Berlin · 2014  Uwe Topper

Whenever classical buildings or documents contain astronomical indications it is agreed to date their corresponding age reliably. There are mainly three ways to do so:

1. A common method consists in relying on the inclination of the earth relative to its orbital plain, i.e. using the value of the angle epsilon. This value is diminishing steadily at the moment. The corresponding value contained explicitly or indirectly in proto-historic or historic architecture can give a clue to their age. The bigger the value of epsilon the older the object. Since the 18th century some of the best astronomers of Europe tried to establish the exact formula of the relation between epsilon and time using observations of the last decades and thus projecting overall values for bygone centuries. Around 1800 this effort was successful, the rate of change of epsilon was determined and had only minimally been refined later on. Different dates of epsilon handed down historically were not taken into account.
Today‘s rate of change yields long-range values for epsilon between 21.9° and 24.3° for a cycle of about 40.000 years. With this algebraic function one can define the age of any document or building that answers the question: How big was the angle epsilon at the time of its conception?
As commonly known, the determination of epsilon in the past has been possible to great exactitude even back in prehistory since it is very simple to obtain from the shadow of the sun between the solstices.
On the other hand, we have records of those measurements from classical Greek times onward. There remain large lacunae between Roman and Arab as well as Renaissance measurements, but in general the surviving values indicate that epsilon has diminished at a grossly stable rate.
Ptolemy has fixed the value of epsilon in different instances in Almagest (e.g. I,12) as 23° 51‘ 20“. He stated that his ability to obtain this value includes a marge of 2.5 arc minutes of error but not more. For our purpose this is fairly sufficient because epsilon has diminished since then by roughly ten times this amount. Earlier authors like Eratosthenes, Hipparchus, Plinius and Vitruvius used 24° as good value in their calculations, which is near to that of Ptolemy. All were convinced that this was correct for their time. Including the Arab astronomers agreed to this, although by observation they had obtained a different value for their own time which ranged around 23°35‘. Today the value is 23°26,4‘.
Modern historian of astronomy Alexander Jones (2002) calls the value of Ptolemy „wonderfully close to reality“, but „today we know“, that the value at that time was 11‘ lower. An inclination of 23°51‘20“ as Ptolemy writes would belong to a position of the earth one thousand years earlier if we use our modern formula of epsilon variation.
Archaeologist Edmund Buchner who excavated until 1982 for several years the sun dial of emperor Augustus in Rome repeatedly says (p. 21) that the value of modern retro-calculation of epsilon for that time, which 2000 years ago would have been 23°41‘, does not coincide with the value deductible from the sun dial, but is 11‘ lower. Yet, the Augustean „false“ value deductible from the marble sun dial must reflect the scientific result of that time (p. 22) because otherwise all other measures of this genial building would not match. It is not out of the way to read a precise value of epsilon in such a big monument (of 30m height), „23° 50‘ (or better 52‘)“ because the incisions in the pavement had been executed only after erection of the obelisk and after several years of observation (p. 49 f). They reflect exact measurements and are in agreement with the value Ptolemy wrote about 150 years later.

There we have a contradiction of sorts that reiterates in many such intentions to date ancient buildings: Dates that had been determined centuries ago for classical and prehistoric monuments collide with those retro-calculated by modern techniques for those same objects. They diverge quite noticeably, and the more the dates go back in time the bigger is the difference between the two, i.e. between real observation of that time and retro-calculation based on actual observations.

2. Let us look at a second example of this kind. As point of reference I am choosing the precessional dislocation of the spring equinox. Sun, moon, and the planets exerce a measurable force on Earth which therefore undergoes a third movement apart from rotation and orbit around the sun, which since Hipparchus‘ time is known as precession. Earth reacts like a gyro-static top describing a movement around the pole of the ecliptic. Thus the constellations of the zodiac rotate, spring equinox moves back.
In his enormous work „Kosmos“ (III,149), Alexander v. Humboldt wonders why the date of conception of the Almagest is 138 AD while by modern calculations of its star positions it should be 63 AD. He realizes that a rigorous application of the actual precession rate to ancient observation values leads to discrepancies, in this case to a difference of 75 years which the Almagest should be moved further into the past. Other astronomers before and after him concluded the same. Robert Böker wrote 1952 (S. 45), that the incorrectness of the Almagest would amount to 90 years if modern calculation would be applied. Methodically it is the same result like that of Humboldt and other historians: The Almagest gives values that are older than the proposed date.
As we go back in time yet another step the divergence becomes appalling. Platon’s disciple Eudoxus (4th c. BC), very admired in his time and ever afterwards, is known to us through the Phaenomenes of Aratos and the commentary of Hipparchus. All historians from Isaac Newton to Delambre and to this day agree that the positions of stars given in Eudoxus should belong to a time many centuries before the date convened for its author. Newton proposed 939 BC, but he could not explain why the atlas should be 600 years older than its traditional date. Shouldn’t Eudoxus have observed the positions in his time instead of retrocalculating positions of centuries ago?
During the last hundred years several archaeastronomers have dealt with this question. Julius Höpken in 1905 pleaded for a movable sphere and different moments of observation of the Eudoxian atlas. Böker (1952) and Schaefer (2004) as well as Duke (2008) arrived at more or less the same results: the stars of Eudoxus belong to a time about 600 to 700 years older than the instance Eudoxus had been agreed upon.
Böker who gives 1000 BC (plus-minus 30 to 40 years) concludes that the positions must have been calculated schematically and not observed if they go back to Eudoxus. Duke with even better methods and a new translation of the original text arrives at near 1100 BC.
As I must assume that it should have been easy for Eudoxus or anyone else to shift the positions to their correct location but had not done so, I can only conclude that the positions correspond to the moment given. And that means that our calculation based on actual values must be wrong.

