“THE
COFFER MODEL”
INTRODUCTION TO THE
COFFER
Computer
modeling has been used to propose that the so-called Sarcophogus (coffer for
short) in the King Chamber of the Great Pyramid contains the elements of
mathematical communication designed into its various measurements. There is substantial argument produced herein
to suggest the coffer represents mathematical and construction knowhow. Not only are there complex mathematical
relationships, but it also utilizes stonework of unbelievable accuracies that
are easily seen once the design criteria have been established.
SIR
FLINDERS PETRIE
Almost
everyone who visits the Giza Pyramids, or reads about them, realizes that these
are truly amazing structural creations. In the early 1880’s Sir Flinders Petrie spent two years of his life
surveying and very carefully measuring various aspects of the Giza
Complex. He was knighted for his
outstanding efforts. He was truly
“inspired” to make such incredibly thorough and complete measurements that
nobody has since come close to even equaling his efforts.
However,
Sir Petrie’s later book editions (a summary without mathematical details)
completely left out the details on measuring the coffer and most folks are not
aware of the broad statistical nature of his measurements. The four basic dimensions widely quoted
represent some 681 separate measurements at six inch intervals. These details clearly show topographical patterns
on each of the surfaces to the experienced eye. Misunderstanding of Sir Petrie’s
methods caused some to question his measurement accuracy.
My
meager efforts consist primarily of using his detailed measurements, and those
of a few others, in modern computer models. The computer allows millions of trial-and-error
calculations in seconds. It further
provides sufficient decimal digits to allow the discovery of “numeric patterns”
in these calculations.
Just
one of several examples of Ancient Intelligence comes from this so-called
coffer in the upper chamber. The initial
six-ton,
hard granite rock was carved into the shape of a sharp-cornered, rectangular
bathtub. The surface preparation is typically beyond most people’s ability to
fully appreciate.
PETRIE
THE MEASURIST
Sir
Flinders Petrie realized all this and set up an extremely appropriate system of
measurement. He built a stable wooden frame and from this suspended plumbobs
all around the internal and external surfaces.
We still use this technique in modern archeological excavations. Below
is a cross-section showing just a portion of the measurements at a given
elevation.
This
approach separates the “scientific investigator” from the “non-scientific
interest”. The message of the coffer appears to be very scientifically based
and likely will require that approach for complete decoding.
The
Sir Flinders Petrie approach minimizes errors by making any given measurement a
mere fraction of the total effort. The
overall outcome is easily reproduced by multiple investigators, while a single
measurement will vary with each person’s measuring skills. If the designer was going to send a message,
it would have to be sent in this manner.
The four basic mean dimensions (Petrie 1883) are given below to two
decimals of an inch. (OL= outside Length, OW = outside width, IL = inside length,
and IW= inside width, all in inches as measured by Petrie)
89.62(OL) x 38.5(OW) = outside floor
area
78.06(IL) x 26.81(IW) = inside floor
area
Ratio of
outside/inside areas = OL x OW / (IL x
IW)
Now
recall the number natural log “E” =
2.71828… from pre-highschool algebra.
The square root of “E” is 1.6487.
Ö2.71828 = 1.6487
One
does not need a thorough understanding of logarithms or the uses of natural log
E. All that is necessary is to know that
this number is very important in all of modern science. What is this important technical number doing
in the midst of a very important artifact from ancient times?
The
question now comes to mind. If it is
very unlikely for such a number to occur randomly, just how could it have
occurred, because it did happen and is repeatable even today?
If
today we thought our entire civilization would come to an end and wanted to
leave a message for some future intelligence, perhaps this number would be a
good way to capture their initial attention.
From that point, we could develop other bits and pieces until a full one
way communication was probable.
However, if the ratio given above
truly was “designed” and not just an
accident, we might then expect to discover other ratios. In other words, nobody
would likely leave just a “business card” and hope the future would be able to
define the meaning. There absolutely
would have to be other such relationships for this theory to take serious root.
