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Since my early childhood, I have been inspired and excited by ancient and medieval history. I also have a good memory, which allows me to remember historical events, dates, names, and related details. So, after reading many history books, I analysed and compared the information and, little by little, I began to feel that there was something wrong with the dates of antiquity. There were too many discrepancies and contradictions that could not be explained within the framework of traditional chronology. For example, let's examine what we know of ancient Rome. The monumental work The Decline and Fall of the Roman Empire, written by English historian and scholar Edward Gibbon (1737-1794), is a great source of detailed information on the history of the Roman Empire. Before commenting on this book, let me remark that I cannot imagine how - with their vast territories - the Romans did not use geographical maps, how they conducted trade without a banking system, and how the Roman army, on which the Empire rested, was unable to improve its weapons and military tactics during nine centuries of wars. With the use of simple mathematics, it is possible to discover in ancient history several such dramatic contradictions, which historians don't seem to consider. Let us analyse some numbers. E. Gibbon gives a very precise description of a Roman legion, which " ... was divided into 10 cohorts ... The first cohort, ... was formed of 1 105 soldiers ... The remaining 9 cohorts consisted each of 555 soldiers, ... The whole body of legionary infantry amounted to 6 100 men." He also writes, "The cavalry, without which the force of the legion would have remained imperfect, was divided into 10 troops or squadrons; the first, as the companion of the first cohort, consisted of a 132 men; while each of the other 9 amounted only to 66. The entire establishment formed a regiment ... of 726 horses, naturally connected with its respected legion ..." Finally, he gives an exact estimate of a Roman legion: "We may compute, however, that the legion, which was itself a body of 6 831 Romans, might, with its attendant auxiliaries, amount to about 12 500 men. The peace establishment of Hadrian and his successors was composed of no less than 30 of these formidable brigades; and most probably formed a standing force of 375 000." This enormous military force of 375000 men, maintained during a time of peace, was larger than the Napoleonic army in the 1800s. Let me point out that according to the Encyclopedia Britannica,6 "Battles on the Continent in the mid-18th century typically involved armies of about 60 000 to 70 000 troops." Of course, an army needed weapons, equipment, supplies, etc. Again, E. Gibbon gives us a lot of details: "Besides their arms, which the legionaries scarcely considered as an encumbrance, they were laden with their kitchen furniture, the instruments of fortifications, and the provisions of many days. Under this weight, which would oppress the delicacy of a modern soldier, they were trained by a regular step to advance, in about six hours, nearly twenty miles. On the appearance of an enemy, they threw aside their baggage, and by easy and rapid evolutions converted the column of march into an order of battle." This description of the physical fitness of an average Roman soldier is extraordinary. It brings us to the very strange conclusion that, at some point, the human race retrogressed in its ability to cope with physical problems. Is it possible that there was a gradual decline of the human race, with hundreds of thousands of Schwarzenegger-like athletes of Roman times evolving into medieval knights with relatively weak bodies (like today's teenage boys), whose little suits of armuor are today proudly displayed in museums? Is there a reasonable biological or genetic explanation to this dramatic change affecting the human race over such a short period of time? In order to supply such an army with weapons, a whole industry would have been needed. In his work, E. Gibbon explicitly mentions iron (or even steel) weapons: "Besides a lighter spear, the legionary soldier grasped in his right hand the formidable pilum ..., whose utmost length was about six feet, and which was terminated by a massy triangular point of steel of eighteen inches." In another place, he indicates "The use of lances and of iron maces ..." It is believed that the extraction of iron from ores was very common in the Roman Empire. However, to smelt pure iron, a temperature of 1 539oC is required, which couldn't be achieved by burning wood or coal without the blowing or the blast furnaces invented more than a 1 000 years later. Even in the 15th century, the iron produced was of quite poor quality because large amounts of carbon had to be absorbed to lower the melting temperature to 1 150oC. There is also the question of sufficient resources - the blast furnaces used in the mid-16th century required large amounts of wood to produce charcoal, an expensive and unclean process that led to the eventual deforestation of Europe. How could ancient Rome have sustained a production of quality iron on the scale necessary to supply thousands of tonnes of arms and equipment to its vast army? Just by estimating the size of the army, we can conclude that the population of the Eastern and Western Roman Empire in the second century AD was at least 20 million people, but it could have been as high as 40 or even 50 million. According to E.Gibbon, "Ancient Italy ... contained eleven hundred and ninety seven cities." The city of Rome had more After 1800,
