The Fibonacci series is an ideal pattern, widely found within living systems, in which the present magnitude or location of something is the product of two previous magnitudes or locations of it. The next magnitude will again be the sum of the last two magnitudes in what is, an algorithmic pattern producing approximation to the Golden MeanThe Golden Mean is that unique ratio {1.618034}, relative to ONE {1}, in which its square and reciprocal share the same fractional part {.618034}. It is associated with the synodic period of the planet Venus, which is 8/5 {1.6} of the practical year {365 days}, by approximation. It is a key proportion found in Greco-Roman and later "classical" architecture, and commonly encountered in the forms living bodies take. (designated by the Greek letter φ,’phi’). As the series gets larger, the ratio (or proportion) between successive magnitudes will better approximate the irrational value of φ = 1.618033 … – which has an unlimited fractional part whilst the virtue of the Fibonacci numbers within the Series is that they are integers forming rational fractions.
The Background
The Fibonacci series is {1 1 2 3 5 8 13 21 34 55 89 144 233 377 …}, and one can see the convergence of successive pairs as 1, 1.5, 1.666, 1.6, 1.625, 1.615, 1.619, 1.6176 and so on, the last one shown being 55/34 which relates the synods of Venus and Jupiter. In a previous blog, earlier members of the series are seen to give solar yearFrom Earth: the time in which the sun moves once around the Zodiac, now known to be caused by the orbital period of the Earth around the Sun. as 13/8 of the orbit of Venus whilst the synod of Venus (1.6 solar years) is 8/5 of the practical year of whole 365 days (Maya Haab).
The unique virtue of the Golden Mean (1.618) within the world of numbers is that it retains its fractional part (0.618) as its reciprocal (0.618), and also within its square (2.618 = 1 + 1.618), whilst the reciprocal of its square is 1 – 0.618 = 0.382! This property allows complex patterns to emerge in time within space, as within spirals of seeds in corn heads.
When the Golden Mean is found within astronomical time between celestial cycles, as with Venus, this occurs because of the recurring nature of celestial orbits which makes the numbers of the Fibonacci series able to divide into both a lesser cycle and a greater cycle. When the 8/5 (φ) year length of Venus’s synod is divided by the 8/13 (φ) year length, the result is 13/5 = 2.6 (φ squared) as the number of orbits in the synod. The practical year of 365 days takes the role of ONE (1).
This business of φ with respect to Venus is not mentioned by modern planetary astronomers and public interest in it is slighted with the notion that it is a simplistic coincidence despite the influential role of the Golden Mean within architecture and religious symbolism. Once one connects Fibonacci numbers as connecting Venus and Jupiter, φ becomes less ignorable; as a cosmic factor within celestial dynamics.
Jupiter and Venus
In January 2002 I was intrigued to find that Indian astronomy note the average motion of Jupiter through a complete zodiacal sign as being a Brihaspati samvatsara – a year of Jupiter 361 (361.026721) days long. This divides into the Venus synod as 583.92/ 361.026721 = 1.617387. This almost exactly matches 55/34 in the Fibonacci series (to better than one part in 6000).
As Jupiter passes through the 12 signs, Venus has 7.4194 synods and this number is familiar as the square of 2.7238 – reminiscent of the megalithic yardAny unit of length 2.7-2.73 feet long, after Alexander Thom discovered 2.72 ft and 2.722 ft as units within the geometry within the megalithic monuments of Britain and Brittany. in feet and e, the exponential constant. But the Indians count 60 samvatsaras as the sixty-year cycle of Jupiter, and within this 37.096868 Venus synods occur and this is a macrocosm of the number of lunar months (37.1) in three solar years (37.1048 lunar months) within better than one part 4500.
The Brihaspati samvantara appears unique to the Indian astronomers who are conventionally thought to have got their astronomy from the Greeks and/or Chinese – ignoring the historical depth of their own traditions. And it is the tradition of Jupiter traversing the zodiacal signs in the 361-day year (numerically 19 squared) that appears impossible to have come from the northeast or the west.
And in it we find a matrix parallelism between (a) the triple orbital year of the Earth and the lunar month and (b) the Jupiter cycle of 60 samvantaras and the synods of Venus. If one divides 20 samvantaras by the Venus synod one gets 12.3647 synods whilst the solar year contains 12.368266 lunar months which is very close to numerically identical. This is the sort of matrix relationship which figured strongly in my Matrix of Creation (2002) and so, it is time to draw it as below.
Jupiter and Venus are the brightest planets whilst the sun and moon are the brightest luminaries in the sky. There is therefore a subtle relationship, involving a specific pair of Fibonacci numbers, linking the Moon and Sun within the Year to, the Venus synod and Jupiter’s samvantara, unique to Indian astronomy, within the repeating patterns of ‘Eternity’.
The reader might agree that this is an unlikely scenario and yet the orbits of Jupiter and Venus combine with that of the Earth to then, according to the repeated four-square (a.k.a. Robin Heath’s Lunation TriangleThe right-angled triangle within which the lengths of the two longer sides are the relative proportions of the solar and lunar years.) geometry, cause the division of the ZodiacThe 12 constellations through which the sun passes in the solar year of 365.2422 days/ecliptic into twelve parts. The Moon is the only body that has seen significant lengthening of its orbit, to eventually achieve this division of 12 within the solar year, according to this geometrical archetype.
References
The Indian Calendar by Robert Sewell and Sankara Balkrishna Dikshit. Delhi: Motilal Barnasidass 1995. pages 32-33.