| Nazca Monkey & the Seal of Atlantis |
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..the
figures with their beautiful and regular curves, which could
only have been produced in these giant sizes if every piece,
being part of a circle, had a radius and a centre whose length
and exact position were carefully laid out." (Maria
Reiche on Nazca)
An
Unsolvable Puzzle & its Solution
The
daring observation cited above is true. The Nazcans used Geometry to
carefully lay out plans of glyphs. In fact, one of
the Nazca
figures, the well known monkey, is a masterpiece of Science-Art, and an elegant and
intriguing geometric puzzle.
Seen
from above, the Nazca plain is a breath-taking tangle
of lines,
trapezoids, and animal and plant figures. The monkey figure
casts a
long straight line, an umbilical chord in my hypothesis, which
ends in a meeting-point with a number of other lines. Given the
high level of science in the figure, the "Nazca Lines" promises to be one grand-design..
A
careful analysis will show that the monkey has two pronounced postures at once. One relates to a 5-pointed
star, and one is oriented to the cardinal directions. Unfortunately, there are almost no clues to help
us derive the latter from the former. The easily discovered cardinal alignment of the figure appears to be self-explanatory, serving as a powerful misdirection, a dead-end. The sole clue to the truth could be found in the
so called Foot-circle. But, how
likely is it that one will invent the entire concept of the
"Cone" based on just this one clue?
For practical
purposes, the stand-alone monkey glyph is an unsolvable puzzle. It
would seem doomed to a limbo of the scientific doghouse, but I had already solved a different edition of
the same puzzle from another image, time and place!
The geometric solution, which works for Athena - a Stone Age
engraving from La Marche, France, works for the
monkey as well.. In practical terms, it had been fashioned
impenetrably clad in mystery for someone already familiar with the (Cone&Square) concept!
In
terms of sheer complexity, Nazca Monkey does not begin to compare
to the
Athena engraving, but it is no less captivating. The design
per se culminates in a bona-fide lesson on the one method, which
produces the
regular 5-pointed star in only thirteen steps - the fastest such
construction there is.
While this is no
rocket-science, the big deal
is our ability to read specific thought from it, see it come to a conclusion, and than see the main-idea confirmed by being clearly and accurately mirrored in the
Athena-engraving. Note,
I did not identify this idea in the engraving until checking back to it from the monkey. Getting
a helping hand from the monkey was therefore quite a thrill.
Many
years later, I learned that the above mentioned 13-Step
method of pentagram construction is essential to an exact recreation of
the layout of the
three great Giza pyramids (as surveyed by Petrie) from clean slate.
No wonder that no
one could do the same in over a hundred years, although many had
tried. Having prerequisite knowledge is crucial advantage.
So, we have three seemingly unconnected sites (possibly four with the Abydos temple), which yet mirror each
other's ideas. What mysterious force is behind this paradigm-changing global
phenomenon? It got a vague name from me - "Agency".
Over a span of 12,000 years, or so, the
Agency had left its inimitable signature at La Marche, Nazca, and
Giza . Thus, it
advertized pure power, and virtual Lordship over
Time, proffering a source for paradoxes of history,
such as the
Baalbek
Terrace, or legendary Vedic
vimanas, Atlantis, nephilim, etc.
Having evidence pass tests in the
abstract realm of Geometry is a perfectly legitimate means of providing proof of Geometry in the evidence. All
that remains is a verification by objective and authoritative
third parties. Unfortunately, none are willing to get
involved. Critics,
who love to ridicule the many exotic Nazca theories out there,
studiously avoid challenging my study of the monkey. Meanwhile, when googling the
keywords 'Nazca monkey', this article comes up near, or at
the very top of hundreds of thousands of hits, so, it is in no way
veiled by obscurity. Given the method for ordering the search
results, it must be fairly popular. It is also "stored by
Biblioteca Pleyades", and linked to by various sites. Pundits, and critics have
no excuse for pretending that it does not exist.
Regrettably,
the opposition subscribes to a doctrine, by which significant
geometric or
mathematical order can be found everywhere, in any random
collections of lines and points, ancient art, cloud formations,
and so on. Through this prism, any rational
order found in
ancient artifacts can be safely assumed to be devoid of intention.
The perverse nihilism of the doctrine dictates that it is impossible to use art media for
encoding concrete exact information. How absurd!