Napoleon routinely maneuvered armies of 250 000. See Encyclopędia Britannica. than a half-million inhabitants, and there were other great cities in the Empire. All of these cities were connected by a network of paved public highways, their combined lengths more than 4 000 miles! This could only be possible in a technologically advanced society. According to J.C. Russell, in the 4th century, the population of Western Roman Empire was 22 million (including 750 000 people in England and five million in France), while the population of the Eastern Roman Empire was 34 million. It is not hard to determine that there is a serious problem with these numbers. In England, a population of four million in the 15th century grew to 62 million in the 20th century. Similarly, in France, a population of about 20 million in the 17th century (during the reign of Louis XIV), grew to 60 million in the 20th century ... and this growth occurred despite losses due to several atrocious wars. We know from historical records that during the Napoleonic wars alone, about three million people perished, most of them young men. But there was also the French Revolution, the wars of the 18th century in which France suffered heavy losses, and the slaughter of World War I. By assuming a constant population growth rate, it is easy to estimate that the population of England doubled every 120 years, while the population of France doubled every 190 years.
Graphs showing the hypothetical growth of these two functions are provided in Figure 1. According to this model, in the 4th and 5th centuries, at the breakdown of the Roman Empire, the (hypothetical) population of England would have been 10 000 to 15 000, while the population of France would have been 170 000 to 250 000. However, according to estimates based on historical documents, these numbers should be in the millions. It seems that starting with the 5th century, there were periods during which the population of Europe stagnated or decreased. Attempts at logical explanations, such as poor hygiene, epidemics, and short lifespan, can hardly withstand criticism. In fact, from the 5th century until the 18th century, there was no significant improvement in sanitary conditions in Western Europe, there were many epidemics, and hygiene was poor. Also, the introduction of .rearms in the 15th century resulted in more war casualties. According to UNESCO demographic resources, an increase of 0.2 per cent per annum is required to assure the sustainable growth of a human population, while an increase of 0.02 per cent per annum is described as a demographical disaster. There is no evidence that such a disaster has ever happened to the human race. Therefore, there is no reason to assume that the growth rate in ancient times differed significantly from the growth rate in later epochs. These discrepancies lead me to suspect that there is a gap between the historical dates attributed to the Roman Empire and those suggested by the above computations. But there are more inconsistencies in the historical record of humankind. As I have already noted, there are similar gaps of several centuries in technological and scientific development. Notice that knowledge and technology traditionally associated with the ancient world presumably disappears during the Dark Ages, only to resurface in the 15th century during the early Renaissance. The history of mathematics provides one such example. By chronologically and logically ordering major mathematical achievements, beginning with arithmetic and Greek geometry and finishing with the invention of calculus by I. Newton (1643-1727) and G.W. Leibnitz (1646-1716), we see a thousand-year gap separating antiquity from the new era. Is this only a coincidence? But what about astronomy, chemistry (alchemy), medicine, biology, and physics? There are too many inconsistencies and unexplained riddles in ancient history. Today, we are unable to build simple objects made in ancient times in the way they were originally created -this in a time when technology has produced the space shuttle and science is on the brink of cloning the human body! It is preposterous to blame all of the lost secrets of the past on the .re that destroyed the Library of Alexandria, as some have suggested. It is unfortunate that each time a paradox of history unfolds, we are left without satisfactory answers and are persuaded to believe that we have lost the ancient knowledge. Instead of disregarding the facts that disagree with the traditional interpretation, we should accept them and put the theory under rigorous scientific scrutiny. Explanations of these paradoxes and contradictions should not be left only to historians. These are scientific and multidisciplinary problems and, in my opinion, history - as a single natural science - is unable to solve them alone. I think that the chronology of technological and scientific development should be carefully investigated. The toonumerous claims of technological wonders in antiquity turn history into science friction (e.g., the production of monolithic stone blocks in Egypt, the precise astronomical calculations obtained without mechanical clocks, the glass objects and mirrors made 5 000 years ago, and so on). It is unfortunate that historians reject scientific incursion into their domain. For instance, the most reasonable explanation of Egyptian pyramid-building technology, presented by French chemist Joseph Davidovits (the creator of the geopolymer technology), was rejected by Egyptologists, who refused to provide him with samples of pyramid material. About five years ago, I came across several books written by two mathematicians from Moscow State University: academician A.T. Fomenko and G.V. Nosovskij. The books described the work of a group of professional mathematicians, led by Fomenko, who had considered the issues of ancient and medieval chronology for more than 20 years with fascinating results. Using modern mathematical and statistical methods, as well as precise astronomical computations, they discovered that ancient history was artificially extended by more than 1 000 years. For reasons beyond my understanding, historians are still ignoring their work.
