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  Comments on “Part XIV: More Information; More than We Know

  1. There is an article at https://www.chabad.org/parshah/article_cdo/aid/3514607/jewish/Torah-and-Mathematics-The-Secret-of-Noahs-Ark.htm that makes some interesting points about the possibly triangular and pyramid-like shape of Noah’s Ark, and its relationship to the pyramids of Egypt. (Also in the article are other interesting ideas including about the concepts of One and Zero.)

    Here is an excerpt of the text pertaining to the Ark (to see the figures please see the cited link):

    The L rd clearly instructed Noah about the exact spatial dimensions of the Ark: “This is how you are to build it: The ark is to be three hundred cubits long, fifty cubits wide and thirty cubits high. You shall make a (tzohar) window for the ark, and narrow it to a cubit at the top”. The picture below shows how this appears in geometerical terms.

    Figure 1. Geometry of the Ark
    Figure 1 shows that the Ark was shaped like a truncated pyramid. The angle of elevation at its side equals 50.76°. The angle of elevation of the Great Pyramid of Giza is 51.52°. The angle of elevation of the Pyramid of Khafre is 52.2°. The angle of elevation of the Pyramid of Menkaure is 50.47°. Thus, it is obvious that the angle of elevation of the Ark’s side matches the angles of elevation of the three pyramids of Giza within the bounds of observational error.

    Figure 2. Geometry of the Great Pyramid of Giza
    Based on what we shared above, we may make the bold supposition and say that the Egyptian Pyramids were constructed in the likeness of Noah’s Ark and they were ‘modelled’ on it.

    If we divide the sum of width and height of the Ark by its width, i.e. 50 + 30.612/50, the result is 1.612. If we divide the width of the Ark by its height (50/30) the result is approximately 1.667.

    As for the Great Pyramid of Giza, this ratio is approximately 1.631. The Golden Ratio (φ) is approximately 1.618. Just like π, φ is a universal irrational number in mathematics. In this case, the insignificant deviation of the Ark’s dimensions from φ can be explained by the fact that the L rd instructed Noah only in integers.

    When the Jews constructed the tabernacle in the Wilderness, G d commanded Moses: “Let them make an Ark [of covenant], of cedar wood, two and a half cubits long, one and a half cubit wide, and one and a half cubit high,” (figure 3).

    Figure 3
    If we take ratio (2.5 + 1.5)/2.5 = 1.6
    If we take ratio 2.5/1.5 = 1.(6)

    Here the difference between ratios of Ark of Covenant and Golden Section (φ) is due to the fact that G d gave the size of the Ark in integers.

    The Golden Ratio is a special number found by dividing a line into two parts, so that the longer part divided by the smaller part is in the proportion approximately of 68/32. The first mathematician to study the Golden Ratio was Euclid, who did so around 300 B.C. Euclid demonstrated that the Golden Ratio can be found in various geometric figures. The Golden Ratio was also studied in the Middle Ages, and even today mathematicians continue researching this. The Golden Ratio is often utilized in painting, music and architecture phenomenon. Among those who have studied the Golden Ratio we can name Leonardo of Pisa, astronomer Johannes Kepler, and Roger Penrose. Fibonacci, the great Italian mathematician of the 12th century who brought algebra to Europe, showed that the ratio between any two adjacent numbers in a series named after him (where every following number is the sum of the two preceding ones) tends towards φ. The Golden Ratio is often utilized in painting, music and architecture, and we can often observe it in nature (in the structure of leaves or parts of the human body), as well as on the atomic level. Some researchers compare the Golden Ratio to the structure of the human DNA genome.

    The fact that we find in Torah a universal mathematical number constitutes irrefutable evidence that the L-rd has written the Law of our universe in a way that it can be also read in mathematical language.

    It is also not by accident that the Ark was shaped like a truncated pyramid. Some hypotheses (although not yet confirmed academically) say that the space inside a pyramid-shaped structure acquires special properties in terms of energy. Famous Torah commentators have also written about the shape of the Ark.

    Commenting on Bereshit 6:16
    Ibn Ezra stated that the Ark was of triangular shape with a sharp vertex and acute angles to prevent it from overturning.

