06-20-2017, 07:14 PM
(This post was last modified: 06-20-2017, 11:18 PM by Ancient Vizier.)

Memoirs of a Pi Jedi

Chapter Twelve

Let 'Em Eat Pi... Fish?!?

I had a curious thing happen... I might have mentioned in passing that a long time ago I worked out a ratio for the Area of a Vesica Piscis, in the sense of the fish-shaped section between two half-merged circles, then found several approximations for it from our "Pyramid Matrix" numbers...

Area Vesica Piscis = Radius^2 x 1.228369699 (exact)

"Matrix Valid Area Vesica Piscis Ratio A" (MVAVPRA) = 1.228047399

"Matrix Valid Area Vesica Piscis Ratio B" (MVAVPRB) = 1.227936696

Still don't know if it was a good idea to trifle with that but given that Sacred Geometry and "the Pyramid Pi System" aren't exactly complete strangers, it seemed promising at the time. Really don't hear much from them these days, or at least until I started working with George Andrews' data for the Venus Platform at Chichen Itza (it looks like I also ran into 3.728757071 there, that's a long story I can tell some other time but that number was Yoda's "Grid Point" for the Monument to Humanity at Marcahuasi Peru).

Next I know, after looking for data on Palenque (I only have three measurements total from Andrews for that beautiful tower, what a pity) as a fringe benefit I am looking at some data for Pacal's tomb with some of the candidates for measures possibly referencing it and then I learn something I did not know before, that Pacal's sarcophagus is ostensibly hollowed out into the shape of a fish.

So I went to double check, and what I think might have happened is that

a. Ancient Mesoamericans did in fact actually recognize and use this "Vesica Piscis Area Ratio"

b. Because they put this value into calendrical equations that can be highly variable, it gave them an even more variable "Vesica Piscis Area Ratio" and a greater range of constants that they recognized as representing this value

To wit, I think they may have regarded it under the circumstances as (roughly) equal to 2 / Phi, with Phi in context being any number of useful approximations from the "Pyramid Pi System": 1.61882914, 1.620000000, 1.621138938, 1.622311470 and possibly also 1.62348451 treated "as if" Phi for these purposes.

This may afford us at least limited use of additional formulas like possibly

Earth Solar Year x / Lunar Synodic Period = ~VP Ratio = 2 / Phi y = 2 Venus Orbital Period / Earth Solar Year z

Where (thus far), the Lunar Synodic Period and doubled Venus Orbital Period are fixed at the values proposed previously,

29.58741332 (days) and 224.8373803 (days) respectively.

It may help reinforce a sense that (3600 / Pi^2) = 364.7562611 is "special" because unless I did something really dumb (always possible), this figure is the only one where input Solar Year y = output Solar Year z

Perhaps more importantly, the form of Vesica Piscis ratio in this particular equation is 2 / 1.622311470 = 1.232808888, which may be useful and important enough to account for it probably having turned up already repeatedly in Andrews' data.

In fact, I may have recent evidence of 1.232808888 working successfully as a probe to as high as the twentieth power, which may well be a new record. FWIW, I don't generally expect Pi to be a useful probe at higher than the fourth or fifth power, and even the power probes like 1.177245771 or 1.622311470 generally maxing out by the sixth or seventh power.

Meanwhile, in the proposed formula, the original values 1.228047399 and 1.227936696 might actually serve in the generation of a possible pair of leap year values of just over 366, so perhaps we can see why incorporating this value into their calendar mathematics may have also necessitated departures from the most stringent approximations in order for such formulas to give a proper variety of values for the number of days in a year.

Also, I recently purchased a used Year-O-Matic 2000 just in case we run out of experimental values for the number of days in a year. I'm not sure there is such a thing and I really haven't tested it much, but supposedly it works like this:

13.333333333 / Year x = Year y

(13.333333333 x 10^n) / 365.0200808 = 365.2767074

(13.333333333 x 10^n) / 365.5409035 = 364.7562613

(13.333333333 x 10^n) / 365.8052909 = 364.4926321

And probably etc? (After this it may get strange, but maybe it's supposed to?)

