by Wieslaw Z. Krawcewicz, Gleb V. Nosovskij and Petr P.
Copyright © 2002 New Tradition Sociological society, All Rights
Reprinted with Permission
In modern times mathematics has become an inseparable pxj5art of
human culture, in which it plays a fundamental role. Throughout the
centuries mathematics has been a crucial tool in the hands of
mankind. It has allowed us to understand the fundamental principles
of the universe, for example Newton's law of gravity, Einstein's
equivalence of mass and energy, Maxwell's equations of
electromagnetism, the laws of quantum mechanics for elementary
particles, and even the Big Bang theory. The advances in
interplanetary exploration and rapid development of computer
technology wouldn't have been possible without mathematics.
Scientists, in their struggle to improve our
understanding, have untangled the principal problems of biology and
unveiled the secrets of life. However, the times when it was
sufficient for a biologist to know only elementary arithmetic and
graphs of functions are long gone. Today, they need much more
advanced mathematics like linear and multilinear algebras,
mathematical analysis, the theory of differential and functional
equations, statistics and discrete mathematics. Branches of biology
like genetics or ecology are considered as parts of mathematics.
Mathematics also opens new possibilities for medicine. Mathematical
models are used to understand our bodies and to find optimal
treatment for diseases.
More and more mathematics is used in the social
sciences like economics, psychology, sociology, demography, social
epidemiology and criminology. Not surprisingly, mathematics is also
trying to make its contribution in history, where it addresses a
very serious problem of reliability of the accounts of historical
events. How can we be sure that the historical events that we learn
about in school or from books really took place? Maybe some of them
are simply fairy tales that, because of some mysterious
circumstances, are considered now to be historical facts.
History of the Global Chronology
The fundamental question that should be asked is
what is the origin of our historical knowledge. We all learned our
history at school and generally accepted it as a true description of
the actual events. However, even in our lifetime some of the recent
historical events that we witnessed are not always described in the
way we remember them. How can we be sure that the description of the
events that took place centuries ago is accurate? Moreover, why
should we believe that these historical events really happened at
the time and place that is allocated to them? In order to answer
these questions we must look at the history of history.
The early historians (for example Thucydides,
Herodotus, Ssu-ma Ch'ien and others) were describing history of
small territories over short periods of time. Ancient and medieval
manuscripts that are available today usually present accounts of
events in separate countries over a time scale of no more than one
or two centuries. The fundamental problem encountered by historians
in 16th and 17th centuries working on reconstruction of the global
history of mankind was putting together in chronological order all
of the manuscripts, chronicles and other historical documents to
obtain a unified and consistent account of all historical events.
This was an extremely difficult problem for that time. The main
obstacle was that most of the manuscripts were not dated, or used an
unknown or archaic system of dating, and contained only a
description of a sequence of successive events. It should be
stressed out that the most of historical documents that we have
today, related to ancient and medieval times, are not original but
only copies made some time ago, often under suspicious
The idea of reconstructing global history emerged
during the late Renaissance. The official historical chronology,
presently commonly acknowledged, was originated by the Italian
theologian and scientist I. Scaliger (1540-1609). He determined the
exact dates of the most important historical events like the
Peloponnesian War, Trojan War, founding of Rome, etc., but did not
prove none of his dates. His followers continued this work and it is
commonly accepted that the official chronology was given its final
shape by D. Petavius (1583-1652). It is strange that other
historians, in spite of the scientific advantages, very rarely
modified the dates of the basic historical events assigned by
Scaliger and Petavius.
In summary, according to Scaliger, Petavius and
their followers, the events of the ancient world took place from
about 3,500 years B.C. till the fifth century A.D. As their results
were never independently confirmed, there is an outstanding question
of the credibility of this chronology. By the way, not all of the
statements made by Scaliger turned out to be true, as for example,
his geometrical proof of the quadrature of the circle , which he
defended ferociously all his life.
