources, problem is that international companies own them. Africa could easily feed itself. And Ethiopia is one of fastest growing economies in the world.

It's an ancient system of doubling found in other parts Africa as well,I am astonished by the level of ignorance displayed by posters like Justreleased.

Why can't they feed themselves?

I mean if they can do advanced math why can't they plant corn or build computers like the rest of the world?

They had a severe drought some 30yrs ago much worst than the dust bowl of the 1930ts in the good ol U.S of A that drove farmers off their lands and made them internal refugees,you are still stuck in a time warp of three decades??..in any case their ancestors produced cutting edge techniques, and were among the worlds first farmers.

Fallen obelisk at Axum
This fallen obelisk in Axum is one of many that were built as early as the 6th century, probably to indicate a burial site. The details of the construction of this massive structure are still a mystery.
Read more at matadornetwork.com...

They were known as one of the four world powers of the ancient world, others were the Byzantine Romans,Persia and China. they minted their own coins had trade and diplomatic out post in India, it is one of the first Christian nation in the world,not imposed upon btw by outsiders but because they chose to become Christians in A.D 330.


Somewhat related African Fractals.

Phage
Base 2 math. Neat.

Yes, but: "In the West, the modern binary number system was discovered by Gottfried Leibniz in 1679. However, Professor John Lienhard at the University of Houston tells the story from 1940 of an Ethiopian Shaman that used binary math when bargaining to sell livestock."

I think that was kinda the point. Though you are correct if you are implying that this man's accomplishments do not stand up to those of the ancient Chinese empire. Not every individual can outdo entire civilizations like you can, Phage...we just simply do not have the sheer, raw brain-power that we can just aim at any problem and instantly solve it.

It is interesting to think though, that far in the past, perhaps a version of this man's method were used by a larger priesthood to accommodate the economy of a larger empire. It could have been a visitor from a long forgotten civilization thousands of years ago who taught it to them... See that's the point of this stuff. It gets your imagination going. Just about every thread could be one-upped in one way or another, and I'm pretty sure everyone here has heard of an abbacus. But before this thread, I'm pretty sure very few heard of this "neat" man's little trick...

It's also in the WAY he performs binary math...didn't you read the part where some guy said it was not at all an obvious how he was doing it and they had to actually figure out why and how his algorithm worked every time?

The fact is... The man, or whoever originally developed this method is a genius. Plain and simple. Just like the person who developed the multiplication rituals and algorithms we use to this very day.

So, yes... "neat." Chances are this goes back further than the 40s, it just took that long for a westerner to discover and share it with the world. My imagination told me that it could have been in use thousands of years ago. I guess we may never know for sure.

But hey, thank you for bringing your amazing abacus to show and tell... *yawn* really, that was an interesting post packed with useful contributions. Seriously...that would make a great *Zzzz...* thread. Op shoulda tossed this one into the rubbish pile and instead produced a 3 hour long.YouTube video lecturing us on the finer points of the abacus... Yes, you were correct to sarcasticly snub your nose at this boring story about the African Shaman who thinks like a computer, before the computer chip was invented...

reply to post by Spider879


Ah, thank you, ATS Member Spider879. So it would appear that my imagination has once again led me to the truth. Versions of this system were indeed in use long before the 20th century AD.

AMAZING videos btw... I cannot get enough of this stuff. Although I will admit it is sometimes difficult to retain some of the material. So many civilizations, and time periods, and important historical figures, events, etc. etc... But it makes it worth it when, even if for only a moment, you can capture a glimpse of our historical process, cause and effect relationships, and so on... and we are lucky to have access to enough knowledge to connect enough dots to be able to step back and visualize the big picture from time to time, and have a few Aha! moments along the way!

Not to mention all the pure imaginative fodder, if you could even refer to it as fodder...being that it is incredibly useful. I imagine (there's that word again) that Einstein was using his imagination when he came up with the theory of relativity. How else could he when he's treading onto uncharted territory? Sometimes I run simulations through my mind to solve problems. Perhaps we all do. How is this any different from "imagining things"?

Huh, ATS Member Spider876?? How?! How is it any different??? Yeah. You can't answer that one. Can ya? 'Swhat I thought...

Me:1 You:0 Checkmate. You're done in this town. Yahtzee. Slam Dunk. Touchdown and 2 point conversion. Grand Slam. Hole in One. Case Closed. Stick a fork in it. You're pau. Sayanora. Adios. Hasta La Vista, Baby.

