Interpreting Lochmariaquer in 2012, an early discovery was of a near-Pythagorean triangle with sides 18, 19 and 6. This year I found that triangle as between the start of the Erdevan Alignments near Carnac. But how did this work on cosmic N:N+1 triangles get started?
Robin Heath’s earliest work, A Key to Stonehenge (1993) placed his Lunation Triangle within a sequence of three right-angled triangles which could easily be constructed using one megalithic yard per lunar month. These would then have been useful in generating some key lengths proportional to the lunar year:
the number of lunar months in the solar year,
the number of lunar orbits in the solar year and
the length of the eclipse year in 30-day months.
all in lunar months. These triangles are to be constructed using the number series 11, 12, 13, 14 so as to form N:N+1 triangles (see figure 1).
n.b. In the 1990s the primary geometry used to explore megalithic astronomy was N:N+1 triangles, where N could be non-integer, since the lunation triangle was just such whilst easily set out using the 12:13:5 Pythagorean triangle and forming the intermediate hypotenuse to the 3 point of the 5 side. In the 11:12 and 13:14 triangles, the short side is not equal to 5.
Only two type-D stone circles (see figure 3) are
known to exist, called Roughtor (in Cornwall) and Seascale (in Cumbria). Seascale
is assessed below, for the potential this type of flattened circle had to
provide megalithic astronomers with a calendrical observatory. Seascale could also
have modelled the harmonic ratios of the visible outer planets relative to the
lunar year. Flattened to the north, Seascale now faces Sellafield nuclear
reprocessing plant (figure 1).
Stone Age astronomical monuments went through a
series of evolutionary phases: in Britain c. 3000 BC, stone circles became
widespread until the Late Bronze Age c. 1500 BC. These stone circles manifest
aspects of Late Stone Age art (10,000 – 4500 BC) seen in some of its geometrical
and symbolic forms, in particular as calendrical day tallies scored on bones.
In pre-literate societies, visual art takes on an objective technical function,
especially when focussed upon time and the cyclic phenomena observed within
time. The precedent for Britain’s stone circle culture is that of Brittany,
around Carnac in the south, from where Megalithic Ireland, England and Wales probably
got their own megalithic culture.
Natural time periods between celestial phenomena
hold powerful insights into the numerical structure of time, insights which
enabled the megalith builders to access an explanation of the world unlike our
own. When looking at two similarly-long time-periods, the megalithic focussed
on the difference between them, these
causing the two periods to slide in and out of phase, generating a longer
period in which the two celestial bodies exhibit a complete ensemble of
variation, in their relationship to each other. This slippage of phase between
celestial periods holds a pattern purely based upon number, hidden from the
casual observer who does not study them in this way. Such numerical patterns
are only fully revealed through counting time and analysing the difference between
For example, the solar year is
longer than the lunar year by 10 and 7/8 days (10.875 days) and three solar
years are longer than three lunar years by three times 10.875 days, that is by 32
and 5/8th days (32.625 days), which is 32/29 of a single lunar month
of 29.53 days.
The earliest and only explicit evidence for such
a three year count has been found at Le Manio’s Quadrilateral near Carnac (circa
4,000 BCE in Brittany, France) used the inches we still use to count days, a “day-inch”
unit then widespread throughout later megalithic monuments and still our inch,
1/12 of the foot [Heath & Heath. 2011]. The solar-lunar difference found
there over three years was 32.625 day-inches, is probably the origin of the
unit we call the megalithic yard and the megalith builders appear to have
adopted this differential length, between a day-inch count over three lunar and
solar years, in building many later monuments.