> From the vagueness of your post I can only assume
> you are asking me to answer my own question
> regarding which survey best reflects the intent of
> the Ancient Egyptian builders.
> Surveys of this sort only reflect the ‘as
> built’ dimensions, not intended dimensions. If
> you disagree, please provide what irrefutable
> evidence that exist which would lead anyone to
> assume any surveyed dimension of G1 are the exact
> intended dimensions of the Ancient Egyptian
> builders? That any survey does is an assumption
> with no irrefutable evidence addressing this
> conundrum. Therefore the correct answer can only
> be 'None of them'!
Well, that's brave of you to volunteer that the pyramids are so hard to measure that they're not going to support anyone's premises including your own, lol - and I do agree, everyone's measurements describe the GP as having unequal sides but the troubling thing is that no two may agree what the longest or shortest sides are.
However, I do have some experience working with the mean values provided by Petrie and others and don't recall having that much occasion to second-guess them, at least if we're still at the scale of things the size of pyramids or less.
> So Jim, without knowing the intent of the Ancient
> Egyptians you, like everyone else, are just
> guessing and guessing is not science. Fact: No one
> has yet provided any evidence, let alone
> irrefutable evidence. supporting the Ancient
> Egyptians use of pi, phi, √2, √3 or √5.
> There is no evidence other than yours and others
> training and ability to find these modern
> mathematical operators which occur naturally in
> the mathematics of structures by our current
> system. As stated many times before: [i[ If one
> draws a square, the √2 is an inherent value of
> the diagonal within the square, similarly if one
> draws a circle then л is the inherent value
> within the circle relating the diameter to
> circumference. Is foreknowledge of either of these
> factors is necessary for the completion of either
Well, wait a minute here, ok? It's one thing to draw a circle and automatically have the circumference and perimeter ratio be Pi, or take the diagonal of a square and automatically have it be sqrt 2, but if someone makes the perimeter of their circle 360 feet and the radius 57.29577951 ft, that's something different. If someone makes the diagonal of their square roughly 1.414213562 ft, that's something different as well.
If in lieu of a 360 foot circular perimeter, someone makes a circle out whatever they please as long as it's highly interactive with the 2 Pi circumference / radius ratio of any circle, that's something different too.
We can do the same thing with ancient metrology as well. We can say the AEs had no idea what the modern foot was so they had no idea just how brilliant Remens and Royal Cubits are mathematically when expressed in modern feet, they just knew them as 1 of either, but when you start finding the Remen value or Royal Cubit in feet as a ratio between parts, that's again something different.
All of that and much more is capable of talking to anyone who will listen, and I do think it might just be trying to say something.
> A couple of years ago I quit looking for what
> couldn't be prove and started looking for what
> could be proved regarding the Ancient Egyptians
> mathematics. Here is a hint: It doesn't reside in
> our modern mathematical operators like pi, phi,
> √2, √3 or √5 since they are naturally
> occurring factors within our current system. As
> Corinna Rossi determined, from a perspective based
> on the available evidence strongly indicates the
> Ancient Egyptians were not aware of our concepts
> nor did they employ these factors. But I do wish
> you good luck on your quest to prove otherwise.
That seems almost an odd thing to say - I mean, it isn't that Rossi is my source for sqrt 3-riddled equilateral pyramidia because I know what you'd say, they had no idea what sqrt 3 was they just wanted pyramids with edges equal to the base, but where does one really get the opportunity to put things to the test with sqrt 3 or sqrt 5 outside of things like the Vesica Piscis? Sure, every square thing in creation has diagonal of sqrt 2, but how about the rest of it?
If you even have any examples of sqrt 3 or sqrt 5 for this discussion, it would seem like they must quite likely be out of a native context such as the ones you describe that allows their use without understanding them.
Yes, I'd like to see some papyrus for proof too, sigh, and you probably don't want to get me started again on the ephemeral nature of data even in the here and now, but I try to be realistic enough to know that that may not be likely that I get to see the papyrus even if such items had once existed in some number.
Maybe the math we're talking about would have consumed so much papyrus that no one even bothered to write it out - literally. That is NOT some mere glib remark, you should see how much contemporary papyrus I've gone through over this stuff and my mentor is said to have occupied whole rooms with his handwritten calculations prior to the availability of pocket calculators.