Critics of the Traditional Chronology
Even among scholars, not all contemporaries of
Scaliger and Petavius, supported their chronology. For example, in
the sixteenth century D. Arcilla, a professor of Salamanca
University in Spain, claimed that all ancient history was a
fabrication made in the middle ages. The director of the French
Royal Library, Jean Hardouin (1646-1729) declared that practically
all the antiquities and ancient texts were created (or falsified)
after 12th century. The most famous scientist of that epoch, Sir
Isaac Newton (1642-1727), was also against the chronology of
Scaliger and Petavius. Newton published a large monograph entitled
"The Chronology of Ancient Kingdoms Amended," in which he
re-dated key ancient events by shifting them several hundreds years
forward. There were many more scientists, philologists, historians,
and jurists who objected to the chronology of Scaliger and Petavius.
We should also mention recent and contemporary critics of the
conventional chronology in Germany, including W. Kammeier, H. Illig,
U. Topper, H-U. Niemitz, G. Heinsohn, and C. Blцss (see
Nicolai A. Morozov and His Version of
The first scholar who suggested new powerful
methods to correct chronological mistakes, was prominent Russian
scientist N.A. Morozov (1854-1946). He published a fundamental
monograph composed of seven large volumes, entitled "Christ.
History of Human Culture from the Standpoint of the Natural
Sciences" (see ). Morozov analyzed in it the conventional
chronology using the latest discoveries in mathematics, astronomy,
linguistics, philology and geology. He suggested a new version of
the global chronology and a historical reconstruction. According to
N.A. Morozov all the ancient events occurred after 3rd century AD.
Anatoly T. Fomenko and His Version of
In 1970s at the Moscow State University, a group
of young mathematicians undertook the task of the verification and
further development of Morozov's research in global chronology. One
of them, Professor A.T. Fomenko introduced several new methods of
independent dating and after several years of investigation he
proposed a new version of global chronology, which was even more
radical that the version of N.A. Morozov. He claimed that the
recorded history of mankind started not earlier than the year 900
AD, while the majority of historical events, which make our history,
refer to the time after the year 1300 AD (see [2,3]).
The New Chronology
In collaboration with G.V. Nosovskij, A.T.
Fomenko continued his work on the development of new independent
scientific methods for dating of ancient events. In 1993-1996,
completely new results were established by them on the chronology of
Russia and China. Their work resulted in stating the New Chronology,
which is a new concept of the global chronology and history. It is
based on the chronological version of A.T. Fomenko, to which new
proofs and improvements were introduced. It led to the further
shifting of the "starting point" of the known history to
the 11th century AD (see [6,7,8]).
We should mention an important pillar of this
theory, which is the astronomical dating of the Ptolemy's Star
Catalogue in "Almagest" obtained by A.T. Fomenko, V.V.
Kalashnikov and G.V. Nosovskij (see ). In the conventional
chronology the epoch of Ptolemy, who was the last great astronomer
of the antiquity, is considered to be the second century AD.
However, the analysis of vast amount of the astronomical information
contained in his star catalogue proved that the only possible time
of creation of this catalogue was from 7th to 13th century AD, which
is at least 500 years later. Consequently, it is impossible that
this astronomical data was collected in the second century. This
result strongly contradicts the conventional chronology of Scaliger
and Petavius, while it perfectly fits the New Chronology.
Methods of the New Chronology
It is an interesting question, how the above
claims could be made and justified. In fact, this work started with
constructing a large chronological table covering all periods of
human history. Next, it was attempted to discover in it some unusual
phenomena, contradictions and disagreements, simply something that
could never happen. Apparently, this idea was not easy to carry out.
Numerous heavy books devoted to the chronology are arranged in a
frustrating manner (see [10,11]). There are no modern monographs
presenting a detailed description of the global chronology, useless
to even mention proofs of its correctness in principle.
A.T. Fomenko and his collaborators compiled a
global chronology table using all available sources such as old
chronicles, chronological tables, including the Blair's canonical
chronological tables and the most recent monographs. In spite of the
fact that the available data from different sources didn't always
match, they were able to put together the global chronology
enclosing almost the whole history of the mankind. This massive work
could be done only with the use of computers.
