MACHU PICCHU'S DESIGN COULD TELL ITS AGE
Transcript of MACHU PICCHU'S DESIGN COULD TELL ITS AGE
A DIMENSIONAL ANALYSIS OF MACHU PICCHU AND THE INTIHUATANA STONE COULD REVEAL HOW LONG IT TOOK TO BUILD THEM
Machu Picchu is considered by
many to be one of the 'Navels of
the World'. This is a vague term
that implies "this is an important
place" and we use it in that sense.
In the book The Timekeepers of
Ancient Earth the importance it
has is attributed to its
geographical and astronomical
function; specifically the
importance is derived from the
way the monument is exposed to
the sun. To us that is not an
abstraction but a concrete
relationship that can be
demonstrated. In this regard the
other term that is often used for
these places 'Sun Dial' is more specific. Throughout the book we have shown how the obliquity
angle of the earth's axis is reflected in the design of many archaeological structures around the
world. Machu Picchu, we claim is the quintessential Sun Dial; the entire citadel, we explained how
it was built to track the sun. As will be shown here its design tracks the earth's axial tilt over the
ages. The Intihuatana stone froze the position of the sun earth relationship in a distant past;
assuming the stone was designed and accurately built to geometrically align with the sun at the
summer solstice at that location in the southern hemisphere. Any difference with the expected
alignment of the sun with the angle of the stone in today's astronomical conditions we believe
allows for extrapolation into the distant past to calculate its probable age. To conduct an analysis
it would be required to obtain precise measurements of the pyramidal portion of the stone and
an accurate reading of its azimuth along the face of the stone supposed to receive the sun at the
summer solstice. Few references exist regarding the physical measurements of the Intihuatana
Stone. Rolf Müller's measurements taken sometime after his visit to Machu Picchu in the 1920's,
are considered to be precise. He published them in the book The Inca Empire, Springer, 1972,
quoted by Dieter B. Herman in his article 'On the Intihuatana at Machu Picchu' available on line at
www.dbhermann.de.
In this study we seek to establish the geographic alignment of the Stone in relation to the
geometry of the citadel. In the book we claimed the Citadel is aligned to the winter solstice circle
of illumination. That is, the Citadel follows the general direction of the earth axis' tilt at the solstice
-23.44⁰(336.56⁰) also, the actual angle of the CI at that latitude is represented in the terraces, i.e.
335.89⁰, see graphic. Also, at the culmination of the summer solstice the sun is perpendicular to
the CI which in December 21 has an angle equal to the complement of 335.89⁰ (360.0⁰-335.89⁰
=24.11⁰). This means the sun has a theoretical azimuth of 114.11⁰ at the solstice. Using a solar
angle calculator, for December 22, 2015 the calculated azimuth at sunrise at 6:25 will be 114.33⁰.
In the graphic overlay above we rotated Müller's diagram to match the current geometry; from his
30.5⁰ to 24.11⁰. The foregoing, confirms the claim the citadel was built with a specific purpose: to
reflect the geometry of astronomical events. However, the above data does not associate the
Intihuatana stone with the astronomical event. That association exists only through folkloric
reference or legend; also, some measurements of the shadows cast have been reported which
'verify' the stone's name "The Sun's hitching Post".
We set out to prove whether the geometry of the stone does reflects the solar mechanics as is
believed. We were planning to rely on Mr. Müller's measurements since we believe they were
made in situ, but we found that constructing the 'parallelogram' shaped diagram of the stone's
base using the angles and the lines' lengths given by Müller, it doesn't work out geometrically; the
lines cross at the upper left corner, as shown in the schematic above. We realized we needed to
confirm his data. Keep in mind that short of going to the site with precise measuring instruments
everything else is an approximation. A lot has been said about the stone in relation to the sun's
position in the sky, but to our knowledge, there is no definitive proof.