As always, I try to put as many demands on architecture as I can possibly think of to try to rule out coincidences - things should multiply, divide, add, and subtract within established parameters, which may take careful choices to achieve, and that's just for starters. That we should see frequent references to what may be established common themes like astronomy and geodesy is an additional rigorous criteria that I've stacked on top of all that.
Not content with all that, I like to further try to rule out coincidence by demanding in addition that I not only see metrological units in modern feet expressed as ratios to help corroborate their validity, but that should often work as mathematical constants that unlock data with exponential use.
Anything you'd like to add to my list of stringent criteria there?
See, using fractions or rounding numbers is all well and good, but there may come a time when doing that is going to affect not just the way one interprets something, but the way someone designs something. If someone else says, "Oh, 162 is close enough" and I'd say "No it isn't, we should be more exacting", they'd pick it and I wouldn't, see? I wouldn't pick a different interpretation, I would pick a different proportion if a particular grouping of proportions is at risk of causing too much confusion about their nature and intent.
If I see all these rigorous criteria met again and again, if I see numbers that looked they were grouped as if someone were designing architecture in the way they would if they were thinking of numbers to at least ten places after the decimal, then hopefully I'm right in reigning in just how much I want to attribute to coincidence.
That may be hard for you to appreciate because like Rossi or Petrie you probably have a seked for every occasion, but that doesn't stop others from describing the very same thing in terms of slope angles, trigonometric functions, precise perimeter/height ratios and other more sophisticated things that have nothing to do with sekeds, and so forth. Getting sekeds to stick has nothing to with the possible actual state of the art, anymore than does rounding Pi to the second or third decimal place.
The question is always just how accurately is something being described by the textbook description, and how accurately is it being described by any unfounded unorthodox theory, on its own terms?
If the GP isn't 440 cubits wide, many may be in a bit of trouble, you know. Mine isn't. Mine's about 439 and a half, show me how to make a seked out of that?
The biggest action in my pyramid model with the Royal Cubit is really that the pyramidion is modelled on the whole thing with 10 Royal Cubits in modern feet as the ratio between pyramid and pyramidion.
Before we consider the evidence, let's give it the chance to accumulate some more. This was originally determined from scattered reports of the GP's current height and "Wow, I bet Munck will be so happy if 452.3894321 ft turns out to be how high it us up to where the pyramidion sat" because he had profound reverence for 452.3893421".
That pyramidion height and 10 Royal Cubit ratio is locked in by that.
Not yet content that the absurd has already been asked of it, given a model that truncates the sides in order to make the apothem 1 stadium in accordance with classic authors, we find the apothem with the pyramidion missing to be the radian in feet, which outrageous demand it meets to an accuracy of .9999726682, the formula giving 572.9734555 for 572.9577951 even after just suffering from the ravages of addition and subtraction. 10 Royal Cubit ratio locked in, again.
Now think about this, proof of modern feet, we'd all like to see the papyrus, I know -- but what I just described to you with its multiple built-in backup checks, is a Royal Cubit to Modern Foot Converter. I think I'm going to stop asking to see the papyrus, ok?
Not content with that, I recycled one of Davidson's and determined that at the altitude where the Great Pyramid's perimeter expresses the Calendar Year in feet, the length of a side is equal to the concave apothem, but I probably wasn't contented with that either. More! - more outrageous demands to try to filter out coincidences.
I should mention that this is after the placing of the hypothetical pavement, not that I have any of that to show you either, but there seems to be circumstantial evidence for it ranging from the state of surrounding features to the equations themselves.
Let's see, what else did I demand? Oh, yeah - I circumscribed and inscribed all three big pyramids in the vertical plane both through the middle and the diagonal, and for Cheop's pyramidion (or missing section) too, and demanded that it should all be fairly impressive as completely unreasonable as the concept may be, and for Cheop's pyramid I also did this with the pyramid before and after paving.
Not that I'm finished describing the model, but that's how I think I might know how tall the GP might be, and how wide. Because I demand the impossible, and the pyramids oblige, although I'm not sure they're doing it for the likes o' me. Probably not.
Did you want to add something to list of evidence I should want to see before resting confidence in a set of Great Pyramid proportions?
I could still be quite wrong of course, but I hope you can tell how hard I try not to be?
Edited 4 time(s). Last edit at 06-Jan-20 06:28 by thinkitover.