From the point of view of mathematics, the
chronology represent an object called a function. More precisely, we
can write it as a function denoted by H(t, x1,x2), which depends on
the three variables: t - the time of a historical event and (x1,x2)
- the geographical coordinates (longitude and latitude) of the place
where this event occurred, or we can simply say that its domain is
the Cartesian product of numeric half line and the sphere. The
values of the function H(t, x1,x2) represent the fragments of
historical recordings describing this particular event.
The above Figure 1 illustrates the
"chronology" function H. On the left hand side of Figure 1
the concentric spheres represent the domain of H. More precisely,
the red arrow stands for the time axis where the points correspond
to specific dates. For example, the inside coloured sphere
illustrates events of the year 1320 at specific locations. The
larger spheres on this figure correspond to the years 1415 and 1985.
In this way, with every date in history we can associate a sphere on
which the corresponding events are indicated. To every place on the
Earth we can associate a ray originating at its centre to mark the
dates of the events that occurred at this place. The books symbolize
available descriptions of the historical events. The green arrows
indicate the exact fragments of the available descriptions
corresponding to certain concrete events. Briefly, the chronology is
a database parameterized by points of the Cartesian product R+ x S2,
i.e. the product of the half-axis R+ and the sphere S2. Naturally,
this function is not convenient for mathematical analysis. Clearly
the set of values of the function H does not have any natural
mathematical structure. However, the information contained in the
function H allows us, on the one side, to construct a variety of
scalar (numeric) functions which can be easily analyzed with
mathematical methods, and on the other side, to provide essential
information on the nature of the historical events. An example of a
simple scalar function, which can be easily extracted from the
historical database, is the functions of the time-span of the reign
of subsequent rulers belonging to a certain specific dynasty. Such a
`dynasty' function can be illustrated by its graph, see Figure 2.
On the horizontal axis are placed the subsequent
numbers of the consecutive rulers (or names of kings, emperors,
etc.) and on the vertical axis is marked the length of the reign of
the corresponding ruler. We will call such a sequence of rulers a
numerical dynasty or simply a dynasty. The dynasty in the above
example consists of 12 rulers.
There is another way to analyze chronicles by
extracting numerical information from them. For example we can
associate with a text X a sequence of integers, which are the
numbers of words H(X(T)) in the chapter describing the year T (or
simply the volume of a year fragment). We call H(X(T)) the volume
function for X. There are also possibilities for other numerical
functions like the number of references to the year T in subsequent
years, the number of all names of historical persons listed in the
text, or the frequencies showing how often these names were
mentioned in the whole text. In his monograph , A.T. Fomenko used
these functions to analyze similarities and differences between
documents referring either to the same epoch or two different
epochs. It is clear that for two different documents X and Y the
functions H(X(T)) and H(Y(T)) can be completely different even if
they refer to the same epoch. However, if the functions H(X(T)) and
H(Y(T)) have local maxima practically at the same positions it means
that these two chronicles describe the same historical epoch. A.T.
Fomenko called it the principle of maximal correlation. This
principle was empirically checked using the reliable historical data
of 16th - 19th centuries, and its correctness was confirmed.
Therefore, the locations of the maxima constitute the numerical data
that can be associated with the text X in order to characterize the
epoch it is referring to.
The methods of Fomenko are based on theoretical
and numerical analysis of these and other similar functions
describing historical data. In particular, he introduces a routine
for distinguishing functions referring to different dynasties and
defines a certain measure of distinctiveness between them (or a
probability measure for distinctiveness). In simple words, he found
a way to measure a `distance' between the above numerical functions
(like for example dynasty functions) in a similar way to measuring
distance between two different locations. Mathematicians say that in
such a situation they are dealing with a metric space. The geometry
of such metric spaces is definitely different from the geometry we
learn in school, but the usual properties related to the measurement
of distances are still valid in these spaces. If a distance between
towns A and B is less than one kilometre we are justified to think
that in fact A and B represent the same town. Similarly, if in the
space of functions a distance between two dynasty functions is
sufficiently small we may think that indeed they represent the same
dynasty. These methods were extensively tested on the data referring
to well documented. It was proved that if two dynasty functions (for
15 rulers) or volume functions were not related, the measure of
distinctiveness between numerical functions associated with these
dynasties was between 1 and 10-4. However, in the case of related
events from the same epoch, the measure of distinctiveness was never
higher than 10-8.
