You may have heard about the so-called Bosnian pyramids (which actually are real hills and not man made). The proponent of these ideas is Semir Osmanagić and he also has something to say about the Maya. He has apparently visited dozens of Maya cities in Central America and from this come to the conclusions that “it is in our future that ‘we should become planetary Maya with sophisticated technology which will harmoniously connect the frequencies of the Sun and our psyches. Because the Mayan life is that of the soul living in harmony with the Cosmic processes.’ Here, we have the opposite end of the spectrum of nonsense compared to prophet # 3 who suggests the end of the world.

First something about his Bosnian pyramids. There are supposedly three pyramids built by Illyrians between 12,000 and 500 BC. (a pretty long period and Illyrians have of course been a static ethnic group the whole time). By comparing the heights of pyramids in Mexico and Egypt with his pyramid(s) Osmanagić has come to the conclusion that the same people has built them… He once thought that the Bosnian pyramid was the last one constructed (but there are Maya pyramids dating to the late 17^{th} century AD in central Petén in Guatemala, slightly later than Osmanagić’s time frame). He now believes that it is the “mother of all pyramids” (never mind the complete different shapes of pyramids throughout the world).

Here are some quotes from his book The World of the Maya (p. 67):

“It is supposed that the Mayan Codexes were written 3500 years ago. With the 8000 years prior to the writing of the Codex, we would have 11,500 years ago – the time of the sinking of Atlantis. Cosmic and natural cataclysms clearly led to this end of civilization as well – that of the great Pacific islands which were the land of Mu.”

If we just leave the mumbo jumbo on various sunken islands and continents to the side, no one claims the codices were written 2,500 years ago. The oldest preserved ones I believe are from the 13^{th} century AD, and there existed earlier ones but how far back in time we can trace codices are not known.

Here is also something wonderful that I, as a settlement archaeologist, must consider (p. 69-70):

“The Mayan hieroglyphics tell us that their ancestors came from the Pleiades… first arriving at Atlantis where they created an advanced civilization. The building of temples in the shape of pyramids enabled the Maya to obtain more energy… from the interior of the Earth, because the pyramids were erected on energy potent points… and from the cosmos, because the energy coming from outside the Earth was maintained longer and was more intense in the pyramids. For additional energy effect the Maya placed powerful quartz crystals at the top of the pyramids. Thus an additional energy field was created for those who needed energy to move through other spiritual dimensions or for healing purposes. The Maya inherited knowledge from their ancestors at Atlantis and Lemuria (Mu). Cities were planned and built around the main square toward which the pyramids and temples were turned. They communicated with the movement of the Sun and the paths of other heavenly bodies.”

I will post something on real lemurs later on (and I refer to primates on Madagascar). Anyway, according to Wikipedia the target of his project in Bosnia “is to complete excavation by 2012. This is in order to ‘break a cloud of negative energy, allowing the Earth to receive cosmic energy from the centre of the galaxy’ according to Osmanagić, who also hopes that it will be listed as UNESCO World Heritage Site.“ Good luck with that…

Johan,

Support to Dr.Semir Osmanagich is huge. Much more, then you can ever imagine in the wildest dreams. Thank to God, that we have people like he is, here with us in Earth.

By:

DAVIDon November 7, 2009at 18:46

I am sure he has supporters since most people tend to believe in fairy tales rather than science. He is nothing but a fraud. However, judging from the number of hits he gets on my blog he is far behind the master hoaxer Patrick Geryl. He needs to come up with some even more nonsensical stuff to attract more people. I am sure he can. I am not judging people’s ideas from the amount of followers they have. It is quality not quantity that is my measurement. Sometimes they can align but not in this case.

By:

Johan Normarkon November 7, 2009at 18:57

He is not a fraud. Time will undoubtedly

show. He has a special mission and we all should help him, not stop him.

By:

DAVIDon November 8, 2009at 22:46

Oh dear, a special mission? Is he the new Messiah?

By:

Johan Normarkon November 9, 2009at 07:14

Dear Johan,

I feel sorry for you- your empty, main stream thinking is , unfortunately, not new in this see of sorrow coled modern human era. Open your mind or, at least, let someone else to do that, or, simply, try to find some another point of interest…

By:

Elviron January 2, 2013at 15:31

Dear Elvir,

Your words are meaningless, pointless and empty. I suggest you read a book or two.

By:

Johan Normarkon January 3, 2013at 20:03

Dr Osmanagich is a brilliant man, and in time will be proven quite correct.

By:

James Tiptonon January 5, 2010at 07:56

Nope. He is far from a brilliant man. Only people with no archaeological education can believe his nonsense.

By:

Johan Normarkon January 6, 2010at 23:38

The worst thing is that this man is still getting a lot of money for playing in dirt…this has got to end.

By:

Darkoon May 26, 2010at 13:51

I wonder who is willing to waste his/her money on such nonsense?

By:

Johan Normarkon May 26, 2010at 14:51

As seen form their website:

http://www.piramidasunca.ba/en/index.php/Donatori.html

Unfortunately this type of madness can be beneficial, not just for tourism in general, but there are also individuals who exploit this on one way or the other…

By:

Darkoon May 26, 2010at 18:51

Maybe I should create my own mad theory that I can sell in books and become millionaire at the same time. It seems to work well for plenty of people. I just need to figure out how to come up with a new end date and find a new mountain that is pyramid shaped.

By:

Johan Normarkon May 26, 2010at 19:19

You are the fraud. I would suggest you read more than a couple of books.

By:

Davidon May 26, 2013at 03:20

You mean there are more handbooks on how to fool people like you?

By:

Johan Normarkon May 26, 2013at 05:33

Even though it is quite tempting, i doubt it would be the right thing to do ;p

There should be a law by which abuse of scientific data in pseudo scientific projects would be a punishable criminal act.

By:

Darkoon May 26, 2010at 19:36

It will be difficult to implement such a law.

By:

Johan Normarkon May 27, 2010at 10:32

True, but its not impossible i reckon.

It is nice to see others contributing to downfall of this nonsense:

http://www.archaeology.org/online/features/osmanagic/

http://circulartimes.org/Bosnia%20Semir%20Osmanagic%20comments%20on%20Dr.%20Schoch%20and%20Dr.%20Dowell%20on%20Bosnian%20Pyramids.htm

By:

Darkoon May 31, 2010at 18:14

wat a fraud! sorry bosnia but thats just a hill.. i think he is too attracted by ancient egyptian and mesoamerican (mainly aztecs, mayans, and inca) pyramids that he wishes to find some connection or relation between them and bosnia. descendants from atlantis? please, stop it…

By:

Perezon December 16, 2010at 04:41

He is still active…

By:

Johan Normarkon December 16, 2010at 18:39

fuk al y’al, I’m open minded.

May I be among those few wu wil enjoy the comin events & shud Semir nid mi help hand I’m glad 2 assist.

By:

carvanon December 31, 2010at 12:39

The man is a fool…did you see the videos? why are there no better photographs? Because people would undoubtedly find out this is a hoax. I’ll go as far to say that a this point, the Bosnian government as well as the moron they can an archeologist would openly deceive us because it’s brought so much to Bosnia. After all the pain this area has endured, it saddens me that it will undoubtedly go through humiliation. It’s currently 2011, I’ll wait a year and bet money that nothing will happen.

By:

Canadianon February 4, 2011at 06:02

What I wonder is why there actually are people believing the stuff he writes about?

By:

Johan Normarkon February 6, 2011at 21:16

He is a charlatan and that’s it. Nobody came from Pleaides to this planet and nobody is going there. LOL However, these ideas are not Semir’s ideas, he just borrowed those from such clowns like Eric Von Daniken, Graham Hancock, etc. Von Daniken sold over 60 milion books telling idiotic stories about antient astronauts. As long as there are fools to buy lies there will be liers to sell em. Simple.

By:

askeon March 4, 2011at 07:09

Von Däniken has the currently best selling book on the “Maya” (and 2012). He is a wealthy man and many other hoaxers envy him and try to come up with even sillier ideas to stand out against the “normal nonsense”.