But let us return to mathematics and to ancient Rome. The Roman numeral system discouraged serious calculations. How could the ancient Romans build elaborate structures such as temples, bridges, and aqueducts without precise and elaborate calculations? The most important deficiency of Roman numerals is that they are completely unsuitable even for performing a simple operation like addition, not to mention multiplication, which presents substantial difficulties (see Figure 2). In early European universities, algorithms for multiplication and division using Roman numerals were doctoral research topics. It is absolutely impossible to use clumsy Roman numbers in multi-stage calculations. The Roman system had no numeral "zero." Even the simplest decimal operations with numbers cannot be expressed in Roman numerals. N.P. Just try to add Roman numerals: MCDXXV Try to write a multiplication table in Roman numerals. What about fractions and operations with fractions?
Despite all these deficiencies, Roman numerals supposedly remained the predominant representation of numbers in European culture until the 14th century. How did the ancient Romans succeed in their calculations and complicated astronomical computations? It is believed that in the 3rd century, the Greek mathematician Diophantus was able to find positive and rational solutions to the following system of equations, called Diophantic today x31
+ x2 = y3 According to historians, at the time of Diophantus, only one symbol was used for an unknown, a symbol for "plus" did not exist, neither was there a symbol for "zero." How could Diophantic equations be solved using Greek letters or Roman numerals (see Figure 2)? Can these solutions be reproduced? Are we dealing here with another secret of ancient history that we are not supposed to question? Let us point out that even Leonardo da Vinci, at the beginning of the 16th century, had troubles with fractional powers. It is also interesting that in all of da Vinci's works, there is no trace of "zero" and that he was using 22/7 as the approximation of p - probably it was the best approximation of p available at that time. It is also interesting to look at the invention of the logarithm. The logarithm of a number x (to the base 10) expresses simply the number of digits in the decimal representation of x, so it is clearly connected to the idea of the positional numbering system. Obviously, Roman numerals could not have led to the invention of logarithms. Knowledge of our history timeline is important, and not only for historians. If indeed the dates of antiquity are incorrect, there could be profound implications for our beliefs about the past, and also for science. Historical knowledge is important to better understand our present situation and the changes that take place around us. Important issues such as global warming and environmental changes depend on available historical data. Astronomical records could have a completely different meaning if the described events took place at times other than those provided by traditional chronology. I trust that the younger generation will have no fear of "untouchable" historical dogma and will use contemporary knowledge to challenge questionable theories. For sure, it is an exciting opportunity to reverse the subordinate role science plays to history, and to create completely new areas of scientific research. REFERENCES :
Garry Kasparov has been the chess world champion since 1985, when he won the title at the age of 22. In 1997, during a historical chess challenge that made headlines all over the world, he defeated IBM's Deep Blue supercomputer. There are many web sides devoted to Garry, but we recommend : http://www.kasparovchess.com/. A biography can be found at http://www.chennaiweb.com/sp/chess/bio/garyk/. We invite all comments and other points of view. Correspondence can be sent directly to p in the Sky by email at info@new-tradition.org, or by snail mail. All letters will be forwarded to Garry Kasparov.
The math professor's
six-year-old son knocks at the door of his father's study.
