Mysterious celestial objects visible in the sky have always fascinated and inspired humanity. Even today, in this age of super rationality and high tech, in spite of its evident groundlessness, astrology seems to preoccupy many average people, who strongly believe in the supernatural influence of the planetary movements on human lives. Since ancient times, the sky has been believed to be a gate to the Heavens. The changing positions of the planets, the moon and the sun were seen as expressions of a divine power influencing human existence on Earth. Great importance was attributed to all celestial phenomena, in particular to horoscopes. Regardless of all the imaginary significance attributed to horoscopes, we should remember that they are also a record of dates written by means of a cosmic calendar. Today, we can decode ancient horoscopes and, using mathematical computations, discover the dates that were commemorated.

But what exactly is a horoscope? When we look at the sky at night, we get the impression the Earth is surrounded by an enormous sphere filled with stars. Although this celestial sphere seems to be revolving slowly around us (an illusion caused by the daily revolution of the Earth), all the stars always appear in the same configurations (called constellations), at the same fixed positions on the celestial sphere. However, there are also other celestial objects, which seem to be "traveling" across the celestial sphere. The moon is one of them, but there are also five planets that can be observed with the naked eye. These planets are Jupiter, Saturn, Mars, Venus, and Mercury. Of course, although invisible at night, the sun is also moving across the sky.

The planets, including the moon and sun, were in old times called traveling stars, but today we simply call them the seven planets of antiquity. It appears to an Earth-based observer that in the course of one year, the sun completes a full revolution around a large circle on the celestial sphere. This circle is called the ecliptic. The planets and the moon are always found on the sky within a narrow belt, 18o wide, centered on the ecliptic, called the zodiac. The area around it is called the zodiacal belt. The zodiacal belt is a celestial highway where the movement of all the planets, the sun and the moon takes place when observed from the Earth. Twelve zodiac constellations are placed along the ecliptic traveling the zodiac belt. Their familiar names are Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, and Pisces. Each of the 12 zodiac constellations is located in a sector 30o long, on average (see Figure 1).

The key concept in astrology is a horoscope, which is a chart showing the positions of the planets in the sky with respect to the zodiac constellations. In ancient times, people attributed great importance to these planetary positions and unknowingly encoded in horoscopes the exact dates related to astronomical events. 

Celestial sphere with the solar system inside. For an Earth-based observer the planets, the sun and the moon appear on the zodiacal belt. Their positions are changing continuously.

An astronomical situation shown in a horoscope is quite unique. At any time, there are 12 possible zodiac constellations where each of the seven "planets" may appear (see Figure 1). The positions of the moon, the sun, Mars, Jupiter, and Saturn are independent of each other. However, due to the inner orbits with respect to the Earth's orbit, the visual angle distance from Mercury to the sun cannot be larger than 28o, and the angle distance from Venus to the sun must be smaller than 48o. This means that for each fixed position of the sun in the zodiac, there are only three possible positions for Mercury and five possible positions for Venus. It is not difficult to compute that there are exactly
12 12 12 12 12 3 5 = 3 732 480

different horoscopes. Since an average horoscope remains in the sky for about 24 hours, there are about 365 different horoscopes every year. Therefore, a specific horoscope should reappear only after 10 000 years, on average. However, in reality, a horoscope may reappear more often. The existence of so-called false periods has been observed by researchers.1 It appears that two or three repetitions of the same horoscope are possible in a period of about 2 600 years, but later such a horoscope disappears for many dozens of thousands of years.

With the use of modern computational methods, it is possible to calculate all of the dates that could correspond to such a horoscope. If other astronomical information is also available from the horoscope (such as the order of the planets or their visibility), it is often possible to eliminate all the dates except one, which is exactly the date of the horoscope. In this way, mathematics can be a very powerful tool in revealing the mysteries of the ancient world. 1 See [5], Vol.6.

There are many ancient representations of zodiacs containing symbolic representations of horoscopes. In particular, some Egyptian zodiacs, which use specific ancient symbols to illustrate astronomical objects, can be analyzed. It is difficult to disagree that this is an exciting idea which could lead us to the exact dates which correspond to ancient Egyptian history! Let me include some examples of Egyptian zodiacs. All of these zodiacs are discussed in detail in an upcoming book entirely devoted to the astronomical dating of the ancient Egyptian zodiacs.2 Figure 2 shows an Egyptian zodiac found on the ceiling in an ancient Egyptian temple in Denderah. It is called the Round Denderah zodiac.

A drawing of the Round Denderah zodiac made during the Napoleonic expedition to Egypt in 1799.3

A second zodiac found in the same temple in Denderah is called the Long Denderah zodiac (see Figure 3).

A drawing of another Egyptian zodiac is shown in Figure 4. This zodiac was found in the main hall of a huge temple in the ancient city of Esna, located on a bank of the river Nile. We will call it the Big Esna zodiac.

In the same city of Esna, another zodiac was found by the Napoleonic army in a much smaller temple (see Figure 5). We will call it the Small Esna zodiac, but this name has nothing to do with the size of the zodiac itself.

