Post by barnabaslives on Oct 30, 2019 4:10:12 GMT
Wolfie just made the terrible mistake of encouraging me to share more about my forays into ancient history. I just lost a few paragraphs to a power bump, but maybe I'll try again. I don't know what it is about me and ancient history, but I always end up pointed back in that direction no matter what I try and get interested in - botany, physics, medicine, religion, you name it. At one point, if I'd had my way I'd have ended up like Sean Connery in "Medicine Man", roaming the jungles looking for medicinal substances to serve as "lead molecules" for the pharmaceutical industry. I suppose it's not so often we do much with such discoveries, but in my ethnobotany studies as with other subjects, I learned to have considerable respect for the knowledge and intellect of indigenous peoples and traditional cultures.
I guess that's a story in itself so I'll try to skip most of it. Suffice it to say it's more trouble that Dark Shadows got me into, lol, that one morning I'm watching Dark Shadows on the Sci-Fi channel when I see an advertisement for a video by Richard "Face on Mars" Hoagland and became terribly intrigued with his suggestion that some of the man-made features of the Salisbury Plain might constitute a incomplete model of Martian surface features. I was hugely impressed with the model that Hoagland had participated in of the geometry of his five-sided "Martian pyramid".
Hoagland's materials introduced me to the work of a man named Carl Munck and his "Pyramid Matrix". Munck had the idea that ancient peoples had somehow worked out a global positioning system identical to our own, in which the physical features of ancient monuments represented formulas that could be "decoded" into their geographic coordinates to explain "why they are where they are" and where other, often thematically related monuments, were located. In 1998 I began working with Munck's materials and was soon taken under the wing of Michael Morton, who had also been working with Munck's theories and doing a great deal of experimental work with them, trying to fill in some of the gaps in the curriculum.
After about 10 years working closely together, Morton and I had a falling out when I got my hands on a copy of Mark Lehner's Giza Plateau Mapping Project book, and ran into so many major anomalies that in the course of trying to sort it out, the sad truth finally came to my attention that none of us including Munck had adequate qualifications in cartography to be able to actually support the work were doing with things being "why they are where they are", and even though I'd developed great faith in Munck's use of mathematics, I lost so much faith in what was our fundamental premise of a global coordinate system that I ended up giving up on the whole thing, and I think Morton, who doesn't seem to be with us anymore, was quite incensed that I'd "blown the whistle". We had a message board where we'd made several thousand posts sharing various discoveries we'd made involving the particular system of numbers that eventually expired from inactivity.
It's really a pity that the geographical approach didn't seem to hold up, that was probably all we were going to get out of many of North America's earthworks pyramids that have been plowed until there's little left of them but a stain on a satellite image with little way of ever finding out their original proportions or designs.
Three years ago when I couldn't get up the stairs anymore, I went over to a message board set up by an old friend - I remember him proudly showing me his first clip pointing out an oddity in Mars satellite imagery, and next I know he's Kodak's go-to guy for their infrared imaging software, and showing NASA how to get the most out of their multi-spectral satellite imaging. I felt like I didn't have long to live and was posting some of my medical findings for posterity, I thought maybe there'd be three people in the world who weren't trying to blame the wrong thing for my no longer being here.
Naturally, being a fringe science forum there was a thread on the Great Pyramid, lol, and one day I clicked on it and ended up reminiscing about some of the work I'd done ten to twenty years earlier, and apologetically trying to figure out what it actually meant.
I'd already been working with the fundamental premise that an ancient universal standard of measurement eventually re-surfaced with amazing accuracy as the "modern British foot", although Morton and I made some successful inquiries into other ancient metrological units. Morton is probably the first person to give the correct value of the ancient Egyptian Royal Cubit to ten digits. That's quite radical when they aren't even supposed to have known what a decimal was, but various authors including Sir Flinders Petrie, still one of very few people I trust to measure anything correctly, hinted and orbited around that very same question, whether the Royal Cubit value was derived from circular geometry, while keeping a much more distant orbit from opining about the fact that the Royal Cubit only has that remarkable relationship to circular geometry when expressed in modern feet or inches.
There's a phenomenon in Egyptology I jokingly call "Cubititis" - it's kind of like when kids discover ketchup or mustard, and they try putting it on everything, ice cream, birthday cake - that I think when Egyptologist learn what a Cubit it, they try to make all of ancient Egypt into whole numbers of Royal Cubits, and that's about still where things currently stand. Petrie was one of the first notable victims of "Cubititis" - in his larger body of work, he'd written about an ancient Egyptian unit of measurement called the Remen, and how it was 1/2 the length of the diagonal of a square that it is 1 Royal Cubit x 1 Royal Cubit, but he never really seemed to try to measure anything with it. Instead, he kept trying to measure everything as whole numbers of Royal Cubits, so that the actual value of the Royal Cubit would swing wildly all over the place, a problem that continues to this very day.
My first contribution to metrology (not that anyone's accepted it) was giving a precise value to the Remen of 1.216733603 feet after reading Algeron Berriman's book, who not only described a number of ancient metrological units as simple fractions of the Remen, but quoted Penrose's value for the ancient Greek foot derived from measurements of ancient Grecian temples. Having come up with an experimental value of 1.013944669 feet for the Greek foot, I went to convert it into inches and ended up with 12.16733603. Taking the same value in feet to be 10 Remens, I was finally pretty sure I'd found what I was looking for.
One reason I content myself to fringe forums is because of part of the sordid history of that number. The number 1.216733603 has the remarkable distinction of belonging to both Munck's system of numbers, and "sacred geometry", and twice this value ended up in Hoagland and Torun's "Message of Cydonia" paper. All I really did is finally pin it on the ancient Egyptians. Of course, in it's own terms it's nothing special, just "1" (Remen) but in modern feet, a unit of 1.216733603 ft has some amazing mathematical properties. All I have to do is be honest about who deserves credit for that, though, and I'm going to be in hot water for an alleged belief in little green men.
Among the reasons I ended up terribly smitten with this number 1.216733603 is because the cube of 24 Remens in feet gives the equatorial circumference of the earth in miles with amazing accuracy -- (1.216733603 x 24)^3 = 24901.19745 (miles). That's more accurate than a lot of mapping datums of the 20th century (Wikipedia currently gives the figure as 24,901.461 miles). I don't actually deserve the credit for that, Morton had cued up an equation for it, but like Petrie with the Royal Cubit, he never actually went ahead and solved it. I about fell out of my chair when I discovered how to build that figure out of 1.216733603.
Most of my model of the Great Pyramid I built myself, based on only two pieces of data Munck gave us for its exterior proportions, its perimeter and projected height. I hate to obsess over it, that in itself probably makes me sound like your average loon, but even though I often lament people's obsessions with the Great Pyramid at the expense of other Egyptian pyramids, or the bulk of the world's pyramids which are actually in Mexico, in a way I can understand it. 20 years later and I am still making surprising discoveries about the Great Pyramid's proportions that appear in my models, it's as if a whole team of mathematicians were involved in its design.
In the course of being apologetic about the fact that Munck's model of the Great Pyramid is about a foot shorter than everyone else's, I came to the conclusion that there is a missing layer of pavement about eight inches thick that would have given it the proportions specified by Munck. That proposition hangs by a thread, but it stays in place based on some of the characteristics of the present pavement around the Great Pyramid, as if they are not the finished product but were covered with an additional layer that also provided cosmetic effect, and there are a few surviving casing stones that look as if at the bottom they were protected from erosion by just such an additional layer of pavement.