The work of Fomenko and his collaborators proves
that the statistical analysis can be successfully applied to analyze
the numerical data contained in historical documents. A.T. Fomenko
and G.V. Nosovskij also developed several other statistical criteria
for distinguishing or recognizing identical sequences of historical
events. We should mention for example the method of detecting of
chronological shifts based on the names distribution in chronicles
and the method of relation matrices used to recognize duplicates and
decompose chronicles into its source fragments (see ).
What is Wrong With the Traditional Chronology
It is difficult to imagine that two different
dynasties could have identical or almost identical dynasty
functions. The probability of such a coincidence is extremely small
already for dynasties composed of 10 rulers. Nevertheless, the
number of such coincidences, for even longer dynasties of 15 rulers,
turns out to be unexpectedly large. N.A. Morozov, who noticed the
coincidence between the ancient Rome and the ancient Jewish state,
discovered the first examples of surprisingly identical pairs of
dynasty graphs. A formal method to study such similarities was
introduced by A.T. Fomenko (see the reference list in ).
There is another surprise, besides coincidence of
the dynasty functions, the other numerical functions confirm with
very high probability that these dynasties are indeed the same. It
brings us to a suspicion that in fact we are dealing with
repetitions in the conventional version of the history. Fomenko
discovered dozens of strong coincidences, sometimes between three
and more dynasties. But, there are no more such coincidences in the
history of the better-documented epochs, for example starting from
the 16th century.
As an example, we would like to discuss two
dynasties, one the dynasty of the Holy Roman-German Empire (10th -
13th AD) and another one of the Jewish kings according the Bible
(9th - 5th BC). On Figure 3, we represent the vertical time line
with two graphs of reign durations on its opposite sides for
comparison. On this chart, we start the dates for the dynasty of
Jewish kings in the year zero, which is not a date according to some
era but simply indicates the starting "zero" point for
this dynasty. According to the Encyclopaedia Britannica, the
beginning of this dynasty is around 922 B.C. Figure 3 was taken from
A.T. Fomenko monograph .
There are many more examples of similar dynasty
pairs in the conventional chronology. For instance, the parallel
between the first period of the Roman episcopate in 141-314 A.D. and
the second period of the Roman episcopate in 314-532 A.D. is shown
in Figure 4.
On Figure 5, we present another pair of graphs,
this time without annotations. All these graphs were also taken from
the monograph .
These parallels suggest that the traditional
history of ancient times consist of multiple recounts of the same
events scattered in many locations at various times. The first
scientist who realized it was N.A. Morozov (see ). Further
progress was made by A.T. Fomenko who succeeded to decipher the
principle structure of these duplicates in Roman and Biblical
history (see ). On Figure 6, we show a graphical representation
of his result related to the Roman and European history. The
chronological blocks annotated by the same letters (what we also
emphasised by adding colours) represent duplicates in the
What Does Analysis of Astronomical Data
One of the most important and convincing methods
used for dating of historical events is the astronomical dating. For
instance, the accurate astronomical computations indicate that the
Peloponnesian war took place not in the 6th century BC, as it is
assumed by the conventional chronology, but in the 11th century AD,
or even later (see , Vol.1, pp. 20-22). A very important example
was already mentioned; it is the dating of star catalogue in the
Almagest (see ).
During the recent years a significant progress
was done in the old problem of decoding and dating of ancient
Egyptian zodiacs. It was discovered that the principal structure of
a typical Egyptian zodiac was much more elaborated and complex than
it was assumed before. In fact, the amount of the astronomical
information contained in such a zodiac is completely sufficient not
only to accurately calculate its date, but also to determine its
correct decoding (see [11,12]).