By:

Johan Normarkon March 5, 2011at 07:31

You were there?…,because I was, and the buildings truly exists.

What are… dont know, but are real.

By:

Alexon September 20, 2011at 07:22

No, I have not been there and that proves what? I have not been in New York either but I am pretty sure there are skyscrapers over there… I do not have to be in Bosnia to know this is bogus.

Are you an archaeologist? Do you know how to date a building? What are the true dates and extents of the architectural features they have found? Where the constructors from outer space???

By:

Johan Normarkon September 20, 2011at 09:30

Just watched the doco “Uncle Sem & the Bosnian Dream” from 2008 that was filmed through 2006-2007 and covers a variety of locals and visitors with a fairly non-critical approach to our Sam aka Uncle Sem, Sem or Semir Osmanagić.

It was immediately apparent how fraudulent and laughable the concept was and remains. A sad combination of misguided patriotic zeal and a desperate need to bring growth to the area, mixed with pseudo-science and brazen bravado.

The supposed excavations were so obviously an attempt to shape the surrounding hills into a pyramid form. I enjoyed the film, and of course had to search online to see how far along this venture had gotten.

I have nothing against someone shaping a legit site into a tourist attraction, if that’s what the local economy could do with, and no harm was done, let it be.

There is however questions of authentic sites being compromised and then the issue of perverting history and discrediting actual academics for nothing more than the self-serving gains of the few.

It’s an outright mockery, sham and con.

On a side note, why on web sites related to Semir and the Pyramids (usually involving Semir on some level) do they keep showing a Mayan style temple in most of their related letterheads and banners..?.. it kind of clashes with the Egyptian theme they had going.

But hey, maybe geology, common sense, and aesthetics have nothing to do with this, maybe our self-proclaimed “Bosnian Indiana Jones” will unveil a real pyramid… y’know, one with a McDonalds in it.

By:

Jason Oddon October 25, 2011at 17:31

These people do usually not see any great differences between “Maya pyramids”, ziqqurats or Egyptian pyramids. They find it highly unlikely that people have come up with a pyramidal design at several places. They must have the same origin, etc. Hence, a Maya pyramid will work just as well as a Egyptian one.

I am sure there will be a fast food chain at the pyramids…

By:

Johan Normarkon October 26, 2011at 09:02

But, the circle is such a perfect geometric shape that humans could not possibly have discovered it on their own. Ancient aliens came here showed them how to make circles. there is no other way to explain the fact that humans all over the world know how to draw a circle. it is based on a genetic implant technology of the aliens. implanted in the brain in such a way that it connects to the fingers and hands in the drawing of the shape. Thats why all the human cultures can draw. and use circles in their art.

By:

yaxkukon June 12, 2012at 19:49

You almost fooled me Q!

By:

Johan Normarkon June 12, 2012at 19:55

[...] http://haecceities.wordpress.com/2009/05/22/2012-prophet-of-nonsense-4-semir-osmanagic-and-the-pyram… [...]

By:

Sceptici în România – Episodul 36 - Sceptici în Româniaon March 12, 2012at 09:40

I was born and raised in the heart of the Balkans and I know that there is a lot of ancient history there and myriads of artifacts still waiting to be unearthed. Being a scientist myself, I also know how little we know generally – so I was inclined to give Dr. Osmanagic a credit and share his beliefs about the artificial origin of Bosnian pyramids…until I came across his previous publications about people coming from Pleaides, Hitler escaping to a secret bunker in Atlantis and similar. Uhhhm. Then I happened to read some of Semir’s fierce, ridiculous and childish attacks against renowned archeologists who dared opposing his theory. Something is definitely wrong in this picture, and probably in Mr. Von-Daeniken-wanna-be’s head too. But I still wish that Bosnian pyramids prove to be manmade. It would be great for the tourism in Bosnia and Herzegovina and the Balkans!

By:

Fifi Mahoney, MA, PhDon April 28, 2012at 03:58

Maybe Dr Osmanagic will discover one of the secret Wing Maker’s chambers in the Bosnia pyramids. There are seven sights around the World, one was discovered by hikers in New Mexico, with 23 chambers. plus one big hidden chamber.So there are 6 more places in the World to discover. However, on the Wing Maker map. it shows Antarctica. Africa, New Mexico , and it looks like one could be in Sweden, but nothing In Bosnia. Reading the Wing Maker book, In the first chapter there is also a small connection to the Maya.

But in my opinion, the Wing Maker story, and art, Philosophy, music, was made up by the government scientists and government archeologists . I would have to see more discoveries, and more artifacts. Maybe even in the Bosnia pyramids? Or in Sweden??

By:

Gilgameshon April 28, 2012at 18:15

They are not manmade although there are manmade structures on them and around them but they themselves are geological formations.

By:

Johan Normarkon April 28, 2012at 04:54

Osmanagich is a fraud, he is not an archaeologist, only a tricky man looking to be a millionaire with the credulous ones. The Mayan never said anything about the end of the world, they spoke on the end of an age call which ends this December. Then will come Acuarian age.

Please, think for yoorself, read, do not allow manipulate you.

By:

Maria Hendersonon May 30, 2012at 23:58

Well, the Maya did not believe there is an dawning of the age of Aquarius this year. That is just another New Age myth made by other frauds (something I actually believe Osmanagich believes himself)…

By:

Johan Normarkon May 31, 2012at 04:53

Dear doubters,

It’s funny how sure you seem to be what does and does not exist in a place you’ve never visited nor would be able to find on a map since it’s more than obvious how ignorant you lot are.

There are new discoveries about everything and anything every day in the world. Question is, are we interested and wiling to widen our knowledge? We also have to keep in mind that some governments are opposed to many things as that would mean that it would put them and their politics and everything they’re saying and doing in danger- one way or another.

What Osmanagich has discovered is truly remarkable. Why don’t all of you who say that he’s a fraud go to Bosnia and see for yourself and try to prove he’s wrong?

I’ve had the honour to meet the man himself and. What I liked most is that he doesn’t stop at empty words but has proof and evidence for every word he says. Also, since it’s already June 2012 a lot of work has been done so far on and around the pyramids in Bosnia. Maybe look it up and get some more info before you judge?

I know it’s easy to hide behind your desktops and say thing like he’s a fraud, he’s going to humiliate Bosnians, talking nonsense…

But unlike you, he’s not hiding but keeps going with his research, manages to fight all the obstacles that are thrown at him and keeps presenting more and more discoveries…

I have been to Visoko myself and there is no way those “hills” as some like to call them are created by nature.

By:

believeron June 9, 2012at 12:55

Aha, the “I have been there and you not argument, I have seen it with my own eyes”, the most ignorant of all arguments. That is also apparently the only argument you have… Sure, you’ll see a pyramid there because Osmanagich has terraformed the excavations in that way! You are watching a contemporary made up pyramid. Read up on geology and archaeology before you visit the site the next time (you are in Bosnia right now so it should be close enough). Watch out, the Bosnian government is twisting your mind…

Since I am an archaeologist (and you are not, I can tell from this from your short comment), I do not have to be there in person to judge the data. No archaeologist can visit all sites in the world. That is why we have field reports where data should be presented in a scientific manner so that a person who has never been to the site should be able to judge the data. Osmanagic fails utterly in this regard. You can also check the links to the article mentioned in this post, some of which have been made by archaeologists actually visiting the hills: http://haecceities.wordpress.com/2012/05/27/2012-osmanagic-and-public-archaeology/

By:

Johan Normarkon June 9, 2012at 16:39

The Great Pyramid, the Cholula Pyramid, and the Pyramids of the Sun and Moon: working together to prove that “2012″ isn’t nonsense

Abstract. Following Petrie, the position of the pole at the time of the pyramid builders is determined two ways. At their oppositions in early 2013, Arcturus and Algieba reach within an arcminute of the zenith, at the pyramids of Cholula, and of the Sun and Moon, resp., using those poles. The distance between the pyramids of Cholula and the Moon, tells the correct precession rate. The distance and angle between the pyramids of Moon and Sun, and the sizes and shapes of the pyramids themselves, tell us that the pyramid builders assumed an inexact second derivative of the ecliptic pole position, apparently for the sake of using round numbers, and correcting this improves the accuracy to a few arcseconds for Arcturus. Similar plans explain the positions of the three main Giza pyramids, Monk’s mound at Cahokia, and the Bosnian pyramids.