What I found remarkable though, is that the design of the Great Pyramid may have been so well thought out as to provide it with meaningful proportions whether or not this hypothetical layer of pavement survived, so as of several years ago I have two models, the "paved" model (Munck's) and the "unpaved" model (mine). Par for the course, we go to choose proposals for the proportions of ancient architecture that seem sensible to us and then spend years following being amazed at what sensible choices they turned out to be.
Going back to the idea that ancient people were writing messages with the proportions of architecture, I struggled hard to think of what those messages might really be about if not telling us "why they are where they are". I couldn't seem to find the answer to that in ancient Egypt beyond coming up with pieces of geodetic information like "(1.216733603 x 24)^3 = 24901.19745 (miles)". That still amazes me in itself that so many authors seem to have intuited that there is information about the earth's proportions in there somewhere. Even Isaac Newton seemed to think the pyramids were going to provide us with measures of the earth more accurate than we ourselves were capable of at the time. Thankfully, as a "pyramidiot" I can proudly look to him as one of my predecessors.
We found the very same things in ancient American architecture. Munck is the first person I know of to point out that Teobert Maler's measures of the temple platform of Tikal Temple I, when converted to feet, seem to give the earth's circumference in miles / 10^n with uncanny accuracy. A lot of this is pretty silly now but you can see here written and drawn in Munck's own hand where the "759 cm" platform width given by Maler comes to ~24.901 feet www.viewzone.com/bigpicture/bp112311.html even after most of his work has disappeared from the Internet, as has mine and Morton's.
I've since then made similar discoveries concerning the length of the same temple platform, and found in Maler's previously unpublished data the same number, written "backwards" as its own reciprocal, (1 / 24901.19745) x 10^n to be precise. I've taken a fair amount of criticism (along with some abuse) because of course we can't measure architecture that accurately, and of course we rely on formulas and checks and logic to guide us there. I've always worked with the expectation that numbers grouped together in architecture, such as the length, width, and height of a room, are going to interact in intelligent ways that demonstrate deliberateness and help keep us from making mistakes as to what we're looking at, when measurements along can't give us that kind of guidance.
Let me double check that one more time just to be sure. It's Teobert Maler's diagram in Monumenta Americana Vol 4, plate 32, El Castillo at Chichen Itza. Width of the summit platform: 1224 cm = 40.15748 ft; 1 / 40.15748 = 1 / (24901.96058 x 10^n).
When I went back to Middle America looking to what else was being written in this language on the "parchment" of ancient architeture, I ended up having another look at the El Castillo pyramid (aka the Kukulkan pyramid). Besides being renowned for its amazing optical and acoustic properties, there seems to be quite a bit of concensus that one of the functions of the El Castillo pyramid is that it's a calendar in the form of a pyramid. It's so blatantly decked out in numbers belonging to obvious calendar systems that there seems to be little room for argument. Munck and others have pointed out that 91 stairs on each side x 4 sides + 1 platform = 365 representing the 365 days in a year, and other have pointed out counts of 52 features representing 52 weeks in a year. Recently I've been pointing out to people that the 91 steps on a side x the 9 terraces = 819, which is a number recognized as having at least minor significance to the Mayan Calendar, even Wikipedia is aware of that one.
Recently I've been finding out that the peculiar Mayan calendar that tries to coordinate the cycles of as many planets visible with the unaided eye as possible with the cycles of the Earth and moon into a Long Count (1/2 Venus Cycle) may not have belonged to just the Maya, but instead may be something that else that had universal distribution in ancient times.
I've been working with the number 819 but it's a strange one, it's actually 364 x Venus Orbit Period of 225 days = 81900 rather than 365 x 225, and the decimal place has been shifted. I have a number just over 819 I've been experimenting with that is almost identical to a ratio from some calendar numbers someone came up with based on their Biblical studies. One of their numbers was 5.2684, which is almost identical to the reciprocal of the Mayan Long Count of 18980 days -- 1 / 5.2684 = 18981.09483 x 10^n -- from Biblical studies, mind you.
By the time I got around to dwelling on the 365 niches in the Pyramid of the Niches at El Tajin, the penny was starting to drop. By the time I got the Aztec Sun Stone (seen countless times on the Internet mislabeled as "the Mayan Calendar") and not only discovered the same things I've been finding in the measurements of the doorways of Tikal's pyramid temples, but that the Sun Stone based on data from several respectable sources seems to embody some very clever formulas for expressing important calendar numbers, the penny finally did actually drop. (Munck once pointed out that Maler's data for the door of Temple II at Tikal gives one of his favorite numbers - it's measures actually embody at least two of his favorite numbers as I later found out, and the Sun Stone's probably circumference much reminded me of that) - and all this again when these measurements expressed in modern feet (I do A LOT of converting things from meters to feet, although ratios themselves don't care what units one uses).
At present, I'm still working on interpreting some of the physical proportions of the El Castillo pyramid based on Teobert Maler's data. It's not perfectly square at the base and the best answer going at present is essentially that the long side represents the square root of the some form of the Solar Year in days, and the short side represents the square root of some form of the Lunar Year in days, when we measure it in modern feet. That is what I think it is but the exact figures they're using in order to have square roots that belong to the particular system of numbers (derived largely from expanding on basic circular geometry with the incorporation of things like the standard Remen value I use) is still somewhat beyond my current level of skill. I still struggle with the Lunar Year because the standard figure for the Lunar Month isn't really a fixed one, it's an average value, which makes for what is still sometimes rather complicated and mysterious mathematics.
I have a wealth of architectural data on ancient Mayan architecture from George Andrews who was resident at a university barely 75 miles north of here that I've done all kinds of work with - where would I be without him? - including tabling it all out so I can do statistical work like looking for patterns such as spikes in occurrence of values that should be expected to show spikes because of particular importance (I do seem to find them). I still struggle to interpret most of it effectively, they still manage to surprise to me at many turns, but I've learned a good number of important things. It never ceases to amaze me how easy it is to find the Venus Orbital Period (~225 days) expressed in Mayan architecture in obvious ways, exactly as one might expect with the cultural and mythological importance they seem to have placed on Venus.
One of the most intriguing and mysterious Mayan sites to me is Rio Bec, which lent its name to the Rio Bec style of architecture, with its imposing false tower facades. en.wikipedia.org/wiki/R%C3%ADo_Bec My attention was drawn to them after studying the architecture of Tikal's pyramid temples and having had a number of authorities propose that the false towers of the Rio Bec style were tributes to Tikal's pyramid temples. Clarence Hay once wrote about one of the Rio Bec structures and gave some rough measurements of the length of one of them. I still don't have a good proposal for what that length originally was but when I noticed it vaguely resembled the reciprocal of 12 x (Pi^2), I soon discovered how effective that number is at linking certain numbers belonging to calendars, that's still one of the notable discoveries in question.