    Commenting on Bereshit 8:4
    Ramban said: And what is more: on the seventeenth day of Elul he sent a dove, and there was water all around the earth and the trees were beneath the water. But twelve days passed and everything dried up. We may conclude that if the Ark had eleven cubits beneath the water level (which is more than one third of its height) it should have sunk, as it would be too wide at its bottom part and have just one cubit at its top part. This is not the way one should build a ship, as such a design makes it too heavy.

    Commenting on Bereshit 6:16
    Abravanel wrote: the Holy Scripture says that He instructed him to build the Ark in a triangular shape, leaving at the top a length of just one cubit and six cubits wide formed by four beveled facets so that the falling raindrops stream down the walls of the Ark.

    Thus, we see once more that the Torah contains the fundamental mathematical principles of our universe’s structure.

    — Until here the quotation.

    Any remarks about this?

  2. Regarding the identity of the great pyramid’s builder and purpose, there is a new Youtube video, An Elevator in the Great Pyramid of Egypt? The Hidden Tomb of Pharaoh Khufu? | Ancient Architects, discussing the hypothesis that in the heart of the pyramid there is a hidden elevator shaft that hides the elusive remains of Pharaoh Khufu.

    Among the comments is the following list of evidences and sources:

    SurfK9 2 days ago (edited)

    Gee, why would anybody think it was built as Khufu’s tomb? So many people claim there is absolutely no evidence. Except that:

    His mother’s tomb is next to the pyramid and it has inscriptions stating the pyramid was built as Khufu’s tomb.

    His son’s tomb is next to the pyramid and it has inscriptions stating the pyramid was built as Khufu’s tomb.

    His brother’s tomb is next to the pyramid and it has inscriptions stating the pyramid was built as Khufu’s tomb.

    Also it says his brother oversaw construction of Khufu’s pyramid.

    The bakery in the city of workers has inscriptions stating they baked bread for the workers building Khufu’s pyramid.

    The brewery in the city of workers has inscriptions stating they brewed beer for the workers building Khufu’s pyramid.

    The oldest papyrus ever discovered is a ship’s log which says it was transporting covering stones down the Nile to build, wait for it….. Khufu’s pyramid.

    It was carbon dated to the 4th Dynasty. Rope fragments in mud used to fill gaps in the upper stones of the pyramid are carbon dated to the 4th Dynasty.

    450 bce the Greek historian Herodotus visited Egypt and was told by the Egyptians the pyramid was built by Egyptians for, wait wait… Khufu.

    Gee, multiple lines of conclusive evidence from multiple independent sources point to the same conclusion. The pyramid of Khufu was built by Egyptians for Khufu. But hey, there are YouTube videos and some vocal commentators who state, unequivocally, there is no evidence.


    Sources for ANY of these claims?

    I want to see writing specifically talking about “Khufu’s Pyramid” It was my understanding that he had NO text that actually mentions the Pyramid’s construction.

    SurfK9 2 days ago

    Stefan Eggers: Das Pyramidenkapitel in Al-Makrizi`s “Hitat”. BoD, 2003, ISBN 3833011289, p. 13-20

    “Revealed: 4,500-year-old Papyrus that details the construction of the Great Pyramid – Mysterious Earth”. Retrieved 2019-07-30.
    Lehner, Mark. The Complete Pyramids. Thames Hudson, 2008.

    Manley, Bill. The Seventy Great Mysteries of Ancient Egypt. Thames & Hudson, 2003.

    Shaw, Ian. Ancient Egypt: a Very Short Introduction. Oxford University Press, 2004

    Stocks, Denys A. “Immutable Laws of Friction: Preparing and Fitting Stone Blocks into the Great Pyramid of Giza.” Antiquity, vol. 77, no. 297, 2003, pp. 572–578., doi:10.1017/s0003598x00092632.

    Tallet, Pierre, and Gregory Marouard. “THE HARBOR OF KHUFU on the Red Sea Coast at Wadi Al-Jarf, Egypt.” Near Eastern Archaeology, vol. 77, no. 1, 2014, pp. 4–14., doi:10.5615/neareastarch.77.1.0004.