I. Introduction to the stars.

Arcturus (Greek, “the bearkeeper”) is the brightest star in the northern hemisphere, though some sources say Vega, depending on photometric details. Algieba (Arabic, perhaps originally “the mane” of Leo, according to Burnham) is a famous second magnitude double star, one of the fifty brightest stars in the sky. These stars are in the spring sky, about a radian apart. Both stars are nearby orange giants, with large proper motions.

Based on their negative radial velocities and on trigonometry, increases in their proper motions during the last 5000 yr, would cause 45″ & 5″ overestimates of declination for Arcturus & Algieba resp., if only the instantaneous proper motion, arcsec/yr, and not its time derivative, arcsec/yr^2 (and in the case of Arcturus, the significant time second derivative arcsec/yr^3) were known 5000 yrs ago. The accuracy of placement of the Cholula pyramid with respect to Arcturus, explained in Sec. VI, implies that not only accurate proper motions, but also first and second derivatives of proper motions, or the mathematical equivalent (e.g. a presumption of oblique rectilinear motion) were known to the builders.

The orbit of the double star, Algieba A & B, is highly eccentric and highly inclined to our line of sight, so it would have been difficult for the builders to average the center-of-light motion. This would have been easier with Castor AB; see the Addendum re Giza. Algieba AB’s orbit is vague and ambiguous, but by measuring and quadratically extrapolating positions on Burnham’s graph, “Celestial Handbook”, vol. 2, p. 1063, and using mass and magnitude estimates from Kaler’s stars.astro.illinois.edu webpage, I find that Algieba AB’s epoch 2013.0 difference between center-of-light and center-of-mass motion is, in declination, +2.02 mas/yr.

II. Positions of the stars in early 2013.

From their 2000.0 AD positions (Bright Star Catalog) in 2000.0 AD celestial coordinates, and the “rigorous formulae” on p. B18 of the 1990 Astronomical Almanac, I found their declinations in 2013.0 AD celestial coordinates, including proper motions. These declinations are:

Arcturus +19deg06’55″

Algieba +19deg46’32″ (primary component)

There is no atmospheric refraction correction at the zenith, but the nutation and starlight aberration corrections will affect the accuracy considerably. At opposition, the change in declination due to aberration and to nutation in longitude (chart at http://www.pietro.org) can be estimated as

(-20.5″-15″) * sin(23.44) * cos(34, resp. 25)

= -12″ & -13″ for Arcturus & Algieba, resp.

For nutation in obliquity, the effects are

-6″ * sin( -34, resp. +25)

= +3″ & -3″ for Arcturus & Algieba, resp.

The oppositions occur near 2013.32 & 2013.15, resp., giving by precession from 2013.0 another

-5″ & -3″ in declination, resp. (omitting -0.6″ Proper Motion for Arcturus)

This gives declinations at their oppositions in early 2013, as observed when at the zenith:

Arcturus +19deg06’41″

Algieba +19deg46’13″

III. Introduction to the pyramids.

The Great Pyramid of Giza, the pyramid of Cholula, and the pyramid of the Moon are among the world’s largest known pyramids both in height and volume. The Great Pyramid of Giza is a close #2 (to Giza’s pyramid of Khafre) in the world for height. The pyramid of Cholula, thought to have been begun in the 3rd century BC, is #1 in the world for volume and #2 in Mexico for height. The pyramid of the Moon is somewhat smaller than its more famous, nearby, larger teammate in Teotihuacan, the pyramid of the Sun; the pyramid of the Sun is #3 in the world for volume and #1 in Mexico for height. Although most findings of this paper apply almost as well to the pyramid of the Sun as to the nearby pyramid of the Moon, I choose the pyramid of the Moon because according to Wikipedia, the pyramid of the Moon “covers a structure older than the pyramid of the Sun”.

According to the geodesy teaching website plone.itc.nl/geometrics (“Geometric Aspects of Mapping, 3. Reference Surfaces for Mapping”) the plumb line (i.e. perpendicular to the, “geodetic” surface i.e. “geoid”) commonly deviates from the perpendicular to Earth’s reference ellipsoid by up to 50″ near mountains, but in flat regions uncommonly more than 10″. A low-resolution world map of the geoid (Uotila, 1962; cited in Heiskanen & Moritz, “Physical Geodesy”, 1967, Fig. 21, p. 157) shows that both Giza and Teotihuacan/Cholula are in regions where the geoid is extraordinarily close to the reference ellipsoid, about -6m and +2m, resp. At Giza, the gradient of the geoid height is relatively large but lies EW so would affect observed declinations little. At Teotihuacan/Cholula, there is a moderate NS geoid gradient equivalent to about 2″ northward tilt of the plumb line.

IV. The latitudes of the pyramids.

The geographic latitudes are:

19deg03’27″ (pyramid of Cholula)

19deg41’59″ (pyramid of the Moon)

A large error, is the motion of Earth’s pole over thousands of years. Flinders Petrie (p. 125; Ch. 13, Sec. 93 in Birdsall’s online edition) says that the most reliable structures in the Giza pyramids indicate that the pole at the time of their foundation, lay 5’40″ +/- 10″ west of the present true north. Petrie remarks that this indicates a rate of geographic pole migration only a few times greater than measured in recent centuries, and that physically, quantitatively, it is consistent with major changes in ocean currents. Likely, a pole shift would change Giza’s latitude a comparable amount, so I assume that the Great Pyramid was originally at exactly 30N. If the Great Pyramid serves as a monitor of the pole change since the foundation of the greatest Mexican pyramids, then Cholula, and the pyramids of Sun and Moon, would have been 180″ and 177″ nearer the pole, resp., when founded. Their geographic latitudes then would have been:

19deg06’27″ (pyramid of Cholula)

19deg44’56″ (pyramid of the Moon)

With this ancient pole, Arcturus would have been observed only 14″ too far north to match this original Cholula perfectly, and Algieba 77″ too far north to match this original pyramid of the Moon perfectly, at their respective oppositions in early 2013.

If no latitude change happened at Giza (maybe that site was chosen for this reason, determining its longitude; then the site away from 30N was chosen because of the architectural convenience of the Giza plateau) then these pyramids would have been 227″ and 226″ nearer the pole. Their geographic latitudes would have been:

19deg07’14″ (pyramid of Cholula)

19deg45’45″ (pyramid of the Moon)

Arcturus & Algieba would have been 33″ too far south & 28″ too far north, resp. This is a better fit: 14^2+77^2 = 6125 > 1873 = 33^2+28^2. The declinations of these stars change about -50″ * sin(23.44)*cos(34 or 25) = -16″ or -18″/yr, resp. Using the oppositions in early 2012 or early 2014, the sum of squared errors would be 17^2+46^2=2405 or 49^2+10^2=2501, resp.

V. The pyramids tell the precession rate.

The foregoing, determines the pyramid latitudes; but the longitudes remain free choices. Suitability of sites, would remove one degree of freedom, but another degree of freedom, the small difference between the longitudes, remains available.

