In this chapter, we find the quintessential link between the three-dimensional geometries of the CU and the harmonic, mathematical “frequency numbers” of the Octave.

This link comes to us through the work of Mr. Carl Munck. We will see how Munck discovers that all of the “Gematrian” frequency numbers that indicate sound vibrations have only two commonly shared tangents.

He then shows how the Speed of Light, in seconds, is a precise function of these same two tangents. This gives us a solid background upon which to establish a fundamental mathematical connection between light, sound and geometry, adding great weight to the reality of this theory, and therefore the reality of Ascension as well.



Since we have been looking at Dr. Richard Lefors Clark’s “bowtie” shaped vortices in great detail, it is important for us at this point to make mention of Dr. Clark’s theories of diamagnetism and magnetic null zones.

After all, the Wilcock reading in Chapter 17 suggested that these energy forces had a lot to do with the siting of ancient monuments. This was given as the “answer” that would rectify the positioning of certain stone and earthworks in Munck’s system with a mappable, planet-wide grid system.

According to Dr. Clark, the newest advances in the science of magnetism have shown that there is a positive / negative polarity reversal that occurs in the center of a magnetic field (see below diagram.)



It is at this point, called a “Bloch Wall,” where the spiraling energies of the north pole meet the spiraling energies of the south pole, and they overlap. At the overlap point, we get the “bowtie” shape that we see on Earth in the above examples.

The point of magnetic flow reversal, or the “Bloch Wall,” creates what we now term as anti-gravity, nulling its effects and / or changing its direction. Dr. Clark shows in Anti-Gravity and the World Grid how magnetic scientists have actually studied and measured this “Bloch Wall” phenomenon using electromagnets.

As we look at the above illustration, we should keep in mind that the lines on the Global Grid provide the organization for these spinning magnetic fields. In other words, the lines on the Grid are flowing like rivers, due to the spiraling nature of the energies that make them up.

And thus, if we look back to the diagram of the Bermuda Triangle vortex, we can see that the north-south vertical line that intersects Grid Point 18 next to Florida would be the “organizer” for the magnetic energy flows. Then, the magnetic polarity will reverse at the exact center of the bow-shaped area.

It is here that we will get our “Bloch Wall” effect produced, then causing the Bermuda Triangle anomalies, as well as providing exceptional spiritual energy. It is no surprise that many people will want to go to Florida to retire – the youthful energy explodes in abundance there!

If it were truly possible that the Earth’s magnetic field could produce such spirals of energy, then we should expect there to be places where it would be very evidential that something anomalous was occurring.

Certainly Sanderson’s work on the “vile vortices” like the Bermuda Triangle satisfies this, as does Munck’s mention of the anomalies surrounding Rock Lake in Wisconsin. There is another area that also obviously falls under this effect, and that is the area known as the Oregon Vortex.

William Childress featured the Oregon Vortex in an article for the industrial newsmagazine “Compressed Air,” which has been circulating in print for over 100 years.

As this is a reputable, mainstream scientific journal, it would be unlikely for them to print a study that was considered to be “fringe” science. Instead, it appears that their investigation of this vortex came from a genuine interest in trying to uncover and understand anomalous Earth phenomena.

Childress’ article starts out by describing the most crowd-pleasing feature in the Oregon Vortex / House of Mystery. A 100-year old shack was built over the vortex, and within this shack, a broom is “standing rigidly straight in the middle of the room, untouched by anyone or anything, as if it were a spear stuck in the middle of the floor.”

The record time for the broom to remain standing, according to those who run the House of Mystery, is 36 hours! Again, we see the harmonic numbers emerging, this time in the number of hours involved. In another area of the House of Mystery, a golf ball is placed at the bottom of a trough, and it will roll uphill when released.

On the “Superman Platform,” a person can lean very far forward without falling, and thus appear to look like Superman in flight.

Other stunts that are demonstrated at the Oregon Vortex include height discrepancies, where two similarly tall people will walk in opposite directions and have noticeable and opposite changes in their height.

A similar effect is demonstrated when a long plank is placed across two seven-foot tall posts; on the south end, the plank appears to be higher by a good three inches.

