Pyramides de Memphis- cropped image- 201

The Great Pyramid

an Equation in Stone, a 4,500-Year-Old Mystery Solved

D. Arthur Gusner

Cover image derived from:
Vue de l'entrée de la Grande Pyramide, prise au soleil levant.
(View of the entrance to the Great Pyramid, taken in the rising sun.)

1809 - 1828
Source: The New York Public Library


   Foreword: A Brilliant Puzzle

Ernest P. Moyer observed:

In spite of the numerous attestations nothing could be more troublesome to modern scholarship than the search for the source of the ancient cubit measure. The answers go from human body parts to catalogues of numerous guesses.1

The surprising conclusion of that scholarly search is clearly demonstrated in the “Great Pyramid - An Equation in Stone: 4,500-year-old Royal Cubit Mystery Solved.” This brief paper offers evidence establishing new insights into the fundamental design of the Great Pyramid, including discovery of the original source of the “ancient cubit measure”—the Egyptian royal cubit.

According to modern accepted world history, the scientific knowledge encoded in the structure of the Great Pyramid simply could not, and did not, exist. The cut stones, however, do not tell lies. They unquestionably establish that a startlingly high level of scientific knowledge existed more than four thousand years ago.

It is often said that no structure in the world is more mysterious than is the Great Pyramid. Currently accepted dating declares the Great Pyramid was built by Pharaoh Khufu (or Cheops) in the fourth dynasty and completed in BC 2560. It is generally acknowledged to be the oldest and largest of the three pyramids located in the El Giza necropolis.

The evidence presented herein demonstrates that the underlying design of the Great Pyramid constitutes a brilliant intellectual puzzle, one firmly based on general physics and combining units of time and distance. The Great Pyramid is a scientific database with the stored information retained in cut stone.

This paper provides evidence supporting the conclusion that the builders intentionally left behind a concise set of clues, evidently desiring the scholars of later generations to unravel and solve the enigma they posed. The author's discovery of the source of the royal cubit also reveals the existence of a challenging new mystery: the existence of a sophisticated ancient scientific knowledge.

The author provides evidence that, contrary to many current scholarly assumptions, the builders of the Great Pyramid of El Giza commonly used units of hours, minutes, and seconds. This fact provides important new insights, and clear evidence, that the Great Pyramid builders possessed and applied a working knowledge of the physical sciences that included astronomy, the knowledge of the speed of sound, known dimensions of the Earth, and an ability to precisely measure vibrations in units of cycles per second. The unexpected evidence provided within this paper will necessitate the reconsideration of many of the mistaken presumptions put forward by the established academic community.

1 Accessed 10 September, 2019,

   1. Introduction

In “The Dimensions of the Great Pyramid,” the noted late scholar Professor Livio Catullo Stecchini firmly debunked any notion that the dimensions of the Great Pyramid might contain any “mysterious” meaning. He wrote “pyramidism is a stubborn disease,” which he termed “pyramidite delusions.” Unsurprisingly, many scholars and Egyptologists agree, and they tend restrict the academic study of the Great Pyramid to approved subjects.

Nevertheless, a cursory survey of articles about the Great Pyramid on the internet reveals “pyramidism” is alive and flourishing. This raises a query: are there really undiscovered mysteries still to be revealed within the pyramid measurements? The answer is unconditionally yes. The Great Pyramid can be understood as a gift from the builders to mankind. It represents a truly grand puzzle left behind for unborn generations to ponder and to solve.

This is an original work written for a general audience; therefore, it is not prepared in conformance with a particular academic format in mind. The evidence submitted herein is plainly stated, self-supporting, and although unexpected and exciting, it should not be deemed controversial. It is the author's hope the paper will energize healthy discourse within open and expanding conversations, thereby helping further associated research. The information presented should uplift and encourage scholars to continue following the clues that the Great Pyramid builders helpfully provided for that specific purpose.

   2. The Challenge Accepted

It was respect for the masterful achievements of the builders that encouraged the author to take up the challenge they placed before the future. The submitted evidence herein consists of but a brief fragment of decades of considerable contemplation. Among the many remaining and tantalizing questions is, precisely who were the builders, and what was their motivation when constructing the largest building on Earth—the Great Pyramid?

The Great Pyramid remains, intentionally or otherwise, the builders' gift to mankind. It is a truly grand puzzle left behind for unborn generations to ponder and to solve. That the builders wanted their puzzle solved is plainly indicated, because they left behind a concise set of carefully linked clues, a trail of “breadcrumbs” leading directly to its solution.

   3. Beginnings

Long ago, and precisely how long ago may reasonably be challenged, a gentle breeze moved across an open fertile landscape as the sun arched toward its zenith. A few people had gathered together at a precisely selected geographic coordinate point to survey an unobstructed vista, one that nature had obligingly prepared for their grand purposes.

The selected geophysical site was accurately located at the northern latitude of 30°, where the builders would bring into existence a colossal stone enigma. When it was completed and carefully sealed within a casing of polished white limestone, the Great Pyramid would survive the stormy assault of millenniums—only to be broken open by the pillaging thievery of robbers (reputedly by Caliph al-Ma'mun circa AD 820). During a massive earthquake in AD 1303, the Great Pyramid’s outer casing stones were loosened and damaged. Continuing damage resulted afterward from ceaseless looting and scavenging of these casing stones.

