Geodesy is usually defined as the measurement and mapping of the Earth. As a science it is traced back to Pythagoras (6th cent. BC), who was thought to be the first to propose the sphericity of the Earth. Later, Eratosthenes (276 BC– 195 BC) was one of the earliest to attempt to determine the dimensions of our Earth and succeeded with remarkable accuracy.
A controversial aspect of modern geodesy is the claim that many ancient sites were deliberately established at locations that had specific geodetic relationship to each other and/or the dimensions of the Earth. For example(a) in ancient Egypt, from Giza to the Equator is 1/12th the circumference of the Earth, Amarna to the Equator is 1/13th, Luxor 1/14th and Philae 1/15th! Graham Hancock in his Heaven’s Mirror pointed to similar relationships around the globe suggesting a possible world grid. This idea of a world grid has a number of supporters, but is often classified as a ‘fringe’ interest due to the attempt by some to link gridlines with UFOs and their use of the grid as a power source(w).
Possibly related features may be the ley lines identified by Alfred Watkins in Britain(c)(g), the Alesia alignments in France discovered by Xavier Guichard(b) and/or the Heilige Linien of Germany claimed by Wilhelm Teudt(aa).
Heinz Kaminski had claimed to have discovered a megalithic grid system that stretched from Stonehenge across Europe with an east-west and north-south orientation and referred to as the Stonehenge/Wormbach System(h).
*Ashley Cowie has published a paper(ac) related to Alesia and the work of Guichard and others, as well as his own investigations.
I should also point out that Marcel Mestdagh also identified a form of road system, laid out in giant ovals with radials in France. At the centre of these ovals was the ancient city of Sens. Philip Coppens informs us [1275.184] that a further strange discovery by Mestdagh was that this ancient road network, centred on Sens, was mirrored by a similar network of roads in England centred on Nottingham!*
‘The Way of Virachoca’ in the Andes which runs through Tiwanaku and is oriented exactly 45° west of true north and runs for over 1000 miles, has been studied by Maria Scholten d’Ebneth  in the 1970’s and expanded on by a number of Spanish speaking commentators and is now the subject of an article by Dave Truman(x).
In 1973, three Russians, engineers Valery Makarov and Vyacheslav Morozov along with Nikolay Goncharov, an artist, published in Russian an article with the eye-catching title of Is the Earth a Giant Crystal? (y) This was probably the earliest presentation of an earth grid based on ancient historical sites. A brief history of the earth grid theories that emerged around this time is available online(z). There is now a Russian geodesy website with an English translation(ab).
David Hatcher Childress published his Anti-Gravity and the World Grid  in 1993, with the modest claim that he “proves that the earth is surrounded by an intricate electronic grid network offering free energy.” Obviously, Childress’ understanding of ‘proof’ is different to mine, as the only proof required is the production of some of this free energy, which he has not done.
Tom Brooks has entered the fray with a study of 1500 prehistoric sites and his conclusion that the inhabitants of ancient Britain had a designed a navigation system based on a grid of isosceles triangles(i). Brooks has gone a step further and speculatively claimed that the accuracy of this geometry-based system could only have been designed through “extraterrestrial intervention”(r). This concept is explored more fully in his latest book, Seeing Around Corners: Geometry in Stone Age Britain  and in a series of video clips(s). A more critical view of Brooks’ ideas is also available on the Internet(j).
Some years ago a former employee of a NASA sub-contractor, Maurice Chatelain claimed that within a 450-mile radius of the Aegean island of Delos that 13 mystical sites, when connected by straight lines formed a perfect Maltese Cross(u)!
Others such as Livio Stecchini(d) and Jim Alison(e) using geodetic calculations have identified São Tomé and Cape Verde respectively as the location of Atlantis. I must also include Hugo Kennes, a Belgian researcher with a passionate interest in global grids and sacred geometry(l)(p). Kennes has also informed me of a new Facebook group(q) deal with all aspects of the subject, as well as another(v) that includes submerged cities and other features.
Anyone interested in pursuing a study of this subject might like to look over James Q. Jacobs’ archaeogeodesy website(f) as well as the BioGeometry website (m).
