B. Lukács

President of the Matter Evolution Subcommittee of the Geonomy Scientific Committee of the Hungarian Academy of Sciences

Co-president of the Geonomy Scientific Committee of the Hungarian Academy of Sciences

Member of the Astronomical Committee of the Hungarian Academy of Sciences

RMKI KFKI (CRIP), H-1525 Bp. 114. Pf. 49., Budapest, Hungary

lukacs@rmki.kfki.hu

First version: 28^th July, 2001

A. T. Fomenko, correspondent member of the Russian Academy of Sciences, differential geometer claims that (European?) history datings are fatally wrong before 13th century, AD. Historians seem generally believe that he is fatally wrong. I think that we do not understand something in lunar mechanics, and that something could be rather understood for the sake of history.

"New Chronology", sometimes also referred as Fomenkology, claims that there are great misinterpretations in history before the 13th century AD. King lists seem to be clones of each other, and datings by eclipses are wrong. In one book [1] Fomenko & al. suggest that Byzantian catalogs of rulers have been generated from one list starting from the Nikean emigrant rulers in the early XIIIth century and ending about the fall of Constantinople; moreover, Anglo-Saxon and early Norman king lists of England as well. In other books the authors suggest early confusions/falsifications of historic personae throughout all the Mediterranean [2]. Unfortunately, my Russian is too limited to get some finer details of some argumentations, but even the theses are quite revolutionary and disturbing in history. However I think, the problem can be (and indeed was) attacked from another angle too, which does not depend too much even on history.

Fomenkology uses statistical analysis to show that king lists are suspect of cloning; I know that statistical analyses of king lists are useful to help history [3], [4] and while significance of similarities/dissimilarities sometime are highly nontrivial, some dynasties indeed seem surprisingly similar for the patterns of ruling times. Maybe it is accidental, maybe it comes from a so far unknown consequence of biologic and sociologic life (dynasties must and do satisfy statistical laws [3], [4]), and maybe in some cases ancient historians did not have data at all, did not want to tell this, and took ideas from they could. Nobody doubts that great Titus Livius invented historical dialogues when it was necessary, why not ruling years. I would like to advice historians to accept the word of a high-ranking matematician in statistical business until somebody does not prove it oppositely. The results are extremely improbable for historians; however it is hard to compare the hypotheses that our standard history is correct but the king lists seem to be cloned in a very improbable way via mere statistical fluctuations vs. all pre-XIIIth century history is wrong but at least no improbable accidents happened. I would have arguments for the usual history and will mention some in the next Chapter which (to my knowledge) did not appear so far; but I think this line of argumentation is not strong enough for natural scientists. I am a physicist so it seems proper to remain at physical grounds as far as possible.

Chapter 2 confronts New Chronology with Hungarian (and Magyar) history. Sect. 3 discusses some problems of historical dating. Chapters 4 & 5 deal with problems about Moon’s motion. Sect. 6 formulates the physicist’s dilemma about history.

Chapter 7 analyses the best and newest Delta-T function (the difference between Ephemeris Time and Universal time) from -2000 to +2000; some anomalies can be seen. The next 2 Sections deal with famous ancient eclipses; and then I draw some Conclusions, but I am sure that this is not the last word in the question.

Just now state celebrations of the millenium of the Hungarian State are going. According to "orthodox" history (to be sure: orthodox in history; as for religion, the opposite to orthodox: filioque from foundation) and also to valid 1895 and 1999 decisions of the Hungarian Parliament the Hungarian State has the following prehistory. In the spring of 896 AD a tribal alliance of horsemen traversed the passes of the Eastern Carpathian Mountains from the East (some centuries before they seem to have been in the Maeotis region, maybe in Khazaria, maybe just beside) and conquered the Carpathian Basin, which, of couse, had autochtonous population too. The alliance had the name Magyar(s) or Seven Magyars, being composed of 7 (+3) tribes. The alliance was originally led by Prince Álmos (born cca. 819), who, however "could/might not enter the new home" and the conquest was performed by his son Árpád (died cca. 907). First the new power was a foreign body in Christian Central Europe, but at the end of the Xth century the leading family/clan recognised the necessity to "go to Europe", converted to western (filioque) Christianity, and suggested the same for the population. Then a convergence started [5]. Just at the first millenium the prince was crowned with a crown sent from Rome by Pope Sylvester II as King Stephen I as King of all the Basin, so King of Hungary. In Fomenko's New History the Pope did not exist, Rome still did not exist, and I wonder if King Stephen I would have existed (but we have his right hand, and the Crown). From that time Hungary is a multilingual country (until 1841 the official language was Latin) with Magyar as the biggest language.

Recently there is a second state in the Basin, Slovakia, and historians of Budapest and Pressburg (Bratislava) argue on a few (not too much) historical questions, but never on this. Slovakian loan words of Magyar, Magyar loan words of Slovakian, and Latin loan words in both seem to confirm the idea that first linguistic contact happened in IX-Xth century; still Slavic nasal vowels existed in proto-Slovak, and now fungus-type biological entities (mushrooms, by other approach) are called "huba" in Slovakian but "gomba" in Magyar; the two words forked from a Slavic ancestor whose first consonant was [g] and fist vowel a nasal back rounded sound changing in some Western Slavic languages into [u] in next century. I refer to [6], where my story is told by a high-ranking scientist of the Slovakian highly patriotic organisation Matica Slovenská.

Now, it seems that the above statements are contrary to established Fomenkology. In 1000 not only Sylvester II, Pope of Rome was lacked because the Apostolic See in Rome was not yet erected; Christianity did not exist either because Jesus Christ would have been born cca. in 1054, in the future. However archaeologists of Burgenland (now in Austria, until 1920 Hungary) find remains of Petcheneg bodyguards of an early Hungarian King, Salamon [7], from the XIth century, Croatians know about the good relations of the Hungarian and Croatian royal families in mid-XIth century and a personal union (of England-Scotland type) existed between Hungary and Croatia between 1091 (or 1102) and 1918. Therefore Hungarian history represents a strong, independent body of data (practically not used so far in Fomenkology) to check the theory.