When first completed, the polished white limestone casing of the Great Pyramid shone so brightly in the sunlight it was known as “glorious light.”2 Today, the surviving rough bulk of what the builders had so meticulously fashioned still provides clues that challenge discerning people to seek after some deeper meaning.

Among the greatest of all the unsolved mysteries the pyramid builders left in their wake, are their identities, motives, and an accounting of their dominion over boundless resources. The builders undisputedly had access to a vast wealth, and they lavishly expended that wealth upon their project. The sheer enormity of the incurred construction costs pronounces the importance that the builders attributed to their construction. By the fruits of their efforts, both appreciated and unappreciated, they have had an impressive influence upon future generations.

Of the three pyramids located in the El Giza necropolis, the Great Pyramid is acknowledged as the oldest and largest. Currently accepted dating declares the Great Pyramid was built by Pharaoh Khufu (or Cheops) in the fourth dynasty and completed BC 2560. Many relevant questions concerning the Pyramid and its construction remain unanswered.

Clearly, the builders of the Great Pyramid created upon the El Giza plateau a precise stone structure above ground. They also excavated complex tunnel systems and chambers below ground. The scientific knowledge, engineering techniques, advanced construction methods, financial resources, and management skills required to achieve their carefully designed project were enormous. The physical project they completed, the tallest and largest building then on Earth, was on the same improbable scale.

Regretfully, when many people view the remaining ruin of the Great Pyramid, they seldom consider or comprehend what genius was actually required to transform the underlying knowledge and management principles into a design and then execute that design to create the massive physical reality of the structure. In terms of complexity, few if any structures on Earth today rival what was erected on the El Giza plateau in millenniums past.

The unavoidable first question is: did the Egyptian culture of BC 2560 possess the scientific knowledge and management skills evidenced in the material form of the Great Pyramid or were they imported? If imported, by whom and from where? Where are the comparative examples and associated scholarly studies supporting a similar scientific level of knowledge?

At its core, the summation of the builders' knowledge, resources, intellect, and labor constitute a message in stone sent across time. Why? What was their motivation and intent? Was the whole project, as some suggest an undertaking to permit a few men to achieve transcendence, thereby allowing the initiates into a sacred mystery—the knowledge of which was life eternal?

Conversely, perhaps it was built as a warning sent by those who then still retained the scientific knowledge of a poorly studied and understood golden age. Proponents of this theory speak of the “First Time,” known as Zep Tepi,3 that flourished before and immediately following a global devastation—a devastation possibly caused by one or more cometary strikes. These as-yet poorly studied global catastrophes are currently simply labeled “the Younger Dryas.”

Perhaps the gifted builders labored to construct the Great Pyramid in order to inform following generations that once, long before their era, people of science and understanding had lived and prospered. Ultimately, in spite of all their knowledge and technology, they were unable to hold back the descending curtain of darkness.

If true, then the surviving products of their minds, gifted hands, and wealth may represent a still unheeded warning: what happened before could happen again. Humanity and Earth itself remain in peril.

2 Accessed 6 October, 2020,

3 Accessed 7 January, 2020,


   4. A Singular Artifact

Circa AD 832, robbers reputedly being directed by Caliph al-Ma'mun crudely hammered and smashed their way within the Great Pyramid (creating what today the tourist guides call “the robber's tunnel”). They reputedly found no treasure or concealed records within. More notably, the normal Egyptian royal tomb hieroglyphics were absent from the interior walls; the Great Pyramid is therefore said to be “mute.”

Surprisingly, only a singular significant artifact was found within the Great Pyramid. That artifact was, and is, located within the King's Chamber. It is a roughly finished and empty granite coffer.

There are Egyptologists who even now confidently proclaim the pyramid was built as a royal tomb and that the singular coffer was intended to receive the royal sarcophagus. Nevertheless, there is no covering lid for the coffer or a royal sarcophagus anywhere to be found.

It is the very absence of a mummy or hieroglyphics or other records within the Great Pyramid that provides the scholar with the first anomalous and important clue. Presuming there is no hidden vault yet to be found, any surviving mysterious message or deeper meaning within the Great Pyramid must be concealed within the pyramid itself and the measurements of its cut stone, waiting patiently in plain sight for those having eyes to see.

   5. Following the Trail of Breadcrumbs

The lure of the pyramids rising above the El Giza plateau evokes within millions of people a yearning to better understand these enigmatic structures. In 1971, Mr. Peter Tompkins published his foundational work, The Secrets of the Great Pyramid. The beautiful book presents an exceptional description of what was then understood about the Great Pyramid. Fifty years later, the book remains a valued resource and a favorite. Millenniums after its construction, tour guides today imaginatively claim to be descendants of the same Egyptians who built the Great Pyramids as they weave fanciful stories for visiting tourists. The known facts, however, do not support their claim that the Great Pyramid was built to be a tomb.