According to Childress, “in some way still not understood, a kind of “gravity warp” appears to make vertical objects taller or shorter as long as they are in the force field.” If we think about this on a much larger scale, we can visualize the expansion and contraction of landmasses, producing the structures that we have been examining above.

What is actually most interesting to us is the effects that are reported at the area called the “Vortex Post.” As Childress indicates, “people standing next to the post tend to sway in a circle like some bottom-weighted toy.”

From this piece of information, we can indeed see the spiraling nature of the gravitational fields at work! Also notable is a passage in Charles Berlitz’s Bermuda Triangle where there were reports cited of mariners encountering spiraling motions on their compass that became faster or slower depending on how close they were to the center of the vortex.

At these certain times, the spiraling energy from the vortex was actually stronger than Magnetic North, and overtook the normal operation of the compass.

It is also interesting that the owners of the Oregon Vortex / House of Mystery do not permit video cameras. They did not explain to Childress why this was so, only stating that regular cameras were permitted.

This falls perfectly in line with the Rock Lake information from Munck, and shows us that these vortices repetitively show their effects on electronics. We again remind the reader of the similar effects demonstrated by the UFOs in thousands of sighting reports.

Anyone who wishes to actually go out and see the Oregon Vortex for themselves can contact them through the following information: Oregon Vortex / House of Mystery, 4303 Sardine Creek Road, Gold Hill, OR 97525, (541) 855-1543. The tours are open from April through October.

And so, with the addition of physical information to back up the diamagnetism theories of Dr. Richard Lefors Clark, we have to consider that there is more to the Global Grid than just straight lines.

We have pieces of evidence like the bow-shaped structures of the landmasses indicated above, and now the spiraling, anomalous gravitational effects that can be seen in various spots. Although the above diagram of the diamagnetic field was drawn in two dimensions, Dr. Clark makes careful notice of the fact that these lines of force are indeed three-dimensional spirals.

These spirals are very important to study, as they form the basis for all of the Platonic Solids that we have spent so much time discussing. And looking in again on the extended version of the “Triple Julia Set” formation from 1996, this can clearly be seen:



In earlier chapters, we discussed how these universal spirals of energy generally fall into two main categories; namely, the square root of 2 and phi.

One of our postulates is that Nature, or the physical world that we can see, will show us all of the secrets in the metaphysical world.

Therefore, these spirals are not only simple mathematical concepts in our own dimension; they reach their fruition in the functions of the dimensions.

Now that we can see these spirals in action, mapped out for us by the Global Magnetic Grid and its effect on the shapes of continents, we can explore how each of the Platonic Solids “fit in” to these spirals.

As is written in Robert Lawlor’s book Sacred Geometry, the Platonic Solids are in a “simple harmonic relationship” to each other. As we can see in Table II below, that simple relationship is expressed in terms of phi and the square root of 2 in spiral form.

Lawlor gives us a complete breakdown of the Hindu “spectrum” of shapes, with the harmonic proportions for each one of them. The measurements listed are comparisons of the length of each side of the Platonic Solids.

Since every line on any Platonic Solid will be the same length, these measurements are the universal standard for each shape.


Sphere [no edges]
Central Icosahedron 1 / phi2
Star Tetrahedron
Cube 1
Dodecahedron 1 / phi
Icosahedron Phi
Sphere [no edges]

Table II. Harmonic Proportions of Platonic Solids.


In order for these proportions to be established, the researcher must determine where the “1” is going to be. We must remember the simple fact that if you have a square, and each side has a length unit of 1, the diagonals will measure out to the square root of two.

Similarly, if you assign a unit value of 1 to the diameter of a circle, the circumference will measure out to pi, or 3.14159 units. In order to compare the Platonic Solids to each other, we also need to assign a straight value of 1 to the sides of one of the shapes.

In order to have the basic harmonics work out simply and perfectly, the value of 1 needs to be assigned to the length of the side of the cube. All other proportions as indicated above represent the exact numerical value that we receive when comparing their lengths against the cube.

As we are on the subject of phi, it is also interesting to point out here that the “solar number” of 666 and the “lunar number” of 1080 also express the phi ratio when divided into each other.