To be clear, the above two paragraphs were not directed to ATS Member Spider879, but to a person I know with a similar name. They are not an ATS Member, but back in elementary school, he blew chocolate milk bubbles out of his nose in the cafeteria, causing a huge burst of laughter, and Mrs McDonaldson almost choked on her creamed corn trying to quiet us all down, and so naturally someone gave him the very fitting nickname, ATS Member Spider876, and it just kinda stuck all the way through college and everything. I guess it has a nicer ring to it and flows off the tongue much better than his real name, Bob. He lurks the boards all the time so I just left him that message knowing he would see it. I know because he's obsessed with shamans who can think like computers ok? Does it really matter? I mean, he's a guy I know, ok? I know what kind of stuff he likes. I mean, is that really so hard to believe?

I guess that must be obvious though, since ATS Member Spider879 and I have never had an argument about the imagination. So why would I be all confrontational towards him about it, right?

Now that's what I call a useful post packed with over 24 essential vitamins and minerals. That's right... Over 24 That means it could be 25...or 25 million...times infinity.

reply to post by justreleased


I'd bet they were doing much better before Europe floated up to their doorsteps..

It doesnt seem advanced or clever to me, in fact it just seems stupid.

He dug 7 holes and then droop at least 400 pebbles in them.
Why not just dig 34 holes, 1 for each sheep, and then drop 7 pebbles in each????

IMO this is just another way of those with power trying to make themselves look smarter or better than those they have power over. if he can count to 238 Im fairly certain he could understand basic multiplication

reply to post by MerkabaMeditation


A Shaman in the 40's knew binary math...

Not a surprise, human ingenuity at its best.

Now imagine the same human mind has been on the planet, in its current form for 200,000 years, and according to current history we were just damn lazy for the first 196,000 of those years...

IkNOwSTuff
It doesnt seem advanced or clever to me, in fact it just seems stupid.

He dug 7 holes and then droop at least 400 pebbles in them.
Why not just dig 34 holes, 1 for each sheep, and then drop 7 pebbles in each????

IMO this is just another way of those with power trying to make themselves look smarter or better than those they have power over. if he can count to 238 Im fairly certain he could understand basic multiplication

What seems stupid to you is the basis for all modern computing, its how you get all this neat stuff from a 1 or a 0.

Its broken down to its most basic form by the shaman, and someone with a little electronic and transistor knowledge could translate that math into a working calculator with a few vacuum tubes or transistors.

reply to post by benrl

What seems stupid to you is the basis for all modern computing, its how you get all this neat stuff from a 1 or a 0.

Its broken down to its most basic form by the shaman, and someone with a little electronic and transistor knowledge could translate that math into a working calculator with a few vacuum tubes or transistors.

in computers its genius, it saves time and computing power.
in humans it does the opposite which is my point, it takes longer and is harder and more unnecessarily complex to do it the way the shaman does than simply doing 34X7.
This is not clever, its is simply stupid or making something look complex to make yourself look smart and confuse others. You seriously think that system is easier to teach than basic multiplication????

IkNOwSTuff
reply to post by benrl

 

What seems stupid to you is the basis for all modern computing, its how you get all this neat stuff from a 1 or a 0.

Its broken down to its most basic form by the shaman, and someone with a little electronic and transistor knowledge could translate that math into a working calculator with a few vacuum tubes or transistors.

in computers its genius, it saves time and computing power.
in humans it does the opposite which is my point, it takes longer and is harder and more unnecessarily complex to do it the way the shaman does than simply doing 34X7.
This is not clever, its is simply stupid or making something look complex to make yourself look smart and confuse others. You seriously think that system is easier to teach than basic multiplication????

The point is its shows the genesis of knowledge, a point where mans ingenuity on its own can figure out advanced concepts.

Its fascinating , how sad you can't see the wonder of it.


Whose smarter the man spoon fed the easier way or the man who found a way on his own?

3n19m470
reply to post by Spider879

 

Not to mention all the pure imaginative fodder, if you could even refer to it as fodder...being that it is incredibly useful. I imagine (there's that word again) that Einstein was using his imagination when he came up with the theory of relativity. How else could he when he's treading onto uncharted territory?

Actually, what he was doing was working off theories by other people and pointing out the flaws in them. It wasn't done in a vacuum -- and there was at least one other person who came to the same conclusion but didn't publish first.