ArchaeoBlog © 2006 by James Q. Jacobs

Discourse, March 2006


For several reasons, I've pasted together some recent e-group postings for the ArchaeoBlog. Discussion groups offer opportunities to engage in discourse with others interested in the same topic.  They provide a great means of exchanging ideas focused on a particular subject area.  They also have some disadvantages, and those prompted me to create this page.

One of the disadvantages of some forums is their closed nature; only members gain access to the discourse.  This means the material posted is not accessed by search engines and only read by a few people.  That's okay, if you want your writing restricted or to be somewhat private, i.e., where your boss won't see it. Another disadvantage is the disconnected discourse.  Threads become disorganized with interjections, individual postings with distinct perspectives and priorities, and tend to wander every which way, becoming peripatetic musings if not argumentive blather. Another significant disadvantage is moderator control (sometimes also an advantage-often a necessity). Refusing a posting for whatever reasons, or editing what has been submitted and posting only the pleasing parts, is a frustration many must simply endure.  However, I have this site, so I can overcome that obstacle by placing my words here too, uncensored and not excised, and within reach of search engines.

First, below follows the rejected posting that spurned this action, with my own typo editing and excising. Thereafter follows, sorted by threads, selected posting quotes.  You may wish to read them, but mostly, they are here for individuals using search engines.

Message not approved

2006.3.23 Subject: Message not approved: Questions, Natives, Pagans, and Druids

.... I am afraid that by posting this you will ignite a new war.  I already received a nasty letter, and press release from druidcircle who have withdrawn from the group.  ....  Sorry to have to send this back.
Cheers, Vincent
Anuket ... wrote:
>  ... since Tara is obviously of some importance to pagans and druids,
>  could they not claim it  as a religious sanctuary?

"Pagans and druids" are modern/historical mental and culturally specific constructs that have nothing whatsoever to do with what happened in Ireland 4-6,000 years ago.  These are "modern" ideas and there is not a shred of evidence that they bear any relationship whatsoever to ancient monuments in northeastern Europe.  Remote times are not constructed in a later epoch by beliefs about them, no matter how fashionable pseudoscience or new age ideation is. Read:  Archaeological Fantasies:  How pseudo-archaeology misrepresents the past and misleads the public.
If individuals wish to "other" or "sub-culturate" themselves in our time, that is their privilege.  Doing this to a heritage site is irrational. Consider the depth of time involved and count your ancestors in that context.  It will reveal whose property Tara really is.  See  "The One Trillion Principle: How many ancestors do we have?"

> ... in the States Native American tribes still have ownership over areas of land ...

Off topic perhaps, but a correction is in order.  I believe the US Government owns all the reservations, one tract excepted.  USG legally ceded by treaty specific rights, but the tribes do not own the stolen land; USG stole it and they own it under the prevailing legal system they impose in conquered regions.

International Day for Monuments and Sites

2006.3.6 Subject: April 18, the International Day for Monuments and Sites + online resources

We are part of a much wider, global preservationist circle. That can be a focal point of local celebrations on April 18th. Celebrate the global preservationist circle, make others conscious of global efforts while raising awareness of the threats to the Tara and Thornborough circles. ...

On 18 April 1982 ... it was suggested that a day be established to celebrate the diversity of heritage throughout the world. From this idea, the International Day for Monuments and Sites was born. This project was approved ...
Last but not least, the idea was also approved by the UNESCO General Conference who passed a resolution at its 22nd session in November 1983 recommending that Member States examine the possibility of declaring 18 April each year "International Monuments and Sites Day". .....
The essential thing is to mark this day so that it becomes not only a day to celebrate your national heritage, but also a day of international solidarity in favor of strengthening and safeguarding heritage world-wide. ...

"Place, memory, meaning: preserving intangible values in monuments and sites"

Beautiful slideshow on home page at:
Global Heritage Fund (GHF) is a non-profit international conservancy which protects and preserves humankind's most important cultural heritage sites in developing countries. ....
Global Heritage sites are major archaeological sites and ancient townscapes selected by the GHF Advisory Board, based on thorough due diligence and close working relationships with on-site conservation teams and international experts in conservation science.....

Cultural Heritage Search Engine. Preservation and conservation database. The 100 plus links I could add in this posting are found in this comprehensive directory with a database search feature:

Pictographic Language

2006.3.5 Subject: The only living pictographic language features cosmographics.

A friend returned from Yunnan with a fine weaving featuring cosmographic symbolism.  It is part of an existing tradition.  Check out this link for incredible imagery of pictographic codices:
"Selections from the Naxi Manuscript Collection features ceremonial writings of the Naxi people of Yunnan Province, China. The Library of Congress's Naxi collection is the largest outside of China and is considered one of the finest in the world. The Naxi use a unique pictographic writing system that is similar to the ancient Egyptian and Mayan writing systems. It is the only living pictographic language in the world today. This online presentation features 185 manuscripts, a 39-foot funerary scroll, and an annotated catalog of the entire collection."


2006.3.9 Subject: Water-Leveling and Megalithic Monuments

Time to start a thread on this. How many of the "so-called" astronomical observatories have surrounding or internal ditches, or a cursus, a bend in the river, a canal, a lake, a sea, or some other possible water-leveling capability at hand. The correlation is quite high I expect from off-hand knowledge, w/o doing a stats analysis.

Leveling is a first-order task of surveying and accurate astronomic observation. It is something to account for when considering a location as a possible observatory and when considering possible geodetic functions. Geodesy, by definition, employs astronomy by inter-referencing earth and astronomic positions. On land, when you know where you are (unlike at sea and moving), you still need to determine level first before navigating, making place determinations, or positioning points.

Evidence of water leveling features at sites can provide one form of indication of possible activities (in addition to the obvious-to-the-Dutch ice-skating :-).

> James, That Chinese gnome was a U-shaped trough. Is that what you mean?

The refinement was accomplished by Zu Chongzhi circa 500 AD, by taking measure of gnomon shadows over a period of 24 days around the winter solstice. The astronomers realized that the moment of solstice did not coincide with the moment of solar zenith (meridian transit), so the shadow was not "correct" in length when longest each year. They then 'constructed' the 'arc' from the measure of shadows, a form of calculated extrema. This allowed for the refinement in days per year to 365.2429. (At the same time in India the lunar orbit to earth rotation ratio was known with precision.) I don't know the size of this 5th century gnomon. Historical record indicate that Xing Yunlu used a 20 m gnomon around 1600 and further refined the year to 365.2419. Guo used a 13.33 m gnomon with a pinhole sunlight focus in the 13th century, results unknown I believe. ....

Even at sea, the mariner has to use level. Determination of latitude by measuring the pole star angle is a comparative with plumb, or its perpendicular, local level. Finding level is the fundamental astronomy or geodesy (or construction) task on which determinations depend. It is the third leg of the gnomon shadow measure, providing the 90 degree angle to plumb.

Using the coordinates converter at, I noticed an interesting link and followed it to:

That page links to an interactive leveling page. You input your datum.

"...collection of information regarding the various leveling activities carried out by the Ordnance Survey since 1840. Leveling is the process of measuring the relative height marks across the landscape, and ultimately to a fixed datum - Mean Sea Level at Newlyn for the British mainland."


2006.3.23 VR.. wrote: ....
> I think for your type of work (archaeogeodesy) a latitude error of 0.01 degree (which I see as
> small for astronomical alignments) could be quite big for your calculations/methodologies.

When tolerances of error are considered, there certainly is a huge difference between a short line or points far away. It is quite advantageous to be measuring in terms of global scale. People will argue endlessly about the short alignments at Stonehenge. Even at the Newark Octagon, near 3,000 feet long, the direct survey ... cannot distinguish with certainty which of the nearly equal hypothetical reasons for the alignment is correct. Consider instead Stonehenge, at 0.25 degrees N-S in relation to Avebury. Their bearings are very easily quantified with precision, no room for argument. And that's only 1/1440th of the geodetic ruler.

So, when considering the latitude/colatitude of Monks Mound as single point positioned along 1/4 of circumference, between pole and equator, definition is at its best. The set of reasons/angles considered for Newark Octagon's azimuth, remain indeterminate .... In contrast, the points formed by those same angles are quite far apart when the hypotenuse extends from the center of the earth. There is no doubt at Monks Mound about which angle is the correct one!

I really like that sort of definition. Pick your battles, the archaeogeodesist could easily say. :-) It's not fuzzy math at the global scale.

2006.3.21 Re: Geodesy and Ancient Egypt Pyramids
<<< The million dollar question, is, of course, how would they have measured (longitude) ... I can see no mechanism that pre-dates the high accuracy sea going clock ... >>>

I'll take that million now. I've written of this online, but so far no check has arrived, and I've been waiting eight years (when I published online :-). The answer was so obvious, I couldn't stop kicking myself, so I'm not really expecting the check. Quoting ...

"Longitude determination is far more difficult. Longitude determination requires making a comparison of measurements of the position of a celestial object from two points on the earth together with a temporal inter-reference of the measurements. This problem is easier on land (a fixed position) than at sea. On land from a fixed position, measurements can be averaged over long periods of observation...."

The high accuracy sea-going clocks were needed by people who
1.) did not know where they were,
2.) required instantaneous determination,
3.) were moving on water in directions they could not control or perceive entirely.

It is an entirely different problem. Solving triangles requires three knowns. They did not know where the where. Therefore, without celestial-earth inter-reference,

4.) they did not know what time it was either.

On land, you know where you are and your position is fixed. You can take all the time you want and need, and you can look to the sky and see what time it is. So,

1.) you know where you are,
2.) you have all the time in the cosmos,
3.) your not going anywhere unless you decide to move your positioned point,
4.) you know what time it is.

A very wise man in China taught me one BIG lesson. Zu Chongzhi (430-510 CE) measured gnomon shadows for 24 day spans around the solstice, and calculated mean values to refine the value of the tropical year. It gave me great joy to read that. I realized, on land you can observe the moon for, oh, say, 18.613 years, and calculate mean values too, but not from a moving ship at sea.

I'd recommend using the Newark Great Circle and Marietta, or Stonehenge, Thornborough, Avebury, Newgrange, Tara. Good ditches for water-leveling helps, as do standing stones for references. Or natural rock in a high, dry desert. Or all of them at once! Of course, you'd want to know how far apart these sites are. Better stated, you'd end up knowing how far apart these points are. I know I have.

Thornborough Henges under Threat

2006.2.20 Subject: Geodesy of Thornborough = new member

... Hopefully, this important monument will be preserved. The geodetic perspective justifies preventing any alterations in the entire viewscape. I consider the monument significant to the history of science.

