textfiles/bbs/KEELYNET/UNCLASS/monkey1.asc

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|  File Name      : MONKEY1.ASC      |  Online Date     :  08/17/94           |
|  Contributed by : Bert Pool        |  Dir Category    :  UNCLASS            |
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Below ia a concatenated file on the Nasca monkey.  The file is incomplete as of
the date of posting, but I will add to it should I get the other parts.  this
file deals with some VERY interesting recent mathematical relationships
discovered in the form of the drawing.  -- Bert
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From:    John Powell
To:      All                                    Msg #124, Aug-04-94 08:21:00
Subject: NASCA MONKEY 1

 * Originally By: Jiri Mruzek
 * Originally To: All
 * Originally Re: NASCA MONKEY 1
 * Original Area: National Science Echo
 * Forwarded by : Blue Wave v2.12 OS/2

Nasca Monkey  - the Golden Mean Champion of America

Yes, there is much more to this image than meets the eye!  To prepare the
ground for a fair judgement of its true worth, I must emphasize that the
following is generally known and accepted by Art Historians, if not the general
public :

a)  The <20>-constant .618 0 339 887..., known by artists as Golden Section, or
    Golden Mean definitely plays a major role in Art. It played an important
    role in Antiquity. It was made popular again by such as Leonardo da Vinci
    and Albrecht D<>rer, and has remained so until this day. Many of the
    greatest masterpieces contain a hermetic structure based on the Golden
    Mean. Artists impose such order upon their work believing that it enhances
    its perfection and beauty. The Golden Mean compasses once popular with
    Renaissance artists serve as physical evidence of this trend.

b)  An assortment of valid methods exists, by which such hermetic structures
    can be studied and exposed.

I haven't done anymore than apply such methods, where no one had bothered
before. In this, the results are impersonal, and they are easily repeatable.

The  hermetic structure of the Monkey's figure is based upon the Golden Mean,
to a greater mathematical depth than anything we know of in Modern Art.

Too bad that we can't have graphics here, as my analysis depends on graphics
heavily. Still, some figures, such as the "Cone & Square formation, I describe
in enough detail that you may recreate them in your CAD program.  It would be
nice if you had a copy of the Monkey, if possible - magnified. With the
Monkey's image available, I invite you to verify what I say.  This post bases
on the latest chapter in my "Secrets of the Pentagon"

***Discovery by the means of another discovery***

The hard, but brittle surface crust of the Peruvian desert has been forming for
thousands of years. If you tread on it, the crust of small pebbles reddish from
oxidization crumbles easily, revealing the contrasting ochre color of the soil
below.  Beginning in prehistorical times, some would exploit this to decorate
vast tracts of the desert near the small town of Nasca with a puzzling
collection of straight lines from horizon to horizon, spirals, large
trapezoidal clearings, as well as various animal and plant figures on an
imposing scale.

Lately the Ad-Industry got in on the act as well, trying to impress air-
travellers. This just confirms that Nasca was always meant to be seen from the
air, one way, or another, if not by such as airline passengers, or flying
saucer occupants, then by gods, deities, and spirits.

The largest clearing at Nasca can still be espied from a low planetary orbit,
while at the limits of vision five-hundred kilometers away, almost directly
across the Andes, there lurks the famed archeological site of Machu Picchu.
Naturally, numerous speculative theories have been advanced on Nasca. However,
the forum bases mostly on the observations and findings of one prolific
researcher - Maria Reiche, who used to teach mathematics in her native Germany,
prior to becoming Nasca's guardian angel.

Maria devoted her entire life to this site in an enormous individual effort.
Living like a bedouin, she patiently did her work, dusting off the desert with
a broom to revive faded figures, sketching, measuring, etc. It is more than
likely that without Reiche the figures wouldn't have survived irrigation
plans for ranches in the area! Luckily, Maria managed to win Peru over to the
conservationist side.

One of few points most agree upon is that the line makers had to be good at
land-surveying techniques to implement the designs, which they couldn't see in
their true shape from the ground level - as well as they did.  Yet, the
consensus stops well short of wanting to imply that the Ancients had used
science, which could be seen as exceptional in its era. The assumption is that
the Nascans were skilful at scaling and transferring of otherwise quite
unscientific designs (decorative, or religious) onto the pampa.

On the other hand, Maria Reiche had become firmly convinced that the lines hold
ingeniously encoded information. Accordingly, she had spent much time on trying
to break the code.  One possibility Reiche gave serious consideration, was the
"sacred path" idea, which likens the lines to the still unsolved "knotted
cords", once used by the Incan civilization as a way of writing.