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Manifest
order in the monkey figure.
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This study uses a
copy of the Nazca monkey originally
published by Maria Reiche, Nazca's
scholarly guardian angel. She had learned about the
giant figure on the pampa from commercial pilots
in 1952, some years after her arrival to Nazca. It
became her favorite figure, and she ascribed it special
significance:
"The
monkey and surroundings would be an appropriate subject for
a special study, as it is a complete unit and
the pursuit of each line to its origin does not, as at the
border of the pampa, lead unendingly from one thing to
another. This drawing consists of no more than two
elements.
One
is a wide line (or better geometric surface, being at the
beginning twice as wide as at the end) with a
stem which, almost a mile long, leads into the maze of
lines at the edge of the pampa
!!! (sic).
The other is one single un-interrupted line, of which only
a small piece is lost between the end of a zigzag line and
a small winding path at the bottom of the long geometric
surface.
The
line starts from one side of the long surface and after
describing the contours of the monkey, consisting only of
curves, runs through two different zigzag-shapes and
crosses sixteen times over the geometric surface at whose
top it finally ends."
Reiche's measurements
of the monkey glyph should be especially meticulous, as she was known
for this virtue. Although it looks like my copy was sufficiently
accurate to preserve major aspects of the design, I would love to
have a highly accurate plan of the monkey, one, which would
map both line-edges, and moreover, be a part of an accurate survey
of the.entire Nazca.
Standing
Tall
Even
a quick inspection of the monkey reveals evidence that
these
are no random scribbles, but a measured effort.
In
the diagram above, the
two longest lines in the image
form a
big X-shape.
This X has an axis of symmetry,
which is then
perfectly perpendicular to
the multiple alignment along the bases of the tail, the
hands, and the tops of the sixteen lines forming a zig-zag
shape on the right. The
vertical axis
then also passes right between the monkey's feet.
Obviously, we have found a
compellingly reasonable
orientation for the monkey.
I
believe that Maria
Reiche would have noted this
alignment.After all we are working with her copy of the
desert glyph, and this alignment is strong, and
obvious.
There is also the alignment to cardinal points
(shown
later). It is also strong, but cannot be shown by
just a couple of lines. The alignments suggest two alternative
postures for the monkey, much different from the currently
prevalent presentation, which has it tumbling on all fours like a baboon. Such presumptuousness has so
far led to a complete misunderstanding of what the spiral-tailed monkey
and Nazca
are all about.
Science-Art
There is one more alignment to show the reader. The
two lines forming the big X, hold the angle of visually perfect
36°, one-tenth of a circle. Hence the big X will fit into a circle an even ten times. Every line of any X then falls on the neighbouring X's line.. This
idea results in the below remarkable chain of ten monkeys. The tail spirals around the head, and the hands grip the torso with such positional awareness, the effect looks absolutely.contrived.
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In view of such harmony, it is possible that the big X is meant to imply two
5-pointed stars in a symmetric tip-to-tip alignment. The question is, are the sizes of these stars encoded
into the position somehow?
•The
pentagram below the
X-point
The
third longest line of the glyph 'c'
cuts across lines 'a' and 'b' of the big X at an angle similar to that found
on a pentagram. Let this cut set the size of the
experimental star below the point-X. The bottom tip is,
where 'c' cuts across 'a'.
( 'c' diverges
from the star-angle by an even two degrees, this is good to know for
the purposes of reconstruction )
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!
•The
pentagram above the
X-point
We
wish to base our second experimental star on the length of line
'a' above the point-X, but 'a' ends in a curve. That
leaves several choices for its length:
Harmony
The correct move is to
unfurl the curve, and add it to the line 'a'. The 5-pointed
star based on this length then has an inner star, as in the
image below:
That star
(purple), and the two stars above and below
the X-point
(cyan and green) are identical.
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If we set the
size of the big pentagram from 'a' without
straightening the curve, in which 'a' ends, and
superpose the result over the previous one, it looks
like the diagram above. The Φ relationship holds in
this position, as well, but there is tiny separation at
the top. The top of 'a' is ambiguous, but the cut of
'a' by 'c' is straightforward. For that reason, I let it set the star's size. It becomes the standard for the
remainder of this study.
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The
60° Grill
The
Big-X idea in another regular figure!