Does anyone have, or can anyone obtain, accurate GPS coordinates for the henges. ....

2006.3.1  Subject: Scientific data needed NOW.

Who can provide 'accurate GPS data' for the henges. Let's do some science here. Meanwhile, we have hot air only in certain minds ... and I want to check my findings and those of others with better data. Who can
do this? I'm 7,734.7 km away!

On appeal, expect to be called wild speculators, followers of new age occultism, neo-Druid star worshippers, etc., unless the science is done, and done right, beyond reproach. Ancient religion, paganism, has always been a great excuse for destruction and pillaging, and still can be.

Thornborough is very important in the history of science. It is one of the earliest sites in the British Isles evidencing careful surveying and planning. Thornborough epitomizes ancient geodesy. As such, every square foot of the viewscape needs to be protected until fully studied from the perspective of surveying and the science of geodesy. Long distance sight lines may be marked everywhere and anywhere in the entire Thornborough viewscape. The conservation plan needs to account for every post set everywhere. Anything less is equal to the burning of the Mayan codices. This time the book is the earth itself.

Regarding the Orion constellation idea. Where is that constellation in the sky? On the equator, more or less. What is significant about Thornborough's latitude? A degree meridian measure near the Thornborough latitude equals that at the equator. Understanding the measure of a degree of meridian is not religion, it is science, specifically geodesy. Measuring the earth and surveying is geodesy. Point positioning and place determination is geodesy.

An ancient scientific world view explains the Orion "coincidence" if the data supports the correlation. First, let's get the accurate GPS readings and do some science in our age.

2006.3.2 Subject: Re: .. Spell

MM .. wrote:
> ... a lot of people do claim that spells actually work ...

And Tarmac claims the opposition has no archaeological basis ... Diversity is great. We celebrate it. At the same time, is this akin to providing ammo to Tarmac?  Science can prevail in the courts. Welcoming ridicule is counter productive.

2006.3.6 Subject: Re: Beltane at Thornborough Henge 2006

O .. wrote:
> Beltane at Thornborough Henge 2006.
> Sunday 30th April, 12pm onwards, Thornborough Central Henge.
> ... a 5,000 year old ritual enclosure. Over a mile in length, this unique triple henge
> monument is astronomically aligned with the three stars of Orion's Belt.

As an anthropologist and archaeologist, I have a critical eye towards hypothetical alignments and claims of ritual. The authors of the study that mention "Orion's main belt" pointed out that the "western terminal" of the main cursus "would have framed the three setting stars" circa 3300-3000 BC. Of course, an entire celestial circle of other stars also set at the same azimuth. Nearly every alignment has some constellation setting coincidence. Pick an alignment and you can find an astronomical reason for it. Hence the dicho "the probabilities are astronomical" has meaning.

So, the henges do not align with Orion, and did not in the past. And, the positions of the stars change over time. The North Star was not the pole star 5000 years ago. The henges were used for thousands of years, and the position of the celestial backdrop changed significantly during that period.

On to claims of ritual. Ritual is a word used in anthropology and archaeology all too loosely. People lived their lives at these locations. What evidence exists of particular activities done "ritually?" We have evidence of massive construction projects, of surveying, measuring, employing geometry, and perhaps water-leveling. If anything, this is evidence of geodesy. But, I know of no evidence of prehistoric "ritual" in relation to the henges.

What of the concept of "sacred landscape?" Sacred to whom? How do we know the concept was even employed? We don't. This is interpretive writing. And, in anthropology and archaeology, is generally used
antonymous to "profane" in the unplanned sense. The landscape evidences careful planning and layout. And it is part of a larger "tradition." Cursus monuments and henges occur in other areas of the British Isles and other parts of the world. The similar Newark Great Circle in Ohio could easily fit a Thornborough henge inside its 360m diameter.

In sum, Thornborough is a human-altered landscape of a Neolithic tradition evidencing large-scale planning, surveying, and geometry. And these geodetic constructs are "monumental" in nature, probably intended to endure for all time forward. The builders did not foresee the machine age altering their global artworks.

Today, with a gathering inside the same place every year, it is a "ritual enclosure." Enjoy the ritual (and wish I could be there), but without shutters on the wonderment of what really happened at Thornborough, and at Newark, and at Stonehenge, at Tara, etc. In archaeology we have the science, the data and facts, the precise measure and the tallies, and we have interpretations, nearly as many interpretations as archaeologists. Interpretations, all too often, tell us more of beliefs in the time of the writing than of the past. That ritual is a difficult enclosure to escape from.

2006.3.14 Subject: Re: Beltane at Thornborough Henge 2006
B .. wrote:
>> ----- Original Message -- From: James Q. Jacobs
>> As an anthropologist and archaeologist, I have a critical
>> eye towards hypothetical alignments and claims of ritual....
>> What of the concept of "sacred landscape?" Sacred to whom? ...

> With the greatest respect, JQ, I think that archaeology
> as taught in Britain today, is not exactly the
> same as the position taken in your country.

No arguments there. But on to the core of the message...

> ...regarding the concept of 'sacred' landscapes, the
> academic discourse in Britain is aimed at building
> upon the existing knowledge and in prehistory does
> so by considering well grounded possibilities ...

> .. landscape, sacred or secular, has been well considered ...
> .. A site is sacred to whom? To those who consider it so.

Here we perhaps part in the semantics only. The original point in my post, albeit poorly conveyed, is how is the term 'sacred' employed and, especially, how is it understood in current usage when transplanted from archaeology journals into popular media.

This is an important issue with regard to many ancient monuments. Archaeology probably requires better terminology. Sacred has too many modern connotations. It infers religion, and that is an interpretive problem archaeologists need to contend with in their writing.

You write "sacred or secular" rather than "sacred or profane" or another term. The connotation is "religious or 'as distinguished from church and religion' " to use Webster for secularism's definition. This issue requires 'deep archaeology' and deep etiology. Contrasting of views on the two sides of the pond necessarily brings paradigms into the discussion, but first the etiology.

Digging deep, in Latin along with 'sacer' (sacred, holy, consecrated) we find 'saccum' and 'sacrificio,' money bags and sacrifice. Sacco, the verb, is to strain or filter. The English "sack" means a bag and "to plunder" (= not just filtering a sacrificial portion). I get the sense that the Latin usage derives from 'place of the gods' where you get your pocket emptied. Then 'gods' were emperors who received the goods and gold, the 'sacerdotis' being the keeper of the money bags, and the 'sacramentum' the tax, one's personal sacrifice.

Cicero's usage "sacra aedes" refers to sacred buildings, constructs dedicated to the members of the pantheon. The much older earthen circles might better be called 'sacra aegis' with reference to circularity (literally 'shield').

Does it not seem a furtive enterprise to use Aegean prose, be it today or that of 2,000 years ago, to try to define what was built 5,000 years ago? It does to me. Deeper still digging is required, to another strata.

The mythological pantheon of personages, the statues in the sacra aedes had roots in the gods above and below, in cosmology. Latin writers referenced 'aegis' to Jupiter (iovis + pater, father of the air, sky, heavens) and to Minerva (Etruscan origin, arts and sciences, wisdom, technical skill). Before the dark age of empire, before rulers replaced planets and plundered pockets, the etiology points to astronomy.

Dedicated space is my neutral preference to sacred or consecrated. My vote goes to dedicated to science. Instead of BC, we need a BR epoch, a 'before religion' paradigm to replace the assumption that religion
existed in distant, unknown cultures.

> ... I'm afraid that trashing it because we don't fully understand it appears to
> be considered by some to be progress.

Full agreement and a pet peeve. I'm afraid that trashing ancient monuments is still far more purposeful, because they still represent a threat to belief systems. This fundamentalism continues today, as it did during the Inquisition when de Landa burned the Maya codices and sacraidiotes burned women. Blowing up the Buddha epitomizes this typically far more subtle problem. This is why characterizing ancient sites as ancient religion, read "other" religion, is detrimental to their conservation and to scientific inquiry. It is this implication of assigning our term "sacred" to ancient sites that I find troubling. The problem is what meaning it has in generalist print, in current popular language.

> I would define 'ritual' as a repeated activity, brushing your teeth is a ritual,
> .... so I don't think we can ignore that ritual could easily be taking place ...

I agree. And, I would add that certain scientific activities "require" ritual. One example along the ancient path of knowledge and understanding of the cosmos would be the ritual of counting days and moons, an absolute necessity to build a foundation for astronomy. Determination of longitude before chronometers would require a lunar ephemeris, and accuracy would require prolonged observations, ritualized activity. "What rituals are we looking for?" is an important question. Objective inquiry requires more separation of church and ritual (an old sides of the pond issue ;-) There, I've circled back to paradigms and said enough.

2006.3.14 8:13 pm  Subject: Thornborough alignments
B .. wrote:

>> JQ: ... the etiology points to astronomy.

> Sorry, I thought your first post expressed that you didn't agree that features
> of Thornborough aligned with the sun or the constellation of Orion?

There was a point in time when one direction of one segment of the cursus pointed in the direction on the horizon where part of the Orion constellation set, the fact. I do not quibble with the fact. But every line anywhere aligned with some bright star at some time. I do not interpret alignments as ancient religion, nor do I leap to equate the three henges as Orion's belt.

The number of alignments at sites is astronomical, even when they have limited features, and the stellar background and the angles of illumination change over time. The Heel Stone at Stonehenge presents 1/7 of circumference (azimuth from north), as does the latitude at Avebury. That angle is a constant relative to the sunrise changing daily and solstice points changing over time. Alignments are spatial fact, the interpretations are our constructs. We can just as easily construct an interpretation that the Heel Stone was intentionally aligned to 1/7 of circumference.

Distinguishing fact and interpretation is another failing when writing by archaeologists gets transplanted into popular lore. We specialists more easily distinguish the facts and the interpretations in our field. Both are "expert" speak in the popular press without much distinction, and without discussion of how many interpretations could be arrived at from this sort of evidence (alignments).

Astronomy may have been employed at the site for geodetic purposes, place determination or point positioning. The astronomic activities of surveyors, explorers, and navigators inter-reference earth and sky,
employing lines and triangulation nets. I'm just trying to keep the interpretation door from closing prematurely. I'm saying there are other exciting possibilities when considering lines, circles, earth and cosmos.

I recently attended the Earthworks Celebration in Newark, Ohio, with lectures held in a public building on a University campus. I blogged that journey, with earthworks graphics and photo galleries:

One speaker told us how the Indians built the earthworks to please their god, the moon, so the moon would see the giant works and be happy with them, etc. Then the speaker went on to discuss our culturally superior understanding of the moon, denigrating the ignorant ancient Ohioans for building earthworks to please a false god. All those incredible alignments, and that interpretation. This epitomizes the problem I'm speaking to. Paradigms easily preclude viewing the recently conquered and vanquished as scientists. Likewise for the remote past. How much do we fail to see?

