Phi in the Bible

My jaw dropped recently regarding something that has been encoded in the Great Pyramid. I have studied the Great Pyramid for years but didn’t notice this profound secret in plain sight until a gentleman named Ray illuminated me with his website, The Pyramid and the Yard.

The Great Pyramid has a base perimeter of 1,007.7 yards, as measured by Sir Flinders Petrie in 1883 and confirmed by J.H. Cole in 1925. Ray essentially asked, “What if this was meant to be 1,000 yards exactly?” In other words, suppose for a moment that our modern definition of the yard is off by a paltry 0.77%. Couldn’t our yardsticks have lost less than a third of an inch over the millennia?

Could the yard be much older than we think?

For the sake of this article I will differentiate the ancient YARD by writing it all in caps from our modern yard by writing it in lower case.

1 YARD = 1.0077 yards.

The Great Pyramid is the Rosetta Stone of metrology.

The implications of this comparison is bigger than yards. What if our modern system of inches, feet, yards, and miles are all off by the same ratio? Divide our modern “English” measures by a factor of 1.0077 to get the ancient measures.

Ray pointed out one other key fact: the ancients divided the day into 12 hours. More precisely one revolution of the Earth was reckoned as 12 hours, not 24 as we think of today.

Earth imagery courtesy of NASA

Again I capitalize the ancient SECOND and leave our modern second in lower case. I will follow this convention throughout this post.

1 SECOND = 2 seconds.

The advantage with these double length SECONDS is that we end up avoiding all confusion about AM and PM and the math is easier with 12. Aside from that simple practicality the real benefit is the one-to-one correspondence between the division of the Earth’s rotation into the 12 hours of time and the division of stars above our heads into the 12 signs of the zodiac. There are also 12 months, 12 traditional divisions of land and society (see Twelve Tribe Nations), 12 mythological Olympians, etc.

Could it be this simple? This halving reminds me of why Tau is so much better than Pi, but that is another story.

An additional set of correspondences comes from our method of dividing any circle into 360 degrees. I’ve heard it said that this was done for the practical reason that 360 has so many factors, facilitating division into many integer angles.

Earth imagery courtesy of NASA

Consider these facts revolving around 360:

There are 36,000 inches in 1,000 YARDS. 36,000 is 100 rotations around a 360 degree circle.

“The Earth’s solar synodic year is 365.242 days and the lunar synodic year is 354.367 days. Adding these periods together and dividing by 2 yields an average of 360 days, to three significant figures.” -from my book Taking Measure

The 360 day YEAR therefore harmonizes the Earth and Moon as a system. There is one degree for each day in the system’s YEAR. The YEAR is a circle. The date is an angle. Time is cyclical.

Gary Osborn, Randall Carlson, and many others speculate that the 360 day calendar literally represented the Earth’s orbital period around the Sun before an ancient cataclysm that tilted our planet’s axis. This mega-event also kicked us out away from the Sun slightly, lengthening our present orbit to 365.242 days. Perhaps 360 is remembered in our oldest calendars because it recalls the perfect year when we didn’t experience seasons. The “garden of Eden” is in our collective unconscious.

NASA’s data shows that the combined diameters of Earth and Moon is 10077 miles. Dividing 10077 miles by 1.0077 to get the ancient measure equals 10,000 MILES exactly.

The Earth and Moon’s combined diameter is 10,000 MILES exactly.

Earth and Moon imagery courtesy of NASA

The uncanny perfection of the Earth Moon system can be perceived in another way…

“Here a circle is inscribed within a square. The square has 27.3% more area than the circle. The Moon happens to be 27.3% the size of Earth … in addition, the moon’s sidereal orbital period is 27.3 days.” -from SIPS Volume 1

Earth and Moon imagery courtesy of NASA

…and another:

Comparing a square’s perimeter to a circle having an equal circumference, the circle’s diameter is 27.3% longer than the edge of the square. The late John Michell showed how the cross section of the Great Pyramid perfectly encodes this relationship. In other words if the square’s perimeter is 1,000 YARDS and the circle’s circumference is 1,000 YARDS then its radius equals the height of the Great Pyramid.