I am not going to make this check just here. However I mention three counterarguments (to orthodox history) simply to demonstrate that history is not easy and simple.

Just now some geneticists are unable to detect Magyar genes in Hungary [8]; if Magyars in the IXth century traversed a great distance from East, we do not expect normal Central European gene distributions for them. Maybe Magyars do not exist? However observe that the Magyar language is specific. Its only far relatives in Europe are Finnish, Estonian and Lapponian; its nearest relatives are Vogul and Ostyak in Western Siberia, beyond the Ural Mountain. The first person recognising the latter similarity (or, by another interpretation, Magyar speakers East of the River Don) was humanist Enea Silvio Piccolomini, later Pope Pius II (in Cosmographica, 1458). Now, the Western Siberian language must have been carried to Central Europe anyway. I must admit that experts cannot yet single out the proper gene combination, which is strange; however Ref. [9] can detect something characteristic for Hungary at least on the almost gene-free Y chromosome.

While Hungarian sources are quite consequent in the date of conquest (889, 895, 896...) there is an important source giving 677. This is the so called "Vienna Illustrated Chronicle" or "Illustrated Chronicle of Mark Kalti"; a Hungarian book, you can look for it in [10] (but I doubt if you will). The text tells that the Magyars "came out of Scythia" in 677 AD, 104 years after the death of Attila, during Emperor Constantine III and Pope Zacharia. Now, the data are inconsistent. According to orthodox history the death of Attila the Hun is 453, and 453+104=557. Note that this Emperor we number IV. Obviously the chronology of humanists was not yet ready at the completition of the chronicle; the most probable date of the birth of the chronicle is 1370, pre-Petavius and pre-Scaliger. However, the date can be completely independent of humanists, and real. Something did happen about 677. The foundation of present Bulgaria by Khan Asparuch is 681, and archaeological observations clearly show the appearance of a new population in the Carpathian Basin from the East in that time.

Some scholars suggest that the fate of Prince Álmos, old and prophesized leader (begotten by the holy bird turul; togrul in Turkish, astur in Latin and maybe hawk, maybe kite, maybe gerfalcon in English, but maybe he is the ancestor of all predator birds, Kök Tängri himself, the Eternal Blue Sky) of the Magyar Migration), who "might not enter" the Promised Land of the Carpathian Basin, is copied from Moses. Yes; it is possible. But it is quite OK in orthodox history. The Magyar tribes crossed territories previously, where they might have learned Old Testament stories. Nestorian Christians is one possibility, Karaite communities on the periphery of the Khazarian Empire is another. Note that the Kabars, changing sides from Khazarians to Magyars near the Don could be almost anything for religion and some Old Testament religion (maybe Karaite [11]) is probable for them [5].

I mention one more possible check, on which work is just going. There is a formation near Szilvágy, Western Hungary, which looks like a meteor crater [12], [13], geologically recent. A Ravenna official Annales, dated by the orthodox history to mid-Vth century contains a one sentence entry telling that (by modern calendar) on September 7, 456 the city of Savaria "eversa est", so broke down. Savaria is the Magyar Szombathely, in extreme Western Hungary along the Amber Road, and archaeologists see traces of earthquake on the ancient walls. Since also such (but weaker) traces can be seen in Scarbantia (Sopron, Ödenburg) in late Roman context, and the territory is generally tectonically quiet, the two earthquakes are probably the same. Now 1) it is almost sure that the demolishing earthquake did not happen in the time of the Kingdom of Hungary; 2) it may have been the effect of an impact of Tunguska magnitude. Such a catastrophe must have been copiously recorded in the Western Roman Empire. However everything is OK in orthodox history because Rome (Ravenna) withdrew the military and the civil government from Pannonia in 455, 2 years after the premature death of Attila, tanhu (Great King, Emperor or Son of Heaven) of Huns.

Eclipses (and especially, solar eclipses) were extensively used for dating history. Near-total solar and lunar eclipses are very easy to observe and were frequently recorded by historians. Now, lunar eclipses are not infrequent, but solar ones are restricted to narrow strips, so they are not too frequent at the same place. Therefore in principle the dating is simple. We have the place of the eclipse from an old record, and also we have some relative time. (2 years before the battle...) Celestial mechanics is able to calculate backward the eclipses at a given place, so we have a list of possible dates, and we can select from the list according to some extra information.

However the dating cannot be done exclusively within celestial mechanics. Eclipses somewhere on Earth are frequent, especially lunar ones. Namely, Earth's shadow cone can totally envelope Moon, and then Moon darkens on the sky everywhere. In contrast, solar eclipses are total (if at all) in a narrow strip; elsewhere partial or even not that. So lunar eclipses can be used to make the chronology more definite if we know the date approximately (in some cases for 5-10 years). Total solar eclipses can be used for wider temporal range. E. g. the famous total eclipse on 11th August, 1999, predicted correctly by Nostradamus in 1555, was the only total eclipse of the Carpathian Basin in the XXth century.

Let us see one definite example. The chronology of pre-Babylonian Mesopotamia is very much supported by the lunar eclipse of Shulgi, King of Ur (and whole Sumer and Akkad), from the Ur III dynasty. The eclipse was recorded synchronously, and in next year, when Shulgi died, became regarded as an omen, very important for the developing Sumerian, later Babylonian experimenal astrology. (Shulgi died in his 48th ruling year, so the death cannot be called premature.)

Now, historians know a lot of Mesopotamian rulers, because brick tablets carrying cuneiform writing are rather persistent. Some more or less contemporaneous King Lists are known with ruling years and for other kings one can substitute reasonable lengths. In this way 3 concurrent chronologies appeared: High, Middle and Low, with some 120 year difference. Maybe Middle is most probable in pure historical context; the problem is caused by our ignorance about some successors of Hammurabbi, and even more, about the early Kasshu rulers after the Hittite "Sacco di Babylon". The respective years calculated for Shulgi's eclipse are 2106, 2050 and 1986 BC. The most probable is Middle Chronology.