Like the tour guides, casting awkward facts aside, scholars find little problem writing the purpose of the granite coffer found within the King's Chamber was only to enclose the royal sarcophagus. Indisputably, no sarcophagus or mummy was found within the Great Pyramid—let alone reposing in peace within the granite coffer. Why then did the builders leave this singular artifact, the empty granite coffer? Perhaps a logical answer may be surmised by examining the physical qualities of that unique stone artifact.

Physically, the dimensions of the coffer (in millimeters) are:

Outer - L: 2,278; W: 977; H: 1,048; and the Volume: 2,332,435,088
Inner - L: 1,977; W: 677; D: 872; and the Volume: 1,167,110,088

When the outside volume is divided by the inside volume the result is 1.998; the ratio is essentially 2:1. The builders precisely cut out a cube of solid granite to a previously calculated dimension, then painstakingly and exactly bored out one half of that volume. The measured void of the coffer has nothing to do with the dimensions of an imaginary royal sarcophagus. The granite coffer is a crafted resonant cavity, one carefully cut and tuned to resonate at a predetermined precise frequency, as we shall see.

The extraordinary resonance qualities inherent within the entire design and construction of the King's Chamber and its granite coffer are not a speculative “pyramidism” or some crank theory. They are well established and demonstrated physical facts.

The granite walls of the King's Chamber do not rest on the visible floor, but rather rest on a sub floor. The floating floor itself has twenty carefully laid stones, arranged in six rows, and nine large granite stones comprise the ceiling of the King's Chamber. Like the coffer, the floor and ceiling were designed and fabricated to resonate. Clearly, the builders were following known relationships involving vibrating objects, and were fully capable of using solid granite to vibrate like a tuned bell. The implications of this demonstrated technology is far reaching.

One measured resonant frequency of the coffer is 438 cycles per second (cps), or essentially 440 cps. Someone has damaged one corner of the coffer; this perhaps may explain the slight variance of 2 cps. Also, the accuracy of the hand held electronic instrument used to make that measurement, while presumed accurate, is unknown. Nevertheless, when beginning with a solid block of granite, even a variance of 2 cps (0.454%) is a respectable tuning.

The dimensions of the floor in the King's Chamber (20 by 10 royal cubits), like the volume of the coffer, incorporate the ratio of 2:1. Professor Livio Catullo Stecchini, in his interesting paper, “The Dimensions of the Great Pyramid,” wrote, “The angle of the corridors of the Great Pyramid, to which pyramidites have ascribes [sic] profound pseudo-mathematical meanings, is the result of a ratio 1/2.”

While striving to avoid being associated with “profound pseudo-mathematical meanings,” when a basic ratio like 2:1 is repeatedly encountered, prudence suggests that it may be a breadcrumb.

Given the ratio of 2:1 is tightly associated with a carefully designed and painstakingly crafted resonant King's Chamber and its associated resonant granite coffer, the ratio of 2:1 plausibly relates to the definition of an octave:

An octave is a series of eight notes occupying the interval between (and including) two notes, one having twice or half the frequency of vibration of the other.4

The musician, Paul Horn wrote of his own visit inside the King's Chamber in the Great Pyramid. In May of 1976, he was able to play his flute and later wrote:

The moment had arrived, it was time to play my flute,5 I thought of Ben Pietsch and his suggestion to strike the coffer, I leaned over and hit the inside with the fleshy part of the side of my fist. A beautiful round tone was immediately produced. What a resonance! I remember him also saying when you hear that tone you will be “poised in history that is ever present”. I took the Korg Tuning Trainer I had brought along in one hand and struck the coffer again with the other and there it was - 'A' 438, just as Ben had predicted. I tuned up to this pitch and was ready to begin.6

Decades after Paul Horn played his marvelous flute, Tom Danley took a wide assortment of electronic sensors and equipment into the King's Chamber. On March 10, 2017, as he wrote in, “The Great Pyramid: Early Reflections & Ancient Echoes”:

I crunched the results of the measurements, and they were sent on to a musicologist that was part of the staff. As mentioned, he identified that there was a pattern of frequencies, which roughly form an F-sharp chord? Not all the resonances fell in the right place but many did and some repeated the pattern for many octaves. In other words, it was roughly tuned to F-sharp over many octaves. 7

Tom Danley also wrote, “Egyptian texts indicate that this F-sharp was the resonant harmonic center of planet Earth.”8 This is an interesting statement, and it echoes around the internet, however, a reliable primary source for the reference was unable to be located. Nevertheless, the identification of an F-sharp chord as being a chord that the King's Chamber is roughly tuned to is of inherent value, being yet another breadcrumb.

Just for fun, try taking up and blowing a random note on a flute, or else strum a string on a guitar. Then, without instrumentation, precisely count how many cycles a second (cps) that tone is vibrating. With a “good ear” a musician can identify a note and tune an instrument to that note, but precisely measuring its vibration rate by ear is another matter.

Whenever the pyramid was built, its builders possessed the scientific knowledge and technical capability to tune a block of granite to a desired tone, and in doing so they knew the frequency of that tone expressed in cycles-per-second. But how?

