WHY 7920 PARTICULA?
How the Sexagesimal Number System Found Pi
-The Hidden Meaning of the 22 Alna, 8 Alna, 7 Alna Sequence
-How the 24° Spacing Within the Æquinoctialis Zona Set Pi
-Why 42° Became a Target Latitude
Our recent posting “GKS 1812, 4TO DATA SET; Pinpoints NT, KRS, 45th Parallel Geodetic Positions” was fun to do. That it pinpointed the NT, KRS, and 45th parallel was satisfying. That we took the allegorical inscription on the KRS and matched it up EXACTLY to design model was also satisfying. That only six people grasped what the implications represent was disappointing, especially considering that Santa Claus and the Easter Bunny were two of the six persons who got it.
Anyways, as much as we speak of, and to, the 7920 PARTICULA subdivision of the Earth’s CIRCUMFERENCE, it is time to lay out how this value was developed. I have thought about it over the last year, and realized some of its aspects, but it wasn’t until Saturday morning that I put together a spreadsheet to explain the genesis of the 7920 PARTICULA value.
Yep, it is another spreadsheet. Filled with EMPIRICAL VALUES.
We know that the 7920 PARTICULA subdivision of the Earth’s circumference existed by the early 1300s as that section within the Gks manuscript is dated to that period. Was the 7920-value generated in the Medieval Era, or did it exist prior to that date? To answer that question, we have to demonstrate HOW it could have been developed in Antiquity, or prior.
This means we deconstruct the Gks values. The deconstruct provides a starting point from which we can deduce the rational that drove the INVENTION of the values.
One doesn’t have to be a good mathematician to do this deconstruct. There are no intense calculations. I have said it before…I am not great at math. Honestly, I am not even good at math. We do the math to set up a visual presentation so we can “see” patterns, groupings, and repetitive sequences. We, in this case, refers to my left and right eyeballs.
We start with the sexagesimal system of numbers, which is a base-60 system. Multiples of 60, or fractions of 1/60, represented this system of counting.
60 is the BASE UNIT of the Sexagesimal System.
-One multiple of 60, or 601, is 60.
-Two multiples of 60, 602, is 360.
-Two multiples of 60, 603, is 216,000.
-Two multiples of 60, 604, is 12,960,000.
Increments (addition), or multiples (powers), and division (ratios) within a sexagesimal system are accomplished using 60 as the base unit.
The Sumerians (c. 4500 – c. 1900 BCE) are credited, historically, with the development of the sexagesimal system. Most of the surviving records of this number system date from the Babylonian Empire (c. 1895 – c. 539 BCE). The historical artifacts are primarily clay tablets containing lists of numbers.
Antonie Pannekoek’s (1873-1960) “A History of Astronomy,” published a year after his passing, remarked on this topic:
“The Babylonians from the earliest times possessed an excellent mathematical implement in their sexagesimal system of numbers. The numerals go from 1 to 59, rendered by crochets (tens) and wedges (units); in the row of sexagesimals, each following number is expressed according to position (the same as our decimal system), the Babylonians could express any large numbers by higher powers of 60 and any small part by powers of 1/60. The fragments of the astronomical tables known to us consist of rows of numbers without names, intermingled with characters for months and zodiacal signs. Their meaning had to be revealed by the numbers themselves. Sometimes this was easy; but often the most patient efforts, the utmost ingenuity, and the collaboration of different scholars were needed to arrive at a satisfactory interpretation, especially as the numbers are often scarcely readable on the sherds and are spoiled by copying errors detectable only in the very process of deciphering.”
“The origin of these tables is unknown. We may surmise that the Chaldean astronomers had instruments with divided circles to measure the longitude of planets or the moon or the longitude of stars with which to compare them. But nothing of the kind is found mentioned in the clay tablets. Texts with observational data which might be considered sources of these new theoretical tables are also lacking. They stand out suddenly in full perfection, separated by a wide chasm form the earlier expressions of theory or practice. Although we realize that they must have been based upon observation, the course pursued is as yet obscure.” (Pannekoek 1961: 64)
In another section of the book, Pannekoek wrote of the usage of water clocks by the Babylonians and the segmenting of TIME into four-minute intervals (2 hrs: 120 minutes; 30 ush * 4 minutes = 120 minutes):
“We find no measurements in these lists; but there exists a list of stars all around the sky, with numbers added, which evidently stand for the consecutive distances. These are given in three columns of proportional numbers, clearly denoting the same quantity expressed in different units. First in the sexagesimal units of weight (biltu, mana, shikulu, corresponding to the Greeks and the biblical talent, mine, shekel); next in units of time – beru (2 hours) divided into 30 ush of 4 minutes. From Greek sources we know that the Babylonians used water clocks, in which the passage of time was measured by the outflow of water.” (Pannekoek 1961: 50-51)
Pannekoek, Antonie. 1961. A. Pannekoek. A History of astronomy. London: G. Allen and Unwin.