Even that Middle Chronology is not unique. 2 other lunar eclipses in 2055 and 2060 seem almost as good, being this eclipse lunar and lunar eclipses on a particular place are not infrequent.

However some historians seemed to like to reduce the years of obscurity, say, around 1400 BC; this would have solved some purely historical problems which I will not discuss here. They asked the help of the particle physicist Gurzadyan, who reconsidered Shulgi's eclipse with the result that the 2050 eclipse does not fit to the record. The record tells that the eclipse was on Simanu 14. Lunar eclipses are possible only on 14th or 15th days of Mesopotamian months, so the day is not informative; but month Simanu is an end-spring/early-summer month. But the record, in addition, states that the eclipse started after moonrise. Now, Gurzadyan claims (the reason for this verb in celestial mechanics will be clear later) that the 2050 eclipse started below the horizon; and the first possible such eclipse is June 27, 1954 BC [14]. This creates a Lowermost Chronology, and has serious influence on history around 1400 BC [15]; earlier chronological items are only shifted rigidly upwards for 96 years. (King Lists are detailed, without internal contradictions, between Shulgi and Hammurabbi in Sumer and Akkad; while ruling years are mising for kings 4-17 of the Kasshu dynasty and of them we do not know even the names for 11 kings.)

But then Assyrian and Hittite histories must be reconsidered. They are poorer in dates, but long enough. Now, without details. The 39th Assyrian king is Shamshi-Adad I, who is long time established as "elder contemporary" of Hammurabbi. According to Gurzadyan's chronology his closing year would be 1685. Then come badly dated Kings, and the next well-dated Assyrian king is Enlil-nasir II, 67th King, dated to 1430 as starting year [16], and these newer Assyrian dates hang on another eclipse: the solar eclipse on June 15, 763 BC [14], [17] (Stockwell, however, puts it one year later). So the rigid upward motion does not change Enlil-nasir II.

There are (on the King Lists) 27 kings between Shamshi-Adad I and Enlil-nasir II. Of them, the lists do not give the years of 9. Adding up the remaining ones we are at 274 years. So in the Lowermost Chronology of Gurzadyan -19 (!) years "remain" for the remaining 9 kings.

Of course, the lists are not full-proof, in Assyria's history usurpers and parallel rulers are not unheard of, and one may suggest that badly documented kings may have had short rules. However, the corrected eclipse (best according to our present astronomical knowledge) leads to problems in Assyria while solves some in Babylon.

In Hatti the Lowermost Chronology would leave 120 years between Murshilish I (sacker of Babylon) and Shuppiluliumash I, who was in correspondence with the widow of Tut-ankh-Amon. But into this time we would have to push 14 kings, too much.

Postponing now the problem of eclipses below the horizon, we have seen that the 2050 BC lunar eclipse could be 2055 and 2060 as well, and with alternative historical hypotheses, 2106 or 1986. If we do not know even the approximate date, an eclipse record would give "only" a list of alternatives.

The layman in astronomy believes that modern astronomy & physics can calculate the orbits of Moon and Sun in the skies for any time. (In this context most historians are laymen, many matematicians and even a few physicists.) Indeed, Nostradamus' prediction for the August 11, 1999 total eclipse was correct, including the almost-meridional position and the horoscope (albeit the astronomical description is somewhat veiled in his text; for any case as a prophet Nostradamus failed because he did not see that Pope Gregory VII would change the date by 15 days). Astronomers know better. Namely, the Sun-Earth-Moon system is not a three-body problem of celestial mechanics. Earth is not point-like.

Since Earth is not point-like and has a hydrosphere, the tidal "forces" of Moon and Sun make it non-spherical; plus there is its expressed oblateness. But the latter is at least constant, while the tidal peak goes around, cca. together with Moon. And this peak acts back on Moon. Since the tidal peak is coupled to the main mass of oceans and to the crust by friction, it is not just under the Moon, but somewhat forward, and its position cannot be calculated from celestial mechanics. (Plus even without friction the peak is a combined effect of Moon and Sun.) The forward peak accelerates Moon, which, therefore, spirals outward, and so her angular velocity decreases but her orbital angular momentum increases. Plus, if the Brans-Dicke modification of the Einstein equations [18] be true, that should be another source of spiralling out; the Brans-Dicke modification is conform with all established principles of General Relativity and its existence is a matter of observational checks. If the correct equations are the modified ones, then, in first approximation, Gravity weakens as 1/(t-t_o) and, guessing that then the only nonarbitrary startpoint for t_o would be the Big Bang, the corresponding relative decrease in Moon's orbital angular velocity would be ~10^-6/(century)², i.e. (0.1-1)"/(century)². (The exact prefactor is unequivocally determined by t_o.)

So we cannot determine a term in Moon's motion theoretically because i) we cannot calculate tidal friction from first principles; ii) we still do not know if General Relativity is valid in its Einstein or Brans-Dicke form. In addition, other effects may appear on the Earth-Moon system, but it is pointless to discuss unknown effects of unknown agents. Only: they may be present. (Magnetic forces, e.g.)

Tidal friction must exist, since tides exist. It was suggested first at the second half of XIXth century [19], but astronomers generally chose alternative ways. Stockwell [17] e.g. refuses the idea, but he applies a correction term of different form on Moon's motion. Also, in the Hill-Brown theory of Moon (see e.g. [20]), dominant until 1954, a fully empirical term appears in the mean longitude of Moon, with amplitude 10".71 and period time 257 years. The term was necessary for fits to eclipses since telescopic times, but it was a fitted correction term and nothing else. On the other hand, different terms with different long-time behaviour would lead to different postdictions to ancient eclipses. For data of estimations for tidal friction, both from observation and from mechanisms, see e.g. Ref. [21].

History used eclipses to pinning down moderate past uncertainties around 1900; Ref. [22] is only one example albeit very important, and after some time the attention went elsewhere. But those results were got via empirical corrections.

