So I thought I was finished with the Pyramid Math thing at least until I find a good source for the measurements inside the pyramids plus some good modern maps and measurements. I saw an interesting video on Youtube.com about Debunking the show Ancient Aliens on the History Channel. They do a good job of debunking that show which is not to say they debunk the idea of Ancient Aliens being the source for our god myths but they make mince meat of the show. While watching the show I saw a blurb about the gallery and the probable reasons for some of its features. Very interesting stuff. Each course of stone up to the top could be used as roller guides for moving large stones. Very convincing.
While poking around for more information I came across the measurement for the so called Sumerian Cubit. Previously I had worked with the Mesopotamian Cubit which varies depending upon the author but of course I used the one that suited my fancy and it appears several times so it may be the one used. This cubit is 533.4 mm. When I plugged these numbers into the Pyramid of Giza by converting the English Measurements into Metric I came up with the number 432. Here is how that worked. 756 feet (one side) x 12 inches x 25.4 mm per inch yields 230428.8mm. Now divide that by an M-Cubit of 533.4 mm and you get 432. A sacred number. In fact it is one of the few measurements that figure out to whole numbers for both the sides and the height. The height, again depending upon your source is 481.4 or 481.25 feet. The use of the quarter foot or 3 inches in 481.25 yields the answer of 481.25 x 12 x 25.4 / 533.4 = an even 275.
I liked both these numbers for their elegance. 432 is sacred. You can find it all over the world. The first mathematicians found this number and over a period of time watching the sun and earth relationships they came to understand this number well. For instance the number of seconds in a day is defined in part by this number. 24 hours x 60 minutes x 60 seconds = 86,400 seconds. Anyone with a little knowledge of the civilization of Sumer will recognize the Sexigesimal number system here. Anyone who is a little good at math will instantly see that 86,400 is a multiple of 432. 432 x 200 = 86,400. But further more there is another relationship and a number found called The Precession of the Equinoxes. A rotation of the earths axis, or where it appears to spin at the top, and it wobbles backward completing a full circle every 25,920 years.
From the number 25,920 you can derive many things. Let's divide it by 60. And we find 432. Each degree of rotation takes 72 years. 25,920 / 360 = 72.
This may or may not be circular in nature meaning that this relationship may only seem "magical" because the system we use for counting time is handed down from a very long time ago and as we know it isn't exactly right but it is a very good approximation and it fits in a circular paradigm. But let's contemplate that for a moment. Would we naturally divide a circle into 360 degrees? If we did it by forming halves and fourths and then eights etc we would not get to 360. It is basically binary division. 1/2, 1/4, 1/8.....1/256, 1/512. So the two numbers that appear by halving that are close to 360 are 256 and 512 so the method of dividing the circle was not based on simple having. It requires that a civilization count or venerate the number 60 to achieve divisions by 60. Such as 360 / 60 = 6. But that is not enough either. There had to be something that caused these people to divide the time span from an average sun rise to sun rise into 24 and then later mankind went to marking time in increments of 12 most likely because of the two different times of the day known as daytime and nightime thus a division by two. But what caused these people to develop a division of the length of a day down to a time period such as the second which suits our purpose so well? I haven't found a suitable answer for this except a desire to divide by the number 60 and its factors.
Something like this; 86400/60 = 1440. If we gave this as the standard for a time measurement comparable to the hour this would be 24 minute increments. Divide again by 60 and you get .4 minutes or 24 seconds. This is a long time span for counting many things. If we divide again by 60 we have .4 or 4 10ths of a second which is awful small. But as you perform the calculation you realize you can easily flip it and satisfy the need for numbers to "balance out". 60 small units (seconds) per longer unit (minutes) and 60 of those per larger units still (hours) or 24 which can then be divided in half for the two major halves of the day at Spring and Fall Equinox. But this may not be the case. It may turn out that a second occurs naturally and then it was discovered this "magical" set of numbers derived not only from counting off time for days but for years and epochs even. I still don't know what that would be.