If you have pursued all the links so far, you can pamper yourself further with a paper(k) by William Becker and Beth Hagens(n). Another researcher in this field is Dan Shaw whose website(o) give a good overview of the subject.
Jean-Pierre Lacroix added his weight to the debate with his 1998 paper entitled The Mapmakers from the Ice Age(t).
A global network of sacred sites was also put forward by Rand Flem-Ath & Colin Wilson in The Atlantis Blueprint . This book was intended as a sequel to When the Sky Fell , but generally wandered off into other areas after the first couple of chapters.
I am somewhat sceptical about certain aspects of geodesy, particularly some of the claims of a world grid. However, it does raise many questions that require further study and explanation. In this connection, I would recommend John Sase’s Curious Alignments  as a good starting point.
(i) http://www.prehistoric-geometry.co.uk/ (offline 2016) See: https://web.archive.org/web/20160628154229/http://www.prehistoric-geometry.co.uk/
(m) http://www.biogeometry.org/page34.html (offline May 2017)
(r) http://www.prehistoric-geometry.co.uk/ [See (i)]
Tiwanaku (Tiahuanaco) is an ancient city whose remains are located over two miles above sea level near the southern end of Lake Titicaca on the Altiplano of Bolivia. It was first encountered by Spanish conquistadors in 1549. Tiwanaku has all the features of a harbour, which has led some to describe it as the seaport of nearby Puma Punku another remarkable ancient site(o).
The ruins are scattered over a number of square miles through which the Guayqui-La Paz railway was constructed, which was responsible for the breaking up of many monuments to provide ballast. Prior to that, stone from the site was used in the construction of nearby homes and a church.
Belisario Díaz Romero believed that Tiwanaku had been built by a race of people he calls Homo atlanticus, who had come to America from Atlantis over a landbridge from the east, outlined in his 1906 book Tiahuanacu. Heather Pringle notes(t) that before Romero, “Francis de Castelnau (1810-1880), for example, proposed in the mid-19th century that Tiwanaku was the work of wandering Egyptian pharaohs, as opposed to the ‘imbicilic race that inhabits the country today’.”
The controversial Arthur Posnansky, who linked Tiahuanaco with Aztlan, the mythical “white” island homeland of the Aztecs investigated them in the early 20th century. The similarity of Aztlan with the name of Plato’s city has excited some straw clutching Atlantis seekers into claiming a definite connection between the two.
Posnansky also noted that the expected alignments of structures at Tiwanaku were offset by an amount which suggested their construction at a time when they would have been correctly aligned with respect to the cardinal points. He, after many years of study, was convinced that Tiahuanaco was the oldest civilisation on Earth dating it to around 15,000 BC. Charles Orser jnr. debunked Posnansky’s dating in a 2001 article(k) as did Paul Heinrich(n).
Some researchers, including Jim Allen, have studied Tiwanaku’s remarkable Gate of the Sun and identified the figures carved on it as a sophisticated calendar(v) . Ashley Cowie has recently proposed that Tiwanaku was located on an ancient Prime Meridian(w).
In the 1920’s Edmund Kiss studied the ruins of Tiwanaku and concluded that it had been constructed by Nordic refugees from Atlantis which had been destroyed by a falling moon! His ideas were enthusiastically received back in Nazi Germany. A further expedition was planned, but never materialised because of the start of World War II.(u)
In sharp contrast is the claim(l) by Roger Elefant that later construction at Tiwanaku was carried out by the Vikings!
However, a more recent, but catastrophic, explanation is offered by Stephen Smith(d) on the Thunderbolts.info website. Perhaps Smith’s ideas might be combined with the studies of George Dodwell to produce a more comprehensive hypothesis. Posnansky’s date is greatly at variance with conventional dating that puts the flourishing of Tiwanaku at 1200 BC until 1200 AD. The latter part of that period roughly coincides with the existence of the Wari Empire, a possible rival of Tiwanaku(e).(e).