One of the places we missed the boat back in the day is where Munck came up with a value for the number of days in a year. The value he gave was 365.0200808, and for lack of a better suggestion proposed that the earth's day length changed over the ages. What I think it actually is, is a number that effectively represents the calendar year of 365 days, just as we use now. We throw out the extra 1/4 day and then make up for it with a leap year so that we can normally keep a calendar year of 365 days. It's one of the things I normally do with unfamiliar numbers to try to analyze them is multiply or divide them by simple numbers to see if we end up with something more familiar that way, but for years we must have all though it was merely a coincidence what happens when we go to divide a 365 day year into trimesters.
365.0200808 / 3 = 121.6733603
This would seem to make the Remen value in feet as potentially as old as man's first attempts to divide his pile of 365 sticks or pebbles or beans into smaller more manageable units. I can probably also trace back the Royal Cubit to early attempts at dividing planetary cycles, and of course with the double Remen being the diagonal to the Royal Cubit, the two pretty much go hand in hand anyway. I'm not exactly sure how I think we got from one to the other, but it seems obvious enough that the ancient Egyptians thought they were preserving some of the oldest numbers known to man by simultaneously working in Royal Cubits and Remens. That's otherwise a seemingly tall order, and rather odd - it's a bit like us designing buildings and insisting the width of hallways should be in feet but their heights should be in meters, why encumber yourself like that unless you have a particular reason?
So besides Munck's own version of the Megalithic Yard, which is a problem child that has to be squared before it even belongs to its own system of numbers, being one of his favorite numbers that seems to be displayed in the measures of Tikal's Temple II, the other one that was found there later by yours truly is 1.177245711. Munck introduced that and calls it "Alternate Pi" and expressed a preference for it over the Pi ratio itself in analyzing unfamiliar numbers or trying to extract additional data from them. It's one of my standard analytical probes. Another one of paramount importance is 1.622311470. Munck introduced that and wondered if it could be an ancient form of Phi, which is probably precisely what it is. What I have for the circumference of the Aztec Sun Stone is 11.77245771 feet.
I don't think I can count the number of "Ancient Mysteries" authors who will insist that the solar system shows deliberateness in design based on the ratio between the Earth year and the Venus Orbital Period being Phi (1.618033989). I suppose it were deliberately designed that might be true, but it isn't. Canonically speaking it's 365 / 225 = 1.6222222222 and technically speaking it's about 365.243 / 224.701 = 1.625457832. This may make 1.622311470 as a representation of 1.622222222 of almost equal antiquity to 1.216733603, and in fact 1.622311470 is 4/3 of 1.216733603.
When we began experimenting with dividing the 365 day years into months, we probably found that 365 / 30 days = 12.166666666, i.e., 12.16733603; when we tried to make 31 day months out of it, we probably found that 365 / 31 = 11.77419355, i.e., 11.77245771.
So again, it's as if ancient people and their metrological follies thought they were thus commemorating things that were about as old as the dawn of time itself, perhaps quite literally, and at some point the modern foot had to enter the picture far earlier than anyone might believe in order to imbue those ancient measurements with that kind of meaning.
The foot may not be the only ancient unit to mysteriously resurface much later in history. There's a number I discovered at Stonehenge, it's the ratio between the inner and outer measures of the sarcen circle with the inner circumference given by Munck based on Flinders Petrie's data as 305.7985077 - that's a 360 degree circle, divided by "Alternate Pi": 360 / 1.177245771 = 305.7985077. I made a determination of the outer circumference based on Prof. Thom's value of 120 Megalithic Yards, after I assigned a probable Megalithic Yard value of 2.720174976 ft. 120 x 2.720174976 = 326.4209971 ft.
326.4209971 / 305.7985077 = 1.067438159
It turned out I should have known what that was, but thanks to a word processor accident I'd missed it. It was "hidden" all over the place in Munck's data for Giza, it's the ratio between his perimeter for the Great Pyramid and his perimeter for the Chephren pyramid, for starters. Lately it's occurred to me that this value in feet might be a metrological unit in its own right, but I'm having trouble placing it in recorded history except to suspect that it may have managed to eventually re-surface as the "King's Foot" or pied du roi (~1.066 ft). The number 1.067438159 seems to be endlessly useful for linking calendar-related numbers together into some semblance of a system. (Regarding Chephren's pyramid, it's amazing how many people have it pegged as a monument to the Pythagorean theorem, whereas the Great Pyramid appears to be a monument to the ratio 2 Pi, and I have never been able to actually argue).
I also think there's another ancient metrological unit that may have been completely lost somehow. We seem to have to make a few adjustments to keep things fully functional, but just as the double Remen is essentially the diagonal of a square of 1 Royal Cubit per side and the Megalithic Yard is essentially the diagonal of a rectangle made by joining two squares with sides of one Remen each, the diagonal of a square with sides of 1 Megalithic Yard is essentially two of a unit of 1.921388691 ft, which has some interesting mathematical properties of its own, including being able to measure the height of the Great Pyramid as given by Munck, at a whole number value of 250 units. I call this mystery unit of 1.921388691 ft the "ellifino" (a play on the "elle" which is another name for the Cubit), because "'ell if I know" what it is, I've never been able to match it with historical record but it stands to reason that it didn't go overlooked by ancient people.
Regarding Stonehenge, the value derived by Munck from Petrie's data gives the sarcen circle an inner radius of 305.7985077 / (2 Pi) = 48.66934409 ft. That's 40 Remens of 1.216733603 ft. That's not very interesting in Remens themselves, but in modern feet it about sparkles, and it certainly seems to imply that whoever designed Stonehenge was quite aware of how ancient Egyptians used mathematics and measurement.
We're pretty blessed to be able to know that much about Stonehenge thanks to people like Petrie and Thom. Good data is otherwise still very hard to come by. Ironically, Aubrey Burl once remarked that either ancient people used the same measurements as us, or a lot of archaeologists are rounding their measures of stone circles to the nearest 5 meters.
Recently, I discovered that Munck's specified proportions for the Mycerinus pyramid were apparently based on a bad data source, probably I.E.S. Edwards, and based on something of a consensus in the data from Flinders Petrie and the recently departed Glen Dash, I ended up trying to revise it. I built the best model I could and then went on to explore the likely values for the base diagonals and edge lengths, and obtained an edge length of 326.4209971 ft, equal to my figure for the outer circumference of the Stonehenge sarcen circle, to the normal standard of accuracy I've obtained on forced approximations in ancient architecture of .9995 or better. I've seen the inner diameter of the sarcen circle of 80 Remens in data on the Great Pyramid's interior before (I believe it's the length along the top of the passage from the entrance to the upward fork in the passage, but I'd have to look it up to be certain, it's been awhile).
For what it's worth, I've proposed for the Mycerinus pyramid an original perimeter of 1383.399854 ft. One way to obtain this value is 1.067438159 x (360^2); another is 1.921388686 x 2 x 360 ("ellifino" how 1.921388686 got in there). 1383.399854 x (360 / 2) = 24901.19737, the earth's equatorial circumference in miles again. Another way to find it at Giza is take Munck's height for the Great Pyramid of 480.3471728 (which was after the missing pavement was added according to me) and multiply it by the canonical slope angle of 51.84 x 480.3471728 = 24901.19744.
