Chapter 36 Chapter 38: Three-Dimensional Games

At last I reached the end of the great passage and ascended a three-foot marble platform.Like the Queen's Hall, this high platform is located on the east-west axis of the pyramid, so it happens to be the dividing point between the north and south of the pyramid①.The appearance looks a bit like the high platform of an altar, forming a four-cornered platform in front of the entrance of the palace. I stopped for a while, looked back down the corridor, and then confirmed that there were no decorations or religious portraits above my head.None of the symbolic marks associated with the ancient Egyptian belief system were visible.Looking around, I can see a 153-foot-long, far-reaching space created by geometry. In the indifferent regularity, there is an almost mechanical simplicity and simplicity.

Looking up, I could clearly see a black hole in the east wall above the Great Corridor.No one knows who and when the hole was dug, nor how deep it is, only that from here you can enter the first of the five decompression chambers in the king's palace. In 1837, when Hauer Weiss came in to explore, in order to expand the cave space to enter the other four decompression chambers, he deliberately knocked down the walls of the cave.From here, looking down again, I could see the entrance to the longitudinal pit in the west wall of the lower passage.This almost vertical pit is about 160 feet long, passing through the center of the pyramid and connecting with deep underground passages.

Why does the pyramid need to construct such complex longitudinal pits and passages?At first, I couldn't understand it at all.There are too many mysteries hidden in the Great Pyramid, none of which we can easily understand.However, I have found that when we are willing to put in the time and effort to understand it, its rewards far outweigh the effort. For example, assuming that you are a person with a strong sense of numbers, you will naturally want to know the height and circumference of the pyramid, and you will be very interested in the relationship between the two and π. From here, if you want to know more about the pyramid The complex and insoluble mathematical problems hidden in the structure have been quietly lying in the pyramid for many years, waiting for you to discover and explore.

And when you set out to solve the problem, the whole process of excavation and inquiry is like entering a pre-designed program, and there is a driving force in the dark to guide you forward.Once again, I began to think, whether it is possible that the pyramid, from the beginning of the design, was intended to be a great challenge to test future generations, or to make a huge learning device to pass on specific knowledge to future generations...or even a A three-dimensional interactive jigsaw puzzle standing on the desert for future generations to solve. Front Hall Quest The entrance to the palace is only 3 feet 6 inches high, and any normal person must bend down before entering.In less than 4 feet, there is an "Antechamber" (Antechamber), the roof suddenly opens up to a height of 12 feet.The east and west walls are paved with red basalt.There are 4 longitudinal channels of considerable width on the walls.Ancient Egyptian scholars believe that a hanging door made of thick stone slabs must have been installed on it. Three of the four channels were sunken all the way to the ground and left empty inside, but the fourth (and the northernmost one), dug only to the roof level of the entrance (3 feet 6 inches from the ground), was hollowed out. Also embedded in the trough is a massive basalt slab about 9 inches thick and 6 feet high.The slab stood in front of the entrance like a barrier, with only 21 inches of space between it and the roof, and just over 2 feet from the roof.While we don't understand its true purpose, we'd be hard-pressed to agree that ancient Egyptologists saw it as a device to keep out tomb robbers.

Holding this difficult question, I drilled under the stone slab and came to the south side of the hall again.This room, known as the vestibule, is about 10 feet long, with a ceiling height of 12 feet.Although it has been worn out badly, the channels that used to be used for the hanging doors are still clearly visible on the east and west walls, but the stone slabs used for the hanging doors are missing.And in this narrow space, I can hardly imagine how the ancient Egyptians hung the large and heavy stone slabs into the ditch on the wall. I remembered that at the end of the 19th century, Flinder Petrie, an archaeologist who systematically surveyed the entire Kesha area, had a similar question about the second pyramid: "The basalt hanging door of the passage below shows that the builder moved the big one." We have seen that in a narrow space that can only accommodate a few people, the stones that need 40 to 60 people to move are accurately placed, which shows the superb handling skills of the builders at that time." It's what I don't understand about the hanging door of the Great Pyramid.And if there are flap doors, they should be able to be pushed up and down.

If the hanging door needs to go up and down, the door must be smaller than the width of the roof, so that the door can be raised at will to let people in, or closed to exclude unwelcome people before the tomb is closed.But this means that when the stone slab is lowered from above to block the entrance of the front hall, there will be a space at least as large as the door between the upper end of the hanging door and the roof, so that grave robbers can easily climb into it. . The hanging door adds another piece to the pyramid puzzle.Like the other puzzles, the portcullis is intricately constructed without any apparent purpose.

