Since I am attempting to give new consideration to the still unsolved problem of ideal approximation of Mercury’s Orbital and Synodic Periods, perhaps it’s timely to also want to give new consideration to the still uncertain cycles of Mars as well.
The majority of mathematical probes seem to want to give a primary value of 779.2727272 (Pi^4 x 8) for the textbook Mars Synodic Period value of 779.96 days, and 687.5493542 (2160 / Pi) for the textbook Mars Orbital Period value of 686.971 days.
If this is correct, the deviations themselves aren’t particularly troubling, but the logic in organizing them may remain somewhat elusive. With 779.2727272 as the A value for the Mars Synodic Period (MaSP), only the B value will be higher, which means that in this case, only the resulting B value of 779.2727272 x 1.000723277 = 779.8363583 may be near enough to the target figure to serve the use of more accurate approximations.
One possible solution to this is that there are two different sets of figures for the MaSP, although this may seem more challenging to justify in the way that multiple values have been justified thus far. For the Solar Year or Lunar Year, it’s easy to accept “calendar” values near to 365 or 354 and more accurate figures nearer to 365.25 and 354.36, but in the case of Mars the “textbook” figure is already nearer to the “canonical” figure of 780.
In order to rationalize two valid sets of figures for the Mars Synodic Period, the validation might benefit from any historical references that can be located to variant formulas.
This may clearly be the case with the Mercury Synodic Period. From the preceeding post on Mercury,
“Pages 30c-33c of the Dresden codex are a Venus-Mercury almanac. The 2340-day length of the Venus-Mercury almanac is a close approximation of the synodic periods of Venus (4 x 585) and Mercury (20 x 117).”
Which do represent historical departures from the more accurate whole number figures of 584 and 116. The same is the case with 364, a departure from the representation of the Solar Year as 365 days. These variations are clearly subject to the use of diverse formulas which may have certain advantages and disadvantages. The Mayan Calendar Number 819 = (225 x 364) / 100, indicating that 364 was used by the Maya to represent the Solar Year, apparently in association with certain formulas, while other formulas use 365 (18980 / 52 = 365).
Already we can expect that the Venus Synodic Period and Mercury Synodic Period may therefore present as multiple sets which represent adaptations of different formulas, and we may expect that because of the observance of alternate formulas, that there will be third set if values for the Solar Year so that 364, 365, and 365.25 are all represented by the refined mathematics that seem to have been applied to the recording of astronomical data through architectural measurements and proportions.
While these considerations may help to validate a figure of 779.2727272 for the MeSP as legitimate, they also represent the growing challenge of an ancient calendar system further expanding even while understanding a less expansive form of calendar system is still a work in progress.
(I’ve seen numerous values resembling 364, but know relatively little about them because they were not collected or studied further. My hope has been in fact that the proceedings would not reach that level of complication, and working out the ancient use of ~365 has itself proven an ample plateful – but a valid role for ~364 it does seem to be inevitable sooner or later – the 819 formula is probably enough to indicate that).
Some of the things that we do know about 779.2727272 thus far include:
779.2727272 / 10 ft is a good possibility for the diameter of the Stonehenge Bluestone Circle, based on Thom’s data. This is refined by observation of an obvious geometric formula and the primary value of 2.720174976 ft as the (“linear”) Megalithic Yard.
(57.29577951 / 2) x 2.720174976 = 77.92727272
The perimeter value is equal to 90 of such a Megalithic Yard.
(77.92727272 x Pi = perimeter 244.8157478 ft) / 90 = 2.720174976
However this seems as if inadequate explanation for its presence at Stonehenge since it is very close to a calendar number, in a setting where calendar references seem to abound.
We may wish to note that 77.92727272 / 3 = 25.97575761, 1/2 of the outer sarsen circle radius given for Stonehenge. The suggestion indeed appears in literature that the figure of 780 represents the “triple Tzolkin”.
One of a great many additional things we can observe is that with a suggested possible figure of 779.2727272 as MeSP A and a newly suggested possible value of 87.79326992 for the Mercury Orbital Period, their ratio is 779.2727272 / 87.79326992 = 8.876223995.
8.876223995 x 100 (aka “SRVS”, Square Root of the Volume of Sphere) is a recently suggested possible value for the minimum (inner) circumference of the Aubrey Circle, which is part of set of possible proportions linked together by the Pi ratio.
Reckoning the value of 779.2727272 in Petrie Stonehenge Units in inches (or simply dividing it by the primary approximation of the Venus Orbital Period) gives
779.2727272 / Venus Orbital Period 224.8373808 = Eclipse Year 346.5939362 / 100.
779.2727272 / mean diameter sarsen circle 100.6036769 = 1.290994452, the most powerful mathematical probe / data retrieval tool known, a very valuable complement to Stonehenge’s mathematics. This is the reciprocal of sqrt 60 (one of the numbers that Munck told us belong to Stonehenge), sqrt 60 in “Imperial” feet also be the likely value of Thom’s Mid-Clythe Quantum.
When exposed to Stonehenge’s customary value of 360 / 1.177245771 = 305.7985077 ft (see Petrie, Atkinson, Munck, etc) = 360 Inverse Megalithic Feet
779.2727272 / (305.7985077^1) = 2.548320899 = 3 / Megalithic Foot = Lunar Year x 72 / 10^n
779.2727272 / (305.7985077^2) = 8.333333333 / 10^n = the reciprocal of 12
779.2727272 / (305.7985077^3) = 2.725105953 / 10^n = the “Lintel Megalithic Yard”
779.2727272 x (305.7985077^1) = 238.3004373 x 10^n = Michael Morton’s “Great Pyramid Apex Grid Point” value. It’s a still underestimated and underappreciated number that merits more attention than it tends to get, even if there may be limits to its level of integration with the more important numbers from Stonehenge.