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The sixteen
roughly parallel lines forming a zig-zag pattern on the
right of the glyph average out to the angle of 60°
with 'c', which cuts acrross them. Fully a half of
the sixteen lines comes close to the perfect 60°
angle with the line 'c'.
If the Big X is like tips of
two inverted 5-pointed stars, the lines of the grill
with the line crossing it are facsimiles of inverted tips
of 6-pointed stars (equilateral triangles).
The
60°
grill
appears
to be derived from the star system of the Big X, since we
can reconstruct it to a large degree from the X-star
system in just a few simple steps:
• Line 'c' gives
us the first line of the big yellow equilateral
triangle (it originates from the lower pentagram's tip at
34° to the horizontal).
• Another
line (at the corresponding angle) originates from the top point of the
5-pointed star over the monkey.
• We
can recreate the monkey's line of horizontal
balance, because
it rests on one of the unit circles in this
system (see construction of the Cone). This line then
intersects with three other lines, one of which we
know (the red starline), and one is the third side of
the equilateral trianle we seek.
Some other major
lines in the resulting grid then show a clear bias to
passing really close to key points on the 5-pointed stars.
On the equilateral triangle, the thirteenth line of the
grill marks the midpoint of one side. Unfortunately, the
deeper purpose of this fascinating hexagonal system escapes me, so far. Dead-end
or not, the design is quite spectacular, and noteworthy.
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Another
visual proof that the angle of the Big X is 36°
Let's
array the upper part of the Big X, (including the monkey) five
times around the center of the Monkey-star (it can be a point
anywhere on the central axis for just testing the angle).
Supposing we didn't know what the angle was, the result
would seem strange - Five times two lines (of the Big-X)
equals ten lines, whereas we see five lines. The two
lines of a cone normally form two 5-pointed stars, ten
lines altogether, when arrayed like this, not just
the one star we see. Unless, of course, the angle of the
cone is 36°, or its multiple, and lines overlap two
at a time..
Judging by the way the five monkeys entwine, we have found the right pivotal point again, the
centre of the Monkey Star. The idea repeats - a chain
of monkeys. The hands, and the feet, and the heads all meet in
one spot. For instance, at the top right of the image, the
green feet press the light brown tail against the purple head,
which is held by the blue hands, one of which is pushed into
the head by the dark brown tail.
There is something
sinister about this funny scene. Are the five monkeys trying to kill each other?
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The
monkey's Head, Hands, and Feet standardize on the Inner
Circle of the Monkey Star
They
fit very
accurately within the X-Star's Inner-circle
( Monkey-star is one of the X-stars). However, the head
does so in its own way. It fits the pentagon of the
Inner-circle (see below). Remarkably, in my CAD drawing of
the monkey, the inner-circle fits both the hands and the
feet to within three millimeters on each side, fluke or
not. We can reconstruct these circles, too. The
method is given in the Appendix.
This method is
essentially a repeat of the same method of using standard
circles set by a 5-pointed star, as I had learned it from
the engraving.
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For reconstruction of the circles go
down to the addendum.
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We
found some interesting geometrical order in the image,
but how does one go on from there?
Maria
Reiche - the patron scientist of Nazca. may have faced
this dilemma. She must have noticed that the
monkey poses in the 36° Big-X, and probably
devoted much thought to its geometrical
regularities. Being a mathematician - she would
have known then that the entire design might be an
etude on the Golden Mean. Then she probably knew
that the monkey was ordered with respect to the
four cardinal points, as well. No wonder, the Monkey was her favorite design.
Perhaps,
Reiche kept some of her findings back. To put it
poetically, I believe, she had been wary of
malevolence from the bobbing ranks of scholars
ever-ready to pounce on the latest Atlantis Mania patient. Then again,
since Maria herself was opposed to the 'fanciful'
notions of Ancient
Astronauts, and Atlantis,
perhaps, she had practised too much prudence. Most
importantly, she
had no way of discovering the unifying idea, which
would correlate the two kinds of order so manifest in
the monkey, because the strategic Square itself is
completely missing from the picture.
In
contrast, I observed parallels in geometrical
ideas between the monkey and the Athena
engraving before observing its alignment to the
cardinal points . The Big X is like twice the Cone of
Athena's "Cone & Square"
configuration,
and one of the standard circles (Triplets) of Athena is standard in the monkey, as well.