Where is Khufu's Great Pyramid?

2006.3.21 Subject: Geodesy and Ancient Egypt Pyramids
Thanks to the Forum and for all the great responses, on and off Forum. ...

Given current coordinate data, preliminary results (I still want GPS readings):

Khufu Pyramid (Helmert Spheriod) to Newgrange (map-scaled) arc:
36.0030 degrees = 0.10008 circumference = CIR/9.999916 (not 9.99961 ;-)
Bearing N 37.928 W (Petrie's First to Third 37.852)

The links that were particularly useful follow: 

Coordinates for Khufu:  Giza Plateau Mapping Project (GPMP), by Mark Lehner  []
Egyptian Antiquities Information System,  official Geographic Information System (GIS),  Supreme Council of Antiquities (SCA),  []
Petrie's The Pyramids and Temples of Gizeh online  ... Coordinates:...  Relative positions of Pyramids: []
Prehistoric and Predynastic Egypt  []
Great Circle Calculator By Ed Williams  []
Calculate distance and bearing between two Latitude/Longitude points  []
Guide to coordinate systems in Great Britain  ... What is a geodetic transformation?  []
GPS Coordinate transformations  []
Ancient Measurements of the Circumference of the Earth by Livio C. Stecchini  []

Thank you all who posted and e-mailed. I'm impressed by the knowledge you share, and by the data available.  Ya gotta luv da Web. Growing better brains daily.

2006.3.21 Re: Geodesy and Ancient Egypt Pyramids: Summary
X .. wrote: <<< ...I accept lunars can calc longitude - but how accurately ...? The naked eye only manages 1 minute of resolution ... >>>

If you have developed techniques, accuracy is more accurate than the size of a point of light in the sky. As a point of light is occulted, you can readily discern the color spectrum transition to disappearance. At least you can in the deserts and mountains where I've watched the stars. That is far more refined than 1 minute. Remember, the foresight length is a factor. How long is the foresight you are using? How clear is your air? What is your elevation?

<<< ...if they could work out longitudes anywhere they liked with no problems, why set up points on alignments or at equal distances... >>>

Specify what "points on alignments ..." you refer to. Assume I accept nothing except my own thinking/writing here.  Can you read what they said? What does Khufu's Pyramid say about this? Can you read that simple, bold statement? If you know what it says, the questions become mute. It is another culture's book, so you have to learn to read their language, or they have to teach it to you. It matters not if the book is written on paper or on the earth.

<<< ...I have never seen how this could be done over water... >>>

But modern geodesists do it. You're not saying they can't? No, right. It can be done, right? Another culture's capability is not dependent on your seeing how. They do/did or they do/did not, irrespective of your perspective.

<<< 'Fraid the million dollar jury is still out ... >>>

So, you're the guy with the million dollars, :-)

2006.3.21 Re: Geodesy and Ancient Egypt Pyramids:
<<< I posted some info about a possible Giza - Newgrange connection a couple of years ago ... I did not use exact coordinates for either site ... >>>

It is time to accumulate precise data. We have the GPS receivers, we have the WWW, we have the computers. ....

Here is an untested reflection. It has to do with geodetic benchmarks. Our current geodetic system began placing benchmarks with the advent of science in our cultural tradition. First three points at the same latitude encircling the globe. We keep adding them, triangulating inward. (Count property boundaries, and we have billions and billions of geodetic benchmarks.)

Western geodetic science knows the pole has secular motion now, having determined this in rather short order from their primary geodetic benchmarks. What if you were shown 5,012 year old benchmarks? What would that tell you about the earth? What if the bearing angle from Khufu Pyramid to Newgrange was a specific and "very, very precisely known" angle, say perhaps the same as an azimuth at the Newark Octagon in Ohio (atan 4/pi ;-), would you know how much things have moved in the last 5,012 years?

Perhaps, in another culture, this is still known if you know what the marks mean and where you are when you are there.

... geodesy is a science. It is not done by rounding off to the nearest degree (+/- 70 mi.). It is done by positioning points to within inches. For ancient geodesy, +/- 5-10m coordinates (GPS, WAAS-enabled or survey) will do, or its a preliminary datum, useful for analysis but not for quantitative assessments.

... if plus/minus 3 miles is a standard, the probabilities of relationships become astronomical, and even Easter Island, the last speck found, will be on a great circle with the pyramid and a bunch of other sites! Not that that would necessarily mean anything anyway.

Consider instead the relation of Fort Center Mound and Circle in Florida and the Newark Observatory Mound and attached Observatory Circle and Octagon in Ohio. These are monuments in the same group, in the same cultural period, in areas with known contact, and the precision of the relationship is much better than the size of the circles; the ends of the line fall near the centerpoints of the monuments, well within the monuments. Plus, both sites have slightly elliptical circles the same size. .... The distance is relevant to the method of determining longitude and an astronomically determined, not arbitrary, module. Plus, the arc:latitude difference ratio expresses the ratio of our elliptical geoid (termed "flattening" in western science :-).

... There are very ancient pyramidal structures in Peru, and they are far larger than Khufu P. See "Early Monumental Architecture on the Peruvian Coast, Evidence of Socio-Political Organization and the Variation in its Interpretation." [] Much dating work remains to be done there, but these probably include the oldest stone pyramids on earth and the oldest known cities in the Americas.

... where is this point? A village in the Andes, right? Is it the correo? or a mysterious motel bathroom, c. 1979, at Macaulay's B&B? Where is your "megalithic city" exactly?   Are you using a Helmert Spheroid of Reference coordinate, UTM, WGS84? The discussion must first be grounded to some statement of methods. What reference system are you using to describe the position? Are all points in the same system?

There are conventions and systematics in the science of geodesy. It does not matter what size the entire great circle is. Each degree along it's length is a different size than its neighbor. What is the angular relation between the points? Are you calculating a spheroidal angle and bearings, or ellipsoidal?

<<< It looks like your figure of .29990828 for the percentage of the circumference is based on an equatorial circumference.... >>>

No, on the geocentric angle of a spheroid. It just happens that the sites are on opposite sides of the equatorial bulge, an inflation to account for if measuring unequal angular surface distances.

For a geodesic arc length formula on the ellipsoid, see:

There is a Vincenty formula calculator for distance between two Latitude/Longitude points at:

Given latitude and longitude of two points, calculate the ellipsoidal distance and forward and reverse azimuths between the points at this site:

For a links page pointing to Online Calculations & Downloadable spreadsheets - to perform Geodetic Calculations:

"Sacred" Landscapes

2006.3.19 2:15 pm Subject: Avebury, Silbury Hill, and Windmill Hill
Yesterday morning I acquired new, improved coordinates for Avebury, Silbury Hill, and Windmill Hill, thanks to the great Magic interactive map capability at:
and the awesome coordinate converter at:
Then I checked their arc distances. Here are two cosmographic distances to visualize if you are visiting Avebury:
1.) The arc from Avebury to Silbury Hill is 1/1000th of the arc the moon moves during each rotation of the earth.
2.) If you are sitting in the center of Windmill Hill henge looking across Avebury to Silbury Hill, that distance is 1/1000th of the arc of earth's orbit per full moon cycle.
Archaeo cosmographics, intentional or not. ....
FYI, Windmill Hill henge is an about 360m in diameter causewayed enclosure (ditch and embankment) of elliptical form, with two central, concentric inner circles. It is the type-site for the henges and one of the largest causewayed camps. It is also the type-site for 'Windmill Hill culture' pottery. Carbon 14 dating places the site between 3600-3300 BCE. See also: Cleal, Rosamund 2002. Great Sites; Windmill Hill, British Archaeology 67.

2006.3.20 Subject: Re: Avebury, Silbury Hill, and Windmill Hill plus Stonehenge
S .. wrote: <<< Ah, so now you're accepting an accuracy of only 100m, too! Sorry - just couldn't resist that one! ;-)

Look closer. I've been doing preliminary work with +/- 500m for some sites! It's a good thing the planet is 40,000,000m around, as that's still only 1/80,000th error. :-) Most of the +/- 100m is due to national grid differences. But, I started to do intra-site considerations with the Newark Octagon, evaluating my GPS in relation to the Middleton survey data and Horn and Hively articles. I updated Neolithic Calc with the new coordinates, and in v2006.3.18 deleted my old duplicate map-scaled coordinates. The ancient 'state of our geodetic knowledge' that they express regarding resources and methods a decade ago may be of interest to one person, they are just confusion to everyone else, so they are gone now. They served their preliminary study purpose well enough, or we would not be having this discussion.

I still cannot get GPS for most of the Neolithic sites in my study. English Heritage provided some great long reports with "center / point" Easting Northing data. I just uploaded my XLS of the henges to our Files. Their data is in the form: Stonehenge SU 1224 4218 centre / point
That's a +/- 10m format. I used Magic to check their "centre / point" classification, and it seems to hold up (I have not done every site in the Excel). So, all the NMR long report data is +/- 10m. Deeper digging is required for better accuracy. I clicked center points for Windmill Hill, Avebury, and Silbury Hill at 1:5,000 or better (1:2,500 will also display) and I've uploaded a screen capture (also uploaded to out Files). It's still not GPS, but I've answered my question. The same astrogeodetic modules are in evidence at Avebury as at
Newark, Ohio, and in the Eastern Woodlands Mounds array. But, since the hypothetical time difference is great and "the modules are naturally occurring," that in and of itself, does not establish cultural diffusion, etc. I still know that I'll get a different set of +/- 1m full grid references every time I click those centerpoints in magic, but this is better than the +/- 10m because it eliminated the 10m modularity. I calculated everything in arcs. The results in 6 decimals follow:
silhi - avebu 0.013070 degrees = 0.000995 R27 (error - 7.8m)
silhi - winhi 0.029002 degrees = 0.000996 S29 (error - 11.5m)
To calculate the errors I used meters per degree for the local latitude (as if that matters :-). We also now know with certainty that the arc and N-S distance from Avebury to Stonehenge are 1/4 degree (CIR/1440). I still need accuracy to the meter to determine if their ratio is precisely days per rotation. With current methods, what I have is 1:0.9976. As a comparative, only E-W error will budge the ratio.

2006.3.19 10:55 am Subject: Archaeogeodesy Study request = GPS readings needed

Time to quit lurking. First, just two "sacred" tidbits to visualize if you are visiting Avebury:
1.) The arc from Avebury to Silbury Hill is 1/1000th of the arc the moon moves during each rotation of the earth. 2.) If you are sitting in the center of Windmill Hill henge looking across Avebury to Silbury Hill, that distance is 1/1000th of the arc of earth's obit per full moon cycle.

