Pseudoscientific metrology

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Some approaches in the branch of historic metrology are highly speculative and can be qualified as pseudoscience.

Origins[edit]

In 1637 John Greaves, professor of geometry at Gresham College, made his first of several studies in Egypt and Italy, making numerous measurements of buildings and monuments, including the Great Pyramid. These activities fuelled many centuries of interest in metrology of the ancient cultures by the likes of Isaac Newton and the French Academy.[citation needed]

The pendulum[edit]

The first known description and practical use of a physical pendulum is by Galileo Galilei, however, Flinders Petrie, a disciple of Charles Piazzi Smyth, is of the opinion that it was used earlier by the ancient Egyptians. In a 1933 letter to Nature, Petrie wrote:

If we take the natural standard of one day divided by 105, the pendulum would be 29.157 inches at lat 30 degrees. Now this is exactly the basis of Egyptian land measures, most precisely known through the diagonal of that squared, being the Egyptian double cubit. The value for this cubit is 20.617 inches, while the best examples in stone are 20.620±0.005inches. [1]

While sandstone pendulums have been found in various Egyptian sarcophagi (e.g. the Karnak pendulum among others), no explanation is offered, at least in the texts mentioned here, as to why a divisor of 105 would have been chosen or measured.

Charles Piazzi Smyth[edit]

John Taylor, in his 1859 book "The Great Pyramid: Why Was It Built? & Who Built It?", claimed that the Great Pyramid was planned and the building supervised by the biblical Noah, and that it was:

built to make a record of the measure of the Earth.

A paper presented to the Royal Academy on the topic was rejected.

Taylor's theories were, however, the inspiration for the deeply religious archaeologist Charles Piazzi Smyth to go to Egypt to study and measure the pyramid, subsequently publishing his book Our Inheritance in the Great Pyramid (1864), claiming that the measurements he obtained from the Great Pyramid of Giza indicated a unit of length, the pyramid inch, equivalent to 1.001 British inches, that could have been the standard of measurement by the pyramid's architects. From this he extrapolated a number of other measurements, including the pyramid pint, the sacred cubit, and the pyramid scale of temperature.

Smyth claimed—and presumably believed—that the inch was a God-given measure handed down through the centuries from the time of Israel, and that the architects of the pyramid could only have been directed by the hand of God. To support this Smyth said that, in measuring the pyramid, he found the number of inches in the perimeter of the base equalled 1000 times the number of days in a year, and found a numeric relationship between the height of the pyramid in inches to the distance from Earth to the Sun, measured in statute miles.[citation needed]

Smyth used this as an argument against the introduction of the metre in Britain, which he considered a product of the minds of atheistic French radicals.[citation needed]

The grand scheme[edit]

By the time measurements of Mesopotamia were discovered, by doing various exercises of mathematics on the definitions of the major ancient measurement systems, various people (Jean-Adolphe Decourdemanche in 1909, August Oxé in 1942) came to the conclusion that the relationship between them was well planned.[citation needed] Livio C. Stecchini claims in his A History of Measures:

The relation among the units of length can be explained by the ratio 15:16:17:18 among the four fundamental feet and cubits. Before I arrived at this discovery, Decourdemanche and Oxé discovered that the cubes of those units are related according to the conventional specific gravities of oil, water, wheat and barley. [2]

Stecchini makes claims that imply that the Egyptian measures of length, originating from at least the 3rd millennium BC, were directly derived from the circumference of the earth with an amazing accuracy. According to "Secrets of the Great Pyramid" (p. 346 [3]), his claim is that the Egyptian measurement was equal to 40,075,000 meters, which compared to the International Spheroid of 40,076,596 meters gives an error of 0.004%. No consideration seems to be made to the question of, on purely technical and procedural grounds, how the early Egyptians, in defining their cubit, could have achieved a degree of accuracy that to our current knowledge can only be achieved with very sophisticated equipment and techniques.