Egyptian zodiac is nothing else than a symbolic
representation of astronomical objects inside the zodiacal belt. One
of the most famous examples is the Round zodiac from the Denderah
temple in Egypt. On Figure 7 we show a drawing of this zodiac. We
used colours to indicate figures with different types of
Let us briefly explain the structure of an
Egyptian zodiac (we refer to [11,12] for more details). It was
discovered in [11,12] that an Egyptian zodiac presents an
astronomical description of the whole calendar year during which the
main date occurred. This date is encoded in the zodiac by its main
horoscope. On Figure 7, the main horoscope on the Round zodiac is
marked in yellow. Four solstices and equinox days, belonging to the
same year, were described by partial horoscopes. In our example
these horoscopes are marked in light-blue (see Figure 7). There also
could be other astronomical scenes present (see the symbols marked
in green on Figure 7). The whole structure of an Egyptian zodiac is
illustrated on Figure 8.
The results of astronomical dating of Egyptian
zodiacs sharply contradict the conventional chronology (see
[11,12]). For example the final astronomical solution for the main
date on the Round Denderah zodiac was the morning of March 20, 1185
AD. Let us mention that in the same Denderah temple there was
another large zodiac, usually called the Long Denderah zodiac. The
date shown on this zodiac turned out to be April 22-26, 1168 AD.
These two dates suggest that the Denderah temple was commemorating
some events that occurred in 12th century AD. Of course, it
completely contradicts the conventional chronology, but perfectly
agrees with the New Chronology. The situation with other Egyptian
zodiacs is even "worse," because it was proved that their
dates in case of temple zodiacs range from the 12th to 15th century,
and for some zodiacs in tombs and on coffins, they are even later.
What Critics of the New Chronology Say?
We will discuss some of typical arguments against
the New Chronology. One of the most popular arguments in support of
the conventional chronology is that the carbon-14 dating method
supports it. But in fact it is not true. The carbon-14 method, which
was discovered by Willard Libby, is based on the measurement of the
radiocarbon level in organic samples. It assumes essentially uniform
level of the isotope carbon-14 in every living material, but it is
now clear that carbon-14 was never homogeneously distributed. In
fact, in order to improve its "accuracy," the carbon-14
method was calibrated using samples of "known" age. It was
done by constructing the so-called calibration curves, which are
dependent on the conventional chronology. That means the carbon-14
dating method is secondary and is not able either confirm or discard
any chronological theory. In addition, the errors induced by this
method exceed all reasonable time intervals. We would like to point
out that if the global chronology was changed, the carbon-14 dating
method would also work nicely with the new dating system. It is not
possible to present here a complete discussion of this complicated
problem (we refer the reader to , Vol.1, pp. 133-136, , Vol.1,
pp. 184-214, and ).
There are other arguments, of different type,
claiming that there is nothing abnormal in coincidence of dynasty
functions for different dynasties. For instance, we know that the
probability of having winning lottery is very small but still there
are communities that have one or more lottery winners. So, even very
unlike events could happen. Critics of the New Chronology often
mention that biographies of certain rulers, like Napoleon and Hitler
(both dictators) are quite similar, so by applying the method of
Morozov and Fomenko we should consider them to be the same person
and ultimately make a senseless statement that the first 20 years of
the 19th century are simply the years thirties and forties of the
20th century. There are many more similar arguments, but all of them
miss the point that extremely rare events only happen in large
samples. For example, although the chances of having a winning
lottery ticket are extremely small, nevertheless the probability
that somebody wins is one. But, this is not the case with the
unrelated dynasty functions, for which the coincidence in the whole
sample is even less probable than the coincidence of two random
There is also a claim that the
"strange" coincidences between dynasty functions could be
removed by making appropriate corrections of the historical data.
However, even with modified dates the probability arguments still
Regarding the archaeological dating, we should
point out that it is closely dependent on the conventional
chronology. The usual dating procedure in archaeology is based on
the comparison of the excavated objects with objects already dated.
In this procedure, finding some objects of identifiable style or
origin can lead to a conclusion of the age of the whole site. The
whole process is highly subjective and cannot be considered as a
proof of the conventional chronology.
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