Cosmic landscape, I'd say!  Yesterday morning I acquired improved coordinates for Avebury, Silbury Hill, Windmill Hill, .... thanks to the great Magic interactive map capability at: and the awesome coordinate converter at: ....

NOW that I've shared, my request is: I need accurate GPS coordinates, preferably within 3m accuracy, WAAS-enabled readings, for major ancient monuments world-wide for my ongoing Archaeogeodesy Studies. .... If you have a database of such you can e-mail them to me ... you will be duly credited. ...

2006.3.22 11:41 pm Subject: Re: Archaeogeodesy Study request = GPS readings needed
<<< What does "the arc the moon moves during each rotation of the earth" mean? >>>

On Jan. 1, 2000, it was 13.1403824445 degrees (R27). More significantly, it is fundamental to a lunar calendar and the ability to determine longitude on land in a pre-mechanical-clock world. It is a basic tick-tock of our cosmosphere, the fundamental relationship of two of the three motions, rotation on the axis and lunar orbit. It is an expression of basic unity, one rotation equals 'x' lunar orbits.

The third fundamental motion is the earth's orbit of the sun, and that is expressed in the other distance, angular motion of earth orbit per full moon cycle. This is the accurate clock that generates eclipse cycles, a nodal alignment of all three bodies, sun, earth, and moon. This module in degrees is 29.1056177173 degrees (S29). This is another basic unity, one full moon cycle (synodic month) equals 'x' solar orbits.

More complete discussions at the Archaeogeodesy Pages: Think if it as a line from the center of the earth to the moon. During one earth rotation, the moon/line would move 1000 times the distance from Avebury to Silbury Hill. Something to ponder if you are there. And, was that intentional (read sacred) or profane (read coincidence)?

2006.3.29  Re: Archaeogeodesy Study
MB .. wrote: <<< ... Could you clarify; by: "The arc from Avebury to Silbury Hill" are we talking about the arc at the centre of the Earth? >>>

Yes, a method of measuring distance, like we use to create maps. It is arc distance instead of meters or feet, so degrees are the units.

> and you be saying that ... well exactly what? ... Is it: 'two sites separated by 1000
> times the distance from Avebury to Silbury Hill would see the moon in the same position...
> Or am I completely off-target?

You got it. The moon moves 13.14038 degrees per rotation of the earth. When the same star is directly overhead one night later, the moon has orbited this many degrees. If you walk from Silbury Hill to Avebury, you have moved 1/1,000 that many, 0.01307 degrees. And 0.00001 degrees is 3.65 feet (of course!!), so center-on-center error is about the size of a giant megalith, less than in the method of determining the coordinates. Hence, I requested GPS readings.

And, if you walk from Fort Center Circle and Mound in Florida to Newark Earthworks in Ohio, the two sites with the same-sized elliptical circles (1,180 feet about, near Avebury-sized), you have moved the same distance as the moon moves in one rotation, all 13.14 geocentric degrees.

MB .. <<< Sighting of the moon would require a good vertical plane surface at right-angles to its course (the celestial plane) .... >>>

It requires darkness, so the position of the moon can be observed in relation to fixed celestial reference. That is sidereal time. And duration is required to average the motion over time. The moon is not orbiting at a constant speed. The apogee:perigee ratio is about 7:8, considerable ellipticity in the orbit, hence changing speeds.

> ... providing 'clocks' that might be used to > relate instantaneous time from one site to another
> This would be necessary - you'd need a fixed point > in time to clock the different moon positions ...

You are thinking like sailors on a moving ship that do not know where they are. I've had this discussion before, and this view is commonly held, but not actually fully considered. .....

The real insight is in understanding the role of lunar calendrics and long durations of observations. The moon is a foresight, an arm moving against the face of a clock.

> ... machinery would enable the circumference of the earth to be read ...

All you need to do this is a measured, north-south line and two vertical poles set plumb (or a rope in a tree). You compare the shadow lengths and do the simple geometry, two angles and one side determine the third angle, and presto, the circumference is extrapolated. This is so simple, it is no wonder the size of the earth was known long before history begins. Eratosthenes, the librarian, was just reporting ancient knowledge (before that library was burned).

> I've swum around your website (only a little) ... To your... "Questions Posed."
> ... Cultures ... respond in similar ways entirely independently. That said, of
> course ideas move too, and by different means.

Precise, indeed. And the modules I've proposed and found to be of utility can be independently discovered. They are inherent in lunar calendrics and time keeping by astronomic reference. This is why I defined them as analytic tools in the first instance, way back in the 80s. I did not expect the trans-Atlantic results. But there they are, posing the questions they do.

We perhaps have rather poor insight into the relative scale of the dimensions of space and time, being here for short lifetimes, and no longer dependent on walking about over great ranges for foraging/hunting. As modern travelers, that perception is changing, but not about travel on foot. To illustrate the point, there is an Indian Run happening just now, across America to raise awareness of ancient mounds:

My favorite story on moving across the globe on foot is of the meeting on the Piramide del Sol, Teotihuacan, Mexico, Oct. 12, 1992. The Natives came on foot from as far as Peru and Alaska. The earliest departures started in March!!!! Now consider the dimension of time. This rhetorical question puts the relationship of time and scale into perspective. We walk three miles an hour. You do the math. How many times can you walk around the world in one lifetime, or in 2,000 years? It truly is a small world the human family shares.

2006.3.28  10:19 Subject: Stonehenge and Avebury ...

Center-on-center relationship:
Stonehenge to Avebury, 0.25049 degrees arc
Stonehenge to Avebury, 0.24988 degrees N-S
Ratio is: 1.002415 : 1 or, conversely, 1 : 0.9975909
Days per rotation of the earth equals 1 : 0.9972697

1.) the obvious: Coincidence or intention?
2.) Who has precise GPS readings for these two constructs, of sufficient accuracy to refine centerpoint coordinates to the precision attainable by direct survey over 1/1440th of the earth's circumference? I used at 1:5,000 scale and confirmed accuracy from archaeological publications.

Horizons, Refraction, Meridian Transit

2006.3.28  Subject: Re: refraction and its variables
DS .. wrote:
> []
> "refraction cannot be measured accurately near the horizon;...
> ... Refraction at the horizon commonly varies by many minutes of
> arc, and occasionally exceeds nominal values by a degree or more."

What a valuable 'point to raise' (pun intended). I grew up on a hilltop in a very expansive landscape with incredible dip of the sunset horizon. Frequently, western buttes of the distant landscape, normally out of view beyond the furthest horizon, would appear above the horizon. As children, we knew which buttes we were seeing and where they really were, yet we called them mirages. And we very much enjoyed this phenomena, the bending of light allowing seeing beyond the actual horizon. Aaahh ... the things we already know by seeing as three-year-olds!

There are real limits to horizon-level observation. By my thinking, a focus on the moon (near zenith) as foresight to the cosmos might be more productive than horizon as foresight for the moon!

2006.3.29  10:49 am Subject: Re: transit alignments
VR .. wrote: > .. (are) kivas ... transit monuments? ...

Kivas are too shallow. ... I'd say kivas are places to stay warm or cool, with the door in the ceiling. They are an improvement on pit houses that evolves in conjunction with above-ground, walled dwellings, the half of that bifurcation requisite by climate extremes. If you are thinking of zenith observation in the SW, think deep canyons with rock edges, flat bottoms, and long lines for accuracy. Maybe even throw in the stone towers on the canyon edge and the rock art on the walls below. One of the best of these deep canyon sites with rock art everywhere is under Lake Powell.

2006.3.29 Subject: Re: Refraction, Theocentrism, and Seeing the Light ?
S .. wrote:
> ...been pondering about the greater *and* more variable level of refraction at sunrise/set, ...
> For sure, rise/set refraction is both greater and more variable than any other kind.
> For sure, this makes possible alignments to rise/set on the horizon harder to pin down ...

You are writing with tongue-in-cheek, no? I'll reply w/o tongue in check! ;-) All very good reasons to not equate astronomy with assumed alignments on horizons.

> You *will* also, given that your entire culture and its neighbors have been
> in the business of building megalithic "observatories" for generations ...

Assumptions based on lack of careful analysis by past authors. First, where's the proof that even one of them is an observatory. Even Hawkin's Stonehenge concept is still debated. And, given the numbers of megalithic monuments, are we to also believe every valley had an "observatory" or ten?

> ... approximately accurate over long periods, because you don't bother going to all the trouble of
> erecting massive monoliths to a designed plan unless you want it to be of use for more than one year!

Monuments erected "for all time forward" are not, at least in my logic, going to align to rise/set locations that change over time, unless, of course, the purpose is to mark that time.

> ... if you do have a method for leveling-out the effects of the regular and smaller anomalies ...

Remember Ptolemy? Isn't his what he did to make reality fit his model?

> ... Let's take the old and commonplace assumption that
> megalithic structures have some relationship to religion.... pretty likely, given what we do
> actually know about early historical theologies that actually left written texts ...

Assumption is the keyword. And why interpret these structures in terms of historical cultures? Religion has "some relationship" to figuring out cosmography, but, in some cultural sequences, it lacks exactness, replaces inquisition with dogma, and burn books in its inquisitions.> ... assuming a theology ... Again, assumption. Theology, as in a dogma with a godhead? As opposed to understanding actuality by assuming a theo? Religion is a mental category, a linguistic tool, a word in our language, and we assume we know the meaning of the metaphors employed in ancient text as we contrive what they mean in our minds and times.

> Taking it one speculative step further, perhaps (in a crass over-interpretation I admit
> but one worth considering) to track the mood of the solar deity ....

Reverse-engineered analogy based on cultural beliefs in more recent times remind me of the flaws of linear, evolutionary anthropological theory. The Western, post-Dark Ages perspective on past cultures is theocentric, and assumes that cultures have religions. Religion is a word in "current" language, not past languages. All cultures have cosmographies populated with linguistic entities corresponding to greater or lesser degrees with actuality, and some create anthropomorphic entities, improvements on less useful metaphors perhaps. But cultures all do the same thing, creating linguistic tools to understand actuality and to communicate those understandings culturally.

Religion is one such linguistic device, one word in one language. It means to "bind together' and has etiological roots back to "logic" and re-collection of logic, albeit in some cultures it has evolved to "filling in the blanks" where logic has been deficient to the task at hand for that group. The correct origin of religio, "conscientious exactness" (and hence the "artes religiones" or, to use a current word, science--by definition knowledge) may well describe the arrangement and effort of the megalith builders. Moreso than senso moderno, at least.