I've also proposed that the ratio between the width of the Great Pyramid (without pavement) and the width of the platform it sits on (based on data from Lehner and Goodman with the endorsement of Glen Dash) is 1.003877283. Being that the Great Pyramid looks like a monument to the ratio 2 Pi (perimeter / height = 2 Pi), it shouldn't have surprised me so much when I discovered that 1.003877283 x ((2 Pi)^3) = 24901.19744 / 100
I actually discovered that when I was working with Tikal and found a long series based on multiplying a particular number from the measurements of a Tikal pyramid temple door by 2 Pi. You can start the series at the cube of "Alternate Pi" 1.177245771.
(1.177245771^3) x ((2 Pi)^9) = 24901.19744 x 1000.
That's a pretty amazing feeling when you feel like someone is speaking to you in your own language, but a lot more fluently, coming from people who weren't supposed to even be smart enough to invent the wheel after using it to make children's toys that children could pull behind them on a string.
Naturally in such a series there's a meaningful value at every power of 2 Pi until one has just plain gone too far with the progression.
I could re-iterate some basics here - the Great Pyramid really does seem like the "mother ship" of ancient monuments for having the apparent perimeter/height ratio of 2 Pi. That's basic circular math, circumference / 2 Pi = radius, and Munck and his students have traditionally used the 360 degree circle / 2 Pi = the Radian 57.29577951 (arc-degrees). Munck called the Radian "the Giza Constant" and I've never been able to disagree, in fact on a good day I find more evidence that he was right. It's the kind of thing people have been saying about the Great Pyramid since at least as far back as Taylor, but I guess not many people have embraced it very tightly.
I really didn't get very far with Tikal until I studied one of Edwin Shook's photos and decided that the pyramid in question seemed to expanding outward as you approach the base of it at a ratio of (Pi / 3), and started using (Pi /3) in my experiments. If there's a "Tikal constant" my guess would have to be 1/3 of Pi.
I'm not going to be surprised if 360 / 2 Pi = 57.29577951 is also some of the oldest math in the world, I get a picture of someone whose foot was probably exactly as long as the modern foot, once they counted out 365 beans in the time it took the sun to return to the same place in the sky at sunrise, pacing off a 365 foot circle and building the first Woodhenge with 365 little sticks so they could study it better, but I still have a hard time articulating that argument well. By the time someone rounded it to 360 like the Maya sometimes did for general purposes, modern circular math was born, I can only guess.
Morton's Cubit in inches can essentially be derived from circular math, the formula I prefer is .03 Radians = .03 x 57.29577951 = 1.718873385 ft = 20.62648082 inches. The area of a circle is radius squared x Pi, and if we use the Radian value of (360 / 2 Pi = 57.29577951) as the radius, that's 57.29577951^2 x Pi = 10313.24031, or 1/2 of 20626.48082. As near as I can tell, the Great Pyramid was designed so that the capstone (pyramidion) or missing section at the top if the slopes are projected upward to an apex point, is a macrocosm of the whole at the ratio of 10 Royal Cubits of 1.718873385. I came up with that over 15 years ago and still haven't managed to overturn the proposal, the more carefully I look at it the more sensible it's turned out to be, including that the gives the Great Pyramid a slope length without the missing section a length of 57.29577951 feet once the hypothetical pavement is in place.
That also involves allowing for the concavity of its sides. Many authors seem have disputed it or ignored it altogether but Flinders Petrie himself reported that the sides of the Great Pyramid are creased inward slightly at the center. With the model I use, that seems to allow for ancient authors to have been correct when stating that the maximum slope length (apothem) of the Great Pyramid was "1 Stadium" (500 Remens) - when the hypothetical missing pavement is in place, that's 500 Remens of 1.216733603; without the pavement I think the value is 500 Remens of 1.218469679 - distinctions that again we may only be able to spot through calculation and deduction.
It's something of an odd story, but I call 1.218469679 ft a "Thoth Remen" - Munck asserted there were several numbers that were "sacred" to "Thoth", "Father of Numbers". One of them is 240 and indeed, the inner circumference of Stonehenge and the height of the Great Pyramid are both based on (sqrt 240) x (Pi^n), almost as if it were an "inside joke" on the part of ancient architects, like soldiers writing "Kilroy Was Here" everywhere on behalf of the mythical "Kilroy".
Munck also pointed out a hieroglyph associated with Thoth that looks suspiciously like the number 9, and went on to demonstrate that the reciprocal of 9 is .11111111111 and the square of .111111111111 is .111111111111^2 = .1234567901 - all the numbers in order except the number 8 and it seems to repeat indefinitely. Hence he felt like he was giving mathematical truth to ancient mythology with that, and it turned out that 1.218469679 is .1234567901 x (Pi^2). That's sort of a long way to go to make an honest man out of Herodotus or Pliny or whoever it was who said the Great Pyramid's apothem length was "1 Stadium" (I'd have to look it up), but there you go - it does seem to actually work.
(For what it's worth, what I came up with for the perimeter of the Great Pyramid without pavement is 1.1111111111 x 2.720174076 x 10^n feet. If one chooses they can read that as "Oh look, Thoth signed his work on the underside, too").
The "Thoth Remen" also finds other reasons for being. It's loosely true that 360 / (Royal Cubit squared) = 1 Remen, and if we use Morton's Royal Cubit with this formula, 360 / (1.718873385^2) = 1.218469679, the Thoth Remen, so besides its dicey roots in the precarious interpretation of ancient myths, it can also boast some parentage in the area of simple variations on circular mathematics.
For someone who doesn't like arguments, I probably manage to really pick the wrong hobbies. I could have a lifetime of arguments trying to convince some people that any of our ancient ancestors could even conceive of a decimal point, let alone make effective use of it. To me it's as natural as creatures with 10 fingers having come up with base 10 arithmetic to have started experimenting with math just as soon as they tried to figure out when winter was coming, and it probably gave math plenty of time to get far out ahead of the rest of the sciences so that the ancient Egyptians and others were quite prodigal at it even when their first attempts at pyramid engineering were going sour because of engineering errors like poor choices for solid ground to rest them on.
Of all the things to get burnt at the stake for, but there it is. My fundamental premises are still that someone invented long division long before we give anyone credit for it, and discovered how to determine the circumference of the earth the same way the ancient Greeks or Egyptians did it, only again much earlier than we usually give anyone credit for. I don't really see where the controversy is personally, although I know lots of places where an argument can be found over these matters.
So yeah, that's one of the things I try to do with history. I don't try to figure out how ancient monuments were built, or who built them, or even why necessarily, I try to figure out what the architects might have been trying to say to generations down the road. Whatever it says about these ancient cultures, I see it as shared heritage, no matter what a person's particular roots happen to be. Some days I seem to find the earth's proportions recorded everywhere so insistently it seems a lot like someone once forgot the world was big enough that they had cousins on the other side of it and were greatly determined never to forget it again.
I could hypothesize why ancient Egyptians might have wanted to sentimentally equip funerary architecture with numbers that "go on forever" after the decimal point or infuse them with measurements that embody the timeless cycles of the heavens as if to represent, or infuse their works with, eternity, but my Mayan studies suggest even dwellings and government buildings were provided with the very same "added value" by their architects.