Equinoxes are the two points in Earths orbit where the tilt of the Earth's axis is directly opposite of its orientation to the sun meaning that pole tilt doesn't matter. In summer one pole tilts toward the sun the other away and vice versa for winter but during equinoxes this tilt is "to the side" thus for a few days it doesn't matter about the tilt and an area on the earth you will have nearly perfect 12 hour days and 12 hour nights. Did the ancients know this? If they did and this is the reason for the divisions then how could they know the duration was the same and how long it was? Did they have a mechanism to count off time? In an early post I remarked on clocks and how clocks don't really tell time but rather actually count things. Clocks are counters. The clocks you plug into the wall count the cycles of the AC current averaged over a day. Quartz clocks count oscillations of a crystal. Atomic clocks count scintillation of photons released when an electron is excited to a higher orbit and falls back again billions of times per second. These do not actually measure time. Nothing actually measures time. Even a pendulum clock, depending upon its length, and where it is placed on the earth, counts the motion of the weight against gravity and momentum. At standard gravity the length of a pendulum to produce an arc of 2 seconds is pretty close to a meter or 994 mm. This almost became the basis for the meter but later, as I have also discussed, the meter was based on a division of the circumference of the earth.
It is possible that a water clock was used and someone paid or ordered to count how many drips occurred from one sun rise to another and by chance or by the interwoven nature of things, as I have discussed, this turned out to be pretty close to what we call a second but not very likely and yes the counting of drips is an oversimplification of how water clocks work.
After all that and until I find a possible method that either occurs naturally and was possible available to ancient mankind it is quite probable that the elegance of the numbers was the reason for the number 86,400 since 86,400 seconds does not exactly describe the length of a day anywhere except perhaps at the equator during the equinoxes for a couple or three days.
So these are my ruminations about the reasons for dividing the day into these numbers. As I also mentioned before if you add up the base numbers or the perimeter you get the number 1728 which is 12 cubed. My basic theory about the Pyramid of Giza is that it is a monument to mathematics and perhaps astronomy.as it mimics the constellation Orion which I think is either unmistakable or one hell of a coincidence. But that is not part of this discussion.
Having used the 533.4 mm Mesopotamian Cubit I found the number 432 in the base length. Broken down into primes this is 2 to the 4th times 3 to the 3rd. The height at 275 in M-Cubits is 11 times 5 squared. Nothing jumps out at us there.
As I looked on I happened across another cubit that given my years of playing with numbers looked familiar. This was called the Sumerian Cubit. This cubit is 518.6mm. On a lark, and because I was bored, I plugged that number into my Pyramid Equation and here is what I got. 756 x 12 x 25.4 / 518.6 = 444.32 and there you have it. My favorite number. 444. If you have read the beginning of my blog you know my search for the number 444. Furthermore when you use the S-Cubit on the Height you get something interesting as well. 481.25 x 12 x 25.4 / 518.6 gives you the number 282.848 which at first glance doesn't mean much unless you do a lot of number crunching. When you divide this number by 2 you get the Square Root of 2 to the 4th decimal place. Which at first seems pretty cool but is one of those logical consequences of finding 444 in the baseline. If you read my blog before you would know that Pi x Sqr 2 = 444.....and some decimals.
So the question is did the builders using one of these two cubits attempt to convey Pi, the Sqr 2, Phi, and the factorial I found for 9! built into the numbers. The perimeter when using the M-Cubit equals 1728. There are 210 layers to the pyramid this equals 362,880 which equals 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9. A demonstration of math by the builders? But what if we use the S-Cubit and perform this calculation? 444 x 4 x 210 = 372,960 which at the time of this posting I haven't found anything significant about.
I will go ahead and post these latest results. Today is July 9th, 2014. I have several programs I can run the number 372,960 through and see what comes out. The easiest thing a person can do is find the factors and then build from there. For example take the number 444 x 4 which is 1776. Everyone knows that number right? But how would it relate to anything else? If I find anything I will update this page.
As a final interesting discovery since my last blog on this subject. While I was looking up the gravitational constant for Iraq, which used to be Sumer, so that I could run the equation that would tell me the period of the swing of a pendulum 1 meter long at that location I cam across the following factoid I find interesting in my love for numbers and the number 444. It is the GPS coordinates for Baghdad, Iraq. (33.325 latitude and 44.422 longitude) Now isn't that interesting? Sumer is located at 33.3 and 44.4. Very interesting.
Until next time keep plugging away at those mysteries.