“A circle with a 1000 YARD circumference has a radius of 159.15 YARDS. Petrie calculated the pyramid’s height to be 160.38 British yards or 159.15 YARDS.” -Ray [capitalization added for clarity]

Earth and Moon imagery courtesy of NASA

This is all very mind-blowing stuff but I have been saving the most amazing revelations until the end of this post.

The Earth bulges at the equator so the equatorial circumference is the largest possible dimension of our beautiful planet, our ultimate measurement. There are two methods for elegantly arriving at this value:

Multiply the number of SECONDS in one Earth rotation times the Great Pyramid’s base perimeter. This product equals the equatorial circumference of the Earth. One Earth rotation = 12 HOURS x 60 MINUTES/HOUR x 60 SECONDS/MINUTE = 43,200 SECONDS.

43,200 x 1,000 YARDS = 43,200,000 YARDS = Earth’s equatorial circumference (99.3%)

The implication is that the Great Pyramid’s base perimeter represents the distance the Earth rotates in one SECOND at the equator. The YARD is conveniently defined as 1/1000th of that measure.

There is another approach to measuring the equator that does not rely upon the Great Pyramid but instead hinges upon a circle and the YEAR:

Multiply 360 degrees in the circle times 360 Earth rotations in the YEAR times 333-1/3 YARDS. This product equals 43,200,000 YARDS, the equatorial circumference of the Earth.

360 x 360 x 333-1/3 YARDS = 43,200,000 YARDS = Earth’s equatorial circumference (99.3%)

This equation ties together cycles, time, the mystery of 33 and single repetitive digits (in 333.33333…). Of course 333-1/3 YARDS = 1,000 FEET so you can remove the repetitive 3’s if you like. However I think there is something uncanny about single repetitive digits and they shouldn’t be canceled out, but that is another story (read Taking Measure for this discussion). The foot is 1/3 or 33.3333…% of a yard.

The mean radius of the Sun is 432,000 MILES (99.4%). The Sun’s radius has ten MILES for every second in the DAY.

Image courtesy of NASA

Lawrence Edlund pointed out that the average distance from the Sun to the Earth (known as the Astronomical Unit) is to the Light Year as the inch is to the mile (99.8%).

Image courtesy Andrew Robertson

O, the perfection of it all!

The ancient YARD works beautifully in encoding the equatorial circumference of the Earth in a memorable way, immortalized in the dimensions of the Great Pyramid, the measurement of time, the circle, and the YEAR. However, another perspective is that our modern yard is also no accident.

I was wondering why the ancient YARD does not measure the Earth with absolute precision but is “only” 99.3% accurate. Was there slight error in the construction of the Great Pyramid, or was the builders’ measurement of the Earth ever so slightly off? Never mind how the ancient Egyptians could have possibly measured the Earth, just set that aside for now. The discussion of four kinds of encoders in Taking Measure is my attempt to answer the separate issue of whodunit.

I calculated how much bigger our modern yard would have to be (I will write this hypothetical yard in italics) to perfectly encode the dimensions of the Earth?

In other words if we want to multiply 1,000 yards x 43,200 SECONDS to equal the exact equatorial circumference of the Earth as measured by GPS satellites, how much bigger would the yard have to be in comparison with our modern yard?

The answer is 1.0145 times larger. If the yard was about a half inch longer this would work out perfectly. The scale factor of 1.0145 rang bells in my head.

I divided the duration of the Earth’s year which is 365.242392, by 360…and wondered what the relationship between the two numbers could be. I was very surprised when I saw that the result was 1.014562, for I instantly recognized that it was the same (99.9%) as the Comma of Pythagoras to the third decimal place.” -Robert Temple in The Crystal Sun

The Pythagorean Comma is the musical difference between twelve just perfect fifths and seven octaves. The Pythagorean Comma is shown as the gap (on the right side) which causes a 12-pointed star to fail to close.

Image by AugPi under the Creative Commons Attribution-Share Alike 3.0 Unported license.

Our modern yard therefore harmonizes with the back-engineered yard that measures the Earth with absolute mathematical perfection. The ancient YARD does it in a more memorable way however, revealing powerful secrets in plain sight.