Robin Heath[edit]

Later, these ideas were further developed as defence for the Imperial units against the emerging metric system, and adopted by parts of the anti-metric movement. Robin Heath, in his book Sun, Moon & Stonehenge, connects the megalithic yard (and thus Stonehenge) to the imperial foot, and manages to connect a few astronomical phenomena, and the Egyptian Royal Cubit (and thus the Great Pyramid) into one grand equation (MY is an abbreviation for megalithic yard):

if the lunar year is represented by 12 MY then 1 ft corresponds precisely to the extra 10.875 days to coincide with the end of the solar or seasonal year. Furthermore, the period between the end of the solar year and 13 lunations - 18.656 days - is represented by another unit of length from antiquity, the 'Royal Cubit' of 20.63" or 1.72 ft. [4]

This seems to bring pseudoscientific metrology to new heights, especially in view of the conclusion:

Hence the equally astonishing revelation that 1 MY = 1 ft + 1 RC. Assuming that the MY was the primary unit, then the derivative foot and cubit appear to have formed a logical and essential part of the astronomical and calendrical researches of our Neolithic ancestors. If, however, the foot preceded the MY in time - and here we must remember that 1/1,000th of a degree of arc around the equatorial circumference of the Earth is just 365.244 ft in length! - then knowledge of the roundness of the Earth must have predated use of the MY…i.e. well before 3,000BC. There are no other choices readily apparent!

The megalithic system[edit]

Christopher Knight and Alan Butler further develop the work of Smyth's and Stecchini's "Grand Scheme" in their Civilization One hypothesis, which describes a megalithic system of units.[2] This system is claimed to be the source of all standard units used by civilization, and is so named after the Neolithic builders of megaliths. Knight and Butler contend the reconstructed megalithic yard (0.82966m) is a fundamental part of a megalithic system. Although the megalithic yard is the work of Alexander Thom, Knight and Butler make a novel contribution by speculating on how the MY may have been created by using a pendulum calibrated by observing Venus. It also explains the uniformity of the MY across large geographical areas. The accuracy claimed for this procedure is disputed by astronomers.[3]

They derive measures of volume and mass are derived from the megalithic yard, which is divided into 40 megalithic inches. Knight and Butler claim that a cube with a side of 4 megalithic inches has a volume equal to one imperial pint and weighs one imperial pound when filled with unpolished grain. They also posit ratio relationships with the imperial acre and square rod.[2] Their book states that "The Sun, the Moon and the Earth all conform to a 'grand design' that is also evident in the Megalithic structures that are scattered across the British Isles and western Europe."[2]

British stone circle, which according to 366-geometry advocates display in its dimensions an integral number of "Megalithic yards."

Moon an artificial construction[edit]

Based on this work Butler and Knight argue that the moon is an artificial construction, probably built by humans travelling back 4.6 billion years into the past.[4][5]

366 geometry[edit]

366 geometry or 366-degree geometry (also called megalithic geometry) is the name given to an hypothetical geometry supposedly used and perhaps created by an alleged megalithic civilization of Britain and Brittany, France, according to British authors Alan Butler and Christopher Knight, and French author Sylvain Tristan. This geometry, whose origin is claimed to go back to c. 3500 BC, would have used a 366-degree circle rather than a 360-degree circle as we do today.[6]

366 geometry is mainly viewed as pseudoscience by mainstream science; defenders of the theory claim that anyone (scholars and laymen alike) may easily verify the truthfulness of their assertions, the "facts" being, in their terms, "fully testable and checkable" for "anyone with internet access."[7]

"Megalithic geometry"[edit]

One of the first persons to associate megalith builders with geometry was Scottish Professor Alexander Thom (1894–1985) who never hypothesised any 366-degree geometry himself. Thom believed that the Megalithic builders used a standard unit of measurement which he dubbed the Megalithic yard. According to him, the length of this unit was 2.72 Imperial feet or 82.96 cm. The existence of this measurement is disputed.[8][9]

According to Alan Butler[10] this geometry was based on the Earth's polar circumference. The Megalithic degree is the 366th part of it, i.e. 40,008 / 366 = 109.31 km; the Megalithic arcminute is the 60th part of the Megalithic degree, i.e. 109.31 / 60 = 1.82 km; the Megalithic arcsecond is the 6th part of the Megalithic minute, i.e. 1.82 / 6 = 0.3036 km; if this Megalithic arcsecond is in turn divided into 366 equal segments, the length arrived at is 0.8296 m, which is the presumed length of the Megalithic Yard, the supposedly ancient unit of measurement independently discovered by professor Alexander Thom[11] in the 1950s. It is precisely this apparent coincidence that prompted Butler to think that the Megalith builders could have been cognizant with an Earth-based 366-degree geometry.