For later use:
“Far more practical was the Babylonian sexagesimal system, where the units in which the successive numbers from 1 to 59 were expressed were the successive powers of 1/60. Therefore Ptolemy gave the chords of his table in sexagesimal parts of the radius; three numbers secured and accuracy of 1 : 603; 1/216000.” (Pannekoek 1961: 199)
Hmmm…603 (216,000) and 604 (12,960,000) produces values 10X larger than 21,600 nm Earth Circumference and 129,600 (1440m, or particula, * 90°) value. This is a file away…
Let’s turn to our modern-day equivalent of a clay tablet numbering list – Microsoft Excel. The only mathematical operations we are performing are multiplication and division (ratio).
-The top row of values, starting with the “360 Intersects” and extending to the right, is just a series progression of (n + 360; Excel sees this as a multiplication). We are incrementing by 360 each time. We drove out to the final value of 7920 because that is the Gks value.
-“Units of ‘360’” denotes the count of “360” required to achieve the correspond “* Intersects.” 7920 / 360 = 22.
-“Units of ‘60’” denotes the count of “60” required to achieve the correspond “* Intersects.” 7920 / 60 = 132.
-“Count” is an incrementing interval of 1 moving down the page. Our end value is 360.
-“Minutes (Longitude)” is a time value based on 4 minutes equaling 1°. Our end value is 1440 minutes, the number of minutes in a SOLAR DAY.
-“60 Increment” is an (n + 60) interval moving down the page. The end value is 21,600. This happens to be the number of arc minutes in the circumference of the Earth, expressed as nautical miles.
-“Formula Pattern” is the construct used to populate the columns moving down the page.
Populate the spreadsheet, then start looking at it.
Start in the upper left-hand corner of the table. The first value in the table is the green-shaded 60, the base-unit of the sexagesimal system.
-At the 24 count, our initial value of 60 has increased to 1440.
-Our 1:1 ratio at “Count” 24 corresponds to the “1440 Intersects.”
-24 units each containing 60 sub-units totals 1440 sub-units.
-We know “units” as hours and “sub-units” as minutes.
This is the “core” matrix. In this “core” we have our 4:1 and 1:4 ratios, our 1440-minute SOLAR DAY of the 360° Earth, and our 24° = 96-minute interval.
On the top row at the “7920 Intersects” column note that it takes 132 “Units of ‘60’” to arrive at 7920. Move over to the left side of the spreadsheet, find the “Count” column, and then slide down to the 132 value.
Mentally…a 360° Earth which is partitioned into 7920 partitions, or PARTICULA, corresponds to 22 units of 360°. We know this because we can see the value of 22 in the “Units of ‘360’” cell.
-22 / 8 = 2.75
-22 / 7 = 3.142857
We now know why the early 1300s Gks manuscript has the ’22 alna, 8 alna, 7 alna’ sequence. We find it in the table. Right next to each other. Someone eight centuries ago wrote it into a manuscript in Iceland. We know that the information in this section of the Gks manuscript was Latinate in origin – this means that it didn’t originate in Iceland. It flowed into Iceland.
Why is the “2520 Intersects” column significant? We can say that one finds the value for Pi, 3.142857, in the cell which corresponds to the 132 “Count” / 528 “Minutes (Longitude)” / 7920 “60 Increment” record row, but that pre-supposes that they already KNEW Pi.
What if they didn’t – which I believe is the case?
Let’s work in the LITTLE EARTH model, which is the LATITUDE side of the house. Conceptually, the Ancients would have known that a line drawn THROUGH the Earth at the Equator, on the Equinox, would represent the DIAMETER. They didn’t have the ability to do this.
What they did know is that the Solstitial Points were 180° apart from each other. They would have observed that the zodiac shifted (tilted) between the Solstitial Points by an angular value of X. They also would have observed that tilt of the zodiac leveled out the mid-point between the Solstitial Points, what we understand as the Equinox. The mid-point represents a 1:2 ratio, with 2 being the already noted X value. X/2 represents the shift in the zodiac between a Solstitial Point and the Equinox.