And from 1954 even some astronomers believe that now lunar motion is described by correct and well-reasoned equations. The Improved Lunar Ephemeris [23] distinguishes between Universal Time and Ephemeris Time. By other words, there is a time in which the solutions of Newton equations are taken, and there is another time in which the diurnal motion of Sun is uniform in mean. The reason is the secular change in Earth's rotation. Now, the Improved Ephemeris introduced a correction in the mean longitude as

(1) D l = -8".72 -26".75t_c -11".22t_c²

where t_c is the time in centuries. This term is empiric, but at least we seem to see its reason; and in exchange the "great correction" of Hill and Brown is removed. And if we tell too much that we already have the perfect equation, then come the matematicians and find the flaw. In this case came Fomenko [24].

Namely, if the only difference to the "trivial" lunar motion is the quadratic form between universal and ephemeris times, then there is a constant (negative) acceleration of Earth's rotation. Then this constant deceleration is caused by some constant agent, say, the tidal friction whose value may be constant indeed until sea level does not change too much. It did not change too much in the last 4000 years, seacoasts did not change too much. Then maybe the first two terms in (1) are initial conditions and the third is empirical, but historically constant; now we can recalculate all the eclipses.

Newton discussed the situation in 2 papers at the beginning of 1970's and found that as if a square wave propagated in the motion of Moon between 700 and 1300 AD [25], [26]. But I would rather put the problem a la Fomenko.

Lunar and solar eclipses happen if the longitudes of Moon and Sun are equal up to 180°. Then one combination of the mean motions appear strongly in the formulae, with an expected correction term similar to (1) for form. We can do the following. We use (1) but with a free parameter instead of the coefficient of the quadratic term which we simply call D''/2; and for secular changes we fit D'' to observations in the past.

Then the surprising result is as follows. From cca. 1300 AD upwards D'' is cca. -20"/(century)². Since the present value in [23] is 22".44/(century)², this means that D'' is practically constant, and we can be happy.

There is something uninterpretable between cca. 700 and 1300 AD. Maybe astronomy was bad; however, as told, positions of solar eclipses are rather sensitive, and the visibility of a total solar eclipse does not depend on quality of astronomy.

And before 700 AD points are on another constant D'' line, with D'' almost 0!

Now, this is really something. Another constant negative D'' would be surprising but we could argue it away, referring obscurely to changes in narrow sea-channels and such. But a value D''=0 is either absurd or very improbable. Tidal friction must have existed in 456, 455 or 453 AD, because oceans existed; maybe something else (unknown) balanced it; but almost totally?

Then Fomenko suggests that calendrical dates (the X axis of his diagram) are wrong and recalculates them. Some items will be discussed in later Chapters, but let us tell here that the results are devastating for our historic theories. For example Jesus was born around 1054 AD (the year of the Crab Supernova, so maybe it was the Bethlehem Star (cf. [27] and citations therein)), &c.

I mentioned some counterarguments in Chapter 2. More counterarguments are in World History. However one must be careful, and physicists should rather be conform to the tradition of physics. The next Chapter is devoted to the formulation of the physicist's dilemma. (Unfortunately G. B. Shaw gave the title The doctor's dilemma instead of the obvious The physician's dilemma to one of his plays.)

Physics does not work against tradition; but it is independent of tradition. For us Aristotle can be confused with layman's science, but he differed very much from everyday opinions. For example, for him it was clear that a sphere of heavy matter around the center of Gravity does not need support, moreover that there is and can be nothing beneath it; an idea unclear even for some physicists of that age [28]. Also, instead of popular creation acts and traditions he voted for an infinitely old world with infinite future [29], simply because scientific arguments were rather for it. Later, however, biblical traditions (not fundamentally contrary to Greek ones) came over, and when physics became strong again, it did not confront with them for long time. Not because of conformity.

This work is not of philosophy and not of history of science; detailed argumentation, if at all, will appear elsewhere. However let us see one example: the age of World.

Until Galileo, World mainly was something finite ending with the sphere of fixed stars. It had one main source of heat: Sun. For Aristotle, the source of this heat was friction [30], [31], and the dangerous Heat Death was avoided by the exactly stationary work of the Prime Mover of the Universe [31], the source of negative entropy production, located "at the perimeter" of the Universe [32]. If Prime Mover maintains a constant angular velocity forever, Sun has heat output with constant rate forever.

Then came Galileo, dethronizing the Prime Mover. Then Sun needs some inner source of heat. Let us take some tentative mechanism. For example, ignition is possible (gunpowder can be ignited without atmosphere). Taking the best known fuels and the known distances we get cca. 10,000 years at constant rate, and not too different results with more realistic burning mechanisms [33].

The Bible tells cca. 6000 years. Archbishop Ussher in XVIIth century calculated October 23, 4004 BC for Creation from the Bible and his contemporary, Newton agreed in the time range [34]. Until the early XIXth century no mechanisms were suggested seriously for longer solar energy output. So contemporary physics and contemporary history/tradition told more or less the same.

Physics revised its opinion in the middle of the XIXth century because Kant, Laplace and Helmholtz suggested good mechanisms for solar energy output. Gravitational contraction and similar processes (e.g. infall of "meteors") could maintain the output for cca. 30 My. Slightly later Lord Kelvin found 40 My for Earth's age from heat loss. This physics did do, in spite of tradition, and was not disturbed. Then about 1900 Becquerel, Maria Sklodowska and Pierre Curie found and clarified up radioactivity, and in a few years Earth's age was revised to cca. 2 Gy. Later it was corrected to 4.55+/-0.07 Gy and from cca. 1945 we know that Sun's age is cca. 4.5 Gy too. Now we believe, on purely physical grounds, that the Universe is cca. 13 Gy old, and no tradition influences physicists in this.

Maybe we are wrong and then the number will again be recalculated; but we are not wrong because of historical or religious tradition.

