| Author | A Model of Ancient Monument Math and Metrology |
Unhenged
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|  Posted 26-10-2021 at 14:16
I recently posted these two images to Peter's HSMF thread to hopefully support any contentions about the reality, antiquity, seniority, or importance of the HSMF, but I hope it's alright if I post them here as well so that Peter's thread might be spared additional remarks and follow-ups concerning them.
The second image merely speaks of the possible origins of some major metrological units, as well as the possible inevitability of the Megalithic Foot and Imperial Foot as it relates to this. The first is a breakdown of units that appear in my Stonehenge model where the Megalithic Foot is highlighted to show its importance in the design.
Some of my models of the Stonehenge ellipses and bluestone circles are probably in need of review, but where we see above the importance of the HSMF in the sarsen circle, in general in the ellipses we may see more of the importance of the Megalithic Yard and the way it interacts with the Megalithic Foot. As far as I know, perhaps at least half of Thom's figures in Megalithic Yards for the ellipses may be valid.
In a sense, what seems solid in models of the ellipses is that where in ways the sarsen circle can be said to be a tutorial on the Megalithic Foot, of the ellipses it may be fair to say that they may be something of a corresponding tutorial on the Megalithic Yard, which seems to have been used rather sparingly in the sarsen circle.
One aspect of that seems to be reminding us that the Megalithic Foot and Megalithic Yard may be important interactive values. 20 Megalithic Yards interacting with a number of Megalithic Feet that approximates 17 MY may very well be an example of this.
One interaction product of the Megalithic Yard and Megalithic Foot is again the Eclipse Year/Eclipse Unit value in Imperial, and for reference this can be written as
2.720174975 / 1.177245771 = 346.5939368 / 150
These considerations may also be seen in the bluestone "oval with corners", where Thom gives us for the perimeter essentially
51.06 MY x 2.72 = 138.8832 ft
Which I have taken to mean (346.5939368 / 10) x 4 = 138.6375747.
The raw estimate of 138.8832 ft could be taken as 10^n times the reciprocal of 72 as well as other things, but there are multiple metrological pointers within Stonehenge to a value of 138.6375747 and the resulting mathematical environment serves to highlight the three Megalithic Yard values stipulated by the pair of Pi^n series based on the Imperial Foot and putative Egyptian Sacred Cubit value, including a Megalithic Yard value that is a high quality approximation of 1/10 of the Draconic Month, even before we begin the revealing conversions of the Imperial measures into Megalithic Feet or other units capable of data retrieval.
There is also within these models a possible deliberate showcasing of a remarkable rarity, which is the standard Megalithic Yard of 2.720174976 showing efficacy as a data mining tool at least as high as the third power, which is more or less unprecedented. Usually I would say to not even bother squaring a Megalithic Yard of 2.720174976 ft. It may have strong data retrieval properties at the first power, but generally it seems to be more something to be mined for data by other unit values than something to mine data with through exponential use.
When the Imperial value of the Megalithic Yard of 2.720174976 is multiplied by the Megalithic Foot value of 1.177245771, the answer obtained is a value that is metrologically in Hashimi Cubits = Egyptian Royal Feet = Petrie Stonehenge Unit, which is ideal for the expression of the Venus Orbital Period.
Because of these relationships, we can of course take John Michell's model of the Great Pyramid perimeter at 1111.111111 Megalithic Yards and convert it to Megalithic Feet just as Peter would do with Megalithic architecture, and obtain a reference to the Eclipse Year.
(This is very similar to how using idealized units, Royal Cubit / Remen = a value in Megalithic Feet, and Royal Cubit x Remen = a value in Sacred Cubits. These units, many of them conventional and historically supported, show remarkable connectivity through multiple routes).
In practice, for me this operation for the Great Pyramid looks like
(1111.111111 x 2.720174976) / 4 = 755.604160 ft per side of Great Pyramid base / 1.177245771 = 346.5939368 / (54/100)
Allowing a second inverted parameter so that the conversion operation becomes multiplication, the Great Pyramid baseline also conveys Venus data via the Megalithic Foot.
To my reckoning, there was nothing wrong with numerous parts of the views of Taylor, Petrie, Thom or Michell except that somehow after 50 years or more they still seem to be met with skepticism and second guessing.
I obtained the same answer as Michell for the Great Pyramid as independently as possible for having read The View Over Atlantis, which was to try to tackle the problem fresh years after I'd read it last and had long forgotten all about Michell having offered that solution.
Cheers!
[ This message was edited by: Unhenged on 2021-10-26 14:44 ]
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Unhenged
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| Posted 04-11-2021 at 00:12
Greetings, all
This is version 2 of a table that appears on an earlier page in this thread. It's still not complete (or perfect) but I have added a number of things to it.
Again, I think it quite remarkable how a set of units based on the Pi ratio transforming whole numbers of one unit into whole numbers of another known unit, are somehow also able to transform whole numbers of units into whole number of other known units.
Also, I think some interesting things begin to surface here, both with the addition of cubed units, and how a more extensive display lends votes of confidence for something as "out there" as a "Tikal Temple III Unit". That was one of the things that compelled me to consider the possibility as that were multiple metrological pointers toward it thus.
We can see here that surprisingly, Megalithic Foot x Megalithic Foot^2 = Megalithic Foot^3 = Megalithic Foot cubed, produces a numberical value that in linear measure would be a whole number of units of the "Incidental Megalithic Yard" that is derived from the Sacred Cubit or Megalithic Foot and Pi^n.
We can also see that Remen cubed gives a value that for linear measure would be in a whole of Hashimi Cubits (an often more useful form of the projected Egyptian Royal Foot). (Turnabout is NEARLY fair play here as the Hashimi Cubit cubed ALMOST produces the ideal Remen value exactly).
Anyway, I hope this proves of use or at least of interest.
Edit: I've now replaced V2 with V2.1, with a few things fixed and color coding added for easier navigation.
Cheers!
[ This message was edited by: Unhenged on 2021-11-04 05:03 ]
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Unhenged
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| Posted 04-11-2021 at 05:13
Unit conversion table now upgraded. Sorry I didn't spend a couple of extra hours doing that in the first place.
Cheers!
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Unhenged
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| Posted 05-11-2021 at 05:29
Here is my latest attempt at a decent display of proposed ancient unit series based on Pi or 2 Pi. I've used the classic circumference / radius ratio 2 Pi here really out of personal preference and even sentimentality over the Great Pyramid's 2 Pi perimeter / height ratio.
I'm still struggling to perfect the balance between sprawl and legibility, but I hastily cobbled this together this evening and could have done worse.
Here, two previous diagrams of the two different unit series are consolidated, and details are added for the first time of the actual number of units generated by the (2 Pi)^n series starting from their origin points, which are the proposed Egyptian Sacred Cubit and the (apparently ancient) Imperial Foot, which are also the pivotal points at which the series reverse and begin reciting the same sequence of metrological units in reverse order.
Also indicated for the first time on the diagrams is whether it is a regular "forward" form of the unit in question or whether it is the "backward" inverted, reciprocal form of the unit in question. Here then the ordinary "forward" form of the unit is marked "+pos(itive)" and noted in orange font while reciprocal or inverted units are marked "-neg(ative)" and indicated in blue font. There are also cases of inverted multipliers (also seen in the way John Michell and I see the Great Pyramid base perimeter length, determined by the inverted multiplier of ((1/9) x 10^n) Megalithic Yards or 1111.111111 Megalithic Yards, thus an inverted multiplier).
Please note that where the number of units generated by the conversions between units are given in yellow, they are provided without attention being paid to correct decimal placement and without the traditional "x 10^n" disclaimer to offset the concern with correct decimal placement (n for 10^n can be a negative number).