As a linguistic device, religion can be employed to "other" those who employ a different set of metaphors to describe the same actuality we all share across all time. It is a useful word to divide and conqueror only if we lose sight of the fact that it is, in the end, only a word in a language. In scientific anthropology, "pursuit of knowledge" or "cosmography" might be more appropriate terminology than reverse analogy employing Western, post-Dark Age, theocentric assumptions, interpretations, and metaphors. Posits need to be more "religiosus" (Latin, scrupulous) in ordering of the cart and the horse to move megaliths into some cosmic order. History is quite refractive--when not a shimmering mirage on the most distant horizon--and a bit of linguistic relativism seems apropos at this juncture, at last to this anthro.

2006.3.30  7:55 am
S .. wrote: <<< Oh dear - refraction rears its ugly head yet again! ;-) >>>

Just ruminating here, but another idea needs to rear its head.

Location, Location, Location, that's Geodesy speak.
Observatory, Observatory, Observatory, that's Astronomy Speak.
Function, Function, Function, that's Anthro/Archaeo speak.

A Lunar/Solar calendar can combine elements of all three!!
1.) Function: Lunar calendars have function in cultures doing water crossings, the moon being correlated to tides. Light/dark influences group planning and activity schedules; party and howl under a full moon, no outdoor plans if its dark at night. Planting schedules may be moon related, or game migrations. Living with hunter/gatherers in the Amazon, I have participated in scheduling hunting and fishing at night according to moonlight. One activity before, the other after moonset.
2.) Observatories: Not in the classical sense of accurate astronomy, but time-keeping by the cosmic clock instead of by numbers on a wall (simply put, numbers don't fit anyway, fitting the cosmos well or recording numbers fitting into the average Neolithic hunter/farmer's toolkit).
3.) Location: With lunar calendars, after sufficient time accumulating observations, specialists can arrive at longitude determination and navigate more accurately, on land and at sea. And, perhaps a few major centers will have a "real observatory" instead of just a megalithic clock tracking the cosmos.

Just thoughts, not an academic paper here. But, the "observatory" everywhere concept does not float. "Observation" everywhere points to calendars.


2006.3.27 ... What is lacking is consensual reality. Science offer just that. However, the number of people killed by war in the last century is truly a nightmare of unbelievable proportions. Sixty million dead in the Americas at Contact was also; with religion dividing the world in two for kings.

There is inspiration and education in contemplating the past, and solace in ancient places, but all the SPIN is dizzying. Imagine, instead of the romantic deep-doo, the population numbers when Avebury and Silbury Hill were constructed. How do we get BACK THERE? Easy, one child per woman: and population goes to 1/2, then 1/4, 1/8, 1/16, 1/32, 1/64, 1/128, 1/256, and in 8 generations we are back to less than 25 million. That might end wars. Or, at least we would not be killing 25 million per war!

Religion, Science, Knowledge, and Semantics

2006.3.27 ...DW .. wrote:
> ... Of course, Science is giving us the capacity to kill billions at a time. The final vote isn't
> in on whether Science will be a boon to mankind or its instrument of suicide.

Our brains give us this capacity. How we use them is what matters. It is human decisions that determine the course of history and genocides. "Science" is just our current word for the systematics of knowing reality. It is not a thing the gives stuff, it is a mental reference to something, nothing more. It is "humans" who create
the capacities to kill others. Cut the excuses and assume the burden of truth here. Don't blame an entity that is non-existent.

> I suspect that some form of Platonic reality may be true.

There is one reality, no matter how differently perceived.

> Hence the question arises ... how do we live in the Platonic multidimensional universe?

Actually, the question is, how do we live in the one reality, and how will our actions impact the future. We look to evidence from the past for lessons. Sadly, the interpretations of the past tell us more of our own thinking, bias, and paradigms that of the world of those who built Avebury and Silbury Hill. Thinking we know their world is pure hubris when we consider our own problems! No wonder dreamers long for something different, and people pay for the fantasies. But they are not consensual reality, they are individualist realities, marketed for profit and material gain. And individualist realities create disunity, exacerbating our current dilemna. Ask Hitler.

2006.3.28  9:05 am Subject: Why do we have creation myths?
MB .. quotes: Julian Baggini ...The Guardian

> ... we naturally ask where the universe comes from, and in the absence of
> any reliable way of discovering the real answers, we make a best guess, which
> usually means describing cosmic creation in ways analogous to more familiar forms ...

Ergo, we create religion, the mental construct to bind it all together. Very simply, human language makes liberal use of metaphor. For example, the window on my desktop is a gateway to the world. Don't confuse words with reality, or vice-versa. A metaphor can represent a universe. The mind limits what it means. As the mind grows with experience and time, meanings evolve. And school boards in Kansas can't change that evolutionary fact.

2006.3.28 Subject: Science, Knowledge, and Semantics
DW .. wrote: <<< JQ: "Science" is just our current word for the systematics of knowing reality.... a mental reference to something ... >>>

> "Science ... proponents claim that it is the 'true' truth and we must live in its
> impersonal universe.... scientists ... trying to tell everyone that they have a corner
> on the human truth market.

Whoa there. By definition it is knowledge (truth, as you say). Science is a word, and just a word, derivation: to distinguish, to discern, to cut, to separate. By definition it means a state of knowing, and in particular systematic knowing. Do not confuse the "definition" with the people who seek knowledge and who work on the systematics, those who scission unity into mental partitions and apply knowledge.

> > JQ: There is one reality, no matter how differently perceived.

> ... I suspect there are three realities: Consciousness, probability, and the world of classical physics.

Unity is the reality. It is mind that deconstructs it to understand the universe linguistically. "One is the only number" is far more than a song. When you distinguish "three" realities you are mentally distinguishing aspects of one reality. You are on the path of science, "sci-ssioning unity. Keep it up, you may evolve. ;-) But, put the pieces back together when you are done. You don't want to confuse your deconstruction with the ONE unity of all things. False gods there.

And, every culture has a right to their own metaphors. Let's not kill or stone anyone for trying to understand the same thing we are all trying to understand, the one reality we all share. Agreement that we all share one external reality is a good starting point. Understanding of that reality is an individualist activity, and comprehending such leads to empathy and compassion. On this score, don't ask Hitler, ask Ghandi!!

Secular Polar Motion

2006.3.28  2:29 pm Subject: Annual Secular Polar Motion

Here is another site location variable. The "Annual Secular Polar Motion" is the alteration in the position of the axis of rotation relative to the surface of the geoid. The motion has been variously described. One is:

0".0035 (= 0.00000972222....°) along the meridian 65° W.

Think Andes and Himalayas creeping towards the equator, though some blame ocean currents. So, when I consider today's center-on-center relationships: Stonehenge to Avebury .... For illumination studies, it probably does not much matter that these sites are some 200m nearer the equator than they were 5,000 years ago. But reflect on how the change in location of the pole impacts the trigonometry of site relations. Differently at different longitudes. Hardly any latitude change in Egypt, relatively a lot at the Newark Octagon. Avebury is located at the point where latitude equals one/seventh of circumference. What does it's location say about how much polar motion has occurred since construction, if anything? How accurate was the placement 5,000 years ago and today? Just a "small" archaeocosmic morsel to contemplate for afternoon tee.

2006.3.29  Re: Annual Secular Polar Motion
S .. wrote:
> > JQJ: another site location variable. The "Annual Secular Polar Motion" is the
> > alteration in the position of the axis of rotation.... >>>

> It's my understanding that it's not in a "single direction", but wobbles round and round ...
> ... there's not been enough data returned yet to be able to make long-term predictions ...

There are three (or more) polar motions, two wobbles and a proper motion of the poles, the "secular polar motion" quantified in annual terms by current convention and formulations. When the modern version of geodesy was recently founded on a scientific level, in other words globally, of course the first order of business was to establish/position three points around the geoid at the same latitude. The best latitude was determined to be about that of Newark, Arcata, Beijing, Istanbul.

Since the positioning of the primary, initial, modern geodetic benchmarks, astronomers have been able to determine that secular polar motion has altered their respective latitudes, and determined the amount relative to that very short span of recent time. It would be far better, of course, if we had 5,000 year old geodetic benchmarks! Especially so if one wishes to begin debate about attribution and steadfastness of rate, direction, etc. Today, the debate is still about direction accuracy.

Our knowledge is such that we cannot with certainty state what latitude a site was at 5,000 years ago. We have our current best estimations based on our own very brief span of time practicing geodesy at a global, scientific level. For the Neolithic of NE Europe, that estimate is about 0.0022 degrees change in latitude. There is also a change in North orientation of corresponding order (see formula for direction). This motion has yet to enter archaeogeodesy, and is 'notably' lacking (at least to the geodetic-minded) in discussions of the "inaccuracy" of the cardinal-directional alignment of Khufu's Great Pyramid. Egypt is at a longitude where secular polar motion has very small impact on latitude, but does alter polar orientation near the maximum (65W + 31E = 91). Wait a second (pun intended), have we there an ancient geodetic benchmark ;-O ?? indicating the amount of motion? What I'm trying to determine more accurately, and why I bring forth the discussion, should now be clearer.

Reference is: Markowitz, Wm., Concurrent Astronomical Observations for Studying Continental Drift, Polar Motion, and the Rotation of the Earth, in Continental Drift, Secular Motion of the Poles and rotation of the Earth, edited by Wm. Markowitz and B. Guinot, D. Reidel Publishing Company, DorDrecht, Holland, 1968.
For a more complete bibliography of references for all my online ../astro/ folder pages, go to the bottom of:

2006.3.15 Subject: The Stargazers of Ancient Egypt, due North, and Precession
Here is a topic I encountered in another e-group. I've been searching other astronomy related discussions for use of the word "geodesy." And it's usage is really rare even though there is such a close relationship of the two sciences. Anyway, here is the article link.
Would the Ancient Egyptians (AEs) have needed to use two stars and an instant moment of axial rotation to determine north? I doubt it. My method choice would be to observe several circumpolar stars, measuring and marking their paths of circularity, then finding the mean direction of these. Any comments on the qualitative reasoning behind this author's conclusions?
Any comments on the quantitative requisites to determine if the two "plumb stars" indicated north in the first place? Any thoughts on whether or not the AEs understood precession?

