2006.4.2  Re: Local Radius on the Ellipsoid, Flatlanders and Andeans
>... how to calculate the radius of the local sphere on the ellipsoid ...
> short-cut for European latitudes ... take an average (polar/equator) value ...
> ... this returns a quite incorrect value ...

An interesting aspect of the region where the Neolithic megaliths are centered is the fact that the local meridian curvature is the same as the equatorial circumference. Here is the approximation formula I have been using to approximate the size of 1 degree of latitude or longitude centered on a given geodetic latitude (Ø):

1° lat = (111.13297955 - 0.5598 cos 2 Ø + 0.0012 cos 4 Ø) km
1° lon = (111.4128908 cos Ø - 0.0925 cos 3 Ø + 0.0001 cos 5 Ø) km

By this formulation, the latitude where local meridian measure equals equatorial circumference is about Thornborough and Long Meg. You will find the formula for the Geometry of a Meridian Section of the reference ellipsoid, with local radius (p) in geocentric distance solved by formulation equating equatorial radius to one on my Geodesy Page. It is a bit too much to paste here.

> .. the geometrically-correct spherical altitude (angle of
> elevation) for a horizon-point ... typically returns an altitude
> around 0.1 *degrees* lower than assuming a Flat Earth ...

This is the "angle of dip," and it is "the other method" of measuring the scale of the earth. Flatlanders can easily measure a degree of meridian. In the Andes, it would be easier to determine the size of the earth by measuring dip in a triangulation net of mountain peaks. Funny thing, there are all those mountain peak monuments in Peru!!

2006.4.2  Re: Local Radius on the Ellipsoid, Flatlanders and Andeans
>>> Are you including diurnal aberration ... ;-)

> ... - JPL account for it ...assume that you're talking about the effect
> ... at the equator, where the Earth spins at its fastest? This might
> even be too much detail for nutters like myself to worry about! ;-)

Si señor, the result of observing from a spinning observing position on the surface of the earth. Velocity of the observer causes apparent shift to a maximum correction of about 0.0008333° at the equator. Effect is at any reasonable latitude (not at poles) and proportional to speed. Think in terms of the angle of observation, for E-W horizon
and for meridian transits, and their relation to spinning direction.

I like the concept of very long-term temporal observations, like the ancient Americans did, and determinations from long counts, such as the Lunar and Venus tables in the Dresden Codex. Variation is such a big factor with the moon, so this seems requisite. Once again, back to the only clock we got -- lofty moon as foresight, stars as reference, all there and all referenced, but only after you make your star map. The one-arm clock, in 3-D, telling all kinds of time: sidereal, nodal, synodic, anomalistic, nutation cycle (lunar standstill), tides, eclipses, light/dark nights....

2006.4.3 Subject: Stonehenge, heliocentrism and paradigms
> ...at Stonehenge, R ... said that it's builders knew
> that the earth was round and that it revolved around
> the sun (I would have to ask him what the evidence is ...

I don't know what this writer's thinking is, but the comment does raise the issue of what the builders of the megaliths knew regarding ancient cosmology. So I am presenting this issue here too. In part, my anthropology research and writing has focused on modern cultural paradigms. Some I question and contest.

The "ignorance" paradigms and assumptions in anthropology/archaeology and in popular cultural beliefs need examination, if not expurgation. Is the paradigm/assumption of "false knowledge" itself false? Why do we assume that actuality is not known and understood in other cultures?

Simplicio, because our cultural history (I'm writing in English here, not Quechua) is one of false knowledge. False knowledge was enforced by authoritarianism in the face of obvious and readily discernible actuality. Authoritarianism was a necessary mechanism to impose cultural institutions like slavery. Slavery imposes ignorance.

In Western Europe, the Inquisition, the ecclesiastical court investigated heresy (science and thinking). In 1600, Giordano Bruno believed that the earth moved about the Sun. After years of imprisonment and questioning, he refused to recant his naturalist views and was burnt to death as an unrepentant heretic.