I apologize for not doing this sooner - no doubt it must be very hard for anyone to follow along on the previous diagrams how 2 Pi is converting one unit to the other, with quantities involved unspecified and some of the units being in reciprocal form - but I still have other pressing projects and only did this to take a 2 hour break from something else which I'd been working on all day.
The other project is trying to get a better grasp of Lunar cycles and how they are best represented metrologically. Some of the Lunar cycle values have been well defined but others, as well as their mechanics as a whole, may still be rather unaccounted for, so I attempting to search further for formulae which will make the tables of these values more or less self-sorting and take out the sometimes insurmountable guesswork involved.
It should have been fairly straightforward, but there are some square root and cube root formulas for some of the Lunar Cycles that can be hard to qualify and we want to salvage as many as we can, if there is additional justification for doing so besides just the clever formulas themselves.
Earlier today I was pleased to discover that the functionality of treating the Jupiter Orbital Period as 10^n times a fraction of the Eclipse Year (JOP = ~4332; 4332 x 8 = 346.56 x 100, Eclipse Year = ~346.62 days) that I thought had been traded away as a compromise for other important gains, may be salvageable by instituting the next best thing (or often something even better than 8), which is 8 x 1.000732377.
Anyway, without further ado... (And DO watch out as there may still be some errors in the proceedings)
Let's try one or two to see how this works...
Let's take the Sacred Cubit and multiply by 2 Pi to get the Remen. How many Remens? As indicated, 108 x (10^n) Remens.
Sacred Cubit 2.091411007 ft x 2 Pi = 13.14072291 ft
(Some may recognize that that is sort of a "Unifying Value" from Michell's work re: the number of feet in earth circumference, and some of the numbers involved that he uses in Dimensions of Paradise in this respect are more or less identical to my unit values).
13.14072291 / (108 / 10) = Remen 1.216733603 ft.
Let's try one with an inverted multiplier or divisor...
We take the Imperial Foot and divide by (2 Pi)^2 to get 2.533029591 / 100, and then divide 2.533029591 by (1 / 480) to get 1215.854204, or 1 x 10^n Short Remens.
I've also labelled the two series of metrological units as "Square Root Numbers" and "Pi Numbers"; I've been "lecturing" about these definitions for numerous years now. "Pi Numbers" is something of a misnomer vs "Whole Numbers and Pi", but you can see what is here as something of the very definition of what "Square Root Numbers" and "Pi Numbers" can be given as; Square Root numbers here derive from a simple fraction or multiple of sqrt 60 and Pi^n or 2 Pi^n and will always reduce to such a number via Pi^n or 2 Pi^n, and "Pi Numbers" derive from a valid whole number and Pi^n or 2 Pi^n and will always reduce to a whole number via Pi^n or 2 Pi^n.
I'm pleased that these series once they have been filled in thus can explain to us such an outlandish thing as how we've end up with THREE different versions of the Megalithic Yard even after doing everything seemingly possible to reduce things to one single version of each unit. Because the Megalithic Yard in Imperial is also the Draconic Month, it also helps explain how we've ended up with three major versions of each important cycle even before we get to any additional versions mandated because of variations in traditional common mathematics (i.e., the old 364 vs 365 days in a year question; the system in question aspires to cover multiple possibilities of that nature).
(The reason why there is a "Short Remen" in the mix is a longer story that I won't confuse anyone with today, although some may have already heard the story before).
Cheers!
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Orpbit
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| Posted 05-11-2021 at 16:04
Hi Robert,
A very neat diagram I grant you, and there is one thing in it which immediately caught my eye as potentially supporting the "PRACTICE" (Or should it always have been "PRACTISE", which the American English inbuilt dictionary is desperately trying to make me "correct" the spelling!) side of my "ORIGIN" v "PRACTISE" distinction.
( to clarify, practiSe would be the use of the variety of measures as a whole, whereas practiCe would be, for example, the experimental use of one of them, i.e. the HSMF in Ancient Britain in monuments, such that it became the "accepted" primary practiSe as statistically claimed by Harris and Stockdale.)
Anyway, yes, many hours work after many years of experimental slog I take it, but does it - like I eventually decided - take you out of the rabbit hole and into glorious sunlight, or out of the rabbit hole and into the swamp! Here, I'm referring to your last sentence in brackets.
In short, I guess there are several questions which will come your way, including some from me, and some of which will include the likes of:
quote, ...that I won't confuse anyone with today... end quote
1) Does this imply that you consider the summary, as in the latest graphic, removes confusion inherent in your prior posts in this now lengthy thread?
2) Is it less confusing than the likes of John Neal's model in, "All Done With Mirrors"?
3) What was/remains your opening hypothesis in beginning your project?
4) Did you modify your hypothesis as the project progressed?
5) Does this point you have reached "prove" the hypothesis?
6) If not, what remains to be done?
7) What do you consider your model does that other models (such as Neal's) do not?
The above are general questions which, if you consider eventually writing a book, need to be stated up front.
Of course, there will follow many questions of detail which metrology "nerds" will throw at you, or critique you with.
What I see supports - but not necessarily proves - a fundamental hypothesis that I took with me out of the rabbit hole of "PRACTISE", and entered the "swamp" of "ORIGIN". If you know what this hypothesis is then we are as one, If not, then I will reveal it -perhaps to a trusted colleague from the Portal!
I'm playing Devil's Advocate - apologies but unavoidable...
Nevertheless, well done
Cheers
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Unhenged
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| Posted 06-11-2021 at 03:54
Thank you for the kind reply and thoughtful questions. Is this my first interview? lol - I will have to devote some time to the thoughtful answers your questions deserve but God, yes I hope it's simpler than what's in Neal's books. I think you can back to page 1 or 2 of this thread and see the great big mess I was getting into trying to follow in his footsteps proliferating all those geodetic variations mainly so we can try to get the equatorial and circumferences to both be in simple whole numbers of traditional units. We can do ALL SORTS of amazing geodetic things without that.
The point I didn't want to confuse anyone with? It's a matter of scale, I'm afraid it's going to sound to people like I'm "cheating" and I wouldn't be surprised because I'm still not sure myself that that isn't what I'm doing... It's not like I have an ancient rule book handy...
The thing is though that there can occasionally be a difference between our idealized geometry and actual architecture, and we can usually get away with it when looking at models that are one unit by one of some other unit, so when the Remen is sqrt 2 to the Royal Cubit (and vice versa) we can go ahead and use idealized figures and use a slightly variant Megalithic Foot value as square root 2 because the difference at that scale is so miniscule...
But when we start talking about large architecture like the pyramids where there may be hundreds or even thousands of a unit present, those miniscule differences begin to count up until we're safer going back to the actual value of sqrt 2 for the sake of accuracy on diagonals and so forth.
That is the point though where I stop using ~sqrt 2 as metrology and have to pick up sqrt 2 proper for geometry.
Jim Wakefield pointed out that the collection of Egyptian pyramids measuring 150 Royal Cubits on a side starts to become sizable as compiled by IES Edwards, and I'm not disputing that that's what they measure, but the diagonal - and we can see here why they might do that, because they get the Solar Calendar Year on the Diagonal...
Side (150 x Royal Cubit 1.718873385) x sqrt 2 = Diagonal 364.6281080 and it seems a more honest and accurate measure to call it 300 Short Remens of 12 / (Pi^2) Imperial each, than to try to call it 300 Remens of 1.216733607 = 365.0200808 like we can think of it as at a smaller scale where the error is much less significant.