2006.3.30 Re: Khufu's Pyramid and Secular Polar Motion ??
GC .. wrote: <<< ...several cycles at work here. Most of us are familiar with the ~20ky
<< cycle of precession, which placed the star Thuban (Alpha Draconis) near the north
<< celestial pole at the time of Khufu. This cycle actually varies between about
<< 19,000 to 23,000 years ...>>>>

CORRECTION: Precession (PR) is the slow and gradual retrograde rotation of the direction of the earth's axis of rotation relative to fixed celestial reference. The "Centennial General Precession" formula is:

longitude = (1.396291666... + 0.0006180555... T)°
right ascension, m = (1.280397222... + 0.000777... T)°
declination, n = (0.5569666... + 0.000236111... T)°
Given T = Tropical centuries from 1900.0 N

The J2000.0 rate was 25,794 years, and 4,500 years ago it was about 26,295 years. The cause is not accurately stated; gravity acting on the equatorial bulge is a simple statement of cause. Quoting from, "Precession is the effect of external torque exerted on the geoid causing the spin axis to describe a circular cone. This motion is caused by the gravitational attraction of other celestial masses, particularly the sun and the moon. It arises because of the ellipticity of the geoid (torque on the equatorial bulge) in combination with the obliquity of the axis of rotation in relation to the plane of revolution (the ecliptic). The period of precession is presently about 25,780 years. Because the earth is rotating, the torque cannot change the inclination of the axis relative to the ecliptic. Instead the angle turns, inscribing a cone in fixed space perpendicular to the plane of torque (the ecliptic)."

<<< ...The "secular polar motion" referenced in this thread is a 41ky cycle
<< of the variation in the obliquity of the ecliptic. ... >>>

CORRECTION: Obliquity of the Ecliptic is the temporally varied angle of the axis of rotation of the earth relative to the plane of revolution around the sun. That motion has the following formulation:

OB = 23.4392911111° - 0.0130041666...° T - 0.00000163888...° T2 + 0.0000005036111...° T3
Given: T = Julian centuries (36,525 days) from 2000.0.

Secular Polar Motion is just what I said it is, movement of the axis of rotation in relation to the earth's crust. These are very distinct motions. Obliquity of the Ecliptic changes the angle of inclination in cyclic terms, as formulated above. Secular polar motion changes what points on the crust are over the axis, the poles. If you go to the South Pole today and mark the spot, those going there in 4,500 years will find your mark "near" the south pole, but no point remains the pole because the earth's crust moves.

<<< ... Half a degree is pretty hard to measure using plumb lines and circumpolar stars... >>>

Tell that to the ancient astronomers in China who used rather short gnomons to refine the accuracy of the length of the tropical year. Have you tried to do it? Give it your best effort and report back.

2006.3.29  1:52 pm Subject: Re: Tilts and Wobbles
S .. wrote: <<< ... you might be interested in ... [ ] >>>

I'm interested in only the one motion assigned to the pole, not the wobbles and short-order variations. My interest is in the motion that alters the latitude and longitude of geodetic positions over time, together with their orientation in relation to North. Core motion may be at the core of them all, but I'm a bit more surface/archaeology oriented.
Forget wobbles. Secular polar motion is true temporal polar wander and gravitationally related: inertial mantle mechanics and motion. Factors like glacial rebound and mountain uplift are causal, so I expect that the present rate will be reflective of the past 5,000 years. That "assumption" is my thread. Let me frame a question to illustrate the more practical terms, "Since Avebury was constructed at '1/7 circumference' latitude, how much have the coordinates changed since then and, if intentional, what does that tell us about the accuracy of such placement?"


2006.3.7  Subject: Anthrocentrism, Geocentrism, Heliocentrism
All this focus on alignments. I'm beginning to perceive a simple evolutionary theory of archaeocosmology. First, the observer was the center of the universe, then the Earth, and only much later the Sun. Rather like the flawed theories of cultural anthropology used for 'Modern Centrism.'

In evolutionary anthropology, every culture before ours was more primitive and ignorant, and humans climbed a ladder of successive steps to attain our current zenith in all things. Along the 'line' of: the savages, the little village, sky worshipping pagans, the city, anthropomorphic gods, formation of states, monotheism, empires, industrialism, science, democracy, nukes. And it was a continuous climb, not a see-saw with ups and downs, and certainly no previous possibility of our awesome achievements and intellectual insights.

A lifetime can be spent on finding alignments. And the likelihood of finding them is astronomical even if they are not intentional. In the end, what does the alignment approach produce? How long a line is needed for an alignment to tell us something precise, 1 km, 10 km, 20 km, longer. Precise cosmographics involves 1:400 scale triangulation. That is beyond the sale of most single monuments in the British Isles.

Is there an anthrocentric astronomy/cosmography I'm unaware of? ;-)
Serious question: Why study alignments, to what end?......

.....There is a certain irony in all those Englishes out there in the fog trying to study solar alignments, wrapped in the underlying assumption that the sun has something to do with it. I may be joking a bit at
your expense Steve, but I'm hoping to help clear some of the fog. We are in the cultural milieu of 'modern' archaeoastronomy, and that's a real heavy fog to contend with for all of us.

Perhaps the monuments and the alignments are there because the sun isn't available most of the time. Just maybe, the purpose of the monuments is to assist the poor blok out there in the fog trying to navigate the landscape. :-)

In science, first define your assumptions. Then try to find the ones you missed.

So, if you are standing in the middle of Cairnpapple Henge, how far away is Long Meg, and in what direction? Say you are supposed to arrive there in just 3 days with that load of new axes in your
Neolithic pack. And it's really foggy. All you can see are the stones. What direction do you walk in? In math terms, it's 1.3175 degrees, bearing N 155.26 E, but you don't have an HP48GX in your Neolithic pack, you just have axes, and the stones of your landscape.

2006.3.8 : Re: Anthrocentrism, Geocentrism, Heliocentrism
S .. wrote:
<<< JQ: Serious question: Why study alignments, to what end? >>>

> It's a very good question ..... Most importantly, you can't be a truly successful farmer
> without some sense of the periodicity of the seasons ... the simplest way to work out
> a calendar is to build a big Sun-clock ...

Simple is the light shining in the cave, door or window, or the shadow of a cliff, is just as accurate, and no work needed. Rock art everywhere illustrates this marking of light extrema. Big sun clock is big job.

> ..pondering alignments is about trying to grasp at the most solidly-remaining
> straws of the Neolithic cultural complex. ...

Assuming the alignments were important to them. Pondering the constructs holistically, I assume you mean.... The megalithic book, in a holistic sense, is the sum of the constructs. Does an alignments focus at individual sites miss the "single book" perspective?

Intagliare sapiens en lapisaxum es loquitur infinite. Then they invented bulldozers.

2006.3.9 Re: Anthrocentrism, Geocentrism, Heliocentrism
S .. wrote:
<<< JQ .. Simple is the light shining in the cave

> ... Also the least reliable. Makes for great poetry ...

Actually, it depends on the cave and the geometry. Some of the cave petroglyphs marking solstices are 50 feet from the shadow casting rock facet. I know a few light windows in Arches National Park and environs that are comparable to any telescope. The distance from the light window to the illumination point defines the accuracy. Some of these are 100 km lines. Move over a meter and you see a different galaxy thru the rock fissure. For simple seasonal marking, 50 feet is quite explicit. How tall a gnomon did the Chinese use to refine the length of the year?

... I really like the 800-foot-deep canyons with sheer walls. Then zenith shadows can be used, and dropping a rock on a still morning provides a good geodetic center line. Makes it all so easy.

2006.3.30 Subject: Archaeocosmology in the American Southwest
I think a focus on a region where astronomers (still?) go to set up observatories might be useful. Something to contrast and compare with the foggy bottoms of the lower atmosphere. And some of this discussion is multi-threaded already, so to avoid confusions of topics, this new thread....

This article, , is more than a good starting point; it has a relatively recent and very thorough bibliography. And more articles at that domain on our topic....

The Primary Architecture of the Chacoan Culture: A Cosmological
Expression by Anna Sofaer, appeared in "Anasazi Architecture and
American Design," edited Morrow and Price, U. of New Mexico Press, 1997.

 VR... wrote:
>>> JQJ: Meridional occurrence/concentration of a specific glyph led
>>> to first geodetic questions, subsequi the Chaco Meridian.

> .. 'meridional' .. is different than transit .. 'Meridional' is that it
> is related to the north-south axis or not?

Sorry about any confusion. I am in fact referring (off topic) to the occurrence of the same glyph on an approximate North-South line extending a great distance. I made the Chaco Meridian, the meridional concentration of "great houses" known, without mention of the rock art sites. Rock art is too vulnerable to vandals. Even rock books get "burned" in today's world! Unfortunately, it is vulnerable to researchers too. The slabs at Fajada Butte shifted due to erosion. Too many visits? So we archaeos must keep some of our knowledge to ourselves, waiting, waiting...

There are awesome "secret sites" in archaeology, complete with silent alarms, motion sensors, cameras, etc. The desert is also an open book; you can't lock the library at night. In the most remote locations, you might be on candid camera. And yet, more rock art sites continue to be defaced even today. When you have thousands in
just part of one state... Like Fajada Butte, many rock art sites also have lots of rattlers, what with rock crevices (and hopefully the snakes know who the vandals are ;-).

> Perhaps the sun dagger is a solar transit site:

And lunar major, and lunar minor. Read Sofaer's works on Fajada Butte, a great rock art cosmographic "hierophany." There are quite a few of these known rock art/astro hierophanies, not all published. They became incorporated in architecture also, with painted glyphs on walls employing window or door frames. But for "observatories" of
zenith transits, think about the 600-foot vertical, rock canyons, the knife-edge accuracy of bare rock, light windows created by narrow fissures, etc. And never a foggy day.

Ancient Metrology

2006.3.30  : Re: Archaeogeodesy Study
MB .. wrote: <<< Sorry to be slow; why the 'of course'? Do English feet relate in a significant way to arc seconds? >>>

Good question. Your not slow here; that was an allusion to assumptions made by some. This issue was discussed years ago in discussion groups. My memory of the "facts" goes like this: There is a "coincidence' of considerable accuracy. First, bear in mind that in some cultures (i.e., China), the earth was divided by days per year/orbit instead of 360 degrees. Now, given equatorial circumference = 131479775.378 feet (modern standard for feet) based on current ocean level.
131479775.378 / 360 degrees = 365,221.6
131479775.378 / days per year = 359,979.7 feet
131479775.378 / days per orbit = 359,965.7 feet
Again, this calculation uses the modern definition of the foot. Study of ancient metrology entered the debate, in particular, "The Origin of English Measures" now online at:

S .. wrote:
> In Thom's MLO, formula 2.1 (Variation of obliquity ?)... .. first constant in the formula
> is ? for 1900AD, but can anyone tell me what the 2nd, 3rd & 4th constants are?