Clive Ruggles has said that both classical and Bayesian statistical reassessments of Thom's data "reached the conclusion that the evidence in favour of the MY was at best marginal, and that even if it does exist the uncertainty in our knowledge of its value is of the order of centimetres, far greater than the 1mm precision claimed by Thom. In other words, the evidence presented by Thom could be adequately explained by, say, monuments being set out by pacing, with the 'unit' reflecting an average length of pace."[8] David Kendall had previously argued that pacing would have created a greater difference in measurements between sites.[12][13]

Douglas Heggie casts doubt on Thom's suggestion as well, stating that his careful analysis uncovered "little evidence for a highly accurate unit" and "little justification for the claim that a highly accurate unit was in use".[9]

366-day calendar[edit]

The Phaistos disc.

According to Butler, 366-degree geometry is linked to the Phaistos Disc, which has been interpreted by some as a Minoan calendar based on a 366-day year, the Phaistos Disc having 30 divisions on one side and 31 on the other. This calendar would have been working on 40-year cycles, because a 366-day calendar needs one intercalary month in 40 years.

Thom had also hypothesized that the Megalithic Yard was divided into 40 Megalithic inches,[14] a number that indirectly echoes the 40-year cycles of the presumed Minoan calendar in ancient Crete.

Butler also noticed that the division of the same Megalithic arcsecond into 1,000 equal parts yielded a length of 30.36 cm, which he thought matched that of the measurement given to the Minoan foot, a unit of length used in the Cretan palaces built roughly at the same time as the Phaistos Disc was made, and independently discovered by Canadian archaeologist J. Walter Graham. A later statistical test of Graham's figures found the preferred measure for the Minoan foot to be 46.8 cm.[15]

"Megalithic pendulum"[edit]

In another book (Civilization One[16]) coauthored with English writer Christopher Knight, Butler wrote that the length of a pendulum giving 366 beats (or 183 periods) during one 366th of a day (which is approximately the time it takes to the Earth to spin one Megalithic degree) is one half-Megalithic Yard long. From that the authors suggested that such a hypothetical pendulum could well have been used by these ancestral people to accurately reproduce the length of their yard.

Volumes and masses[edit]

In the book Civilization One, Butler and Knight contend that the basic units of volume and mass of the imperial system, the Imperial pint and the avoirdupois pound, are also derived from their Megalithic Yard. Just like the litre is the tenth part of the metre to the cubic power, the tenth part of the Megalithic Yard to the cubic power produces a volume of ( 82.96 cm / 10 ) third power = 570.96 mL, a very close approximation of the modern pint of 568.26 mL. Similarly, they argue that this theoretical Megalithic pint, if filled with barley dry seeds, weighs on average a number close to 453.59 grams, which is the exact value of the avoirdupois pound.

They also argue that division of the Earth mass into 366 equal parts, then again into 60 equal parts, and then again into 6 equal parts, yields a result that is almost exactly 10 to the 20th avoirdupois pounds : 5.9736 X ( 10 to the 24th ) kg / ( 366 X 60 X 6 ) = 4.5337 X ( 10 to the 19th ) kg = 9.995 X (10 to the 20th) avoirdupois pounds.

Said differently, a one-Megalithic-arcsecond-thick ‘slice’ of Earth (at the equator) weighs almost exactly 10 to the 20th pounds, as though, according to the authors, the exact value of the pound had been adjusted so as to be a round subdivision of a one-arcsecond-thick slice of Earth in the Megalithic geometry.

"Fundamental numbers"[edit]

Still in the same book, Butler and Knight claim that the Megalithic Yard is a fundamental number for the Sun, the Moon and the Earth. The Megalithic arc second as measured on the Earth equator is very close to 366 Megalithic Yards, while the lunar Megalithic arc second as measured on the Moon equator is very close to 100 Megalithic yards, and the solar Megalithic arc second as measured on the Sun equator is very close to 40,000 Megalithic Yards.

