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Petr Krylov Methods of Analogies
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The best-known examples:
Stonehenge, England (c. 3000–2000 BCE). This ring of massive stones is aligned with the sunrise on the summer solstice. Some researchers believe the complex was used to predict lunar eclipses.
The Pyramids of Giza, Egypt (c. 2560 BCE). The Great Pyramid is aligned with the cardinal directions to within one-twentieth of a degree. The shafts inside the pyramid point toward specific stars—for example, the shaft from the King’s Chamber is aligned with Orion’s Belt, which was identified with Osiris.
The Temple of Amun-Ra at Karnak, Egypt. The temple’s axis is aligned with the sunrise on the winter solstice. On that day, a ray of sunlight would pass through the entire temple and illuminate the sanctuary. In ancient times, this moment marked the beginning of the New Year.
Chichen Itza, Mexico (ca. 600–900 CE). The Pyramid of Kukulkan was built so that on the equinoxes, the shadow cast by its steps creates the effect of a slithering snake.
Newgrange, Ireland (ca. 3200 BCE—older than the pyramids!). On the winter solstice, a ray of sunlight slips through a narrow opening and lights up the inner chamber for exactly 17 minutes.
The precision of these structures is astonishing. The Pyramids of Giza are aligned with the cardinal directions to within less than 0.1°. Stonehenge marks the solstices with an accuracy of a few arcminutes. That would have required decades of observation and a sophisticated grasp of geometry.
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6.4 Precession and the Magnetic Pole — A Key to Dating
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This is where things start to get really interesting.
The Earth is not a perfect sphere, and its axis not only rotates slowly but also wobbles like a spinning top. This phenomenon is called precession. A full cycle through the zodiac takes about 26,000 years. Because of precession, the points of the equinoxes and solstices slowly shift through the zodiac, and Polaris has not always been the North Star.
What is more, the Earth's magnetic poles also drift across the globe—more erratically than the geographic poles.
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For archaeoastronomy, axial and magnetic precession provide a unique tool.
If a temple is aligned with the rising of a particular star or with the point of the solstice, modern calculations can determine exactly when that alignment was precise. In other words, the stone itself can tell us when it was set in place.
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Examples:
The Temple of Amun-Ra at Karnak. If its axis is aligned with sunrise on the winter solstice, the calculations yield a date of around 2000–2500 BC—which matches the archaeological evidence.
Stonehenge. Its alignment with the summer-solstice sunrise points to a date around 2000 BCE (based on the main construction period).
Some Egyptian temples aligned with the star Sothis (Sirius) allow dates to be pinned down to particular years with an accuracy of within a decade.
But there are mysteries too. Some megalithic structures (for example, Göbekli Tepe in Turkey, 10,000 BCE) display alignments that researchers still cannot interpret with certainty.
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Apparently, this is tied to the periodic reversal of Earth’s magnetic poles and, accordingly, to the planet’s “somersaulting,” with all the consequences that entails. Known in the Bible as the “Great Flood.”
With a cycle that is a multiple of the precessional period of the zodiacal star circle.
That is, every ~25,776 or ~12,888 years.
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6.5 Provocative Questions
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Once you start doing the math, questions arise that official history has no simple answers for.
Question one: weight and transport.
The Great Pyramid is built of blocks weighing anywhere from 2 to 80 tons. The total weight is about 6 million tons. How were they transported and hoisted into place with millimeter precision, so that the joints between the blocks were no more than 0.5 mm?
Question two: precision of alignment.
The pyramids’ margin of error in alignment with the cardinal points is less than 0.1°. That would require either prolonged astronomical observation or knowledge of geodesy—a science that, according to the textbooks, would not appear until millennia later.
Question Three: the starry sky.
The shafts in the Pyramid of Khufu are aligned with Orion’s Belt to the south and Alpha Draconis to the north. But because of precession, those alignments were exact only in a specific era. The calculations point to around 2500 BC—which corresponds to the time of construction. But who calculated those angles—and how? Why was such precision necessary if the shafts were sealed and never used for observation?
Question Four: knowledge that doesn’t fit the historical narrative.
The builders knew the length of the year to within a few minutes. They knew the period of precession—a fact not rediscovered until the 19th century. They knew that the Earth was spherical (Plato was already writing about this—but who taught the Egyptians?). They knew the mathematics needed to calculate angles to within arcseconds.
How?
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6.6 What We Know for Certain
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You can argue about paleocontact theories, Atlanteans, and aliens. But facts are still facts:
Across the world stand stone observatories built thousands of years ago.