    Verner, Miroslav, et al. The Pyramids: the Mystery, Culture, and Science of Egypt’s Great Monuments. American University in Cairo Press, 2004.

    Lehner, Mark, and Zahi A. Hawass. Giza and the Pyramids. The American University in Cairo Press, 201

    Hawass, Zahi A. Mountains of the Pharaohs: the Untold Story of the Pyramid Builders. Doubleday, 2006

    Porter, Bertha and Moss, Rosalind: Topographical Bibliography of Ancient Egyptian Hieroglyphic Texts, Statues, Reliefs and Paintings, Volume III: Memphis, Part I Abu Rawash to Abusir. 2nd edition

    James Henry Breasted: Ancient Records of Egypt: The first through the seventeenth dynasties. University of Illinois Press, New York 2001, ISBN 0-252-06990-0, page 83-84

    Summerized in this video:

    — Until here the quotation.

    Any remarks about this?

  3. General speaking it is undeniable that all of the religions and practices of the Egyptians are extremely abhorrent and detestable to Torah and Judaism.

    It seems therefore to be an amazingly contradictory abnormality for any Bible believer to be so entranced by the pyramids.

    As soon as time allows I will try explain more about my perspective on this.

  4. The author knows what he is speaking about and coincides with much of what we’ve written, though I believe 1 is also synonymous with “always.” I don’t see any reason that the Torah suggests a pyramid shape. We were given the measurements for definite purposeful reasons but I don’t see any design plans for more specific shapes. If anything it describes the shape of a cargo tanker which is far more seaworthy than a pyramid.

  5. I too recently saw the elevator video. Interesting theory but more likely about a hidden chamber of secrets then Khufu. I did a lot of research 30 years ago in the the books of people who had actually taken the measures and did the primary research not all these rehashed books written with agendas and all reversed engineered to fit the narrative of the fake cartouche–nothing pointed to Khufu. Anything with Zahi A. Hawass’ name on or in it is complete BS built on the dual agenda of self-aggrandizement and promoting Egyptian superiority and tourism. All the books cited were of circular sources (mostly Hawass) written in the last 16 year; earlier works showed no such info. The truth as we know it is that the more powerful the pharaoh the bigger the statues and building he made to himself and put his name all over, and the tombs were all elaborately decorated as part of their death journey preparations–neither fact applies to khufu. Finally, the Egyptian wrote extensively about their elaborate preparations for the dead and no where do they write about be shoved into a modest hole inside a pyramid.

  6. That is if you believe the Pyramid to be of Egyptian design and culture, and if you believe anyplace on earth does not belong to G-d. G-d saw fit to send all the Patriarchs to Egypt on separate missions, and use it as a place of incubation for the Israelites; was He mistaken; did He put it in His Torah because He found it so detestable? What G-d wrong went He sent the Israelites to Egypt for 210 years; should He have chosen a different date so it would not match up with the height of the Pyramid? Or was He just trying to confuse us? Did He give the dimensions of the Future Holy Temple to the Ramchal so they would match up with the pyramid within .0424% that you think was built by Egyptians before the iron age, or it is possible it was His design and he had some reason with sharing it with us? Maybe there is a reason not even the Egyptians dared put graven images on the pyramid?

  7. Continuing from my previous comments:

    Whether or not the shape of Noah’s Ark is connected with the shape of the pyramids, certainly Noah must have been an engineering genius in order to design and construct the Ark, and his sons and their families after him continued and improved on his wisdom.

    In succeeding generations major work was done toward building an enormous ziggurat, the Tower of Babel, which surely was a colossal engineering project. When the Tower’s construction of was disrupted, the previously united population split up and dispersed throughout the world, taking with them various aspects of the previously developed technology. Subsequently people in many places continued building megalithic structures and towers, including other ziggurats in Babylon, and stacked mastabas and pyramids in Egypt, and in virtually every part of the world.