I'm sure I'd enjoy lecturing but I don't see how it's possible with Tourette's that's only half managed. Earlier this year I was daydreaming of doing some biology lectures for YouTube if I could get a medication to work, but that's likely still out of the question now. I can barely keep my arms raised to groom myself these days (hooray, now I look as loony as I must sound), but if I prop myself up on my elbows at my desk, I can still operate a pocket calculator and I can type without challenges. Thank heavens I can still do that much, and still express myself that way. I hope I can make the best of it and make it count for something somehow.
I guess that's a story in itself so I'll try to skip most of it. Suffice it to say it's more trouble that Dark Shadows got me into, lol, that one morning I'm watching Dark Shadows on the Sci-Fi channel when I see an advertisement for a video by Richard "Face on Mars" Hoagland and became terribly intrigued with his suggestion that some of the man-made features of the Salisbury Plain might constitute a incomplete model of Martian surface features. I was hugely impressed with the model that Hoagland had participated in of the geometry of his five-sided "Martian pyramid".
Hoagland's materials introduced me to the work of a man named Carl Munck and his "Pyramid Matrix". Munck had the idea that ancient peoples had somehow worked out a global positioning system identical to our own, in which the physical features of ancient monuments represented formulas that could be "decoded" into their geographic coordinates to explain "why they are where they are" and where other, often thematically related monuments, were located. In 1998 I began working with Munck's materials and was soon taken under the wing of Michael Morton, who had also been working with Munck's theories and doing a great deal of experimental work with them, trying to fill in some of the gaps in the curriculum.
After about 10 years working closely together, Morton and I had a falling out when I got my hands on a copy of Mark Lehner's Giza Plateau Mapping Project book, and ran into so many major anomalies that in the course of trying to sort it out, the sad truth finally came to my attention that none of us including Munck had adequate qualifications in cartography to be able to actually support the work were doing with things being "why they are where they are", and even though I'd developed great faith in Munck's use of mathematics, I lost so much faith in what was our fundamental premise of a global coordinate system that I ended up giving up on the whole thing, and I think Morton, who doesn't seem to be with us anymore, was quite incensed that I'd "blown the whistle". We had a message board where we'd made several thousand posts sharing various discoveries we'd made involving the particular system of numbers that eventually expired from inactivity.
It's really a pity that the geographical approach didn't seem to hold up, that was probably all we were going to get out of many of North America's earthworks pyramids that have been plowed until there's little left of them but a stain on a satellite image with little way of ever finding out their original proportions or designs.
Three years ago when I couldn't get up the stairs anymore, I went over to a message board set up by an old friend - I remember him proudly showing me his first clip pointing out an oddity in Mars satellite imagery, and next I know he's Kodak's go-to guy for their infrared imaging software, and showing NASA how to get the most out of their multi-spectral satellite imaging. I felt like I didn't have long to live and was posting some of my medical findings for posterity, I thought maybe there'd be three people in the world who weren't trying to blame the wrong thing for my no longer being here.
Naturally, being a fringe science forum there was a thread on the Great Pyramid, lol, and one day I clicked on it and ended up reminiscing about some of the work I'd done ten to twenty years earlier, and apologetically trying to figure out what it actually meant.
I'd already been working with the fundamental premise that an ancient universal standard of measurement eventually re-surfaced with amazing accuracy as the "modern British foot", although Morton and I made some successful inquiries into other ancient metrological units. Morton is probably the first person to give the correct value of the ancient Egyptian Royal Cubit to ten digits. That's quite radical when they aren't even supposed to have known what a decimal was, but various authors including Sir Flinders Petrie, still one of very few people I trust to measure anything correctly, hinted and orbited around that very same question, whether the Royal Cubit value was derived from circular geometry, while keeping a much more distant orbit from opining about the fact that the Royal Cubit only has that remarkable relationship to circular geometry when expressed in modern feet or inches.
There's a phenomenon in Egyptology I jokingly call "Cubititis" - it's kind of like when kids discover ketchup or mustard, and they try putting it on everything, ice cream, birthday cake - that I think when Egyptologist learn what a Cubit it, they try to make all of ancient Egypt into whole numbers of Royal Cubits, and that's about still where things currently stand. Petrie was one of the first notable victims of "Cubititis" - in his larger body of work, he'd written about an ancient Egyptian unit of measurement called the Remen, and how it was 1/2 the length of the diagonal of a square that it is 1 Royal Cubit x 1 Royal Cubit, but he never really seemed to try to measure anything with it. Instead, he kept trying to measure everything as whole numbers of Royal Cubits, so that the actual value of the Royal Cubit would swing wildly all over the place, a problem that continues to this very day.
My first contribution to metrology (not that anyone's accepted it) was giving a precise value to the Remen of 1.216733603 feet after reading Algeron Berriman's book, who not only described a number of ancient metrological units as simple fractions of the Remen, but quoted Penrose's value for the ancient Greek foot derived from measurements of ancient Grecian temples. Having come up with an experimental value of 1.013944669 feet for the Greek foot, I went to convert it into inches and ended up with 12.16733603. Taking the same value in feet to be 10 Remens, I was finally pretty sure I'd found what I was looking for.
One reason I content myself to fringe forums is because of part of the sordid history of that number. The number 1.216733603 has the remarkable distinction of belonging to both Munck's system of numbers, and "sacred geometry", and twice this value ended up in Hoagland and Torun's "Message of Cydonia" paper. All I really did is finally pin it on the ancient Egyptians. Of course, in it's own terms it's nothing special, just "1" (Remen) but in modern feet, a unit of 1.216733603 ft has some amazing mathematical properties. All I have to do is be honest about who deserves credit for that, though, and I'm going to be in hot water for an alleged belief in little green men.
Among the reasons I ended up terribly smitten with this number 1.216733603 is because the cube of 24 Remens in feet gives the equatorial circumference of the earth in miles with amazing accuracy -- (1.216733603 x 24)^3 = 24901.19745 (miles). That's more accurate than a lot of mapping datums of the 20th century (Wikipedia currently gives the figure as 24,901.461 miles). I don't actually deserve the credit for that, Morton had cued up an equation for it, but like Petrie with the Royal Cubit, he never actually went ahead and solved it. I about fell out of my chair when I discovered how to build that figure out of 1.216733603.
Most of my model of the Great Pyramid I built myself, based on only two pieces of data Munck gave us for its exterior proportions, its perimeter and projected height. I hate to obsess over it, that in itself probably makes me sound like your average loon, but even though I often lament people's obsessions with the Great Pyramid at the expense of other Egyptian pyramids, or the bulk of the world's pyramids which are actually in Mexico, in a way I can understand it. 20 years later and I am still making surprising discoveries about the Great Pyramid's proportions that appear in my models, it's as if a whole team of mathematicians were involved in its design.
In the course of being apologetic about the fact that Munck's model of the Great Pyramid is about a foot shorter than everyone else's, I came to the conclusion that there is a missing layer of pavement about eight inches thick that would have given it the proportions specified by Munck. That proposition hangs by a thread, but it stays in place based on some of the characteristics of the present pavement around the Great Pyramid, as if they are not the finished product but were covered with an additional layer that also provided cosmetic effect, and there are a few surviving casing stones that look as if at the bottom they were protected from erosion by just such an additional layer of pavement.
What I found remarkable though, is that the design of the Great Pyramid may have been so well thought out as to provide it with meaningful proportions whether or not this hypothetical layer of pavement survived, so as of several years ago I have two models, the "paved" model (Munck's) and the "unpaved" model (mine). Par for the course, we go to choose proposals for the proportions of ancient architecture that seem sensible to us and then spend years following being amazed at what sensible choices they turned out to be.
