View Full Version : Paleocartography? Longitued BCE?

11-17-2009, 09:30 PM

I am a late 50s systems software design engineer turned CEO (not a rich one). When I grow up I want to try to make my mark in paleocartography.

To that end I have been studying this subject, (BCE longitude determination, aka the Holy Grail) off and on for 30 years, but to date have not encountered anyone with an intersecting knowledge of paleoastronomy, cartography and history who finds the subject worthy of effort or consideration, after all, all that can be know is already known on the subject and it simply was not possible in a BCE timeframe (which I think has a high ostrich factor).

I believe I have (however naive) rediscovered a means of longitude determination consistent with the archeological record, historical records and academic writings on the subject of which I am aware. To be sure in the unlikely event I am correct; I do suspect I have inadvertently rediscovered someone else’s rediscovery. But onward I go until some kind and knowledgeable thinker of time, stars, lat and long, sets me straight, after which I have numerous other windmills to tilt with.

So my introductory question is “am in the right neck of the woods”? And if not, I would most appreciate a heading on which to continue my travels.

Kind Regards,


Steel General
11-18-2009, 08:57 AM
Welcome Aboard!

Can't help you with the 'paleo'-stuff (though it sounds interesting).

11-18-2009, 09:07 AM
Welcome to the guild!

I can't even think how one might go about determining paleolongitude (differences and applying differences to an absolute reference point is hugely fraught with errors). Paleolatitude is bad enough and also full of with errors. Latitude is a nice physical quantity that has measurable characteristics, but Longitude is an arbitrary convention with 0 being at some culturally-defined location.

Having said that, this is a good location to discuss such things. There's always interest and some of the folks hereabouts are pretty sharp on those kinds of subjects.

11-18-2009, 12:35 PM
I'm not sure that I can really see the problem here.

Are you talking about "Defining longitude using the reference system of ancient civilisations"?
If so then this is just a maths problem. Involved to be sure but straight forward, just read a book on trigonometry and pick your chosen points of origin.

If you are talking about "Where did this piece of continental crust come from?" then that is a different kettle of fish entirely and is more about working backwards form the current physical density maps of today's tectonic plates, figuring out the current stresses and strains, running those as reverse accelerations and accounting for the fact that those stresses and strains will result in density changes to the plates which themselves will results in new forces. To ensure accuracy the historical densities of rock can be used, "How long ago was it since the density of this piece of crust changed, as determined by the current magnetic resonance and chemical composition."
This is sort of like weather modelling but in reverse. If your data are inaccurate by any amount then you will obtain very different results. However unlike modelling future weather you can 'calibrate' the model by looking at known historical data. Again though, if the historical data are inaccurate so will your model be.
Be aware that people spend millions trying to predict the weather and are generally only usefully accurate to 1-5 days. Rock moves slower but like any fluidic system it is chaotic so don't expect useful results beyond 30-50 'movement iterations'.
As far as I know a movement iteration for weather (air) is an hour. For plate tectonics (rock) it may be 100-300 years, depends on how fine grained your model is. Again though if your model is not detailed enough it will be too inaccurate to be of use.

11-19-2009, 07:41 AM
Welcome to the guild. Love the whole archeology stuff (it was my Major in University after all ;))

Looking forward to an findings you may have!

11-19-2009, 08:32 AM
Hi and welcome Greenman.

Primarily, this forum is populated by people who like to draw maps - largely, but not exclusively, maps of fictional realms.
However, cartographical interests do intersect.

Longitude determination by ancient civilizations was an interest of mine, back in the days when I had time for interests, though I'm no expert.
I am aware, however, that contrary to Mathus' thoughts, it is not entirely a matter of geometry, certainly not when you have several landmasses separated by sea.

Like Relativity, Longitude requires a definition of simultaneity before you can begin your calculations, and there you open a writhing can of worms.

I, too, independently figured out a solution, only to find later that it was a known technique, and I pretty much lost interest from thereon.

Certainly, it was possible. The only question is about the degree of accuracy obtainable, and whether anyone actually did it. The Romans could have built steam engines, but they didn't...

Edit: If you haven't already, I would recommend you read 'Longitude' by Dava Sobel. Essentially, it's Harrison's story, but it includes a description of the problem and a number of previous solutions. You might find your solution is there, though I hope with you that it isn't. ;)

11-19-2009, 10:40 PM
I’ll bet a bottle of port that you were like me and thousands of others were entranced decades ago by the possibility of BCE longitude determination as brought forward by Hapgood's Maps of the Ancient Sea Kings. Years later, but still years ago, studying human migration theories and mitochondrial DNA distribution in the Americas led me (however circuitously) to question the possibility that the knowledge of precession (and the corresponding observations of precision) may have had not only a common knowledge/technology root, but perhaps more importantly have been a common cultural/economically driven pinnacle of achieved by Mediterranean (Greek/Egyptian/Babylonian), South American (Mayan) and Chinese cultures BCE, and if not BCE then certainly before the European Renaissance.