They are aligned with the heavens to a precision that would seem to require advanced mathematics and generations of observation.
They worked like analog computers, enabling priests to determine the year's crucial dates with remarkable accuracy.
They fused religion, power, and economic life into a single system.
Some of them still have not been fully deciphered.
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6.7 Book Conclusion
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Cosmic projection is a method in which architecture becomes a tool for understanding the sky. Human beings do not merely look up at the stars. They build a stone model of the celestial mechanism, so they can make themselves part of its workings. The pyramid is not a tomb, but a clock. The temple is not a place of prayer, but a receiver for signals from the heavens.
And the method worked. It delivered a calendar, predictability, power. And in the process, it left us riddles we still cannot solve.
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6.8 Moving to the Next Chapter
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If the pyramids modeled the sky outside us, the next model was found within the human being. How the microcosm is put together—and why blood flows by the same law as rivers—in the next chapter.
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Chapter 7. Mechanical analogy: the Antikythera mechanism, a model of the heavens built with gears.
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“For every person on earth there is a place unknown to them, though it can be seen in dreams.
If a person finds it, one way or another, and settles there, they will be happy for the rest of their days.”
Oleg Kuvaev, A Home for Wanderers
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7.1 Numbers That Make Your Head Spin
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Modern astronomical observations establish the following points:
The astronomical solar year—not the calendar year, but the actual one—is 365.242199 days.
The astronomical lunar month is 29.530589 days.
Mars takes 686.98 days to orbit the Sun, Jupiter 4,332.59, and Saturn 10,759.22.
Six decimal places is a level of precision that astronomers could achieve only in the 17th and 18th centuries, with the advent of telescopes and accurate clocks. But Babylonian priests already knew the length of the year in the 2nd millennium BCE, with an error of less than a minute. And in the 1st millennium CE, the Maya calculated the synodic period of Venus with an accuracy of 0.01 days.
A simple calendar—for example, 365 days with no leap years—very quickly drifts out of sync with reality. Over 100 years, the error adds up to almost a month. That is why every advanced civilization developed its own system of adjustments.
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7.2 Calendars Humanity Has Used
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The Egyptian calendar (from the 28th century BCE) — 365 days: 12 months of 30 days each, plus five extra days. The error was about 0.25 days per year. Without correction, it drifted against the seasons by one day every four years, completing a full cycle in 1,460 years (the so-called Sothic cycle).
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The Babylonian calendar (from the 18th century BCE) was lunisolar: 12 lunar months, with a 13th month added from time to time. Its precision in tracking the sun was achieved through observation. The length of the year was known to within just a few minutes.
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The Chinese calendar, known since the 14th century BCE, was also lunisolar, with leap months. By the Han era, in the 2nd century BCE, its accuracy was about 365.25 days.
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The Maya calendar, in its Classic Period (3rd–9th centuries CE), was a complex system of several cycles. The haab year had 365 days; the tzolkin, 260. They knew that the true year was slightly longer, and they made adjustments.
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The Julian calendar (45 BC) – 365.25 days, with a leap year every 4 years. With an error of 0.0078 days a year, it had drifted by 10 days by the 16th century, leading to the Gregorian reform.
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The Gregorian calendar (1582) – 365.2425 days, accurate to 0.0003 days a year (one day in 3,300 years). It is still in use today.
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But the most remarkable example is the calendar created in the 11th century by the poet, mathematician, and astronomer Omar Khayyam.
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In 1079, by order of the Seljuk sultan Malik-Shah, Khayyam was appointed to head a commission of Isfahan’s finest astronomers. Their task was to anchor the start of the year, Nowruz, to the spring equinox once and for all.
Khayyam proposed a cycle known as the Jalali calendar, or the Malik-Shah reckoning. Instead of the Julian rule of 1 leap year every 4 years or the Gregorian rule of 97 in 400, he used a ratio of 8 leap years in 33. It’s a stroke of calendrical genius: the 4th, 8th, 12th, 16th, 20th, 24th, 28th, and 33rd years of the cycle are leap years.
And now for the raw numbers:
Length of the year according to Khayyam: 365.24242 days.
Actual tropical year: 365.24219 days.
Error: a mere 0.00023 days (about 19.5 seconds)!
That means the error would add up to a single day only after 4,500–5,000 years. The Gregorian calendar we use today drifts by a full day every 3,300 years. Khayyam’s calendar is one and a half times more accurate than the Gregorian one.
