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However, all these pecularities disappear when we renounce<br />

the hypothesis claiming that the Almagest was compiled<br />

in the beginning <strong>of</strong> the Christian era. Let us find out<br />

what would be the best epoch in which Northen Star would be<br />

the most natural choice for the first star in the catalogue. On<br />

Figure 1.16 we show the trajectory <strong>of</strong> the north pole around<br />

the ecliptic pole P , and the locations <strong>of</strong> the stars Alpha and<br />

Beta. It is clear that with the time the astronomical situation<br />

was changing: Beta was gradually moving away from the<br />

north pole, while Alpha was directly approaching the north<br />

pole. We have indicated on Figure 1.16 the initial position N<br />

<strong>of</strong> the north pole in the 2nd century A.D. The angular velocity<br />

<strong>of</strong> the north pole moving around the ecliptic is about<br />

1 o per 100 years. Now we are in the position to find out the<br />

epoch when North Star became closer to the northy pole than<br />

the star Beta. Since an argument <strong>of</strong> this type can hardly be<br />

considered as reliable for the dating purposes, we are satified<br />

with a rough estimate indicating the period from the 9th<br />

to 11th century A.D. At that time Alpha was closer to the<br />

north pole than Beta and Alpha was also the brightest star<br />

<strong>of</strong> Ursa Minor (M = +2.1 for Alpha, while for Beta it was<br />

M = +2.2). It is also obvious that at that time an observer<br />

compiling a star catalogue, would choose the star Alpha as<br />

the first star in the Northen Hemisphere. Notice that it is<br />

exactly, how the creator <strong>of</strong> the Almagest listed the stars. In<br />

addition, during the 15th and 16th centuries, when the publications<br />

<strong>of</strong> the Almagest took place, North Star was the closest<br />

star to the north pole — its distance was only 4 o from the<br />

north pole. Consequently, by chosing North Star as the first<br />

star in the catalogue, the creator <strong>of</strong> the Almagest revealed the<br />

real time <strong>of</strong> its observations — the epoch that was not earlier<br />

than the 9th or 10th century.<br />

1.7.3 Statistical Analysis <strong>of</strong> the Star Catalogue<br />

Almagest<br />

Let us return to the investigation <strong>of</strong> the Almagest conducted<br />

by astronomer R. Newton’s. It is important to emphesize that<br />

Newton never, at any moment, doubted the correctness <strong>of</strong><br />

Scaliger’s chronology. His conclusions can be summarized as<br />

follows:<br />

1. The astronomical stitation on the real sky in the beginning<br />

<strong>of</strong> the Christian era does not match the astronomical<br />

data contained in the Almagest;<br />

2. The presently availabe version <strong>of</strong> the star catalogue Almagest<br />

does not contain descriptions <strong>of</strong> direct astronomical<br />

observations, but the results <strong>of</strong> computations, based<br />

on the theoretical models. These theoretical computations<br />

were later inserted into the Almagest seemingly to falsely<br />

assume the real astronomical observations, i.e. they were<br />

(according to Newton) fabricated;<br />

3. The Almagest couldn’t be compiled around the year 150<br />

A.D., as it is claimed by Scaliger’s chronology;<br />

4. Consequently, the Almagest was created during another<br />

epoch and its dating should be revised accordingly.<br />

R. Newton points out the passages in the Almagest indicating<br />

that the astronomical observations were conducted during the<br />

1.7 Controversy over the Ptolemy’s Almagest 15<br />

reign <strong>of</strong> the Roman emperor Antoninus Pius, who according<br />

to Scaliger’s chronology ruled from 138 to 161 AD. Therefore,<br />

R. Newton concludes, that whoever was the author <strong>of</strong><br />

the Almagest, he was a liar. There is no way his “personnally<br />

made observations” could ever represent a real astronomical<br />

situation from the 2nd century. In the introduction to<br />

his book, Robert Newton stated that it was a story about a<br />

crime comitted by a scientist against the ethics in his pr<strong>of</strong>ession.<br />

He claimed that Ptolemy’s star catalogue was “corrected”<br />

according to the precession used by Hipparchus. For<br />

example, he shows that the equinoxes and other observations<br />

allegedly made by Ptolemy to determine the ecliptic’s slop<br />

and Alexandria’s latitude, were fabricated. There were also<br />

four fabricated lunar eclipse “triads,” falsifications <strong>of</strong> calculations<br />

and falsification <strong>of</strong> data (for example related to Venus<br />

and the exterior planet data). Newton completes his thought<br />

with a statement that Ptolemy was not an outstanding astronomer<br />

<strong>of</strong> antiquity but rather a most successful swindler<br />

in the history <strong>of</strong> science 58 .<br />

However, a perception <strong>of</strong> the Ptolemy’s work may become<br />

quite different if it turns out that it was a text written in the<br />

10-16th century. In the book [106], the authors, V.V. Kalashnikov,<br />

G.B. Nosovsky and A.T. Fomenko, verified the correctness<br />

<strong>of</strong> R. Newton’s calculations and confirmed his findings. In<br />

contrast to R. Newton, their goal was to achieve an independent<br />

dating <strong>of</strong> the Almagest based on the mathematical and<br />

statistical analysis <strong>of</strong> the individual stars’ proper motion. This<br />

is not an easy problem, which required a careful analysis <strong>of</strong><br />

the accuracy <strong>of</strong> the Almagest’s star coordinates. Let us recall<br />

that every star in the catalogue was identified by two ecliptic<br />

coordinates: longitude and latitude. It was discovered that<br />

the accuracy <strong>of</strong> the longitudes was much worse than that <strong>of</strong><br />

the latitudes, leading to a suspission that they were obtained<br />

by a method quite usual in the Middle Ages: by measuring<br />

equatorial coordinates and subsequently recarculating them<br />

into ecliptical ones. Since the calculations <strong>of</strong> the ecliptic longitudes<br />

were much more complicated, larger errors arose and<br />

the accuracy failed, making them useless for the purpose <strong>of</strong><br />

dating the Almagest. In addition, the longitudal precessions<br />

were already well known in the Middle Ages, what could have<br />

been tempting to manipulate this data. The method used in<br />

[106] was applied to latitudes only. Its effectivness was tested<br />

on the several star cataloges whose dates are well known (for<br />

example the star cataloge <strong>of</strong> Tycho Brahe, Bonner Durchmusterung,<br />

etc.). It involved extensive computations which<br />

were done using specially writen for this purpose computer<br />

programs.<br />

For the purpose <strong>of</strong> computations, a list <strong>of</strong> 80 relatively<br />

fast moving stars was compiled, based on the modern star<br />

catalogue by D. H<strong>of</strong>flit (The Bright Star Catalogue). Based<br />

on this list about 35 stars were identified in the Almagest,<br />

from which three had to be rejected because their identity<br />

couldn’t be indisputably established. Let us point out that it<br />

was not a trivial question to identify some <strong>of</strong> the stars in the<br />

Almagest. Basically, the star identifications in [106] confirm<br />

58 See [178].

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