But if so, then it would be against rules and tradition of Physics to take sides on the grounds of historical tradition. On the other hand, Common Sense must be preserved and used, albeit not against Physics. This is, briefly speaking, the physicist's dilemma.

In the next Chapter I formulate the problem from quite recent data (Fomenko's original paper [24] is now 20 year old).

Delta-T is a terminus technicus of standardization, time measurements and such. We believe that atomic clocks show the "true" time, so they are periodic. Reasons of physics could be listed but will not here. We do know that Earth's rotation is not uniform and we know at least some reasons why. So there is a Universal Time and an Ephemeris Time, and Delta-T is the difference; for more detailed definitions see the proper standardisation literature or at least [35]. Universal Time is the inheritor of Greenwich Mean Time in which (except maybe for shortrange fluctuations) one day is 24 h, or, on more physicist's language, one rotation of Earth is 23h 56m 3s.09. On the other hand, Ephemeris Time (now rather Terrestrial Dynamic Time) is independent of Earth's rotation. So one expects their difference as

(2) Delta-T = A + Bt_c + Ct_c².

A and B are initial conditions, and if C is found constant, then

(3) C = D''/2

Now let us look for Delta-T data. In the last decades it is kept by Offices of Standards for leap seconds, in the last 4 centuries it can be calculated directly from telescopic observations and clock times. For earlier times it is calculated from observed eclipses. I am not interested here, exactly how; according to best astronomy and orthodox history; for the details see [36], a quite new compilation on Internet is [37]; it refers the 2000 value of Delta-T already as "observed". It gives the observed Delta-T's for each last year of centuries from 1700; the data from [37] between -500 and +1600 in the same manner; and an earlier series [38] between -2000 and +900. Since the two series almost match smoothly at -500 (and one author is common in them) I simply appended [37] with the earlier part of [38]. Let us proceed.

Fig. 1 is the curve. Indeed the switch to one series from another cannot be seen (the difference at -500 is less than 4%). For first sight the curve is quadratic. However it is not really.

Fig. 1

Fig. 2 shows the best quadratic fit. The weighing is trivial, being the series equidistant. Still the curve seems quadratic. However there are 3 strange features. There seems a "disturbance" around -600, another around +400; and the modern, "telescopic" part is impossible: the parabola reached its minimum in +1569 increasing in the whole age of modern astronomy. The overall curve of the last 4000 years is not "our" Delta-T; something does not seem to have been stationary.

Fig. 2

Fig. 3 shows the curve + the best fit from 1300. This period is "good" according to Fomenko, and no "square wave" is detected by Newton. Now the curve is reasonable, the 8 points of the fit are not far from a quadratic function, with minimum in 1823, with some 2.5 second. But this fit definitely does not match the ancient data.

Fig. 3

And then Newton and Fomenko give an idea [24], [25], [26]. We are now at sheer phenomenology, but they agree that some behaviour before 700 AD seems to differ to the present. Also, I do not want to go too far back, when even orthodox history has some doubts in dating. So let us see the curve between 700 BC and 700 AD. That fit, with the original curve is Fig. 4. It definitely does not match the modern data. The quadratic function reached its minimum in 1518 AD. However it is good for classical antiquity, and it is not too bad before that too.

Fig. 4

Something strange can be felt at late antiquity or Early Middle Ages; of course, I do not know what.

Now, indeed, either 1) something drastic happened with Earth, Moon, or I do not know with what roughly in the time of the "square wave" of Newton; or 2) dating is seriously wrong before 1300 AD as claimed by Fomenko; or 3) some more complicated scenario holds. "Possibility" 3) will not be discussed here because it contains such options as e.g. a small but measurable change of gravity on historical timescales, which may seem harmful enough for laymen and a desirable alternative to historians, but it is more dangerous and unbelievable for physicists than any of 1) and 2); and Earth, abode of laymen and theater for historians is kept together by gravity; and we do perform measurements for the constancy of several constants of theories. Let anybody be content with the alternative 1) or 2).

OK, physics & astronomy at the present moment cannot show up the cause of the change of the curve on Fig. 1 (or of the disturbances seen on Fig. 2). Still, it may be able later and I would like to emphasize that this is a real problem. In the 60's, when physicists discussed time standardisation, one opinion (although maybe not the majority one) was to remain with a time standard from celestial mechanics; on the ground that the existence and causes of disturbances can be reconstructed even after the disturbance via celestial mechanics even if the disturbance itself broke down the observations transiently, while atomic clocks can in principle be destroyed without possibility of later reconstruction. Now we see that (so far) it was easier to boast than to work. But, of course, the task is rather hard, nobody expected it really, and I think, we shall perform it in reasonable time.

But historians and mathematicians do not have to believe the mere self-confidence of a physicist if he cannot even tell how he will do it. So now let us continue on the languages of history and mathematics. This Chapter, I think, has demonstrated the existence of the problem.

Fomenko's solution is clear and simple, as expected from a mathematician. The dating before 1300 AD is wrong; let us make a better one.

I could easily rescale axis X on Fig. 3 in a way that it be quadratic everywhere. Calendrical years before 1300 AD would change smoothly. It would be something similar to "calibration" of C14 data [39] because of smooth changes in ancient C14 levels. Unfortunately this easy way cannot be followed now; for example because the transformation would not keep seasons. Let us see one item from [23]; then confronted it with diverse sources.

Fomenko tells that one very important sequence of eclipses is the 3 eclipses in Thukydides. Let us see the eclipses, from the original. These 3 eclipses are the only ones preserved from the Pelloponesian War, and help(ed) to date a very decisive period of ancient Greek civilisation. Because I am neither historian nor linguist, I use the modern English translation [40] and do not go back to the Greek original. If one detects a misinterpretation, contact the historian community.

Happens at the first year of the War. The original text is in italics. The same summer, at the beginning of a new lunar month (which seems to be the only time when such a thing is possible), there was an eclipse of the sun after midday. The sun took on the appearance of a crescent and some of the stars became visible before it returned to its normal shape. And my comments (which you do not have to accept): 1) Thukydides' comment (the bracketed term) indicates that he did not know the theory of eclipses but accepted the opinion of an expert; 2) Thukydides does not seem to have been eyewitness; 3) either the eclipse was almost 100 % (crescent, but stars), or it was total for a short time, or it was partial for one observer, total for another, and Thukydides innocently merged the two reports.