Short of going to Machu Picchu with a Transit and rulers we did the next best thing and cheapest! We Googled for photographs and to our amazement we found several excellent ones taken from various angles. We took the ones having the best alignment with a coordinate grid and proceeded to measure the Stone in absolute units. We used a photograph which appears to have been taken head on at eye level facing the south east face of the stone1. This is the stone's face which is supposed to receive the sun perpendicularly at the solstice as shown in Müller's diagram. The
part of the monument in question is the protruding pyramidal extension on top. Due to the unknown positioning of the camera by the various individuals who took the photographs made the stone's size measurements taken totally random from photo to photo; but the measurements are internally consistent for any one photograph. To eliminate the inconsistency, we took the best photograph, i.e. closest to having a cardinal alignment and normalized its height and width measurements -found their ratio utilizing a computer graphics program. We assigned a length equal to unit (1) to the SE face bottom line and then proceeded to take the other edge measurements which make up the other faces of the stone as they are found in the chosen photographs. Utilizing the 'master reference' we normalized the measurements of the remaining sides. Via this procedure we arrived at a fairly precise set of measures. Since our 'master side' was given a base of unit length, then we were able to multiply it by the corresponding value for the same side and line given by Müller. Following the procedure all of our measurements came substantially close to those given by him. The SW and NE are the wider sides of the stone. The NE face is about 12.9cm shorter due to the gradual increase in height of the base starting on the SE and ending on the NE. Müller doesn't show the difference in one of his diagrams but the length given for the SE corner is equal to the average of the two heights. In the graphic on the next page we show the variance in terms of the ratios of the two heights.
Following these steps we confirmed the shape and size of the stone's base, roughly, but not its
cardinal alignment. Müller's diagram shows the SE face of the stone -the reference face- as being
aligned at 30.5⁰ vs. North; that is a 6.39⁰ difference vs. the required 24.11⁰ for the sun to impinge
perpendicularly on this face at the summer solstice considering the theoretical azimuth the sun at
about 114.11⁰. Did Müller make a mistake? Eventually that can be easily confirmed by someone
with the proper instrumental measurements. The geometry discussed here tends to prove the
stone's lengthwise general alignment with the solstice. Any significant discrepancy found vs. the
theoretical value of the stone face receiving the sun would allow one to calculate the age of the
stone based on the current drift rate of the earth axis angle and the net change over time,
assuming the stone was precisely aligned on the day it was cut and that the rate of change is an
average. The earth's axis drift has been a subject of debate since the late 1800's**.
CALCULATIONS
Every degree of earth rotation is equivalent to 69 miles or 111.78 km. or 111,780 m. The earth's
axis is reported to oscillate 1.7⁰ within the last ±10,000 years1 around today's value; currently
drifting towards the equator along the 80⁰ meridian at 10cm/yr4. To calculate the sun's azimuth at
an earlier time by reverse engineering from the stone's azimuth is theoretically possible. From the
angle we can calculate an earlier obliquity angle of the earth's axis but a small error in the
measurement of the stone's azimuth will result in large time differences as will be shown.
The angle of the CI is found in the SE face of the stone. According to Müller's the angle is 30.5⁰, the
equivalent angle for the earth's axis obliquity angle at the equator is 29.61⁰. This value minus the
23.44⁰, the current tilt angle, equals the angle drift that would have occurred since the stone was
cut: 6.17⁰*. In meters 6.17X 111,780 = 689,682m. or 6,896,820cm. At the current rate of 10cm/yr
the stone would have been cut 689,682 years ago. In this case an error ±0.5⁰ results in an age
ranging between 633,792 years and 745,572 years. Incidentally, the oscillation cycle of the earth's
axis is 41,000 years. *This difference is highly questionable since the calculated tilt range for the
past 5MM years is reported to be only 2.5⁰ 2, although larger excursions are claimed to have
occurred5.