There are many more Egyptian zodiacs containing horoscopes, but it is not possible to discuss them all in such a short article. 4

2 See [1].
3 Picture taken from [2], A. Vol. IV, Plate 21.
4 For example, there are many zodiacs found inside ancient Egyptian tombs. Read more about it in [1].
5 Picture taken from [2]. Annotations were made by A.T. Fomenko, T.N. Fomenko, W.Z. Krawcewicz, and G.V. Nosovskij (taken from [1]).

A drawing of the Long Denderah zodiac from the temple in Denderah in Egypt.5 Colour annotations were added to indicate constellations (red), planets (yellow), and other astronomical symbols (blue or green).

The Big Esna zodiac.6 The zodiac constellations are marked in red, the planets in yellow, and the other astronomical symbols in blue and green.

Drawing taken from the Napoleonic Album7 of the Small Esna zodiac.

Egyptian zodiacs should be seen as symbolic representations of astronomical objects inside the zodiacal belt. The actual decoding of the astronomical symbolism of such a zodiac is rather complicated. In Figure 6, we show a drawing of the Round Denderah zodiac taken from the book [1], where it is carefully analyzed and decoded.

6 Picture taken from [2], A. Vol. I, Plate 79. Colour annotations were done by A.T. Fomenko, T.N. Fomenko, W.Z. Krawcewicz, and G.V. Nosovskij (taken from [1]). 7 Picture taken from [2], A. Vol. I, Plate 87. 8 See [1].

Decoded astronomical meaning of the Round Denderah zodiac. The zodiac constellations are marked in red, the planets in yellow, and the other astronomical symbols in blue and green.

In this representation, colours are used to distinguish figures of different astronomical meaning. The red figures are the zodiac constellations, which can be easily recognized because their appearance has remained largely unchanged to present times. The yellow figures are the planets. Some are marked by hieroglyphic inscriptions, but it is generally not an easy task to determine exactly which planets are represented by these symbols.

The blue and green figures represent other astronomical symbols. The blue colour indicates the astronomical meaning of the figure was successfully decoded, and the green colour indicates the meaning of the figure was not completely understood.

The final decoding was achieved through a complicated elimination process,8 in which all possible variants were considered. For each of the dates obtained, all of the available astronomical data was carefully verified, and only solutions satisfying all of the required conditions were considered.

It was found that the figures shown on this zodiac indicate that: the moon was in Libra; Saturn was in either Virgo or Leo; Mars was in Capricorn; Jupiter was in either Cancer or Leo; Venus was in Aries; and Mercury and the sun were in Pisces.

Dating of this zodiac was done using the astronomical software HOROS, which was developed by Russian mathematician G.V. Nosovskij, based on an algorithm used by the French astronomers J.L. Simon, P. Bretagon, J. Chapront, M. Chapront, G. Francou, and J. Laskar, in an astronomical program calledPLANETAP.9 This software, together with sample input .les and brief instructions, is available at the p in the Sky web site at:

http://www.pims.math.ca/pi/.

The results presented in [1] are most intriguing. The dates obtained were as follows:

Of course, these dates completely contradict the chronology of ancient Egypt and create a controversy regarding the age of the ancient Egyptian monuments. But still, the results stand for themselves. Clearly more research is needed before .nal conclusions can be drawn.

REFERENCES:

If you have any comment, remark or question related to this article, or you would like to share your opinion, send your email directly to Wieslaw Krawcewicz at [email protected].

A statistics professor plans to travel to a conference by airplane. When he passes the security check, a bomb is discovered in his carry-on baggage. Of course, he is hauled o. immediately for interrogation.

"I don't understand it!" the interrogating officer exclaims.
"You're an accomplished professional, a caring family man, a pillar of your parish - and now you want to destroy all that by blowing up an airplane!"
"Sorry," the professor interrupts him. "I had never intended to blow up the plane."
"So, for what reason did you try to bring a bomb on board?!"
"Let me explain. Statistics show that the probability of a bomb being on an airplane is 1/1 000. That's quite high if you think
about it - so high that I wouldn't have any peace of mind on a flight."
"And what does this have to do with you bringing a bomb on board?"
"You see, since the probability of one bomb being on my plane is 1/1 000, the chance that there are two bombs is 1/1000000. So, if I already bring one, I am much safer. . . "

9 See [4].

A physics professor conducting experiments has worked out a set of equations which seem to explain his data. Nevertheless, he is unsure if his equations are really correct and therefore asks a colleague from the math department to check them.
A week later, the math professor calls him: "I'm sorry, but your equations are complete nonsense."
The physics professor is, of course, disappointed. Strangely, however, his incorrect equations turn out to be surprisingly accurate in predicting the results of further experiments. So, he asks the mathematician if he was sure about the equations being completely wrong.
"Well," the mathematician replies, "they are not actually complete nonsense. But the only case in which they are true is the trivial one in which the time variable is supposed to be a nonnegative real number. ."

A physicist, a mathematician, and a computer scientist discuss which is better: a wife or a girlfriend.
The physicist: "A girlfriend. You still have freedom to experiment."
The mathematician: "A wife. You have security."
The computer scientist: "Both. When I'm not with my wife, she thinks I'm with my girlfriend. When I'm not with my girlfriend, it's vice versa. And I can be with my computer without anyone disturbing me. . . "