So we can qualify it as 3600 / (Pi^2) = 364.7562611 = 300 Short Remens of 1.215854204, just so we don't go adding 4/10 feet onto the diagonal to try to make ~365 ft. We can also still count it as a Solar Calendar Year, but it's just rather rare to see the Short Remen in actual practice except at diagonal to large numbers of Royal Cubits. Most of the time the Short Remen is probably busy trying to pass itself off as other units (possibly legitimately) that don't need to be dealt with if we're aware of the Short Remen.
Sort of a strange diversion, but today I saved a couple of videos with Crichton Miller to watch at my leisure later. I recently met him in a discussion about one of Harry Siverten's papers or books, and was intrigued with a couple of the things he said. I may know him from a ways back, he's big on the idea of the Celtic Cross as a nagivational instrument and ages ago on a forum someone was discussing that very thing (I wondered if Rose + Cross meant Antiscorbutic + Navigational Instrument for those... you know, "nautonniers" or whatever).
I've see a couple of videos with him and was very pleased that he mentioned Harrison and the Longitude Problem (quick, hide all the ancient telescopes before those pesky Spaniards get their hands on them), and he may have some valuable insights into how we've lost the thread of history.
Anyway, so I'm starting at this list of videos and all these Celtic Crosses and my researches into Mayan symbolism kick in and I'm reminded that lately I am wondering if a cross is somehow a symbol of Mercury since we several find Mercury-associated mythical figures like Ehecatl and Xolotl with crosses plastered on them, and by now a circle is bound to try to make me think of Saturn's rings.
Since I'm pretty challenged at thinking of astronomy in four dimensions or in everyday practical terms, I don't know what to think of the idea or if there is any advantage to tracking the fastest of the visible planets against the slowest, but that's what popped into my head is the idea of an emphatic on Mercury and Saturn.
In calendrical terms, the Orbital Period of Saturn at about 10758 d divided by the Orbital Period of Mercury at about 88 d is 10758 / 88 = 122.25.
I'm going to have to admit that I have not yet been able to work out sensible schemes for the approximation of Mercury's major cycles, but I still find this incredibly intriguing because 122.25 / 4 = 305.625 / 10
and hopefully some of us are reminded by that of the c.a. 305.7 ft projected inner circumference of the inner sarsen circle, (40 Remens of 1.216733603 ft each) x 2 Pi = 305.7985079, the basic unit of which would be via somewhat unusual application, the Megalithic Foot.
This got me thinking about just how much the Megalithic Foot and the sarsen circle have had to do with astronomy already - not just the Lunar Cycles, but heavily steeped in planetary cycles as well.
I'd gone back to some of my earliest planet cycle ratio tables because I wanted to look for examples to give of where various units are serviceable for various astronomical functions in a table of units dedicated to that purpose. (That may be about all we need to go with any reasonable versions of the other reference tables provided and I think we could about start designing Megalithic moments in what I suspect to be the traditional way).
Instead, so far I've been drawn into gawking at the resumes of some of these numbers, including the Megalithic Foot, in part since it is part of another simple formula to remember or to generate the 305.7985079 figure as simply 360 / 1.177245771.
What was so big about the fact that two different academic data sources put the diameter of the Aztec Sun Stone at within hundreds of a foot of the Megalithic Foot (and that the Maya apparently created another at Yaxchilan and seemed to treat it with unusual reverence toward such an object)?
What a calendar stone it makes! Especially because it's a circle, it will be hard to resist exposing it to the Pi ratio, and one we do we have set out on the road to discovering that
11.77245771 x Pi^3 = 365.0200808
11.77245771 / Pi^3 = 37967.98252 = 18983.99126
The common version of the near infamous Mayan Calendar Round aka half Venus Cycle of 52 years of 365 days is 18980 days.
When Susan Milbrath reported Eclipse symbolism on it, I went back and threw Pi some more and that's when it got discovered that the ideal Eclipse Unit is out there on the further reaches as the very same metrological series that gives us the above.
Pi^5 WILL indeed take us from a Megalithic Foot of 1.177245771 to an idealized Eclipse Year approximation of 346.5939368, and not only does the Megalithic Yard / the Megalithic Foot provide a shortcut to the figure ((2.720174976 / 1.177245771) x 1.5 = 346.5939368 / 100), but my Stonehenge models seem to show the Eclipse Unit actually having been used as a metrological unit at Stonehenge, including a projected value of 3.465939368 ft a lintel width figure. That is just TOO tempting with the Megalithic Yard and Megalithic Foot all over stonehenge.
I haven't caught a lot of the proposed Anomalistic Month unit in use yet but I may have at least one Mesoamerican artifact in mind where its presence may be in evidence (it's one of the calendar stones not surprisingly).
There are other roles in astronomy for the Megalithic Foot value in Imperial to play, as mentioned previously in this thread and in Peter's thread... 1/100th of 1/2 of the Maximum of Venus' Synodic Period, as a refined value for the ratio between the Mars Orbital Period and the Venus Synodic Period (in common numbers, that's 687 / 584 = 1.176369836)... It's apparently hiding in the interstices of some of Thom's Flattened Rings (unbeknownst to him, I presume)...
IMHO, it's a HUGELY important value to astronomy and no wonder it's one of two numbers that aren't Pi that they were seemingly trying to build into virtually everything that had intelligent design...
...But this creature, this 305.7985079, what was so important about IT?
About once a week, I like to mention that based on John Michell's specifications, the straight apothem slope of the Great Pyramid registered as twice this value. Almost as often I like to mention that from Petrie's data I get a distance from the Great Pyramid entrance to the roof of the ascending passage of 80 Remens or 97.33868824, the very same as the inner sarsen circle...
BTW, anyone ever catch what the relationship between these two Stonehenge-like figures featured in Egypt's most prominent 2 Pi Pyramid actually is?
(305.7985079 x 2) / 97.33868824 = 2 Pi
We also seem to see it built right into the proportions of the Thom Type A Flattened Ring so that it will be present therein at ANY scale.
(The figure as Thom gave it was Perimeter/Major Diameter = 3.0591)
So again, what was so important about numbers like these that the grandest pyramids and stone circles seem so eager to incorporate them (besides that we can say the apothem of Michell's Great Pyramid with base in Megalithic Yards has a slope in Megalithic Feet)?
Anyone happen to know the conversion ratio for the Lunar Year and the Mercury SYNODIC Period?
In common numbers, it's 354 / 116 = 30.51724138; in natural numbers its more like
354.36707 d / 115.88 d d = 3.058052037
Next, Mars and Venus want in the conspiracy some more. While the Mars Orbital Period and the Venus Synodic Period are aspiring to form the Megalithic Foot in Imperial
687 / 584 = 1.176369834
The Mars Orbital Period the Venus ORBITAL Period seem to aspire to
687 / 225 = 305.33333333
With more natural numbers,
686.971 / 224.701 = 305.7267213
Using my already established values for these Mars and Venus Cycles, they precisely form 1.177245771 and 305.7985079.
Now, though, I suppose Jupiter's going to want in on the act too?
Jupiter Orbital Period 4332.59 d / Lunar Year 354.36707 d = 12.22627712 = (305.6568280 / 100) x 4
With my numbers? That would be 4329.2929292 / 353.9334578 = 3.057985078 again...
That 305.7985078 looks like it might just be some pretty good stuff if you're an astronomer or Calendar Keeper, IMHO...
Even if I haven't quite figured out how we accomodate Mercury's Orbital Period with being a sensible part of this...
So where did these people get the absurd idea they could make calendars that involve all the planets and actually get them to work?
I'm blaming nature. In fact it might almost pass for intelligent design except for us number crunchers who know better because we have to spend so #$&^%! much time gently hammering on it to try to get it to look quite that nice.
Cheers!
[ This message was edited by: Unhenged on 2021-11-06 04:01 ]
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jonm
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| Posted 06-11-2021 at 06:49
Fascinating table posted Posted 04-11-2021 at 00:12.