A visitor to the Royal
Tyrell museum asks a museum employee: "What is p?" New Tradition , 2003. Toronto Reproduced with permission from New Tradition
Investigation of the Correctness of the Historical Dating
by
Wieslaw Z. Krawcewicz, Gleb V. Nosovskij and Petr P. Zabreiko
In modern times mathematics has become an inseparable part 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 circumstances. 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. Blöss (see [13,14,15]). Nicolai A. Morozov and His Version of Chronology 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 [1]). 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 Chronology 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 than 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 [4]). 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 [2], 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 [6]). 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 [2]). 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 [2].
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 [2].
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 [1]). Further progress was made by A.T. Fomenko who succeeded to decipher the principle structure of these duplicates in Roman and Biblical history (see [2]). 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 conventional chronology.
What Does Analysis of Astronomical Data Confirm? 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 [2], Vol.1, pp. 20-22). A very important example was already mentioned; it is the dating of star catalogue in the Almagest (see [4]). 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 astronomical meaning.
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 [2], Vol.1, pp. 133-136, [3], Vol.1, pp. 184-214, and [13]). 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 fingerprints. 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 hold. 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. References
Decoding Dates from Ancient Horoscopes By Wieslaw Krawcewicz 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.
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 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].
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: 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 wieslawk@shaw.ca.
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. 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 physicist, a
mathematician, and a computer scientist discuss which is better: a wife or a
girlfriend. New Tradition , 2003. Toronto Reproduced with permission from New Tradition
CIVILIZING EVENTS AND CHRONOLOGY
On the cosmic scale of time our civilization is very young. Conventionally it has been lasting about 8-10 thousand years since the beginning of the neolithic age. At that time homo sapiens (human beings) supplanted homo habilis (pre-human primates). Essentially, our civilization is the age of production. There are two necessary conditions to be fulfilled for any producing activity: 1) some natural resource must be available, and 2) a certain technolology must exist. Nature itself provides all resources, but any technology must be invented. An invention stems from a certain discovery, when ą man reveals a new law of nature or a new kind of a natural resource. The sequence "discovery - invention - new technology - new anthropogenic production" constitutes a civilizing event providing a new product or a new level of production for a user. Thus, civilization presents a wave-like process: evolutional periods (replication and reproduction of goods by means of conventional technology and experience) alternate with revolutional ones (when a certain technological burst takes place). Here the term "technological burst" is applied not only to engineering and manufacturing but also to culture, i.e. art, music and any other humane activity. So, in the widest sense, the term "civilizing event " seems to be more appropriate than the "technological revolution" when applied to a sharp rise of civilization upon a higher level. Each civilizing event (CE) is put into effect within its own interval of realization (RI). RI of a given CE can be defined as the while between the appearance of a new product (in the widest sense) or some well-known product by means of a new method, and the beginning of its mass consumption, rising our civilization upon a new, qualitativly advanced level. The latter corresponds to a moment when the number of consumers exceeds the percolation threshold for a 3-dimentional infinite cluster. Every new-born infinite cluster of human beings designates the creation of a new community of more civilized users. In a random system this threshold is equal to 1/6. For example, as far as the current population amounts to 6 billions, CE called "the world-wide Internet" came into being as soon as a number of Internet users exceeded 1 billion. One can see that even the larger part of the mankind may not belong to the new more civilized community. Some part of the population can stay on much lower levels, e. g. certain aboriginal tribes in South America, New Zealand or Central Africa.
Some most important civilization events are summarized in
Table 1. Since ca.