Working with whole numbers is a decided advantage when doing computations, so they set the tilt value as 24° North of the Equator. They could validate this supposition by cross-referencing the gnomon shadow on the longest day of the year at various geographic locations.
At this point there was likely a bit of an argument. They had a half-circle of 180° on the Earth running from the North to the South Pole, of which they knew that the zodiac shifted by 48° between the Solstitial Points.
-48° zodiac tilt
-180° / 48° = 3.75
-180° / 132° = 1.363636
The 180° movement from one Solstitial Point to its opposite represented only 1/2th of the year. To synchronize it to the entire year, they had to do this:
-360° / 132° = 2.727272
They further reduced the values: 180° / 66° = 2.7272.
They did yet another reduction: 90° / 33° = 2.727272.
The other party in this ancient argument said “Wait! If we know that 24° is the one-quarter of the year movement of the zodiac from the Equinox to the Solstitial Point, let’s just do ratio’s involving 90°, 24°, and then the remainder of 66°.”
-90° / 24° = 3.75
-90° / 66° = 1.363636 (this then becomes 180° / 132°)
Both parties realized that either approach produced the same results!
At this point a voice from the back of the gathering yelled out “What is the mid-point between 66° and 24°? The zodiac is tilting between these values – there has to be a point where they are balanced! That balance point would represent the DIAMETER of the Earth!”
-66° - 24°= 42°
They already had populated the values for the (360° * 7 = 2520) column.
-It was 3.142857.
It was the LITTLE EARTH values which produced Pi.
[An alternate, and quite plausible option to ‘observing the zodiac’ is that they “set” the 24-value using the “core” matrix value of 24 (hours as the 1440 value is in that record, as well), or took the 1440-minute value down at the 360 “Count” record row which produced the 2.727272 value.
This makes the generation of Pi and the Megalith System of Measure values PURELY MATHEMATICAL, or an abstract exercise (at least initially), for its origination.]
We now switch over to the BIG EARTH values. Run down to the 360 “Count” record row and then go all the way to the right to the last column. 21,600 nm / 132 = 2.727272.
1) Our amazement that the Gks values produced an Arctic Circle position of 65.454545° - which is amazingly close to the modern era’s maximum axial tilt of 24.5° (90° - 24.5° = 65.500000°) is tempered.
That someone measured the 24.5° axial tilt angle in ca. 7000 BCE is a big stretch, and then that singular value being historically preserved for another 4000-5000 years only adds to that stretch. Since the 2520 particula / 114.545454° / 65.454545° value stream could be obtained computationally (just did it at the kitchen table by building a spreadsheet), we are going to re-calibrate the origination era.
2) The sexagesimal construct of TIME, related to the Earth, is clearly a basic element of the Megalithic System of Measures and, by extension, the value of Pi. We just laid out how it was done. This means that anyone who knew of, or used, the sexagesimal construct for time could be the originator of the Gks 7920 Particula System. Babylonians and Sumerians pop as candidates. The Indian sub-continent might also be the origination point (I just don’t know their time measuring system well enough to discount the impressive knowledge that history informs us this area of the world possessed).
3) Could OTHER cultures with different numerical systems have, in parallel, independently worked a computational stream which resulted in MSOM and Pi? Again, I am not well-versed with other numerical systems, say of the Mayan society, to say that they couldn’t do such a thing.
4) Was the 7920 Particula System known and used prior to the early 1300s preservation of it in the Gks manuscript? This is obviously, YES. It is easy to conclude that the Megalithic values were known and applied as late as c. 3000 BCE, based on the Megalithic values found in the henges of Northern Europe and the Giza pyramid in Egypt.
5) What we do know with absolute certainty is that someone, or some party, used the 7920 Particula System of the Gks manuscript and geodetically placed two artifacts on the North American landscape – the NT and KRS.
You do realize the days of what "historians" say "just because we say so" are long gone......its amazing what the academics have totally ignored and then perpetuated a "fake" story line. And we do not believe "academics" anymore. Your reading material for the weekend. Probably far more interesting then the "super bowl" will be.....just saying.
--------------- John Michell has reconstructed the geometric pattern of the ‘heavenly city’ which is the template of the New Jerusalem of Revelation 21.
