The Roots of the Year

In going over a notebook from 2002 I thought it useful to review some material here to do with the numerical factors of the solar year that are present in the movement of the Moon's nodes that locate where eclipses can occur. The root involved will be shown later as a solution to a quadratic equation but first it is necessary to get the strange background of how the Moon's nodes are synchronous to the year.

The Eclipse Year (time for the sun to arrive at a given node again) is 346.42 days and this is the square of 18.618. The Solar Year of 365.242 days is 18.618 times 19.618 or 18.618 (18.618 + 1). This sort of thing caused my brother and I to find a lot of 18.618 factors. In a single day the nodes move 1/18.618 as fast as the Sun has, in the opposite direction, i.e. retrograde. In 18.618 days the nodes have moved the same distance that the Sun moves in a single day (the Heath brothers' term for this being one Node Day).The difference between the eclipse and solar years is just one node day.  The nodes precess completely in 18.618 years, which is 19.618 eclipse years, a period called the Draconic Period, since eclipses were associated with sun or moon being eaten by a dragon, one node being its head and the other its tail.

This all seems rather a coincidence! It is as if the year, numerically, is normalised in some way to the year and this triggers all of those "design" issues that imply that this could not have come about by accident. It could be due to some natural "great attractor", namely the Moon, solving something like a quadratic equation all by itself or the earth - Sun - Moon system is set up in a special and unique way.

For 18.618 to factor into the year, then if x = 18.618 then the solar year can be viewed as (x² + x) in which case the day is 365.242 / (x² + x). This can be turned into a quadratic as per x² + x - 365.242 = 0 whereupon the formula for solving quadratics yields the two solutions 18.618 and 19.618.

Since the solar year cannot be greatly affected by the lunar orbit, the nodes of which are precessing as above, then one has to note that it is the day length within the year that, in dividing up the Earth's orbit to give number to the solar year, is normalised to this solution according to the movement of the Moon's nodes.

It appears then that the surface of the Earth rotates at such an angular velocity so that the number of days and the rate of nodal movement generate this coincidence. In terms of physical forces, this can only occur if the precession of the lunar nodes is interactive with the earth's rotation.

We know that all precession is caused by forces that try to pull a spinning or orbiting body out of its polar alignment. Whilst the Moon orbits the Earth, the Earth cannot generate such a force. It is the Sun and planets that do this. Therefore it is difficult to have the Earth's rotation and the Moon's orbital precession linked.

What we are left with is a scientific blank as to the cause of the 18.618 factor in the solar year. I tried to get the issue raised in Nature and Monthly Notices of the RAS but was of course re-buffed with peer review and binning. It appears that the design hypothesis is the only explanation for this numerical coincidence partly because it is no explanation at all.

It appears that in modern science the unusual nature of such phenomena cannot be considered an opportunity rather than a threat to the scientific paradigm itself. If only properly trained mathematicians or physicists were to look at it they might find out something really interesting.

The question is "What is x?". Otherwise it is "Who is x?". Fred Hoyle even supposed in his On Stonehenge book that

Could a distant memory of S[un], M[oon] and N[ode] be the origin of the Trinity, the 'three in one , the one in three'? I suspect so. [page 133]

The three certainly seem to work in perfect harmony according to 18.618, though N wears dark glasses and is an invisible god. For more on 18.618 see my posting on Nineteen and the Moon. In the relevant N:N+1 triangle shown below, the third side is 6.1835 which is closely 10 times 1/ golden mean, and the 19 long intermediate hypotenuse has a third side length 1/ golden mean of this and is 10 times 1/ (golden mean)². 19.618 is the angular separation of the Sun and nodes per Node Day, measured in DAYS of angle. Using degrees instead completely loses the significance. The DAY in angle reveals the number magic of time as angular motion related to the Earth.