DOUBLING
METHODOLOGY
Material
as old as the Rhind Papyrus demonstrates Ancient Egyptian mathematical
techniques. In our haste to dub the
techniques of these ancient folks inferior to modern methods, we have routinely
made remarks about their use of a doubling technique for “rudimentary”
accomplishing of our modern methods of multiplication. We did not stop to think that their methods
might be superior in many other considerations and perhaps multiplication is a
shortcut that dulls our senses to many other advantages and deeper
understanding.
The
modeling effort seems to indicate that routine doubling or halving of numbers
increases the overall spectrum of a number and allows the discovery of simple
relationships. It appears that
Pythagoras attributed something like a “personality” to numbers and something
of that nature can be seen in “digital linkage” within the symmetry of certain
number systems. For certain Mother Nature uses sequencing in DNA molecules.
For
this article we shall describe doubling and halving simply as it sounds. The number “440” can be doubled to 880, 1760,
etc and can be halved to 220, 110, etc.
These particular examples are musical “A” notes depicting the primary
human vocal range. Therefore, just for
starters we see an “expansion” of our focus to link music more directly with
mathematics.
Starting
with the mean outside measurements, we see the outside width divided by the
outside length, and then doubled twice, gives:
OW/OL x 2 x 2 = 38.5/89.62 x 2 x 2
= 1.71836
THE POWER OF “A”
We
shall see that the natural log “E” consists of two parts, namely “1” and the
sum of a factorial series that we call “A” = 1.71828.. which rounds to 1.7183 and 1 +
1.7183 = 2.7183. “A” is the intelligent portion of Natural Log E.
“A” is
mathematically generated in the simple series which you don’t need to
understand nor memorize:
A = 1 /1
+ 1 /(2x1) + 1/(3x2x1) + 1/(4x3x2x1)
etc
=
1.718281828459045235360287471352662497757……
but here
written 1.71828 for short.
The point here is not to force the
non-technical reader into serious mathematics.
It is to demonstrate that this is not currently a number our modern
technology has brought into serious focus. Also that it is not a routine number
we would expect ancient tomb builders to be using. So just what is it doing
here in this ancient artifact?
These
two number occurrences should at least tweak our interest. The chance of both “the
square root of E and the factorial portion of E” coming from these coffer
“statistically measured” ratios on a random basis is so low one can forget
about random occurrence.
Once
again this is a dimensionless ratio, so no matter with what units the coffer is
measured, the same ratios result. If one were to “design” a means to gain the attention of serious
researchers, this would be a good way to improve the odds of discovery.
IS
THERE ANOTHER “A”?
Let us sum the inside length and outside width:
78.06(IL) +
38.50 (OW) = 116.56 this number appears
throughout the Great Pyramid internal dimensions. It must have some important
contribution.
Taking
heed from the previous two relationships, but in reverse order, the number
above is divided by 2, twice, then the square root taken and finally divided by
Pi.
Ö(116.56/2/2) /
Pi = 1.71828
Now,
considering all three relationships collectively, we now have a
random chance of perhaps 1 in trillions.
This seems rather a remote chance of being an accident. Furthermore, each of the three relationships
involves the same important number series, namely “A = 1.71828”.
Does this seem sort of
complicated? It is not for someone who
really wants to understand something as incredibly important as a message from
an advanced intelligence. But one must
consider that this intelligence may not want to communicate to someone who is
impatient. It is for the people who have
faith and believe there is something to be gained from the study. It is,
perhaps, the natural feelings that people who visit the pyramids come away with
and don’t know why or where it came from.
The
coffer outside model height is 24 x “A”
total. The height from floor to inside
bottom is 4 x “A”. The height of the lip is “A”. These differ from Petrie a little
more than other measurements because the top of the coffer is so badly damaged
and he had to estimate for lost material.
“A’s” IN THE WALL THICKNESS
Continuing
to examine the remaining wall thickness with equal care, 10/ “A” is the west wall thickness and 33 x
“A/10” for the north wall thickness. These projections are exceptionally close to Petrie’s statistical mean
measurements.
THE
COMPUTER SOLUTION
At
this point we have Petrie’s measurements which may provide statistically
accurate data to about 3 or 4 digits of accuracy. But with the hint from the heights that
“exact values” could be represented, one might
consider “what if” the coffer represents a “design model” which could be solved
exactly with mathematics.