John Michell’s work shows how many ancient monuments used these proportions, and we also see it in nature as well, being the harmonic relationship between such things as the size of planets. Since phi seems to be of such penultimate importance, we can see yet another reason for why the Hindus ascribed such religious significance to Purusha, or the icosahedron.

Now that we can see the actual mathematical structure of the spiraling energy that makes up the CU, we no longer need to wonder about whether they are, in fact, crystallized frequencies. We have seen it on the planetary level, and now we can see it on a mathematical level as well.

Hoagland’s team made the connection between these geometric shapes and the frequencies of the dimensions, and many might wonder exactly how he did that. The answer to that question actually helps us even more in understanding the true physics behind these harmonic, geometric shapes.

On his website, Hoagland has printed an early essay that he composed on hyperdimensional physics back in 1989. In this essay we have the clearest picture of how the Enterprise Mission team tied together the physics of higher dimensions with the abstract concept of Platonic geometry. This article is also located at

The “Message of Cydonia”

First Communication from an Extraterrestrial Civilization?
By Richard C. Hoagland and Erol O. Torun

Copyright (C) 1989 All Rights Reserved

[We are only going to reprint the part of this article that directly concerns us here.]

…If in the “Cydonia tetrahedral mathematics” we are truly seeing the deliberate communication of demonstrable astrophysical effects of a long-sought “Unified Field Theory,” this in itself would be remarkable confirmation of current efforts to discover such fundamental mathematical connections between Nature’s elemental forces.

For, most provocative: one leading mathematical approach to successfully modeling such connections is essentially based on a tetrahedral model, and a resulting mathematical expansion into “higher-dimensional, n-space relationships” (recently discovered) between the five Platonic solids (Sirag, 1989).


It is very important to note here that Mr. Saul-Paul Sirag, referenced below, has referred to ALL of the Platonic Solids in his model of “higher dimensions,” not just the tetrahedron. The work of Tony Smith also built upon Sirag’s geometric models, and a direct reference to Sirag’s work is made on Smith’s website.

In particular, these studies relate tetrahedral geometry as being topologically equivalent to three-toruses — tori extending into “one more dimension than our familiar three.”

[Many current efforts in pursuit of “unified field models,” such as the much-acclaimed “super-string theory,” routinely involve up to ten mathematical dimensions. Some more recent theories are exploring twenty-six (Sirag, ibid).]

As we have already stated in previous chapters, by breaking the “symmetry” of the strings in Superstring Theory, we arrive at an octave-based, 8 or 24 (8 x 3) – dimensional universe. This lines up with Srinivasa Ramanujan’s “modular functions.”

Phrased in simple terms:

The routine mathematical representation of vorticular flow in more than three dimensions — a three-torus — by means of three-dimensional tetrahedral models, opens up the possibility that the demonstrable geophysical effects of the “Cydonia tetrahedral message” are attempting to communicate the reality of additional dimensions (as opposed to mere mathematical abstractions) — and the observable reality of vorticular energy flow between adjoining “n-spaces.”


So, if we plug in our own discoveries in this chapter to what Hoagland and Torun have said here, and use the language that they expressed it with, Dr. Clark’s bow-shaped “diamagnetic energy vortices” would be another physical example of “the observable reality of vorticular energy flow between adjoining “n-spaces.””

Hoagland’s hyperdimensional physics asks us to visualize the spiraling energies making up the shapes themselves as being connected together to form a three-torus, which really is nothing more than what you would see if you removed the tetrahedron from the intersecting, spiraling lines that formed it.

When a number is assigned to a torus as in this case, it refers to how many visible “sides” the curving line produces. Thus, a three-torus is essentially like a triangular knot in its appearance.

Such totally unexpected (to non-specialists) and remarkable mathematical correlations — between as yet unpublished theoretical work into Unified Field Models, and the specific tetrahedral geometry apparently intended at Cydonia — gives added confidence that such a linkage was in fact intended. If so, there may be an additional confirmation of such a radical “Cydonia Unified Field Model”–

In the continuing, puzzling departure of some celestial objects from strict “Newtonian” mechanics.