The claim of a direct connection between Tiahuanaco and Atlantis is hard to accept on a number of grounds; for example, the idea of an army travelling from the west coast of South America to attack Greece in the east of the Mediterranean is not tenable. That there was an advanced culture in the Andes is undeniable but to link it to Plato’s story is stretching credibility to extremes. Lake Titicaca and Tiahuanaco have plenty of mysteries still to be explained. In 1980 the Bolivian scholar, Hugo Boero Rojo, aided by one of the local natives, Elias Mamani, located underwater ruins off the coast of Puerta Acosta. His discoveries included megalithic temples, flights of stairs and stone roads.
More recently, Dave Truman has written about an alignment known as ‘The Way of Viracocha’ that runs from Cajamarca in the north, through Cuzco and Tiwanaku and finishing at Pukara Grande(p), oriented exactly 45° west of true north. Truman has built on the work of Maria Sholten d’Ebneth (1926-2007), who wrote of the La Ruta de Wiracocha in the 1970’s(q). Others have expanded on her work, but usually in Spanish. Truman has speculated on whether “Viracocha, the great teacher and restorer of civilisation in the Andes, in some way embodied the scientific knowledge of a sophisticated, but long forgotten high culture?” Truman
also discusses the ‘chakana’ or Andean stepped cross and it possible meaning.
It was reported in October 2013(g) (that a team of Belgian and Bolivian archaeologists had found an assortment of ceramics, gems and gold objects at an apparent ceremonial site beneath the waters of Lake Titicaca, which was sacred for the Incas and Tiwanakus.*It was not until 2019 that images of some of the artefacts recovered from the lake were widely published(x).*
We cannot leave the matter of mysterious Tiahuanaco without referring to the fact that some miles further south is Lake Poopó beside which Jim Allen is convinced that the city of Atlantis was located. Allen claims that the large plain to the west of the lake is the plain mentioned by Plato as being adjacent to the city of Atlantis. In a recent documentary “Atlantis in the Andes” broadcast by ‘Discovery Civilization’, Allen identified Tiahuanaco as one of the ten kingdoms of Atlantis.However, I cannot help noticing that while Tiwanaku, claimed to be 17,000 years old, provides us with an astonishing wealth of structures, Allen’s chosen Atlantis site, Pampa Aullagas, offers little more than rubble!
Another supporter of an Andean Atlantis is Sean Bambrough, who has been developing a theory since 1999 that identifies Tiwanaku as the city of Atlantis(h). In February 2015, Marcelo Ozorio also suggested a link with Plato’s Atlantis and most interesting is the huge number of images included on his site(i). There is also a large collection of related images on a YouTube clip(m).
In 2008 David E. Flynn brought to public attention an astonishing series of satellite photos(a) that show a vast network of the remains apparently of human structures that extend for many miles around Lake Titicaca. These ‘geoglyphs’ encompass Tiahuanaco.
The most remarkable collection of early photos of the Tiwanku site can be found on the Above Top Secret website(b). The accompanying text makes a strong case for treating the location as archaeologically contaminated and as a consequence that many of the dates proposed for the site should be considered suspect. Other mysteries are the fact that saltwater Lake Titicaca contains known sea life and that old waterlines are slanted(c).
In late March 2015, the Bolivian government announced(j) that ground-penetrating radar had identified what appeared to be a buried pyramid in the Tiwanaku complex as well as other ‘anomalies’ and that excavations may start in May or June.
A mixed Spanish and English website(f) offers a number of interesting papers including a chapter from Posnansky’s book Tiahuanaco: The Cradle of American Man.
Archaeology magazine has an interesting Q & A paper relating to the history and current state of preservation at the Tiwanaku site(s).
A May 2017 report(r) confirmed that the Tiwanaku complex is much more extensive than previously thought, covering an area of at least 650 hectares (1,675 acres).
(i) http://documentaries.camera/tiwanacu/ (offline Sept 2015)
*(j) http://latino.foxnews.com/latino/entertainment/2015/03/27/bolivia-detects-buried-pyramid-at-tiahuanaco-site/print (offline April 2019) See: https://web.archive.org/web/20170319193806/http://latino.foxnews.com/latino/entertainment/2015/03/27/bolivia-detects-buried-pyramid-at-tiahuanaco-site/print*
*(o) http://www.atlantisquest.com/prehistcity.html (offline March 2018) See: https://web.archive.org/web/20170601230717/http://www.atlantisquest.com/prehistcity.html*