Going back to the idea that ancient people were writing messages with the proportions of architecture, I struggled hard to think of what those messages might really be about if not telling us "why they are where they are". I couldn't seem to find the answer to that in ancient Egypt beyond coming up with pieces of geodetic information like "(1.216733603 x 24)^3 = 24901.19745 (miles)". That still amazes me in itself that so many authors seem to have intuited that there is information about the earth's proportions in there somewhere. Even Isaac Newton seemed to think the pyramids were going to provide us with measures of the earth more accurate than we ourselves were capable of at the time. Thankfully, as a "pyramidiot" I can proudly look to him as one of my predecessors.
We found the very same things in ancient American architecture. Munck is the first person I know of to point out that Teobert Maler's measures of the temple platform of Tikal Temple I, when converted to feet, seem to give the earth's circumference in miles / 10^n with uncanny accuracy. A lot of this is pretty silly now but you can see here written and drawn in Munck's own hand where the "759 cm" platform width given by Maler comes to ~24.901 feet www.viewzone.com/bigpicture/bp112311.html even after most of his work has disappeared from the Internet, as has mine and Morton's.
I've since then made similar discoveries concerning the length of the same temple platform, and found in Maler's previously unpublished data the same number, written "backwards" as its own reciprocal, (1 / 24901.19745) x 10^n to be precise. I've taken a fair amount of criticism (along with some abuse) because of course we can't measure architecture that accurately, and of course we rely on formulas and checks and logic to guide us there. I've always worked with the expectation that numbers grouped together in architecture, such as the length, width, and height of a room, are going to interact in intelligent ways that demonstrate deliberateness and help keep us from making mistakes as to what we're looking at, when measurements along can't give us that kind of guidance.
Let me double check that one more time just to be sure. It's Teobert Maler's diagram in Monumenta Americana Vol 4, plate 32, El Castillo at Chichen Itza. Width of the summit platform: 1224 cm = 40.15748 ft; 1 / 40.15748 = 1 / (24901.96058 x 10^n).
When I went back to Middle America looking to what else was being written in this language on the "parchment" of ancient architeture, I ended up having another look at the El Castillo pyramid (aka the Kukulkan pyramid). Besides being renowned for its amazing optical and acoustic properties, there seems to be quite a bit of concensus that one of the functions of the El Castillo pyramid is that it's a calendar in the form of a pyramid. It's so blatantly decked out in numbers belonging to obvious calendar systems that there seems to be little room for argument. Munck and others have pointed out that 91 stairs on each side x 4 sides + 1 platform = 365 representing the 365 days in a year, and other have pointed out counts of 52 features representing 52 weeks in a year. Recently I've been pointing out to people that the 91 steps on a side x the 9 terraces = 819, which is a number recognized as having at least minor significance to the Mayan Calendar, even Wikipedia is aware of that one.
Recently I've been finding out that the peculiar Mayan calendar that tries to coordinate the cycles of as many planets visible with the unaided eye as possible with the cycles of the Earth and moon into a Long Count (1/2 Venus Cycle) may not have belonged to just the Maya, but instead may be something that else that had universal distribution in ancient times.
I've been working with the number 819 but it's a strange one, it's actually 364 x Venus Orbit Period of 225 days = 81900 rather than 365 x 225, and the decimal place has been shifted. I have a number just over 819 I've been experimenting with that is almost identical to a ratio from some calendar numbers someone came up with based on their Biblical studies. One of their numbers was 5.2684, which is almost identical to the reciprocal of the Mayan Long Count of 18980 days -- 1 / 5.2684 = 18981.09483 x 10^n -- from Biblical studies, mind you.
By the time I got around to dwelling on the 365 niches in the Pyramid of the Niches at El Tajin, the penny was starting to drop. By the time I got the Aztec Sun Stone (seen countless times on the Internet mislabeled as "the Mayan Calendar") and not only discovered the same things I've been finding in the measurements of the doorways of Tikal's pyramid temples, but that the Sun Stone based on data from several respectable sources seems to embody some very clever formulas for expressing important calendar numbers, the penny finally did actually drop. (Munck once pointed out that Maler's data for the door of Temple II at Tikal gives one of his favorite numbers - it's measures actually embody at least two of his favorite numbers as I later found out, and the Sun Stone's probably circumference much reminded me of that) - and all this again when these measurements expressed in modern feet (I do A LOT of converting things from meters to feet, although ratios themselves don't care what units one uses).
At present, I'm still working on interpreting some of the physical proportions of the El Castillo pyramid based on Teobert Maler's data. It's not perfectly square at the base and the best answer going at present is essentially that the long side represents the square root of the some form of the Solar Year in days, and the short side represents the square root of some form of the Lunar Year in days, when we measure it in modern feet. That is what I think it is but the exact figures they're using in order to have square roots that belong to the particular system of numbers (derived largely from expanding on basic circular geometry with the incorporation of things like the standard Remen value I use) is still somewhat beyond my current level of skill. I still struggle with the Lunar Year because the standard figure for the Lunar Month isn't really a fixed one, it's an average value, which makes for what is still sometimes rather complicated and mysterious mathematics.
I have a wealth of architectural data on ancient Mayan architecture from George Andrews who was resident at a university barely 75 miles north of here that I've done all kinds of work with - where would I be without him? - including tabling it all out so I can do statistical work like looking for patterns such as spikes in occurrence of values that should be expected to show spikes because of particular importance (I do seem to find them). I still struggle to interpret most of it effectively, they still manage to surprise to me at many turns, but I've learned a good number of important things. It never ceases to amaze me how easy it is to find the Venus Orbital Period (~225 days) expressed in Mayan architecture in obvious ways, exactly as one might expect with the cultural and mythological importance they seem to have placed on Venus.
One of the most intriguing and mysterious Mayan sites to me is Rio Bec, which lent its name to the Rio Bec style of architecture, with its imposing false tower facades. en.wikipedia.org/wiki/R%C3%ADo_Bec My attention was drawn to them after studying the architecture of Tikal's pyramid temples and having had a number of authorities propose that the false towers of the Rio Bec style were tributes to Tikal's pyramid temples. Clarence Hay once wrote about one of the Rio Bec structures and gave some rough measurements of the length of one of them. I still don't have a good proposal for what that length originally was but when I noticed it vaguely resembled the reciprocal of 12 x (Pi^2), I soon discovered how effective that number is at linking certain numbers belonging to calendars, that's still one of the notable discoveries in question.
One of the places we missed the boat back in the day is where Munck came up with a value for the number of days in a year. The value he gave was 365.0200808, and for lack of a better suggestion proposed that the earth's day length changed over the ages. What I think it actually is, is a number that effectively represents the calendar year of 365 days, just as we use now. We throw out the extra 1/4 day and then make up for it with a leap year so that we can normally keep a calendar year of 365 days. It's one of the things I normally do with unfamiliar numbers to try to analyze them is multiply or divide them by simple numbers to see if we end up with something more familiar that way, but for years we must have all though it was merely a coincidence what happens when we go to divide a 365 day year into trimesters.