Oops. Some historians might proclaim the last statement is a wild unsupported pyramidism, since it is obviously impossible. Quoting from Wikipedia:

Although Mersenne had made a rough determination of sound frequencies as early as the 17th century, such measurements did not become scientifically accurate until the 19th century, beginning with the work of German physicist Johann Scheibler in the 1830s. The term formerly used for the unit of pitch, cycle per second (CPS) was renamed the hertz (Hz) in the 20th century in honor of Heinrich Hertz.9

There is no intent to minimize the earnest work of the German physicist Johann Scheibler, however, the tuned stone coffer demonstrates that more than four millenniums before his valued work, the pyramid builders were fully aware of the relationship between a tone and its frequency, and they could accurately measure frequencies in cps. They also could produce precise 90-degree corners, both within and on the outside of hard granite stone objects, and they could join large adjacent stone sections with such a fit that a thin paper cannot be inserted into the seam.

4 Accessed 9 September, 2019,

5 (Paul Horn playing flute in King's Chamber) Accessed 7 October 2020,

6 (Liner Notes) Accessed 7 October, 2020,

7 Accessed 7 October, 2020,

8 Accessed 7 October, 2020,

9 Accessed 7 January, 2020,


  6. The Problematic 440

Direct measurements establish the resonance of the granite coffer in the King's Chamber at essentially 440 cps.10 The statement that measuring frequencies in cps did not become scientifically accurate until the 19th century is strictly speaking incorrect. Such unquestioned assumptions being accepted as historical fact can stifle the search for truth.
Another common presumption accepted as fact is found in the definition of a cubit:

…any of various ancient units of length based on the length of the forearm from the elbow to the tip of the middle finger and usually equal to about 18 inches (46 centimeters)11

The definition stated above is often repeated. But in relationship to the Egyptian royal cubit and the Great Pyramid, as will be demonstrated, the common definition is utter nonsense.

Likewise, some intelligent people might reasonably believe it is absurd for anyone to propose that in BC 2560 the Great Pyramid builders commonly used 24 hours in a day, 60 minutes in an hour, 60 seconds in a minute, let alone claim they could accurately measure a frequency of sound in cps. That the builders did so shall be demonstrated. When creating the granite coffer, the builders precisely fabricated a cavity in a block of granite that produces a tone of essentially 440 cps. That frequency is not some random value, it is purposefully precise.

Moreover, the measured frequency of 440 is not merely a happenstance frequency determined by some modern electronic instruments. The 440 frequency was calibrated in cps by the builders, and the numerical value of 440 reoccurs structurally in the fundamental dimensions of the Great Pyramid. The value of 440 units is the measured length of each side of the Great Pyramid, that length being 440 Egyptian royal cubits.

10 Accessed 7 January, 2020,

11 Accessed 9 September, 2019,

   7. The Egyptian Royal Cubit

When discovering the original source for the unit of measurement called the Egyptian royal cubit, some circular reasoning was required—similar to asking, “Which came first, the chicken or the egg?”

While the answer to the egg problem is fairly obvious (the egg), the answer to the question of the royal cubit is not. As used in the Great Pyramid, the Egyptian royal cubit is a dependent and arbitrary value. Unless that fundamental fact is understood, discerning its source is not only problematic—it is improbable. The precise physical length of a royal cubit, as measured on the Great Pyramid, depends upon whose approximation is being used. The commonly accepted unit length for the Egyptian royal cubit is 20.626 (English inches).12

Historically, the approximate value of the length of the royal cubit was obtained by the British archaeologist Sir William Matthew Flinders Petrie, who surveyed and measured the Great Pyramid with care and precision. In his detailed report, The Pyramids and Temples of Gizeh, he wrote:

The four sides [speaking of the King’s Chamber] there yield a mean value of 20.632 ± .004, and this is certainly the best determination of the cubit that we can hope for from the Great Pyramid.13

The expressed value is a calculated average of multiple measurements, and the reported value is a coarse measurement, being an approximation in the hundredths of an inch.

Before the builders aligned and stretched the first survey cord on the ground, they first derived a fundamental scientific equation, one having specific coefficients. That physical science and architectural equation then governed the overall dimensions of the Great Pyramid. In discovering the builders' brilliantly conceived and executed “equation in stone,” an underlying and sophisticated level of scientific knowledge is revealed. That the builders chose to work with painstaking care in stone, a medium capable of withstanding the ravages of thousands of years, suggests that from the outset the builders desired the Great Pyramid to be a lasting beacon marking a historical database of information stored in cut stone. They have achieved their goal. Their carefully stored information has successfully conveyed a message across millenniums for interpretation by future generations.

The precise geodetic position of the Great Pyramid (30 degrees north latitude), coupled with its mathematical design, displays a sophisticated knowledge of astronomy, general physical science, and geodesy (in particular a knowledge of the equatorial and polar circumferences of the Earth). In fact, the Great Pyramid provides ample evidence demonstrating a working understanding of astronomy—specifically precession, the physical sciences, a 24-hour day, a 60-minute hour, a 60-second minute, and the capability to precisely measure frequencies in cps. It is not surprising that when achieving their purpose on a grand scale, the builders' equation in stone pivots about the integer 440 and the measured length of the royal cubit.