In
other words, if we have three formulae which very closely define a constant, at
what point do we “take the hint” and set these formulae exactly equal to the
constant and try to solve for an exact solution instead of relying upon
measurements. In such a solution, the
measurements of the coffer would be replaced with “exact and precise” numbers
representing a “model”.
There
are four
basic dimensions which we would like to know with exactness. There are three relationships
described above. From mathematics, we
know with four independent relationships, we can normally solve for all four
dimensions of such a model.
The
diagram below summarizes the “highly suspected” three relationships and allows
us to see if there is one or more exact solutions. The solution should hit all four dimensions
as measured by Petrie within the margin of error of his measurements. Hopefully, there will be something else to
tell us that we have at least one of the solutions the designer had in mind for
us to find.
The
three relationships suggested by measurements:
1) OL /IL x OW /IW = ÖE 
2) OW/OL x 4 = A = 1.71828…
3) sqrt(( OW
+ IL) /4) / pi = A = 1.71828…
After
grinding out a bunch of numbers a fourth relationship was found to be involved
with the “difference” between
the outside length and inside length. The Petrie dimensions are 89.62 - 78.06 =
11.56. The computer model dimensions adjust this number to 11.56171828
which is (1.7*2)2 + “A”/1000.
OL - IL = (1.7*2)2 + A /1000
Using these four “A” relationships provides at least one solution for all “model” dimensions to unlimited significant digits when combined with the two “thickness relationships”.
NT = 33 x A /10 NORTH WALL THICKNESS
ST = OL – IL – NT SOUTH WALL THICKNESS
ET
= OW – IW – WT EAST WALL THICKNESS
Table I
summarizes the computer model output to calculator accuracies. See also Figure 1 appended.
TABLE I. Coffer Model Dimensions
Model Petrie Difference
Outside
length =
89.622338825 89.62 .002338825
Inside length =
78.060620543 78.06 .000620543
Length
Difference = 11.561718282 11.56 .001718283
Outside
width =
38.499109057 38.50 .000890940
Inside width = 26.809438129 26.81 .000561870
Width
Difference = 11.689670928 11.69 .000329070
North Thick. =
5.670330034 5.67 .000330034
East
Thick =
5.869903859 5.87 .000096141
South Thick. =
5.891388248 5.89 .001388248
West Thick. =
5.819767069 5.82 .000232930
Overall
height = 24 x “A” = 41.23876387 41.31
Base
height = 4 x “A” =
6.873127312 6.89
Inside
height = 20 x “A” = 34.36563656 34.42
Lip
height = 1 x “A” =
1.718281828 1.7
(see also
Figure 1 “Model Coffer Dimensions”)
SYMMETRY
There
are other reasons to think this model output has overall significance. Look at some of the following numbers and see
if they suggest anything to you. View these as “puzzles” and not calculations. One must look
for repeating numbers, sequences, reversals and particularly “mirror-like” structures such as “12321” or
“1234…88-9-88…4321”. Perhaps you will
see some that are not listed. Remember that this may be like “breaking a code”
and only revealed to the faithful and those that pursue with due diligence.
The
product of outside volume times inside volume uses all six basic
dimensions.
OL x OW x OH x IL x IW x IH =10233323323.3
Most
can see the interlocking symmetry in “23332” and
“33233233” without much difficulty. The
probability of such symmetry occurring in random numbers is extremely low. One must consider not only the repetitive
nature, but the sequential nature of 2 followed by 3 and vice versa to
calculate the accurate probability of occurrence.
33233233 1/32 = 1.718102792
The
significance of the above relationship will be covered in subsequent articles.
For now, perhaps there is some subtle “beauty” in “3-32-3-32-33” taken to the
1/32 power. The scientist will find a
different beauty when the entire range of subatomic nature is linked.
Perhaps
most folks ran across the mass of a neutron in high school chemistry and
physics as something like 1.67492716 x 10-24. The extremely small nature would cause many
folks to just “move on” without gaining a “feel for the neutron”. But if we press the square root key seven
times, it becomes 0.652003562 which seems more tangible. If we continue by multiplying by 103/2
and dividing by 12, we get 1.718180248 which should now pique our attention in
line with what else has already been presented. More on this will be provided later.