1500 A. D. (stages 15-22 in
The first conclusion reflects the fact that each epoch can be characterized by its own rate of civilizing. The second one stems from ramifying of CE's consequences and synergetics of simultaneous CEs. For example, artillery and printing are the CEs of the XV century and their RIs are evaluated as about 100 years. At the beginning of the XIX century RIs of steam-engine, vaccination and musical chromatic scale amounted to 40 years. At the beginning of the XX century RIs of current generator, radio and telephone etc. were already close to 20 years and so on. One can see that within the historically well-dated term since 1500 A. D. there are no "breaks of civilization" inspite of all wars, epidemic diseases etc. Neither are there any experimental data to surmise such breaks in the past since the Deluge. Analysis of more than 50 CEs since 1400 A.D. leads to a simple RI dependence on time t: RI (years, ± 20%) = 1500 - 0.2 t Here t is the
time since a certain start of civilization t0. This equation
presents a decreasing arithmethical progression and may be called an equation of
civilization rate. This rate is constantly accelerating while each century RI is
decreasing by 20 years. In order to define t0 one must fix the first step (the first stage of civilization) and evaluate the number of consecutive steps from the beginning up to nowadays. As the first step one can accept fire-sustaining. This is a genetical leap separating a human being from an animal which is genetically tabooed by fire. At this first step RI (1) = t1 (see Fig. 1). The number of consecutive steps can be estimated by means of formal logics based on causal relationship of CEs. As shown in Table 1 and seen from Fig. 1, the number of interpolated consecutive steps until 1500 A.D. amounts to 14 only (± 2). From this the current age of human civilization can be estimated as 7500 ± 2500 years. It is consistent both with the neolithic age and with the Byzantine Age of Creation. Study of consecutive steps (stages of CE) is a powerful method to define the right (not a certain "new"!) chronology. For example, cavalry and horse-driven transport could not physically exist in Western Europe until the XIII century because until then there had been neither natural, nor artificially-created conditions for horse-keeping in this area, contrary to steppe areas. Judging even from traditional references, at the beginning of the XII century in Italy or France a horse was extremely expensive - about $30000 if recalculated. Both in Germany and Russia the largest penalty - Wergelt - ought to be paid not for the murder of a free man or treason but for horse-stealing. William the Conquerer gathered only about half a thousand mercenaries mounted on horses out of the whole Western Europe and nevertheless he won the Battle of Hastings, because opposing Harald's troops, numbering more than 5000 soldiers, were on foot. And no cavalry could exist had not harness technology been developed before, no armoured free lance mounted on a horse could fight without stirrups etc. No good iron could be manufactured before cox-coal melting technology and no iron tools like a saw or a drill could have been produced earlier. No shaved faces of grown-up men could be painted before a razor had been made - every man was bearded, i.e. he was a barbarian. No self-portrait was known until Leonardo da Vinci - and that was the time when transparent glass was manufactured at first, so first glass mirrors appeared. No careful sea maps could have been drawn by any "Mercator" until Sir Isaac Newton invented a sextant in 1675 A.D. and Ch. Huygens made a pendulum clock in 1657. And no "ancient Codex Argenti" could be written in silver "Gothic" letters before Dr. Johann Glauber and his works in chemistry (1648-1660 A.D.) These examples demonstrate only a small part of results obtained by the CE method. The method was successfully applied by the author also to terminology and linguistics, basing on excellent works by É. Benveniste, a prominent French scientist of the XX century in this field. For instance, there were no real kings in Great Britain before Henry Tudor because, particularly, preceding rulers were addressed as "Your Grace" or "Your Serenity". Henry Tudor himself was titled as "Your Highness" and only his son Henry VIII became "His Majesty". There is also a strong suspicion that "half-Welsh" Henry Tudor was a close relative of John III of Russia and that all preceding history of Britain is invented by Sir F. Bacon and Co. and promoted by the genius of Shakespear or rather Shakes-PR. On the other side the history of Russia was created by Catherine II herself and her coworkers and finally edited by Nicolaus I in the XIX century. The same holds for the history of any other European country. (The history of Germany is fictitious as well as shown, for example, by Diter Foster for the times of Martin Luther. By the way, even in the XVIII century in England the word "german" was not yet associated with the German people but designated a relative by blood.) The real history of church began not earlier than in XIV century. It is enough to look through the Bible and you find out that, e.g., in the Apocalypse St. John mentioned glass transparent as crystal (Rev. 4, 6; 21, 18; 21, 21; 15, 2). And there is some revelation because technologically it corresponds to the end of the XV century as the earliest. And as St. Paul intended to visit Spain (Rom. 15, 28), it means that it could not have happened before 1479 A.D., because the word "Spain" appeared at that time firstly to designate the union of Castilia