Apparently the builders wished to tell us what precession rate they used in their calculation, by setting the geocentric arc between the two pyramids, equal to that precession rate times an interval of time that we would know or guess. Wikipedia gives geographic coordinates for the pyramids to about 0.0001deg = 10m. Geographic latitude, g, is converted to geocentric latitude, f, by tan(f) = tan(g) * (296.0/297.0)^2. The results are

of Cholula: long 98.3019W geog lat 19.0575N geocen lat 18.93854N

of the Moon: long 98.8440 geog lat 19.6996 geocen lat 19.57727

The geocentric angular separation of these pyramids, is 2946.5″, precise to 4 figures. The time period used seems to have been based on Jupiter’s tropical period, 360deg / (dL/dt), where L = the mean longitude of Jupiter referred to Earth’s ecliptic and mean equinox of date. Clemence, Astronomical Journal 52:89+ (1946), p. 90, gives L = 10930690″/cyr plus insignificant secular terms and a sinusoidal 900-yr “Great Inequality” term which is 1/10^4 as large and therefore barely significant (and perhaps averaged out by the pyramid builders). Because of the 5::2 resonance of Jupiter and Saturn, 5x Jupiter’s tropical period is a reasonable time interval to use. This implies a precession rate of

2946.5″ / (5 * 360*3600/10930690*100)

= 2946.5″ / (5 * 11.856525 Julian yr)

= 49.702″/yr, where the last digit is not significant

The Newcomb precession formula chosen by Clemence (op. cit., p. 90) amounts to 50.238″ + 0.02216″ * T per yr, where T is centuries from 1850.0 and I have omitted a barely significant quadratic term. The precession rate implied by the pyramid spacing, corresponds to 1850.0AD – 2420 = 571BC, which is halfway between 2013.0AD and 3154BC; 2013AD – 3154BC = 5166yr (last two digits not significant)(Mayan Long Count = 5125.26yr)(I’m keeping more digits than I show here, so your last digit might not agree). Thus the inter-pyramid spacing refers to either the start of the Mayan Long count, 3114BC, or else the reference year of Hindu astronomy according to Bailly and Playfair, 3102BC, and that spacing was designed to suggest the mean precession rate between that time and the present.

We thus confirm that the builders’ precession error was probably no more than, and perhaps much less than, about 0.005″ * 5000 = 25″. This corresponds to a declination error for either star, of at most about 25″ * sin(23.44) = 10″, and perhaps much less.

VI. The pyramids tell the ecliptic motion.

Proceeding as in (V), I find that the geocentric angular separation of the pyramids of Moon and Sun, suggests that the builders estimated the arclength rate of ecliptic pole motion, as 25.46″/(5 Jupiter tropical periods), if I use the Wikipedia coordinates. Instead I’ll use the separation I measured on the paper map of Rene Millon and Armando Cerda, Univ. of Rochester, 1970 (as Teotihuacan appeared in 1962); I prefer this figure, 26.108″, because I was able to make sure that the measurement was from the centers of the topmost marked rectangles on the pyramids.

Precession moves in a circular cone around the perpendicular to the ecliptic, but because both Venus and Jupiter affect the ecliptic considerably, specifying ecliptic motion is more complicated. The second difference of the ecliptic pole position using 100 yr intervals, often is inadequate to predict the change of pole position over 5000 yr.

Let’s guess the thoughts of the builders. Their other calculations were so competent, that surely they knew their contemporary arclength rate, 31.72″/ 5 Jupiter periods (at 3113BC, according to data from NASA’s online Lambda utility, by either first or third order numerical differentiation with central differences on 100 year intervals) and direction of ecliptic motion. The Lambda utility data indicate that the rate slowed roughly linearly to the present 27.87″ (average rate over a modern 800 yr interval) with a mean rate since 5125 yr ago, of 29.38″. However, the builders, according to the distance between the pyramids of Moon and Sun, apparently assumed a more drastic linear slowdown.

The actual mean radius of curvature of the ecliptic pole path over the last 5125 yr, has been about 1.4606deg (circumcircle of endpoints & time midpoint). Likely the builders used a constant radius of curvature for the pole path, to get a second order approximation method which we moderns, the intended audience of their message, could guess from the layout of their monuments. The slope of the interpyramid line Moon-Sun, is W of N, 1.53 +/- 0.22deg including 1 sigma rounding error, from the Wikipedia coordinates, or else 2.106deg from my measurements on Millon’s map. Maybe this slope was intended to indicate the assumed radius of curvature of the motion of the ecliptic pole.

There is reason to believe that the real interpyramid line slope is 1.594deg W of N: originally, before Petrie’s presumed changes of the latitude and true north at Giza, this would have been 1.667deg, which I argue, is the true original figure. Millon’s map and other sources (primarily James W. Dow, American Antiquity 32:326-334, 1967) give 15deg25′ E of N, as the slope of streets and buildings at Teotihuacan and, approximately, of some other Central American pyramids. Giulio Magli of Milan (paper on ArXiv.org) calls this slope the “Nord” slope and the other prominent slope found at Teotihuacan (following Dow), 16deg30′ E of N, the “Est” slope. The deviation of the interpyramid line W of N, probably a little less than 2 deg, could be added to either of these slopes. So one could speak of 15, 16, 17 or 18 deg slopes; 15 and 17 are heard oftenest.

On the messageboard of the late Dr. Tom Van Flandern, I have explained quantitatively how decreasing oblateness would provide energy for Earth to undergo torque-free precession at 18.90deg with period one year. This would put the pole at the same place every winter solstice, providing, climatologically, a pole-like location with latitude consistent with Charles Hapgood’s estimates of the latitudes of the last three Ice Age poles (60, 72, 63). If 1.669deg is added to both the 15deg25′ and 16deg30′ slopes of Teotihuacan, and I use, converting the Wikipedia coordinates, 19.5737N as the mean geocentric latitude of the pyramids of Moon & Sun, then 16deg30′+1.669deg becomes the angle between the line of longitude, and the great circle drawn tangent to a latitude circle at 15deg25′+1.669deg from the pole. This colatitude is 17.1deg, not far from my estimate, 18.9. Note that 360/1.669 = 215.7, and 360/1.66667 = 216 = 6^3, a round number in base 6.

Alternatively, I could use the mean geographic, not geocentric, Teotihuacan pyramid latitude. Then the solution is 1.460deg, exactly equal to the actual circumcircle radius of curvature, of the ecliptic pole path, mentioned above. So apparently the builders knew the exact value of the curvature of the ecliptic pole path 5000 yrs ahead, but exploited the two equations resulting from use of geocentric and geographic latitudes, to encode both curvatures in the chosen 15deg25′ & 16deg30′ angles: the actual 1.460deg circumcircle radius of curvature of the ecliptic pole path since 3114BC, and a cautious “round number” underestimate of that curvature, a 360/6^3 = 1.6667deg radius. If the former radius had been used but not correct, future scientists might never have deciphered what radius was used.

Millon warned that he had not had time to correct some cartographic details of his map; one of these details might have been exact equality of NS and EW scale. I can cause the 2.106deg interpyramid slope to become equal to 1.594deg (that is, the 2.106+15.417 deg between interpyramid and “Nord” lines, to become 1.594+15.417) by stretching NS distances and shrinking EW distances, by a factor q = 1.01464. This slightly increases the interpyramid distance, to 26.49″. Corroborating this, I find that the angle between the map’s NS arrow, and the bottom of the map (which closely parallels the nearest horizontal grid line) is 90 – 15.800deg which would be corrected to 90 – 15deg25′, if I use q = 1.01299; with this q, the interpyramid slope becomes 1.650deg.

The height and base of the pyramid of the Moon (George L. Cowgill, “An Update on Teotihuacan”, online, written for “Antiquity”) are 46 m & 149NS x 168EW m; of the pyramid of the Sun (when “completed” c. 200AD, according to the Metropolitan Museum of Art, “Heilbrunn Timeline of Art History”, online) 63 m & 215 m square. Knowing the 15.417+1.594(?) = 17.011deg offset of the interpyramid line from their faces, let’s use the Pythagorean theorem to find four distances:

1) It would be practical to lay chains straight down the north & south sides of the pyramids of the Sun & Moon, resp., then along the ground in a straight line from there. This distance, slightly longer than the great circle distance from peak to peak, corresponds to a total arc (using as denominator the Earth radius 6378.3km, corrected for latitude and altitude, and assuming perfect pyramidal shape) of 27.79″. We recognize this as a round number in base 6, 360deg/216^2=27.778″, analogous to the other round number, 360deg/216 = 1.667deg, which the builders chose for the original interpyramid line rotation W of N. It soon will become apparent that this arc, 27.778″, is what the builders assumed for the time-average arclength speed, per 5 Jupiter tropical periods, of the ecliptic pole path.

