The Second Register of the Planetary Tables
I don’t actually have anything to report on this, per se – no conclusions yet – but I’ve started the painstaking process of revising my astronomical cycles tables so that they have room to record an increasing number suggestions for “second register” figures.
I do not know how well things will work, but it seems timely to give the subject more consideration because the prospect seems to come up more and more in recent efforts.
What this means essentially is that whereas the original tables were given as many columns as necessary to note any and all possible valid figures for the Calendar Round, and because it aspires to be a networked set of equations based on fixed ratios, the resultant values for all subordinate figures – thus generating as many as 13 or 14 possible sets of calendar figures to contend with – if we break off a row after the C value, our “first register”, we can start a “second register” beneath it to accommodate additional numbers that seem to be the most useful.
This reduces the number of candidate figures for a particular astronomical value from 13 or 14 down to only 6, a much-welcome simplification for both ourselves, and presumably, also for the ancient astronomers.
Ultimately things may be similar to my earlier efforts to project metrological units values according to an extended scheme similar to John Neal’s – it mostly makes sense and we made it work well geodetically – yet in the long run, the sprawling tables are both complex and potentially unnecessary. Such a framework will by definition try to force there to be eight different versions of the Royal Cubit (or perhaps even more).
In reality, we still only need there to be one Royal Cubit, and through studies of metrological unit families we have learned such definitions as the extended metrological table calls for may be incorrect anyway.
As it stands, I have been unable to come up with a second version of the Royal Cubit that isn’t already claimed by some other metrological unit family instead, and in the case of a possible ancient Meter, as attractive as such a proposition may look, I have not been able to come up with a single version of an ancient Meter that doesn’t turn out to actually be a value in some pre-existing ancient unit.
At any rate, an extended metrology table resembling Neal’s has largely fallen by the wayside, and early on the shortcomings of such a system began to be realized when it was found that even such a comprehensive scheme, and even allowing for reciprocal versions of units, still wasn’t enough to provide definition for the ancient “Egyptian Mystery Unit”.
Just as such a system seemed to be badly in need of streamlining for its own sake, the very same seems to be true of the Planetary Cycle Tables.
It’s possible that such a revision of the Planetary Tables will finally help explain some things. For some 20 years, the squared Royal Cubit has been trying to win a nomination as a valid representation of the Lunar Month, and yet even with a generous systematic rendering such as a Planetary Table with 13 or 14 column, there was still no place that it appeared as a legitimate value.
Ideally, we will see the successful streamlining of the Planet Table values down to six numbers representing a particular standard planetary aspect rather than 13 or 14. It seems that it was the right thing to do with the measures themselves, and it seems that it may be the right thing to do with the calendar as well.
It’s potentially confusing, as some “first register” values for different planetary aspects are still being worked out, but ultimately it seems manageable and more so given organized displays of data like the tables.
If we are fortunate, we may also see some long standing questions like the “squared Royal Cubit problem” finally laid to rest.
The Third Twin
I’m not certain if I should spring this on people, but I suppose it’s time?
We have just observed a certain Tikal Wonder Number finding its way into an organized table of metrological units, based on a whole number and Pi, seen here as the “Tikal Temple III Unit” at Pi to the sixth power (Pi^6).
I have referred back to this “Tale of Two Numbers” wherein it is discussed how this Wonder Number from Tikal Temple III has a near-identical twin in the form of the “Faiyum Number / Bat Palace Number” multiples and fractions, and numerous notes on the astronomy-related significance of both numbers.
Some time ago, I became aware of a possible third similar number in this range. I cannot locate the notes now, but I remember it as arising from taking another look at some of the relationships between planetary Orbital Periods and Synodic Periods, and number related to their Retrograde Periods.
I suppose it’s time I mentioned the number to the world at large so that people can be aware of it, or even be on the lookout for it if they are working with some of the figures themselves.
Unless there is a fourth similar number at large, the “Third Twin” should be 1.423250880.
So that is,
1.424280286, the “Tikal Temple III Wonder Number”; 1.4237993344, the “Faiyum Number”; and 1.423250880, for now “The Third Twin”.
It’s entered the discussion for the umpteenth time in several weeks now most recently because in attempting to begin to assess what might be the best way of representing 178 from the Mayan Calendar formulas, we arrive at the possibility of 177.9063600, and 177.9063600 x 8 = “The Third Twin” 1.423250880 x 10^n.
This might give us a few more ideas about what numbers like these may mean to ancient unifying calendar systems designed for dynamic architectural expression of calendar figures. We already know a few things about the value of numbers like these in calendar systems (it’s thought for example that the Temple III number has important interactions with 1.424280286), but they may prove to be more versatile than our current understanding or definitions give them credit for.