That set my course
of action - to test the "Cone & Square"
on the monkey!
See
the experiment below. The peach colored diamond
is the Square as set by the blue Cone.
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The Square's diagonals
are oriented to the cardinal points!
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The
Square's position is interesting in relation to the
square, which the monkey signals with its arms. Their sizes look the same, and
both squares have almost the same elevation at the
top, while their orientation differs by 45°.
All
four corners of the Square are meaningfully placed with respect to the
monkey's body. The lower three corners are anchored in the monkey's
spine, knee, and a finger. The top corner appears to be on the
horizontal line, which also serves as the limit for the top of the
head, top of an ear, and top of the elbow. The Square's y-axis tunnels
down the upper right arm while the vertical from the left corner of the
Square tunnels down the spine. The horizontal from its bottom
corner tunnels through one of the monkey's thighs.
I
was happy with these initial results even without any
knowledge of the Square's orientation to the
world-compass. That was one of the pleasant surprises
still to come.
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The
Monkey Frame
To
see the monkey’s layout with respect to the
cardinal points, we simply enclose it between
four East-West oriented lines, as in the above image.
This gives us the Monkey Frame. Its sides are parallel
with the x,y-axes of the Square. To this frame, we add
central axes. We see:
• the
monkey’s vertical spine divides the monkey in half
neatly along the East-West axis
• the lower
right forearm - the monkey’s longest straight line -
divides the frame into southern and northern
halves
Conclusion
The
Monkey Frame’s axes clearly govern the monkey’s
layout as two ‘great divides’.
More Frames
If
we pay attention to the monkey's body-language, we see
that its arms signal a square (Arms-square). Indeed, a
vertical line through the outside of the upper
right arm completes a perfect square (the Arms
Square) in combination with two sides of the Monkey
Frame, and its horizontal axis:
•
width
of the arms (East-West) = half
the monkey's height
•
width
of the feet (East-West) = half
the width of the arms = one-fourth of the
monkey's height.
• width
of the left foot (East-West)
= half
the width of the feet =
one-eighth
of the monkey's height
A
horizontal line along the one-fourth height marks out a
square with the vertical lines bounding the
feet, and with the bottom line of the Monkey-frame. This
is the Foot-Square,
the right figure left in the right place, as we'll see.
• the
tip of the tail is at the three-eights
height
level of the Monkey-frame, and one-fourth
of
the height away from the left side of the Monkey-frame.
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Above:
Other
squares fit the monkey as well. The purple square is of the same size as the Square.
The southernmost points of
the left ear and the left elbow align to the East-West
axis on the big square.
There is a Hand-square as well.
The
Big Clue
The top right
corner of the Foot-square connects to the top and bottom
corners of the Square by lines approximating angles found on
the 5-pointed star. Therefore it is a clear indication that a
star should be drawn here.
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13 Euclidean
operations to construct the regular 5-pointed star (pentagram)
To
appreciate the meaning of the Foot-square in the design of the
Nazca monkey, we have to review a certain construction of
the regular 5-pointed star (pentagram) in thirteen
(13) operations or steps . I believe it to be the fastest
such construction, and this is the underlying reason for the
Foot-square - to clue us onto it.
The
diagram above shows the first six steps. Step-1 is a
horizontal line, which will eventually form one arm of the
sought after star. Next, we center circle-2 anywhere on
the horizontal. Circle-3 is centered at the intersection of
circle-2 with the line. Steps 4 & 5 are help circles,
which give us the vertical line as step-6. The circle-3
now has been given both horizontal and vertical
axes.
Construction
of the 36-degree angle
step
7:
Draw
a line between points C and 2.
step
8:
Draw
a circle centered in 'C' through the intersection of circle-2
with the new line.
steps
9&10:
Draw
lines from the top of circle-3 to points P1 and P2 at the
intersections of circle 'C' (cyan) with circle-3 (green).
These lines are tangents to circle 'C', and the
angle betwen them is exactly 36 degrees. These lines will
form two more arms of the 5-pointed star under
construction.