Galileo wrote his "Dialogue on the Two Chief World Systems" and the pope ordered the book banned. On June 22, 1633, Galileo was forced to sign a confession:

"I, Galileo Galilei, ... before you Most Eaminent and Most Reverend
Lords Cardinals, General Inquisitors of the universal Christian
republic against depravity ... swear ... I will in future believe
every article which the Holy Catholic and Apostolic Church of Rome
holds, teaches, and preaches ... I held and believed that the sun is
the center of the universe and is immovable, and that the each is not
the center and is movable; willing, therefore, to remove from the
minds of your Eminences, and of every Catholic Christian, this
vehement suspicion [of heresy] rightfully entertained against me, ...
I abjure, curse and detest the said errors and heresies, ...and I
swear that I will never more in future say or assert anything
verbally, or in writing, which may give rise to a similar suspicion..."

The church lifted the ban on Galileo's Dialogue in 1822, and finally, in 1992, formally cleared Galileo of any wrongdoing. Nonetheless, dogmatic attacks on science continue in the Western cultural tradition, notably creationism.

In the Americas, until the national liberation movements, imposition of church dogma forcibly replaced naturalistic views. Dunce-capped heretics who refused to renounce their belief systems were burned in public display. Astronomy books were burned, symbols destroyed (driving out snakes?), ancient architecture leveled, church attendance enforced, etc.

Ignorance should not be assumed to be a natural state, and it should not be an assumption/paradigm about past cultures. The question about past culture might be better phrased, "Is there any evidence of false knowledge?" Anyone looking at the world can perceive actuality. Why assume otherwise? Why place the burden of proof on the "other" culture? The pre-St. Patrick world view may have been, and probably
was, cosmologically correct.

That said, I must ask, "Where is the evidence they did not recognize the obvious actuality, a round earth revolving around the sun?"

2006.4.4 Re: Stonehenge, heliocentrism and paradigms
m... wrote: ... Even with the benefit of detailed observations
> and mathematical models, there is very little to choose
> between the heliocentric and earth-centred models....

Keeping a luni-solar calendar reveals the facts. Observing the moon and sun moving in sidereal terms quickly reveals the ratio of days and rotations per orbit and the concurrent lunar synodic and sidereal ratio. There is only one way that the numbers fit. Without an intervening dogma/belief system, it is simple logic and math.

>> "Anyone looking at the world can perceive actuality."

> .. you mean earth sphericism and heliocentrism? ...
> If so; first, yes .. the second absolutely not.
> I don't think 'burden of proof' should enter the enquiry. We must assume
> nothing, although the kinds of ideas I've noted above indicate the pre-modern
> view to be logically favorable - for what that is worth.

You say "assume nothing" and then use your own assumption, "there is very little to choose between the heliocentric and earth-centered models" to support a viewpoint. The problem with paradigms and assumptions is that often we do not recognize our own.

Consider for a moment keeping a lunar and solar calendar. Try this yourself perhaps. After just one year, what do these numbers tell you: a count of lunar and (apparent) solar motion against the stellar backdrop, of full moon cycles, of days, and of meridian transit of a bright star? How do they fit? Only one unity can be obtained, the reality. Simple math and logic. Truly, there is "very little to choose between," IF you make observations first!

2006.4.5 Re: Heliocentrism, a Round Earth, and Paradigms
G.. wrote: ... The realization that some of the greatest monuments in North
> America e.g. the Louisiana mounds, were built by hunter gatherers has
> provided an impetus for questioning that view...

The assumption that the hunter/gathers living there were exclusively the builders also needs questioning! How many times was monument/mound building independently invented anyway?? If there is an underlying systematic, entirely different questions are posed regarding cultural connections, diffusion of traditions, and the role of distant cultural centers. The very early mound building tradition along the central Andean coast may be reflected in site layout at San Lorenzo, for example. Answers are elusive with such deep strata and distant expressions of an apparent 'mound building tradition' (?).

Were the Paleoamericans capable navigators (on land or along shorelines)? If so, that goes a long way to explaining how they found it!!

2006.4.6 Re: Heliocentrism, a Round Earth, and Paradigms "
S... wrote: ... assuming religious comparisons with remote cultures is never
> guaranteed to produce a correct analysis. ... what chance have we in
> trying to figure out Neolithic religion from the incredibly scant evidence ...