365.5482919 again being a proposed candidate for mean value for the year, and possibly something that's found in the Great Pyramid with some frequency after Capt's findings of 365.2-something are converted back from "Pyramid Inches" to ordinary ones?

It's (1 / (1.177245771^2)) / (2 (Pi^2))* so it's sort of a chip right off the old block of this fondness that ancient Mesoamerica may have had for the square of Alternate Pi 1.177245771.

(*Whereas 2 (Pi^2) / 1.177245771^2 = 142.4280286 / 10^n, previously proposed for product of w x h of a Tikal temple door)

But some of those year figures thus generated are still very new to me in spite of previous attempts to find formulas to generate them, and I'm still not sure what to think.

At least I think I can safely say from looking at Andrews' data for the Palace at (Santa Rosa) Xtampak, that the same kind of mathematics seems to appear there as in temples, so this astronomical cycle-related math may not have been reserved for any particularly sacred type of structures.

Also, I'm finding more instances of what look like the reciprocal of Alternate Pi^2 (presented probably as fake sqrt 52 and possibly as fake 72) in a number of room proportions at places other than at Rio Bec - and quite possibly also at Palenque, perhaps including in the width of Pacal's sarcophagus lid "2.20 meters".

This Piscis business brings up another thing that slows me down on Tikal, though - there is a temple width there that looks about 340-something which I would usually think is awkward, and opt for something just a hair smaller and more resonant, but it turns out that the square of the proposed Venus Synodic Period is right in this neighborhood

584.0321292^2 = 341.0935279

This is also a somewhat awkward figure, yet 341.0935279 x 360 = 1.227936701 / 10^n

So that quick we are getting more Vesica Piscis talk from another aspect of Venus' cycles, and some unfamiliar numbers that might call for extra care.

And of the two Vesica Piscis ratios I previously proposed, it's this one that has its own valid square root, which is

sqrt (1.227936701 x 10) = 350.4192775 / 10^n,

which is the proposed circumference of the Thom Type A flattened ring, aka 111.5419203 x Pi etc

Also I don't know if I showed this before - I don't think I did but frankly I'm so swimming in numbers with this stuff that I probably make the same discovery three times in one week and don't realize it...

But this came out of candidates for assigning possible intended values to the sarcophagii so whether or not we actually find it there, we can call it "The Red Queen's Venus Supreme Equation" (or not) wherein

2.033593767 / 224.85373803^2 = 1 / Earth's Polar Circumference in Miles x 10^2

2.033593767 / 224.85373803^4 = 1.789199025 (a noble number that still awaits a proper introduction)

2.033593767 / 224.85373803^5 = 353.9334588 Proposed Lunar Year in days value

Allowing this Venus Orbital Period value to make a rare display of worthiness even at the fifth power, while directly linking the Polar circumference to the Lunar Year. (Another candidate to come out of the Palenque tomb data may afford a rare opportunity to show off "Not-Phi" 1.61882914 as being useful - on at least the one occasion anyway - to the third power).

Most lately I am using Not-Phi with the Radian to generate the proposed Lunar Year value

57.29577951 / 1.618829140 = 353.9334578 / 10^n

Which I like to think is itself a vote of confidence for this proposed Lunar Year

We also see the aforementioned noble number come from a string of familiar numbers connected by Alternate Pi, starting at 1/2 the Earth's Polar Circumference divided by Pi

Ignoring correct decimal placement for the remainder of this post

24858.38047 / Pi = 7912.668258

7912.668258 x 1.177245771^1 = 9.315155237

7912.668258 x 1.177245771^2 = 1.096622711

7912.668258 x 1.177245771^3 = 1.290994449

7912.668258 x 1.177245771^4 = 1.519817755

7912.668258 x 1.177245771^5 = 1.789199025

7912.668258 x 1.177245771^6 = 2.016326986

Also in the Pacal data, I have width measurements of 2.85 and 3.75 meters from Alberto Ruz Lhiullier for Pacal's burial chamber