The exit from the vestibule, a tunnel as high and as wide as the entrance, and also paved with red granite, opened in the south wall (the wall itself was also granite, but the top was inlaid with a layer 12 inches thick. limestone).After walking about 9 feet forward, you enter the spacious palace.Upon entering the room, which is all paved with red granite, one can immediately see the unusual power and energy it exudes. hard rock like cream The longitudinal axis of the palace runs through the due east and due west of the Great Pyramid, while the horizontal axis faces due south and due north. The room is 19 feet 1 inch high, 34 feet 4 inches long and 17 feet 2 inches wide, forming a 2:1 ratio.A total of 15 granite slabs were used for the floor.The wall is made of 100 large stone blocks, each weighing at least 70 tons, with a total of 5 floors.There are 9 stone blocks on the roof, each weighing at least 50 tons.I walked to the very center of the room and felt a large number of huge stones, giving off a strong sense of oppression.

On the west side of the King's Hall is the sarcophagus of King Khufu that many ancient Egyptian scholars believe was the purpose of the construction of the entire Great Pyramid.This rectangular utensil with no cover on it is carved from dark chocolate-colored granite, which is full of hard particles such as feldspar, quartz, and mica.The interior of the sarcophagus measures 6 feet 6.6 inches long, 2 feet 10.42 inches deep, and 2 feet 2.81 inches wide; the exterior measures 7 feet 5.62 inches long, 3 feet 5.31 inches deep, and 3 feet 2.5 inches wide.Interestingly, the width of the sarcophagus is exactly 1 inch more than the lower exit of the room (the one that is currently blocked), and cannot be lifted from this exit to the uphill passage outside.

As usual, many mathematical puzzles can be found from this sarcophagus. For example, the inner volume of the sarcophagus is 1166.4 liters, which is exactly half of the outer volume of 2332.8 liters.This kind of exact "coincidence" should not be accidental.In addition, the hardness of the walls of the sarcophagus and the exquisite manufacturing technology required have surpassed the modern machine age, which shows that the ancient masonry should be very superb in terms of skill and experience.After a careful survey of the Great Pyramid, Flinder Petrie concluded, with some chagrin, that ancient masonry must have had tools "that have only recently been reinvented by us."

After careful measurements, Petrie found that the sarcophagus had to be cut from a large block of granite with a straight saw at least 8 feet long.Due to the very high hardness of granite, he could only assume that these saws should at least be made of steel (theoretically the hardest metal known at the time) as the blade, and set with "gems" at the "cut point": "From the characteristics of the work Looking at it, this gemstone should be a diamond. However, because diamonds are very rare and did not exist in Egypt at that time, we cannot jump to conclusions..."③

