Stonehenge Builders Had Ancient Knowledge of Pythagorean Geometry
A new book, Megalith, claims ancient Britons built Stonehenge “and other stone circles with a knowledge of Pythagoras' theorem, 2,000 years before the Greek philosopher formalized geometry.”
Megalithic researcher Robin Heath, who contributed to the book, told reporters at The Telegraph that he presents evidence of “a great Pythagorean triangle in the British landscape” and editor John Matineau connects “Stonehenge with Lundy Island in Wales and the site from which Stonehenge’s ‘Preseli bluestones’ were quarried.”
The oldest known depiction of Stonehenge, a giant helps Merlin build Stonehenge. From a manuscript of the Brut by Wace in the British Library. ( Public Domain )
The huge stones we see today at England’s Stonehenge were once surrounded by a circle of 56 wooden posts or smaller stones which many archaeologists believe recorded the position of the Sun and the Moon which would help predict eclipses and monitor seasonal changes to assist with agriculture. The bluestone horseshoe at the center of Stonehenge is thought to have contained 19 stones representing the approximate number of solar years it takes for the Sun and Moon to complete a ‘metonic cycle’ and almost recalibrate.
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Depiction of the 19 years of the Metonic cycle as a wheel, with the Julian date of the Easter New Moon, from a 9th-century computistic manuscript made in St. Emmeram's Abbey. ( Public Domain )
The overriding point or take away from Megalith is that Pythagorean geometry was being applied in Britain’s ancient landscapes ‘over 2000 years before Pythagoras was born.’ To achieve this end, Megalith is loaded with claims like: “People often think of our ancestors as rough cavemen but they were also sophisticated astronomers” and “We see triangles and double squares used which are simple versions of Pythagorean geometry. And then we have this synthesis on different sites of solar and lunar numbers.”
Regarding the content of Megalith the authors told reporters, “much of the knowledge was lost following the rise of Christianity in Britain” and, “These days it’s seen as hippy dippy or New Age, but actually it’s a colossal omission to the history of science that we don’t see these monuments for what they are,” records The Telegraph report .
Some argue Stonehenge was designed to record the positions of the Sun and the Moon. ( CC0)
The Other Side of The Coin
The ancient “lost knowledge” presented in Megalith, was published today to coincide with the summer solstice. However, the idea that Pythagorean triangles were being applied in ancient Britain passed from the tables of a handful of academics in the early 20th century and entered mainstream archaeology in the 1960s when Professor Alexander Thom of Oxford University measured the underlying alignments of hundreds of megalithic stone structures in the United Kingdom, Ireland and Brittany.
Thom presented a series of “complex astronomical alignments intertwined with Pythagorean triangles, accurate right angles and ellipses based on Pythagorean triangles, congruent triangles and basic polygons.” He also famously proposed a ‘Megalithic Yard’ - 2.72 Imperial feet or 82.96 cm - which he believed was ‘ the’ standard building unit of measurement applied in the stone circles of Neolithic Britain and France. (Thom, 1955)
Although he never actually said the words, by implication Thom introduced the controversial idea that an elite theocratic class of educated wise men - astronomer-priests - ruled over a highly organized Neolithic society and had developed geometric processes and building procedures.
Stonehenge Spring Equinox Celebrations 2018. ( CC BY 2.0 )
At the time, Thom’s beliefs contradicted the zeitgeist as most archaeologists believed Neolithic people were isolated groups of survivalists, incapable of inter-tribal order to the extent that Thom inferred. Although today we know this was certainly not the case, as entrapping as the ‘Pythagorean’ discoveries presented in ‘Megalith’ might be, we have to be so, so careful in these fields of research, as many unseen variables exist, and one is always well served to consider the arguments’ skeptics.
Doubts About the Megalithic Yard
Mr Heath, an unashamed proponent of the Megalithic yard, told reporters “many stone circles were not fully circular but have geometry derived from Pythagorean triangles ‘often in whole numbers of Megalithic yards (2.72 feet)’ which were probably laid out using ropes and pegs.” He, like many if not most, of the contributors in “Megalith” write about the ‘Megalithic yard’ as an accepted historical fact, yet some of the world’s most respected archaeoastronomers and archaeologists are equally as certain that standard Neolithic measurements and building modules developed independently from place to place, and a northern European ‘standard’ measure did not exist.
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Constable's portrayal of Stonehenge. Source: Public Domain
In 1981, Douglas Heggie, from the School of Archaeology & Ancient History at Leicester University, cast doubt on Thom's Megalithic yard stating that after his “careful analysis” he uncovered "little evidence for a highly accurate unit" and "little justification for the claim that a highly accurate unit was in use”. (Heggie,1981)
Furthermore, in my own 2015 book A Twist In Time , in which I measure the underlying rope measurements of Neolithic monuments, I discuss the fact that Thom actually “noted tiny differences in his measurements of the ‘Megalithic yard’ from circle to circle” and that his Megalithic yard was an ‘average’ measurement. I argue that ‘averages’ only work on paper and that the ‘tiny differences’ Thom found in the measurements of each circle occurred because the prime measurements were based on “something present everywhere, but varying slightly from place to place.”
I concluded that this “something” was us! All over the world, prime measurements used for building were derived from rulers’ feet, arms, hand spans and steps, evident today in the names of the measuring units: feet, hands and spans. Cementing my hypothesis, the 42.5 cm prime measurement used to construct the Ring of Brodgar standing stone circle in Orkney matched the length of a 5 feet 5 inch high persons forearm, from middle finger tip to elbow!