And now, we check in on the References section to get a clearer picture on Mr. Saul-Paul Sirag:


Mr. Saul-Paul Sirag, for furnishing important references linking tetrahedral mathematics with “two and three-torus topologies,” and for providing examples from his own research of not only Schuster’s Hypothesis as potentially applicable to a Unified Field Model — but for specifically referencing tetrahedral mathematical topology and the Platonic Solids as directly applicable;

And finally, Mr. Stan Tenen (The Meru Foundation), for introducing us to Saul-Paul Sirag, for furnishing examples of his own research into the historical importance of the Platonic Solids (tetrahedra, in particular), and for valued general discussion of some of the more controversial aspects of our work.

[Note: Schuster’s Hypothesis relates to more recent published material from The Enterprise Mission regarding the energetic flow between bodies in the Solar System.]

It is important to point out here that the work of Stan Tenen, often referred to by Hoagland, gives us yet another layer of depth to explore in these matters. Tenen has discovered that the Torah, or the section of the Old Testament that was apparently dictated to Moses by God, has precisely encoded the formulae for constructing the Platonic Solids in its passages.

From this same Biblical scripture we also see the bizarre synchronicities that emerge with apparent mathematical certainty in the work of The Bible Code, explained in the book by Michael Drosnin of the same title.

(The Bible Code appears to have given us written prophecies of events 2000+ years in the future, in our own modern era. Drosnin’s biggest “claim to fame” with the Bible Code was the precise prediction of the assassination of Israeli Prime Minister Yitzhak Rabin.

The perfection of the mathematics involved in this, and the fact that it does not show up in any other books of the Bible, has excited mathematicians worldwide. It obviously helps strengthen the faith of Hebrews in the Torah as well!)


The work of Stan Tenen, showing us the mathematical encoding of the Platonic Solids within sacred text, gives us yet another interesting clue as to how the physical fundamentals of Universal Law and hyperdimensional physics were preserved as knowledge for us to use by Higher Intelligence.

Obviously, Tenen’s work is another major area of inquiry, and we leave it up to our readers to investigate the Meru Foundation on their own at the Meru website.

The one point that we need to mention here is that Tenen’s work also shows us a very interesting principle at work in the formation the Hebrew alphabet. Tenen explains that the Hebrew alphabetical characters represent different shadows of a single geometric figure.

That single geometric figure is, believe it or not, a spiral shape contained within a tetrahedron!

As amazing as it must seem, all we have to do is rotate the tetrahedron into different angular positions and then draw the shadows that result. All of the Hebrew letters will show up in a quite natural progression as a result of doing this.

We remind ourselves that the science of Gematria also started out in the Hebrew language, giving each of these tetrahedral rotations, or alphabetical letters, a sequential number.

The founders of this science seemed to have full awareness of the frequency numbers that underlie the dimensions, as well as their meanings. We remember as one example that 144 was said to equal Light, and now we can see through the work of Bruce Cathie that light speed, in harmonic terms, is indeed 144.

And now, we can see that the same authors of Gematria also knew of the Platonic Solids, as well as the fact that they have an inner, spiraling nature! The actual structure of the Hebrew alphabet was intended to show us this.

If we look back to the work of Carl Munck, we can see that the Ancients were very much concerned with the traditional English inch, foot and mile measurement when building their sacred sites. The work of John Michell, which we have not explored in detail here, also shows very significant relationships of the Great Pyramid and Stonehenge to the inch / foot / mile system.

We also remind the reader that the Sumerians gave us the Constant of Nineveh, and that it was a value expressed in seconds. We also remind the reader that the Speed of Light, in conventional terms, is also expressed in miles per second.

In the chapter on Bruce Cathie, we demonstrated how the harmonic of Light shows up precisely when we solve the Speed of Light for (x) minutes of arc per grid second. The value that we end up with is 144,000 minutes of arc per grid second for the speed of light in free space.

This puts it into the simple harmonic terms that the Universe works off of, and that the minds of the ETs navigating our globe can understand. Now, we can see here that the values of miles and seconds are also important in harmonic terms as well, to the Atlanteans and their cohorts.

So, we wonder to ourselves, could the Speed of Light also have harmonic significance when expressed in miles per second?

We do find that this is indeed the case. Not only that, but it ties in directly with the science of Gematria, which we have just been re-examining here.

