Ancient Egyptian arithmetic just like binary numeral system in modern computers

[Roma_Victrix]

This guy gives a very straightforward explanation for how ancient Egyptian arithmetic worked. Fascinating.

I know mathematics isn't as sexy as pike formations and gunpowder artillery, you guys, but please watch the video! Evidence for Egyptian mathematics dates back even to the Old Kingdom period with details about construction preserved in inscriptions on walls, yet the earliest known papyrus documents to have been preserved for posterity date only as far back as the 12th dynasty (ca 1990–1800 BC) of the Middle Kingdom of Egypt. Using a numeral system with bases of ten, the Egyptians were able to solve problems of not only basic arithmetic, but also complex equations in algebra and geometry.

Binary numbers were first put to use in Europe by the 17th-century German mathematician Gottfried Leibniz in his 1679 publication Explication de l'Arithmétique Binaire. A Sinophile who was familiar with various tracts in Chinese literature via returning Jesuit missionaries, Leibniz derived these ideas from the binary system presented in the ancient Chinese Yijing, or I-Ching (易經) written sometime during the Western Zhou dynasty (1046–771 BC). The Yijing is mentioned in the Youtube video as well. By the 1930s, this binary system was applied to electronic relays in the first practical digital circuits, the very base origin of the modern computer, developed by Claude Shannon at MIT. In the modern binary numerical system, the digits 0 and 1 represent the "on" and "off" functions of electrical current.

My only question is this: since the earliest Greek mathematics was somewhat influenced by Egyptian and Near Eastern mathematics and astronomy, why didn't these ideas rub off onto Greco-Roman mathematics?

It's funny, taken as a whole, ancient Greek mathematics were actually further ahead in development than contemporaneous Chinese mathematics until about the 2nd century AD. In the 3rd century BC, there was no Chinese mathematician like Archimedes, who nearly discovered integral calculus. It's only a few centuries later, with Han Chinese figures like Liu Xin, Zhang Heng and Liu Hui, that Chinese mathematics was on the same level. However, as far as I know, the Greeks never applied or devised a binary numerical system for solving equations like the Chinese. Why?

On a side note, it's interesting that use of negative numbers first appeared in China by the 3rd century AD, the same time they were considered for use by the Greek mathematician Diophantus, yet even he thought they were absurd. However, once again Gottfried Leibniz found good use for them in his infinitesimal calculus. In doing so Leibniz became the first mathematician to use them in a coherent system.

[Roma_Victrix]

No replies yet? No interest at all? The Pharaoh weeps because the mathematics of his people go ignored. A sad day for Egypt indeed. Worse than the oncoming of the Hyksos, the Nubians, the Assyrians, the Persians, Greeks or Romans, truly.

And Arabs, but that was way later.

Look what you've done TWC: you've killed his kitty cat. In mourning, he shall erect a great sphinx...again.

[Roma_Victrix]

The waters of the Nile River have flooded over today, with the tears of the Egyptian people, because you ignore them so, TWC.

Yet you have now simply invoked the wrath of the Pharaoh, by ignoring the achievements of his people and focusing on other threads instead.

[Lord Oda Nobunaga]

Well this was very informative... but what?!? I'm so confused I want to huddle into a corner and start crying cause I'm so bad at mathematical procedures.

Although he mentioned that they didn't memorize their multiplication tables. Well that's probably cause they were trying to memorize their thousands of hieroglyphs! you Egyptians, why does everything have to be so confusing with these peoples. About as confusing as their religion I would say.

[Roma_Victrix]

Finally! A response! I'll take it.

The Egyptian system with a base of ten and doubling numbers is way simpler than modern multiplication tables we teach in school, as demonstrated in the video. Moreover, it reminds one of the same binary system found in modern computers!

I know you're confused, Oda, but please, don't leave! Don't leave me here in this thread all alone! Otherwise I might go schizo and start having a conversation with myself about Egyptian mathematics.

[Lord Oda Nobunaga]

I'm here for you man!
So at the end of this video there's like a link for another video that explains it better. I think I get it now.

I suppose it is better than memorizing the multiplication tables, I mean I haven't even memorized anything past the 6 or 7 but then again I have a calculator. It's also noteworthy that the Chinese and Indians also used algebra. I mean I'm not good at math at all but I think the Chinese had been doing algebra since the Han dynasty if not much earlier. I recall an interesting documentary about ancient ideas of various places. One such topic was technology and science. India for instance was far ahead of anything most people usually believe.

[Lord Oda Nobunaga]

What the Ancients Knew

Egypt


India


China


Japan

[Roma_Victrix]

I had time to watch the ancient Egyptian one, very cool! As the video explains, the Egyptians, along with the Sumerians, were the first to apply geometry to architecture!

