The design of Stonehenge
The construction of Stonehenge reflects the empirical discovery of mathematical truths. Its design embodies the elegant and universal symbolism of numbers and geometry. Some 4,500 years ago Neolithic surveyors and engineers understood and employed the relationships between squares and circles. They accurately created polygons which included hexagons pentagons decagons; the classic 30 sided figure which determined the positions of the Sarsen Circle (a ‘triacontagon’) is itself a product of these fundamental shapes.
The ‘horseshoe’ form of the central array was derived from the same markers that determined the position of the Sarsen Circle. Beyond the circle, the four ‘Station Stones’ sit in perfect spatial and geometric relationship with the central group. A modern preoccupation with ‘alignments’ has masked the elegantly simple formulae used by the prehistoric designers.
News – Amazing stone rabbit (not found near Stonehenge and well, it’s actually a natural flint nodule, but it’s prettier than the ‘carved stone ducks’). Here it is: Stone Rabbit
I love this: WARNING, do not play if you are offended by colourful language:
His poor wife, and all the guy had to do was click this link: What?
Here’s something for all you mathematicians ….
In the world of archaeology there is such a thing as transparent or manifest proof. I will explain in a moment, but first what is archaeology? The simple answer is that it is the study of the human past through the evidence provided by material remains. Hence when you look at any theory which relates to archaeology, and especially prehistoric remains, you have to ask yourself ‘can this be supported by the tangible evidence, or is it no more than opinion and guesswork’. So back to the original point, what is this extra dimension, this realm of the ‘transparent or manifest’? what does it mean? If archaeology only deals with material evidence how can there be dimension within which other information resides? Well, let’s consider an archaeologist finds a bronze artefact, and let’s say the context is secure, for example it was found with burial scientifically dated to some time before 2,000 BC. The archaeologist may not know where the tin or copper that made up the alloy came from, nor any other ‘fact’ such as where it was made, or for what purpose, but we can say ‘the people who made this had access to both tin and copper’ and that they knew how to raise the temperature of a smelting furnace to near 1000 degrees Celsius, fact. In other words we don’t have to find the source of the tin or copper, nor locate the furnace to know that both these statements are true.
Now when we use the same logic to examine Stonehenge, we also see numerous examples of ancient knowledge which can be unlocked from the design of the structure. From the evidence of the physical remains we can directly enter the realm of prehistoric knowledge, without guesswork and without speculation. To do this we do not start with a ‘theory’ into which the evidence appears to fit, but by considering what the evidence actually tells us about what people who built Stonehenge knew. From this starting point we can then begin to understand the way that knowledge was used to create the structure. By doing this we start from the basic facts and the uncertainties soon become apparent. The alternative is to endlessly sift accept and reject poorly constructed theories which may or may not be correct, and invariably if they are not susceptible to any kind of material proof this ultimately is a pointless exercise. That’s not to say we cannot test and evaluate the ‘theories’ but only after the all the evidence has been called in does it make any sense to do so. Moreover the body of evidence is not static, we gradually learning more about Stonehenge and contemporay monuments and improving scientific methods of investigation.
So, and here’s a simple exercise for mathematicians, here are some facts, based on the tangible archaeological evidence. The inner faces of the ring of ‘sarsen’ stones at Stonehenge form a circle to which the centre of the faces conform. Forget interpretations that show circles drawn through the centres of the stones, or to the outside of the circle, for the stones are all irregular in thickness and form. Anyone who disputes this fact needs to take a long hard look at accurate plans of the structure, and preferably pay a visit to examine among others, sarsen stone 16. It will then be immediately apparent that the builders of Stonehenge set the inner faces of the stones against their marked circle. Still unsure, then ask a builder when building a natural stone wall how the stones are selected and set. Are his stones chosen so that the better sides represent the face of the construction; is the string line to which he works on the face, or is the line running in the middle of the foundations? Let’s assume we have overcome all the illogical arguments as to which aspect of the Stonehenge circle represents the surveyors intended circle, so what’s next, what’s this ‘mathematical’ question in respect of the setting out of the stones?
Interestingly we accept the idea of the prehistoric circle largely without question, it can be measured and checked on the ground and verified. We can see exactly what the prehistoric surveyors intended, even if we don’t understand why they wanted a circle in the first place (remember that’s simply the realm of speculation, we can’t say why). But wait, what else we know about this structure; well despite being a stone circle it has an axis, it straddles the line of the midwinter sunset and midsummer sunrise, there were originally thirty uprights, the solstice axis passes between stone 30 and 1 and 15 and 16. What might we discover from these facts alone? Firstly that they could set out an accurate circle, obvious in it’s simplicity, knock a peg in the ground and scribe or make a circle using a rope, and yes they had ropes, so that’s how they started, too easy? It would be if in fact that was where they did start, but they didn’t! Firstly Stonehenge (the iconic sandstone structure) sits central to a much earlier earthwork; they needed to find the centre, now try guessing where the centre of an earthwork some 100m in diameter is, and you will immediately understand the first problem. You might try marking it out on the ground, it’s a pretty big area. Secondly they didn’t even start with a circle! Remember the axis of the construction, the two solstices, this line had to be marked out first, exactly through the centre of the existing earthwork, and only then the centre point found.
Outside and beyond the Circle, sitting just inside the remains of the earthwork are the two surviving so-called Station Stones, two others are lost but are known from their foundation holes. Station stones, not a bad name actually as they do appear to be exactly that, surveyors survey control stations. If you take two lines across the diagonals of the ‘Station Stone rectangle’ they form they cross in the centre of the Stone Circle. And, just as importantly this ‘rectangle’ formed by the Station Stones; well the short sides make up two facets of an octagon, in other words the Station Stones were set on the vertices of two opposing facets of an octagon. Moreover the Station Stones were there before the central array, it would have been impossible to set them up so accurately in respect of the Circle if they were later.
So, returning to the Circle, we can see marked out the line of the Solstices, simple really by observation, even looking at the length of the sun’s shadow as ancient Japanese observers are known to have done to establish the solstice. On this line, and in the centre of the existing outer work (established some 500 years earlier around 3,000 BC), they scribed the circle against which the inner faces of then stones were to be set. Are we getting to the maths problem yet? We certainly are, here’s the task they were faced with, put yourself in their place:
You have 30 massive stones to set upright in a circle, each irregular, each of different width and thickness (and height). You want to set them so as they support 30 perfectly formed lintels, which have been pre-fabricated with complex pre-cut joints. We know about the pre fabrication because things didn’t always go to plan, and some joints had to be re-cut (at least one of the circle stones cracked, but I digress, the reference below explains all that). Now and here’s the real challenge, you want to keep the axis of the solstice clear, in other words you have to place four of your thirty stones at their correct spacing either side of the ‘solar corridor’. Easy, is it really? Don’t forget that the joints in the lintels are supported in the centre of the uprights, and that the middle of the flatter (prepared) inner faces are set almost perfectly to the vertices of a regular 30 sided polygon (a triacontagon to be precise).
So how do you do it, for they did, and with great accuracy. How do you created a 30m diameter 30-gon on the ground, and ensure that the axis of the structure (within which there are further mirrored symmetrical structural elements, some up to 50 tons) is preserved. What’s more these central stones, the ‘Trilithons’ had to in position before the Circle! When you begin to explore the possibilities you enter the prehistoric mindset behind the design of Stonehenge, you are using evidence manifest in the structure itself. Now look again at all the ‘theories’ and see if they still make sense, for example the idea that the stones themselves were aligned on some distant object, the moon or constellations. Remember you are now the prehistoric surveyor, what exactly are your priorities….