Often so productive in ancient explorations, searching for possible connection
of the markings to astronomy had so far brought disappointment to all who
tried, including Reiche.  Most such searches had concentrated on the first
millennium A.D., to which researchers credit the markings' genesis.  Critics
complain that Reiche failed to document any of her ideas in a sufficiently
convincing manner, as she has published just too little material. Yet, none did
more than Reiche. With her exception, Nasca has been avoided by serious and
devoted researchers.

     Secrets of the Pentagon - Nasca Monkey
                             *
This report represents a new stage in Nasca's research.  It shows the Ancients
engaged in a game of encryption, for which they chose a logical code derived
from the geometrical science.

Early summer of 1991, Prague, the Czech Republic: Mrs Zdenka Hrub<75> gave me a
copy of the nine-fingered Monkey figure from Nasca. She was aware that methods
of analysis, which can be best described as reverse-engineering, had previously
let me document how one ancient engraving on a stone tablet from La Marche,
France, encodes ideas of exact geometry. Having come across mentions of Ancient
Science in the context of Nasca, she asked what my methods could bring to
Nasca's research.

The La Marche Engraving is easily the Most Mathematical Art-Piece In the World,
which, apart from appearances, has nothing to do with freehand drawing.
Without delving into details, it encodes a complex plan, perhaps of an actual
device, vibrant with golden harmonies of the <20>-proportion.  The device itself
may not be of any practical value to us, but there is no doubting the
importance of a potentially huge reservoir of ancient information in Logically
Rational Code.
                       *
As to the Nasca image, I realized at a glance that the three very longest lines
in it could hold regular pentagram angles together, and I was right about two
of those lines. Since the pentagram-pentagon form plays a central role in the
La Marche Geometry, I was automatically interested.

The image of the Nasca Monkey looked a bit roughed up from being copied over
and over. The lines looked cancerous.  Still, after some tests, the image
showed several unexpected sophisticated aspects, strongly reminiscent of La
Marche.  But, a better copy was needed for more testing.  Having written a
brief report on the Monkey for Mrs. Hrub<75>, I had put myself back to work on the
La Marche problem, which has preoccupied my mind since 1985. Over the years, I
have issued several reports on the fact that the ancient engravers knew
scientific geometry. But, to my regret, the reports elicited only passing
interest, i.e., were shown the door.  I would respond to such setbacks by going
back to the drawing-board to do more work for the inevitable breakthrough.

As you see, I've progressed to being the "boy who cries Monkey" on the FidoNet.
Times are tougher nowadays, since the "boy who cried Wolf" (read von D<>niken),
was caught in the act of misrepresenting evidence on Nasca. I hope that what I
do reinvests the site with its "old magic".

Having finally put the Monkey's image, into my computer, there ensued such a
string of sensational findings that I decided to change strategies. La Marche
helped me discover the secret of the Nasca Monkey, and now, it shall be Nasca's
turn to blaze the trail for both.

In the end, we have to deal with the mysterious Echo of the pivotal ideas from
La Marche at Nasca. I cannot imagine otherwise, but that the implications of
both sites disseminating their message in the same code - must be stunning, to
say the least!

     Geometrical testing

[There is nothing drearier than descriptions of geometrical figures without
graphics. Yes, Big News can be incredibly boring when passed in mundane
technical detail. I have no cure for this.]

For the tests, first, I procured a copy of the Monkey as published by Maria
Reiche,  The new image was wonderfully sharp and clear in comparison to my
original one. Next, I had it professionally converted to CAD format, which made
the image available to computerized testing.

Reiche found out about the giant image of the Monkey on the pampa from
commercial pilots in 1952. It was her favorite figure, thus, her measurements
of it are meticulous.  It is in connection with this Monkey that she
hints at a secret system of geometry!

First computerized test - the pipe-dream test

If this test failed, my vision of a five-pointed star would have had vanished.
I went through its motions, thrilled by the moment of truth.  The Monkey has
one dominant feature. It shelters in an assymmetrical X-like tree, about 180
meters tall - the X-Fork.  In the test, the two lines of the X-Fork had to
match the 36-degree angle to a narrow fault tolerance.

I rotated the longer line [a] exactly 36<33> about the X's center.  In a flash, it
smothered the shorter line [b] out of sight.  This effect results from the X-
Fork matching the whole 36 deg.  angle to the imperceptible 0.02 deg. The test
was a success.  It shows that the Monkey lives in a Magic Golden Mean Tree, put
poetically. The Monkey's tree shows potential of growing into a 3-D star with
twelve pentagram faces - Plato's DodecaHedron.