2) Suppose instead, the chain is laid straight down the north & east sides of the pyramids of Sun & Moon, resp., then from there along the ground. This distance corresponds to a total arc of 29.55″, near the 29.38″ which we think has been the actual time-average arclength ecliptic pole speed during the last 5125 yr.

3) Suppose the chain is laid down the west & east sides of the pyramids of Sun & Moon, and from there along the ground. This distance corresponds to a total arc of 32.51″, near the 31.72″ which we think was the actual arclength ecliptic pole speed at the start of the prediction, 5125 yrs ago. This arc also arises from the circumference of the circumcircle of the base of the pyramid of the Sun; using a square 215m base, this corresponds to 30.89″. Except for a factor of 2, the arc arises more accurately from the circumcircle circumference at Cholula; at the latitude and altitude of Cholula, its usually given square base side of 450m corresponds to 32.33″ times 2. The square perimeter at Cholula likewise corresponds to 29.10″ * 2, and the square perimeter of the Sun pyramid to 27.81″; these arcs approximate the actual average rate of ecliptic pole motion 29.38″, and the assumed round number rate 27.778″.

4) Finally suppose the chain is laid down the west & south sides. This distance corresponds to a total arc of 30.18″, again somewhat near 31.72″, the actual ecliptic pole speed at the start of the prediction.

Summarizing:

west+east –> original ecliptic pole speed 5125 yr ago

north+east –> actual mean ecliptic pole speed since 5125 yr ago

west+south –> original ecliptic pole speed 5125 yr ago

north+south –> assumed mean ecliptic pole speed since 5125 yr ago

Geometrically, the west+east and west+south distances must differ by more than the other two differ; this precludes their simultaneously being the original ecliptic pole speed. But their average is (32.51+30.18)/2 = 31.34″ ~ 31.72″.

The slopes of the corner edges of the idealized Moon & Sun pyramids are 22.3 & 22.5deg, resp.; these slopes seem intended to equal pi/8 radians. The Sun pyramid seems intended to be square. Above, I showed that the interpyramid line slope (offset from NS) seems intended to show the assumed radius of curvature of the ecliptic pole path. If the pyramids must be orthogonal to the famous 15.5 degree orientation, then there remain only four adjustable variables: the base side of the (square) Sun pyramid, the two different base sides of the (rectangular) Moon pyramid, and the interpyramid distance. Above, I show that these four variables have been chosen to satisfy four constraints:

i) the circumcircle circumference arclength, of the Sun pyramid, measured in geocentric angle, equals the original (~5125 yr ago), actual and assumed, arclength rate of ecliptic pole motion per 5 tropical Jupiter periods;

ii) the via north face Sun pyramid & south face Moon pyramid, chain distance described above, measured as in (i), equals the assumed average rate of ecliptic pole motion during the last 5125 yr;

iii) the via north face Sun pyramid & east face Moon pyramid, chain distance equals the actual average rate of ecliptic pole motion during the last 5125 yr;

iv) the via west face Sun pyramid & south or east face Moon pyramid, chain distances, averaged, equal the original rate of ecliptic pole motion.

By measuring on both Millon’s 1:2000 maps (for the Sun pyramid, the large map, and for diagonals also field map N3E1, p. 45 in his map book; for the Moon pyramid, only the large map, because the field map is divided, and I did not measure Moon pyramid diagonals) and averaging these similar results from the two maps, I find dimensions significantly different from the consensus values above. Millon helped by drawing rectangles to outline the main levels of the pyramids. I assumed the center of the top level to be the peak of the pyramid. The Sun pyramid’s peak is decentered eastward and the Sun pyramid is significantly non-equilateral and non-rectangular. Retaining the consensus values of the pyramid heights, and again assuming perfect pyramid shape (others know more than I about what formerly was on top) I repeat (i)-(iv) above:

i) the Sun pyramid’s NW-SE diagonal is 0.5% longer than the other, corresponding to 0.005rad = 17′ hingelike northward motion of the west side. Its longest peak – corner line, the NW line, is thus

sqrt((102.8+208.2*0.005/2)^2+109.5^2) = 150.55m;

which times 2*pi for this largest circumcircle, corresponds to 30.59″ geocentric, vs. 31.72″ predicted.

ii) the via north face Sun pyramid & south face Moon pyramid, chain distance is 27.84″ vs. 27.778″ predicted.

iii) the via north face Sun pyramid & east face Moon pyramid, chain distance is 29.35″ vs. 29.38″ predicted.

iv) the via west face Sun pyramid & south or east face Moon pyramid, chain distances (necessarily much different) averaged, equal (30.28+32.28)/2 = 31.28″ vs. 31.72″ predicted. By adding 5.0% (5.5m) to the horizontal distance from the Sun pyramid’s peak to its west edge, the values of (i) and (iv) become equal at 31.41″, vs. 31.72″ predicted, without affecting (ii) or (iii).

The length/width ratio of the pyramid of the Moon is 168m EW /149m NS = 1.128. The ratio, of the original ecliptic pole speed which seems to be indicated by my map measurements of the Sun pyramid, 31.42″, to the assumed round number speed 360deg/216^2, is 1.1311.

From Millon’s two largest maps, I find differences in the diagonals of the Sun pyramid’s ten level rectangles as outlined by Millon. The lowest three levels are nearly rectangular, but above these, the NW-SE diagonal is always much longer. The 4th & 5th levels’ diagonals always differ a little more than 1%, and the 6th through 10th differ on average more than 3%. This corresponds to a slant, for the top five level parallelograms, averaging 1.77 +/- SEM 0.11deg, and for the top seven, averaging 1.49 +/- SEM 0.15. Again this might indicate the assumed and actual radii of curvature of the ecliptic pole path, 1.6667 & 1.4606deg, resp.

In a plane approximation, the differential equation of Earth’s pole precession about the ecliptic becomes linear. If the ecliptic pole moves slightly, the perturbation terms obey a nonhomogeneous linear differential equation which I solve by one Runge-Kutta step. The perturbation, is the actual Lambda utility ecliptic pole position minus the builders’ estimate (the builders’ estimate appears to be mean arclength motion of 27.778″ per 5 Jupiter tropical periods, linearly decreasing from the actual NASA Lambda rate, 31.72″, 5125 yr ago, along a circle of radius 1.6667deg, originally tangent to the actual Lambda direction 5125 yr ago). My result is that the Earth’s actual rotation pole is at 102″ greater longitude, and 41″ greater obliquity relative to the invariant plane, than the builders’ parameters predicted.

Solving the spherical case numerically with a computer (approximating the actual ecliptic pole sufficiently precisely with 4th order central difference interpolation of NASA Lambda values) I find that if I assume that the torque on Earth is proportional to sin(obliquity)*cos(obliquity), and adjust the precession rate accordingly based on the present rate and obliquity, the solution using the actual ecliptic pole positions, predicts the longitude of Earth’s present rotation axis much less well than if I assume the torque is proportional simply to sin(obliquity). Be that as it may, the results are 85.6″ longitude & 41.2″ obliquity, and 99.1″ longitude & 41.1″ obliquity, for the first and second assumptions, resp. So, the difference between the second, apparently valid, assumption, when solved with a computer, and the approximate back-of-envelope calculation of the preceding paragraph, is negligible.

The slower longitude regression, relative to the invariant plane, is due only to Earth’s rotation pole being nearer to the ecliptic pole; it does not indicate a different angular precession rate. The actual 99″ greater pole longitude, relative to the invariant plane, would cause 99″ * sin(23.44) * cos(34 or 25) = +33″ or +36″ change in declination for Arcturus or Algieba, resp. The 41″ greater obliquity, relative to the invariant plane, would cause 41″ * sin(-34 or +25) = -23″ or +17″ change, resp.