In a book published in France and Canada in 2007 French author Sylvain Tristan[17] suggests that the numbers 366, 40 and 10 are not only fundamental to the Earth, the Moon and the Sun, but also to the human body and water. In the water-based Celsius temperature measurement system, which is directly linked to base-10 numeration, the average human body temperature is 36.6 degrees (according to Russian medicine), whereas the maximal density of water, Tristan says, is 4.0 degrees (whereas it is in fact 3.98 degrees [18]).[19]

More recently Butler and Knight claimed that, on a scale where the absolute zero is defined as being minus 1,000 degrees, water boils at the temperature of 366 degrees, an "utterly remarkable" result according to the authors, which they believe points at something intrinsically fundamental in these numbers.[20]

"Salt Lines"[edit]

Alan Butler also asserts that 366-degree geometry has been materialised on the Earth by what he terms Salt Lines – 366 meridians and 183 parallels crisscrossing the globe at regular intervals (the equivalents of modern-day 360 meridians and 180 parallels).

The term Salt Line was created by Xavier Guichard,[21] who was the first person to posit the existence of such lines in the 1920s and 1930s. After having looked at a map of France, Guichard had noticed a recurrent name which he linked to Alesia, the place where Julius Caesar defeated Gaulish leader Vercingetorix in 52 BC. At the time, Guichard thought the Bronze Age people had invented the 360-degree circle. But because the intervals between the lines were seemingly too small, nobody took him seriously at the time. It was only in the late 1990s that someone (namely Alan Butler) had a second look on Guichard's tentative hypothesis.

Butler explains the smaller intervals between the lines by the fact that in a 366-degree circle, you get a few more lines than in a 360-degree circle, which of course entails a slight decrease of the interval between two lines.

The Jordan River

According to Sylvain Tristan,[22] most of the world's capital cities or sanctuaries of late prehistory and antiquity are located on the course of Salt Lines: it includes Stonehenge, Avebury, the Ring of Brodgar and Skara Brae (both of which are located on the 60th Megalithic parallel), Babylon, Assur, Niniveh, Thebes, Abu Simbel, Harappa, Mycenae, Athenes, Hattusa, Alesia, Teotihuacan (20th Megalithic parallel), Chichén Itzá, Tiwanaku and Caral. According to the author, such a situation challenges probability laws and can hardly been explained away by chance only, and thus is the result of some common knowledge held by the Megalithic civilisation that might have spread to different parts of the globe.

Tristan also thinks that the Salt Lines Prime Meridian could have been the Jordan River, a river that approximately flows in a north-south direction and along which numerous Megalithic sites from the 4th millennium BC are to be found. Although no solid link has ever been established between Megalithic sites of the Middle East and those of Europe, the Megalithic people are known to have been sailors.[23] It is also known that the first phase of Stonehenge dates from c.3100 BC. Tristan claims that Stonehenge was positioned so as the number of degrees between the monument and the prime meridian be an integer.

Tristan also claims that the lost city of Alesia is not located in the village of Alise-Sainte-Reine as mainstream scholars contend, but on the double hill of the Montfault and the Glass Mountain near the village of Guillon in Burgundy. This location was first suggested by Bernard Fèvre in 1982.[24] The hills are located on the course of a Salt Line and stand halfway between the cities of Aalst, Belgium and Alès, southern France, two cities whose name sound like Alesia and which are located along the same meridian.

Evidence[edit]

The Thornborough henges in Yorkshire.

As of October 2009,[25] Butler and Knight claim the evidence on the ground for 366-degree geometry abounds, most of it readily checkable by anyone on Google Earth. First, the circumference of the henge at Stonehenge1 was, according to the authors, exactly 366 Megalithic yards long.

Second, the triple henge of Thornborough, Yorkshire, is claimed to perfectly exhibit Megalithic measurements: the space between the henges is 360 and 366 Megalithic rods respectively (both numbers are "Megalithic" – there are 360 seconds of arc in a Megalithic degree, and 366 degrees in a Megalithic circle); each of the three henges has a circumference of precisely 366 x 2 Megalithic yards (Butler predicted the existence of such "magic" circles with a 233-Megalithic-yard diameter, which naturally results in a 366 x 2-Megalithic yard circumference, without ever finding any for years); and the longitudinal distance between the two outer circles is exactly 4 Megalithic seconds of arc.

