Season's Greetings, all
The other day om GHMB during one of Steve Clayton's discussions about water sources for pyramid construction, Trevorjjj mentioned Lake Moeris, and that is about all one has to do for me to get misty-eyed over engravings from Thompkins' book of two large Egyptian pyramids in Lake Moeris that don't seem to be accounted for.
I attempted to look for new developments as well as old discussions but didn't seem to find much and in fact the closest thing I found to the typical robust discussion here, is a thread from "Above Top Secret" starring Hanslune that probably turned a bit "paranormal" on the part of persons he was corresponding with.
Stijn van den Hoven, who I think has posted here a few times in the past, has a paper on Academia.edu that seems to be proposing that the two pyramids referred to by Herodotus are the Pedestals of Biahmu
It's a very interesting idea and elegantly simple, but I still struggle with it quite a bit, including that there are a few things that try to suggest to me the structures at Biahmu were never pyramids.
I am still trying to trace some of the details of the two pyramids seen in various engravings back to their respective classic authors and get a better grasp of their full descriptions and how plausible they might be but please feel free to discuss.
Image may be NSFW.
Clik here to view.
What is MORE implausible, two pyramids this size (and in the the middle of a lake no less), or Herodotus making an error this large as to the proportions of the pyramids? -- but are the Biahmu structures pyramids at all?
Image may be NSFW.
Clik here to view.
At upper left, if we take Petrie's drawing and project a pyramid from it, a problem may be fairly obvious. Perhaps it can be corrected by facing the statue the opposite way on the pedestal within a niche in the pyramid side (at upper right), but how much confidence can be invested in such a proposition? (Also seen is Lepsius's drawing in which the cardinal directions seem to have been confused, compared to a Google Maps clip).
At any rate, I went back to my digital copy of Petrie, Hawara, Biahmu and Arsinoe concerning this, and discovered that apparently my data for the Hawara pyramid might come from a different publication by Petrie (?) since apparently I never got around to actually reading this work by Petrie after having been put off by every other page in my copy being badly bleached.
There are a couple data points in Petrie's description that need more scrutiny (basically his figures in inches may be good while his uncharacteristic quotes of measures in feet may not?) but most of the data seems rather interesting
Here is some metrological (and a little mathematical) speculation
Image may be NSFW.
Clik here to view.
Notice a possible "preponderance" of instances of the Indus Foot in use.
The typical "unit of measure in Imperial as ratio) phenomenon may be on display here, with possibilities of the Remen and (Harris Stockdale) Megalithic Foot (approximately).
Image may be NSFW.
Clik here to view.
Here, the Royal Cubit in feet may (or may not) appear as a ratio
To be honest, I'm a little confused by some of that, and when I tried to think of where to look for assistance, the nearest pyramid comes to mind, which as far as pyramids that can be located seems to be the Hawara pyramid.
The intriguing thing is that as soon as one looks there, several curious parallels seem to emerge
If I take the equation 35 / 21 = 1.6666666666 and adapt it to the 2.107038746 ft Palestinian Cubit,
21.07038746 x 1.6666666666 = 35.11730793 as the height of the statue. This is equal to twice the perimeter of the missing Great Pyramid apex section / 10^n.
Curiously, 5 / 35.11730793 = 1.423799344 = 1 / 7.023461587
Because 1 / 60 = 1.666666666 / 100, if we look at the ratio between Petrie's "60 feet" total height for pedestal and statue, projective though it is, we get the same thing from the opposite direction: 60 / (10 Palestinian Cubits = 21.07038476) = 2.847598689 = 1.423799344 x 2
This has been reported as an Egyptian "Wonder Number", and in fact I recently stumbled across notes that state that the discovery took place while working with Petrie's data for the Hawara pyramid, showing that just prior to that I was oblivious to the existence or significance of the figure. Apparently they are from a post I made on Ancient Metrology (formerly Ancient Measures) earlier this year:
That was right before 7.023461565 = .1 / 1.423799349 attained "Wonder Number" status
A figure of 130.833 feet appears in the drawing based on Petrie's descriptions, which also appears in his data for Harawa
(Yes, anything that isn't a round number of Royal Cubits seems strange to Egyptology, doesn't it?)