The 1976 I.A.U. adopted formula is in Taff's Computational Spherical Astronomy and other texts and is relative to J2000.0 instead of 1900.
Obliquity = 23 degrees, 26', 21".488 minus 48".8150 T minus 0'.0059 T squared plus 0".001813 T cubed where T is measured in Julian centuries of 36,525 ephemeris days from J2000.0. See source for corresponding values of a, b, and c. Because obliquity is an oscillating inclination between to extrema, the "constant" is adjusted temporally by the other equation parts. This formula is adequate for current cultural span considerations. Robert Bednarik, publishing on H. erectus sailing in the Indonesian islands circa 800,000 years ago, would need more temporal accuracy, ;-).

2006.3.13 Subject: Ancient Metrology and Geodesy
I'm wondering if anyone in the group has researched ancient metrology, esp. beyond the works of Thom and Thom. I got a comment from a friend about using meters for the British Isles, instead of the foot and yard. Does it matter if we call one degree near Avebury 111,255 m or 365,011 ft? Does the meter obfuscate something important here? In anthropology there is a renewed tendency to accept traditional names for places, and other cultural features, just as there are linguistic efforts to preserve languages and the knowledge they transmit. Who has an opinion on any relevance between archaeometrology and archaeocosmology?

2006.3.15 Re: Ancient Metrology and Geodesy
T .. wrote:
> ... Despite many references to possible sophisticated mathematics being used in the Neolithic
> ?Bronze Ages it is usually in reference to astronomy or layout of stone circles ...

This reading may interest you: The Origin of English Measures

2006.3.15 Re: Ancient Metrology and Geodesy
T .. wrote:
> ... my eyes glazed over at the huge > amount of figures and cross referencing .... it
> appeared to my non-mathematical eye that there > was a wee bit of massaging the figures. ...

One of the problems with ancient metrology is exactness when the dimensions are so small. The layman's ruler may be derived in many steps from the standard set in stone elsewhere. We are left with a tiny sampling. It is a difficult task to make sense of it. But, we also, on a non-quantitative level, realize that these system diffused, and were important in markets, land measure. And establishing measure standards is a very fundamental task in starting any science, even if it does not extend to measure of the earth or cosmos.

> I am not a Thomist (Alexander that is) and have no faith in the megalithic yard or inch so
> I was a bit unsure of the Egyptian/Babylonian measures he posits, are they accepted
> by mainstream archaeology ?.

Without getting into "Is there a mainstream in archaeology, and if so where?" ancient measure is a known area of (largely ignored) research. Evidence exists in the rulers and in texts, plus architecture. And architectural analysis reveals modularity. Some of that work proposing previously unevidenced units is typically ignored by academics. A complication with metrology that has a parallel in ancient
cosmography is the local variation in meridian measure. If units of measure are based on the local scale of a geodetic fractional division, i.e.. different latitudes produce different lengths for an arc second, hence units with the same name will have varying values in different centers when so determined. This is due to the oblate flattening of the earth, the centrifugal bulge of the equator. In Western science, only recently Newton realized this.

2006.3.16 Re: Ancient Metrology and Geodesy
U .. wrote:
> Was that how Ptolemy figured out the distance between Alexandria and Syene?
> And Eratosthenes figured the circumference of the world with latitudes?

Is there a pun in there somewhere? I refer to the flattening and elliptical shape of the earth as Newton's understanding. I do not know of a reference in any other Western literature of that knowledge. I discuss history of geodesy in this page: While I do not accept everything Livio C. Stecchini wrote back when, it is interesting reading: Egyptian Estimates of the Size and Shape of the Earth
I have to concur with other writers about Eratosthenes using more ancient sources. He was just the librarian in most advanced analyses and discussions. Likewise for Àryabhata, at a young age coming up with a precise ratio for lunar orbits and earth rotations. His writing was likely a compilation by a young student, the one paper that survived, thus passing to us more ancient knowledge.

2006.3.14 Re: Ancient Metrology and Geodesy
VR .. wrote:
> For me a numbers has no significance in themselves ... I think though that in some cases
> people see significance in the sequence of symbols, which I don't see always. ...

There is a bit of this, in relation to ancient monuments and under the rubric of 'sacred' geometry, on the Internet. One has to wonder where the beliefs stem from. Some discuss the pyramid related to the size and shape of the earth, with myriad explanations and no coherent theory. Some extrapolate from cubits of theoretical size to Egyptian knowledge of earth's scale and flattening ratio.

> ... I can understand that Neolithic people would like 3:4:5 ... For me, the word archaeocosmology
> would encompass all things people would see as part of their environment/cosmos. So I would
> see archaeometrology as part of archaeocosmology. But that is just my definition..

And measure is taking scale of the environment. There are some interesting relationships of numbers in the old system when considering the scale of the earth. That is why I posted the inquiry. I was doing a little fishing for viewpoints. The meter was created without good knowledge of the size of the earth. So we have 40,075,035.5351 meters of equatorial circumference at mean sea level marked somewhere, instead of 40,000,000. ...

2006.3.17 Re: Ancient Metrology and Geodesy
U .. wrote:
> .... Since only latitudes were known at the time of Eratosthenes, ...

I assume you read Eratosthenes' other writing, "Geographica", the three books on making a map of the known world, before drawing such a conclusion. You have this on good evidence, right. Or did he have a different name for them? Also, we must remember that he was a librarian and a Greek. As such, he was in the position of translator and conduit to others speaking Greek. The knowledge he conveyed was from the library where he worked moreso than attributable to him. This has been amply discussed and shown with his measure of the earth tale.

> and he was a few 1000 miles short of the circumference ...

That has been debated for a long time, Since when does anyone think it was that far off? First, I'd like to see who agrees on the length of a stadia. Size of the earth was well known in that era, and conclusions such as this are probably ill-founded on misperceptions of the conversion rates.

> It is interesting no matter what phase of numbers you are studying. The Equator has a
> bulge and the Poles are flattened. Makes one wonder how to really do measurements of the
> world, or any part of it ...

More concretely, the geoid is a slightly irregular oblate ellipsoid. Three dimensional ellipsoidal trigonometry is the standard in the geodetic industry, and always has been. The formulas are uncomplicated, now more so than ever with programmability at everyone's fingertips. There are more than a few histories of how it is done. I like the one from India, of the first British survey, not the Vedas. Many of their triangles can still be seen, and the mounds they built are often there still.

... (Eratosthenes) was a librarian at the library in Alexandria, writing to Greeks in Greece, aiding them in their education. What other writers said of his exploits may be exaggeration of the Greek role by Greeks. The values Eratosthenes is said to have reported are the best evidence of their antiquity at the time he passed on the information. Regarding the stadia, defined geodetically, as we define minutes and seconds, different latitudes will have different sizes of stadia. The accuracy will be dependant on the measure of the local meridian. That is a very simple determination requiring only basic geometry of triangles. Most school children can do this, given a chance to travel north or south.

Using spherical determination, longitude can be directly surveyed as a local proportion of local altitude. Without the more advanced math, even this is possible if you create a sphere. Different authors provide different interpretations of the stadia for different times and cultures. I would look to research on the Parthenon for Greek metrics. But I'm not much interested in the Greeks. They destroyed centers of knowledge, then, in their apotheoses, failed to get it right. The Western Dark Ages with geocentrism followed. Ptolemy and the inheritors of his thinking should have paid closer attention to what was known before this time in other cultures. Too little of what Eratosthenes wrote them survived, seemingly, or was simply not understood by those horsemen.

Stecchini discusses Greek measure. Read his work with some skepticism, and enjoy all the history it presents. In addition to Livio C. Stecchini's "A History of Measures" at: there is a book entitled "Ancient Metrology." My old metrology notes are buried I don't know where just now, they are that ancient. I think the author is Berriman.

... Where the Greeks obtained their information is vague. Claims that the info is of Egyptian origin are rebuffed with critiques regarding temporal separation. So, instead, the argument is made that their knowledge derives from the centers Alexander destroyed, Persipolis, The library in Alexandria probably also built upon second generation sources of Egyptian knowledge from outside of Egypt. Unfortunately, in the West conquest and taking and making slaves usurped knowledge, creating empires razed centers of knowledge, and we are left with the reconstruction in the 21st century, more than 21 centuries later. I'd say we lost a little time in the bargain, not just knowledge of the history.

... Astronomy is a necessary tool of geodesy. That fundamental understanding should inform our reasoning on this topic and on ancient cosmography generally when considering concepts of the size and scale of the earth. Determination of the scale of the earth is such a simple exercise. And doing so accurately is readily attainable to any culture that attempts it. This "understanding" should also inform our reasoning. We also need to keep in mind the entire planet and diverse cultures. While the West was in the Dark Ages, other cultures were in the Light. Accurate astronomies are documented from long before your "mid-centuries (800 onwards)" in a variety of locations around the world.


2006.3.20 Subject: Doctor, Doctor, I've got a Pain in my Datum...
S.. wrote:
> ... when you're using an app which is explicit about its implementation of datums for things
> like distance calculations, are you necessarily sure that it's not using shortcuts? WGS84, for
> example, being ellipsoidal rather than spherical, has two ideas of the diameter of the planet.....
> semi-major axis a = 6378.137000 km, semi-minor axis b = 6356.7523141 km
> .... I finally decided to go with the Vincenty formula for my distance/azimuth calculations,
> because it implements both the a and the b > axes of the ellipsoid. ... Vincenty did yield
> slightly different results ...

Are you using this formula: I'm using spheroidal trig with some concern regarding avoiding loss of significant digits with near proximate points. Excel does pretty
well. I convert degrees to distance measures using the mean of the two latitudes with the formula for the degree of meridian defining arc lengths. This is precise if close, less so with more disparate latitudes.
I tested my app against the Middleton survey for Newark Octagon using my GPS. For Avebury-Silbury Hill I got 0.163m difference with my spherical, locally-converted method. At about 300m distance, I get more degradation. The advantage of off-spreadsheet calculation is the floating points of the machine are the limit, not the apps decimal limit.

2006.3.20 Subject: Coordinate Transformations
Trying to do an accurate Helmert Spheroid of Reference to WGS84 transform, I'm Web searching coordinate converters, and this reading grabs attention: National GPS Network Information: A guide to coordinate systems in Great Britain. ... good reading. Their formulas are +/- 5m ?? Any comment on accuracy of transforms anyone? Especially to GPS Lat, Lon, Height (WGS84) from UK OS grid references.

2006.3.10 Re: Equinoctial Calculations
S .. wrote:
> ... the Neolithic calculation of the equinoxes ... I think it's an important question ...
> ... how did these dudes calculate the precise positions of the equinoxes?