12 Accessed 24 January, 2020,

13 Accessed 24 January, 2020,

   8. Discovery of the Elusive Source of the Egyptian Royal Cubit

Today, we understand that the frequency of a particular musical note (measured in cps) in an elastic medium is inversely proportional to a unit of measured length—that being the wavelength of the frequency. The higher the frequency, the shorter the wavelength. The product of the two variables, frequency and wavelength, equals a third variable, the velocity of sound within the elastic medium. Simply stated, frequency multiplied by wavelength equals velocity.

The velocity of sound itself is a variable dependent on other variables, such as pressure and temperature. According to ScienceDaily,14 at sea level, and at a temperature of 70 degrees Fahrenheit, and under typical atmospheric conditions, the speed of sound is about 770 mph or approximately 1,129.33 feet per second.

Under these typical conditions, a frequency of 440 cps has a calculated wavelength of 30.799 English inches. Even using the generous standards of approximation, the calculated wavelength is not anywhere near the accepted length of an Egyptian royal cubit, that of 20.626 English inches. Nevertheless, when the royal cubit length of 20.626 is divided by the calculated 440 cps wavelength, 30.799, the result is 0.6697. This calculated value is but 0.003 from the numerical fraction of 2/3.

Therefore, as demonstrated above, the length of the accepted Egyptian royal cubit is approximately 2/3 of the calculated wavelength of a frequency of 440 cps, when the velocity of sound is 1,129.33 feet/second, a typical velocity of sound as defined by ScienceDaily.

The relationship between the length of the royal cubit and the wavelength of a specific frequency has many profound historical implications. Undoubtedly some scholars may initially consider the demonstrated relationship to be merely coincidental. Nevertheless, the variance of 0.003 and related supporting facts, presented below, clearly establish and demonstrate it is not a coincidence.


Momentarily setting aside the important issue of just why the builders adopted a scaling coefficient of 2/3 when defining the royal cubit, the source of the Egyptian royal cubit can now be defined: The Egyptian royal cubit is the standard unit of length that the builders adopted when constructing the Great Pyramid; the source for the royal cubit is 2/3 of a specific wavelength of a 440-cps sound in air.

Using 3/2 times the accepted Egyptian royal cubit length of 20.626 English inches, yields a “royal cubit wavelength” of 30.939 English inches. When this calculated royal wavelength is multiplied by 440 cps, the product is a velocity of sound of 1,134.43 ft/sec. This unique calculated value will hereafter be referred to as the “royal cubit velocity.”

An interesting point of observation, and pure speculation, is that there are nine stones (beams) in the ceiling of the King's Chamber, and 6 rows of stones on its floor. The apparent ratio of 9:6 can be reduced to 3:2. Is this important fundamental fraction another missing breadcrumb? It may well be. What is clear is the floor contains 20 stones. If it had contained 18 stones, then the 2:1 ratio of stones observed elsewhere would have been maintained. It was intentionally not maintained—suggesting the 3/2 relationship of the stones was intended.

It is noteworthy that the calculated value of the royal cubit velocity differs from the typical velocity of sound defined by ScienceDaily15 by more than four thousand years, but only 5.1 feet/second. There are many apparent controversial issues embedded within the forgoing definition for the royal cubit velocity. Such as, it may be construed that in BC 2560 (or earlier) the builders possessed a proficient understanding of a velocity of sound in air, the interrelationship between the velocity of sound and a frequency measured in cps, and were capable of precisely calculating the wavelength of a tone.

Accordingly, given the expressed frequency of 440 cps, the measurements of frequency were made using units of seconds, and therefore the builders had an accurate means of precisely measuring time and a frequency in cps. For many obvious reasons, such a technical capability is remarkable and significant. Simply acknowledging the revelations of these surprising historical anomalies will upset many current, but now apparently erroneous, scholarly presumptions.

In summary, the very cut stones of the Great Pyramid firmly establish the builders made calculations using standard units of frequency in cycles per second, and were capable of precisely measuring time, the frequency of a tone in cps, and the corresponding velocity of sound.

While the builders' motivations for leaving a marvelous empty musically-tuned granite coffer in the similarly tuned King's Chamber is unknown, the granite coffer has definitely served as the essential connecting clue or breadcrumb permitting the unraveling of the source of the Egyptian royal cubit. Perhaps that was the entire reason why the builders left the empty coffer behind. It is noteworthy that, given its dimensions, they also assured the coffer could not be moved through the descending passageways and removed from the Great Pyramid. They were very considerate when leaving behind a chain of clues.

13 Accessed 10 September, 2019,

15 Accessed 10 September, 2019,

   9. Geodesy, Coefficients, and Physical Science

By definition, a nautical mile is the measured length of a minute of arc at the equator.16

Therefore, the circumference of the Earth at the equator is precisely 360 times 60 or 21,600 nautical miles. Because of this precise definition, a nautical mile represents a very useful unit of measure. When calculating the length of a nautical mile in English feet, it is first necessary to choose an official accurate source for the equatorial circumference of the Earth.