Washington, D.C..

What is more, according to the authors, modern Washington, D.C. displays a staggering number of fundamental distances when expressed in multiples of 366 Megalithic yards (or 366 Megalithic seconds of arc), many stemming from the centre of Ellipse Park in the centre of the city. For example, the distance between the centre of the Ellipse to The Pentagon is 10 times 366 Megalithic yards, whereas there are exactly 8 times 366 Megalithic yards to the centre of the Capitol.

According to the authors the circle inside which The Pentagon is inscribed is an exact 5 times 366 Megalithic yards.

Finally, the length of a diagonal of the square originally designed as the District of Columbia (no longer a full square) is an exact 75 times 366 Megalithic Yards. According to Butler and Knight, all this is incontrovertible evidence of the continuing existence and (secret) use of 366-degree geometry within modern Freemasonry (for example, the Ellipse-Capitol-Pentagon ensemble forms a triangle of 15, 10 and 8 times 366 Megalithic yards respectively, or 33 times 366 Megalithic yards in total, which is said by the authors to echo Freemasonry's 33rd degree of the Ancient and Accepted Scottish Rite).

Henges[edit]

Butler and Knight contend that henges, which exist only in Britain, would have been the world's first star observatories. Circular mounds would have been artificial horizons and inner ditches, when filled with water, would have provided "foolproof way of identifying a perfect level.".[26] In the case of Stonehenge, it was possible for its builders to have marked the 366 Megalithic yards of its circumference by woodposts, thus creating one of the first geometric divisions of the heavens, with one degree for each day of the year, and observe the movement of stars.

Critical reception[edit]

Publications in pseudoscientific metrology receive little, if any, attention from mainstream scholarship, by nature of being intended for the popular mass market.

For French historian Lucien Febvre, Xavier Guichard's work was "time and effort lost based on wordplay."[27] Now Guichard is remembered as one of the first researchers in sacred geometry.

Alexander Thom's theories have been criticized by Ian O. Angell.[28] W. R. Knorr, examining the evidence as presented by Thom, finds no real evidence of the Pythagorean theorem, the ellipse, or a standard unit of distance in Neolithic times.[29] Karlene Jones-Bley also denies the existence of such a precise unit of measurement during the Neolithic period: "the suggestion put forth by Thom that there was a 'megalithic yard' uniform to 0.1mm from Brittany to the Orkneys cannot be accepted".[30] However, for R. J. C. Atkinson, the British prehistorian and archaeologist (1920–94), the Megalithic yard as defined by Thom is a plausible notion: "An interesting theory is his notion of a megalithic yard and rod, supposedly fairly consistent in Britain and Brittany".[31] According to the analytical methods employed by the British statisticians S.R. Broadbent and D.G. Kendall, Thom's 1955 dataset is unlikely to be the result of chance: "a 1% significance meaning that such a best fit would only occur in 1 in 100 random datasets."[32] A review in The Guardian newspaper of 'Who Built the Moon by Butler and Knight refers to the authors as "an ad man specialising in consumer psychology and an engineer turned astrologer, astronomer and playwright". The review comments on their ideas about megalithic geometry "Here, they suggest, numerical ratios concerning sun, moon and Earth - neatly arrived at by applying the so-called principles of megalithic geometry - are evidence of a message for today's Earthlings. The message is that future humans conquered time travel and went back, way back, to construct the moon to ensure Earth orbits in precisely the right alignment to the Sun to encourage the evolution (yes, they believe in that) of humans - a Mobius strip theory of history. Oh, and they genetically engineered DNA (we know, because that's too complicated for nature alone)."[33]

The first book to ever deal with the possible existence of a 366-degree circle and of a 366-day calendar (rather than speaking of "Megalithic geometry" or "Bronze Age geometry"), The Bronze Age Computer Disc by Alan Butler, has not been commented on either by mainstream scientists or the press.

