The above image shows Venus transiting the sun as seen from the top of West Kennet Long Barrow after sunrise on 6th June 2012. Although I managed to capture a full minute of this on a handheld HD video camera on a cloudy day, it did take me 22 minutes focussed on a bright patch of the sky to get it.

If you’re *really* keen the full video can be seen here You might want to start watching at 8.07. It zooms out and comes down to Earth at the end, so that you can see that it really *is* taken from the top of West Kennet long Barrow. I spoke briefly afterwards to the man in the hat you can see at the end; he had been involved in a Venus transit ritual, along with a woman who had sat inside the long barrow earlier while I was filming from the top. It was a cloudy day and I don’t know whether either of them realised that the transit had in fact been briefly visible. I didn’t even know myself that I had captured it on the video until I got home and played it back.

These transits occur in pairs 8 years apart, with the pairs more than a hundred years apart, so without the internet and Stellarium to warn me it was going to happen I would never have stood a chance of seeing or recording it, so no, I do not think that Neolithic skywatchers could have kept track of the movements of Venus by observing its transits. I do however think they could have kept track of its patterns by observing its maximum elongations from the sun since these can potentially be observed and measured over the course of successive mornings or evenings. Its positions on the ecliptic could also have been understood and recorded.

Since moving North and beginning in 2019 to examine the geometry of Cumbrian stone circles I am finding further indications of an understanding of the ecliptic, eclipse cycles and a zodiac divided into 12. This is backing up my findings at Avebury of geometry for eclipse cycles and a circle or calendar divided into 12.

At Avebury there are also a lot of divisions into 13, as if they ran a 12 month and 13 month calendar concurrently, but I am not yet (November 2019) finding these 13 month years in the northern Circles.

Anthony Johnson recognised a Pythagorean type of geometry at Stonehenge in the same way as I have at Avebury. The reason I compare the geometry of Avebury to Pythagorean geometry is not because of any three-four-five or other Pythagorean triangles but because the geometry of Pythagoras included star-shaped patterns and was associated with a belief in the music of the spheres.

The concept of the Music of the Spheres appears to have arisen from the many harmonious proportions which can be found in the patterns of the cosmic cycles, and which are therefore part of nature. Pythagoras seems to have considered these ratios to be akin to the manner in which proportional relationships in lengths of strings produce sounds at harmonic frequencies. He also believed that numbers were sacred. There was however an element of dogma and secrecy in these beliefs which would, or clearly should, be at odds with today’s professed ideal of the scientific method.

We do not really have surviving evidence from Pythagoras of how exactly his planetary geometry connected up with musical harmonies but the nature of the belief is described and the idea seems to have survived for a very long time. Among all the later mystical allusions to this idea however it is very difficult to find any credible geometry which shows how it actually works.

I think that what I am finding, and am still investigating, is likely to be the original geometry behind these ideas.

In my investigation of the geometry of Avebury I was struck by the number of patterns I found which were regular polygons or polygrams having relatively small numbers of points. One would expect an accurately measured random set of angles to tend to produce patterns with large numbers of points, whereas at Avebury, as I discovered, the geometry produces a surprisingly high proportion of integer fractions with small integers; a pentagram for example is drawn using an angle of 144º or 2/5 of a circle. A seventeen-pointed shape is drawn using the fraction 4/17 and also using 8/17.

The Pythagoreans believed that numbers were sacred, and seem to have shared with the ancient Britons this liking for integer fractions, so much so that they (the Pythagoreans) were very upset by the discovery of irrational numbers. They hated them so much in fact that they are even rumoured to have killed one poor man for revealing the terrible truth about the square root of two; i.e. that it is an irrational number. If this is true then it would seem to indicate that the Pythagoreans suffered from a conflict between science and dogma. Some of their dogma looks very much like superstition, and so I can’t help but wonder whether these attitudes may ultimately have led to their downfall.

The one person person in history who comes close to explaining or demonstrating the idea of the Music of the Spheres in clear terms is Johannes Kepler. There are others who have much to say on the subject but only in general terms. Kepler studied the cycles of the planets and calculated ratios between their orbit lengths. He also famously fitted the platonic solids inside one another in a manner which enabled all the points of each one to touch the faces of the one outside it. Kepler also investigated the relationships between musical harmonies. He did have religious beliefs; Kepler was a scientist who believed that god created the universe with a rational plan.

I’m inclined to feel that the architects of Avebury were more pragmatic than the Pythagoreans and maybe more like Kepler, and that whether or not they had any concept of irrational numbers, they knew they were choosing their integer fractions as close approximations for the real and complex ratios in the cosmos. Their calendar would have needed constant recalibration to correct for the small margins of error resulting from their use of integer fractions, so the continual search for ever better approximations to reduce this need would have been of major importance to them. It might even be the reason they made Avebury so huge, and they might not have been actively hostile to irrational numbers so much as very fond of closely approximating integer fractions for ease of practical use, whether ratios in Neolithic sites were set out by chains of people linking hands or with knotted ropes.

(Page updated 23/11/2019)

Gramus Hyperboricus Publications © Marina Graham 2016