X-File: Pentagram (a brief glimpse into its rich past)

The <20>-ratio, or the "Section", as the Pythagoreans called it, occurs on only
one regular figure - the pentagram. Pythagoreans protected their knowledge of
pentagram's secrets, having sworn to seek and destroy all those who would
betray them. Yet, they freely taught other mathematical knowledge... Paradox?
Since they had no gain in protecting these secrets, I think that they must have
considered them dangerous.  Dangerous Mathematics? Strange. Well, perhaps not
so strange if the Pythagoreans thought that Science had been misused before.
There is no shortage of myth on Wars between Gods.

There is also one small issue of the Secret of Life.  By my own interpretation
of his passage on the solids, Plato claims that the Dodecahedron - the 3-D
solid with twelve pentagram, or pentagon faces - holds the Secret of Life, as
this was the Divine Design with which God had animated the Heavens, i.e., the
Universe. Note, he does not use "Earth"!  Our translators have two dictionary
options for the word Plato had used here:

   a) to draw pictures of beings
   b) to animate with soul

Translators opt for

   a) without hesitation and then muse at the obscurity of their translation:
      (DodecaHedron, with which God had decorated the Sky, or Heavens.
I choose

   b) It keeps Plato linked to Pythagoreans, and I do see around me the
      countless simpler forms of Life like flowers, or seastars proving Life's
      pragmatical use of the Golden Mean and other secrets of the pentagram for
      its own purposes..

By Magic traditions, the pentagram's domain cannot be invaded by Evil. Again,
and again, this star is ascribed a Holy, or Sacred status (as in Sacred
Geometry.) For the protocol, the starting position in pentagram's construction
is a cross (the x,y axes).  Lucas Paccioli - the "monk drunk on beauty" -
wrote his book on the Golden Mean as on the Divine Proportion, but Leonardo da
Vinci illustrated the same book, and so it is mostly known under his term for
it - the Golden Section. I prefer "Golden Mean" because it is shorter.  With so
many challenges to our researchers, we stand to hear more on Pentagram's
secrets in the future.

      X-Fork

The 36 deg. X-Fork permits use of its two lines as "guide-rails" for expansion
of a pentagram on each side from the X-point.  We seek a pentagram, which fits
the position intelligently.  Significantly, the expansion comes to a multiple
stop against a series of points. Each point of this natural barrier suggests a
very similar size for our X-Star.

   The Third Line

The key to setting the X-Star's size - is in the lower of two near-parallels
sloping up across the image from the left, and passing at about the same
distance from the X-Pt.  This is one of the three longest lines, which first
drew my attention to the image - as I had mistakenly thought that with the
other two lines of the X - it formed a triangle, which you find on the regular
pentagram.

The Third Line is already very interesting. It rounds out to the 60 deg. angle
with eight of the sixteen parallel lines forming a grill on the right, which
the Third-Line crosses approximately through the middle. Since 60 degrees is
normally found on the even sided triangle, this adds interest to the position.
The Third Line turns out to have a hand in setting the X-star, after all. We
have to extend the X-Fork's longer line (a) slightly until it reaches the Third
Line at the Third Line-Point.

Onwards, the length between the Third Line Point and the X-Point becomes the
standard length for all X-Star arms.

Important! The proportion of this standard length to the rest of the X-line (a)
above the X-point, is as the proportion of that rest ... to the whole length.
Here, we are describing nothing less than the Divine Proportion!

In other words: the proportion of the shorter side to the longer one, is as the
proportion of the longer side to the whole thing.  "The Monkey lives in a Magic
Golden Mean Tree" - my earlier poetic expression now sounds more serious. The
X-Fork has both, a significant angle, and a significant proportion.

The first X-Star, which is set between the Third Line-Point and the X-Point, is
tagged as X-Star-1.

X-Star-2 is a mirror image of the X-Star-1 through the X-Point serving as the
center of symmetry.  In other words, we simply flip the X-Star-1 over the X-
Point to get the X-Star-2.

The X-Star-3 is a mirror image of the X-Star-2 along the same axis.  In other
words, we simply do the same flip with the X-Star-2.

The symmetries between the first two X-Stars and the Image are impressive
enough to oblige us into checking if this sphere of order extends towards the
Monkey. Hence, we project the X-Star-3 there. The X-Star's geometrical shadow
upon the Monkey produces so graceful an effect, that the X-Star-3 also earns
the name "Monkey Star".

The Monkey Star's center closely coincides with the Monkey's own center of
gravity, as the Monkey's head, hands and feet all orbit at about the same
distance around it.