Construction
of the regular 5-pointed star
steps
11,12,13:
Since
the horizontal line will serve as one arm of the star, the
point 'Q' circled in green will be equidistant to the four
circled points on the star, two outside, and two on the
pentagon inside. The circle with center Q drawn through the
top of the star gives us three more distinct points
needed to complete the star. (point Q can be on the
other side as well)
I have no idea if this construction is
recorded in some geometry book somewhere, all I know is that I
had gotten the idea of constructing this specific star
from the Nazca monkey's design. Certainly, no other star
construction by the same classic rules can be more efficient
than the thirteen steps we just saw.
The
Solution to the Foot Square
The
monkey is referencing the quickest method of constructing a
regular 5-pointed star! One of the benefits - we can now
reconstruct the
Foot Square to scale for any 5-pointed star (diagrams
below).
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What do we see in the inset
to the right of the diagram? A circle with an inscribed square?
No, make it two concentric circles and two squares - the Square's Golden-circle, and the Foot-square's
circle, plus the squares inscribed in these circles.
The
circles and the squares overlap with visual perfection, as the
difference between the circles' radii is a mere 0.02 m in my
CAD.dwg of the monkey, which reduces to virtually nothing
on the scale shown.
Conclusion:
The circle around
the Foot-Square is meant to be the same as the Square's
Golden Circle. We can clearly see how the Foot
Square was added to the position.
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The
Trans-Atlantic Connection & the Foot-square
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What if we
backcheck on this, so far, the culminative idea of the
monkey's geometry, to the Athena
engraving? Will the transatlantic connection
continue? Is there anything remarkable in the relationship
between the Foot Square, and Athena's
feet?
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The Athena engraving already has its Square, we just add in the
Foot-square component (in the direction of Athena's feet).
The result below : there is a definite great fit
with Athena's lower right leg!
Moreover,
a square of the same size and orientation also fits Athena's helmeted
head!
The test
is a spectacular success, especially, when magnified several times!
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Rather than fitting over both feet as in the Nazca-monkey, the Foot-square & circle
fit over Athena's right foot, and lower leg. The bottom of the square
limits the feet downwards, doing exactly the same thing as in the monkey glyph. How it does so with almost
microscopic precision
(see the magnified view
below) is most attention-worthy!
While the square's bottom limits the feet downwards, the top side of the square clearly coincides with
the divide between the right thigh, and the lower leg.
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The
square inscribed into the Foot Square
An experimental line at 45° to the
horizon snaps tightly onto the three toes of the right
boot. Even under this much magnification, the fit remains simply perfect!
Three
toes? Well, yes, just like the Nazca monkey! Since as a rule, neither
monkeys nor humans are three-toed, this further coincidence is very telling..
The 45°
line then goes on to strategic points of the left foot. The square
inscribed into the Foot-square can be skidded along this line by
the right lower side until it fits the left boot in
width! At that moment, the
horizontal axis of the sliding square also comes to a good fit with the
boots - more positive feedback for establishing the back-and-forth connection between Nazca and La Marche.
Athena's
head & the Foot Square
In
a major surprise, the Foot Square
also fits over Athena's helmeted head - perfectly, even
under magnification! You
may not believe it, but, believe me, you see it. There it is, in the diagram below, a
definite fit on four sides.
Conclusion from the experiment: The fit of the Foot-square-idea learned from the monkey is
stunningly accurate, when transferred upon the Athena
engraving.
The
Foot Square, extended into
a rectangle fitting the head as below - note the bottom left
corner, and the chin - produces interesting Φ (PHI)
proportions along the vertical
axis.
Important: Two inside corners of the blue star are on the
bottom line of the square. This data helps in reconstructions, for
instance, in locating the topmost elevation of the head.
↓The
top of the head to the face
1 / Φ = 0.618..
↓
is as the face is to the
entire head
Φ / Φ+1) =
0.618..
The lower 1/4 of the Foot-square is
marked by engraved points on the eye - nose-bridge
level.
0.5 + 1/Φ = Square root of
5 divided by 2 (1.1180339...).
Overall,
the height of the head is Phi + 1 ( 2.618..), and
its width is 1 + 1.
So, these
levels of Φ progress over the base (whose width is 2) as
follows:
From the chin to the bottom of the square (end of the helmet)
• 0.618..
From the chin to the nose-bridge
• the Square
root of 5 divided by 2, or 1.118..
The height of the face
• 1.618..
The height of the head
• Phi
squared, or 2.618..
