Significance of the Numbers 5 and 12
Are there really "hidden sacred numbers"?
https://youtu.be/R7oyZGW99os?si=C11yjjgDJL-hMByr
All the mathematical relationships that are so well described in this most interesting video are based on one simple connecting feature of our species.
Stretch your hands out and make your left hand into a fist and your right hand face palm upwards.
Now with your right thumb, tap each of the phalanges on each of your four fingers once and when you have completed these 12 taps, extend a digit on your other, left, hand.
You can do this 60 times at the end of which all the digits on your left hand are extended.
The number 12 is highly composite, meaning it has many divisors (1, 2, 3, 4, 6, 12). This makes it convenient for practical divisions into halves, thirds, quarters, and so on. For example, a dozen (12) eggs can be split or sold evenly among 2, 3, 4, or 6 people.
This was a convenient and practical way the Ancients used to count before the invention of the Abacus. Indeed, one step further, mathematics (trigonometry and algebra, an Arabic word) emerged out of Mesopotamia because the private fields of farmers would get flooded every year and it was necessary to redraw the boundaries.
Evolution of measures
I don't think the ancient Sumerians and Babylonians - the first civilization to live in cities, maybe as long as 10,000 years ago? - knew the size of the planet, but with a system based on five and 12, or base 60, it is self-justifying that the Giza pyramid, for example, should scale up to the size of the Earth, since the system of meridians and longitudes, used for location and distance, is based on five and 12, 60 and 360.
And using the sexagesimal system, there will be unsuprising and non-coincidental resonance with other numbers, for example measures of length: the pace, the foot, the yard, the furlong, the mile.
And same for the calendar: 60 seconds, 60 minutes, a lunar month of 30 for the moon to reappear in its first phase, 12 lunar months for the Earth to orbit the sun.... and then the Greeks use of decade and century for political terms of office and historical chronological events on base 10 i.e two hands, simpler. Although counting in base 60 didn't really begin to decline until the Renaissance which adapted and extended classical Greek and Roman texts, philosophies and law. 7 bright objects in the sky - the sun the moon Mercury Venus Saturn the North Star - that "turn round the earth" as we turn round the kaabla.
Currency, trade calculations: pence, shillings, pound.
Angle, rotation, navigation, architectural 3D design shapes polyhedron: seconds minutes, degrees.
Weight, agriculture, tax tributes: the talent, mina and shekel (also currency, based on a silver standard).
Religion the 30 days of ramadam, the 12 disciples of Jesus and unlucky 13, pilgrims must walk around the Kaaba seven times in a counterclockwise direction.
Imperial system of Measures
The Imperial system is not entirely based on 12 but it does use 12 and multiples thereof. This system codified all the units mentioned above and by the 19th century was used throughout the British Empire.
Length: 1 foot = 12 inches
Volume: 1 pint = 16 fluid ounces (not base-12 but a similar concept of divisible units)
Weight: 1 pound = 16 ounces (again, not base-12, but still is convenient for division so for trade.
Religion
According to the Book of Revelation (Revelation 7:4 and Revelation 14:1-5), 144,000 is the number of people who will be sealed and protected during "the great tribulation", being a group of individuals chosen from the twelve tribes of Israel, 12,000 from each tribe.
Another cabalistic mystery
Here's another cabalistic mystery unraveled or debunked from mystical associations.
Why is the small gauge railway that width? And the answer is that the railways followed the Roman roads and the Roman roads were scored by the wheels of the Roman chariots and the width of a Roman chariot was determined by the width of the horse that draws it.
1. Mathematical and Historical Context
- Counting Systems: The numbers 5 and 12 are significant in historical counting systems. The method you described of using the phalanges (each finger having 3 segments except the thumb) for counting up to 12 on one hand while using the other hand to keep track of multiples is a rudimentary yet effective counting system. This system is likely a precursor to the more sophisticated abacus.
- Base-60 System (sexagesimal): Mesopotamian mathematics, which significantly influenced later civilizations, used a base-60 (sexagesimal) system. This is evident in our timekeeping (60 seconds in a minute, 60 minutes in an hour) and in the division of a circle into 360 degrees. The sexagesimal system might have evolved from a combination of base-10 and base-12 counting systems.
2. Cultural and Symbolic Significance
- Number 5:
- Human Anatomy: Five is often seen as a number symbolizing humanity due to the five fingers on each hand and five toes on each foot.
- Pentagon and Pentagram: In geometry, the number 5 is associated with the pentagon and pentagram, which have historical significance in various cultures, often representing completeness and balance.
- Number 12:
- Calendar Systems: The number 12 is significant in many calendar systems. There are 12 months in a year, and this division of the year likely originates from lunar cycles.
- Zodiac and Time: The 12 zodiac signs and the division of the day into two 12-hour periods (AM and PM) also highlight the importance of 12 in timekeeping and astrology.
3. Geometrical and Astronomical Significance
- Circles and Cycles: The division of circles into 360 degrees is a direct consequence of the sexagesimal system, which itself is rooted in base-12 counting. The number 12 fits well into many systems of division (e.g., 12 divides evenly into 2, 3, 4, 6).
- Giza Pyramid: While there is much speculation about the numerical and geometrical significance of the Giza pyramids, the idea that they might scale up to the Earth's size using a system based on 5 and 12 ties back into the sexagesimal system and ancient understandings of geometry and measurement.
Evaluation and Expansion
1. Ancient Numerical Systems:
- The use of the phalanges for counting is a practical method that naturally lends itself to base-12 counting. This system is intuitive and efficient, explaining its widespread use.
2. Development of Mathematics:
- The necessity of redrawing field boundaries due to annual floods in Mesopotamia is a key driver for the development of geometry and algebra. The systems developed were practical solutions to real-world problems.
3. Astronomical Measurements:
- The ancient Sumerians and Babylonians had a sophisticated understanding of astronomy and geometry, allowing them to develop accurate calendars and timekeeping systems based on the numbers 5, 12, 60, and 360.
Conclusion
The numbers 5 and 12 have deep roots in human history and culture, reflecting both practical counting methods and symbolic meanings. Their significance extends beyond simple numerics into the realms of geometry, astronomy, and the development of early mathematics. The base-12 system, combined with base-5, forms a robust foundation for the sexagesimal system that influenced many aspects of ancient and modern life.
Understanding these connections explains many mysterious resonances and magic numbers and enriches our appreciation of the ingenuity and practicality of ancient civilizations.
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