3.75 / 2.85 = 1.315789474 (raw)

Going to take a wild guess here that perhaps Pacal too loved to Do The Cholula 1.315947254

And the ratio of the width of sacrophagus lid to width of sarcophagus

2.20 m / 2.10 m = 1.047619048

Wild guess on this one is 1/3 of Pi = Pi / 3 = 1.047197551

I continue to see a lot of what looks like the "Great Pyramid Apex Displacement Ratio" version of 104 days, namely 104.0913798 as seemed to appear repeatedly at Tikal, now also appearing in the measurements of other sites, but Pi / 3 is easily potent enough to be a fiercely competitive candidate even against the 104.0913798 ratio. A little more about that momentarily...

So now I suppose the question is, are there any other ratios specific to the Vesica Piscis that I probably know even less about?

Also I looked at a few more calendar stones (aka" sacrificial altars") and tried to learn more before I came down with a bad case of Anthropologitis - one can catch that from scouring sixty-page articles all about human sacrifice while just trying to find the measurements of the f---king thing.

I found at least one example, and possibly several more in the form of circular ornaments from Chichen Itza, that hint at dividing the year into 16 (or possibly 8?) - I have not seen the number 16 enter into discussions of ancient Maya (read: ancient Everybody's?) calendar keeping but it turns out it may indeed belong there.

"Kukulkan - Sun Symbols. Chichen Itza"

(Item at lower right has 16 notches in perimeter)

365.020081 x 16 = 584.0321293 proposed Venus Synodic Period (days)

= 364.7562611 x 16.01157243

360 / 16.00000000 = 225.0000000 "alternate" Venus Orbital Period figure

360 / 16.01157243 = 224.8373803 "primary" Venus Orbital Period figure

Also it was proposed that 12 Pi^2 may be a useful calendrical or astronomical figure

12 (Pi^2) = 11.84352528

11.84352528 x 16.01157243 = 1896.334629 "Long Count Builder" = 360 / 18983.88125

Performing the operation with 16 Proper advises us that this is apparently not the only approximation of the Long Count or Half Venus Cycle that has a "Builder" figure. It turns out that 189.4964045 is NOT "Go away you pesky thing you are not one of the finalists," but actually part of that same process

11.84352528 x 16.00000000 = 1894.964045 = 360 / 18997.72193, the alternate Long Count version derived from the Aztec sun stone and the version that may best break down into hours, minutes, and seconds.

(also ~224-225 = ~16 x 14)

If I did anything wrong at Tikal so far, it might have been related to overlooking that 1/sqrt 60 = 1.290994448 may have been recognized as a legitimate representation of 13. I certainly could have made a mistake for overlooking that possibility.

I also think I found fairly recently, where 720 / Pi^2 = 72.95125222 may have been used in some applications or equations as the calendrical number 73. Also, possibly 73.10818007 (Alternate Pi^2 / Pi)

Yes, their math may have been half as complex as their written language. The Egyptians too. Should I be shocked?

I probably should have seen it back it at the Kukuklan-Pyramid-as-Calendar. On the one hand, it's extremely gratifying to see that (and apparently the Aztec sun stone) apparently operating on the very same logic that Yoda has been using in "decoding" ancient monuments the whole time, but it does also suggest it's a bit of a free-for-all with that "add 1 to make 365" business (and depending on preference, you could say the temple on top has five sides if you count the roof, divide five temple sides by four pyramid sides to get 1.25 to add to 364, to get 365.25)

But yes, this idea of how far we are allowed to drift when this high-precision system collides with a highly imprecise system like calendar counting might even go so far as throwing away everything after the decimal in such situations (once we have arrived at the-number-to-be-mutilated in a meticulously precise fashion of course), in which case

104.7197551 might therefore have actually read the same as 104.0913798 for such purposes, and that is another specific possibility I've previously overlooked.