It also ties in with the work of Carl Munck, our pioneer archeocryptographer who discovered a universal coordinate system being used within all sacred sites worldwide. It also ties in with the fundamental, spiraling nature of the geometric forms that the authors of the Gematrian sciences were very much aware of.

Carl Munck was studying the Gematrian “frequency numbers,” and started to notice that there was a definite mathematical redundancy to them. The redundancy came when he started calculating the tangents of each number, and found out that they were all the same!

If we remember from trigonometry class in high school, the tangent function is used to measure the intersection between a straight line and the very edge of a circle. This also could obviously be the intersection of a straight line and a curve as well, thus mapping – you guessed it – a spiral.

We now go directly into a reprint from Mason et al.’s Gematria page, which explains this point, and eventually tells us how these numbers harmonically tie into the Speed of Light, measured in miles per second. Here is Mason et al. to explain.

Carl figured a certain logic was demanded by these [Gematrian frequency] numbers, so he arranged them into two separate scales, organizing them by their tangents, and marking the numbers that came from the ancient systems with asterisks (*), and filling in the “blanks,” with appropriate numbers, something like this:


+ 3.077683537 72* 252* 432* 612 792

– 3.077683537

108* 288* 468 648* 828



+ 0.726542528 36* 216* 396* 576* 756*

– 0.726542528

144* 324 504





In the newsletter, Carl had a longer list of these numbers in vertical columns. He also drew in sine waves connecting the numbers, which seemed to be suggested by their logic.

He noted the consistent differences between the various numbers in the top two rows of 36 and 144, such as 108 – 72 = 36 and 252 – 108 = 144. The differences between the bottom rows are 108 and 72, such as 144 – 36 = 108; and 216 – 144 = 72.

The suggestion of sine waves, Carl said, is very, very obvious. Did the ancients know about sine waves? Did they have oscilloscopes? Were they suggesting a certain frequency?




Carl was shocked when he multiplied the two Gematrian tangents:

3.077683537 x 0.726542528 = 2.236067977

He knew that 2.236067977 is the square root of five!!!

That’s the pyramid codex talking!”, Carl says. He asks, “Why does the square root of five answer the sine waves of the Sacred Numbers? What was the reasoning behind it?… [The reasoning was that] the square root of five is itself a Tangent; the Tangent of 186234.09485, which is the speed of light in air!!!

Carl points out that the speed of light in a vacuum is 186282.5894 miles per second, but when light travels through air, it is slowed down to 186234.09485 miles per second. Enter this speed-of-light-in-air number into your calculator, and then press the tangent key, to see that it is very close to the number arrived at by multiplying the two Gematrian tangents…

[Here we remind ourselves that the tangent is a mathematical function that can be used to map out a spiral. The Speed of Light has a tangent of the square root of five, and this in turn has a tangent that harmonically relates to ALL frequency numbers making up the light / sound / geometric structure of the Octave of dimensions. You simply multiply their two commonly shared tangents together to get this number.]

Carl concludes –

And there we have it, the reasoning behind the Sacred Numbers of Gematria, the same ones preserved in eastern metrology and western calendrical computing; square roots and tangents – all keyed to the terrestrial speed of light.

It is delivered through the pyramid codex in nearly the exact methodology they used in keying the earth’s equatorial circumference to the cube root of double-pi when they built the Great Pyramid at Giza.


Munck’s work quite well explains how the Great Pyramid was built to unify the Earth’s circumference at the equator with the “constant” of the cube root of double pi, and it is also explained on Mason et al.’s Gematria page, from which this was excerpted.

No communications across ancient oceans? No prehistoric writing that makes any sense? Ignorant stone age progenitors? I’m afraid I’m not buying anymore, not when I can so easily find this kind of mathematical evidence to the contrary.

Someone back there had it all; maps of enviable accuracy, a complete knowledge of every inch of our planet, a thorough understanding of mathematics and, yes, even calculators and computers we take for granted today — because without such tools, they could never have put it all together.

Why do I say that? Because the U.S. Geological Survey advises me that they have the only computer in the United States which is programmed to calculate accurate distances between widely separated points anywhere on the planet — which means — that before the ancients could have marked out the pyramid grid system, they required a computer of the same caliber!