    Egyptian pyramid building design and technology advanced in stages, improving on previous methods, and progressing from plain mastaba structures, to stacked mastabas, such as the “Step Pyramid,” then to the “Bent Pyramid,” then to large pyramids with shallower inclines, like the “Red Pyramid,” and then finally to the immense steeper-sided pyramids, reaching the pinnacle of size and complexity in the three massive pyramids at Giza, attributed to Pharaohs Khufu, Khafre and Menkaure. These great pyramids are guarded by the large graven image of the Sphinx, probably built by either Khufu or his son Kafre, with the face of one of these pharaohs depicted as the head of the lion’s body. Egypt has more than 135 pyramids and they clearly played a major role in ancient Egyptian civilization, religion and culture.

    [It seems possible that that these three renowned Old Kingdom Pharaohs, Khufu, Khafre and Menkaure, correspond to the three Biblical patriarchs Avrohom, Yitzchok, and Yakov. Yosef very likely was the viceroy of Egypt near the end of the Old Kingdom, and the Exodus probably happened toward the end of the Egyptian Middle Kingdom, as per a number of alternative theories regarding the convergence of Biblical and Egyptian chronologies.]

    Incidentally, the newest Ancient Architects Youtube video came out yesterday, discussing the topic of “Fact or Forgery: The Khufu Graffiti Inside the Great Pyramid of Egypt.” The producer explains that the red ochre graffiti painted inside the relieving chambers of the Great Pyramid discovered by Howard Vyse in the 19th century is a critical piece of evidence that associates the Great Pyramid with Khufu. Many have claimed that this is a forgery, and that it was painted by Howard Vyse so that he could claim some major discovery and grab the headlines. It is almost an accepted fact in some circles that it is a forgery. Nevertheless, in this carefully weighed opinion, the burden of proof is on those making these forgery claims. He reviews statements of alternative researchers who have looked at the graffiti in great detail, namely Graham Hancock, Robert Bauval and John Anthony West, who accept it as genuine. There is also a crucial detail that nobody talks about, and the fact that Khufu’s Horus name also appears inside. Watch this video to learn more.

    Next week I will try continue with some further important observations about these matters, but for now Shabbos is approaching fast.

    Good Shabbos and Good Rosh Chodesh Elul!

  8. Thank you, Moshe, Shabbat Shalom and Chodesh Tov. I have no proof but isn’t it possible that once the technology to build the 3 pyramids was removed, that the Egyptians tried to replicate them and could only come up with simple ziggurats. The Tower of Babel is a whole other discussion.

  9. The “Orion Link”
    Moshe, Ezra, thanks for the “Pyramids info”. Do you have any thoughts on something that I have wondered about:

    Was the Great Pyramid planned and built as a “One off”? In other words, were the other pyramids, and the apparent efforts to “reproduce” Orion’s Belt at Giza, and the rest of the Orion Constellation across hundreds of miles of Egyptian “real estate”, an afterthought?

    When I look at the Great Pyramid and the one adjacent to it, they look like they were “planned” to be together. The “second pyramid” is shorter, but its base-rock is about 30 feet higher than what we call “Joseph’s Pyramid”. The higher base level contributes to my mental picture of those two pyramids being “pseudo twins”.

    BUT, the “Gret Pyramid” (Joseph’s Pyramid) is so “riddled with Torah mathematics that “mentally” I see it as UNIQUE, a permanent monument showing Divine input in its design and maybe in its construction.

    Any thoughts on the possibility that someone tried to “hijack” the brilliance of the Great Pyramid and make it part of a “star map” to honour human achievement or some magical ride into the afterlife for a select few monarchs who thought their ancestors had links to Orion?

  10. Regarding the development of technology, the Torah teaches, Genesis 4:7, that at the beginning of history Kayin (Cain) built a city and named it after his son Chanoch, and it is evident that in addition to the technical skill involved in building a city in and of itself, “Urban life, unlike rural life, cultivates sophisticated skills in its practitioners,” as the Artscroll commentary on notes on this verse from Rav Hirsch.

    [It is interesting that the name חנוך, Chanoch, the namesake of this first city, has a meaning of “educated” and “skilled,” which according to the above is a fitting name for a city dweller. Chanoch’s son incidentally was named עירד, Irod, which seems also to hint to the idea of a city dweller, since the the first three letters are עיר, Ir, which means “city.”]