→The
rectangle of the head represents two squared shoulder
to shoulder vertical golden rectangles←
Then
there is the matter of the small (blue) pentagram, whose horizontal arm
protrudes through the tip of the nose. It shows that there is Φ proportioning between the vertical distances from the bridge of the nose to its tip, and down to the line of the lips.
This star's vertical Φ
division also represents the following vertical
distances on the head between:
• bridge of the
nose, where it meets the forehead, and a line-end of the
helmet
• tip of the nose
• bottom of the
nose (slightly inaccurate)
• the lips
This pentagram is actually on a
larger (yellow) pentagram of a height equal to the diagonal height
of the Square. The x diagonal of the Square is the
larger star's axis.
For more
Φ relationships on Athena's
head:
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The
Seal of Atlantis
The Peruvian
"Nazca Monkey" is identical to the 14,000
years
old "Athena"
engraving from La
Marche,
France in that both images are instances of the same geometric
engine, the Cone & Square.
To show this
system in the Athena
Engraving,
and how it came to light was always a long
process. The engraving is complex, and the original star is not
given as explicitly as in the monkey. But, the
Square is signaled in many ways.
With the monkey,
it is the opposite. The Cone and its 5-pointed stars
are given in a strong style, but the Square is
completely missing. Its spirit presence is perfectly
evident however, because once we add it into the
position, everything falls into place and
starts making sense. The Nazca monkey is a
heaven-sent help to the engraving in proving the presence of the Cone & Square
system in both images. The two images work in
tandem.
The Canada Council had seen this design well back in 1987, along with
my story of how it had been inspired by the engraving. Thanks to
that, the design's objective existence is proven, whether truly
observed or fantasized.
By
itself, the detection of the Cone & Square in the Athena engraving
may have looked questionable to anyone wishing that what I
were wrong. Of
course, the Canada Council had rejected my study,
probably attributing it to naive interpretation of data, seeking and
seeing rational order, where none exists.
What
matters is that the Cone & Square system is so extensively coherent, and original, it goes far beyond the limit of recreation by chance. The
Naazca Monkey then decides the issue of authorship of this system in
favor of the ancients. The two distinct instances of it are
unimpeachably real together. Having met it again at Nazca, it
became the "Seal
of Atlantis"
to me. The "Seal
of an Unknown Advanced Prehistoric Civilization of
either Earthly or Alien Origin",
would be more accurate, but had seemed too long. In any case, it goes a long way toward proving
that Plato's
tantalizing account of advanced Atlantean
civilization
is based upon some true facts.
The
Seal of Atlantis establishes
the link:
La
Marche
→← Nazca!
or, maybe Europe →←
Atlantis?
→← America!
The
Nazca-monkey's umbilical cord stretches all the way to the Stone Age
engraving of Athena. Both were born from the "Cone & Square,
and this was readily recognizable in the monkey, but only thanks to
lessons learned from the engraving. Then, the monkey taught me
something new, too. The "13-step" pentagram construction
was something I had not noticed in the engraving, and so I
was very eager to test it there. It worked out great, revealing
the back and forth flow of ideas between the two works.
Imagine
my bewilderment at discovering, many years later, that the
"13-step" pentagram construction gave birth to the ground plan of
the three great pyramids of Giza, completing a trilogy with
this motif! In contrast, I know zero examples of this
construction from anywhere else in our media, literature, etc. Even if
some exist, they are rare enough to be practically non-existent.
The fact that no one seems to care, tells me that my research
may be somewhat misunderstood and underestimated. Of course, missing
out on apparently coordinated scientific communications from
widely scattered points of the far past is plainly bad. If the data is
just positive information, the fine is blissful, just a little
ignorance. Of course, if the messages are meant to assist us in
averting general disaster, then I'd rather be wrong.
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Appendix
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•
Reconstruction
of the Circles around the Head, Hands,
and the Feet
•
Reconstruction
of the Monkey Frame
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Reconstruction
of the Circles around the Head, Hands,
and the Feet
Despite fitting the
original Head-Hand-Foot circles to the image by
eye - their positioning to the Monkey-star
turned out easy to define in simple geometrical
terms resulting in a neat blueprint - key to the
monkey's reconstruction.
Hand-circle's
Exact Coordinates
First coordinate:
Its center
is on the vertical line b1, which emanates
from the Monkey-star's tip just above (it is a major
line in the star's grid).
Second
coordinate:
Pentagon No.