As to the metrological nature of “The Third Twin”, it is observed that 1.333333333 x Hashimi Cubit 1.067438159 ft = 1.423250880, hence we can say that the “Third Twin” is as a measurement would be an expression in Hashimi Cubits since 1.333333333 is the reciprocal of a whole number (the number 75 / 100, which is simply a whole number with the decimal place shifted). Because the standard Venus Orbital Period (VOP A) is also an expression in Hashimi Cubits (240 / 1.067438159 = 224.8373808), we might expect that “The Third Twin” may enjoy notable harmony with the standard VOP and the corresponding HVC (Calendar Round), as well as other important astronomical expressions where 1.067438159 plays a vital role.
I might also take a moment to note once again that the Hashimi Cubit is simply a form of the proposed Egyptian Royal Foot that is more convenient to use for many purposes, and whose value proceeds much more readily from astronomical calculations than does the Egyptian Royal Foot per se.
The particular operation 240 / 1.067438159 = 224.8373808 is why WMF Petrie’s proposed Stonehenge unit of ~224.8 inches has seemingly proven to be a discovery of the Egyptian Royal Foot at Stonehenge by an individual who remains one to this day of our most careful and trusted gatherers of measurement data.
Flinders Petrie of course also pioneered “Inductive Metrology” which has curiously enough turned out to be more or less the heart and soul of a more efficient organization of metrological unit values into families, curious because it involves the identification of whole numbers of “quanta” (quantities) of measurements and because it has proven to be so useful even after the work of Harris and Stockdale very clearly showed that what ancient architects did with with metrology easily transcends the simple search for whole numbers of units of measurement.
Hopefully my own work also bears out what I have been saying for such a long time, that the most interesting and meaningful numbers to find in ancient architecture are not whole numbers at all.
Technically then, Petrie’s “Inductive Metrology” should be of little use to us at all, and yet surprisingly, as an initial or intermediary step in design (rather than a final one) it may be proving vital even now to sorting out ancient units into a usefully organized set of unit families.
To get back more to the subject at hand, “The Third Twin” 1.423250880 has already demonstrated sufficient pedigree to be taken seriously, even if it is confusingly close to two already well established numbers also belonging to astronomical formulas. Whatever it may represent exactly, I’m certain that we stand to learn much more about it in the near future if we keep our eyes open.
Relative to our two classic numbers (besides Pi or 2 Pi) that the ancients seem eager to build into virtually everything, 1.177245771 and 1.622311470, 1.622311470^3 / 3 = 1.423250881. It seems to me that “The Third Twin” isn’t unfamiliar, but perhaps simply under-appreciated.
The Jupiter and Saturn Path
The recent history of this work goes that that in between realizing that the “Bat Palace Number” was twice an important internal ratio of Saturn’s cycles, and looking at Susan Milbrath’s paper on Jupiter and Saturn Retrogrades in relation to Mayan monuments, I was looking again at Mayan calendar stones (“circular altars”) and starting to see possible traces of Jupiter and Saturn.
It may remain somewhat difficult to be entirely certain – certainly at a casual glance, 1/100th of Saturn’s Synodic Period (for these numbers, primarily 377.8020800 / 100 = 3.778020800 might resemble either the 3.747289674 value that seems to be so prevalent in the calendar stones starting with the Aztec Sun Stone, which is thought to have this value in “modern” British feet as its intended diameter), or even the Chichen Itza Number 3.706382503.
If we have not encountered such a thing already, by the time we get to Robichaux’s data, Oxpemul Altar 15 may indeed prove to be an example of an altar diameter directly dedicated to the Saturn Synodic Period. We may have for it only of two valid diameter figures (?) but is is quite possible that projections of either diameter into circular form are perfectly valid, even if we are still missing part of an ingenious design scheme.
The diameter is given as 115 cm and the thickness as 42 cm; 115 cm = 3.772965879, and 42 cm = 1.377952756, and of course 3.772965879 particularly resembles 1/100 of the Saturn Synodic Period, either the “textbook” value 378.09 days, or the primary value (in this case apparently the B value but this is probably not yet entirely certain) that I work with, 377.8022316.
Since Milbrath’s insights have us pointed in the direction of looking at Jupiter and Saturn retrogrades, I should not that my data on retrogrades gives a round 138 days as the Saturn Retrograde Period, so we might be able to guess what’s coming here somewhat.