To make it readable for the casual observer, it might be useful to have a key at the bottom lifting what each unit is (for example Remen = xxxx , Megalithic Foot = yyyy etc)
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Unhenged
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| Posted 09-11-2021 at 00:35
Greetings, all
Thanks for the feedback, jonm. Very good idea!
I think I would rather share this as-is with the provision that it is almost undoubtedly going to be subject to some future revisions. I don't know when the revisions might be able to happen; this is work I happened to do in the middle of two other major projects trying to go on at the same time.
Very little if any work has been done with it yet looking at the finer details of internal relationships and as such there may even be data projections here that violate formulas that were already established for the better known parts of these three main Giza pyramids.
On the other hand, there may be enough showing that I'm justified in some excitement about the results.
For background, even though the Stonehenge sarsen circle very clearly seems to have a significant set of mean values, mean values for Egyptian pyramids have not been such a simple matter in the past (nor are they all that simple even now).
On a number of occasions, I've tried to explore the premise that the Great Pyramid is just as entitled to a significant mean value as is Stonehenge; the "license" here for a mean is that my model attempts to reconcile two disparate but indispensible models of the Great Pyramid - Carl Munck's, and John Michell's.
That's mathematical models. All I know to attribute the disparity physically is to is a hypothetical layer of pavement that has gone missing because a) it was made of a prized material b) consisted of smaller lighter blocks that were easier to plunder than the Great Pyramid casing stones and hence would have been the first thing to be stolen and c) happened to be arranged so there were minimal obstructions to its removal - it didn't have to be liberated from out from under anything else, it would have rested on the base of the casing stones and within the enclosure walls.
This speculative paving material may have been very similar to that found under the adjacent mortuary temple (some of which still survives), and according to calculations was likely 4/10 = 2/5 Royal Cubit thick, which is the same value calculated for how much the further the bottom of the Great Pyramid's platform projects outward than the top.
Given some of the mathematics involved, it seems reasonable enough that the same paved courtyard feature was also destined for the pyramids of Chephren and Mycerinus so that they too would have both minimum and maximum - or "paved" and "unpaved" - models from which mean values can be obtained.
A great difficulty however has been to try to determine whether a single set of data projections for the Mycerinus pyramid should refer to the minimum, mean, or maximum intended for its proportions.
What has happened the last several days is that it finally occurred to me that the Hashimi Cubit value that for almost 20 years I have felt massively apologetic about NOT being the unit of the Great Pyramid model, once we re-examine what the likely maximum diagonal value might be, can actually fit comfortably as the mean diagonal value of the Great Pyramid's base.
This has helped to resolve a riddle over that the intended mean height of the Great Pyramid was, and thus emboldened by actually being able to obtain a fairly sensible model for the Great Pyramid's mean, I not only set out to look at mean figures for Chephren's pyramid, and having some apparent success there, subsequently set out to try again to sort out whether the proportions given for the Mycerinus were intended as min, mean, or max values.
Several years or so ago, I was called upon to revise the measures of the Mycerinus pyramid from the model Munck used. Munck had relied on data from I.E.S. Edwards, who in my own opinion is NOT a good source on pyramid data and had something of a lackadaisical attitude toward the matter. Hence Munck's model of the Mycerinus pyramid ended up approximately some 10 feet larger than the pyramid described by some small consensus between Flinders Petrie and Glen Dash, as was pointed out on GHMB by moderator "Dr.Troglodyte". (I based my revision on the diagrams provided by "Dr.T" after vetting the data).
Rather than dwell on some of the things that might try to overturn some of the modelling suggested here, I'd like to focus on a few positive things (and yes, some of the mean values look pretty skewed - looks like someone let Andre Spatzier near the data, lol - but by definition the means will be somewhat skewed in these models as was the sarsen circle mean, and the skewing can be magnified by both scale and by calculation, similar to how small diameter adjustments can have larger impacts on the corresponding circumference values.
Several things I'd like to point to - 1) the mean data for the Chephren Pyramid seems to further reinforce a strong case to be made that its design shows a strong preoccupation with the expression of the Lunar Year value, and 2) the data emerging here suggests that the Mycerinus Pyramid design may show a comparable preoccupation with expression of the Eclipse Year value.
Third, and perhaps most important of all, is that what started out as observation of emulation of Stonehenge's outer sarsen circle perimeter by the Mycerinus pyramid's vertical edge length, has here blossomed into observation of a much more thorough emulation of sarsen circle functions.
Surprisingly, if we take into account also the diagonal values projected for Mycerinus' pyramid, it seems able to take on the fuller responsibilities of the sarsen circle of "showing us what the Megalithic Yard and Megalithic Foot are and are not". The closer we look, the more homage to Stonehenge's design logic it seems to pay.
The other thing I want to say here because I'm not sure how easily everyone might spot this, but I've made a point of it to underscore how the whole metrological network system in question can be regenerated from only Pi (or 2 Pi, same difference), 60 and sqrt 60.
It's possible that what we are seeing in the Mycerinus serves as a third very vital but missing component in understanding such a metrological network, because in the course of emulating Stonehenge, the Mycerinus converts Stonehenge's circular circumference measures into a linear vertical edge length.
Converting a linear radius or diameter in one unit into a circumference value in another unit is the very essence of how the metrological network shown in previous diagrams works - by projection of a series of circles in which the radius or diameter of one becomes the circumference of the next.
Such a gesture being so integral in unbundling and understanding the metrological system, what the Mycerinus seems to be doing with the vertical edge value could be considered the ultimate complement to what has been established with the perimeter/height ratios of the Cheops and Chephren Pyramids.
I should probably go ahead and point out a couple of other things?
The maximum apothem length for the Mycerinus has been projected here as either "277.2751496 OR 277.3819995?". I find it quite remarkable that for my having chose for the perimeter/height ratio of the Mycerinus a value that I'm not sure if anyone else on earth would have chosen, if we half 277.2751496, we get 277.2751496 / 2 = 138.6375748 = 34.56939370 x 4, so that somehow the Eclipse Year is readily displayed in both the max perimeter and maximum apothem.
Again, the max perimeter of the same pyramid was projected as probably 1386.375745
(138.6375748 is also what I have for the perimeter of Thom's Stonehenge "Oval with Corners", further advancing the premise of the combination of Megalithic Foot and Megalithic Yard forming the Eclipse Year).
Again as recently mentioned, since Michell's Great Pyramid model consists of Megalithic Yards, converting it to Megalithic Feet finds Eclipse Year data, but this cause seems to have furthered even more dramatically by the projected Mycerinus Pyramid figures.
This may also constitute a substantial amount of additional evidence of an Eclipse (Year) Unit having been in ancient use, along with the displays of same at Stonehenge.
We may wish to bear in mind that along with 1/2 the Great Pyramid's maximum baseline being an excellent and highly useful approximation of Saturn's Synodic Period, the projected dataset shown here also seems to give us a simple fraction of the Jupiter Orbital Period as the Mycerinus Pyramid's maximum height, and what is probably the Mars Synodic Period seems to be modeled by the Chephren pyramid's vertical edge, in addition to its mean vertical value being in rather obvious Royal Cubits.
Also, the projected diagonals for the Mycerinus may also be Stonehenge / Great Pyramid references, potentially being more simple multiples of the inner sarsen circle circumference, so the Mycerinus Pyramid may be singlehandedly managing to pay homage to both the inner and outer sarsen circle values.
I wish I had designed it but I didn't; I simply tried to take Petrie and Dash's data and derive a sensible base length and perimeter / height ratio, said height being one of those rare displays of Imperial used as a design unit rather than an interpretive unit, possibly along with the Chephren Pyramid, where the mean of the strange unsolved diagonal values seems to have an even better chance of being 1000 Imperial Feet than the min and max diagonals seem to have.