365.0200808 / 3 = 121.6733603
This would seem to make the Remen value in feet as potentially as old as man's first attempts to divide his pile of 365 sticks or pebbles or beans into smaller more manageable units. I can probably also trace back the Royal Cubit to early attempts at dividing planetary cycles, and of course with the double Remen being the diagonal to the Royal Cubit, the two pretty much go hand in hand anyway. I'm not exactly sure how I think we got from one to the other, but it seems obvious enough that the ancient Egyptians thought they were preserving some of the oldest numbers known to man by simultaneously working in Royal Cubits and Remens. That's otherwise a seemingly tall order, and rather odd - it's a bit like us designing buildings and insisting the width of hallways should be in feet but their heights should be in meters, why encumber yourself like that unless you have a particular reason?
So besides Munck's own version of the Megalithic Yard, which is a problem child that has to be squared before it even belongs to its own system of numbers, being one of his favorite numbers that seems to be displayed in the measures of Tikal's Temple II, the other one that was found there later by yours truly is 1.177245711. Munck introduced that and calls it "Alternate Pi" and expressed a preference for it over the Pi ratio itself in analyzing unfamiliar numbers or trying to extract additional data from them. It's one of my standard analytical probes. Another one of paramount importance is 1.622311470. Munck introduced that and wondered if it could be an ancient form of Phi, which is probably precisely what it is. What I have for the circumference of the Aztec Sun Stone is 11.77245771 feet.
I don't think I can count the number of "Ancient Mysteries" authors who will insist that the solar system shows deliberateness in design based on the ratio between the Earth year and the Venus Orbital Period being Phi (1.618033989). I suppose it were deliberately designed that might be true, but it isn't. Canonically speaking it's 365 / 225 = 1.6222222222 and technically speaking it's about 365.243 / 224.701 = 1.625457832. This may make 1.622311470 as a representation of 1.622222222 of almost equal antiquity to 1.216733603, and in fact 1.622311470 is 4/3 of 1.216733603.
When we began experimenting with dividing the 365 day years into months, we probably found that 365 / 30 days = 12.166666666, i.e., 12.16733603; when we tried to make 31 day months out of it, we probably found that 365 / 31 = 11.77419355, i.e., 11.77245771.
So again, it's as if ancient people and their metrological follies thought they were thus commemorating things that were about as old as the dawn of time itself, perhaps quite literally, and at some point the modern foot had to enter the picture far earlier than anyone might believe in order to imbue those ancient measurements with that kind of meaning.
The foot may not be the only ancient unit to mysteriously resurface much later in history. There's a number I discovered at Stonehenge, it's the ratio between the inner and outer measures of the sarcen circle with the inner circumference given by Munck based on Flinders Petrie's data as 305.7985077 - that's a 360 degree circle, divided by "Alternate Pi": 360 / 1.177245771 = 305.7985077. I made a determination of the outer circumference based on Prof. Thom's value of 120 Megalithic Yards, after I assigned a probable Megalithic Yard value of 2.720174976 ft. 120 x 2.720174976 = 326.4209971 ft.
326.4209971 / 305.7985077 = 1.067438159
It turned out I should have known what that was, but thanks to a word processor accident I'd missed it. It was "hidden" all over the place in Munck's data for Giza, it's the ratio between his perimeter for the Great Pyramid and his perimeter for the Chephren pyramid, for starters. Lately it's occurred to me that this value in feet might be a metrological unit in its own right, but I'm having trouble placing it in recorded history except to suspect that it may have managed to eventually re-surface as the "King's Foot" or pied du roi (~1.066 ft). The number 1.067438159 seems to be endlessly useful for linking calendar-related numbers together into some semblance of a system. (Regarding Chephren's pyramid, it's amazing how many people have it pegged as a monument to the Pythagorean theorem, whereas the Great Pyramid appears to be a monument to the ratio 2 Pi, and I have never been able to actually argue).
I also think there's another ancient metrological unit that may have been completely lost somehow. We seem to have to make a few adjustments to keep things fully functional, but just as the double Remen is essentially the diagonal of a square of 1 Royal Cubit per side and the Megalithic Yard is essentially the diagonal of a rectangle made by joining two squares with sides of one Remen each, the diagonal of a square with sides of 1 Megalithic Yard is essentially two of a unit of 1.921388691 ft, which has some interesting mathematical properties of its own, including being able to measure the height of the Great Pyramid as given by Munck, at a whole number value of 250 units. I call this mystery unit of 1.921388691 ft the "ellifino" (a play on the "elle" which is another name for the Cubit), because "'ell if I know" what it is, I've never been able to match it with historical record but it stands to reason that it didn't go overlooked by ancient people.
Regarding Stonehenge, the value derived by Munck from Petrie's data gives the sarcen circle an inner radius of 305.7985077 / (2 Pi) = 48.66934409 ft. That's 40 Remens of 1.216733603 ft. That's not very interesting in Remens themselves, but in modern feet it about sparkles, and it certainly seems to imply that whoever designed Stonehenge was quite aware of how ancient Egyptians used mathematics and measurement.
We're pretty blessed to be able to know that much about Stonehenge thanks to people like Petrie and Thom. Good data is otherwise still very hard to come by. Ironically, Aubrey Burl once remarked that either ancient people used the same measurements as us, or a lot of archaeologists are rounding their measures of stone circles to the nearest 5 meters.
Recently, I discovered that Munck's specified proportions for the Mycerinus pyramid were apparently based on a bad data source, probably I.E.S. Edwards, and based on something of a consensus in the data from Flinders Petrie and the recently departed Glen Dash, I ended up trying to revise it. I built the best model I could and then went on to explore the likely values for the base diagonals and edge lengths, and obtained an edge length of 326.4209971 ft, equal to my figure for the outer circumference of the Stonehenge sarcen circle, to the normal standard of accuracy I've obtained on forced approximations in ancient architecture of .9995 or better. I've seen the inner diameter of the sarcen circle of 80 Remens in data on the Great Pyramid's interior before (I believe it's the length along the top of the passage from the entrance to the upward fork in the passage, but I'd have to look it up to be certain, it's been awhile).
For what it's worth, I've proposed for the Mycerinus pyramid an original perimeter of 1383.399854 ft. One way to obtain this value is 1.067438159 x (360^2); another is 1.921388686 x 2 x 360 ("ellifino" how 1.921388686 got in there). 1383.399854 x (360 / 2) = 24901.19737, the earth's equatorial circumference in miles again. Another way to find it at Giza is take Munck's height for the Great Pyramid of 480.3471728 (which was after the missing pavement was added according to me) and multiply it by the canonical slope angle of 51.84 x 480.3471728 = 24901.19744.
I've also proposed that the ratio between the width of the Great Pyramid (without pavement) and the width of the platform it sits on (based on data from Lehner and Goodman with the endorsement of Glen Dash) is 1.003877283. Being that the Great Pyramid looks like a monument to the ratio 2 Pi (perimeter / height = 2 Pi), it shouldn't have surprised me so much when I discovered that 1.003877283 x ((2 Pi)^3) = 24901.19744 / 100
I actually discovered that when I was working with Tikal and found a long series based on multiplying a particular number from the measurements of a Tikal pyramid temple door by 2 Pi. You can start the series at the cube of "Alternate Pi" 1.177245771.