One thing sorely lacking in anthropology is a neutral taxonomy about world views. The term religion, as used in the English language, is theocentric, with connotations of belief in supernaturalism and metaphysical dogmas. To avoid

> ...making huge leaps of thought and massive analogical
> assumptions...

it seems necessary to distinguish religion from world view or cosmological ordering of the universe. (Thanks for the great line I borrow here :-). Supernatural belief is a human invention, and not a natural state. The origin of religion is obscure and obfuscated by time-inverted analogies. Cultures with names for planets are viewed
as deifying the cosmos. Perhaps they were more scientific than the theocentric/supernaturalistic world view imagines.

At any rate, just "trying to figure out Neolithic religion" has an underlying assumption, it assumes they had religion(s). Before an autocratic culture phase, this may be unlikely. Slavery may be more important in the origin of religion (as we know it in Western traditions) than any other factor. It is difficult to find another explanatory and causal factor, within a Darwinian framework, for the imposition of such an unnatural belief system.

For a neutral term, I look to cosmography, world-view, understanding of nature, etc. Without some societal imperative to adhere to a specific belief system, slavery being one such imperative, there is also the issue of first demonstrating that some systematic of belief even existed. In the hunter/gatherer ambient where I lived, the
equivalent of "religion" was more a mythical/metaphorical story realm than a belief system, adherence was not of any real importance, and individual thinking was not a societal prescription. It seemed everyone had their own world view, each evolving in complexity with experience.

Perhaps our post-autocratic, post-Dark Age view of the past still has too much 'fear of being burned alive at the stake' framing of ideas for us to grasp archaeocosmography fitfully. It is going to take a long time for our anthropological perspectives to overcome the theocratic aspects of our history. Not to mention the linguistic realm. Some day though, the "Sun" will not "come up" or "rise again" and yet there will be light.

2006.4.8 Thornborough and Possible Alignments
George wrote: Did past discussion cover Sirius?

Here is the link to what was released by Harding, followed by the pertinent quote:

"One of the earliest monuments, a giant elongated enclosure or cursus, about half of which has been destroyed by quarrying, was most likely built between 3500 BC and 3000 BC. This appears to have been deliberately orientated towards the midsummer solstice sunrise, to the east, and towards the setting of the three stars which make up the well known constellation of Orion's Belt, to the west. This early monument was replaced after 3000 BC by three giant circular earthwork enclosures or henges, each around 240 metres in diameter. All three henges are interrupted by a pair of entrances, all on a shared axis and aligned on the midwinter solstice sunrise. The entrances also frame the rising of Sirius, the sky's brightest star, and again, the associated constellation of Orion's Belt."

As you can see, the author(s) state: "appears to have been deliberately orientated" and "(t)he entrances also frame." This, rather than directly asserting deliberate alignments. In popular lore this has already been transformed into a certainty.

The cursus has four alignments, since it has two segments each with a distinct orientation, each pointing in two directions. Each of the four alignments thus points to an entire circle of stars.

> I know you have your own theories, I hope you were unbiased.

I hope so too, albeit I do not know to what you refer. I do focus my research and anthropology writing on bias, assumptions, and paradigms, and I critique them.

Is this a bias, "As Jan Harding explains, 'Thornborough was a sacred landscape, a place of religious worship, and we should try to interpret these astronomical orientations within that context....' or a fact?" Once again, in popular lore, the distinction between fact and interpretation of fact gets blurred or lost entirely.

> This research has been confirmed by Newcastle University
> and I hear it will also beconfirmed by a senior astronomical body.

I am unfamiliar with the process of research confirmation by institutions. I doubt that such happens, or is necessary. The facts are simple enough. The interpretation is whatever someone wants to believe. I really doubt that a "senior astronomical body" is going to confirm Thornborough as "a place of religious worship." This illustrates the facts/interpretations distinction, right?

First, a qualifier. The stars in the belt of Orion have proper motion, so they are not in the same relationships to each other as they were 5,000 years ago. The cosmos is three dimensional and in motion. These stars move in different directions, and are at vastly different distances from our observation point. To the best of my knowledge, no author proposing relationships between those stars and ancient sites has addressed the proper motion issue.