Once we set the X-Star-1 we remain committed to it, that is, anything else in
the Geometry of the Monkey unfolds from here!

Into the three X-Stars, we draw the axes of symmetry, as well as the outer, or
perimeter circle.  Henceforth, we may see for ourselves how the Ancients'
vision of the pentagram must have included its axes. The Monkey seems to climb
the central axis of the X-Fork like a pole-climber in spiked boots. Also, the
Monkey shifts its body into the Monkey Star's axes, in effect wearing the Star
like a suit.

  The Ten-Fold Symmetry of the X-Fork

The X-Fork represents one tenth part of a circle, hence ten X-Forks will form a
whole circle. The total overlap is a tiny 0.2 degree, or 1/1800th of the
circle. But, this wonderful fact gives no guarantee that the Monkey parts will
mesh with each other. Yet, they do. Try this on your computer!

An amazing effect develops of a Daisy Chain of Ten Monkeys!  The hands of each
monkey find a hold on the midsection of the next monkey in the chain. One loop
of the spiral tail falls snugly around the head of the monkey behind, in
effect, making the head disappear in a large halo. This design is so perfect,
so professionally composed that I cannot imagine it as the result of an
accident.

 The Proper Orientation for the Monkey

The Monkey is mostly shown as if both its feet and hands were touching the
ground. This, so to speak, puts the Monkey in its natural place, but takes it
out of alignment with the four compass-points. (North, or South aren't at the
top of page) Yet, the Monkey does a great balancing act, achieving a remarkable
Axial Equilibrium with the Monkey Star.  If in general, monkeys use their tails
as a main instrument of balance, the Nasca Monkey's tail is notable for
balancing the Monkey with the X-Star's axes. For instance, the bases of both
the tail and the hands hold the X-Star's horizontal.  In consideration of this
balance, we should show the Fork as upright in at least one version. If true -
the rebellious Monkey has stood up, its hands free...

The Monkey faces towards the Pacific, but it seems to be looking intently at
its hands, which are held in a very active posture.  There is nothing in the
hands, but my imagination can easily draw in a number of things, such as a
dowsing rod, or a ball.  The truth is even better.

              Precision Grip

We find that in three cases the Monkey aligns its fingertips in pairs to the X-
Star directions, while grasping, or strumming the circle around the Monkey Star
like a string. It looks like the Monkey holds the circle between its thumb and
index digits.  We also find the rest of the hands' design to be similarly
deliberate and precise in its many other aspects.  Such dexterity in hands and
fingers is normally limited to humans and higher primates. The hold between the
thumb and the index finger is known as the Precision Grip.

But the Americas were ever inhabited only by such lower primate species, which
lack the elongated thumb opposable to the other fingers on the same hand, i.e.,
they lack the Precision Grip.

In general, the Monkey is not seen as Anthropomorphic. Yet, it has very capable
hands with sensitive fingertips essential to the Precision Grip, and so, in the
absence of a local simian model, we have to choose between anthropomorphism, or
a non- American model for the Monkey.

BTW, we may also choose to view the Monkey's hands as if they were portrayed
palms up. This palms-up posture looks no less realistic. Versatility belongs to
Monkey's special hand effects.

              Super-Anthropomorphism

In the context of horizontal balance with the X-Fork, the Monkey takes an 18
deg. step. After both feet step once, the Monkey will have moved 36<33>.
Therefore, these steps are well choreographed  for the Daisy Chain of Ten
Monkeys (ten-fold symmetry of the X-Fork).

Seeing the symbolism in this, we must ask if the Highly Unusual style of the
feet is also symbolical by design. For one, the Monkey's heel is Over-
Emphasized to the point, where the leg becomes centered over the foot. Thus,
the Monkey would seem very well adapted to a bipedal way of life...

Another super-anthropomorphic feature of our Monkey is the clear, nicely
arching instep of the left foot, a prerequisite to a good two-legged mobility
on the ground.  In principle, the foot comes closer to the human norm than even
the human form...  The second to fifth human toes are presently atrophying,
since the foot doesn't need the prehensile capability anymore.

Given the evolutionary trend, does the Monkey cartoon it?  This sounds silly on
the surface, but whereas in general the monkeys' feet aren't all that different
from their hands - that difference is more pronounced in the Nasca Monkey than
even in humans...

Researcher's dilemma - What Next?

Let's say that Maria Reiche noticed (how couldn't she) that the Monkey shelters
in a Golden 36 degree X-Tree. A mathematician - she has observed the
symmetries, the proportions and the possible X-Stars. She could have created
the Daisy Chain of ten Nasca Monkeys. She could have noted pretty well
everything we have noted so far.