Another common analysis of the stone considers whether the sun casts a shadow at noon time at
the solstice; the results reported in the literature are quite variable. The stone is a truncated
pyramid with a slanted top and a slanted SW side and not all sides are straight; some of them are
slightly bowed. We analyzed the 'shadow' from a different perspective; we measured the angle of
the stone's top slant
and found it to be
11.44⁰ measured from
the SE side and 9.26⁰
from the NW, the
opposite side. We
hypothesize the stone
was given this angle to
reflect the sun's
maximum altitude at
the solstice. The
normal to the first angle
is equal to 78.56⁰, for
the second 80.74⁰; with
an average value of
79.56⁰, this would be
the maximum solar
altitude attained at the solstice. Using a solar angle altitude calculator (susdesign.com), at solar
time noon the altitude angle on December 21 will be 79.72⁰. This is a difference of 0.16⁰. Giving
this rotation the same treatment as above, the probable age of the stone's top cut is 17,884 years
old an age about six thousand years older than Göbekli Tepe.
The angle of the slanted SW side of the stone, which is bowed, was measured; the average slope
was found to be about 6.38⁰ from the SE and 7.27⁰ from the NW, the average slope being 6.83⁰.
To project no shadow at maximum solar altitude, the sun's altitude would have to be 83.17⁰,
resulting in a difference with today's maximum of 79.72⁰ of 3.45⁰, which also far exceeds the
maximum calculated range for the axis tilt of 2.5⁰ in the past 5MM years2 . Performing the same
calculation the stone's age turns out to be 385,641 years old. The slope for the NE side is too steep
at about 2.54⁰. This side appears to be not relevant to the analysis. These ages are incompatible
with any other dating methods. The premise behind the 'encoding' in the stone and the alignment
of the citadel of the earth's motion with respect to the sun needed further support. We could
have continued performing this analysis on every angle of the stone and would come up with
different ages, it could be argued. However, for us to make any educated assumption about each
measurement, we felt it needed to be reconciled with other data points found elsewhere. We
started by taking a second look at Müller's data; The SE face angle of 30.5⁰ implies an axis
obliquity angle of +29.65⁰ and -29.65⁰ (330.35⁰)at the solstices adjusted for latitude yielding a
summer solstice solar azimuth at sunrise of 120.5⁰. Also the winter solstice CI would have an angle
of 329.5⁰ at Machu Picchu; the sunrise perpendicular to the CI would have an azimuth of 59.5⁰.
In the book we reported we had measured the angle of the terraces in the plaza. On the SE side of
the plaza we find one with a bearing of 330.35⁰; similar to another we had described for the
current obliquity angle of -23.44⁰(336.56⁰) and CI of 24.11⁰ at Machu Picchu's latitude. These two
terrace angles are found next to each other. This appears not to be coincidental; however, the
maximum obliquity angle, as calculated above, is out of range; but, there is something else to
consider.
Focusing on the terraces
in the plaza we see a
pattern similar to the
one we had found in the
lines on the Nazca plain.
In our first publication in
2014 we had speculated
the 'star' like
arrangement of lines
found at various
locations represent a
historical record of the of
the earth's axis angle
drift through the ages.
The steps in the plaza are not parallel like most of the other terraces in the citadel. They fan out at
different angles; within a 10.29⁰span and there are 10 steps. Considering the axis drift has a range
of 1.7⁰ it is reasonable (fractional degree changes would have been hard to build) to assume there
could be a factor of 10 built into the angular bearing of the steps; which yields a total drift span of
1.02⁰. This translates into 114,015 years recorded in the steps. This would indicate the layout at
Machu Picchu was accomplished over that number of years. Many researchers, both at Machu
Picchu and Giza have noted the different quality of workmanship and apparent age of the
stonework at each one of these locations. It is reasonable to argue that the Intihuatana was the
last construction at the site: the stone's slant cut; would correspond with the last layer.