Now, my first geographic pole correction, based on the additional assumption of original 30.000N latitude for the Great Pyramid, seems best. Had the ecliptic change been what the builders predicted, then Arcturus & Algieba, at their oppositions in early 2013, would have missed by only +14-33+23 = +4″ and +77-36-17 = +24″, resp. The variance, 4^2 + 24^2 = 592, is far smaller than for any alternative considered.

For Arcturus the error is as small as can be expected in view of Petrie’s 10″ uncertainty of the old pole direction at Giza, and the 10″ uncertainty of reference spheroid vs. geodetic vertical. Correction for an approx. 2″ northward tilt of the plumb line at Teotihuacan/Cholula (as for southern Mexico generally, according to Uotila; see Sec. III) lessens the errors to +2″ & +22″, resp.

At its opposition in 2014AD, correcting for a year’s change of precession and nutation, Algieba would be misplaced by only 22-18+1 = +5″. Maybe the delay of Algieba’s alignment, by one year, was intended to tell us that some phenomenon, accompanying the end of the Mayan Long Count, persists for only a year.

In Sec. I, we learned that the epoch 2013.0 difference between center-of-light and center-of-mass proper motion for Algieba AB, corresponds to +10.4″ J2000 declination in 5125 yr. By Kepler’s law of equal areas (which applies even to inclined orbits) Algieba B moves 14x slower relative to Algieba A, at its apparent farthest (near the present location) than at its apparent nearest. Such grossly nonsinusoidal motion might have been only roughly averaged by the builders.

VII. Conclusion.

John Major Jenkins, as quoted in Geoff Stray’s popular book on 2012, has expounded the idea that the Central American pyramids might be “precessional alarm clocks”, but Jenkins has looked for relationships mainly to special points on the sky path of Venus, or of the Pleiades, heeding the known Mayan interest in these objects. Such relationships exist but are approximate to the order of a degree, not arcseconds, like the relationship I discover here.

Someone invested huge resources of calculation and construction, to align the zeniths of two of the world’s largest and most famous pyramids, within an arcminute (and within a few arcseconds, if what appear to be deliberate second order ecliptic motion underestimates by the builders, had been corrected) with two of the world’s most prominent stars, at their oppositions in early 2013. Alignment would happen then (rather than more than a decade later) if the geographic pole shift determined by Petrie from Giza, had not occurred.

By encoding the average precession rate, in the distance between the Cholula and Moon pyramids, and the ecliptic motion, in the separation and shapes of the Moon and Sun pyramids, the builders told us their plan was deliberate, accounted for precession and ecliptic motion, and was very ancient. They enabled us to correct their calculations, if only we could otherwise determine the foundation date, e.g. by knowing that the Mayan Long Count started in 3114BC, or knowing the 3102BC Kali Yuga reference year of Hindu astronomy, or guessing from the chronology of Manetho which starts c. 3110BC (or by assuming the encoded precession rate to be accurate and using the date implied by it, to evaluate the encoded ecliptic motion). No significant correction to precession rate is indicated, and only a plausible second order correction to the ecliptic. This correction improves the accuracy, especially for Arcturus, to no worse than a few arcseconds at the stars’ oppositions in early 2013.

Addendum June 1, 2012 re Giza:

A theory has been popularized, that the layout of the Giza pyramids is related to the layout of the stars in Orion’s belt, after some amount of precession. Years ago I tried, with several mapping schemes, to verify this quantitatively, but was unable.

I discovered today that instead, the layout of the Giza pyramids is related to Castor and Pollux, those other near together bright stars visible from north temperate latitude. Pollux is a nearby, large proper motion orange giant like Arcturus and Algieba. Castor is a nearby, non-giant blue-white star. Using online Bright Star catalog epoch 2000.0, J2000.0 positions (given to the nearest arcsec), the NASA Lambda utility for conversion to mean 2013.0 coordinates, Bright Star catalog Proper Motions for 13 years, and finally my own approximate corrections for nutation in longitude and obliquity, aberration of starlight, and the extra fractional year’s precession, I find that the observed (near the zenith, refraction ~ tan(phi) ~ phi, so is only a tiny minification) declinations when their midpoint reaches opposition early in 2013 are:

Castor 27deg59’25.5″

Pollux 31deg51’19.9″

The midpoint of these lies at declination 29deg55′ at 2013.0AD. The builders of Giza apparently seized this random, rough coincidence and used it to mark the end of the Mayan Long Count in a way that still allowed them to put the Great Pyramid at (then) exactly 30N.

Let x1 (resp. x2) denote the absolute declination difference Pollux (resp. Castor) minus 30.0deg.

x1/(x1+x2) = 0.519929

The Great Pyramid of Cheops (Khufu) corresponds to Pollux, Mycerinus (Menkaure) to Castor, and Chephren (Khafre) to the observer. Let y1 (resp. y2) denote the distances Cheops-Chephren (resp. Chephren-Mycerinus) measured by Petrie, and theta be Petrie’s break angle between the lines Cheops-Chephren and Chephren-Mycerinus.

y1/(y1+y2*cos(theta)) = 0.520723

To get this agreement, we projected y2 onto the line of y1, hence the cosine. The difference, +0.000794, corresponds to a mere +11″ declination shift for the Castor-Pollux midpoint, actual vs. Giza-based prediction.

The foregoing, based on declinations, is most natural to us, but requires measurement at two points in time. Another way to measure discrepancies from the zenith, would be at one point in time, when the stars’ EW discrepancies from the zenith are equal, sighting upward through a rectangular grid. Suppose first that it is the RA discrepancies, not the EW discrepancies, that are equal. Curvature of the parallels, would displace Castor or Pollux northward, in radians,

(1-cos(RA difference/2))*cos(31d51′ or 27d59′)*sin(same)

which divided by the stars’ declination difference, is 0.001804 or 0.001668. For the EW discrepancies to be equal, the RA discrepancy is proportional to q = cos(mean declination)/cos(declination), so the above RA discrepancies must be multiplied by q, and the northward displacements multiplied by q^2, giving 0.001804*1.0412 = 0.001878 and 0.001668*0.9634 = 0.001607. The ratio of NS displacements becomes x1/(x1+x2) = (0.519929-0.001607)/(1-0.001607+0.001878) = 0.518182. Without any projection, y1/(y1+y2) = 0.517483. The difference, -0.000699, corresponds to a -10″ declination shift of the Castor-Pollux midpoint.

Precession changes the declination about 50.28″*sin(23.44)*sin(115.2-90) = 8.5″/yr. The accuracy of the two methods above, implies a best fit of +0.5″ +/- SEM 7.4″. So, January 2013AD is indicated at a significance exceeding 1 sigma per yr.

Petrie’s distance from Chephren to Mycerinus, if doubled, corresponds to 29.3859″ geocentric arc, adjusted for latitude, the altitude of the Giza plateau near these pyramids, and the barely significant nonperpendicularity, of the reference ellipsoid, to Earth’s radius. Fourth order central difference interpolation of the NASA Lambda positions of the mean ecliptic pole through the last 5125 yr, gives an integrated arclength travel of 29.3819″ per 5 tropical Jupiter periods (this time unit is suggested by the spacing of the Mexican pyramids discussed in the other sections of this paper). The difference corresponds to only 2.4 inch error in Petrie’s one-way distance. The foregoing findings already constrain the Cheops-Chephren distance, but if doubled it happens to correspond to 31.52″, near the actual 31.72″ initial ecliptic pole rate.

Petrie’s angle between NS and the Cheops-Chephren line, is 43deg22’52″; though Petrie determined the old NS line of the pyramids, as 5’40″ +/- 10″ W of modern N, he used for a round number, 5′ in this determination. Adding 40″ gives 43.392deg. From my interpolation based on the entire 5125 yr interval, the initial rate of change of the ecliptic pole, makes a 42.53deg angle with its equinox of date. If instead I find the ecliptic pole rate of change from values +/- 100 yr, I find 42.63deg. So the two distances and two angles of the Giza plan, manage approximately to encode five data: two different definitions of the Pollux-Castor straddle of the 30th parallel, at their opposition in 2013; the initial and mean rates of ecliptic pole motion over the last 5125 yr; and the initial direction of ecliptic pole motion.