It was with this premise in mind that I came to hypothesize a means of longitude determination compatible with my understanding of BCE technology. Having been before the days of the web and knowing no one who could see why anyone would care, I left it on the shelf until reading Menzies 1421 and Marchants's Decoding the Heavens, interspersed with works of Joseph Needham (Heavenly Clockwork, Science and Civilization in China), Martin Isler (Sticks, Stones, & shadows), Nick Kanas (Star Maps), Kelly & Milone (Exploring Ancient Skies), and many others.

I propose for your critique that ancient cartographer/astronomers could have established approximate longitude +-10 degrees (yes that is not real impressive, and perhaps that is the same magnitude of limitation you point out in your post, but I am talking BCE) along with the much easier to determine latitude and charted the Earth before the Common Era with no more than a level, plum bob, clepsydra, gnomon, a solar-noon determined N/S line, and a star chart compiled at a "prime meridian" observatory. More important and what differentiates my hypothesis from others is what is not needed: observations or positions of any planet or moon, knowledge of planetary motion, telescope, units of time smaller than half a day, or math beyond simple addition and subtraction.

First some context:

Solar-noon is well documented in many ancient cultures as the means of establishing highly accurate (even in modern terms) north-south orientation, equinoxes, and solstices. Then just as today, noon was considered midpoint in a "day". For thousands of years before the Greenwich Prime Meridian was established (~1675) and subsequently Greenwich Mean Time along with time zones (1850s), communities calibrated their clocks to solar-noon. With the advent of time zones, wristwatches and GPS, solar-time has gone the way of the crystal radio. Like the crystal radio, solar-time lay within the modern premise, but is likewise lost in abstraction. The human abstraction of time being essential to my hypothesis it is important to note that GMT was created to mitigate the fact that for every step you take east or west you will have (however small) a different measurement for solar-noon. We observe solar-noon (and for that matter any moment of daily time) sweeping west from meridian to meridian at a rate of 15 arc-minutes for every minute of time, which equals one degree for every four minutes of time. At the equator that is roughly 900 nautical miles per hour.

Solar-midnight, on the other hand, is not well documented in ancient writings other than for its mystery, indeterminate nature and as being the transition point between days, the opposite of noon, and the middle of the night. It is for these very reasons that I suspect ancient astronomers would have had interest in investigating midnight and the stars that lay where the sun had been at mid-day before. Further, our ancient astronomer's time keeping technology, the clepsydra, would have easily determined the moment of midnight with a precision of seconds.

Geometrically speaking solar-time is defined by a plane established by a line crossing thru the Earth's north and south poles and the apparent center of the sun. This plane sweeps the universe once per solar year. The Earth rotates thru the solar-time plane once per solar-day and correspondingly 365.24 times per solar-year. Tangent to the surface of the Earth on the sunward side is solar-noon and on the umbra side is solar-midnight. The part we are most interested with here is the plane of solar-midnight that sweeps the universe once each solar-year which equals .98 degrees (roughly two moon diameters) per solar day. Again, each rotation of the Earth corresponds to the plane of midnight sweeping the universe by .98 degrees. It is as if three hundred sixty five (and a quarter) very tall and skinny Mercator projected maps of earth, each .98 degrees wide and 180 degrees tall (pole to pole) have been rolled out across the epileptic and at exactly solar midnight, the spot directly over your head precisely correlates to your location on the surface of the earth.

Now application:

The prime meridian observatory would have been elevated above its surroundings, topped with a gnomon (horizontal in the case of the renowned Dengfeng Observatory) and equipped with a clepsydra. To the north (south for southern hemispheric observatory) would be an area precisely aligned N/S and laid out for observing and tracking the gnomon's shadow from sunrise to sunset with the greatest possible precision. Each day the astronomers using their clepsydra would predict the moment of solar noon, and then confirm by shadow measurements the moment of solar noon, and read and record the actual measured duration of the last day. Armed with the duration of the previous day the astronomer can then predict the moment of midnight at which time the astronomer would sight along the N/S line. Imagine two parallel N/S lines of silk thread illuminated with a wax or oil pottery slit lantern, to keep the observer perfectly aligned thus inscribing a precise meridian line thru the sky, which would be recorded by the astronomer. As we think about it, it seems obvious that while the astronomer was at it, they would likely note yesterdays meridian now .98 degrees (=~1 degree = two moon diameters) to the west, and tomorrows meridian a likewise one degree to the east. Thus working ahead, and confirming behind, and making up for nights when the stars were occluded by weather. This can be simply replicated with modern astronomy software, but first you must compute accurate solar midnight for your longitude by hand, which is a pain because solar-midnight is not simply solar noon + 12hrs.

These meridians, one for each night of the year, will be useful for several years (with yearly 15.16176 arc-minute adjustments for the "extra" yearly quarter rotation and precession). Charts on brass or wood with rings or slides for yearly adjustments would have much greater longevity but no greater precision.

To be clear, I am not suggesting that our ancient mariner could just jump off a ship, eyeball N/S, count drops of water to midnight, look at a star chart and expect to figure out where he was. To the contrary, establishing best longitude required an investment of weeks or months and by this method could not possibly do so from the deck of a ship BCE.