and Leon. Moreover, this word is neither Spanish nor Latin - it is of Balto-Slavonic origin as compared, e. g. with Czech "spojeny" = united. As well the Anglo-Saxon army was called "fyrd" - the word corresponding to contemporary "horde". Is there any difference between "Anglo-Saxons" of the VI century and "Tartars" of the XIII? There exists also an old engraving dated 1514 A.D. It demonstrates King Arthur fighting against Scosa for Paris! Thereupon Artur's army is under Swedish Tre Kronor banner and that of Scosa is under the Double Eagle!! Does not Scosa look like a Cossack? One can see that there are more questions than answers concerning conventional history. As plainly stated in Encyclopaedia Britannica in 1771 A.D., "History, with regard to subject, is divided into the history of Nature and the history of Actions. The history of Actions is a continued relation of a series of memorable events." It is quite right: conventional history is the history of Actions and made of "memorable events". This history is not natural and it should rather be called "political historiography". The real history of civilization is still to be written. And it is more than probable that the "New Age" of our civilization started with "Bethlehem" Supernova blown up in Taurus on July 4, 1054 A. D. Since then the pulsar has been radiating from the core of the Crab-like nebula. It may be poetically called "The Heart of Salvator". Now, if you look at Fig. 1 again, you can see that nowadays our civilization is close to its end because RI approximates to zero. The Internet is one of signs of a new-coming post-genome era. As soon as the mankind is able to change its genetics, it will unequivocally transmute into some other population and then this new population will start a new civilization of its own. A post-human being will differ from us as well as we differ from homo habilis. So we find ourselves in the vicinity of a phase transition, that is demonstrated in Fig. 2. In Fig. 2 Curve 1 reflects current crucial changes both in human population and energy consumption, dealt with the technological revolution having been lasting since ca. 1500 A.D. Curve 2 corresponds to simple human reproduction (which does not differ from animal one) and natural fuel consumption (wood, straw, manure etc.) that had been until 1500 A.D. If there had not been any technological revolution, now the world population would amount to about 800 millions only. If nothing is done to stabilize population, Curve 4 should take place. But hardly it seems real, because the mankind has not yet found a new more powerful and simultaneously much less harmful source of energy than nuclear fission. So sooner or later Curve 4 would convert to Curve 3: this one stems from a scenario for the Caribbean nuclear war of 1962, which fortunately did not happen. If it did, the world population would drastically fall down to animal-like Curve 2. (Note, that the same curve is consistent with "Golden billion" calculations and speculations.) If the UNESCO forecast comes to being (Curve 5), the world post-human population will stabilize at the level of 11-12 billions in the XXI century. Thus, the mankind is trying to change the type of its own phase transition from first to second order - in order to escape an apocalypse. Why did the phase transition of our civilization begin approximately about 1500 A. D.? It proceeded mainly from the two simultaneous civilizing events: fire-arms and printing. The first CE caused massacre of lower-civilized people and animals. Expansion of the new power lead to mass felling and destruction of flora. It started irreversable anthropogenic pressing on the environment. The second CE started politology: the technology of mass media pressing on mind. That is the point where the false conventional chronology and history comes from. Up to this point there is no discrepancy between Fig. 1 and Fig. 2. But the peculiarity is that demographers did not admit Curve 2 before 1500 A.D. because of the false conventional chronology created by J. Scaliger in the XVI century. They have to insert a number of breaks in it: population plateaus in 200-300, 1200-1300, 1400-1500 and 1600-1650 A.D., and "the Plague downfall" between 1300 and 1400 A. D., when supposedly ¼ of the population died. Demographers are forced to install these breaks in order to make demography consistent with fanthom data from different "ancient books". They have to evaluate the population of 50 millions at the beginning of the neolithic age - the number that is very far from archeological proofs. And by fixing simple human reproduction at the lowest possible level of 0.1% increase per year one can easily calculate down Curve 2 from 1500 A. D. (when the population consisted of ca. 440 millions people) that at the beginning of the neolithic age there was no more than half a million human beings transmuted out of homo habilis. The right chronology is needed badly if only for one reason: the false conventional history distorts the starting parameters of the phase transition that our civilization is experiencing. This can lead to wrong prognoses pregnant with bad consequences. Table 1Civilizing events and their interval of realization
Fig. 1Interval of CE realization (RI, years) vs. time (t, years) from the beginning of our civilization up to nowadays: RI (± 20%) = 1500
- 0,2 t Well-dated intervals (stages 15-22, since 1500 A. D.) are designed as the bold line. Figures designate consecutive stage numbers.
New Tradition , 2003. Toronto Reproduced with permission from New Tradition
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