One of these days maybe it will be time to go back and try again to figure out what unit the ancient Egyptians used for the length of the Great Pyramid's "King's Coffer", another unsolved Giza problem of long standing. I've asked myself before "What if it were something strange like an Eclipse (Year) Unit?" but I never took the question as seriously as I might be tempted to as the incidents of apparent use of an Eclipse Unit seem to accumulate.
Cheers!
[ This message was edited by: Unhenged on 2021-11-09 02:46 ]
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Unhenged
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| Posted 09-11-2021 at 02:02
Hi again!
I feel like there are perhaps a couple more things I should have said even though I've already said much...
One is that if I'm going to refer to the two metrological series illustrated as "Square Root Numbers" and "Pi Numbers", I should have gone over some basic ideas about those concepts.
"Pi Numbers" includes the whole numbers used to make them, even if that's a bit of a misnomer.
When these numbers interact, we can observe following rules:
Two "Pi Numbers" interacting through multiplication or division will always result in another Pi Number, they will never produce a "Square Root" number.
Two "Square Root Numbers" interacting through multiplication or division will always result in a Pi Number, they will never produce a "Square Root Number".
A "Square Root Number" interacting with a "Pi Number" through multiplication or division will always result in a "Square Root" Number, they will never produce a "Pi Number".
This information used in conjunction with the unit series tables can be helpful. As I become accustomed to them, I am beginning to be able to simply consult the tables concerning simple analytic observations concerning unknown numbers, often saving as many as 30 calculations that would be required to test 18 units and their reciprocals against them to try to see what unit they are made of.
I've also seen my first real life example of a unit value crossing back across the center point instead of proceeding directly toward the far ends. It involved the Megalithic Foot with (2 Pi)^3 producing either the Incidental Megalithic Yard going one way in the progression, or the Megalithic Foot again going the other way, and it happened to be the other way.
I'm still a bit awed at seeing that, that crossing the center points (Sacred Cubit and Imperial Foot) of the two series, 2 Pi is sometimes able to convert a unit to another whole numbered value of the SAME unit, a property one might swear was seen only in whole numbers.
It seems like perhaps I should emphasize another thing - it's about how I'm somehow getting Petrie's Inductive Metrology (whole numbered quanta of units monitoring) to work, when by rights it shouldn't. It does seemingly work ONLY because of the selection of historical units that MAKE it work. It seems highly unlikely that anyone designs architecture using only whole numbers of any single unit.
That seems to me to require deliberate choices of unit values and MUCH premeditation on the part of the ancients.
To me it seems much as if the ancient architect and designers ANTICIPATED the problems that whole numbered unit quanta monitoring could face, and specifically provided us a way around such obstacles. I DON'T think I'm the one who made Inductive Metrology work, personally I think it had to be them.
Also, since I posted data on a possible Great Pyramid mean, maybe it's only fair if I explain a little about why I found such a skewed mean to be favorable? Well, for one it's something of a consequence of adjusting the mean of the base into what very much seems only reasonable - I'm about 16 or 17 years wondering whether the Great Pyramid was deliberately built somewhat trapezoidal in order to try to make the min diagonal value into Hashimi Cubits, that many years before I knew or believed that 1.067438159 as Imperial Feet really was a metrological unit.
There is some impressive recovery of astronomical data via the mean measures for the Great Pyramid.
The suggested value for the mean height is 480.8701159 ft and for the mean perimeter 3021.396047 ft...
Being it's something I think can never be over-emphasized that the Great Pyramid, the pyramid that thinks it's a circle, has as its most fundamental message simply that radius x 2 Pi = circumference, and in sexigesimal that is Radian x 2 Pi = 360*
Thus its gratifying to be able to take these fundamental Great Pyramid numbers and find
3021.396047 x 2 Pi = 18983.99125, the best viable approximation of the half Venus Cycle, and
480.8701159 x Radian = 27551.82813, or 1000 times the best viable approximation of the Anomalistic Month.
These are of course NOT things we could accomplish so well with the established min or max measurements.
The suggested mean perimeter 3021.396047 also follows John Michell's model, except the "Alternate e" Megalithic Yard of 2.720174976 has been substituted with the "Incidental Megalithic Yard" of 2.719256444, and especially with the aid of the tables we can observe that the Incidental Megalithic Yard is only one power of Pi away from the Eclipse (Year Unit), and being Michell's formula uses an inverted multiplier, can thus anticipate that the height of 480.8701159 with a perimeter/height ratio of a whole number of Pi, therefore would constitute another example of actual real-life use of whole numbers of the Eclipse (Year) Unit in architecture, without performing further calculations to determine this.
I'm sure there must be more in the expanded Giza models to discover over time, as with other parameters of previous models.
Even in only a short time however, better understanding the nature of the metrological network really is showing promise of being able to save on hundreds and even thousands of manual calculations in the course of interpreting ancient architectural measures.
I was also going to explain my remarks about Stonehenge homages. Again, besides the projected Mycerinus vertical height values imitating both the outer sarsen circle and the outer lintel circle measures from my Stonehenge model, there is the Mycerinus diagonal, for which the minumum value is suggested in the chart to be 489.2776124.
489.2776124 / 16 = 30.57985078 = inner sarsen circle perimeter / 10; 489.2776124 / 18 = 2.718208958, the false Megalithic Yard (really the Megalithic Foot) that is the diameter measure to a circumferential measure in Hashimi Cubits.
The uncertain RAW projected mean and max values of 489.4594688 and 490.1578454 divide by 18 (18 being simply half of 360 / 10) respectively to suggest the Incidental Megalithic Yard 489.4594688 / 18 = 27.19219372 for 27.19256444 and 490.1578454 / 18 = 27.23099124, which I suspect is the other Stonehenge false Megalithic Yard (also made of Megalithic Feet), 27.25105951.
The accuracy is off just enough to suggest this may be another calculation where only methods of calculation may be applicable for clearing the accuracy standard, as may be the case with the Great Pyramid and the Lintel Circle. As seen previously the case of the Lintel Circle is strange, wherein one perfectly accurate and legitimate calculation of the mean passes accuracy standards while a second perfectly accurate and legitimate calculation of the mean somehow does not.
As of this hour, these are all still only suggestions, and again, at least a few future discoveries and revisions seem fairly likely.
Cheers!
[ This message was edited by: Unhenged on 2021-11-09 02:53 ]
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Unhenged
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| Posted 09-11-2021 at 04:54
Hi, all
I fixed a couple of errors and added descriptions at the right of the table of the particular units that are being suggested as possibilities, i.e., the units that make up the projected measures at left. I hope it's still legible as I reduced the size somewhat. Please let me know if not.
Note that the Megalithic Foot seems to have done rather well for itself in this exercise even amid all the competition.
Cheers!
[ This message was edited by: Unhenged on 2021-11-09 05:06 ]
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jonm
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| Posted 09-11-2021 at 09:13
Thanks for the feedback, jonm. Very good idea!
Great. Would be interested if you could flag it up if you get round to doing it (finding it hard to work out what all the above is about!)
It's this one that I couldn't easily see what was being multiplied by what, so examples of what these units are would probably help the reader:
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Unhenged
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| Posted 11-11-2021 at 01:17
Greetings, all.
Here is a concise table of unit values. I hope I have understood correctly that that is what is being suggested.
Here is the unit table. (The color coding used matches that on the large diagram showing both series of metrological units, rather than the color coding on the table of unit interactions as I thought that might be just a little more relevant and/or useful).