He discovered that this diagram served as the design (blueprint) for many sacred sites, including the Stonehenge, The Great Pyramid, St. Mary’s Chapel at Glastonbury and the City of Magnesia in Plato’s The Laws.
hummm... so where does that leave the "Newport Tower".......hummmm. And you did read the posting about the "Gks 1812, 4to".
NEWPORT TOWER EGG
The AS to ES Dimension Stack-Up
I will admit…this is a confusing slide. The intent was to illustrate the relationship between the Anglo-Saxon unit of measures and how they scaled up to the nautical mile.
The best place to start is at the bottom graphic, with the “12 Inches”. This is the system we are all familiar with, the English Statute System. 12 inches to a foot, 3 of them make a yard, 16.5 feet of 12 inches makes a rod, 660 feet of 12 inches makes a furlong, and then we arrive at our 5280 mile.
The bottom line of the bottom graphic shows the comparable value in Anglo-Saxon inches, referenced to ES inches.
The next graphic to look at would be under the light blue “These values are ES inches” banner. This row gives the values in Anglo-Saxon inches (referenced to ES inches) as they ramp up through the larger measures. We can see the 7920-value pop at the furlong measure. The “old mile” is the nautical mile in the AS system; it is 10X the 7920-value of the furlong. As one moves left from the furlong, the decrement is given. DIVIDE a furlong by 10 to get the chain, DIVIDE the chain by 10 to get the fathom, then DIVIDE the fathom by 6 to get the foot.
The very top graphic, which we labeled “Anglo-Saxon Measures”, starts with how many AS inches are in a 12” Imperial foot. This is 10.909090” AS.
We then began to our drive to the right to see what values resulted for INCREMENTING. The values should look familiar…they are derived from the Gks 1812, 4to analysis.
The Earth diameter was ‘114 and a half degree and one particula.’ This value is 114.545454°. 180° minus 114.545454° equals 65.454545°.
In the sexagesimal number system, the base unit is 60. There are SIX units of 60 each to reach the sum of 360. This value, in degrees, represents the circumference of a circle.
There is a quirky thing contained within the text of the Gks 1812, 4to. They give the Earth’s diameter as the above stated 114.545454°. They then remark that the Sun’s solar ring (circle) is 2X the Earth’s diameter, or (114.545454° * 2) 229.090908°.
This is allegorical for the Sun’s diameter is 109X the diameter of the Earth.
Not a great slide, not a great explanation…but the central point that the 7920 Particula System was connected with the shift from the Anglo-Saxon to Imperial/English Statute dimensions may be seen.
While doing this work last week, it struck me to check the window spacing at the NT using the Megalithic Yard and Cubit degree intervals… boOM!
you did catch the comment above ----- "but the central point that the 7920 Particula System was connected with the shift from the Anglo-Saxon to Imperial/English Statute dimensions may be seen."
This is why historians would much rather talk and write about the wars and battles and the sex lives of the "royals" because they do not have a single clue about the "nuts and bolts" of how things were done, built or supplied in the ancient of times. In my opinion, a really good place to start would be with books about the "nuts and bolts" of a civilization rather then the "glorified" lives of the aristocracy. Lets talk about, step by step of "how the Newport Tower" was actually built.
1) Site Plan...anybody who has even a marginal concept of "blueprints" knows this is usually page label "C1"....and now we have the last years postings of "Ptolemy Navigation" with the Anglo-Saxon dimensions..
So to start with, we need a "ground zero" survey point. And that would be the "NRS" (Narragansett Runestone). Any guesses on what it took to get to spot the NRS...and then carve it. AND REMEMBER, the KRS (Kensington Rune Stone) has an earlier date then the NT (Newport Tower). So we need a calendar of events and at least two coordinated groups of intrepid (characterized by resolute fearlessness, fortitude, and endurance) explorers and/or pathfinders..any volunteers...
I would also need several (?) ships for the supply lines. This would have to include construction tools, survey equipment, and labor (probably even a priest or two for good luck), etc. Food probably was local with all kinds of good eatin' fish in the water before we polluted the entire bay in later years. And don't forget we would need a complete crew of ship millwrights and fabric makers (wool) for sails. Ropes probably were "walrus hide" or "hemp". The walrus probably came from the (future) St. Lawrence Seaway. And yes, there were thousands of walrus there before they were wiped out by, you guess it, those people from NW & Western Europe. (side note - we are still wiping out species like the wolves and almost got the buffalo...just saying).