It give us a good opportunity of course to see that the given value for the inner sarsen circle circumference isn’t merely a consequence of the chosen radius value – the circumference figure can have exponential value, which is always an asset to metric data storage and retrieval. This is why “Pi Jedi” should want to keep Pi “pure”, so that its profound exponential powers remain intact. There are numerous figures similar to Pi that see might see in various situations, but in contrast to other independent research, none of them are, or need be, applied to projections of circular measures.
At any rate, the passage quoted again above may lend more confidence to the idea that values for Mercury and Mars may among those that have been particularly difficult to pin down to a single set of approximations, because even if surprisingly, they may be better geared to multiple sets of approximations.
At present I’m aspiring to revisit that multiplicity in more depth, although it a a complex and time consuming process not only to work with the figures but to locate literature as well, even though the present example of Mercury’s cycles clearly shows how advantageous it can be to consult historical references on the matter as well as exploring mathematical relationships between given figures.
Without comprehensive access to relevant materials, it might be difficult to say if the entirety of rationale for the variations in Mercury figures has been presented by anyone or whether my observations or those of others are entirely novel.
I could point out some initial impressions for whatever they are worth:
780 / 585 = 1.33333333 (essentially the same ratio as Eclipse Year 346.62 / Tzolkin 260 we presume), so we can see where choosing 585 over 584 makes the Venus Synodic Period of ~584 days makes figure value more harmonious with the Mars Synodic Period of 780 and others.
For the main approximations 779.2727272 and 584.0321292, we would find the ratio
779.2727272 / 584.0321292 = 1.334297701 = 10.67438159 / 8
780 / 117 = 6.66666666, so we can see that the choice of the excessive figure 117 to represent Mercury’s ~116 day Synodic Period (MeSP) establishes a simple albeit reciprocal relationship with the Mars Synodic Period (MaSP), something else that might have made the figure of 117 an attractive alternative for some calendar formulas devoted to subsets of the Calendar Round.
Notably, 18980 / 117 = 162.2222222, which is harmonious with the Earth / Venus ratio of 365 / 225 = 1.622222222, and indicates that we may be able to form the correct approximation of “117” (and hence also 585 since 585 x 2 = 1170) from some form of the Calendar Round value and 1.622311470.
Using the A value for the Long Count = Calendar Round = Half Venus Cycle
18983.99126 / 1.622311470 = 1170.181658 = 2340.363316 / 2. This is almost four times the “Real Mayan Annoyance”, a fact that might be considered when trying to calibrate the figures toward the intended one. However, the B value for the Half Venus Cycle does not give the “RMA” either. It is the C value for the HVC which bears that distinction.
585 / the Tzolkin 260 = 225 / 10. It was part of proceedings of considering the right value for the Petrie Stonehenge Unit that 25.97575757 x 224.8373808 = 584.0321298 (in feet, 480 Remens). Various alternatives like 585 may have escaped notice because in cases the need for them may have been circumvented by the utility of the usual numbers.
585 x 225 = 365 x 360 (this also provides the mean circumference of the earth in feet for those willing to consider the prospect of ancient geodesy, though the usual numbers serve here as well. 584.0321298 x 225 = 365.0200808 x 360).
Intriguingly, 225 / 117 = 18980.00846 / (Pi^2) – almost perfectly – and 117 / 225 = 52 / 10 (see the 52 posts asserted for Stukeley’s alledged second Aubrey circle), which comes with 260 x 2 being 520. Again, if the Aubrey Circles were phased out by a redesign of Stonehenge, the function of the 52 posts would seem to have been repurposed through the used of Imperial feet in the sarsen circle.
I might take the opportunity to point out that the Squared Munck Megalithic Yard x 260 is (2.719715671^2) x 260 = 18981.04421 / (Pi^2), a fact that may also be meaningful. Perhaps the Squared Munck Megalithic Yard is getting overshadowed lately by the necessary emphasis on exploring various linear forms of the unit, including several which have only recently received my “endorsement” after years of deliberation about their validity as Megalithic Yard values.
So we can see that there might be considerable merit to alternative values for not only the Mercury and Mars Cycles, but others as well, although this exercise has also hinted that the functions of analogous values may not all be directly transferable, making prediction of the most ideal values more challenging, as does a clack of familiarity on my part with the alternative values and their properties.
The nomination of ~117 also merits some research on my part. I’ve written before about some efforts to sort out more than one significant constant in that range, although the location of the material currently eludes me. The numbers in question are probably among neglected numbers themselves. Several of these numbers are currently considered positive responses to mathematical probes, although I’ve sometimes omitted them from the disclosures for convenience.
I somewhat regret then to announce that the handiwork of some sort of “ancient NASA” seems to appropriately get more like “rocket science” all the time. It seems to be what many of have hoped for or even advocated, that ancient man was able to accomplish far more with mathematics than he is being credit for. One the other hand, it’s exciting to see what all these new prospects might actually have in store for us.
I should note that one of my compatriots in alternate mathematical and metrological research, Bogna Krys, probably warned me that things might get this complicated, but at the time I probably wasn’t able to correctly infer it from the expressions in his particular mathematical dialect.
–Luke Piwalker
Luke Piwalker 