From Mintaka to Alnitak is now 1.6435 degrees, or 1/219th of circumference. That's a big target. They now form a north-south line, but have shifted due to precession, so target size changes with time. Their spacing is now 0.815 : 1.0. They form a 179.82 degree angle.

From the north henge to the south henge is about 0.0135 degrees, the spacing is 1.0 : 1.02, the angle formed is about 175.5 degrees, and the orientation is about 1/10th of circumference from N-S.

These are the approximate facts. Additionally, the henges are about 240 meters in diameter. They have two entrances. How wide are these? What portion of the sky do they frame from what position? All told, do they frame 20% of all stars, more, less? It depends on where you are standing!

For every line, there is a celestial alignment. The pencil on my desk has a significant clestial alignment. Did I align it with intention, or not?

Harding writes in the press release, "This study provides detailed insights into Neolithic religion ... religion was complex long before the arrival of beliefs like Christianity and Islam." There is the bias. This author assumes there was religion in that place 5,000 years ago.

Do beliefs "arrive" or arise? Are beliefs necessarily religion? Can other kinds of "beliefs" exist? Religion is belief in a supernatural reality. Did the builders believe in reality instead of supernatural reality?

I think the evidence allows for some conclusions. For one, the constructions involved geometry and surveying at Thornborough 5,000 years ago. To discover how this translates into intentional stellar alignments and a complex religion, you will have to look into the biases and minds of others.

2006.4.2 Re: Question about circular buildings
>...Why are so many ancient structures ... circular...?
> My bias leads me to think they were originally inspired by the
> heavens. Circular sun and moon, full circle of the horizon ...

Without considering the domain of symbols, there are architectural/geometric reasons, less work to enclose the same area and structural strength. Advances in construction techniques allow buildings to assume shapes not inherently stable.

Avebury is located where latitude equals 1/7 of circumference (also Heel Stone azimuth). From a geodetic perspective, if intentional, a square just would not be the correct symbol for circumference.

2006.4.2 Re: Question about circular buildings
VR ... wrote:...  How circular is the sky? The horizon is indeed circular,
> the sky is not really circular in my opinion;-) I don't know if Neolithic
> people saw the path of moon, sun etc. as circles...

Some obvious circles are there, such as the circumpolar stars. Any culture mapping the stars quickly discovers the hemisphere of the celestial vault and its celestial rotation point. A linguistic approach might be useful to these question. What do different cultures call "the heavens." That's plural, right off wrong.

How about depictions? What symbols are associated with hemispheres. In Mayalands, the "Nine Lords of the Night" and the coatimundi, the trickster known in myth to climb to the "celestial vault?" In Mayalands, we also know there were advanced astronomers, so the symbols matching a realistic concept is no surprise. The linguistics should also reflect this, in the absence of depictions.

2006.4.1  Re: Shocking old Irish Times article. Another one destroyed.
> ... It really is like the Taliban, in Gucci suits, are running the show here ...

More like Taliban with industrial disease. Not much better across the pond. In the USA, if it is on private property, the owner decides. Take this case I happened upon last Fall:

The West Virginia Division of Culture and History currently maintains Grave Creek Mound, called "the largest conical" type mound in the USA, at 62-foot high, 240-foot diameter mound, originally of a height of nearly 70 feet, containing approximately 57,000 tons of dirt--about 3 million basket loads of heavy dirt! (The once 4-5' deep, 910 foot-in-diameter, and 40' wide moat is no longer apparent.)

In the museum, I discovered that prehistoric stone towers surrounded the mound on the bluffs. Hilltop mounds are part of the Newark Earthworks, so I wanted to see these, now basically giant stone cairns. I went to Indian Knob to see one, and to GPS the location. Unfortunately, a developer 'very' recently used the stones to build a
road into his new subdivision. Only a slight amount of one edge now remains. What apparently was a huge stone mound is now a narrow crescent of rock only four feet high. The bulldozer tracks remain visible.... When will the destruction STOP??

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