Mayan Matemtics

[steve_bank]

Watchedd a show on the rise and fall of Mayan civilization.

They were experts at applying geometry to civil engineering and architecture. Like other civilizations they had structures to signal different times based how light appeared inside or outside a structure. An entire outer section on the face of structure remains dark during the day as the angle of the sun chnages.

They had an arithmetic and a concept of zero.

It developed separately from the other continents.

Mayan mathematics

mathshistory.st-andrews.ac.uk

 

[Swammerdami]

Ancient documents are preserved when inscribed in stone or clay, but are otherwise hard to come by. Exceptions include 3500 year-old papyrus documents from Egypt, preserved due to a very arid climate.

Mayan documents were written on fig-tree barkcloth, an invention which may have preceded Chinese paper (which was made from ingredients including mulberry tree bark). Mayan barkcloth preserves better than papyrus and would have given much information about this advanced civilization, but zealous Christian missionaries burned all the barkcloth documents they could find! The Baby Jesus had never touched the Mayans so they could have nothing of value to remember.

There were still Mayan documents preserved in stone or ceramics, mostly biographies of their Kings IIRC. Deciphering them was very difficult — there was no "Rosetta Stone." (Many natives spoke languages sibling to or descended from ancient Mayan, but were any actually conversant in the ancient tongue? IIRC none could read the ancient script.) I watched a YouTube showing how one man — the teenage son of an anthropologist IIRC — made great progress deciphering the Mayan script.

Since the Mayans recorded numbers using both place-value and a zero symbol, why are they not credited with "invention of the decimal system"? Two reasons: (1) They used base-20, not base-10; (2) They denoted the numerals from 1 to 19 using just two symbols rather than nineteen. (Would doing arithmetic with Mayan numbers be slightly awkward compared with the nine digits we memorize in kindergarten? I think coping with 19 digits would be uncomfortable compared with 9 digits. Many adults have forgotten their 10x10 multiplication table; 20x20 would be hopeless!)

The Mayan place-value number system presumably had 1, 20, 20², 20³, 20⁴ as its place values, but the article Steve links to says there's no proof of that! Instead the values found in the stone-inscribed biographies are 1, 20, 18·20, 18·20², 18·20³. This is because the only large numbers deciphered are dates, and these are recorded based on a year of 18·20=360 days.

 

[Learner]

Watchedd a show on the rise and fall of Mayan civilization.

They were experts at applying geometry to civil engineering and architecture. Like other civilizations they had structures to signal different times based how light appeared inside or outside a structure. An entire outer section on the face of structure remains dark during the day as the angle of the sun chnages.

They had an arithmetic and a concept of zero.

It developed separately from the other continents.

Mayan mathematics

mathshistory.st-andrews.ac.uk

Hi Steve, I was going to bring the Mayans (and the Chinese) up, on the other thread, which was regarding the very same thing... the 'development of arithmetic' separate or isolated from other civilizations. My point was, arithmetic is bound to be discovered, universally, simply by realization; starting with the basic methods through the mere exercise of 'counting sheep or other livestock,' etc.... regardless of where in the world you are.

Hi Swammerdami, interestingly, the base 20 system, apparently was thought to have been started when the Mayans were counting the digits on both their hands and feet. ( I met a professor of ancient civilizations around 2010, mainly the Mayan and Aztec civilizations. A dinner guest at a mutual friends home).

 

[steve_bank]

The North American natives were not nearly as sophisticated as Central and Southern American civilizations.

I thought the notation was interesting. The zero concept is important.

Civilizations on the American continent never developed the wheel and machines as did civilizations across the water. Chinese and Romans used water power on an industrial scale.

Mayan civil engineering was as good or better than Rome.