And for today...who would have thought that the "Hooked X" would have been found on an "Irish late 14th century Irish manuscript, Book of Ballymote. Folios 169r - 170v". And yes, that is "The Book of Oghams". I said in an earlier post this research was going to get worse and worse for the "academics"...well, guess what....... And they said that "all those marks on the rocks were made by a plow"......damn....enough said. If the 'academics" don't get it now, they never will.
"This is the exact same symbol known as the Hooked X (HX) on the KRS and SPR."
HOOKED X SYMBOLOGY
The Hooked X is an X with a single branch, or tally, extending from the upper right-leg. If this were a ROMAN NUMERAL, we would have 11. This isn’t just speculation…
Take a look at the late 14th century Irish manuscript, Book of Ballymote. Folios 169r - 170v contain row upon row of number notations (tally marks, symbols, etc.). Closer examination reveals that in nearly all cases, the number notation is pentadic notation, in the sense that there are groups of symbols that represent 1-5, then a differentiated grouping that represents 6-10, and so on.
Researcher Steve DiMarzo noted some time ago that on the bottom of Folio 169r there is a sequence of X’s with tally marks. In the position that corresponds to the value of 11 resides an X with a single branch (tally) extending from the upper, right leg.
This is the exact same symbol known as the Hooked X (HX) on the KRS and SPR.
When Steve found the 11 value-HX in the Book of Ballymote, we didn’t know how to context it into the NT/KRS/SPR research that we were doing.
Now we do. In a very literal sense, it represents the number of ELEVEN. Why? Because 11 is a proportion of 22, and 22 is found all over the KRS and NT. Why? Because the KRS and NT are geodetic monuments. Geodetics, or geodesy, is all about the numbers. 11 and 22 are part of the 7920 Particula System.
Second post for today...when you say that you use the "scientific way", you had better be ready when the "real" scientists call you on the carpet. And no, we do not under any stretch of the imagination, give the "academics, historians, and archaeologists" the final say on anything. And yes, we have identified the "new fringe"...
Phippsburg History Center 2 hrs ·
Holy smokes! When one takes the SACRED GEOMETRY number of 22 and divides it by 4, the result is 5.5. This drops us right into the number expansion of 7920 Particula System...which of course is the basis for the Ancient fractional value of Pi...and which, of course, connects into the Newport Tower (NT) and Kensington Rune Stone. Then it connects to leg bone, thigh bone, backbone, and the rest of the bones in this NT/KRS/SPR/NRS/Rosslyn Vault/Sinclair/Pre-Columbian exploration of North America.
What is the Newport Tower? It is part of a geodetic monument paired with the KRS and, tangentially, with the NRS. The NT is DESIGNED around the values found in the Icelandic manuscript Gks 1812, 4to (7920 Particula System). These values are the ANCIENT values which described the GREATc CIRCLE.
Math, astronomy, astrology...all defined by relationships rooted to the interactive geodesy of the Earth and Heavens. Ancient stuff...call it Pagan, but it really isn't. It embodies the KNOWLEDGE of the above as the Ancients understood it. They constructed monuments all over the world codifying this knowledge. The Newport Tower is no different.
In a manner of speaking, the NT is a church-construct where it is the SCIENCE that brokered its design. The divinity is SCIENCE...expressed in the purest form of numbers (math).
We aren't talking about the head of John the Baptist here, we are talking about artifacts made of stone - to endure the weathering of time - which preserve KNOWLEDGE.
I reckon we could term this SACRED GEOMETRY, as others have done it, but just because something is old...doesn't altogether mean it is sacred (in the sense of theology or religion). There is an importance in preserving KNOWLEDGE regardless of when one lives. If one was living in the Medieval Era and there was a political entity that prioritized faith over science, that would be a pretty good reason to devise a method to preserve the ancient knowledge.
This is what makes the research on the NT/KRS et al so IRONIC. Strip down all the trappings hung onto these artifacts AND look at what has been codified into/onto them. It is KNOWLEDGE built upon SCIENCE.
Yet, those who argue most vociferously against the NT/KRS et al, the skeptics/debunkers/fringe-academics, posit their position as one of SCIENCE...that they alone are uniquely qualified to judge what they term as pseudo-historical theories because they employ the CRITICAL THINKING that is a requisite for pursuit of SCIENCE.
The skeptics/debunkers/finge-academics are actually WORKING AGAINST all that they espouse to be important.
And finally, I am going to only post the link and picture below, the rest is on you as it is a very lengthy posting. And yes, the ancients were very much in tune with what the group has. In fact, it is the ancients who invented this stuff.