    Only a few generations afterward, Genesis 4:22 states that “Tuval-Kayin was a metal-worker of all manner of implements of copper and iron,” or as alternatively translated, “Tuval-Kayin was a sharpener all manner of cutting implements of copper and iron.” Usually in the Torah the word “copper” (Nechoshes) includes its principal alloys of “bronze” and “brass,” metals that are relatively easy to refine and manufacture. In contrast, “iron,” with much higher malleability and melting temperatures, is much more difficult to produce and utilize. At any rate, this verse indicates that at least the initial production and use of iron implements occurred at a very early stage of civilization, even well before the Great Flood.

    It is very likely that Noach himself was also skilled in this early metal-working technology, and that he also designed and used bronze and iron tools. Interestingly, regarding Noach’s skill as an inventor and craftsman, there is a Midrash that attributes him with the invention of a special plow to assist in cultivating crops. Rashi mentions this on Genesis 5:29, “זה ינחמנו, This One Will Comfort Us — He will ease from off of us (ינחמנו) the toil of our hands. For until Noah came people had no agricultural instruments and he prepared such for them. The earth had brought forth thorns and thistles when they sowed wheat in consequence of the curse imposed upon Adam Harishon: in the days of Noah, however, this ceased (Tanchuma 1:1:11). This is what is meant by the word ינחמנו (viz., ינח מנו).” Although it is not explicitly stated, it is likely that Noach’s plow was made of metal, and similarly Noach would have been able to use both bronze and iron tools and fasteners in the construction of the Ark.

    After the Flood some of the descendants of Noach likely carried on and developed this technology, and were able to use at least some iron tools for cutting stone to shape and for carving statues and other items. Indeed there seems to be some evidence to support the idea that the ancient Egyptians used not just copper, but also iron tools to produce granite and other very hard stone statues and stone blocks for their great construction projects. It seems that the Egyptians, even if they themselves were unable to produce iron tools, would have been able to acquire such tools through trade with people in other regions of the world.

    It is also possible that very early on, including in ancient Egypt, stone cutting tools were made with tips and edges fashioned of extremely hard crystals and gemstones, even diamonds, and these could have been used to enable them to cut stone blocks and carve intricate statues, vases, jewelry and the like out of the hardest stone.

    Additionally, some ancient people may even have developed a technology, lost to us today, that enabled them to soften stone, and thereby more easily carve and mold stone blocks that fit closely together even with intricate shapes. This is based on another Ancient Architects Youtube episode, “This is How They Built the Inca Stone Walls,” featuring a hypothesis presented in a paper by Helmut Tributsch for the SDRP Journal for Earth Sciences and Environmental Studies in December 2017, http://www.academia.edu/37497925/On_t… ‘On the reddish, glittery mud the Inca used for perfecting their stone masonry.’ It is mentioned there that there are also some ancient Egyptian structures that may have employed similar technology.

    Also perhaps relevant to this discussion is that according to Jewish tradition long ago there used to be something special called a “Shamir,” that was used in some way to cut through stone and even hard crystals and diamonds, perhaps by utilizing chemical reactions to soften or dissolve and cut minerals and metals. It is said to have been a small creature, perhaps some kind of worm, that no longer exists, or that still exists but has lost its previous qualities, and its unique secretions supposedly had this exceptional ability.


    Peter, that the three Giza Pyramids were planned in sync with one another seems to be generally true, but the idea that they were built to resemble the three bright stars in Orion’s Belt has been completely debunked and discredited, as can be found explained many places on the internet.

    As written before, I do not think that the “Great Pyramid” has any connection with Joseph, though it seems possible that Pharoah Khofu, who commissioned the Great Pyramid, may have been the pharaoh that Avrohom and Sarah met when they descended to Egypt. It may even be possible that they discussed with one another certain aspects of pyramid building and various sciences and philosophies, but in my opinion it is highly unlikely that Avrohom had any direct influence on the way any pyramid was constructed.

    As for the Great Pyramid being “riddled with Torah mathematics,” and “showing Divine input,” and the like, I hope to be able to write more about this at my next opportunity.