According to NASA online data, the equatorial circumference of Earth is 24,873.6 English miles.17 There are 5,280 feet in an English mile. By way of comparison, the National Geodetic Survey reports, “A currently accepted value for the earth's circumference at the Equator is 24,901 miles, based upon the equatorial radius of the World Geodetic System.”18 The difference between the two approximations of the circumference of Earth is 27.4 English miles.

For the limited purposes of this paper, the NASA measurement is herewith adopted as being “official.” Therefore, herein a nautical mile is “officially” defined as 6,080.213 English feet. This value is also in general agreement with the length of a nautical mile as found in an old well-worn copy of Duttons Seamanship and Navigation: 6080 feet. By comparison, the World Geodetic System value produces the “unofficial” length of 6,086.91 feet per nautical mile.

Now, boldly entering into the perilous arena of pyramidism, it is possible to demonstrate that the builders did in fact work in a 24-hour day, a 60-minute hour, and a 60-second minute, and also precisely measured tones in cps. The question momentarily set aside previously was: when the builders defined the length of an Egyptian royal cubit, why did they scale the calculated wavelength of a 440-cps tone by 2/3?

Because 1/3 and 2/3 are fractions often encountered in legend and in religious mysteries (such as Gilgamesh being two-thirds god and one-third human, and the Biblical tale of one-third of the stars falling to Earth), discerning why the builders used 2/3 proved problematic. The eventual resolution of the puzzle was found within physical science and geodesy, not within mystical or pseudo-religious numbers.

In their design, the builders first adopted a brilliant method for preserving their knowledge of physical science, including the then-known equatorial and polar circumferences of the Earth. They conceived a fundamental equation, one based upon physical science, and that equation dictated the 2/3 scaling factor.

Sir William Matthew Flinders Petrie established that each side of the Great Pyramid measures 440 Egyptian royal cubits. As demonstrated previously, the Egyptian royal cubit is based upon a scaled value of the wavelength of a 440-cps tone. General physical science confirms a frequency measured in cps multiplied by its wave length equals the velocity of the wave. Therefore, the underlying design of the Great Pyramid is predicated upon established physical science units of frequency and wavelength corresponding to a precise velocity of sound in air.

Multiplying the 440 (frequency) times the unit length of an Egyptian royal cubit yields a scaled value of velocity of sound, 2/3 times the royal cubit velocity of sound in air; where the 2/3 is a pure numerical coefficient. But again why 2/3?

Indisputably, the pyramid has four unique and equal sides. Therefore, the underlying equation in stone can be expressed as: 4 times 2/3 times 440 cps times the royal cubit wavelength, or 8/3 times the royal cubit velocity of sound.

Thus far, the pure coefficient of 8/3, the royal cubit wavelength (30.939 English inches) and the royal cubit velocity of sound (1,134.43 feet/second) are identified, but again what does it mean?

16 Accessed 19 October, 2019, questions/question79.htm

17 Accessed 19 October, 2019,

18 Accessed 19 October, 2019,

   10. The Great Pyramid is a Scientific Database

The Great Pyramid is constructed of cut stone, and can be viewed as a database the builders intended to survive millenniums, and even the ravages of earthquakes and centuries of plundering. Therefore, the builders must have knowingly left behind the necessary pointer or datum needed for scholars to understand their grand puzzle and underlying equation—some breadcrumb located in plain sight.

The logic problem posed by the builders is similar to the previous riddle of the egg. To discern the needed clue, it is necessary to once more examine one of the most apparent clues or breadcrumbs, the noted frequency of 440 cps.

As shown, the builders used a frequency of 440 cps and a measured wavelength to define a unique velocity of sound. But when that velocity of sound is held constant, the builders might optionally have chosen any frequency, such as 330 or 400 or 500 cps, and while the wavelengths would vary accordingly, the intended velocity of sound would remain constant. So, why, other than choosing a frequency whose scaled wavelength clearly established the physical size of the Great Pyramid, did the builders choose a frequency of 440 cps?

As some have theorized, perhaps the builders chose 440 cps because of a mysterious resonant frequency at the center of the Earth—but there exists a far more probable and logical reason for their choosing 440 cps. That unique choice of a frequency points directly to a specific interval of time; and, when a velocity is multiplied by an interval of time, the product equals a distance.
Accepting Occam's razor as a guide, when 24 hours/day is multiplied by 60 minutes/hour the product is 1,440 minutes/day. By choosing 440 as the frequency, the builders provided us with the missing and necessary breadcrumb. It is a direct pointer to a precisely defined interval of time, a day consisting of 24 hours, or 1,440 minutes, or 86,400 seconds.

In 24 hours, a wave traveling at a leisurely royal cubit speed of 1,134.43 feet/second travels 98,014,752 feet. Is there a prime significance to this calculated distance? Although not readily apparent, the answer is definitely yes.

First, converting the distance into “official” nautical miles, the calculated distance traveled is equal to 16,120.28 nautical miles. When this calculated distance is divided by the “official” circumference of 21,600 nautical miles, the result is 0.746. This is a difference of 0.004 from 0.75 or 3/4.

