The ancient Maya used a mathematical system that is “vigesimal.”
A vigesimal counting system is based on 20 units (0 – 19), instead of the 10 unit (0 – 9) based counting system that we use today called the decimal system.
The vigesimal counting system used by the ancient Maya made counting high numbers extremely easy, even when one could not count very well – or at all.
In the “Four Slave” example, we make the assumption that the ancient-era individual counting is using the fingers and toes of four slaves they have in possession to count out a ‘pic’ of cacao beans.
A “pic” in Mayan is 8000.
The ancient Maya packed cacao beans in sacks of 8000, which is a ‘pic’. Thus, we assume it takes four Maya slaves to count and pack a ‘pic’ of cacao beans, without actually knowing how to count.
Here is how we do it:
To count 8000 cacao beans with 4 slaves that cannot count, all you need to do is make sure they have all their fingers and toes.
Take “slave 1” and have them pick a cacao bean for each finger and toe they have (20). When they have a cacao bean for each finger and toe, they put that sum into a single pile of cacao beans. They then pass their pile of cacao beans to the next slave, “slave 2.”
“Slave 2” then keeps a stack of cacao beans they get from “Slave 1” for each finger and toe that they have. Once they have a stack of cacao beans from “Slave 1” for each finger and toe they have, they combine it into one stack. They then pass their stacks to the next slave, “Slave 3,” whom cannot count either but also has all their fingers and toes.
“Slave 3’s” job is to watch what the other slaves are doing and when “Slave 2” has enough stacks for each finger and toe they have, “Slave 3” gets passed “Slave 2’s” stack. “Slave 3,” whom proudly caught on easily, then makes a stack for each finger and toe they have from the stacks “Slave 2” passes them.
“Slave 4” has the easiest job, all he has to do is wait until “Slave 3” has enough stacks from “Slave 2” for each finger and toe. Once “Slave 4” gets passed “Slave 3’s” pile, “Slave 4” only has to put the stack of cocoa beans he gets from “Slave 3” and put them in a sack and let his master know, “they have a ‘pic’ (8000) of cacao beans.”
None of them may be able to count past 20, much less to 8000, but they can still accurately pack 8000 cacao beans using a vigesimal counting system – as long as all the slaves have all their fingers and toes.
Of course the Maya certainly needed a higher understanding of mathematics beyond basic cacao bean counting to accurately calculate the paths of celestial bodies. They also needed higher math for the engineering necessary to build the structures that they built, many which still stand to this day.
After all, you can only go so far with lucky block stacking.
- Read: <Ancient Maya Arithmetic>
- Read: <The Ancient Maya understood Value of Zero>
- Read: <The ‘Four Slave’ Example How the Maya count to 8000>
- Read: <Maya Math – The Grid System>
- Read: <Counting the Maya Way – The Finger Method>
- Read: <The Maya Abacus>
- Read: <The Ancient Maya Concept of Fractions>
This article is an excerpt from the book: Kane, Njord. “Chapter 12 – Ancient Maya Arithmetic.” The Maya : The Story of a People. 2nd ed. Yukon: Spangenhelm, 2016. ISBN: 978-1943066032 Used by permission from the author and publisher exclusively for use on readicon.com only.
written by Njord Kane © 2016 Spangenhelm Publishing
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