Greetings, all – and a Safe and Happy Thanksgiving, even to those who don’t celebrate the holiday.
Today I am thankful for, among other things, having beaten my Planetary and Lunar Tables into the form of the first prototype. It’s still a work in progress, but I have been slaving away on it for days going on weeks going on months and I had started to think I would never get this far with it. I apologize that it’s still only a prototype, but when things reach a certain point of readiness I like to share them, finished or not, just in case I’m run over in my bed by a city bus or what have you.
I’m not quite sure what to say about it – I could ramble for hours without actually doing a good job explaining – but for ages now, I’ve making reference to data in this table and talking about the Venus Orbital Period A value or the Venus Synodic Period B value or whatever, and meanwhile no one else have ever seen what this looks like, and it must be difficult to picture. For brevity, I’ve edited the screen shot and cut out the explanatory formulas in a column to the right not shown here.
That’s most unfortunate, because readers would be able to see for themselves what kind of formulas are being used if I just posted the whole sprawling mess (which I still might do because of that). It’s quite remarkable how often familiar and particular important numbers are found in these formulas linking the planetary cycles, even though I’ve had to throw out a great many promising formulas that ALMOST worked. One reason I’ve omitted the formulas is because I could still give some thought about the best way to display them without a sprawling mess if more accumulate, and I’ve already had to resort to a lot of shorthand that readers may or may not readily decipher to keep things concise for now.
Not everything does work, which ultimately isn’t surprising considering what an absurdly tall order it actually is that the major cycles of the planets should possess such tidy internal relationships in the first place. Even at their worst, things have gone rather well in the face of such demands, although there has been a great deal of testing and weeding out of less promising candidates and formulas that just don’t work, however promising they seem.
This much in itself represents a major milestone for this work of trying to piece together how the ancients would have represented the solar system cycles AS A WHOLE, particularly given what we can project for the metrological units they would have used to measure out representation of the solar system in their architecture. I’ve at least managed to include data on how the similar columns in three values relate to one another (A Value x 1.000723277 = B Value and etc).
No doubt changes and revisions will take place in the future, I can almost guarantee that – but I’ve put a preposterous amount of effort already into trying to make sure that most of what’s here is solid and won’t be overwritten by future changes. Future changes are expected to mainly concern representing more formulas that support the choices of values you see displayed, and expansions relating to cases of multiple rows of values for certain things. There is already – quite obviously – more than one right answer to some of these. The future will probably also include more agonizing about whether I’ve really gotten things right, but that could be going on a long time. Why hold up the show any longer?
Still an item in the experimental stages, the very first draft of the Planetary and Lunar Tables I work with. Naturally being me I have to miss some corrections – Nodal Precession a and i should be a and b, Saros c and h should be a and b, and Full Moon Cycle c and d should be a and b of course, for ease of reader reference. Today I’m just going to be thankful if it isn’t much worse than that.
That might give a hint of just how much the table has been trimmed down the last few days. Because of the many experiments that were conducted in the course of trying to optimize these figures, there were 14 columns where there are now three, and as many as 150 rows where there are now 55. (The 14 columns came from simply experimenting with every valid number I could find that might be used to approximate the 18980 day Half Venus Cycle, after Stonehenge and the Great Pyramid both “testified” that there might be more than two valid columns).
In some cases there are a and b rows simply because the MOST ideal value hasn’t quite been settled on, and in some cases because, again, it’s become apparent that there can be more than one right answer. We assume that when there is more than one right answer, it’s likely to be because there are variations in traditional common whole number calculations for these values. The most obtrusive examples of that like 364 for 364 (again 7 days in a week x 52 weeks = 364 days, NOT 365 like most people think, and the average ancient person may have therefore used more than one formula which more advanced mathematics aspires to emulate), or the Dresden variations which use 117 and 585 for the Mercury and Venus Synodic Periods respectively.
I’ve mentioned that in addition to the link between Mercury and Venus that the Dresden variations provide (585 x 2 = 1170), these variations might have also been chosen to better harmonize with the 260 day Tzolkin. There may be still more to it than that, they may also afford better harmony with Mars’ Synodic Period (585 / 780 = .75; 780 / 3 = 260, the Tzolkin), and then there is the part where 18980 / 117 = 162.2222222, while 365 / 225 = 1.622222222, so there are hints of greater harmony with both the earth’s 365 day Solar Year and Venus’ 225 day Orbital Period, even if most scholars wouldn’t give the ancients credit for recognizing the existence of this Phi-like natural values arising from whole numbered calendar cycle values.
Ideally, there will turn out to be related justification for some multiple versions of other figures as well, which is still under investigation. I’m still getting mixed signals about exactly which column the best value for the Eclipse Year, (346.5939368) actually belongs to, as well as a few as conflicting indicators for a few other very important details, so investigations into the structure and functionality of this experimental grand scheme do continue, even if putting this to rest for the moment may provide a moment to think about other things.
I still have yet to publish some of the formulas that led to the firmest of realizations that the Maya (and others) HAD indeed chosen a calendar system that IS able to incorporate even the cycles of Uranus and Neptune, yet another possible hint that they were perfectly aware of them, as well as there being other possible offerings to consider working on. (It seems like ages since I’ve got to do anything with ancient doorways, which are a favorite subject. Some of the best ancient math I’ve ever seen was integrated into ancient doorway proportions, starting with – but by no means limited to – the amazing Tikal Temple Pyramids in Guatemala).
Anyway, that will probably be plenty for all to ponder for now… Thanks for stopping by!
Cheers!
–Luke Piwalker
Luke Piwalker 