The
outside volume times the inside area is
OL x OW x OH x IL x IW = 297777790
The
symmetry in both numbers does continue far beyond these digits, but until one learns how to read symmetry, the
complexities might detract from this simple numeric beauty. These can be checked
on a typical calculator and may be designed to “capture initial attention”.
Using something like Microsoft Mathematics can yield much longer sequences. The
normal calculating mode of most computer languages is 8 digits with 16 allowed
on double precision mode. Working with MathCAD one has almost unlimited range
up to 250 digits. Something like 1 / 127 is amazing that it repeats every 42
digits. For now it just seems like numerical artwork and nothing practical has
been discovered. If the coffer design is intended to produce these sequences,
it must be important.
Forgetting
decimals, the inside volume is:
IL x IW x IH
= 71-91-90-76-89-88-(5694-314-5693).
One can easily see the sequence
“91-90-89-88”? How about the sequential “5694…5693” with Pi in between? It could be random for any given single
number, but the overall pattern of numbers seems quite “planned” or “designed” ……as if a puzzle waiting
an “awakening”.
The
inside area times the height of the lip is the string:
359-5-953-84494-2847-157-2846
One
can see the mirror “359-5-953”? How
about the sequence “2847…2846” with Pi/2 between? The sequence “84-4-94” would
be read “48-4-49” by reversing the last two digits which was not uncommon in
Ancient Egyptian writing. On an individual basis, these numbers have no
statistical significance. But
collectively, they do. It particularly
becomes significant when this type of system is seen throughout the Giza
Complex.
THE MESSAGE OF SYMMETRY
There
is more symmetry in the various combinations of the coffer model dimensions
than one can imagine. Any one of these
numbers is very unlikely to occur randomly, let alone the several dozen or so
that have been found so far. One concern is that the 1.71828..1828.. may
contribute to the symmetry.
There
is the essence of a “Mathematical Language” contained in the symmetry of the
digits. It seems to provide hints and curiosities until the real relationship
shows up. In computer lingo, it is a “self-extracting file”. For example, when you put the CD for new
software into your drive and the setup software analyzes all your computer
hardware and software and automatically makes it work best for you. And sometimes, it really does work.J
The key to further understanding in the Great Pyramid seems to
be the number 1.71828. A ten digit calculator display is just not
quite enough to be able to see these huge “mirror-like” structures. The Giza Complex shouts at us to give “A”
closer examination. But meaningful progress comes only for those willing to put
out substantial extra effort.
SURFACE
TOPOLOGY AND MEAN MEASURES
The
designer’s ability to carve out complex topographical features on each of the
coffer surfaces and have the “mean” dimensions still provide such “relationships of A” is far
beyond our current typical practice. It is questionable whether we could gain
the smoothness on perfectly flat surfaces let alone complex very slightly
curved surfaces.
There are other aspects to the
coffer design which clearly set it aside as a “designed shape”. The outside topographical pattern is
definitely designed and not the result of random polishing. It appears to mimic
“coupling surface adjustments” in modern industrial microwave baking.
The surface
polish is flat to 1/10,000th
inch in places. To attain this level of
smoothness in an overall curved surface is most difficult. This is a very
precise 6 ton rock which could not likely be duplicated even today using
computer programmed stone grinding equipment.
THE
REAL CUBIT
When
Sir Flinders Petrie had measured enough chambers, he concluded the Ancient
Egyptian cubit was 20.62 +/-
.004 inches (Petrie 1883). From the modeling it appears that the cubit was
meant to be exactly 12 x “A”
= 20.61938 1941… inches, which you can see is about .0006180
inch from Petrie’s determination and well within his estimated tolerance.
WHY ALL THESE “THINGS
ABOUT A”
There
are some special reasons for the Ancient Intelligence to be calling attention
to “A”=1.71828 and multiples of 12 and 256 collectively. Let us first draw a
very intriguing example from modern times to show how the three numbers (“A”, “12 x A”, and “256 x A”)
can work together in real life.
Pretend
that our musical world had standardized on Concert A = 256 x “A” =439.880148 cycles per second
instead of the round number “Concert A = 440” cps (even tuning forks for
Concert A can range from 439.9 to 440.1).