And most crushing of all: this calendar is still the official one in Iran and Afghanistan. A thousand years ago, one man created a system for measuring time that we still have not managed to surpass. When you celebrate Nowruz on March 21, you are relying on the invention of a man who wrote rubaiyat about wine and clay jars.
Omar Khayyam went and made a better calendar than the Pope—half a millennium earlier. And while medieval Europe prayed and burned witches, Khayyam already knew the length of the year to within 20 seconds.
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Every system was a compromise between simplicity and accuracy. But predicting the positions of the planets takes more than simply counting days — it requires constant observation and calculation.
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7.3 The astrologer’s tasks that no one wanted to do by hand
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In ancient times, astrology was not a matter of reading coffee grounds, but a rigorous mathematical discipline. An astrologer had to:
– Calculate the exact positions of the Sun, the Moon, and the five planets at the moment of the client’s birth (taking into account their non-uniform motion).
– Determine the rising sign (ascendant) – this requires knowing the exact time of birth and the geographical coordinates.
– Calculate the mutual aspects of the planets (angles of 0°, 60°, 90°, 120°, 180°) and their placement in the houses of the horoscope.
– Compare this with the planets’ current positions in order to produce an all-encompassing metaphysical forecast.
To answer a specific question—for example, about marriage or travel—it was sometimes necessary to cast several horoscopes.
Working by hand with tables (ephemerides) and trigonometric formulas took a trained specialist several hours. If the client was an emperor or a grandee, it was hardly proper to keep him waiting until evening. What was needed was a tool that could deliver a result in minutes.
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7.4 The Antikythera Mechanism—the first analog computer
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In 1901, near the Greek island of Antikythera, divers recovered from a sunken ship a shapeless lump of bronze covered in calcareous encrustations. A year later it split open, revealing bronze gears inside—a remarkably intricate system of gear trains embedded in petrified wood.
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It took half a century to prove that the mechanism dates from around 150–100 BC and is an analog computer for astronomical calculations. It contained no fewer than 37 gears, including a differential mechanism (until then, the differential was thought to have been invented only in the 19th century).
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Turning the handle on the front panel set disks in motion that showed the positions of the Sun, the Moon, the five planets then known, the phases of the Moon, the dates of the Olympic Games, and eclipse predictions based on the 223-month Saros cycle. The mechanism modeled the Moon’s uneven motion by means of an elliptical gear system—something European science would not manage to replicate until the seventeenth century.
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It was a genuine portable calculator. With an instrument like this, a priest or astrologer could obtain in a few turns of the handle data that had once taken hours to work out.
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7.5 Higher Astrology — the Horoscope of Place and Interference Waves
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True astrology was never confined to a simple birth horoscope. Location also mattered: the same sky chart, projected onto different points on Earth, produces different houses and a different ascendant. Hence the idea of a horoscope of place — the natal chart combined with the coordinates of where one lives.
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In the Hermetic tradition, there was also the concept of interference waves: the interplay between the rhythms of birth and the rhythms of place creates a unique pattern, like the interference of waves on water. Hence the maxim, attributed now to Cicero, now to Arab astrologers, now to Hermes himself: “Every person has a city on earth where they can be happy.” To find such a city is to come into resonance with your own star chart.
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Working this out required not only knowing the positions of the planets, but also being able to recalculate the house coordinates for any location at speed. Without a mechanical aid, the task was virtually impossible to solve in real time.
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7.6 Underestimating the Ancients
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When scientists first reconstructed the Antikythera mechanism, they were stunned. Nothing comparable was created in Europe until the 14th and 15th centuries, with the advent of the first astronomical clocks. Medieval science never attained that level of mechanics and mathematics.
The achievements of Hellenistic science (3rd–1st centuries BC) proved superior to anything seen in the first thousand years of the Christian era. It took the Renaissance to rediscover what the ancient Greeks had already known.
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The conclusion is hard to escape: modern civilization stands on the ruins of the one before it. We are used to thinking of progress as a steady upward climb, but history is full of collapses. The Antikythera mechanism is not the exception, but the rule. It shows that the brilliance of Hellenism was followed by centuries of oblivion.
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And if we take pride in our computers today, it is worth remembering that the first computers were analog, made of bronze, and turned by hand. And they did what modern digital machines do in nanoseconds—yet in those days it was nothing short of a miracle.
A precision no one has been able to reproduce
The point is not merely that the Greeks could cut bronze with extraordinary precision.
It is that they knew which numbers to cut.
