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
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)
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
> ...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
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
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
holds, teaches, and preaches ... I held and believed that the
the center of the universe and is immovable, and that the each
the center and is movable; willing, therefore, to remove from
minds of your Eminences, and of every Catholic Christian, this
vehement suspicion [of heresy] rightfully entertained against
I abjure, curse and detest the said errors and heresies, ...and
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
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
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
>> "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
2006.4.5 Re: Heliocentrism, a Round Earth, and Paradigms
G.. wrote: ... The realization that some of the greatest monuments
> 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
Were the Paleoamericans capable navigators (on land or along
shorelines)? If so, that goes a long way to explaining how they
2006.4.6 Re: Heliocentrism, a Round Earth, and Paradigms "
S... wrote: ... assuming religious comparisons with remote cultures
> 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
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
> 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
> 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,
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
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
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
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
> 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
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
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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