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
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from druidcircle who have withdrawn from the group.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.
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?" http://jqjacobs.net/anthro/ancestors.html
> ... 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. ...
THE ORIGIN OF THE INTERNATIONAL DAY FOR MONUMENTS AND SITES
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. ...
PROCEEDINGS OF THE INTERNATIONAL SCIENTIFIC SYMPOSIUM,
"Place, memory, meaning: preserving intangible values in monuments and sites"
Beautiful slideshow on home page at: http://www.globalheritagefund.org/save/index.html
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
|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
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 nearby.org.uk,
I noticed an interesting link and followed it to: http://www.deformedweb.co.uk/trigs/levelling.html
That page links to an interactive leveling page. You input your
"...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
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
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
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
... 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
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
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
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
> 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
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
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
> 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,
> 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
> 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
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: http://jqjacobs.net/blog/newark.html
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
Given current coordinate data, preliminary results
(I still want GPS readings):
Khufu Pyramid (Helmert Spheriod) to Newgrange (map-scaled)
36.0030 degrees = 0.10008 circumference = CIR/9.999916 (not
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 [www.aeraweb.org]
Egyptian Antiquities Information System, official Geographic
Information System (GIS), Supreme Council of Antiquities
Petrie's The Pyramids and Temples of Gizeh online ... Coordinates:... Relative
positions of Pyramids: [www.ronaldbirdsall.com]
Prehistoric and Predynastic Egypt [www.egypt.ukideas.com]
Great Circle Calculator By Ed Williams [williams.best.vwh.net]
Calculate distance and bearing between two Latitude/Longitude
Guide to coordinate systems in Great Britain ... What is
a geodetic transformation? [www.gps.gov.uk]
GPS Coordinate transformations [lists.tartarus.org]
Ancient Measurements of the Circumference of the Earth by Livio
C. Stecchini [www.metrum.org]
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:
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
... 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
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." [jqjacobs.net]
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
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
For a geodesic arc length formula on the ellipsoid,
There is a Vincenty formula calculator for distance
between two Latitude/Longitude points at: http://www.movable-type.co.uk/scripts/LatLongVincenty.html
Given latitude and longitude of two points, calculate
the ellipsoidal distance and forward and reverse azimuths between
the points at this site: http://www.ga.gov.au/geodesy/datums/vincenty_inverse.jsp
For a links page pointing to Online Calculations & Downloadable
spreadsheets - to perform Geodetic Calculations: http://www.ga.gov.au/geodesy/datums/calcs.jsp
2006.3.19 2:15 pm Subject: Avebury, Silbury Hill, and Windmill
Yesterday morning I acquired new, improved coordinates for Avebury,
Silbury Hill, and Windmill Hill, thanks to the great Magic interactive
map capability at: http://www.magic.gov.uk/
and the awesome coordinate converter at: http://www.nearby.org.uk/
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. http://www.britacrh.ac.uk/ba/ba67/feat3.shtml
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: http://www.magic.gov.uk/ and
the awesome coordinate converter at: http://www.nearby.org.uk/ ....
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
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
> 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
> 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
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
> ... 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
> ... Cultures ... respond in similar ways entirely independently. That said,
> 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
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 http://www.magic.gov.uk at 1:5,000 scale
and confirmed accuracy from archaeological publications.
Horizons, Refraction, Meridian Transit
2006.3.28 Subject: Re: refraction and its
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
> 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
> ... 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
> ... 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
> 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,
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
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
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
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
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
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
> 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
> ... 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
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
2006.3.29 Re: Annual Secular Polar Motion
S .. wrote:
> > JQJ: another site location variable. The "Annual Secular Polar Motion" is
> > 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,
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
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
<< celestial pole at the time of Khufu. This cycle actually varies between
<< 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
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 jqjacobs.net, "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
<<< ... 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
2006.3.29 1:52 pm Subject: Re: Tilts and Wobbles
S .. wrote: <<< ... you might be interested in ... [earth.leeds.ac.uk/...
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,
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
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
> 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
> 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
Intagliare sapiens en lapisaxum es loquitur infinite. Then they
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
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, http://www.solsticeproject.org/primarch.htm ,
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
American Design," edited Morrow and Price, U. of New Mexico
>>> 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,
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.
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: http://www.metrum.org/measures/english.htm
S .. wrote:
> In Thom's MLO, formula 2.1 (Variation of obliquity ?)... .. first constant in
> is ? for 1900AD, but can anyone tell me what the 2nd, 3rd & 4th constants
The 1976 I.A.U. adopted formula is in Taff's Computational Spherical
Astronomy and other texts and is relative to J2000.0 instead
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
> 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
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: http://jqjacobs.net/astro/aegeo.html 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 http://www.metrum.org/key/pyramids/estimates.htm
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
2006.3.14 Re: Ancient Metrology and Geodesy
VR .. wrote:
> For me a numbers has no significance in themselves ... I think though that in
> 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
> 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: http://www.metrum.org/measures/index.htm
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, et.al. 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...
> ... when you're using an app which is explicit about its implementation of datums
> like distance calculations, are you necessarily sure that it's not using shortcuts?
> 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
> because it implements both the a and the b > axes of the ellipsoid. ... Vincenty
> slightly different results ...
Are you using this formula: http://williams.best.vwh.net/ellipsoid/node5.html.
I'm using spheroidal trig with some concern regarding avoiding
loss of significant digits with near proximate points. Excel
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. http://www.gps.gov.uk/guidecontents.asp
... 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
> ... 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: http://www.iol.ie/~geniet/eng/homer.htm
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
> to see what practical survival value there would be in coinciding certain human
> 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
> a secondary bulge following the sun. Were it otherwise, there would be no springs
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
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 (http://jqjacobs.net/astro/astro.html)
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
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
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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