Clearly, 3/4 is not equal to 1. Therefore, in order to adjust their royal cubit calculated distance (based on 24 hours times the royal cubit velocity of sound) of 98,014,752 feet to be equal to the then-known equatorial circumference of the Earth, they would need only to multiply the initial calculated distance by an adjustment factor of 4/3, thereby obtaining the underlying Egyptian royal cubit equatorial circumference of 130,686,336 feet, or 24,751.2 English miles, or 21,493.71 nautical miles).

When the adjusted calculated value of the Egyptian royal cubit equatorial circumference of Earth is divided by the NASA official value, the result is 0.995. The difference of 0.005 or 0.5% is not a random product of happenstance or the result of a really good guess. It is a four-thousand-year-old approximation; one creatively derived using the unlikely parameter of the royal cubit velocity of sound and a time interval of 24 hours.

The applied adjustment factor of 4/3 used by the builders to creatively demonstrate their knowledge of physical science and geodesy, and the equatorial circumference of Earth, is expressed as an integral part of the equation in stone: 8/3 multiplied by velocity multiplied by time. Oops, but there is an apparent ambiguity. The adjustment factor used for computing the equatorial circumference was 4/3, but the equation in stone has a coefficient of 8/3, that being twice the equatorial circumference adjustment factor. So, what clue was missed? What is the problem?

Obviously, the builders' knowledge of the circumference of the Earth and their derivation of the equation in stone preceded the actual construction of the Great Pyramid, therefore the builders might have directly compensated for the 4/3 and 8/3 disagreement by simply dividing the length of the royal cubit in half (by using 1/3 as a scaling factor instead of 2/3). That method of correction would, however, also have significantly reduced the size of the monument they wanted to build. The builders obviously rejected that simplifying solution. Consequently, they retained the 2/3 coefficient when calculating the royal cubit. Is there yet another overlooked breadcrumb that might resolve the ambiguity?

As stated previously, the angles of the interior corridors, dimensions of the floor in the King's Chamber, and the outside-to-inside volume ratio of the coffer all exhibit a 2:1 ratio, and as noted, this suggests the ratio might be a breadcrumb. Applying this ratio to the indicated 24-hour time span, while retaining a relationship with music and the 2:1 of octaves, redirects the time span pointer from 24 hours to an interval of 12 hours.

Repeating the previous calculations involving 24 hours, but substituting a 12-hour interval predictably produces the following: The distance traveled in 12 hours is equal to the royal cubit velocity (1,134.43 feet per second) times 43,200 seconds, or 49,007,376 feet, or 8,060.14 “official” nautical miles. When this calculated distance in nautical miles is divided by the “official” circumference of 21,600 nautical miles, the result is 0.373. Comparing this value to 3/8, or 0.375, the difference is 0.002, a near match. Using these values, the equatorial circumference adjustment factor becomes 8/3, which adjusts the 12-hour distance traveled to approximate the Earth’s equatorial circumference. This adjustment brings the calculation into whole agreement with the coefficient in the equation shown in stone: 8/3 times the royal cubit velocity.


   11. Physical Dimensions of the Great Pyramid

It was stated near the beginning of this paper that “[t]his brief presentation offers clear evidence the builders of the Great Pyramid of El Giza used the units of hours, minutes, and seconds in measuring time.” The use of units of seconds are evident in computing cps, in determining the distance a sound wave travels, in measuring the velocity of sound, and especially in computing the length of the royal cubit.

The number of seconds in 24 hours is 86,400. Dividing 86,400 seconds by 2 yields 43,200 seconds. When 43,200 is used as a scaling factor and multiplied by the physical dimensions of the Great Pyramid, it produces a product approximately equal to the equatorial circumference of the Earth.

To demonstrate the 43,200-scaling factor, first compute the boundary of the perimeter of the Great Pyramid. There are 20.626 English inches in an Egyptian royal cubit, and 440 royal cubits is the length of each side of the Great Pyramid. Multiplying 20.626 times 440 times 4 sides equals 36,301.76 inches. Dividing this value by 12 equals 3,025.14 English feet. When scaled by 43,200, the product is 130,686,048 English feet. Divided by the 6,080.213 feet in a nautical mile the result is 21,493.66 nautical miles. This is a variance of 106.33 nautical miles from the precise equatorial circumference of the Earth, which is 21,600 nautical miles, a difference of 0.492 percent.

The unique scaling value of 43,200 seconds firmly demonstrates the builders worked in seconds. The discovered equation in stone, demonstrated above, illustrates and explains how this scaling factor was derived. The builders were almost playful when defining their brilliant physical science equation in stone. That equation posed a logical challenge to future scholars. As in their other remarkable achievements, they were again proven exceptional and successful.

In conclusion; Quod Erat Demonstrandum.

   Afterword: Reflections and Observations

The builders labored at enormous cost to achieve precision in their construction of the Great Pyramid. Without that exceptional care, the challenge they posed to unborn generations could not have been resolved. Just why the builders felt so strongly it was important to convey an awareness of their level of scientific knowledge to the future remains open for consideration. Again, it is appropriate to ask, who were these remarkable early scientists?