Behind every gear tooth in the Antikythera mechanism stands a mathematical model of the cosmos, encoded in the tooth counts. Researchers have decoded these numbers: 19 (the Metonic cycle), 235 (lunar months in a 19-year cycle), 223 (the Saros, an eclipse cycle), 127 (half the number of sidereal months), 365 (days in the Egyptian calendar).
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Each of these numbers is no accident, but a coefficient in a system of equations describing the motion of the heavenly bodies. They made it possible to convert solar years into lunar months, predict eclipses to the very day, and synchronize the calendar with astronomical cycles. A dedicated study showed that the mechanism modeled changes in the Moon's angular velocity with an error of less than 0.5%. That is more accurate than Hipparchus's version of the theory as presented by Ptolemy (2nd century CE).
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Researchers emphasize that the mechanism encodes cycles of 462 years for Venus and 442 years for Saturn. Classical Babylonian astronomy tells us nothing about how the Greeks managed to determine these highly precise cycles.
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Why Europe Failed to Create an Equivalent
In the Christian era, no such mechanism was created, because the system of equations on which it depended had vanished; without it, the whole device is nothing more than a beautiful toy.
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Researchers working on the Antikythera Mechanism state plainly: “There is no evidence of mechanisms of comparable complexity until the fourteenth century, when mechanical astronomical clocks appeared in Western Europe.” François Charette writes in Nature that “the astonishing technological sophistication achieved in the Hellenistic and Greco-Roman world was simply not passed on. Gear systems had to be invented all over again.”
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Although the medieval Islamic world did produce descriptions of mechanical calendars—for example, al-Biruni’s “Moon Box” around the year 1000—they were far simpler. An Arabic astrolabe from 1221–1222 used only seven gears to model the movements of the Sun and Moon.
There are several reasons:
The mathematical foundation vanished—the need to recalculate disparate astronomical parameters gave way to a theological view of the world.
The tradition of observation was lost—the Babylonian tables were unknown in medieval Europe.
The paradigm shifted: the world became God's creation, not a mechanism for calculation.
Knowledge remained closed off—craft secrets were passed down within narrow circles of masters and died with them; there was no system of patents or publications.
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One question remains: could the mechanism have worked?
In 2025, Argentine physicists published a study modeling the mechanism on a computer. They suggested that because of the uneven spacing between the gear teeth, the mechanism may have jammed. But the authors themselves admit: either the mechanism never worked, or the margins of error assumed in the calculations do not reflect reality. The scientists emphasize: “It is unlikely that anyone would have built such a complex device that did not work.”
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Moreover, after 2,000 years underwater, the bronze had turned into a brittle mineral that cracked and changed shape after recovery. Using it as a yardstick is like judging a clock’s accuracy by its mangled dial.
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Conclusion: the Antikythera mechanism is not merely an “ancient computer,” but proof that the Greeks possessed mathematical knowledge that Christian Europe would recover only fifteen hundred years later—and then in a different form. And the issue is not the precision of the metalwork, but the system of equations built into the teeth. Without it, all the gears in the world are just a heap of bronze.
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7.7 Moving on to the Next Chapter
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The mechanics of the heavens were mapped onto gears. But there was another projection as well—into the human being. How the four bodily fluids were likened to the four elements of the world, and why a physician also had to be an astrologer—in the next chapter.
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Chapter 8. The Hermetic analogy—'As above, so below': the principle that all levels mirror one another.
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Venus is the only planet in the Solar System that rotates in the opposite direction from all the others.
Because Venus is a strong, independent woman!
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8.1 Universal Law
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In 1912, three occultists who wished to remain anonymous and called themselves “The Three Initiates” published a book titled “The Kybalion.” In it, they were the first to systematize a teaching that until then had been passed down only orally—from teacher to student, from initiate to initiate. They called them the Seven Hermetic Principles. In fact, they were quoting the laws of the Emerald Tablet of Hermes, albeit in a somewhat altered form.
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In essence, they popularized and systematized the fundamental methods of analogy—methods that until then had remained a secret of the Hermetic Tradition.
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The second of these principles states, as the Tablet puts it:
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What is Above arises from what is Below, and what is Below arises from what is Above,
And thus works wonders through the One. For all things come from a single Source.
…».
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At first glance, a simple phrase. In reality, the key to understanding the whole structure of the cosmos.
This principle holds that there is always a correspondence between laws and phenomena on different planes of being and life. What occurs in the Macrocosm (the universe) is echoed on the middle plane (the human being) and in the Microcosm, and vice versa. The laws of physics find their echo in the laws of the psyche. The structure of the atom mirrors the structure of the solar system. The principles of governing a state are analogous to those that govern an anthill.
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