I’ve been suggesting in several forum discussions that ancient references to Saturn as a “better sun” (see David M Talbot, The Saturn Myth, or other sources) might make much more sense if viewed in the light of the fact that if we we divide Saturn’s Synodic Period by its Retrograde Period using only canonically simple numbers, the ratio is 378 / 138 = 2.739130435 and hopefully we know our calendars well enough by now to guess that 1 / 2.739130435 = 365.0793651 / 10^n, a very good likeness of the Solar Year – at least there’s something sun-like about Saturn when it’s difficult to think of anything else, and no doubt whoever referred to Saturn as a “better sun”
For our raw data for the stone in question, the ratio is 115 / 42 = 2.738095238 = 365.2173913, which will be even more apparently to some a reference to the Solar Year, or as we now recognize, also a reference to Saturn’s Synodic Period / Retrograde Period ratio.
Beyond pointing out this fabulous “coincidence” against which the odds might be, pardon, astronomical, I’m not certain what to say about this probably calendar stone. It looks as if they wanted the product of diameter times thickness to be a valid representation of the important number calendar number 52, but exactly how they juggled such a tall order as to achieve it, I’m not certain (and remember, we may have only very limited data here that may only show one facet of the total design).
I hope to find the data to be able to move on into looking at not just Jupiter and Saturn Retrogrades and how they coincide with calendar period endings, but also the retrogrades of Mercury, Venus and Mars as well as how these might relate to the symbolism or iconography of the ‘”altar” and stela decorations. Were they enamored enough with Mercury and Venus as a pair that these could be the mythical “Hero Twins”, or might those be Jupiter and Saturn as a pair?
If we are fortunate, we will be hearing more about Jupiter in Saturn in at least several contexts.
A Few More Words On Mayan Matters
In the event that there aren’t any issues from having some of the experimental Saturn values in the wrong column tables, one of the more recent hints that a Second Register of planetary values might be in order is a recent resurfacing of 377.67445062 amid experimental calculations. Just like we have been wondering for years whether a squared Royal Cubit should be considered as representing the Lunar Month, the wondering has been going on at least the better part of a year now whether 377.67445062 could be a valid representation of the Saturn Synodic Period, and if so, why it doesn’t seem to fit into the experimental Planetary Cycles tables, just as the squared Royal Cubit doesn’t seem to fit either.
An incentive for this is that I think the particular question has potential to solve a long standing major Giza mystery, which is what the intended mean size of the Great Pyramid is suppose to be. We have a minimum and a maximum, just as with the Stonehenge sarsen circle, whose mean values were deduced the better part of 20 years ago, demonstrating that not only were the minimum and maximum figures highly significant and well planned, but apparently even the mean value was too. No doubt we should expect no less from the Great Pyramid.
Another possible impetus for trying to brave up to taking the step of exploring the possibility of “Second Register” figures is that I continue to struggle with the major internal ratio of Jupiter’s cycles and possibly with subsequent internal ratios of Jupiter as a result of what might yet prove to be having mixed First Register figures with Second Register figures in the course of trying to generate a complete set of values for both Orbital and Synodic Periods of Jupiter.
There may be a number of votes coming from other aspects of the Solar System that in order to have a well coordinated system, the ratio of Jupiter Orbital / Synodic periods may be coming out just a little bit too low – it tends to come out about 1.084-something whereas what are presumably (hopefully) harmonious figures seem to tend to come out at about 1.085- to 1.086-something.
Something I forgot to mention in the previous post:
One of the reasons I decided to go out on a limb and make this tentative call of a Pi^8 unit, is because the “Venus Orbital Period C Unit” appears to also be the “fundamental” unit of the diagonal of the Great Pyramid at the proposed pavement level.
That’s tried for years to elude me; at face value that comes out looking like a rather obvious statement in some kind of unwanted variant of the Hashimi Cubit. Now that we may have a better idea what it is, I feel relieved and somewhat justified for having long resisted the idea of a variant Hashimi Cubit in trying to explain the Great Pyramid’s pavement level diagonal.
So, given that the “Venus Orbital Period C Unit” apparently
– is the fundamental unit value of what appears to be a legitimate representation of the Venus Orbital Period
– can be constructed from at least one pair of other metrological units (and major ones at that)
– tentatively belongs to an established metrological series (formed from a whole number and Pi^n)
– appears to be a fundamental unit of a measurement of a major ancient monument (the Great Pyramid, no less)
I’ve decided to make a leap of faith that it has enough going for it that the series that starts with the Royal Cubit may indeed project that far into legitimate units of measure. regardless of any possible apparent lack of attestation in a more orthodox sense.
–Luke Piwalker
Luke Piwalker 