I’ve been working on a new data table. On the one hand, it’s meant to save on having solar system astronomy formulas scattered everywhere over posts to five forums and over pages and pages of written notes; on the other hand, there may be no replacing taking the time to work out those notes. One shortcoming of the data tables I’d like to present here is that it is all in terms of ratios – diving the larger number in a situation by the smaller. There is much to be said for what can be learned by multiplying the two numbers involved instead to generate a multiplied product, data that is still not presented here. Thus these tables are not definitive reference tools, although if one lingers over them a bit it may still inspire all sorts of relevant insights.
Also not included here (still looking for them) are versions of the two oldest tables featuring the ratios between major planetary cycles, and between major lunar cycles, which were notated to show “coincidences” in the data output. I’ve included that step with the latest data table presented here.
Here are the two older tables in their basic form
Figure A: Basic ratios between major planetary cycles.
Figure B: Basic ratios between major lunar cycles, with several Mayan calendric cycles added.
Figure C: Here for the first time (why does no one else seem to be doing this?) on my part is a table that looks at the ratios between planetary and lunar cycles.
Figure D: Figure C with color coding used to indicate some of the remarkable coincidences in the solar system that produce recurring numbers. Note that this applies to Uranus and Neptune. It’s ALMOST enough to generate a sense that the Solar System is designed by an intelligent mathematician deity, were it not that us mere mortal mathematicians tend to notice that it ISN’T all exactly perfect and that we have struggle with it and tweak it to turn into a harmonious interconnected system. Not the kind of thing that it necessarily seems ancient peoples could make into a religion, but enough that we could understand if they build temples to it.
I am indebted recently to author Crichton Miller for suggesting that the words time (Latin, tempus) and temple may well stem from the same root, implying that an original context for “temple” might have been a place where they kept track of time or taught about timekeeping – that certainly seems very consistent with my experiences studying and attempting to interpret ancient temple architecture.
Figure E: Figure C with highlighting of certain numbers that may be of particular significance for various reasons, for being easily recognizable or familiar from previous work, or for being particularly poignant.
One entry I’d classify as “poignant” is the interaction between lunar Apsidal Precession Cycle and Uranus Orbital Period. Essentially,
30668.5 / 3233 = 18.97216208 / 2 – see Mayan Half Venus Cycle, canonical value 18980. It certainly gives the impression that the Half Venus Cycle that was so seemingly important to the Maya, can even help to harmonize things like the Apsidal Cycle and the Uranus Orbital Period into a single calendar system.
Figure F: Here is a version of Figure C where various random suggestions for “perfected” figures have been offered in the table boxes colored in green.
Figure G: As long as we’re doing this, here is a version of Figure A with some suggestions for “perfected” figures (green boxes) and a few values suspected of being potentially problematic (orange boxes).
Figure H: the recent Planetary and Lunar tables that attempt to narrow down the candidates to some of the best overall suggestions.
These are all tools that can be used in various ways to help understand what ancients were doing with their preposterously ambitious calendars that sought to integrate all kinds of solar system cycles into what is essentially a single system, and again, they can be used not only to try to help recreate ideal “Master Formulas” for the solar system cycles, but also to help us to design architecture that embodies key data about the solar system that we wish to express, or novel formulas that relate some of the diverse parts together.
Chances are, ancient astronomer-architects had and used very similar references even if we have yet to find or recognize them after cumulative cultural damage in many quarters. Once again, it’s one of the most natural kinds of questions that can be asked, to inquire “How many Lunar Years are in one Solar Year?” or “How many Venus Orbital Periods are there in a Solar Year?” or “How feasible is it to have multiplanet calendars?” – and if we set down that path as the ancients must have, this is something like where one may eventually end up. There seems little doubt that ancient astronomers must have given a great deal of time, effort, and thought to these same matters.
When we start to do that, we also quickly see an amazing collection of numbers that have long been familiar because they have been written in numerous places around the world as measurements used in specialized architecture such as pyramids and temples, and it has been spotted even with the relative shortage of freely available architectural data that currently exists.
At any rate, much of the data that I have to work with is now available in the same form for readers of this blog, and that is the point of this blog, to be as much as possible a sort of clearing house for data of this nature – so even though I have done a truly abysmal job here explaining some of the finer points or pointing out some amazing facts, this much progress has been made at least.
(PS: If you experience legibility problems with the tables, please check the original uploaded images. Some or all images presented on this page may be at a somewhat reduced scale).
–Luke Piwalker
Luke Piwalker 