As for the engineering technique of hollowing out the interior of the sarcophagus, it is even more puzzling, because in terms of difficulty, this work is a step up from sawing the rock from the stone foundation.Petrie imagined the working situation of Egyptian workers at that time as follows: Instead of straight lines, they use circular saws.Set the processed stone blade into a cylindrical shape, gradually cut into the stone during pulling, and form an inner groove, then smash the stone in the groove and take it out, and gradually expand the hollow part inside.This is the most labor-saving way of working.Circular saw bits are available in diameters from 1/4 inch to 5 inches, and blades should be 1/30 to 1/5 inch thick. Of course, Petry also admitted that ancient Egyptologists have never found diamond-encrusted saws or drills.However, after carefully examining the sarcophagus, he found that the traces of using such tools were so obvious that he had to deduce that such things must exist.As a result, he became interested in the tools used in ancient Egypt, expanding the scope of his research from the sarcophagus of the king's palace to granite relics, and many of the "stones" he collected in the Gesha area that he identified as "stones" pulled out with a saw. core".However, the more he researched, the more he was fascinated by the hard stone cutting techniques of these ancestors: When cutting hard rock with a saw or drill from the top down, considerable pressure must be applied from above in order for the tool to cut into the stone.About every time a 4-inch drill is used to cut granite, at least 1 to 2 tons of gravity should be applied to it.No. 7 granite core, helical cut marks outside 6" circumference, about 1" deep, it takes a lot of force to make a cut that deep...to go deep into the granite quickly, to make a helical depression this deep hole, you have to apply tremendous pressure from the top of the saw... Isn't this a wonderful phenomenon? 4,500 years ago, when we thought that human civilization was just dawning, the ancient Egyptians already possessed the diamond technology that was only invented in the industrial period. Like a knife cutting hot butter, it can easily cut through hard rock. After Petrie developed the hypothesis that the ancient Egyptians had advanced tools, he was unable to use his hypothesis to explain the puzzles in the ancient Egyptian ruins.Although he found hieroglyphs on Fourth Dynasty diorite bowls in the Geza region, he could not provide a specific explanation for how those characters were carved into the diorite bowls: "The hieroglyphs on the plates must have been It was carved with tools with extremely sharp tips. Moreover, these characters were definitely not cut with a saw or the like, but cut into the stone surface with a knife blade..." Petrie, a theoretician, was troubled by his own observations.He knew that phenochlore is one of the hardest stones on the surface of the earth, but the ancient Egyptians had a way to carve patterns on it with incredible power, and the tools they used are still unknown to humans: The lines (on the disk) are only 1/350th of an inch wide, and apparently the tips of the cutting tools are not only harder than quartz, but also very durable, so as not to crumble and disintegrate while cutting.The tip of this cutting tool, no more than 1/200th of an inch wide, can carve such thin parallel lines that the distance between lines is only 1/30th of an inch from center to center. In other words, in Petrie's imagination, the Egyptians possessed a tool that was as sharp as a needle point and as hard as a diamond, which could easily cut into amorphochlore and withstand tremendous pressure during operation.What kind of tool would this be?How to pressurize from above?How to describe as thin parallel lines only 1/30 inch apart? As Petrie himself said, the drill saw used to make the sarcophagus can be more or less imagined as a round tool that looks like a drill and a saw, with diamonds set on the tips of the teeth.However, it is not so easy to imagine a carving knife used before 2500 BC to carve hieroglyphics.Especially if we don't admit that the technical ability of ancient Egypt is much higher than what scholars and experts believe, it is absolutely impossible to imagine how they completed those difficult works. Moreover, the high technical level of ancient Egypt is not only displayed in the above-mentioned hieroglyphs or morphochlore works, but also in the production of common handicrafts.During my several visits to Egypt, I saw many stone vessels carved out of large blocks of rock such as diochlorite, basalt, crystal rock, chrysanthemum rock, etc., and some were even completed in pre-dynastic times.How people did it at that time is really puzzling. And such utensils are found now, only in Saqqara, there are at least 30,000 in the lower room of the "Step Pyramid" of King Zesai of the third dynasty, which shows that those utensils can only be older than Zesai three years ( circa 2650 BC), would not have been younger than him.Theoretically, they could be older than Zeus, as identical vessels have been found in predynastic remains, at least as far back as 4000 BC.And we know that since ancient times in Egypt, there has been a tradition of passing on family treasures from generation to generation, so the age of these utensils may be older than 4000 BC. These exquisite handicrafts belonging to the "step pyramid" era, whether they were made in 2500 BC or 4000 years ago or more, we still can't imagine what kind of work they were made of. Why can't you imagine?Among the containers, for example, are many tall, thin-necked stone vases with hollow interiors and swollen shoulders.But so far, humans should not have invented any tools that can go deep into the neck after