And so, from this excerpt, we can see very clearly how Carl Munck has discovered a similar harmonic function for the Speed of Light in miles per second, as Cathie did in his own harmonic system.

The most amazing point of all was not addressed by “The Code Gang” in this article, though, and that is the centering on the square root of five as being so important. What we see, when investigating Robert Lawlor’s book Sacred Geometry, is that the internal measurements of all the Platonic Solids are a function of phi, square root of two, square root of three and square root of five.

And so, the connection is obvious — the hidden mathematical properties of light reveal that it is traveling in a spiral formation, which is exactly what Ra tells us in the Law of One series. These spiraling lines or “superstrings” in the sea of energy known as the “aether” then form the framework for the different Platonic Solids.

Remember that we just showed above how the lengths of the sides of the Platonic Solids can all be expressed in terms of phi and the square root of two. However, a cube with a side length of 1 will have a diagonal of the square root of two on each of its faces, and if you draw a diagonal through the center of the cube between two points, its value is the square root of 3.

In addition, when we measure the diameters of these shapes, and their harmonic relationships, one of the most important ratios of all is indeed the square root of five. In Lawlor’s words,

The square root of five is the proportion which opens the way for the family of relationships called the Golden Proportion, [or the phi ratio.] The Golden Proportion generates a set of symbols which were used by the Platonic philosophers as a support for the ideal of divine or universal love.

It is through the Golden Division that we can contemplate the fact that the Creator planted a regenerative seed which will lift the mortal realms of duality and confusion back towards the image of God.

So, the connection of the square root of five to the Platonic Solids is the fact that the phi ratio grows directly out of it. Now we can see from the work of Carl Munck that the Speed of Light is also directly a function of the square root of five, and furthermore that the square root of five is directly a function of the Gematrian Numbers.

This is the cornerstone that we have been waiting for. We have already expressed the harmonic link between these “perfect” harmonic numbers for the vibrations of sound in air. These “perfect” numbers only come about when we measure them against one second of time as we now have it.

If our seconds were shorter, the harmonic ratios would still be preserved, but they would not be whole numbers any longer. It appears that the second of time that we now use from the Sumerians gives us perfectly round numbers for the vibrations of each note in the Octave.

This alone suggests a high level of scientific knowledge that went into this apparently archaic system of measurement. That only further strengthens the case for why we will see in later chapters that they also formulated the Constant of Nineveh, a number that allows all planetary orbits to be quickly calculated, as being expressed by a value in seconds.

It is only with the second that we now use that these frequency numbers are all round and rational. And, that second of time is a precise harmonic breakdown of one Earth day of 24 hours of 60 minutes with 60 seconds each.

We know that the Gematrian Numbers are all based on the number 9 as a foundation. Cathie showed us that if you convert our time units from a ratio of 8 to a ratio of 9, at 27 “grid hours,” then we have a measurement of “grid seconds” that shows us the harmonic “frequency number” of 144 as the Speed of Light in free space. We also see the “frequency numbers” coming out much clearer in the division of the number of Grid seconds per day.

So, in short, we now have a quite sufficient amount of scientific proof to show us that the Platonic solids are indeed a function of the mathematical expansion and contraction of curving superstrings in a spherical energy field, forming natural shapes such as what Hoagland would refer to as a “three-torus” when constructing a tetrahedron, for example.

This same information regarding spiraling lines of light was revealed to us by Ra and other sources, and now we have gone in and directly seen it mathematically. These superstrings travel at the speed of Light, and now with the work of Cathie and Munck we can see how the spirals themselves are functions of Light.

The harmonic frequency numbers, expressed in Gematria, are completely woven into this “fabric” of space and time.

So, what we essentially have here is a bullet-proof mathematical design that incorporates all of these various points together. We can see how these consciousness units function in their “inward coalescing” capacity by their effects on a planetary energy field.

Just as Ra told us that the consciousness units’ inward expansion creates gravity, so too do we now see with the Becker / Hagens grid that gravity demonstrates in a quite literal fashion how these various Platonic shapes emerge. The actual lines of force created by the shapes have a direct effect on the shaping of continental landmass.