157 inches / 12 = 13.083333333 ft
(It's also possible that instead, 157 inches refers to Pi / 2 = 157.0796327 / 100)?
I should also like to remark that concerning a possible height of 189.9772194 feet for the Hawara pyramid, that relative to 360, this is the inverse of the figure that is still trying to be the upper height of the Bent Pyramid in my model
360 / 189.9772194 = 189.49644044 / 100
For what it's worth, even though the Pedestals of Biahmu may never have been pyramids, projecting pyramids from their bases as we would project the heights of pyramids from what remains of them, may be an interesting and rewarding metrological / mathematical exercise.
It's a bit sticky since the bases of the Harawa structures are apparently rectangular than square, but a projection based on a half-base of 65 feet and a mean slope of 65* gives 139.39298 ft as a projected height, which is very close to 66.66666666 Sacred Cubits using my usual unit values.
(Others might wish to see 139.39298 ft as approx "81 cubits", or 130.8333333 as "76" cubits, or the perimeter/height ratio of the Hawara pyramid as 7, while I'm devoted to exploring alternate possibilities).
Ideally at least, perhaps the Pedestals of Biahmu could enhance understanding of the design of Amenemhet III's pyramid at Hawara, and vice-versa?
Cheers!
The other day om GHMB during one of Steve Clayton's discussions about water sources for pyramid construction, Trevorjjj mentioned Lake Moeris, and that is about all one has to do for me to get misty-eyed over engravings from Thompkins' book of two large Egyptian pyramids in Lake Moeris that don't seem to be accounted for.
I attempted to look for new developments as well as old discussions but didn't seem to find much and in fact the closest thing I found to the typical robust discussion here, is a thread from "Above Top Secret" starring Hanslune that probably turned a bit "paranormal" on the part of persons he was corresponding with.
Stijn van den Hoven, who I think has posted here a few times in the past, has a paper on Academia.edu that seems to be proposing that the two pyramids referred to by Herodotus are the Pedestals of Biahmu
It's a very interesting idea and elegantly simple, but I still struggle with it quite a bit, including that there are a few things that try to suggest to me the structures at Biahmu were never pyramids.
I am still trying to trace some of the details of the two pyramids seen in various engravings back to their respective classic authors and get a better grasp of their full descriptions and how plausible they might be but please feel free to discuss.
Clik here to view.
Clik here to view.
At upper left, if we take Petrie's drawing and project a pyramid from it, a problem may be fairly obvious. Perhaps it can be corrected by facing the statue the opposite way on the pedestal within a niche in the pyramid side (at upper right), but how much confidence can be invested in such a proposition? (Also seen is Lepsius's drawing in which the cardinal directions seem to have been confused, compared to a Google Maps clip).
At any rate, I went back to my digital copy of Petrie, Hawara, Biahmu and Arsinoe concerning this, and discovered that apparently my data for the Hawara pyramid might come from a different publication by Petrie (?) since apparently I never got around to actually reading this work by Petrie after having been put off by every other page in my copy being badly bleached.
There are a couple data points in Petrie's description that need more scrutiny (basically his figures in inches may be good while his uncharacteristic quotes of measures in feet may not?) but most of the data seems rather interesting
Here is some metrological (and a little mathematical) speculation
Clik here to view.
Notice a possible "preponderance" of instances of the Indus Foot in use.
The typical "unit of measure in Imperial as ratio) phenomenon may be on display here, with possibilities of the Remen and (Harris Stockdale) Megalithic Foot (approximately).
Clik here to view.
