Robert Tulip wrote:Leonardo's use of the zodiac here involves no astrology. It is just astronomy, just stars, just observation of the path of the sun against the galaxy, 100% empirical description.

johnson wrote:

Penelope,

Can you elaborate on the geometric orbits?

Orbits are eliptical.

johnson wrote:

gotcha.

Thanks, Penelope.

johnson1010 wrote:Penelope,
Can you elaborate on the geometric orbits?
Orbits are eliptical.
Take a look at this thread where we have been having fun with orbits. (yes. i said fun. *push up horn-rimmed glasses*)
http://www.booktalk.org/planetary-orbit ... t8576.html
of particular interest might be this link
http://www.wimp.com/earthyear/
which is a nice illustration of what our orbit actually looks like. All orbiting objects necessarily share similar orbits as their mass pulls against the sun, as well as all the other objects it pulls the center of the orbit slightly out of center, creating an elipse.
Objects on different trajectories are either ejected from the solar system, or collide with one of the stable orbits.
Sorry Robert, slightly off-topic here.

The Earth Venus conjunction features interestingly in The Da Vinci Code. Because 13 Venus years are almost precisely equal to 8 Earth years, there are 13/5 = 2.6 Venus years for each 8/5 = 1.6 earth years. The common "0.6" in the two cycles means that when Venus has orbited 2.6 times, the Earth has orbited 1.6 times, so they line up exactly again with the sun. The five inferior or superior conjunctions are therefore at 1.6, 3.2, 4.8, 6.4 and 8 earth years = 2.6, 5.2, 7.8, 10.4 and 13 Venus years. For example, the inferior conjunction of Earth and Venus on 18 August 2007 was the fifth such event since the same date in 1999. These five points form a perfect pentagram in space, the divine shape of Pythagorean lore and the Vitruvian Man by Leonardo, as discussed by Dan Brown. There is reportedly a 0.0789 day slippage of this pentagram every 584 days.

The inferior conjunction of Venus occurs every 583.93 days as Venus passes between the Earth and the Sun. Most recent was 18 August 2007. The period for every fifth event is eight years minus 2.4 days, so it will happen on 16 August 2015. This regular period, due to the 13/8 relation between the orbits of Venus and Earth, also applies to the superior conjunction (Venus behind Sun), the dates of change to forward and retrograde motion, and the dates when Venus is at maximum apparent angle of 45-47 degrees each side of the sun. Venus was recently at maximum angle on 9 June 2007 and went retrograde on 30 July. In eight years, it will reach these positions on 7 June 2015 and 27 July 2015 respectively, 2.4 days before the corresponding days this year.

For the ancients, the date when Venus as evening or morning star changed direction could have been a main temporal marker, observed 2.4 days earlier against the zodiac stars every eight years. I would be interested in any information on this - did the ancients monitor the apparent 2.4 day precession of the position of Venus each eight years? This movement is certainly much easier to observe than the precession of the zodiac recorded by Hipparchus in the second century BCE.

The ten points of the apparent change of direction of Venus (five each for the evening and morning stars) form two pentagons, each evenly spaced around the zodiac. These pentagons precess with an orbital period of about 1217.5 years, as do the inferior and superior conjunctions. The Pythagorean School of ancient Greece used the pentagon as its symbol, (http://en.wikipedia.org/wiki/ Pythagoreans. They had a strong interest in the mathematics of celestial observation, and had cultural affinity to the themes of beauty and love symbolized by Venus/Aphrodite. For these reasons, I imagine it is likely the Pythagoreans monitored this nearly exact eight year cycle. Would their secrecy mean we will never know?

Fifty years of Venus Dates

Inferior Conjunction; 10/11/1970; 18/6/1972; 24/1/1974; 28/8/1975; 6/4/1977; 8/11/1978; 15/6/1980; 21/1/1982; 25/8/1983; 4/4/1985;
5/11/1986; 13/6/1988; 19/1/1990; 23/8/1991; 2/4/1993; 3/11/1994;
11/6/1996; 17/1/1998; 20/8/1999; 30/3/2001; 31/10/2002; 8/6/2004;
14/1/2006; 18/8/2007; 28/3/2009; 29/10/2010; 6/6/2012; 12/1/2014;
16/8/2015; 25/3/2017; 27/10/2018;

Average Days between aspects: 583.93
Year x 8/5: 584.4 days
Days lost per eight year cycle: 2.4
Years lost per 8 yr cycle: 0.0065708
Cycles per precessional rotation: 152.19
Years per Precessional rotation: 1,217.5
Years per pentagon point precession: 243.5

Robert wrote:

The geometry of the relation between Earth and Venus is actually entirely on topic and I had already raised it myself, but naughty Penelope neglected to quote.

The Secret Code of Leonardo da Vinci
It is one of the most famous and enduring works of art in all the world. Leonardo da Vinci's fresco The Last Supper is the one surviving piece of the original church of Santa Maria delle Grazie near Milan...

Leonardo's [painting of the last supper] has for some reason captured the imagination more than most ... Some images may be so familiar that they are never truly examined, and although they lie openly before the viewer's gaze and invite closer scrutiny, at their most profound and meaningful level they actually remain totally closed books. So it is with Leonardo's Last Supper... Generations of academics had simply not observed what leapt to our startled notice... such explosive information had lain patiently waiting all this time for writers like us from outside the mainstream of historical or religious research to discover.

So to begin our story proper we have to return to Leonardo's Last Supper and look at it with new eyes... to let the scales of preconception fall from one's eyes and perhaps for the first time really look at it... Leonardo must have hoped that perhaps others who shared his unusual interpretation of the New Testament message would recognise his version, or that someone, somewhere, some objective observer, would one day seize on the image ... and ask the obvious questions...

We have often heard it said that Leonardo was a pious Christian whose religious paintings reflected the depth of his faith... Nothing could be further from the truth than the idea that Leonard was a true believer - a believer, that is, in any accepted... form of Christianity. Already, the curious and anomalous features in just one of his works seem to indicate that he was trying to tell us of another layer of meaning in that familiar biblical scene, of another world of belief beyond the accepted outline of the image... Whatever those heterodox inclusions may mean, they were... totally at variance with orthodox Christianity...

Leonardo was the first real scientist, a man who had no time for superstitions or religion in any form, who was the very antithesis of the mystic or the occultist. Yet [materialists and rationalists] have failed to see what is plainly set out before their eyes...

Leonardo's other works ... underline his own specific heretical obsessions through carefully applied and consistent imagery... they are not just the equivalent of sticking a red nose on St Peter, for example. What we are looking at in The Last Supper and other works is the secret code of Leonardo da Vinci, which we believe has a startling relevance for the world today....

He despised fortune tellers but his accounts list monies paid to astrologers ... he was both a profound thinker and a master of riddles... there was surely no need for him to put his head on the block by working such heretical messages into his paintings unless he had a passionalte belief in them ... Leonard was deeply, seriously committed to a system of belief that ran totally counter to ... mainstream Christianity.

The lynchpin of all the groups of the day was hermeticism, which takes its name from Hermes Trismegistus, the great, if legendary, Egyptian magus... the most important part of hermetic thinking was the idea that man was in some way literally divine - a concept that was in itself so threatening to the Church's hold on the hearts and minds of its flock as to be deemed anathema... Giordano Bruno (1548-1600) ... proclaimed that his beliefs came from an ancient Egyptian religion that preceded Christianity - and which eclipsed it in importance ... given the risks involved in being openly part of them, it is unlikely that Leonardo would commit any evidence of this to paper...

was the message that can be read into his paintings in some way actually true?