I want to say that I'm pleased with how the preceeding charts are working out. Yesterday I was feeling slightly apologetic that the incomplete table of chart interactions only shows two combinations of units which produce a value in Anomalistic Month units (there's some catching up to do with Anomalistic Month because it was the last one to arrive at the party).
So using the charts, I was able to find four more combinations resulting in the Anomalistic Month in the fifteen minutes it took to finish my first coffee of the day, rather than taking all day or even not taking place at all as it has gone previously.
HOW do we do this? Well, let's say we want to know what unit to combine with the Palestinian Cubit to get the Anomalistic Month Unit. The chart shows that the Palestianian Cubit is a Pi^5 number and the Anomalistic Month is a Pi^8 number, so we know it is Pi^8 - Pi^5 = Pi^3 from one to the other, and the corresponding Whole Number and Pi Unit at Pi^3 is the Draconic Megalithic Yard, so by combining the Pi^5 number from the left column and the Pi^3 unit from the right column, we generate the Pi^8 number from the left column.
With only several equations, we can verify whether the two units which in combination produce the Anomalistic Month should be multiplied or divided in order to do so.
Draconic Megalithic Yard 2.721223218 x Palestinian Cubit 2.107038476 = 57.33722022, which does NOT reduce via the Anomalistic Month Unit 2.755182715 to a whole number. Therefore, we must have to divide the Draconic Month by the Palestinian Cubit to produce a whole numbered quantity of Anomalistic Month Units...
2.721223218 / 2.107038476 = 1.291491944
A bit of a tough one, but 2.755182715 / 1.291491944 = 2.133333333, and we know that valid trailing decimals are generally the sign of an inverted whole number (1 / 2.133333333 = 46875 / 10^n), so we know that we have successfully reduced the value 1.291491944 to a whole number of Anomalistic Month Units of 2.755182715 feet.
We can continue to work in the same way with the other units from the left column of units, and in minutes we will find four more combinations of units that in operations of multiplication or division with give a value that is a whole number of Anomalistic Month Units.
As we begin to understand the nature and structure of the system of metrological units, that understanding can take a great deal of guesswork and searching (often seemingly in vain) out of the proceedings.
That is enough for one post, but I might gather my wits later and share some comments about some other recent discoveries and considerations. One thing I did is revisit a number from Stonehenge that showed up in the mathematics for Thom's "Oval With Corners". It is 1.451809286 and I have managed to confirm some interesting mathematical properties, and that it qualifies as a "Wonder Number", so while it's not a new discovery, it's a new realization of a Stonehenge "Wonder Number" and it has already been found in the Great Pyramid model also.
Cheers!
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Unhenged
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| Posted 11-11-2021 at 02:20
I have declared that 1.451809286 is a Stonehenge (and Giza) Wonder Number. I should be quick to point out that it is something of a secular Wonder Number - that is, its response to a variety of the most powerful data retrieval tools appears to be limited. However, it has nonetheless seemingly qualified as a Wonder Number because it fulfills two classic criteria previously used in the identification of Wonder Numbers.
1). It is profoundly responsive to at least one of the more powerful data retrieval tools (in this case, 2 / 1.622311470) and
2). It serves as the seed for a remarkable series that begins higher or lower that we would ordinarily expect
The second characteristic particularly may be seen with a significant number of the Wonder Numbers reported from Tikal.
1.451809286 also has some other intriguing mathematical properties. It was nominated for a role in the "Oval With Corners" calculations because there were multiple metrological pointers to it - that is, multiple combinations of known units that produce this figure or a simple multiple or fraction thereof - but it's response to the Palestinian Cubit in such interactions is indeed remarkable.
I was about to post a warning that although there are some "Square Root and Pi" unit values that we can square to obtain known "Whole Number and Pi" unit values - i.e., as seen on the unit interaction table, the Megalithic Foot^2 = the Outer Sarsen Circle Diameter Unit and the Hashimi Cubit 2 = the Tikal Temple III Unit, and etc - when we square the Palestian Cubit we seem to create a monstrosity that requires about Pi^15 to resolve into a whole number. This may have mathematical value, but its difficult to think of as having metrological value when the cap on what's reasonable for metrological values seems to be "root" (Sacred Cubit or Imperial Foot) x (Pi^9).
It was demonstrated that nonetheless, the CUBE of the Palestinian Cubit value pulls recognizable data from 1.451809286. To me that is more or less inconceivable given how many powers of Pi it takes to turn the SQUARED Palestian Cubit into a whole number, but so it is.
The presence of 1.451809286 in the Great Pyramid was confirmed as the product of Munck's height for the Great Pyramid and John Michell's perimeter for the Great Pyramid (1111.111111 Megalithic Yard, where I use the AEMY value 2.720174976 ft)
Ht. Great Pyramid Munck 480.3471728 ft x Per. Great Pyramid after Michell 1111.111111 x 2.720174976 = 3022.416640 ft = 480.3471728 x 3022.416640 = 1451809.288
That is, we are taking two of THE most fundamental and blatantly obvious of the Great Pyramid's measures, and are somehow "magically" able to construct the Stonehenge Number from them.
At about the currently known upper end of the (2 / 1.622311470) series generated from 1.451809286 is something that greatly resembles Peter Harris' Unifying Value 413.42 (Astronomy & Measurement in Megalithic Architecture, page 28). I am still taking it "under advisement" whether we should accept it as such, or dismiss it. I'm very much on the fence whether there should be, or would need to be, three versions of such a Unifying Value, but many surprises have come from realizations about traditional variant calculations (such as 364 vs 365, the Dresden Codex Variations on the Mercury and Venus Synodic Periods, and so forth), so I'm happy to remain on the fence observing for now.
It can be a little difficult to tell, because that is a characteristic of heavy use of 2 / 1.622311470 - after generating a brilliant series of data, if we continue to apply 2 / 1.622311470 we will get a similar series that is mathematically mutilated so that it is little more than an inferior copy of the series that led up to it. We likely wish to stop or back up when we see that, or when we see the mutilation of numbers that border on being literally "sacred" like 2 Pi or the Megalithic Foot value in Imperial.
I haven't gotten up the ambition yet today to type out the whole series that I think qualifies 1.451809286 as a Wonder Number, but I at least wanted to put forth some of the math I was referring to in the last post, so that people don't have to just take my word for things completely. I do make my share of mistakes, especially when I harbor such grand ambitions. Usually if erred only 1% of the time, that would be a wealth of mistakes!
Cheers!
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jonm
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| Posted 11-11-2021 at 09:53
Hi Unhenged
A problem with the above table is that if you take two random figures from it: Say the "megalithic foot" at 1.1772ft and the "royal cubit" at 1.718ft you get a figures of 2.022 sqft.
Your table below says that is equal to one "Hasimi cubit (ERF)". But your table above says that a "Hasimi cubit (ERF)" is 1.067. So at that point, anyone reading will give up. I'm guessing that you're doing something else with these tables, but the problem is that you haven't explained what.
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Unhenged
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| Posted 12-11-2021 at 00:03
Hi, jonm
Thanks once again for the insightful observation. You are very right, the language at the top of the second chart is at best ambiguous. At very least "whole number" should appear more than once in the sentence to try to make clear that "a whole number of one unit multiplied or divided by a whole number of a second unit will usually equal a whole number of a third unit".
I think the "something else" I am doing must come down to not having equipped the second table with the actual numbers of units that are involved in the conversions, which tends to range between anything from the blatantly obvious to the unexpected and almost obscure.
I will try to come up with a version of the second chart that includes that data, as I included it for the conversion of ADJACENT units in the chart on black background that shows the two series of units in entirety.
I might be wise to try to fill in more of the second table in your post first (?), but following your advice here is now near the top of my to-do list.
Many thanks!
