Anthony Johnson has kindly made his and Alberto Pimpinelli's paper on laying out a 56 sided polygon using just pegs and ropes available on Academia.org. Of course this isa proposed solution to the the laying out of the Aubrey Holes.
"A recent computer-aided-design investigation of the Neolithic 56 Aubrey Hole circuit at Stonehenge has led to the discovery of an astonishingly simple geometrical construction for drawing an approximately regular 56-sided polygon, feasible with a compass and straightedge. In the present work, we prove analytically that the aforementioned construction yields as a byproduct, an extremely accurate method for approximating a regular heptagon, and we quantify the accuracy that prehistoric surveyors may have ideally attained using simple pegs and ropes. We compare this method with previous approximations, and argue that it is likely to be at the same time the simplest and most accurate. Implications of our findings are discussed."
They even bring in Plutarch's Moralia. Isis and Osiris "It is plain that the adherents of Pythagoras hold Typhon to be a daemonic power; for they say that he was born in an even factor of fifty-six; and the dominion of the triangle belongs to Hades, Dionysus, and Ares, that of the quadrilateral to Rhea, Aphroditê, Demeter, Hestia, and Hera, that of the dodecagon to Zeus,c and that of a polygon of fifty-six sides to Typhon, as Eudoxus has recorded."
Everybody loves Tony Johnson — hey — me too. On paper this formula looks very reasonable and concise.ReplyDelete
In practice? Holy cow! W A Y too complicated.
Stick-and-rope, for sure. There's our compass.
Straight-edge? Well, we have a perfectly good sunline for that, and according to what I see in the Aubrey layout, that's what was used from -56 to -28, or the axis of the circle. (This would be a Stone-97 axis, by the way.)
The circle is very good — among the most accurate for that time — much better in fact than the henge ditch itself.
The spacing of holes along the circuit? Not so much. They have an average, certainly, but there are some key places where that average falls apart.
The reason (I believe) is that, in many instances Holes align across the diameter of the circle, based, not only on the sun at the time, but the cardinals as they understood them. When all the solar and cardinal errors were corrected a couple of hundred years later, the alignments fall away, so we simply don’t see them anymore. But if you use S-97 as a base line, they all show up clearly. Go ahead and use that great diagram they use in the paper. It's right on the button.
So external to the computation is the physical needs of the circle. That is, yes to simple geometry in making it, but they followed the sun, moon and incorrect cardinals in aligning them, and this explains the weird spacing.
The number of them are both multiples and derivatives of lunar-based periods of time. Weeks, seasons, solstice, equinox, and the Standstill cycle. 7/14/28/42/56. This shows that those folks could certainly count, do basic arithmetic and probably associate naturally accruing numbers to naturally occurring events, such as above.
But they wouldn't need Texas Instruments to place those Holes.
They would all fall within the sines, coefficients, arcs and other geometry whether they knew about Euclidides or not. Conversely, the circle and hole-placement themselves show that, under perfect circumstances of peg-and-rope, transits and range-finders, they did a sloppy job. So, as we know they could make a good circle, it makes no sense that they couldn’t put a rope-length of 16.24 feet between hole-centers and call it a day. It’s because there’s a large balance of incidences where the placement was meant for something other than symmetry.
As many know, I too believe they used a square to shape the three initial, equidistant circles, and this rationale is explained in detail elsewhere. But I also believe that this is as far as the complex geometry went.
As a stand-alone concept, it would still have been amazing at the time.