At the very beginning of the following summer there was a partial eclipse of the sun at the time of the new moon, and at the beginning of the same month there was an earthquake. Obviously Thukydides was not an eyewitness, does not tell any other detail. But very possibly the eclipse was seen from the Balkan.

It happens at Epipolae, near Syracusa, as we shall see, in summertime. When everything was ready, and they were on the point of sailing, there was an eclipse of the moon, which was at the full. Most of the Athenians took this event so seriously that they now urged the generals to wait, and Nicias, who was over-inclined to divination and such things, said that, until they had waited for the thrice nine days recommended by the soothsayers, he would not even join in any further discussion on how the move could be made. So the Athenians, delayed by the eclipse, stayed on afterwards. And because of the delay, the Athenians finally lose. Prisoners of war were put to work in a stone quarry, where first they suffered "from the heat of the sun", later "came the cold autumnal nights". So the eclipse was in summertime. Also, the text shows that Athens, claimed to be most intellectual in Greece, was generally as ignorant in astronomy as any else city. Common sailors and soldiers are one thing, but General Nikias also considers the lunar eclipse an omen, not a natural and predictable event. Maybe we confuse Pericles' Athens with Aristotle's Athens, a century later.

Now, let us go step by step in dating. Diodorus Siculus used the Olympic dating, so we have a Greco-Roman relative chronology. This also would indicate that classical antiquity was at least one millenium long, or sources are forged. True, there are inconsistencies in that counting, e.g. about one hero at a turning point of civilisations, Hermeias, Tyrant of Assos and Lord of Atarneus, father-in-law of great Aristotle, but not more than one or two Olympiads, maybe caused by pen errors and clumsy number system. Also, we know that Perikles, longtime leader of Athens, dies at the beginning of the Pelopponesian War.

As first approximation of dating I go back to founder of classical physics, I. Newton, [34], [41], cca. at the end of XVIIth century. Already the beginning of the Pelopponesian War is 431 BC at him, so this is a consensus of the West, going back to the Olympiad chronology. Good: then we check the dating. (Anyway, humanists as Scaliger and Petavius, could calculate fictitious eclipses, as, we saw, Nostradamus could do future ones.) But in 1891 Stockwell [22] tells: "Now, although astronomers have never been able to find an eclipse that would accord with the description of the first one [the 431]...to magnitude, they have found that eclipses occurred in the years 431, 424 and 413 B.C., which were visible in Greece... And hence that date has been universally adopted for the beginning of that war, because there are no other years near the period of time, in which eclipses visible in Greece occurred in that order."

A quite sound reasoning, if we are convinced that the era is not wrong by centuries. We saw that Thukydides' description of the first eclipse is slightly self-contradictory, and he was no eyewitness. But it goes further as follows: "But I have shown in a former number of this Journal that my corrected elements of the moon's motion give the first two eclipses recorded by Thucydides, magnitudes which accord well with the description of the historian." He refers [17]; there, by one correction which helps many eclipses gets for the 431 one totality at the Hellespont and 92 % in Athens.

So far so good. But the correction is arbitrary, however fitted to several events. Now comes Fomenko [24] and tells that if we want to keep D'' on the recent value, then the first possible triad starts in 1093 AD!

The reason that time cannot be slightly and continuously rescaled is seen here. Now we have not one eclipse but three, separated by known intervals, and in two cases in known seasons. Continuous rescaling might put a summer eclipse to winter, or so.

No doubt, Fomenko is right that some explanation should be found. As a matematician, correspondent member of the Russian Academy (in Moscow), and chair of university department he has the right to demand that his word and curiosity be taken seriously. I happen to remember that before 1991 Westerners were much impressed by Soviet academians (Moscow) in physics and mathematics, and were eager to answer them. I do not believe that the modest shrinking of the state from Soviet Union to Russia can support such change in awe. I would give an answer if I could. Maybe it is not my task alone. Of course, we do not have to; but are we not interested in an answer at all?

However, the problem is even more complicated. Let us assume for a moment that Fomenko's solution is the solution. The Pelopponesian War, however, belongs to the East. If it started in 1039, then it might go on when Jesus was born, but it went on Byzantian sphere of interest. The Pope and the Italian humanists could not falsify the War in 1300. Findings are found in these centuries in Greece. OK, they may have confused the data, either by ignorance or deliberately. But one cannot choose numbers by random which are good for 3 coupled eclipses. And to make a falsification which is not too good without correction but becomes excellent with a fitted correction (albeit of arbitrary form) is something not happening in real life.

I am not nearer to the solution than in the previous Chapter. I am going to tell one more story and then finish this work. It has a sequence number I and I will write II if I can tell something more.

Plutarch in the "De facie in orbe Lunae" mentions a total solar eclipse. Stephenson & Fatoohi try to reconstruct the eclipse [42]. They guess that the central figure, Lucius, is Plutarch himself. It is quite possible. They guess that he, so Plutarch, saw the eclipse with his own eyes. Possible. They argue that the eclipse was total and Plutarch saw the corona. I am not convinced. It can refer to an annular eclipse; from the text it does not follow that he speaks of the actual eclipse at all. However it is true that in sections 931D-E he speaks of a total eclipse; with stars appearing, temperature dropping, and beginning just after noonday [43]. Let us assume that it was a real eclipse and either Plutarch saw it or somebody giving him later a very detailed description.