Further information has now come our way regarding a direct mathematical connection between Platonic geometries and the harmonic number sequence.

As we briefly mentioned before, at the end of a MUFON conference in 1997, Richard Hoagland gave a sneak-preview of unpublished research that revealed that the orbit of Mars had once been exactly 666 Martian days in length, which is a clear harmonic number.

We already know that the Earth’s orbit could well have been 360 days exactly at some point in the past, and that this might be one explanation for why we have used 360 degrees in a circle.

So, Enterprise Mission associate Erol Torun decided to see what would happen if 666 degrees were used in a circle instead of 360.

They already had a collection of all the significant angle relationships between the various sections of a tetrahedron circumscribed within a sphere, and with few exceptions these were decimal-point values. Hoagland revealed that when 666 degrees are used, all of these values become whole numbers!

In the table on the next page, we have demonstrated this with our own calculations, based on Hoagland’s suggestion.

The first column shows the tetrahedral angles in a 360-degree system, the second column shows what the exact figure must be to harmonize with a 666-degree system precisely, the third column shows the value in the 666 system and the fourth column indicates how “harmonic” the 666 value is.



Harmonic Val. 666 Y/N


3.783783783784 7 Y
19.5 19.45945945946 36 YYY
22.5 22.70270270271 42 Y
34.7 34.59459459459 64 YY
45.0 45.40540540541 84 YY
49.6 49.72972972973 92 NNN
52.0 51.89189189189 96 YYY
55.3 55.13513513514 102 NNN
60.0 60.0 111 NN
69.4 69.18918918919 128 Y
85.3 85.40540540541 158 NNN
90.0 89.72972972973 166 NN
94 94.05405405405 174 N
184 183.7837837838 340 NA


As we can see from the chart, the more “Y’s” there are, the more harmonic the number is, and the more N’s there are the more non-harmonic the number is. If we look at the column of Y’s and N’s, we can see that a clear waveform is visible. [No information was available on our harmonics chart regarding the last number, hence the NA.]

In order to truly see it well, we would have to graph the N’s as indicating force points in the opposite direction. Therefore, it is very interesting for us to see that the true harmonics of the tetrahedron shape appear to be a combination of very harmonic numbers and very non-harmonic numbers.

In the cases where the N’s emerge, there are very few numbers that divide into the number itself, and in the cases with many Y’s the numbers are harmonic, meaning that they have a maximum number of divisors.

Considered together, this information reveals a tremendous amount. We now have solid mathematical proof from the Enterprise Mission that connects the angles of one of the main Platonic geometries (and almost certainly the others as well) to the harmonic number series.

Furthermore, the singularly important “19.5” number, representing the most significant portion of the circumscribed tetrahedron, is the precise harmonic of the number 36, which is by far one of the most harmonic numbers of all.

In the triangle-shaped “tetracys” from Pythagoras, there are 36 rows of dots starting with one dot at the top and ending with 36 dots at the bottom. Together, this forms a triangle, and it also represents a simple system of harmonic counting.

When we summarize all the dots in the triangle together, we come to that same cornerstone ‘solar’ number, 666.

Therefore, as we look at harmonic numbers showing up in the Solar System in Part Three, we have more reason than ever to see that they can be directly connected with Platonic geometries. Even the speed of light itself appears to describe a harmonic spiral that Cathie equated with 144 in his harmonic time system based on a proportion of nine.

Before we enter into our final discussion regarding time cycles, we will finish out our look at the history of this knowledge. By examining the trickle-down effect of Atlantean knowledge into past and present “secret societies,” we can indeed trace how it was that literally all of the knowledge that we have been discussing was carefully preserved.

We will explore how it was that ancient peoples chased after these Grid energies one line at a time, through the amazing study of “ley lines” and how they emerge all over the planet. We will also explore an amazing twist to the story, by showing how a present-day secret society still exists which has never lost this knowledge.

This secret society was responsible for the formation of the United States Government, and lent its hand quite directly in the building of the United Nations Meditation Room.

We will show the amazing quality of this room, and suggest that it is indeed a hyperdimensional “machine,” built on the premises of this carefully guarded secret knowledge that is gradually becoming available to the public.