It is obvious to the researcher that the Golden Mean and the Pentagram are
important to the Nascans, but it is not obvious What To do Next. The list of
clues is getting desperately short.  However, we can take a clue from La
Marche.  While others have to search for parallels between the Monkey's
Geometry and our own, we know some interesting concepts, in which the La Marche
Cavemen thought about the Pentagram. This proves to give us a decisive edge!

***  Reviewing Nasca by the Standards of La Marche

            The Cone

In the Cone, La Marche sports its own version of the X-Fork!
                       !!!
Some time ago, I imagined that some interesting arcs in the Engraving are like
Pods, inviting correspondingly shaped circles to be placed upon them. So, I
took the liberty to complete the arcs into circles. Low and behold, these
circles create a kind of Harmony of the Spheres with the image, which would
seem natural, if the Artist saw and thought in terms of those circles all the
time, rather than mere arcs.

Among the circles, I found three, which together imply the Cone Formation:

   1) Their centers lay in a straight line.
   2) The three circles are lined up by size to represent a Regular Linear
      Growth rate!

In other words, a line can be drawn on each side, which touches all three
circles.  In the result, the three circles with the two side tangents look like
icecream Cone with three scoops inside.

The purpose of the Cone Formation had remained a mystery to me until I saw the
potential in its pentagram angle, and began looking for such specific
pentagram, which, if at all possible, would fit the position intelligently,
i.e., explain it.  The concept of the Cone as a geometrical puzzle turns out to
be so straightforwardly Scientific that not even a University professor could
hope to improve upon the idea.

The clue is as solid and Major-League as can be. We already have the Cone and
its sides. These sides are External Tangents to the circles. Theory says that
External Tangents are drawn from the External Center of Similitude of the
Circles, which in our case is the Tip of the Cone.

Of course, theory also recognizes and deals with the Complementary Opposite of
the aforementioned external concepts.

  1) The Internal Center of Similitude at the point S, from which
  2) the Internal Tangents are drawn between the smallest and the largest
     circle of the Cone.

Our recognition of this External -- Internal pairing in theory leads us to
testing for the same recognition in the Ancients.

!We let this theoretical pairing set the trial pentagram [S]!

  1) The internal center of similitude (S) on the Cone becomes the center of
     the trial star [S].
  2) The Cone's tip orients and sizes the S-Star.

 Now, all the jig-saw pieces start fitting the common pattern:

*** The Circle-Triplets

Once more, the S-star has an outer perimeter circle as well as an inner circle
around the inner pentagon & pentagram.  We begin by noting the first clue: the
S-Star's inner circle looks just as big as the middle of the three Cone
circles.

Then we discover another interesting clue. The radii of both circles fit the S-
Star's arm a near-perfect five-times, one set a hair short - one a hair too
long.  In effect, the two circles alert us to the existence of a third circle.
It is visually the same as the first two - but it fits, or maps the star's arm
five-times exactly.  In this sense it is a Unit Circle, but the term
"Construction Circle" is actually better suited for it...

When concentric, the three circles look like a single circle.

     If the unit circle's  radius =  1,
     the inner pentagram circle   =  1.0040...
     the middle Cone circle       =  0.9975...

***Mapping the Cone with the S-Star's Unit Circle!!!

This is a very rewarding stage in the S-Star experiment.

  1:) Let's draw one Unit Circle from the center of the largest Cone circle.
  2:) Now, Let's map the Cone part of the S-Star's by the Unit circles
      beginning at the Tip of the Cone.

Result:

  The Unit Circle drawn from the center of the Large Cone circle now matches
  perfectly to the nearest two of the Unit Circles, with which we mapped the
  Cone. The circles fit the Cone!  Ergo, we may logically reason that the top
  Cone's circle was generated  from the S-Star by the method of mapping with
  standardized circles.

Likewise, the Middle Cone circle was generated during the same mapping process.
We may so reason because:

  Its center is given by the upper intersection of the fourth circle row from
  the Cone's tip. From there, we draw it so that it is the Cone's tangent.

The small circle on the Cone is designed to fit between:

  a) the Internal Tangents
  b) the Cone's sides.

Hence, it is logical to reason that all three circles of the Cone are generated
from the parent S-Star.

            <to be continued in part 6>

--- Blue Wave/QBBS v2.12 OS/2 [NR]
 * Origin: Absence of Evidence is not Evidence of Absence BBS (1:261/1201.0)
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