2 in these diagrams is a
direct projection of the inner pentagon of the Monkey
Star. Its rotation about the star's center describes a
circle, which is tangential to the Hand-circle
(magnified view below). This solves the second
coordinate for Hand-circle's reconstruction.
At
this point, we can reconstruct the Hand-circle, and
the line-1, which is the laser-like line of sight from
the center of the Monkey Star through a pointlike
aperture between the hands. We can also reconstruct
line 3.
Foot-circle's
Exact Coordinates
First
coordinate of the Foot Circle:
This
idea is straightforward. Line-3 originates at the same
point, at which Line-1 exits the Hand-circle. It
is a tangent to the top of the Foot-circle,
giving us its elevation.
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Second coordinate of
the Foot-circle:
The
pentagon we see inscribed into the Foot-circle is a
direct projection of Pentagon No.
2 downwards and parallel to line "b".
Two
coordinates give us the Foot circle. The star
lines we see within it then give a number of
important parameters on the feet. For instance, we
see the extent of the small toe on the left
foot given in the diagram. The left foot is
indicated by its high arching instep, an adaptation
for upright posture and fast running.
Special Effect
Two
distances involved measure 17.9999..
X-Star meters - almost a perfectly round value:
These are the distances of the centers of both the
Foot-circle and the Monkey Star to the nearest
corner of the other circle's pentagon.
Head-circle's
exact coordinates
First coordinate of
the Head Circle
A
line from the Head Circle's center perpendicular to
Line-1 is a tangent to the inner Monkey Star
circle. And the line drawn from the center of the
Monkey Star as a tangent to the Head Circle will be
perpendicular to Line-1.
Second coordinate of
the Head-circle
It
is given by the Square, not seen in the diagram
above. It involves a major line of the
Square's grid (through the 1/4 point of its
y-diagonal.
*
The distance between the centers of the
Head-circle and the Cone's Key-circle (
see the "seat1.htm" for details on the
Cone) is quite interesting
11.777,777,67...
X-Star meters.
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Reconstruction
of the Monkey Frame
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The
Golden Triangle
The
triangle inscribed into the rectangle in the diagram above is a
pretty good facsimile of the Golden Triangle. The angle at its tip is
35.8 degrees, i.e., it is very close to being like any of the five
yellow triangles on the inscribed pentagram in the above image.
The
scale model of this situation is very reproducible from memory This
is the second such scale model we have for the monkey.
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The
idea seems to be that the Monkey Frame's intended height
should equal the Foot-square's
perimeter. (4x one side of the
square inscribed into the Golden Circle)
The
idea is easy to reproduce (see above), because we know the position
of the Foot Square. We get the southern and northern lines of the
Monkey Frame, plus one axis.
The height of the rectangle
also gives us its width. Next, we need to determine its East-West
position.
*
It seems that the lower line of the triangle
pointing west passes through one inside corner of the Monkey Star.
That point is marked by a small yellow circle in the diagram above.
So, we try this idea. See the reconstructed Monkey Frame below,
where the inscribed triangle is exactly 36 degrees at the tip.
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The Monkey
Frame turns out slightly higher, and slightly
narrower. We can just see daylight
between the Foot-square's base and the lowest
point of the foot. The Monkey Frame fits
especially well on the western (right) side,
to within a couple centimeters. Everything
else in the reconstruction below, like the
Foot-square's width, the axes, and the
Arms-Square, turns out very exact. Note, how
the straight horizontal line of the right forearm
is completely blotted out by the Frame's
horizontal axis. The same line on the upper arm is
similarly blotted out in its straight part by one
side of the Arms Square
Diagram
below:
Another view of how well the
geometrical template fits over the monkey figure.
Note, how the Big-X lines almost disappear
without trace under the star lines.
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Meanwhile, competition
is doing reconstructions of Nazca figures, as
well:
http://www.onagocag.com/nazca.html
The
reconstructor, Joe Nickell, chose primitive methods to
emulate the ancient Nazcans. He does not think Nazcans
could measure angles! "...
there appears to be no evidence that the Nazcas
had such a capability" he wrote.
Jiri
Mruzek
If
you'd like to contact me, or weigh in with an opinion, I am at Yahoo.com.
Just use my name without the space and use a
heading like ancient mathematics, or so.
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last edited: 12-23-2011
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