Cheers!
[ This message was edited by: Unhenged on 2021-11-12 00:04 ]
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Unhenged
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| Posted 13-11-2021 at 01:14
Greetings, all
It is as they say "too soon to tell" but I've been pouring over the data for the proposed Giza model that attempts to account for mean measures of the three main pyramids there, and also attempts to define whether the revised Mycerinus measures were intended to represent maximum, minimum or mean proportions.
Overall, it looks a bit of a strange brew that seems to take some effort to understand the madness of. There are a lot fine ratios flying about because of comparing similar proportions, which I will try not to frighten anyone with here, but I want to offer a few general comments about what things like in general as of this hour.
From where I'm sitting, it LOOKS like that where the pyramid of Chephren (Khafre) was intended to serve as something of a sourcebook on the Lunar Year, the Mycerinus pyramid was intended to serve as something of a source book on the Eclipse Year.
This includes that someone may have decided that while they are working with values that have multiplicity, they might seize the opportunity to try to show us how to navigate an ever-perplexing riddle which we may call "The Eight Problem".
(Basically "The Eight Problem" is what we see when we try to coordinate the Jupiter Orbital Period, Eclipse Year and Metonic Cycle. Turns out their cosmic choreography isn't quite perfect and it's up to us to iron the consequences somehow. It's provided me with vast amounts of perplexity trying to figure out how anyone dealt with that).
I hope I have already mentioned that the data projections show me that the vertical edge - even as a multiplicitous value once we project maximum, minimum, and mean values - not only continues to a fine job imitating the Stonehenge sarsen circle, but between the Mycerinus pyramid's vertical edge and base diagonal, we seem to have the entire teaching from Stonehenge about what Megalithic Yard and Megalithic Foot are and are not.
This revelation goes so far as noting that the likeness to Stonehenge includes "The Valley of Kings Number" in the vertical edge.
In spite of more individualized skewing of mean values seemingly taking place from one pyramid to another, we see that the proposed mean values can lend themselves to some very informative and unifying statements in astronomical metrology, relying only on the most blatantly obvious elements present at Giza to reveal this.
As was shown for the Great Pyramid, mean baselength x 2 Pi = the half Venus Cycle and height x Radian = the Anomalistic Month x 10^n...
For the proposed mean height of the Mycerinus Pyramid, it was noted that
a) it was noted that 15 / 216.1562274 = 6939.425332 / 10^n, which is the lovely Metonic Cycle (textbook 6939.688 d) approximation made from cubing the reciprocal of 2 Remens... AND..
b) 216.1562274 / (Radian Squared) = Best Saros approximation (textbook 6585.3211 d (6584.495227 / 10^n).
Here we used only the radian (exponentially) and 60 / 4 to generate another PAIR of HIGH QUALITY approximations of known astronomical cycles.
c) the figure is remarkably like Nodal Cycle 6793 d / Pi = 216.2279057, but it has yet to be confirmed if substituting 216.1562274 here forms a valid equation as the ideal values for a nodal cycle set may remain somewhat uncertain for the moment. (It may not always be quite possible mathematically for us to get everything we'd like).
Part of the Mycerinus pyramid's teaching about the Eclipse Year may also concern an "Eclipse Year Builder" which would be analogous to the "Half Venus Cycle Builder" figures that can arise because of inverted numbers, which can be "corrected" due to the fact that the half Venus Cycle is similar to the square root of 360 x (10^n).
The "Eclipse Year Builder" seems to capitalize on the similarity of the Eclipse Year to (sqrt 12) x 10^n in order to "correct" an inverted figure.
It's not a new discovery, although it is a new thing and a big surprise to think of them actually addressing this prospect at Giza.
There is one other thing on my mind, because some of the concerns here remind me of it very much, which is the El Castillo Pyramid at Chichen Itza in Mexico.
It isn't usually that I trust Teobert Maler on large measures like the exterior of moments, no matter how impeccable I consider most of his data on smaller measures used in architecture to be, just because so many of the structures in question were in states of dilapidation and disrepair when he visited them. (I don't think to this very day Temple 6 at Tikal has been cleared off, my understanding is poor but something to the effect that they are "keeping it in a natural state"?)
However, partly because there are photos suggesting that the El Castillo probably WAS successfully cleared off so that Maler could measure accurately (old photos show the structure exposed all the way down to the serpent heads at the bottom of the staircases), and partly because it's such interesting data, I DO tend to take him at his word concerning the two sides of the base of the El Castillo Pyramid that he measured.
Briefly, based on his data I interpret the two sides as representing a pyramid based on a mathematical symmetry involving the numbers Pi and 6: length = 100 x (6 / Pi) and width = 10 x (6 x Pi) Imperial feet, wherein the length serves as the square root of the approximated Solar Calendar Year and the width serves as the approximated square root of the Lunar Leap Year.
The resultant diagonal has been the subject of considerable confusion and internal debate - there is more than one strong possibility that falls within acceptable tolerances.
It comes to mind here talking about how the half Venus Cycle resembles the square root of 360 x 10^n and how the Eclipse Year resembles the square root of (360 / 3) x 10^n, that one way of describing the El Castillo pyramid's projected base diagonal for a symmetric rectangular structure, is as strikingly similar to the square root of (360 x 2) x 10^n.
It also comes to mind because I am thinking a lot about the hugely important Harris-Stockdale Megalithic Foot, which we can write as 10*((sqrt 2)/12) or optionally, as 10*(sqrt (1 / 72)).
If I consider also how far out of their way ancient Americans seem to have gone to make 10 Megalithic Feet the perimeter of the Aztec Sun Stone, and how far out their way they seem to have gone to make 100 Megalithic Feet the major width of the Pyramid of Niches of El Tajin, and how much I have been saying things like that the Megalithic Foot seems to be a numerical value ancient architects everywhere seem to have wanted to build into everything, or how it's the most important thing to build into architecture after Pi itself for the purpose of recording and retrieving astronomy data...
I'm suddenly wondering anew if the El Castillo's diagonal really needs to seem as mysterious as it may try to seem.
Lastly, regarding the spray of fine ratios that comes forth from the suggestions for mean values for the three main Giza pyramids, I would say from staring at them a bit that their nature and intent may be mostly to provide certain key ratios involved in conversion of astronomy cycle sets, while Cheop's pyramid, true to its apparently highly geodetic constitution, seems able to also provide a critical but rarely seen ratio in the max/min ratio for its vertical edges (specifically, the ratio standard equatorial circumference / standard polar circumference).
The "Valley of Kings Number" may also prove to be one of these ratios used for conversion of various forms a given Solar System period, and a number of fine ratios may be required for this. Again there may be as many as at least 4 forms of the Solar Year alone, representing 364, 365, 365.25 and 366, which would create four different ratios against both one another, and against another Solar System cycle.
Based on the ratio data and the premium on sensible ratio values, the maximum apothem for the Mycerinus pyramid has been seemingly narrowed down to 277.2751496, allowing a more realistic mean of (277.2751496 + 276.6799708) / 2 = 276.9775602 to be reached.
Here we may use a fine ratio advantageously to attenuate the previous suggestion to obtain a VALID approximation of the raw figure for the newly redefined suggested mean: 277.1815211 / 1.000723277 = 276.9811869.
The suspected representation of astronomical values therein would include formulas such as follow:
276.6799708 / 8 = (12 / (Metonic Cycle / 2)) x 10^n
276.9811869 / 8 = (12 / Eclipse Year) x 10^n (the "Eclipse Year Builder")
277.2751496 / 8 = Eclipse Year / 10
Cheers!