Let us again accept first orthodox (Western?; catholic?; filioque?; Papist?; humanist? Italian?) history. Then the eclipse may have happened somewhere in the Mediterranean, most probably in Greece, Rome or Alexandria, toward the end of 1st century AD. Now, it seems that we have 4 and only 4 eclipses, of which 2 are more probable (reasoning is in [42]). Eclipse 71 AD was total somewhere in Greece, and that is the best anyways; except that calculations reconstruct it to 1 hour before noon. The authors tell that "the Sun would then be almost at its maximal height", and that "just after midday" was a "rhetorical exaggeration". Note that such an agreement was reached after corrections of type [37] & [38]. (It was, in fact, a third paper, but let us not go into details.) So even after the Delta-T corrections (empirical) there remained a cca. 5000 s shift? Or is this eclipse also something about 1100 AD, according the lines of Fomenkology?

I do not know, but I would be quite happy with such an agreement. For 2 reasons.

1) Assume that not Plutarch was the eyewitness; or it was he but wrote the text after some months. Then no "rhetoric aggregation" is needed at all. He remembers or his informer remembers that Sun was high, about noon. After some time he forgets that it was just before noon, and there is no way to consult journals &c.

2) The deviation from 3-body calculations comes from 2, correlated but different sources. Earth's rotation is slowing; Moon is spiralling out and slowing. It is not true even with purely gravitational coupling that the two effects are trivially proportional, since Sun makes tide too; but other couplings are sometimes also assumed. (Think, e. g. on magnetic forces from Sun, Galaxy or as you like; interactions of core with mantle or of mantle with crust; &c. The deviation from quadratic form on Figs. 1-4 are not yet explained.) Now, for a complete agreement Earth must have performed -20° extra rotation in 700,000 full rotations. This is a cumulative effect; but we calculate across the suspected disturbances about 400 AD (see again Figs. 1-4). It is possible to modify minutely so Earth's rotation and Moon's orbiting that an eclipse in Greece remains an eclipse in Greece, but with 1/20 less rotation in 700,000 rotation.

And now back to Gurzadyan and Shulgi's eclipse. If one explains the superfluous 9 Assyrian kings, then Shulgi's eclipse may have been in 1954 BC. If that is a big problem, then look. Modern calculations for the 2050 BC eclipse give that, contrary to the report, Moon rose already partially eclipsed, so local time was out of phase by cca. 2 hours (too early). At Plutarc's eclipse we get that it was too early by at least 1 hour. So if we explain one of the problems, the other may get its explanation automatically.

Of course, this is not the explanation.

We, physicists, astronomers and matematicians, cannot date history from first principles. We can, if historians discussed the problem and accepted an opinion. C14 dating is quite objective, but it dates something unearthed by archaeologists. If somebody smugglesa fresh bone into the grave, then gives to the nuclear physicists, the analysis will be ghood, but not the dating of the grave.

Dozens of nations in the last 2 centuries invented "national histories". I, as the most physicists, accept that objective outer reality (as opposed to internally existing mindstates &c.) does exist. If so, the task of all scientists and most scholars (except e.g. psychologists) to approach and recognise this, objective, world, and so the objective history. If two histories contradict, at least one of them is false; maybe both. Dr. Fomenko started a research which demonstrates that falsificators do this on their own danger; and danger or not, we can recognise the falsification. If history is important, then checks are important too. Altough I will not do here, I could make a long list of proven or suspected falsifications made in accepted history. But statistics and mathematical logic can reveal falsification even if they cannot tell what is truth.

Also, it is better to accept that we do not know enough the Earth-Moon system to calculate back 4000 years without historical help. No problem. Physics does not need the dating of Shulgi, greatest king of late Sumerian age. No physical problem is connected with Shulgi (so far at least). It seems that the Earth-Moon system did unexpected things in the past.

We, in 2001 AD, do not possess the fullness of knowledge. There are things we still do not know. Academician and department chair (differential geometry) A. T. Fomenko showed us a problem. The problem is connected with our own Earth as a planet and with celestial mechanics. The latter is a star territory of mathematical physics and physical mathematics for 2500 years.

I do not believe Fomenko's explanation. My guess is that it raises more problems than solves. It would definitely solve the initial problem, of course.

Now, if I have the right not to believe, everybody else has too. But no physicist has the right to tell that Fomenko cannot be true because he is against established history, which is only high-level tradition. Nobody has direct knowledge about events 1500 year old.

Of course, there are probabilities. Neo-Latin comparative linguistics uses old Latin manuscripts, and then, with simple evolution laws, empirical, of course, gets quite satisfactorily 10 modern languages from one. If Fomenko's scenario is true, then never was a Latin language and Latin manuscripts were forged in Renaissance; maybe earlier illiterate Italoceltic barbarians lived in the Northwestern Mediterranean with languages similar to each other; and still they evolved as if from a common language. And, what is more, some intellectuals 600 years ago must have reconstructed correctly, or at least self-consistently the ancestor of 10 modern languages. To do this they should have had a linguistic theory as versatile as our present one. I think we have better chance to find the explanation for Figures 1-4). In addition: what is with Hungarian history?

We can tell Academician Fomenko that we do not believe his history until he does not produce a history working as well and smoothly as the orthodox one. Good. But he may answer he will not believe ours until we do not show him why Delta-T is not even approximately quadratic throughout 4000 years. Our task should be simpler but it has not yet been done.

The author would like to thank Dr. A. Shanenko for giving some information about New Chronology, and to Dr. K. Martinás for illuminating discussions about Aristotelian physics. Of course, the author is responsible for all conclusions. Also, the author hopes he will be able to write a Part 2.

****

Written during the millenary celebrations of the Hungarian State, founded with Western Christian rite in 1000 AD.