Most scholars and reviewers label Butler and Knight's work as pseudoscience. Aubrey Burl, a much-published digger of Megalithic sites and a lecturer in archaeology at Hull College of Higher Education, although he coauthored a book with Thom,[34] derided Thom's work, saying that he himself had never "seen a Megalithic Yard." Jason Colavito, in a review in Skeptic Magazine, wrote "Crammed into just over 250 pages are so many unbelievable assertions and unproven speculations that it would take a book-sized rebuttal to do adequate justice to this triumph of numerology over science." He also pointed out "The precision claimed for the length of the Megalithic Yard is surprising given the poor condition of Neolithic monuments today. It is impossible to record their measurements to the ten-thousandth of a millimeter, the standard apparently used to derive this unit of measurement.[35]

Belgian author Robert Bauval,[36] considers Butler and Knight's new discoveries as "major breakthroughs" and as "a stunning discovery [that] could completely change the way we view our remote past", whereas Graham Hancock praised the book, regarding it as "Absolutely fascinating, and very, very convincing."[37]

See also[edit]

References[edit]

  1. ^ Ken Zetie (2004), "A lesson from history: it’s good to look back from time to time", Physics Education 39 (2): 216, retrieved 13 October 2008  in reference to Flinders Petrie (15 July 1933), "Origin of the Time Pendulum", Nature 132 (102-102), doi:10.1038/132102c0 
  2. ^ a b c Butler
  3. ^ Uriel's Machine – a Commentary on some of the Astronomical Assertions.
  4. ^ "Who Built the Moon? Interview with Christopher Knight". New Dawn. November 25, 2012. Retrieved 13 November 2013. 
  5. ^ Butler, Alan. "Who Built the Moon?". Retrieved 13 November 2013. 
  6. ^ http://www.civilizationone.com/reviews.html, http://www.atm.org.uk/reviews/books/civilizationone.html
  7. ^ Butler, Alan and Christopher Knight. Before the Pyramids. Cracking Archaeology's Greatest Mystery. London: Watkins, 2009. ISBN 1-906787-25-5, p.1 (introduction)
  8. ^ a b Ruggles, Clive (1999). Astronomy in Prehistoric Britain and Ireland. Yale University Press. p. 83. ISBN 978-0-300-07814-5. 
  9. ^ a b Heggie, Douglas C. (1981). Megalithic Science: Ancient Mathematics and Astronomy in North-west Europe. Thames and Hudson. p. 58. ISBN 0-500-05036-8. 
  10. ^ Butler, Alan. The Bronze Age Computer Disc. 1999. London: Quantum Books ISBN 0-572-02217-4
  11. ^ Thom, Alexander. Megalithic Sites in Britain. Oxford : OUP, 1967
  12. ^ David George Kendall; F. R. Hodson; Royal Society (Great Britain); British Academy (1974). The Place of astronomy in the ancient world: a joint symposium of the Royal Society and the British Academy, Hunting Quanta, p. 258. Oxford University Press for the British Academy. Retrieved 22 April 2011. 
  13. ^ David H. Kelley; Eugene F. Milone; Anthony F. (FRW) Aveni (28 February 2011). Exploring Ancient Skies: A Survey of Ancient and Cultural Astronomy. Springer. pp. 163–. ISBN 978-1-4419-7623-9. Retrieved 22 April 2011. 
  14. ^ Thom, Alexander, A.S. Thom. Megalithic Remains in Britain and Brittany. Oxford: Clarendon Press, 1978
  15. ^ McEnroe, John C. (2010). Architecture of Minoan Crete: constructing identity in the Aegean Bronze Age. University of Texas Press. p. 88. ISBN 978-0-292-72193-7. 
  16. ^ Butler, Alan et Knight, Christopher. Civilization One: Uncovering the Super-science of Prehistory: The World Is Not as You Thought It Was . London : Watkins, 2004. ISBN 1-84293-095-8, ISBN 978-1-84293-095-3