Such it is that if the previous proposals will continue to hold water, then for the proportions of the door to Tikal Temple IV,

Temple IV (Maler)

Width 10.17060367 Height 10.40026247 Ratio 1.022580646 Product 105.7769476

Perhaps the most pleasing and sensible interpretation for what was intended could well turn out to be

Width 10.25135528 Height 10.47197551 Ratio 1.021521079 Product 107.3519415

Yup, probably a fake square root trick (Why do I have a strange urge lately to refer to the pairs involved as "Hero Twins"? Was Mesoamerican mythology among any mythologies able to successfully embrace mathematics, as might have been the case with Egypt?) although not quite the square root trick we might have expected?

Although this is still not a terribly well-tested proposal for the doorway of Temple IV (and please don't get me started on lintels, which are one of the reasons none of this doorway data is telling a complete story yet)...

Perhaps the biggest mystery on my mind since I let it wander, is how archaeologists end up thinking the "psychoducting" in Pakal's burial arrangements means he and his wife are getting out that way to go for walks, when perhaps the fish-shaped sarcophagus does double duty as a hint he's going for a wee swim in the underworld instead? Between the "psychoducts" and the Queen's sacrophagus style, I'd swear that Mr. and Mrs. Pacal have heard of this Giza. I hate to go near that sort of stuff at all, but just maybe it would be easier to figure out at Palenque than at Giza what those things are really for?

FWIW, I never paid much attention to Pacal before as Nat. Geo. managed to make him out like the sort of arrogant sh-t to exploit the peasants for his own vanity and so forth, so who gives a rip? It just occurs to me now that even with what may have been a sizable case of Giza Envy, he seemed to have been content with what would most likely be considered as preposterously humble burial arrangement for a Pharoah.

I should just leave that stuff alone and stick to the math but it is interesting that I seem to be able to spot so many apparent ancient cultural contacts that aren't supposed to have happened. I dunno whether Candi Sukuh inspired El Tajin or vice-versa, but I really struggle to believe the striking similarities are coincidence. Worse, archaeologists seem to say a lot of dumb stuff when they're in Isolationist mode. I think I actually read a comment from Lhiullier to the effect that if ancient Asians visited Mesoamerica, why didn't they convert everyone to Buddhism? ROFLMAO! I can see he gave that one even less thought than he gave to getting a complete set of measurements of Pacal's final arrangements.

(I'll try to continue working with his data and see where it leads even though it gives me a creepy feeling how seldom there is anything but a zero in the second and last place after the decimal in that dataset).

Even the ideas archaeologists have about local diffusion of culture seem recalcitrant to me somehow. I'd love to know the story of how neighboring towns got similar architecture but they don't seem to come up with simple straightforward stuff like maybe one of the gubernatorial personages from Rio Bec happened to be passing by Becan and was really impressed with their cosmetic tower, so he got hold of the architect who designed it and said, "Hey those things are awesome, can you come up here to Rio Bec and design us a bunch of those?" - that's one of the sorts of things I wish I could find in the numbers, or maybe a particular mathematical "signature" of a particular architect.

More likely the history books will suggest it was because the architect was taken captive and they tortured tons of work out him before ungratefully ripping his guts out. I know archaeologists say such things even about their own ancestors - ooh, big scary heathen bloodletting altar at Stonehenge! - but really... I mean, unless they were ritually sacrificing their math teachers (which would be perfectly understandable), it's still hard to reconcile that kind of barbarism with the level of civilization visible in the mathematics and astronomy.

I think there's actually a good reason that when I look on the expanses of Palenque or Uxmal or Tulum or Tikal or etc that they nearly scream "College Campus" at me. We are apparently talking about specialization in society here, and for us ourselves that involves specialized education...

"Work and pray, live on hay, you'll get Pie In The Sky when you die." - Joe Hill, "The Preacher and the Slave" 1911