(1.177245771^3) x ((2 Pi)^9) = 24901.19744 x 1000.
That's a pretty amazing feeling when you feel like someone is speaking to you in your own language, but a lot more fluently, coming from people who weren't supposed to even be smart enough to invent the wheel after using it to make children's toys that children could pull behind them on a string.
Naturally in such a series there's a meaningful value at every power of 2 Pi until one has just plain gone too far with the progression.
I could re-iterate some basics here - the Great Pyramid really does seem like the "mother ship" of ancient monuments for having the apparent perimeter/height ratio of 2 Pi. That's basic circular math, circumference / 2 Pi = radius, and Munck and his students have traditionally used the 360 degree circle / 2 Pi = the Radian 57.29577951 (arc-degrees). Munck called the Radian "the Giza Constant" and I've never been able to disagree, in fact on a good day I find more evidence that he was right. It's the kind of thing people have been saying about the Great Pyramid since at least as far back as Taylor, but I guess not many people have embraced it very tightly.
I really didn't get very far with Tikal until I studied one of Edwin Shook's photos and decided that the pyramid in question seemed to expanding outward as you approach the base of it at a ratio of (Pi / 3), and started using (Pi /3) in my experiments. If there's a "Tikal constant" my guess would have to be 1/3 of Pi.
I'm not going to be surprised if 360 / 2 Pi = 57.29577951 is also some of the oldest math in the world, I get a picture of someone whose foot was probably exactly as long as the modern foot, once they counted out 365 beans in the time it took the sun to return to the same place in the sky at sunrise, pacing off a 365 foot circle and building the first Woodhenge with 365 little sticks so they could study it better, but I still have a hard time articulating that argument well. By the time someone rounded it to 360 like the Maya sometimes did for general purposes, modern circular math was born, I can only guess.
Morton's Cubit in inches can essentially be derived from circular math, the formula I prefer is .03 Radians = .03 x 57.29577951 = 1.718873385 ft = 20.62648082 inches. The area of a circle is radius squared x Pi, and if we use the Radian value of (360 / 2 Pi = 57.29577951) as the radius, that's 57.29577951^2 x Pi = 10313.24031, or 1/2 of 20626.48082. As near as I can tell, the Great Pyramid was designed so that the capstone (pyramidion) or missing section at the top if the slopes are projected upward to an apex point, is a macrocosm of the whole at the ratio of 10 Royal Cubits of 1.718873385. I came up with that over 15 years ago and still haven't managed to overturn the proposal, the more carefully I look at it the more sensible it's turned out to be, including that the gives the Great Pyramid a slope length without the missing section a length of 57.29577951 feet once the hypothetical pavement is in place.
That also involves allowing for the concavity of its sides. Many authors seem have disputed it or ignored it altogether but Flinders Petrie himself reported that the sides of the Great Pyramid are creased inward slightly at the center. With the model I use, that seems to allow for ancient authors to have been correct when stating that the maximum slope length (apothem) of the Great Pyramid was "1 Stadium" (500 Remens) - when the hypothetical missing pavement is in place, that's 500 Remens of 1.216733603; without the pavement I think the value is 500 Remens of 1.218469679 - distinctions that again we may only be able to spot through calculation and deduction.
It's something of an odd story, but I call 1.218469679 ft a "Thoth Remen" - Munck asserted there were several numbers that were "sacred" to "Thoth", "Father of Numbers". One of them is 240 and indeed, the inner circumference of Stonehenge and the height of the Great Pyramid are both based on (sqrt 240) x (Pi^n), almost as if it were an "inside joke" on the part of ancient architects, like soldiers writing "Kilroy Was Here" everywhere on behalf of the mythical "Kilroy".
Munck also pointed out a hieroglyph associated with Thoth that looks suspiciously like the number 9, and went on to demonstrate that the reciprocal of 9 is .11111111111 and the square of .111111111111 is .111111111111^2 = .1234567901 - all the numbers in order except the number 8 and it seems to repeat indefinitely. Hence he felt like he was giving mathematical truth to ancient mythology with that, and it turned out that 1.218469679 is .1234567901 x (Pi^2). That's sort of a long way to go to make an honest man out of Herodotus or Pliny or whoever it was who said the Great Pyramid's apothem length was "1 Stadium" (I'd have to look it up), but there you go - it does seem to actually work.
(For what it's worth, what I came up with for the perimeter of the Great Pyramid without pavement is 1.1111111111 x 2.720174076 x 10^n feet. If one chooses they can read that as "Oh look, Thoth signed his work on the underside, too").
The "Thoth Remen" also finds other reasons for being. It's loosely true that 360 / (Royal Cubit squared) = 1 Remen, and if we use Morton's Royal Cubit with this formula, 360 / (1.718873385^2) = 1.218469679, the Thoth Remen, so besides its dicey roots in the precarious interpretation of ancient myths, it can also boast some parentage in the area of simple variations on circular mathematics.
For someone who doesn't like arguments, I probably manage to really pick the wrong hobbies. I could have a lifetime of arguments trying to convince some people that any of our ancient ancestors could even conceive of a decimal point, let alone make effective use of it. To me it's as natural as creatures with 10 fingers having come up with base 10 arithmetic to have started experimenting with math just as soon as they tried to figure out when winter was coming, and it probably gave math plenty of time to get far out ahead of the rest of the sciences so that the ancient Egyptians and others were quite prodigal at it even when their first attempts at pyramid engineering were going sour because of engineering errors like poor choices for solid ground to rest them on.
Of all the things to get burnt at the stake for, but there it is. My fundamental premises are still that someone invented long division long before we give anyone credit for it, and discovered how to determine the circumference of the earth the same way the ancient Greeks or Egyptians did it, only again much earlier than we usually give anyone credit for. I don't really see where the controversy is personally, although I know lots of places where an argument can be found over these matters.
So yeah, that's one of the things I try to do with history. I don't try to figure out how ancient monuments were built, or who built them, or even why necessarily, I try to figure out what the architects might have been trying to say to generations down the road. Whatever it says about these ancient cultures, I see it as shared heritage, no matter what a person's particular roots happen to be. Some days I seem to find the earth's proportions recorded everywhere so insistently it seems a lot like someone once forgot the world was big enough that they had cousins on the other side of it and were greatly determined never to forget it again.
I could hypothesize why ancient Egyptians might have wanted to sentimentally equip funerary architecture with numbers that "go on forever" after the decimal point or infuse them with measurements that embody the timeless cycles of the heavens as if to represent, or infuse their works with, eternity, but my Mayan studies suggest even dwellings and government buildings were provided with the very same "added value" by their architects.
I'm sure I'd enjoy lecturing but I don't see how it's possible with Tourette's that's only half managed. Earlier this year I was daydreaming of doing some biology lectures for YouTube if I could get a medication to work, but that's likely still out of the question now. I can barely keep my arms raised to groom myself these days (hooray, now I look as loony as I must sound), but if I prop myself up on my elbows at my desk, I can still operate a pocket calculator and I can type without challenges. Thank heavens I can still do that much, and still express myself that way. I hope I can make the best of it and make it count for something somehow.
The more I read, the more I'm finding similarities between metrology and the idea behind block transfer computation, actually. Messages in the mathematics. I think @chaoticcivet 's right, a blog is a jolly good idea.