This would mean all musical tuning would have the exact same foundation
as many scientific relationships. It
would mean that “A = 1.71828..cps” is an exact “A note”, hence why it was named
“A”. Our existing tuning makes 1.71875 the low
“A” note, which is not a great deal different. It is 55/32 or 55 halved 5 times
where 55 is 3 octaves below 440 cps.
This “basic A” just happens, however, to be
too low in pitch to hear via our ears alone. But we do not hear by our ears
alone.
We
can sense this same note in the “A rhythm” in many songs such as “America
Typically,
music rhythms are given in “beats per minute” so 1.71828cps x 60 = 103.09 beats
per minute, roughly a popular dancing rhythm in disco atmospheres.
Continuing
the musical analogy, there is a low bass note that is a particularly great
harmonic with any “A note”. It is “12 x A” cps and just happens to be called
“low bass E”.
This makes the “cubit frequency” a fundamental contributor to bass
music. These bass notes are often
plucked in harmonic rhythm with the whole song rhythm. This again makes rhythms
within rhythms.
So
we see that each of the three numbers, “A”,
“12 x A” and “256 x A” play important roles in music and do it collectively
through rhythm, bass and tuning. Note I have selected colors red, green and
blue to symbolize this “blending” of frequencies to make “white light”.
It
is too early to have any certainty, but it may be that the basic brain waves
are also “tuned” to this “basic A” whether 1.71828 or 1.71875. The difference
is only important to mathematical solutions and is too slight for our typical
ears to detect even if at an octave frequency we could hear.
LEARNING BY EXAMPLE
Now,
let us see if the coffer puzzle and this musical analogy could provide insight
into anything important to science. In
the computer modeling of other aspects of the Giza Complex, the speed of light
was found to be extremely important. So
much so that a “relationship” was needed with more significant digits to check
out patterns beyond what the use of the standard nine digits in 299,792,458
meters per second could provide.
Using
techniques from the Ancient Intelligence,
the following equation was found which is called the “symbolic light
speed (SLS)”. It uses the three musical
analogies from above:
SLS
= 230 / ( [(50+7)/50 + 1/{A x (12xA) x (256xA)}] x
Pi)
which rounds
to the 299,792,458 m/s standard adopted around the entire world. There is
nothing in the equation that is not emphasized in Ancient Knowhow. The “50” and “7” are both sacred numbers. The 230 is simply “doubling 30 times”.
No
claim is made that it might in fact be a more accurate value for the speed of
light or for the conversion of matter into energy. For now, it just might be another
key to understanding the pyramid
that will be used in subsequent modeling. Note we have in a sense “graduated”
from the class in Ancient Knowhow and now have a very scientific number based
only on real numbers without dependence on any measurements.
If this formula turns out to be
important towards better understanding of the universe, then the Pyramid
Designer will have been successful with the coffer as a “training tool”. Not only is the coffer a beautifully
constructed piece of artwork, it is also a mathematical beauty. And it is only
the very tip of the iceberg.
THE COFFER REFLECTS ANCIENT KNOWHOW
It
is very clear that these mathematical relationships of A actually exist in the statistical
measurements of the coffer. The question
can only be whether it was an accident or part of a design. The answer to this
question seems “designed”. This issue is further addressed in other
areas of the Giza Complex. Computer modeling
finds a very consistent path and information is revealed that is currently
unknown, but obviously true. (see subsequent articles)
THE MODEL DEVELOPS SYMMETRY
A model constructed around these “relationships
of A” produces very unusual symmetry in common geometric terms such
as volume, area and perimeter. The combinations
of these terms provides even greater symmetry which has extremely low
probability of occurring randomly.
THERE IS A MATHEMATICAL LANGUAGE
The final case for the argument for
ancient intelligence in the coffer design is that it appears to suggest a
“Mathematical Language”. One can use the
techniques and structure of this language to find relationships such as was
done here with the single example of “symbolic light speed”. These “symbolic hints” may ultimately point
to final relationships if these, in fact, are not more than symbolic. The
elements of this language were used to find the coffer model solution.
Jim Branson
see all www.king-chamber.blogspot.com
<knowhow
at ctcweb dot net
Reference
1.
Petrie,
Sir Flanders. 1883. “The Pyramids and Temples
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