There are many incredible stories of human achievement, including epic tales of courage exhibited during times when humanity was confronted by global disasters and potential extinction. These amazing legends reveal a people possessing the determination to survive. Often buried deep within the intricate stories are wonders of preserved knowledge and remarkable heights of human consciousness that should never be frivolously discounted as nonsense. That such conscious fragments survived in legend when billions of similar fragments perished suggests they are worthy of consideration; there is often a deep taproot of wisdom that preserves legends.

As an example, history and science may well be discovered intertwined within the ancient fabled battle between the Hittite sky god and the dragon Illuyanka. Given its striking contents, that cosmic battle likely occurred 70,000 years ago. Consider, with an open mind, perhaps the awesome battle described in the surviving legend actually happened. Perhaps the source of the legend lies in an interaction between our primary sun and a glowing red dwarf star and its brown companion, which were then towing their trailing collection of planets and cosmic debris.

A modern-day astronomer recently discovered and identified a low-mass star system. That system consists of a brown and red dwarf pair, now nicknamed “Scholz's star,”19 and given the formal designation WISE J072003. Through the calculation of the star’s trajectory, it was determined that about 70,000 years ago the pair of stars (with their orbiting cosmic debris) passed by and “brushed”20 Earth's solar system. Given the reality of the difficulty in precisely calculating relative motion between Earth's constantly moving solar system and a fast-moving dwarf star pair during 70,000 years, the scientifically prudent and cautious word “brushed” should be understood for precisely what it really is. The estimate is an acknowledgment of a course approximation of the proximity of the dwarf star system to our own sun at the point of its closest approach.

If the red dwarf star approached near enough to our sun, it would have become visible in the night sky. The observations of a cosmic battle preserved within multiple legends, such as that of Illuyanka, suggest the dwarf system and its caravan of cosmic devastation did more than “brush” past the outer fringes of our solar system. Given the details preserved within multiple legends, our solar system was directly and materially involved.

One legend speaks of two battles being fought between the sky god and Illuyanka. Such a two-part sequence suggests the binary pair and their associated debris may have performed a “slingshot” around our sun or else the red and brown dwarf stars each separately caused violent solar flares.

The deep root of the legend of the cosmic battle between the Titans and Olympians may also be found in the passing of Scholz's star. For certain, our skies were forever altered after the battle between the Titans and Olympians, some of the Titans having been bound and cast into Tartarus.

Some of the oldest legends were impressed on clay tablets. Miraculously, some of those tablets have survived. One of the oldest such legends dealt with a hero named Gilgamesh, and his saga includes a time of pure terror and global devastation:

   Astonishment at Adad the Storm reached to the very heavens.
   He turned to blackness all that had been visible.
   He broke the land like a pot.
   For a whole day the South Storm blew,
   Gathering speed as it blew, drowning the mountains,
   Overcoming the people as in battle.
   Brother saw not brother.
   From heaven no mortal could any longer be seen.
   Even the gods were struck by terror at the deluge,
   And, fleeing, they ascended to the celestial band of An
   The gods cowered like dogs
   Crouching by the outer wall of that celestial band.21

Legends aside, at nearly the same time as the binary pair “brushed” our solar system, the singular massive Earth catastrophe known as the “Toba super eruption”22 also occurred. Given the newly discovered scientific data concerning Scholz's star, and the estimated date of its passage occurring at nearly the same time as the Toba event, a connection is plausible. While coincidence is possible, given the many legends, it is reasonably questionable.

The genuine wonder found here, and perhaps preserved within ancient legends, is the preserved real-time observations of an incredible cosmic-level disaster and its associated global catastrophes. The once often-told legends come to us across 70,000 years and describe what people who survived “the battle” observed. Humanity, then experiencing a global population bottleneck, one where the survival of the human species was in question. The surviving legends are vivid stories that must have been often told around campfires during a millenniums-long ice age—stories so powerful they were remembered and retold over thousands of generations. Except for the remnants of our legends, our human history before 70,000 years ago was eradicated.

The passage of Scholz's star may also represent the missing powerful element of causality that was glaringly absent from the necessarily speculative books written by Immanuel Velikovsky, Worlds in Collision and Earth in Upheaval. According to Wikipedia, Worlds in Collision is broadly labeled “catastrophism” and “many of its claims are completely rejected by the established scientific community as they are not supported by any available evidence.”23

The recent discovery of Scholz's star appears to have revealed new “available evidence,” and perhaps the “established scientific community” may with open minds someday revisit catastrophism, and acknowledge and make good use of the bountiful research provided by Immanuel Velikovsky. A long overdue apology may also be in order.

What is set forth in these few pages expresses but a small fraction of the enticing wonders that were found while journeying through dusty archives with an open childlike curiosity and a love of inquiry. The scope of treasures deeply buried within our poorly studied and misunderstood legends may reveal traces of hundreds of thousands of years of human history. As the equation in stone demonstrates, humanity is utterly ignorant of its true history; much of it having been casually rejected and swept under the rug of “superstition” or “catastrophism.”

19 Accessed 24 January, 2020,

20 Accessed 24 January, 2020,

21 Accessed 7 October, 2020,

22 Accessed 24 January, 2020,

23 Accessed 24 January, 2020


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