Here, the Royal Cubit in feet may (or may not) appear as a ratio
To be honest, I'm a little confused by some of that, and when I tried to think of where to look for assistance, the nearest pyramid comes to mind, which as far as pyramids that can be located seems to be the Hawara pyramid.
The intriguing thing is that as soon as one looks there, several curious parallels seem to emerge
If I take the equation 35 / 21 = 1.6666666666 and adapt it to the 2.107038746 ft Palestinian Cubit,
21.07038746 x 1.6666666666 = 35.11730793 as the height of the statue. This is equal to twice the perimeter of the missing Great Pyramid apex section / 10^n.
Curiously, 5 / 35.11730793 = 1.423799344 = 1 / 7.023461587
Because 1 / 60 = 1.666666666 / 100, if we look at the ratio between Petrie's "60 feet" total height for pedestal and statue, projective though it is, we get the same thing from the opposite direction: 60 / (10 Palestinian Cubits = 21.07038476) = 2.847598689 = 1.423799344 x 2
This has been reported as an Egyptian "Wonder Number", and in fact I recently stumbled across notes that state that the discovery took place while working with Petrie's data for the Hawara pyramid, showing that just prior to that I was oblivious to the existence or significance of the figure. Apparently they are from a post I made on Ancient Metrology (formerly Ancient Measures) earlier this year:
Quote
Applying a common mathematical probe
7.015761821 / 1.622311470 = 4324.546768 (Jupiter Orbital Period 4332.59 days)
7.015761821 / (1.622311470^2) = 2.665669846 = 1.066267938 / 4
(1.067438159 / 4) x 1.622311470 = 4329.292924 Jupiter Orbital Period A
(1.067438159 / 4) x (1.622311470^2) = 7.023461565
I am confused and saddened that this is 1 / 7.023461565 = 1.423799349 and NOT 1 / 7.021089950 = 1.424280286, one of the Mayan Wonder Numbers.
However, I am pleased to see that this scheme would actually provide
1334.297699 / 7.023461565 = 189.9772194 as the height, 1 / 100 of Half Venus Cycle B
That was right before 7.023461565 = .1 / 1.423799349 attained "Wonder Number" status
A figure of 130.833 feet appears in the drawing based on Petrie's descriptions, which also appears in his data for Harawa
Quote
WMF Petrie
The brick-work base (of the pyramid) was found to be: 3692 inches (307 ft 10 in) in length
adding 2 x 157 we find 4006 inches for the original size of the pyramid base; and hence a height of 2284 inches. It seems very strange that it should not have been 10 feet longer, as so reach 200 cubits...
(Yes, anything that isn't a round number of Royal Cubits seems strange to Egyptology, doesn't it?)
157 inches / 12 = 13.083333333 ft
(It's also possible that instead, 157 inches refers to Pi / 2 = 157.0796327 / 100)?
I should also like to remark that concerning a possible height of 189.9772194 feet for the Hawara pyramid, that relative to 360, this is the inverse of the figure that is still trying to be the upper height of the Bent Pyramid in my model
360 / 189.9772194 = 189.49644044 / 100
For what it's worth, even though the Pedestals of Biahmu may never have been pyramids, projecting pyramids from their bases as we would project the heights of pyramids from what remains of them, may be an interesting and rewarding metrological / mathematical exercise.
It's a bit sticky since the bases of the Harawa structures are apparently rectangular than square, but a projection based on a half-base of 65 feet and a mean slope of 65* gives 139.39298 ft as a projected height, which is very close to 66.66666666 Sacred Cubits using my usual unit values.
(Others might wish to see 139.39298 ft as approx "81 cubits", or 130.8333333 as "76" cubits, or the perimeter/height ratio of the Hawara pyramid as 7, while I'm devoted to exploring alternate possibilities).
Ideally at least, perhaps the Pedestals of Biahmu could enhance understanding of the design of Amenemhet III's pyramid at Hawara, and vice-versa?
Cheers!