[1] G. V. Nosovskiy & A. T. Fomenko: Rus’ i Rim. Pravil’no li my ponimaem istoriyu Evropy i Azii? Izd. AST, Moscow, 2000

[2] G. V. Nosovskiy & A. T. Fomenko: Imperiya. Faktorial, Moscow, 1995. See also on Internet: A. T. Fomenko & G. V. Nosovskij: New chronology and new concept of english history. British empire as direct successor of byzantine-roman empire. http://kulichki-lat.rambler.ru/moshkow/FOMENKOAT/engltr.txt; G. V. Nosovskij & A. T. Fomenko: Novaya hronologiya i koncepciya drevney istorii Rusi, Anglii I Rima. Fakti. Statistika. Gipotezy. http://moshkow.perm.ru/lat/FOMENKOAT/rus_ar.txt

[3] B. Lukács & L. Végsô: The Chronology of the "Sumerian King List". Altorient. Forsch. 2, 25 (1975)

[4] B. Lukács: Between Educated Guess and Proof: Phenomena at the Borderline of Statistics. KFKI-1998-02

[5] M. Banai & B. Lukács: Attempts at closing up by long range regulators in the Carpathian Basin. In: Technological Lag and Intellectual Background: Problems of Transition in East Central Europe, ed. J. Kovács, Dartmouth, Aldershot, 1995, p. 323

[6] R. Marsina: Ethnogenesis of Slovaks. Human Affairs 7, 15 (1997)

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[8] L. Luca Cavalli-Sforza: Genes, peoples and languages. Proc. Natl. Acad. Sci. USA 94, 7719 (1997)

[9] Ornella Semino & al.: The Genetic Legacy of Paleolithic Homo sapiens sapiens in Extant Europeans: A Y Chromosome Perspective. Science 290, 1155 (2000)

[10] I. Szentpétery: Scriptores rerum Hungaricarum tempore ducum regumque stirpis Arpadiensis gestarum, Budapest, 1937, Vol. 1, p. 239-505

[11] Kohn S.: Héber kutforrások és adatok Magyarország történetéhez. Zilahi, Budapest, 1881

[12] A. Arday, Sz. Bérczi, Gy. Don & B. Lukács: Preliminary Report of Szilvágy-Patkó (Horseshoe): A New (Possible) Impact Crater Remnant in Hungary. LPSC XXX, 1384 (1999)

[13] A. Arday, Sz. Bérczi, B. Lukács, Gy. Don & P. Solt: Would We Detect a Semi-Recent Impact of an Icy Tunguska on Clay? PIECE'99, ed. Y. Miura, Yamaguchi, 1999, p. 1

[14] V. H. Gurzadyan: Astronomy and the Fall of Babylon. Sky and Telescope, July 2000

[15] H. Gasche, J. A. Armstrong, S. W. Cole & V. G. Gurzadyan: Dating the Fall of Babylon. A Reappraisal of Second-Millenium Chronology. Mesopotamian History and Environment Memoirs Vol. 4, 1998

[16] J. A. Brinkman: Appendix I to A. Leo Oppenheim: Ancient Mesopotamia, Revised Edition Completed by Erica Reiner, University of Chicago Press, Chicago-London, 1977

[17] J. N. Stockwell: On the Secular and Long-Period Inequalities in the Moon's Motion. Astron. J. 10, 33S (1890)

[18] C. Brans & R. H. Dicke: Mach’s Principle and a Relativistic Theory of Gravitation. Phys. Rev. 124, 925 (1961)

[19] G. H. Darwin: On the precession of a viscous spheroid and on the remote history of Earth. Philos. Transact. Roy. Soc. London, Part 2, 170, 447 (1879)

[20] E. W. Brown: Tables of the Motion of Moon. London, 1919

[21] P. Melchior: Physique et dinamique planétaires. Vander, Louvain, 1972-3

[22] J. N. Stockwell: On the Rectification of Chronology by means of Ancient Eclipses. Astron. J. 10, 185 (1891)

[23] Improved Lunar Ephemeris 1952-1959. Nautical Almanac Office, U.S. Naval Observatory. Washington, 1954

[24] A. T. Fomenko: The Jump of the Second Derivative of the Moon’s Elongation. Celestial Mechanics 25, 33 (1981)

[25] R. R. Newton: Astronomical Evidence Concerning Non-Gravitational Forces in the Earth-Moon System. Astroph. Space Sci. 16, 179 (1972)

[26] R. R. Newton: Two Uses of Ancient Astronomy. Phil. Transact. R. Soc. Lond. A276, 99 (1974)

[27] V. S. Imshennik: Supernova explosions and historical chronology. Physics-Uspekhy 43, 509 (2000)

[28] Aristotle of Stageira: De Caelo, especially 294a-b

[29] Aristotle of Stageira: Physica, especially 250a-260a, and De Caelo 288.

[30] Aristotle of Stageira: De Caelo 289a

[31] K. Martinás: Aristotelian Thermodynamics. In: Thermodynamics: History and Philosophy (ed. by K. Martinás & al.), World Scientific, Singapore, 1991, p. 264

[32] Aristotle of Stageira: De Mundo, especially at 398b

[33] Horváth G.: Kihül a Nap. Fizikai Szemle XLIV, 92 (1994)

[34] Sir Isaac Newton: The Chronology of Ancient Kingdoms Amended. J. Osborn & T. Longman, London, 1728. (Ref. 41 is its Foreword.)

[35] International Earth Rotation Service: Appendix A. http://creation-answers.com/time6.htm

[36] ***: Delta T. http://user.online.be/felixverbelen/dt.htm

[37] F. R. Stephenson: Historical Eclipses and Earth's Rotation. Cambridge University Press, Cambridge, 1997

[38] F. R. Stephenson & M. A. Houlden: Atlas of Historical Eclipse Maps. Cambridge University Press, Cambridge, 1986

[39] M. J. Aitken: Physics and Archaeology. Oxford University Press, Oxford, 1974

[40] Thucydides: The Peloponnesian War. Penguin, Harmonsworth, 1972

[41] Sir Isaac Newton: A Short Chronicle from the First Memory of things in Europe to the Conquest of Persia by Alexander the great. http://hbar.phys.msu.su/gorm/fomenko/inewton.htm

[42] F. R. Stephenson & L. J. Fatoohi: The Total Solar Eclipse Descibed by Plutarch. http://www.dur.ac.uk/Classics/histos/1998/stephenson.html

[43] Plutarch: Moralia XII, Loeb, 1957, 931D-E (De facie in orbe lunae)

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