  17. ^ Tristan, Sylvain. Atlantide, premier empire européen. Paris : Alphée, 2007. ISBN 2-7538-0210-6, ISBN 978-2-7538-0210-0
  18. ^ Denny, Mark W. Air and water: the biology and physics of life's media Princeton University Press; Reprint edition (1 Sep 1995) ISBN 978-0-691-02518-6 p.27
  19. ^ Dingman, S. Lawrence Fluvial Hydraulics Oxford University Press, USA (26 Feb 2009) ISBN 978-0-19-517286-7 p.109
  20. ^ Butler, Alan and Christopher Knight. Before the Pyramids. Cracking Archaeology's Greatest Mystery. London: Watkins, 2009. ISBN 1-906787-25-5, 81
  21. ^ Guichard, Xavier. Eleusis Alesia. Enquête sur les origines de la civilisation européenne. 1936.
  22. ^ Tristan, Sylvain. Les Lignes d'or. Pourquoi TOUTES les capitales des premières grandes civilisations furent érigées sur ces axes. 2005. Paris: Alphée. ISBN 2-7538-0050-2
  23. ^ Cavalli-Sforza, Luca and Francesco. The Great Human Diasporas: The History of Diversity and Evolution. Addison Wesley Publishing Company, 1996. ISBN 0-201-44231-0 and ISBN 978-0-201-44231-1.
  24. ^ Article from the Nouvel Observateur, 20 January 1984, "On se bat toujours pour Alésia" by Fabien Gruhier
  25. ^ Butler, Alan and Christopher Knight. Before the Pyramids. Cracking Archaeology's Greatest Mystery. London: Watkins, 2009. ISBN 1-906787-25-5
  26. ^ Butler, Alan and Christopher Knight. Before the Pyramids. Cracking Archaeology's Greatest Mystery. London: Watkins, 2009. ISBN 1-906787-25-5, p. 94-8
  27. ^ L. Febvre, "Activités régionales", Annales, 1951, 6,1, p. 84n.2lire en ligne [archive: http://wikiwix.com/cache/?url=http://www.persee.fr/web/revues/home/prescript/article/ahess_0395-2649_1951_num_6_1_1916]
  28. ^ Angell, Ian O. Megalithic mathematics, ancient almanacs or neolithic nonsense. Bull. Inst. Math. Appl. 14 (1978), no. 10, 253--258
  29. ^ Knorr, W. R. The geometer and the archaeo-astronomers: on the prehistoric origins of mathematics. Review of: Geometry and algebra in ancient civilizations [Springer, Berlin, 1983; MR: 85b:01001] by B. L. van der Waerden. British J. Hist. Sci. 18 (1985), no. 59, part 2, 197--212. SC: 01A10, MR: 87k:01003
  30. ^ Karlene Jones-Bley, American Journal of Archaeology, 106-1, 2002, p. 122
  31. ^ Atkinson, R. J. C. Obituary: Alexander Thom. J. Hist. Astronom. 17 (1986), no. 1, 73--75. SC: 01A70 (01A10), MR: 87h:01062
  32. ^ cited in Alexander Thom. Megalithic Sites in Britain. Oxford Press. 1967.
  33. ^ Nettleton, Paul "Peer Review" Guardian 1 September 2005
  34. ^ Thom, Alexander and Burl, Aubrey Stone Rows and Standing Stones: Britain, Ireland and Brittany B.A.R. 1990, ISBN 978-0-86054-708-2
  35. ^ [1]
  36. ^ # ^ http://www.independent.co.uk/news/media/horizon-censured-for-unfair-treatment-622719.html
  37. ^ Book cover of Butler, Alan and Christopher Knight. Before the Pyramids. Cracking Archaeology's Greatest Mystery. London: Watkins, 2009. ISBN 1-906787-25-5
  • Shalev, Zur 1967 - "Measurer of All Things: John Greaves (1602-1652), the Great Pyramid, and Early Modern Metrology", Journal of the History of Ideas - Volume 63, Number 4, October 2002, pp. 555–575, The Johns Hopkins University Press
  • Thom, Alexander (1955). "A Statistical Examination of the Megalithic Sites in Britain". Journal of the Royal Statistical Society. Series A (General) (Journal of the Royal Statistical Society. Series A (General), Vol. 118, No. 3). 118 part III (3): 275–295. doi:10.2307/2342494. JSTOR 2342494. 

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