At Newcomb’s precession rate of 5125 yr ago, 49.15″/yr, the equinox 5166 yr ago (see Sec. V) would have been at 0.560deg greater longitude than 5125 yr ago. This would improve the agreement of the smoothed initial ecliptic pole direction, to 42.53+0.56=43.09, vs. 43.392 at Giza.

Castor A & B differ from Algieba A & B: Castor AB’s orbit is only moderately inclined to our line of sight, and its true orbit only moderately eccentric. So, the difference between Castor AB’s center-of-light position and center-of-mass position, is roughly sinusoidal and could more easily have been averaged out by the builders.

Summary of addendum re Giza. The builders chose the distance ratio and break angle at Giza, to quantify as simply as possible in two natural ways, the exact deviation of the Castor-Pollux (a.k.a. “Dioscuri”) midpoint from the zenith over 30.0N at those stars’ opposition in 2013. The absolute distances and the Cheops-Chephren direction, quantify the initial direction, and the initial and mean rates, of ecliptic pole motion from ~5125 yr ago.

Addendum June 3, 2012 re Cahokia:

From information in the Bright Star Catalog, I find Vega’s observed declination, employing all corrections as elsewhere in this paper, observed at the zenith at its opposition in mid-2013, to be +38deg47’57″. Wikipedia gives the geographic latitude of the Cahokia mounds near St. Louis, USA (the largest, about 30m tall, is named “Monk’s Mound” because a Trappist monastery was nearby) as N38deg39’14″.

The same correction for the post-Giza pole shift that I use elsewhere in this paper, gives the presumed original Cahokia mounds’ latitude as 38deg42’48″. Now I consider the effect on Vega, of correcting the ecliptic pole motion underestimate used in Mexico (see Sec VI):

99″ greater actual longitude of Earth’s rotation pole –>

99″*sin(23.44)*sin(-9.2) = -6.3″ change in Vega’s declination

41″ greater actual obliquity –>

-41″*cos(9.2) = -40.5″ change.

Thus if the Teotihuacan (and Cahokia) builders’ ecliptic pole estimate had been exact, the declination of Vega would have become 38deg48’44″. This 5’56″ discrepancy between Vega and Monk’s mound, amounts to 24% of Vega’s proper motion in declination over 5125 yr. Maybe the error is due to an unknown physical or optical effect of Vega’s rapid pole-on rotation.

Ptolemy’s star positions indicate that Arcturus’ proper motion (2.25″/yr) has been near its present value for 2000 yr, but that Vega’s (0.33″/yr) very much has not. Aided by a computer, I consider four triangles:

1. Arcturus-zeta-epsilon Bootis

2. Vega-beta-eta Lyrae

3. Vega-beta-theta Lyrae

4. Vega-gamma-eta Lyrae

5. Vega-gamma-theta Lyrae

Ptolemy’s distances within a constellation should be his most accurate data. The two dimmer stars in each triangle were chosen to make all the angles of the triangle large (giving a well-conditioned system of equations) and for their small (modern) proper motions (about 50 mas/yr for the dimmer stars in Bootes and not more than 4 mas/yr for the dimmer stars in Lyra).

Because Ptolemy’s positions for these stars are all rounded to sixths or quarters of a degree, the sides of implied uncertainty boxes for the stars are 5′ or 10′. Defining error as sum of squared side length differences between Ptolemy, and modern proper motion corrected data, I find the least error among the 4^3=64 choices of corners of these uncertainty boxes.

For Ptolemy’s Almagest, I use Peters & Knobel’s translation, “Catalogue II”, 1915. For Arcturus’ triangle I find minimum root-mean-square side length error of 13′ (with best choice of uncertainty box corners) at 0 AD (near experts’ estimated true epoch of Ptolemy’s catalog) with twice that rms error, at 1300AD & 1100BC. By contrast, for Vega’s four triangles I find minimum rms errors ranging from 3′ to 5′, at times ranging from 4450AD to 5700AD, mean 5225AD.

Flamsteed’s (adjusted for precession to 1690.0AD by the editor, Baily) “British Catalog” (microfilm version at the Iowa State Univ. library) has uncertainty boxes 1′ on a side in right ascension (the relevant stars in Lyra all are given only to 1′ RA) and 5″ in declination. Flamsteed somewhat corroborates my finding about Ptolemy. For the four Vega triangles, the minimum rms errors range from 0.07′ to 0.24′, at times from 1715AD to 1745AD, mean 1730AD. I gather from Baily’s explanations, that Flamsteed’s observations began in 1689 and most were made during the early 1690s. If Flamsteed’s actual mean epoch were 1695AD and Ptolemy’s c. 150BC (i.e. Ptolemy used Hipparchus’ observations corrected for precession, as many believe) then a change in Vega’s proper motion, mas/yr/yr, sufficient to move the date of best fit by +35yr in 305yr, would move it 35*(2150/305)^2 = +1740yr in 2150 yr. With a higher order change, mas/yr^3, the indicated +5375yr shift seems possible.

Summary of addendum re Cahokia. Cahokia is to Vega, as Cholula is to Arcturus. Vega’s rapid pole-on rotation might have caused a ~20% error in predicted proper motion, causing Cahokia to be misplaced by 0.1degree latitude. Ptolemy’s and Flamsteed’s catalogs support drastic long-term changes in Vega’s proper motion, which the builders might only roughly have estimated.

Addendum June 10, 2012 re Bosnia:

In the foregoing, I’ve discussed pyramids of stone, brick, and earth. Whether the Bosnian pyramid is an artificially shaped hill or built from the ground up, is less important now, than whether it is another “precessional alarm clock” for December 2012, and to what catastrophe, these precessional alarm clocks are trying to alert us.

The epoch 2000.0 position of Capella in J2012.94 coordinates (Capella’s next opposition) is RA 5:17:38.75, Decl +46:00:41.0. Proper motion from 2000.0 to 2012.94, nutation and aberration decrease this figure for Capella’s declination by about 9″, to +46d00’32″.

My position for the main Bosnian pyramid is interpolated by measuring to the end of the marked gradient, which is at least near the peak, and interpolating the corner coordinates of the online ( http://www.bosnianpyramid.com ) topographic map of Amer Smailbegovic, Ph.D. My result is E 18d10’37.0″, N 43d58’37.0″ (Wikipedia gives ~1′ farther north than my result, but theirs might not refer to the peak of the main pyramid). The pole shift which Petrie and I infer from Giza, again gives an original latitude of 44d00’56″. This is 88″ farther north than needed to make Capella graze the horizon, neglecting atmospheric refraction. That is, 44d’00’56″ + 46d00’32″ = 90d01’28″. The true (refractionless) grazing could have been determined, from near-zenith observations, with spherical trigonometry.

Assuming the round-number ecliptic pole motion underestimate (which seems to have been used in Mexico but not at Giza) as explained in Sec. VI, Capella’s actual position now is about 33″ north of what the builders predicted. So for Capella to graze the horizon, the main Bosnian pyramid is really only 88-33=55″ farther north than it should be, according to what the builders expected. According to the centers of the squares drawn by Dr. Smailbegovic (Fig. 1, p. 4) around the suspected pyramids, the third pyramid (the third of his three “primary anomalies”) Dautovci, is about 134″ farther south than the main pyramid, Visoc^ica. So, their mean is about 55-134/2 = -12″, i.e. only 12″ S of the theoretical latitude.