creating a slender and beautiful neck line, and create a rounded space inside the swollen shoulder line.We cannot imagine how much upward and outward pressure must be exerted on the inside of the vase to create this effect. There are countless mysterious vessels unearthed from the Pyramid of Zeuse and other monuments: there are exquisitely crafted vases with handles carved out of a single piece of stone; There are also glassware that seem to have to be completed with a microscope; there are also wonderful wheel-shaped objects made of rock flakes, curved inward from both ends, and the edges are as thin as paper.The most astonishing thing is that these stone utensils are exquisite and delicate both in appearance and interior. The successive curves perfectly match each other, and the surface is extremely smooth, and there is no trace of any props used at all. Not only can these utensils not be replicated at the level of ancient Egyptian craftsmanship known today, but even with the most advanced tungsten carbide tools, it is impossible to make such high-level works of art.In other words, we have to infer that ancient Egypt possessed secret technologies that we still don't know about. Lying in a thousand-year-old sarcophagus I stood in the king's hall, facing west—that is, the direction that was considered death by both ancient Egyptian and Mayan civilizations.I placed my hands lightly on the edge of the sarcophagus that almost all Egyptologists believed Khufu's body had slept in, and peered into the dark base of the coffin.The electric light in the room was dim, unable to reach the bottom of the coffin, only the dust floating inside the coffin like golden clouds. I know that clouds are but illusions of light and shadow.The palace of the king is full of similar visions.Napoleon spent a night alone in this room when he conquered Egypt in the late 18th century.The next morning he came out of the room trembling and pale, evidently bewildered by what had happened to him.But all his life, he never said what happened. Did he try to sleep in a sarcophagus? On a sudden impulse, I also climbed into the sarcophagus and lay on my back, with my head facing north and my feet facing south. Napoleon was a small man, and he should be able to lie down quite comfortably.But is Khufu just as comfortable lying down? I relax, try not to think about what to do if the pyramid guards burst in and find me in this embarrassing and possibly illegal position, and hope for a few minutes of peace.I put my hands on my chest and let out a low voice.In other places in the Palace of Kings, I have also tried to make similar speakers, and found that the walls and ceilings seem to not only collect the sound, but also amplify the sound and project it back to the direction of the sound, allowing me to hear from my feet and head. Vibrate on the shell and skin, feel the echo effect. When I lay in the sarcophagus and made a sound, I not only felt the same effect, but also the vibration of the echo was much, many times stronger and more concentrated than when I tried it in other corners of the room, as if entering a loudspeaker designed to reflect only one sound. The speaker is average and feels very strong.I imagined sound waves starting from the coffin, bouncing off the red marble walls and the roof, and shooting out from the north and south ventilation shafts, like a mushroom cloud of sound, covering the Kesha Plateau. I closed my eyes, let the sound waves vibrate the sarcophagus and my body, and felt my wild dream quietly.A few minutes later, I opened my eyes, and what I saw was a very disappointing scene: six Japanese male and female tourists of various ages, two standing on the east side of the sarcophagus, two on the west side, and the north and the south respectively. One, surround me.I can see the surprise in their hearts from their facial expressions; and I was also surprised to see them, because the Islamic extremists were very active at that time, and almost drove away all the tourists in Kisha. I thought the palace except me Otherwise, no one will come to visit. What should I do in this situation? Putting on a dignified and dignified look, I stood up, smiled slightly at the surroundings, and waved off the dust on my body.The Japanese tourists gave way, and I pretended that this kind of thing is common and not worth making a fuss about, walked out of the crowd indifferently, walked to a place 2/3 away from the north wall of the palace, and began to carefully observe the ancient Egyptology. Home called the "North Vent". I knew at first that the ventilation hole was 8 inches wide, 10 inches high, and more than 200 feet long, leading to the outdoors via the 103rd stone step of the pyramid.The air hole directly points to the sky in the northern hemisphere at an elevation angle of 32 degrees 30 minutes. Around 2500 BC in the pyramid era, the air hole just faced the main star of the constellation of Draco in the sky.All this should not be a coincidence, but the result of exquisite design. To my great gratitude, the Japanese tourists left quickly after visiting the palace without even looking back at me.After they left, I turned around to the other side of the palace to observe the Nantong air hole.The air vent has changed a lot in appearance since I visited it a few months ago, as a massive air conditioning system was recently installed behind it.And Rudolf Gandenberg, who installed the air conditioner, was inspecting the vents of the forgotten Queen's Hall at the same time as I visited the King's Hall. Since ancient Egyptologists agreed that the purpose of vent holes was ventilation, in their view, there is nothing wrong with installing an air-conditioning device and using modern technology to improve ventilation efficiency.However, if it is really for