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STOCKDALE
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| Posted 14-11-2021 at 12:03
Hi Robert, thanks for the Luke PiWalker blog. I just wondered if you or anyone else had read this book? Any useful measurements or information in it re Archaeoastronomy? Must admit some of the criticisms are quite damning of its content!
Spirits in Stone: The Secrets of Megalithic America Illustrated Edition, Kindle Edition
by Glenn Kreisberg (Author), Graham Hancock (Foreword) Format: Kindle Edition
4.7 out of 5 stars 21 ratings
Kindle Edition
£10.99
A ground-breaking study of ceremonial stone landscapes in Northeast America and their relationship to other sites around the world
• Features a comprehensive field guide to hundreds of megalithic stone structures in northeastern America, including cairns, perched boulders, and effigies
• Details the Wall of Manitou, the Hammonasset Line, landscape astronomy along the Hudson River, and a several-acre area in Woodstock, NY, with large, carefully constructed lithic formations
• Analyzes the archaeoastronomy, archaeoacoustics, and symbolism of these sites to reveal their relationships to other ceremonial stone sites across America and the world
Presenting a comprehensive field guide to hundreds of lost, forgotten, and misidentified megalithic stone structures in northeastern America, Glenn Kreisberg documents many enigmatic formations still standing across the Catskill Mountain and Hudson Valley region, complete with functioning solstice and equinox alignments.
Kreisberg provides a first-person description of the “Wall of the Manitou,” which runs for 10 miles along the eastern slopes of the Catskill Mountains, as well as narratives about related sites that include animal effigies, reproductive organs, calendar stones, enigmatic inscriptions, and evidence of alignments. Using computer software, he plots the trajectory of the Hammonasset Line, which begins at a burial complex near the tip of Long Island and runs to Devil’s Tombstone in Greene County, New York. He shows how the line runs at the same angle that marks the summer solstice sunset from Montauk Point on Long Island, and, when extended, intersects the ancient copper mines of Isle Royal in Upper Michigan. He documents a several-acre area on Overlook Mountain in Woodstock, New York, with a grouping of very large, carefully constructed lithic formations that together create a serpent or snake figure, mirroring the constellation Draco. He demonstrates how this site is related to the Serpent Mount in Ohio and Ankor Wat in Cambodia and reveals how all of the vast, interlocking sites in the Northeast were part of an ancient spiritual landscape based on a sophisticated understanding of the cosmos, as practiced by ancient Native Americans.
While modern historians consider these sites to be colonial era constructions, Kreisberg reveals how they were used to communicate with the spirit world and may be remnants of a long-vanished civilization.
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Unhenged
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| Posted 18-11-2021 at 06:27
Hello, Peter and all
Apologies - I'm not familiar with the work in question although it sounds intriguing.
Thank you for mentioning my blog post. I had to go so far as buying a new computer just to get a browser upgrade after my old one was beaten half senseless by a Windows Update, but I have finally begun to be able to access and post my blog again for the first time in about six months.
The latest, with some corrections and what may be some new discoveries, including at Stonehenge.
Short Reports 7
Cheers!
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Unhenged
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| Posted 21-11-2021 at 13:38
Greetings, all
Another temporary Megalithic Portal exclusive for you.
Here is the latest state of the art for the Unit to Unit Interaction Table. After uploading it I noticed some mistakes concerning the operation symbol in the far right column. It should in all cases of course be the same operation sign as to the left of it in the row, and presumably in most if not all cases, the correct operation has been performed to give the formula in spite of the wrong operation symbol being used.
The table has expanded vertically since the last version with more rows now featured, and as per jonm's feedback, the fourth row to the right has been added which contains a specific formula for each unit to unit interaction.
I don't know if I'm quite ready to start designing my own ancient architecture as I think of it being designed, but I've left the formulas column a bit subdued so that mainly just the unit interactions stand out, because I want the table to still allow focus on the simpler ways of describing the unit interactions as we learn more about how to make use of them.
In spite of my lack of preparedness, I'll give it a try because I do want to try to illustrate how I think the data table could be useful from a design perspective.
Let's say I've got a Mayan architectural commission, so I'm starting out on my first room in the design, and events dictate that there should be emphasis on Venus and Saturn - but it's also perhaps an opportunity to me as an architect to "enshrine" some of my own formulas or to champion the cause of what I think are some neglected numbers.
Let's say in this case I want to make a statement of some kind about the Draconic Month and the Anomalistic Month, two very important cycles that I don't think get enough attention...
So I go to the table and look under Draconic Megalithic Yard at the left. The Hashimi Cubit as we now know is superior for expressing an idealized Venus Orbital Period figure (240 / Hashimi Cubit 1.067438159 = 224.8373808), so I can begin to consider the consequences of such a combination of units of measure.
The table tells me that if I make the length of the room to be a measure in Draconic Megalithic Yards and the width of the room to be a measure in Hashimi Cubits (or vice versa), the ratio created by dividing length by width will be a figure in Incidental Megalithic Yards, an alternate form of the Draconic Month, and their product will be in Sacred Cubits.
So, the table informs me that this combination will give me TWO versions of the Draconic Month=Megalithic Yard for the price of one AND the product of multiplying the length and width will be in Sacred Cubits, which should bring us face to face with THE most powerful data retrieval key, which is a value in a whole number of Sacred Cubits, sqrt 60, which is 1/27 of 100 Sacred Cubits - and the Sacred Cubit can be used to express the Saturn Orbital Period, so I've got my requisite Venus and Saturn references in there where they are fairly visible.
What will I do about featuring the Anomalistic Month? Well, the table advises me that the Draconic Megalithic Yard interacting with the Anomalistic Month uses the Palestinian Cubit, so if I make the height of the room to be in Palestinian Cubits, the length / height ratio will produce a figure that is a whole number of Anomalistic Month units (a little table of what astronomy statements can be made using which units will help me out there if I forgot).
This is another brilliant bit of "good luck" because the Palestinian Cubit serves as the basis for the best approximation of the (Almighty) Calendar Round as well as other important astronomy values, including reinforcement of the Saturn motif because one of these other values is the Saturn Orbital Period / Synodic Period data.
I haven't even gotten to the vaulted arch making up the upper part of the typical Mayan room, and I've managed to check off all the items on my first to-do list as an architect in what was hopefully once a traditional manner and still produce what might just turn out to be a fairly satisfactory overall design. Might be beginner's luck, but maybe not bad for a first outing,
Now I begin to wonder what I will have if I made the total height of the room plus the value to be in Megalithic Feet (see also HSFM)... the total height / room height ratio will then be in a whole number of Megalithic Feet / Palestinian Cubit and hence a value that metrologically would be in the Pi^3 Unit also known as the Tikal Temple III Unit... If it doesn't clash with some of the other units already selected, it would be a very gratifying touch to the design to add this as if perhaps in mathematical homage to Tikal's temple pyramids, which the whole Rio Bec school of Mayan architecture seems to pay tribute to artistically.
Tikal's pyramid temples include some brilliant math that's worth any ancient architect knowing about and which may have set trends in ancient Mexico.
I wouldn't even have known where to start with that had it not for having the included reference table at my disposals, even though it did not require my considering the specific formulas at far right of the table to accomplish this initial semblance of a Mayan room design.
So there is an example of one way I picture such reference tables as being of use. As such I intend to make more refinements to the tables as time allows, but since this might be the incarnation the latest table will stay in for awhile, I may as well share it in case it avails anyone else in the meantime.
Cheers!
[ This message was edited by: Unhenged on 2021-11-21 13:42 ]
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jonm
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| Posted 21-11-2021 at 15:06
Nice table
The figures only work if Imperial Unit of one foot is used (as opposed to a metre, yard, inch or whatever). Is it your argument that the Imperial foot has some sort of correlation to the distant past of various communities around the world David?
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