On Dr. Smailbegovic’s topographic map of the Visoc^ica pyramid, I marked by eye, the points of greatest curvature of all the level curves at the NE & NW edges, then drew least squares lines by eye to approximate these edges. Including a small correction for Earth’s flattening, I find that the orientations of these edges are 45.505deg E of N & 35.7475deg W of N, midpoint 4.879deg E of N. In my Sec. VI discussion of Teotihuacan, I noted the relationships:

cos(geographic lat.)*sin(x+d1) = sin(y+d1)

cos(geocentric lat.)*sin(x+d1+d2) = sin(y+d1+d2)

At Teotihuacan, y=15deg25′, x=16deg30′; d1=1.460deg, d1+d2=(5/3)deg, which seem to signify the actual and assumed radii of curvature of the ecliptic pole path during the last 5125 yr. Instead of the mean latitude of the pyramids of Moon & Sun in Mexico, let’s now use the theoretical ideal mean latitude of the pyramids of Dautovci & Visoc^ica in Bosnia, (geographic) 44deg00’01″. Instead of y = the famous 15 deg alignment of Teotihuacan, let’s use y = the 4.879deg alignment which I measure on the Visoc^ica pyramid, and d1 = (5/3)deg. Then d2 = 272″. Before the pole shift indicated by Giza’s layout, true north at the Bosnian pyramids would have been 374.5″ W of N, but because of their latitude, this amounts to only 270.3″ on the globe. So the small alignment of Visoc^ica away from true north, seems as at Teotihuacan to encode important angles.

Using the 2.5m contour intervals, I find that the average slope of the NW edge is 20.25deg and of the NE edge 20.92deg. This near equality, and similarity to the edge slopes (22.3deg & 22.5deg) at Teotihuacan, suggests artificiality.

Summary of addendum re Bosnia. Regardless of how the Bosnian pyramid might have been produced or arisen from the natural material, its latitude, assuming only the pole shift deduced from Giza, is only 1.5′ too far north to be perfectly consistent with Capella’s circle of travel grazing the horizon at Capella’s opposition in late 2012.

By:

Joseph C. Keller, B. A., Harvard, cum laude, Mathematicson June 12, 2012at 18:33

Zzzzz

By:

Johan Normarkon June 12, 2012at 19:18

Massive wall of text. I confess I didn’t read over the whole thing, because your calculations appear depend on several unwarranted assumptions:

1) The pyramid builders knew (at the time the pyramids were built) that the earth was spherical. Given that the earliest mentions of this idea occur in the 6th century BC, this appears to present a problem for your theory if the pyramids in Egypt were built ~3000 BC. In addition, there is counter-evidence in the case of meso-America.

2) The pyramid builders used the same angular measurements we use today. This may hold true for Egyptian pyramids, where the measurements of angles was inherited from the Babylonians, but you have not shown that New World pyramid builders measured angles with the same system.

3) All of the pyramid builders had this knowledge. This seems to be a major problem for your claim, given that there is absolutely no evidence (that I am aware of) for any communication between the two groups.

4) The pyramid builders had access to instruments capable of measuring stellar angular distances to the precision you describe. Where are the ancient telescopic instruments capable of measuring angles in arcminutes?

You subject your measurements to various mathematical gymnastics in order to force-fit them to your idea. This is exactly backwards.

By:

Bill Hudsonon June 12, 2012at 20:42

1. Indeed I assume that the pyramid builders, or at least those who selected the sites, knew that Earth is approximately spherical. I assume knowledge even more advanced than that: for example, that they accurately knew the proper motion of Arcturus. A mainstream scholar wrote that 90% of classical literature was destroyed during the “pagan”-”Christian” transition. History tells us that the destruction of Mayan texts was even more complete. Again, Playfair and Bailly noted that solar system parameters given in almanacs from India, often were exceedingly and inexplicably accurate, and referred to 3102 BC as the base epoch.

2. I never assume that their measurement system is the same as ours. I make statements such as “Angle A = Angle B”, which are true regardless of units. When I do, in a few places, speculate about their units, I hypothesize natural units which are different from ours.

3. I find no direct connection between the Egyptian and Mayan work. They might have been two separate groups of skilled astronomers working independently, though my guess would be that they were in communication with each other.

4. Ptolemy’s surviving data typically are only a few arcminutes in error, and the best human visual acuity is less than one arcminute as usually measured. “Vernier” (i.e. line to line, not point to point) acuity is much better yet, something which is routinely exploited in the design of measuring instruments. Furthermore, quantities determined from many measurements, increase in accuracy as the square root of the number of measurements.

5. Hudson says “You subject your measurements to various mathematical gymnastics in order to force-fit them to your idea. This is exactly backwards.” I’m not force-fitting anything. The quantities happen to fit, and I call attention to the fact that they happen to fit. “Gymnastics” is a pejorative term; what I perform, are appropriate calculations. The idea that “subjecting” data to correct mathematics can give it “various” different values, is akin to the claim that “you can prove anything with statistics.”

By:

Joseph C. Keller, B. A., Harvard, cum laude, Mathematicson March 28, 2013at 23:57

What’s up with your academic titles? I am always sceptical to anyone who must show them when they are not needed or asked for…

By:

Johan Normarkon March 29, 2013at 06:43

John Normack bless you and your closed mind, I amsending you love and light xx

By:

Kikion July 1, 2012at 10:54

[...] Another influential character was Augustus Le Plongeon (1825-1908). He was fascinated by Atlantis and he argued that he had lived at Chichen Itza in an earlier life. According to him both ancient Egypt and the Freemasonry derived from the Maya by way of Atlantis. Jesus’ last words on the Cross were also spoken in Yucatec. Much of Le Plongeon’s work has reemerged in the writings of the Bosnian pyramid inventor Semir Osmanagic. [...]

By:

2012: The history of Mayanism and the 2012 phenomenon, pt 1 « Archaeological Haecceitieson November 26, 2012at 11:54

Dr.Normark,With all due respect,I doubt seriously you could find your arse with both your hands.Speaking of your arse,while your hands are trying to find it you may find it useful to remove your head that seemingly,is clearly stuck in this afermentioned body part.

By:

Rolandon March 8, 2013at 04:50

Another example of how desperate people are in this post-2012 era. Apparently no enlightenment struck them. Poor man.

By:

Johan Normarkon March 8, 2013at 05:50

Actually, the enlightenment did strike *them*. Being gratuitously insulting is part of that enlightenment. Roland gave no concrete examples of your errors and oversights because if you were enlightened, you wouldn’t need to be told. The subtleties of Roland’s elevated intellectual discourse are lost upon you, precisely because you wouldn’t accept the Enlightenment.

By:

MuxTunon March 8, 2013at 16:14

Judging from Roland’s email address (lovinlife60@hotmail.com) I think he his having a blast in Fredericksburg, Viriginia. Call me judgmental but I do not think that metropolis stimulate intellectual discourse.

By:

Johan Normarkon March 8, 2013at 16:42

I m sure, that everybody here is very impressed with

Roland’s words.

By:

Gilgameshon March 8, 2013at 19:54

Yes, but wait for the follow up. He has been visiting the blog during the past hour or so, checking out other pages, probably to find something to comment on. Maybe we will find out something about other body parts as well? Maybe my feet are entangled in my scrotum? I can’t wait.

By:

Johan Normarkon March 8, 2013at 20:01

Seems like Roland is busy visiting my blog bút he has not responded yet. I wonder what he is up to?

By:

Johan Normarkon March 10, 2013at 07:49

Compelling arguments and passionate posts on both ends of the argument… Easy to dismiss Dr semir as a con artist especially in the ‘pseudoscience’ obsessed times we exist in now, but also easy to read evidence produced by scientists claiming it IS a pyramid with artificial concrete… a little more time I think and if nothing unearths significant he himself will have no choice but to witness the demise of the project… 5 years time max and we should see significant VISUAL results with all the support and volunteers working… If nothing significant? Simple, he is a moron who kept it going past it’s sell by date….

By:

Vincenton May 16, 2013at 00:28

Semir (Sam) Osmanagic is one of the people with the highest moral caliber. By every aspect.

The scientists who called his, Sam’s, work a hoax should be finished … and they should already empty their office cubicles because they aren’t good for anything anymore.

By:

Jon Cachelon June 12, 2013at 09:29

LOL. Good thing I don’t have much stuff at my office then.

By:

Johan Normarkon June 12, 2013at 09:51