ventilation, why was the tunnel built with a slope at that time?In theory, horizontal aisles are more efficient in ventilation than ramps.It is no coincidence that the south air hole of the Wangdian directly guides the sky at a 45-degree angle.In the era of the pyramids, that direction was facing the lowest star of the three stars in the constellation of Orion (Zeta).It was only later that I gradually understood that the arrangement of Orion's three stars plays a very important role in the study of pyramids. master craftsman playing with boulders I, who was alone in the king's hall, walked from the south wall to the west wall, looking east from the back of the sarcophagus. In this huge room, countless mathematical puzzles are hidden. For example, the height of the room (19 feet 1 inch) is exactly half of the diagonal of the floor (38 feet 2 inches); the structure of the palace is rectangular, and the aspect ratio is 1:2 is the so-called "golden section" ratio invented by the Greeks. It is impossible for the builders of the pyramids to know this. The golden ratio is also known as φ, which is the square root of 5 plus 1 and then divided by 2; like π of pi, it is an irrational number that cannot be exhausted by arithmetic, approximately equal to 1.61803.This is "the limit value of adjacent two values ​​​​in the Fibonacci sequence of 0, 1, 1, 2, 3, 5, 8, 13... - the characteristic of the Fibonacci sequence is Before dynastic history began, the Egyptians mysteriously inherited a system of measurements from unknown ancestors.According to ancient measurements; the floor of the palace (34 feet 4 inches by 17 feet 2 inches) is 20 by 10 cubits, while the height of the side walls is 11.18 cubits.The length of half AB of the diagonal length of the ground is also exactly 11.18 cubits.That is to say, if AB is vertical, it becomes the height C of the room. The value of φ is (√5+1)÷2=1.618. The distance of CD (the height of the wall of the palace plus half of the floor banner) is exactly 16.18 cubits. Is it also purely accidental? "Each number is equal to the sum of the previous two numbers". In addition, the value of φ can also be expressed graphically.Divide the straight line AB before the point C, so that the ratio of the length of the whole straight line AB divided by the longer half AC is exactly equal to the ratio of AC divided by CB.This ratio has been proven to be the most harmonious seen by the human eye and is said to have been discovered by the Greek Pythagoreans and applied to the Parthenon in Athens.However, there is absolutely no doubt that φ was present in the King's Hall of the Great Pyramid at Giza 2,000 years before the temple was built here. To understand this, we must first imagine the rectangular floor of the palace as a composite of two squares of equal size, each side of which has a length of 1; if the two squares are divided into two rectangles, and if the The diagonal of the rectangle close to the central line of the palace is rotated to the upper side of the bottom, and the point where its top touches the bottom is φ, which is 1.618 times the side length of the original square. (Another way to get the φ value built in the palace of the king, please refer to the picture below) Ancient Egyptologists attributed it all to chance.However, as far as the pyramid builders were concerned, nothing was accidental.Regardless of who these ancestors were, they must have been the most mathematically minded and systematically thinking group of people. With my head full of arithmetic games, I left the palace, but I still couldn't forget that the location of the palace happened to be on the 50th stone step, 150 feet above the ground, waiting for numbers.I remember that Flinder Petrie once pointed out with great amazement that the builders of the pyramids placed the king's palace in the very center, whether vertical or horizontal. Looking at the horizontal section, the floor area is exactly half of the entire horizontal section, and the diagonal length of the room is exactly the length of the foundation, and the width of the side is equal to half of the diagonal of the foundation. The builders of the pyramid confidently and efficiently played with the 6 million tons of boulders in the palm of their hands, arbitrarily created nearly perfect symmetrical corridors, corridors, rooms, air holes, and passages, not only maintaining each corner at a right angle, but also maintaining the orientation Correct, never out of order.In addition, the builders of the Great Pyramid, in particular, had the luxury to put many small math games on the huge building. Why did the ancient Egyptians build such a building full of puzzles?What are they trying to say or do?And why, thousands of years after its construction, it still captures the hearts of many people from all walks of life and comes to contact it? The Sphinx is nearby.I decided to take a stroll there, maybe it would give some light to the puzzle. note ①Petree's "The Pyramids and Temples of Giza", p. 25. W． M． Flinders Petrie, The Pyramids and Temples of Cizeh (New and Revised Edition), Histones and Mysterics of Man Ltd., London, 1990. p. 25． ② Edwards's "Egyptian Pyramids", pp. 94-95. Edwards, I. E． S, The Pyra mids of Egypt, Penguin, London, 1949. ③ "The Pyramids and Temples of Giza", p. 74. ④ "Pyramid: Mystery Unveiled", page 118. Dr． Joseph Davidovits and Margie Moruis, The Pyramids: An Eigma Solved, Dorset Press, New York, 1988. ⑤ "Egypt: Land of the Pharaohs". 51 pages. Egypt: Land of the Pharaohs, Time-Life Books, 1992, p. 51． ⑥ Rob Boufar, "Discussion of Egyptology", No. 29. Robert Bauval, Discussions in Egyptology No. 29, 1994. ⑦ "The Great Pyramid: A Personal Guidebook", 64 pages. Peter Lemesurier, The Great Pyramids: Your Personal Guide, Element Books, Shaftesbury, 1987.