My point here is, if Thom’s Megalithic yard doesn’t exist and the Pythagorean triangles he claimed to discover arose axiomatically, that is the builders had no idea about them, then is Heath’s giant landscape triangle too, a matter of chance? All things considered, whoever you choose to believe, I firmly advise you to read Megalith as it does what every good book should, and too few do - it really makes you think.
And, there was one thing Heath told reporters that nobody can argue with,
“I do feel very sad that visitors to Stonehenge are not told anything about the astronomical alignments, even when they are very simple to explain.”
Top image: Stonehenge Sunset impression. Source: Public Domain
By Ashley Cowie
Thom, Alexander (1955). "A Statistical Examination of the Megalithic Sites in Britain". Journal of the Royal Statistical Society. Series A (General). 118 (3): 275–295. doi:10.2307/2342494. JSTOR 2342494.
D. C. Heggie, Megalithic Science: Ancient Mathematics and Astronomy in North-west Europe (UK: Thames and Hudson, 1981), p. 58.
A Twist In Time, Alchemy International Publishing: Available at Amazon.
who cares what people think who use words like ‘dippy-hippy' and why even bother mentioning them in a serious article such as this one?
There may be some evidence that they were trying to work out some really important things, like the size of the Earth, planets and the sun. I don't know much about the Neolithic mega structurers, but from what I've seen of Minoan artefacts, they were using precise measuring tools. The so called double axes are substantial flat, they both reflect sunlight and cast shadows for tracking the suns position (time of day) and were used in peak sanctuaries with lots of other markers (so called Horns of consecration on the wall tops), the iconography shows this is there intended purpose. You can move the axes around to line the tips up with targets (stars, they probably did this for foreign ships on the horizon too). You measure the distances between fixed reference markers horns or use axes to the walls and you get angles. It doesn’t have to be an axe, two staffs would work too (that other cultures seem to refer to). The Minoans (maybe others) will have had Babylonian trigonometry tables (jaw dropping-ly good) to convert angles to distance or visa versa (this gives you not only bearings but range to say foreign ships (if they saw a flash of light, they were just about to be boarded by marines – all the Minoan fleet were white hulls and protected their territorial waters and commodities flowing probably to levy duty if they saw any plain wooden hulls on the horizon), these axes could also be used for long distance signalling too. They were fascinated by numbers (their Palace bookkeeping records make KPMG auditors look interesting), they embedded things like pi and Fibonacci numbers into their buildings proportions for example. The Babylon records show they were observing and recording the patterns of the celestial bodies on a daily basis. The reason I’m flagging this up is that you can’t produce the antikythera mechanism unless you understand and have been monitoring the stars position for centuries (there is an offcentered cog in the mechanism to track the egg shaped orbit of the moon it is a very sophisticated analogue computer), they didn’t just keep records of this, they could predict eclipses, they have basic manual calculators (like abacus for orbits) to do just this. The stars are a clock due to precession of the equinoxes and you can mark your time by alignment to key references, the Sphinx’s is recording when it was built, civilisation is a lot older than most think. I’m flagging this up because if you had separation between observatories sites this might be useful for certain events or to make other measurements, I’m pretty sure they would have been interested in this, they wanted to better understand those that organised the solar system and its patterns, underlying rules and the cycles of life. It makes perfect sense to support agriculture, navigate and better understand the world about you. The Minoans appear to be really good at navigation for example, they had portable double axe mirrors, they know the time of day and their latitude, there are even offsets markers on the B side that show the adjustment you need to make for the time of year so you know your latitude, can be used mid-day (sun at zenith) or referencing the stars at night (probably Orion belt – nice and bright to the horizon). There is even a technical diagram on a pottery jar to explain how it all works. The petal of life means (organise), petals are shown above the axe (winter solstice), below (summer solstice) and either side at equinox. The sumerians also used this same symbol (you see it on the rulers wrist bands, that walks around with a standard weight MEASURE in his hand).
Oddly, there is a tomb in Cumbria and in the stone ceiling of it, there are rebated sections to gravity cast double axes (like about 30 of them), that suggests they were produced in some volume in Britain at this time (I cannot explain this), but the tools to measure the stars position may have been in Britain around the time of stone henge. They could have got there through Iberia trade or over the amber road.
“It’s a colossal omission to the history of science that we don’t see these monuments for what they are,"
Yes, this is the tragedy of our times. We simply don’t understand that they had technology also. We believe (because of the media) that we are the apex of civilisations but this is obviously not so. Do not overlook Thom’s work
Love to look at it. email [email protected]
Bang on Ashley! Take a look at Babylonian trigonometry (as in tan, cos, sin), it was even better than today, it uses fractions so everything is much easier to calculate, but don't let the computer scientist know or they will make even better AI to outsmart the humans.
Hey, your article on Egyptian rock processing gave me an idea. I worked out how they were producing facing stones so precisely, I've looked into it and it checks out. Would you like to write it up (I'm not so good at words, but I can produce the illustrations and do the mechanical engineering maths) if you'd like to give it a whirl?
Your essential right, water was used to make the blocks level, but they were not using chisels, they had something much better to make the blocks perfectly flat (within about 10 micron), parallel and consistent across courses and processed damn fast! Ancient tech rocks, it's so simple and effective!
Let me know your email and I'll send on some details for your thoughts. Best, Nick