[conon394]

OP

My only question is this: since the earliest Greek mathematics was somewhat influenced by Egyptian and Near Eastern mathematics and astronomy, why didn't these ideas rub off onto Greco-Roman mathematics?

Because it is a cumbersome system and not very useful in everyday life.

Binary systems may have turned out to be a useful way to do math for computers But even humans coding Assembly language run away from binary as fast as then can to Hexadecimal and no high level programer ever uses it except in a few computer classes.

Also I would say his examples are a bit 'pre-canned' particularly on division he already knew which numbers to pick and opted for a example that produced a round number.

Try 5007 / 43

I am betting Long Division wins and gives you the option to run out the decimal or just take the remainder a whole number - assuming equal familiarity with each system.

The columns get awfully long and how do you deal the fact there is no round answer? Also recall this a time when pot shards were your disposable paper. The Ink and paper paper pad he uses would likely have cost more than a slave who could do useful sums in his head.

It cool they had the system and Its also cool how many different ways different cultures approached math - but I won't take the scorn heaped on Multiplication tables. Its been 35 years or so since they were drilled into and they still work w/o paper or pen or calculator and they solve most of the range of number issues I have most of the time or give a round estimate at least

[Roma_Victrix]

Well, aside from pottery shards they also had papyrus, but the latter was for official documents and not a disposable materials used in an instructional class setting by students, as far as I am aware of. Although the papyrus plant was native to Egypt, it was still expensive to produce and distribute, much more so than ceramic potsherds.

You're right that multiplication tables can still be put to good use in the lack of a handy calculator. However, for higher order mathematics like Boolean algebra, the binary system is absolutely pivotal and fundamentally important.

[conon394]

But now you are cheating you have moved to logical operators vs mathematical ones. Great again for Computer logic but so much for daily math and also not the way the Egyptians were using the system.

[Roma_Victrix]

But now you are cheating

Ugh! CONTROVERSY! ACCUSATIONS! DRAMA! Sound the alarm bells!

But please, do go on about how I am cheating. Anything to keep this thread going. I swear I'm going to get TWC interested in mathematics if I have to drag them there by the ankles.

[ArmoredCore]

What the Ancients Knew

Egypt


India


China


Japan

I like the videos but the problem with many of these "be amazed at the ancient knowledge of xyz" they only give half information.
For the Egyptian video one of the worst was: "they divided the day into 24 parts, but didn't have hours".
I had to laugh. The point he was trying to make was that the 24 parts weren't equal length as in our modern hours (which is a Roman I believe).
But, the word hour comes from the Greek Hora/Horo, which is the word for hours, season and time, and related to the word Horus, the Greek word for the Egyptian deity Heru.

Heru was the incarnation of the Sun god and the sun was the basis of the daytime hour keeping and the people who kept track of time were "watchers of Heru/Horus/the Hours".

The watchers of the hours were timekeepers of ancient KMT who kept track of the movements of the sun and stars and produced catalogs of time and passing of seasons.

This notion of time keeping and the movement of the seasons and the cycles of life and death also were found in the cosmology of Egypt, as the "book of hours" in the Amduat or underworld. From this the Greeks created the Horologion, which is the 'book of the hours or time keeping'. The point being that all these terms horus,hora,horo, used in Greece and Egypt have the same root and are used for the same things: time, seasons and ultimately the hours.

But that kind of understanding requires more than one or two sentences in some documentary. And the same holds true for most of these kinds of documentaries as they only skim the surface of the real impact and understanding of all the artifacts that and evidence that has been recovered from these ancient cultures. Instead of putting things into proper historical context they make them seem like oddities.
http://www.hartford-hwp.com/archives/21/004.htmlAs for the OP, it has been noted in many places that many ancient counting systems influenced the the mathematics used to create computers, from I-Ching in China to African Divination systems and so forth. And we know many ancient cultures had many different methods for computing math and that over time, some were discarded for more simpler forms, as in the indo-arabic number system we use today. But many of those other systems are found in computer math, beyond binary, like hexadecimal, which is another fundamental numeric form in computer science.

https://www.youtube.com/watch?v=7n36qV4Lk94

[Roma_Victrix]

I completely agree about those limitations of presenting facts in a documentary, for what I assume is done for the sake of flow, pacing, and staying on topic.

Also, good points about mathematics; I would rep you for this post, but I have repped you too recently.

[Lord Oda Nobunaga]

Yes I agree, a lot of it was not put into a proper historical context that's true.
Also thank you for specifying this stuff. I noticed that too and yeah they pretty much are just skimming the surface but I didn't mind since I learned some new things. I pretty much expect anyone to have a full knowledge of this to have read other sources or learned it somewhere else.