... A good question worth the ponder. The number of days between solstices does not define it, since solar orbit speed varies with the elliptical orbit distance. So, what does define it? Angle of inclination coinciding with a plane perpendicular to the plane of orbit, right? Sidereal locations of the earth, 90 degrees in relation
to solstice sidereal locations.

2006.3.20 Subject: Equinoctial Calculations
S .. wrote:
>> JQ: .....The number of days between solstices does not define it, since solar orbit speed
>> varies with the elliptical orbit distance. So, what does define it? Angle of inclination coinciding
>> with a plane perpendicular to the plane of orbit, right? Sidereal locations of the earth, 90 degrees
>> in relation to solstice sidereal locations.

> Measuring time is simpler, but that would mean they used non-daylight (i.e.. solar) clocks of
> some kind...

You've definitely got it there. They used the night, when the clock (stars and moon) is visible. When the angle of inclination coincides (as above) the sun is crossing the ecliptic, a known stellar line. :-) I know I was being vague (pedagogical inclination). What they and we know: If we take the time to determine the ecliptic in the celestial vault, then, all that is needed is to translate this to the landscape with any alignment. Does this seem plausible? And, I finally found a use for an alignment!


2006.3.22 Subject: Myths, Star Maps, and the Earth?
This deserves it's own thread. Starting at Victor's page: and the various origin myths and characters in the 'Near Eastern' regions, the genesis stories of different cultures that diffused into so many versions. Many of these are obvious allusions to dividing up the heavens, naming constellations. And the characters/deities in pantheons: Jupiter, Mars, Venus, etc. Quite long ago now I wrote/asked:

" ....The Popol Vuh, the ancient history of origins of the Quiche Maya, relates that the ancestors of the Quiche came to their side of the earth "on stones, as if there were no sea." When they arrived they "measured the earth and the sky" and they pointed to the heavens to indicate from whence they had come (as though to a certain position on a map?). Does this Quiche ethnohistorical document indicate a navigation ability enabling their migrations, or an ancient history of migration? "

My difficult question is, "Was any of this transferred to the surface of the earth? Was there an 'equation' of positions, celestial and terrestrial?"

2006.3.22 Re: Myths, Star Maps, and the Earth?
D .. wrote:
>> JQ: My difficult question is, "Was any of this transferred to the surface of the earth?
>> Was there an 'equation' of positions, celestial and terrestrial?"

> I don't think this is the least difficult .... EVERY society of any sophistication always erects
> a coordinate framework for both celestial and terrestrial reference. ... facets of the same
> thing, and both are necessary for the surveyors...

Very good point, and not very well recognized in literature. The Chaco meridian is not readily accepted. Perhaps that's more a problem of accepting that the society was "sophisticated."

> .. The prime meridian at Greenwich is certainly not > the first, but only the most
> recent example of a longitudinal reference meridian. ....

The other one I noted in North America is the Maya meridian, centered on Tikal, with Dzibilchaltun observatory on the north end. However, Mayanists have never addressed this issue. They do not think in terms of the necessary date line, and operate on the assumption that the date glyphs are all on the same side of a never discussed date line.

> It would be more appropriate to ask if there has ever
> been an advanced society which did not do this.

I have to agreed with that. You're making me rephrase the question in more explicit terms. I wonder if the positions of the stars were monumentalized on the earth, if the star map per se was ever "made real" rather than a mathematical grid system. Not every culture will come up with the same solution to inter-referencing the celestial and terrestrial reference frames. Some might just do triangulation in both frameworks. Flatlanders will prefer meridians and lines, mountain dwellers might prefer measuring dip in triangulation nets.

Sun, Moon and Tides

2006.3.29  Subject: Re: Sun, Moon and Tides
W .. wrote:
> > JQJ: for practical matters like crossing a waterway affected by tidal rips, one's life can
> > depend on predictions based on astronomic observations or lunar ephemeredes.

> Quite. It would seem that a lot of sites in the UK have alignments towards moon rises
> and sets at the standstills - events which happen over such a long cycle, that it's hard
> to see what practical survival value there would be in coinciding certain human activities
> with them. To me, the moon stuff seems to be a form of pure research.

Al contrario, the moon determines the tides, and the intensity of tidal fluctuation is a function of lunar position in 3-D, not just orbit/rotation direction. If the moon is near lunar major in its cycle, and at southern extrema, tidal motions between islands in the Irish Sea or in the English Channel are quite different than at
northern extrema. The lunar major rise/set lines are references for observed positions at any time, ergo they are references for the extrema in tidal fluctuations too.

> ... there is a great deal of similarity in the styles of the various ancient sites
> in the UK, and that similarity stretches the length of the country.

No doubt, and further afield too, from Knocknaria to St. Michel, Brittany, from the Ring of Brodgar to Le Gran Menhir, and across a great expanse of time. The difficult big question is, "What underlying unity is found?" determining/expressed-in the monumental aspects of such an expansive cultural expression.

2006.3.31 Re: Sun, Moon and Tides, and the Long Count
W .. wrote:
>.... something ... concerning how the interaction of the relative positions of
> the sun and moon affect the tides. ... tides are nominally a function of the
> gravitational pulls of the moon and sun ... the main bulge .. following the moon..
> a secondary bulge following the sun. Were it otherwise, there would be no springs and neaps....

Excellent point here. And, impetus in cultures doing water crossings to do luni-solar calendars. This presents interesting research avenues for archaeocosmology variations. Sailing cultures require lunar calendars, etc... I have not studied this since working on the Mayan codices intervals, many moons ago, but I'll dig into my study notes.

> .... the sun and moon don't simply make their way > around the equator, ... paths ... at an angle to
> the equator. ... gravitational pulls .. not > perpendicular to the equator, but ... direction
> of each body .. disparate declinations will > 'spread' the gravitational pull ...

The tides are due to "centrifugal force" and "tractive force" (gravitational). Solar gravitation is less than half that of the moon. The tides have a primary cycle of half of each passage below the moon. The water rebounds when the earth has rotated a place/position to the side opposite the lunar orbit position. Picture a drawing of a sound wave, with the tidal 'wave' amplitude drawn, in the temporal direction, as "one day plus mean daily lunar motion per day," or in degrees [ (360 * days per rotation) + 13.17636 ]. This in AeGeo code terms ( is [(360 * DR) + C27]. (The days per rotation number, DR = 0.99727, is also the ratio of 'latitude difference : arc distance' between Avebury and Stonehenge I posted the other day.)

Hereafter, in terms of variations in tides, everything cyclical is variations in this primary amplitude wave, [(360 * DR) + C27]. Also, discussion/thinking needs to bifurcate for theory and localities. Tides vary by location on the earth. First, the big picture, theory or the cosmic-scale viewpoint, then the local, earthbound viewer. Tidal cycle variation is in harmony with the Lunar Synodic Period (S9), the time between consecutive alignments of the sun, earth and moon on a plane perpendicular to the plane of solar revolution. The intensity of lunar tide is amplified or diminished by solar gravitation, and this cycle is the same as the lunar synodic cycle = full moon/new moon = S9. The nodes of increased intensity in this cycle, spring tides, correspond to nodal alignment of sun, earth, moon; in other words new and full moon. The diminution half of the wave would be half moons, neap tides, when the sun and moon gravitation effects are at right angles. The wave modulation is not uniform, the amplitude peaks of the spring tide are greatest at new moon when the gravitation of both bodies combine.

Proxigean spring tide is another amplitude variation. The perigee:apogee ratio of lunar orbit is significant, about 7:8. When the moon is closest to the earth, the tidal effects are amplified. This cycle is based on the Anomalistic Month, the period of the moon's eccentricity of orbit, from perigee to perigee, is 27.5545465 days (S5). Because the moon's distance is least at perigee, parallax and proxigean spring tide are then greatest.

> Since this .. is all very cyclical, one naturally wonders if there is maybe a 'grand cycle' ....

Getting there. There are more factors to include. Basically, the overall tides are defined by the cycles above. Therefore, the multiplier of synodic and anomalistic months produces the overall greater pattern in intensities of tides. S9 * S5 = 813.7 days.

Now, to the cycles that impact local variations in tides. ... we are not discussing a 2-D problem. The moon's orbit is inclined at a temporally constant inclination of 1/70th of a circle (1/10th Avebury's latitude), or, more precisely, 5.1453964 degrees (IL). Therefore, during each orbit the moon crosses a node with the plane of earth's revolution around the sun, the nodal month. Using current values for astronomic constants, the Lunar Nodal Month is 27.21222 days (S2). This cycle is not synchronous with S9 (or S5), and the synchronization of nodal crossing with S9 is termed the Eclipse Year, 346.620031 days (YE) for obvious reasons, when all three align on/near the plane of earth's revolution, eclipses are possible.

The "grand cycle" product of these four motion cycles is called the Saros Cycle, the eclipse cycle of 242 nodal months, 223 synodic periods, 239 anomalistic months and 19 eclipse years.

242 * 27.21222 = 6585.36 days
223 * 29.53059 = 6585.32
239 * 27.55455 = 6585.54
19 * 346.62006 = 6585.78

Moving on to larger, grander cycles. The other local factor is due to another non-conformity with the plane of earth's revolution, that of inclination of the axis of rotation, termed obliquity of the ecliptic, currently 23.438 degrees (OB). This is inertial direction, the direction of force countering earth's gravitational pull on the water. This 'orientation' in the solar system determines the path of the rotating locations on the earth with respect to the gravitation directions of the sun and moon. The cycle of this motion, from the locality perspective, is the Tropical Year of 365.2422 days (DY). The axis of rotation is not inclined in a fixed direction due to gravitational forces acting on the equatorial bulge. The forces rotate the axis orientation in fixed space in a retrograde direction. Therefore DY is less than days per orbit, 365.25636 (DO). The cycle of the retrograde rotation is called precession and the current rate is 25,793 years (PR). The formula for DY is defined by these motions in fixed celestial space, and therefore formulated in reference to Rotations per Orbit (RO = 366.25636) and precession as: DY = [(RO - 1) x (1 - 1/PR)].

The two inclinations, lunar orbit and earth rotation axis are not synchronous and therefore their coincidence produces a longer cycle, the "Lunar Major" cycle, one producing another variation cycle in the amplitude of the tidal wave. Their nodal coincidence is defined by the Eclipse Year (YE) and the Tropical Year (YT), where:

YT / YE = 1.0537
1 / 0.0537 = 18.613 years
18.613 YT = 6798.35 days
19.613 YE = 6798.35 days

The intercalation of the Lunar Major cycle and the Saros cycle is 19 YE * 19.613264554 YE ....

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