The Machu Picchu steps and the Intihuatana stone appear to serve the same purpose as the 'star'
lines in Nazca. We discovered there is a connection between the two sites, as follow: The Müller
solar alignment is represented in lines on the Nazca plain. A 'star' line arrangement we labeled
Star 2 Node 12 in the above graphic, is located at -14.700⁰, -75.142⁰ it includes one line at 120.5⁰
equal to the solar azimuth shown above. The corresponding perpendicular line at 30.5⁰
corresponds to one of the main lines which form the Monkey Glyph; this is the alleged alignment
angle of the SE face of the Intihuatana stone. A line connecting the Monkey glyph with the Star2
node also connects with the Hummingbird glyph at 329.5⁰ the winter CI angle also described
earlier. Perpendicular to it is a line which is part of one of the trapezoidal glyphs at Nazca (-
14.689⁰, -75.133⁰). This line has an angle of 59.5⁰; the sun's azimuth at the winter solstice. All the
reported Intihuatana measurements, we find, are replicated at Nazca. In the book we had claimed
"the Nazca Lines are a cartographer's map to different places" this adds a new dimension, in line
with that claim: Nazca may have been also the template 'blue print' for the construction of Machu
Picchu. Is Müller's angle measurement correct? Finally, if all these line angles are found at Nazca,
then it presupposes the equivalent line representing the 'Old North' would be present as well. In
fact, a line of a major glyph (-14.685⁰, -75.111⁰) corresponds to the 'old North' with an angle of
351.37⁰ vs. 360⁰, also the corresponding 'Old Celestial Equator' 81.37⁰ vs. 90⁰ is also present (-
14.694⁰, -75.178⁰). True Polar Shifts of up to 30⁰ have been reported5. The 8.36⁰shift would help
explain the fossilized trees found at Mt. Archernar and Beardmore Glacier in Antarctica.
The foregoing analysis of the Intihuatana's top slant and the arrangement of the plaza terraces
provide an idea of what the actual age of the last cut on the stone might be. We have shown that
Müller's measurement of the stone's alignment is in question. The wider than expected angle of
the SE face adds a new enigma: why are the same measurements embedded in lines and glyphs at
Nazca and at the citadel? Except for the net difference found vs. the earth's axis obliquity angle -at
the Equator- of 6.17⁰, the geometry of the resulting astronomical layout at each location is
identical; all lines correspond when superimposed -see first graphic. Until Müller's angle
measurement is confirmed, we can only say that today the Intihuatana pyramidal stone is roughly
aligned lengthwise in the direction of the sun's azimuth at the summer solstice in Machu Picchu.
Regarding the larger than expected axial shift, the recorded shift beyond the calculated maximum
could be interpreted as an instantaneous, perhaps, a shift of few thousand years duration which
could have produced the forest in Antarctica. The actual 'blip' in time may eventually be read in
the trees' age.
1 Traveler photo by Cvetopipa (July 2014)
2"Obliquity berger -5000000 to 0" by Tfr000 (talk) 15:27, 6 April 2012 (UTC). Licensed under CC BY-
SA 3.0 via Wikimedia Commons - https://commons.wikimedia.org/wiki/File:Obliquity_berger_-
5000000_to_0.png#/media/File:Obliquity_berger_-5000000_to_0.png
3"Obliquity of the ecliptic laskar" by Tfr000 (talk) 17:58, 21 March 2012 (UTC) - Own work.
Licensed under CC BY-SA 3.0 via Wikimedia Commons -
https://commons.wikimedia.org/wiki/File:Obliquity_of_the_ecliptic_laskar.PNG#/media/File:Obliq
uity_of_the_ecliptic_laskar.PNG
4Wikipedia.
5 Besse, Jean; Courtillot, Vincent (November 2002). "Apparent and true polar wander and the
geometry of the geomagnetic field over the last 200 Myr". Journal of Geophysical Research (Solid
Earth) 107 (B11): EPM 6–1.Bibcode:2002JGRB..107.2300B. doi:10.1029/2000JB000050
**Various theories exist as to the degree and type of axial drift and its causes, some involve
rather complex mechanisms; the more popular ones are: "Total earth Drift and Polar Drift" for
the first, the whole earth shifts with a shift in tilt angle for the second only the mantle shifts.
Copyright©2014-2015