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The Sumerians
The Sumerians are highly regarded to this day
as being mathematically advanced. They introduced a sexigesimal style of enumeration, which is still incorporated in modern
society.
This system works very much like the binary system,
only each bit is a rise by multiples of 60. They utilized only two digits as with the Mayans (or binary). There was a symbol
for 1 and for 10. The first bit would count out 1 through 59, then on the 60, it would transform into a 1 in the second bit
position. (e.g.: 72 in Sumerian would read 1, 12 which equals 60 + 12.) In just a four bit system, you could count to 12,959,999.
Consequently, the average household electrical
outlet inputs 60hz. 60hz per second for 60 seconds at 60 minutes per hour, 24 hours a day. The basis for this math came from
Sumeria. The Babylonians who overtook the area later seemed obsessed with the number 6, as they assimilated the sexigesimal
system and even went as far as to stamp different magic order 6 squares on coins they manufactured as currency.
This sexigesimal count is actually incorporated
into the Mayan numerical concepts as a sub-sequence of their Long Count (as illustrated below).
The Romans, Greeks and Egyptians
I group all of these together because they were
all utilizing a decimal base system. The Romans and Egyptians each had 7 symbols in their number systems. The Greeks employed
6 and used symbols for: 1, 5, 10, 100, 1000, and 10000. The Romans had a similar system while utilizing symbols
for the numbers: 1, 5, 10, 50, 100, 500, and 1000. The Egyptians numbered theirs in decimal format. They had symbols for the
numbers: 1, 10, 100, 1000, 10000, 100000, and 1000000. There is also evidence to suggest that the Egyptians knew and
understood the binary sequence of even numbers and even used a multiplication process based off of this understanding.
Of the three, the Egyptians were definitely the
more advanced mathematicians. There is consistent proof of the use of fractions in conjunction with decimal equations, geometric
equations and an understanding of pi. Not to mention the Kemi, which is a 360 day calendar respecting 72 houses of 5. These
number principals are to be found in the Sumerian and Mayan works.
The Chinese
The Chinese have also maintained an understanding
of the decimal system, but pioneered other basic principles in math. Although to this day, the binary codice is continually
overlooked, even in Chinese culture, the esoteric concepts involved in the I-Ching speak for themselves. This and the acknowledgement
of the existence of magic squares which has been an enigma to mathematicians globally for millenia.
I-Ching is almost exclusively used for divination puposes
these days. Another overlooked divination process is found in the Gong Hee Fot Choy. It utilizes the 32 highest cards in an
average 52 card deck and brings connection to tarot, binary enumeration and the playing cards we have all used at some
time or another.
The Europeans
All of Europe has maintained a use of the decimal
system. It is also responsible for the Gregorian calendar and the broadened use of tarot. Tarot began as a 52 card divination
and later grew to the 78 cards that it uses today. Both numbers, 52 and 78, are divisible by 13 and you will notice that
in an average deck of cards, there are 4 suits with 13 cards apiece. With aces low, it counts out 1 through 13, which totals
91. 91 x 4 suits = 364. Meaning, all cards in a standard deck of playing cards total 364. 7 weeks x 52 , 13 lunations x 28
and 4 seasons x 91 all = 364.
(The cards themselves are generally made to Fibonacci proportions.)
The Mayans
The Mayans have probably the most intricate system
of math in the ancient world. Beyond the 260 day Tzolkin, they also had 19 other calendars that they employed for various
purposes. 5 of which are still being secreted by Mayan elders. Each calendar worked mostly off of base 20 counts (vigesimal),
but also incorporated base 13 and base 18 counts as well. It is easy to find multiples of 260, 360 and 400 within each calendar
along with common denominations therein.
The main calendar of note is the Buk Xok, also
known as the Long Count. In total, it counts out 1872000 days. It is a 5 bit system with an odd numerical arrangement to make
it work. The first bit counts from 0 to 19, on the 20 it flips over to the next bit to create a 1. So 20 in the Buk Xok reads:
00.00.00.01.00. The second bit is now counting out groups of 20 up to the 17th group. On the 18th group of 20, it flips over
to the third bit to create: 00.00.01.00.00 which equals 360. The third bit is now counting out groups of 360 up to the 19th
group. At the 20th group it flips over to the fourth bit to create: 00.01.00.00.00 which now equals 7200. This bit also counts
to 19, and on the 20th will flip over to the fifth and final bit of the sequence. 01.00.00.00.00 = 144000. The final bit counts
up to 13 to equal 1872000 or 13x144000.
If you divide 1872000 by 5125 it equals
365.2683, which is near equivilant to our current understanding of a sidereal
year. If you divide 1872000 by 5112 you get 366.1972, which is approximately equal
to 1 synodic year.
- 5125-5112 = 13
- 71x72 = 5112
Also, 7200 days is about 19.7 years which
is how long it takes for the Earth and Moon to calibrate. Venus calibrates with Earth every 52 years (4x13). Jupiter has a
year approximate to 4333 Earth days (a fractal of 13/3). Divide 1872000 by 21280 to get one Mercury year, divide it by 8331
to get one Venus year(a fractal of 25/3, 13 being the center number of the 1 through 25 sequence), divide by 432 to get one
Jupiter year, all calibrated in sync with Earth days and years to full round numbers.
This seems to be the primary purpose of Mayan
mathematics. To define these different natural processes in full round numbers to negate the need for extended decimal format
numbers, which we (and appearantly they, too) understand to be true.
This numbering system was also being used in
measurements for architecture, as well as incorporated into their socio-religious structures. The oldest and more fundamental
Mayan groups were peace loving and community oriented. Not so brutish as history commonly conveys. I have not found evidence
of a monetary system or wars in the earlier periods. Also, the level of sophistication in these number practices
relay the idea that they had a level of comfortable living in order to sit back and define the universe to such deep levels
of numerics. A troglodyte society would be less concerned with these issues and levels of thinking.
Some Interesting Facts
This is a random series of interrelated numerics.
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