Exploratory mariners setting out to sea would always want the latest meridian star chart. When upon uncharted shores, their cartographer/astronomers would focus their efforts on establishing an observatory as best they could (given available time, materials and environmental conditions) to build an observatory commensurate with the one back home. Important to recognize here are three critical resolution limiting factors:
1. Determination of N/S: winter months offers the greatest potential precision. Proximity to equator diminishes precision. Each arc-minute of N/S error imparts 6 degrees of longitudinal determination error.
2. Calibration of the clepsydra used for determination of solar-midnight: It seems obvious the sophistication, maintenance and tuning of the clepsydra requires talent, time and suitable environmental conditions for its operation. Each second of chronologic error imparts ~.5 arc-minutes of longitudinal error.
3. Precision of their determination of the N/S meridian bisecting the elliptic. Each arc-minute of error (1/30 diameter of moon) imparts 6 degrees of longitudinal error. Obviously one must be able to see stars that have been charted and do so via sighting mechanisms/structures that enhance precision.

The explorer with paper or parchment star charts would also need a "rule" of some sort mated to the map with gradients of 15.16 arc-minutes (likely a single unit of measure in their time) to compensate for the Earth's yearly extra ¼ rotation and precession. They would align their rule such that the .98 degree section was over the observed meridian. Then they would align the gradient of the current year with the nearest prime meridian (remember there is a prime meridian in the sky every .98 degrees in this system) marked by the astronomers back home. Then the longitude is indicated by where tonight's meridian crosses the ruler for "this year". So if this ruler was (for example) good for four years, then there would be four 15.16 arc-minutes measures followed by one .98 degree measure within which would indicate the local longitude.

This edit control says I am out of bytes....

What do you think Icosahedron?

Greenman (aka David Lee Cunningham)

11-20-2009, 06:43 AM
You get to keep your bottle of port. :)

Hapgood's book was full of crap in a number of respects and, as I recall, it had the scientific rigour typical of the 'spacegods' genre, which is to say little to none, but those maps were very thought-provoking and stood alone.

I have to reiterate that my investigations took place more years ago than I care to remember and the intervening decades have dulled my memory of, and enthusiasm for, the topic. It is by no means a current interest for me, so I may not be the muse you are looking for. I have no idea at this stage whether I ever read the books you mention. Perhaps I'll put them on the list to check out when I retire.

I don't recall reading about the exact method you suggest, but that's not to say it's new, and I have vague recollections that other methods may have used solar midnight as a marker.

A brief consideration of your method leads me to conclude that it seems to be scientifically valid, though I probably haven't absorbed the finer nuances of your ideas and at present my interest is not rekindled sufficiently to check your figures regarding accuracy and error margins. Error analysis is a PITA even for a current project.

Of course, whilst this method (and others) would make for more accurate cartography, it doesn't address the problem of determining longitude at sea, which was always the real 'holy grail'.

I'm happy to discuss the topic, it makes for interesting conversation, but I'm probably not going to spend time doing calculations on it. As I said upthread, I concluded long ago that land-based, and to an extent, sea-based longitude determination was possible before the current era, that others had reached similar conclusions, and that there was little point in re-inventing the wheel. But my goal, even back then, was only to satisfy myself that it was possible, not to achieve 'fame and fortune' by writing a rigorous scientific paper on the subject.
For me, it's just another windmill carved on my lance. :)

What drives your interest in this material? How do you define 'making your mark in paleocartography'?

If you want to set out any calculations I might be tempted to confirm them, if that's helpful to you, provided I don't have to go digging out any books and we don't stray into spherical geometry. That stuff used to hurt my head even when it was young and pliable. :)

BTW, if you run out of bytes, there's nothing to prevent you from spilling over into a second, or third post, we don't have thought police here. :)

11-24-2009, 07:59 AM
In my case Hapgood’s book brought forward intriguing possibilities.
From what I recall, I even felt back then that if the problem of longitude determination had in fact been resolved by the ancients, that it could not have been through his proposed math, which as with all hypotheses, working from the solution backwards to the problem can seem like a proof.
Re your question as to what drives me. I am the founding engineer and now CEO of a company that has many claims to engineering fame. Yet in the grand scheme of things what I do will not stand the test of time and when you get down to it, it is meaningless.
Rediscovering something, anything, that cast a light on where we came from, how we fit into the world around us, and perhaps contributing to an understanding of who we (species) really are and where we are going has meaning and could benefit the world.
Longitude determination BCE is just one of a dozen or so windmills that I wander amidst. From time to time I stop and tilt at one for a while.

11-30-2009, 07:15 AM
Sorry, Greenman, I missed your last reply somehow. I just decided to check back and ask if my last post had unintentionally put you off, and found that you had already replied.
These threads disappear down the list so quickly, especially in this introductions forum.

When I looked into this, I think I just 'assumed' that determination of solar midnight was possible, I didn't look into the practicalities of how it would be done. Your description was illuminating. It seems that my assumption was valid, but I hadn't realised all that went into the calculation.
Do you have any thoughts on determining longitude at sea?
Maybe we should go PM with this? I'm not sure that anyone else is interested.