3. Now a third example. Again we regard the phenomenon of precession by which in the long run new constellations rise above the horizon. The axis of the earth points to a different spot in the sky in the course of centuries. Our Polaris is an ephemeral object. So any indication of the position of the North pole in the sky can be used as another firm measure for dating ancient objects or writings. And there we come across the same type of contradiction:
The Phoenicians are said to have used the constellation Draco as indicator of time. A steadfast tradition claims that their Pole Star was Thuban (Alpha Draconis). Joseph Scaliger (1583) has transmitted this and it is upheld until today. By retro-calculation Thuban would have been close to the pole around 2800 BC. Scaliger thought this to be correct, but we have some problem with the date since our archaeologists do not admit such high antiquity for the Phoenicians. We would rather cut out 2000 years and would locate the Phoenicians near 1000 BC. Thuban then would have parted from the position as indicator of North for a very long time. As a seafaring people the Phoenicians would have used a different star if any. Even Homer knew that it was rather Kochab that stood close to the Pole in their time, reason enough to call it Phoenike (Ideler 1838, S. 10). In order to save Thuban as polar star it was imposed on the Ancient Egyptian Empire albeit with no hint to its veracity and only because they are supposed to have the corresponding age.

There are many more examples to similar contradictions. Those three here mentioned concerning the inclination angle epsilon, the precession of the equinox, and the position of the Pole Star, suffice to search for the reason of this astounding fact.

4. The further we look back into prehistory the bigger becomes the difference between factual and virtual time estimates. Megalithic monuments show this with a certain precision. Their dates have often to be readjusted when astronomic dates are taken into account. In all cases those remnants of an unknown past are made older than they used to be before the application of the calculus.
Since 1999 and more expressively in 2006 I proposed the following scenario as explanation: Several interruptions of the secular movement of precession have struck the earth and invalidate our retro-calculations which only use actual observations and deem ancient ones erroneous. As those „jumps“ or jolts (or jerks) of the earth are easily recognizable in old observations on precession, I have baptized them „precession jolts“. Their factual number and magnitude is still unknown and might remain so for the time being, as is the exact physical way of the occurrence. The supposition solves the problem, and there are indications to its probability. After undergoing a jump, the earthly precession moves with a slightly different speed. This is documented in ancient and medieval astronomic records.
As long as historians apply steady and unchangeable rates of precession to all retro-calculations, the outcome will be wrong if jolts and precession velocity changes have taken place as I propose, more so in case those jolts not only stretch the amount of time but leave wholes in our historic timetables. The chaotic behaviour of planets like the earth excludes strictly mathematical retro-calculations, and the method of calibration as used in physical examinations like radio carbon dating is of no help either.
The historical chronology as established by the Renaissance humanists and historians has no fundament. It had been concocted on precession calculations of a very rough kind. Their chronology does not rely on real traditions, it rather proposes a fabulous sequence of figures beyond reality.

References:
Almagest see Manitius
Böker, Robert (1952): „Die Entstehung der Sternsphäre Arats“ in: Berichte der sächs. Akademie der Wiss., Leipzig, Bd. 99, S. 3-68 (Berlin)
Buchner, Edmund (1982): Die Sonnenuhr des Augustus (Mainz)
Duke, Denis (2008): (2008): „Statistical Dating of the Phenomena of Eudoxus” in: DIO 15, 7 (USA)
Höpken, Julius (1905): Über die Entstehung der Phaenomena des Eudoxus-Aratos (Emden)
Ideler, Ludwig (1838): „Über den Ursprung des Thierkreises“, in: Abh. Akad. Wiss. (Berlin)
Jones, Alexander (2002): “Eratosthenes, Hipparchus, and the obliquity of the ecliptic” in: Journal for the History of Astronomy, vol. 33, S. 15-19
Kunitzsch, Paul (1974): Der Almagest. Die Syntaxis Mathematica des Claudius Ptolemäus in arabisch-lateinischer Überlieferung (Wiesbaden)
Manitius, Karl (1912-13): Des Claudius Ptolemäus Handbuch der Astronomie (Teubner, Leipzig, 2 Bde 1963, German transl. of the Greek edition of the Almagest by Heiberg)
Newton, Isaac (1728): The Chronology of ancient Kingdoms amended (London)
Scaliger, Joseph Justus (1583): De emendatione temporum (Lüttich)
Topper, Uwe (2006): Kalendersprung (Tübingen)
Vitruv (1908): De Architectura decem libri, German transl. by Franz Reber (Berlin; Wiesbaden 2004)

Abbreviated translation of a lecture held in October, 2014.

My lecture held in Potsdam Sept. 2008, published on this site as „Cataclysms are the reasons for our wrong chronology“ basically holds the same items and reasoning, yet it is slightly outdated through my research since then. The short lecture given above allows an easier access to the main points.
This text has been published recently by Society for Interdisciplinary Studies (SIS) in its Review “Chronology & Catastrophism”, 2017:2, pp. 43-46. (UK)