• Graffiti of the Kiev Sophia

    It's hard to say with certainty when calendar calculations on fingers were started in Russia, as described above. The Mongol invasion led to the destruction of many cultural monuments. .. Therefore, all the conclusions about the methods conducted here in the XII-XIV centuries.calendar calculations have to be done so far only on the basis of three sources:

    1) "Teach him the same person number of all years", written in 1136 by the Novgorodian monk Kirik,

    2) table-graffiti, opened by SA Vysotsky on the wall of St. Sophiacathedral in Kiev, and

    3) calendar tables of the so-called Norov Psalter, a manuscript supposedly dated back to the fourteenth century, "owned by Mr. AS Norov."

    All the same regulars. In the Teachings, Kirik demonstrated the ability to count tens of millions: he gives the number of calendar months, days and hours that elapsed "from Adam" up to 1136, gives definitions of the indicator, circles of the sun and moon, and calculates these calendar characteristics by 1136year. Here we will dwell on Kirik's statement that "the solar cycle begins on the first day of October."After all, it follows that in the XII century.in Russia, a voucher in calendar calculations have not yet been used.

    In fact, if the account of the circles of the Sun starts in October( or September, even January), and the vouchers are painted on March 1( other variants are unknown), then each year of the October( or September) style should have two parties - one beforeFebruary 28, the second - from March 1.In addition, in a leap year after February 29, there would be a "jumping over" a single letter of letters. This would be extremely impractical. Probably, for this reason, the Constantinople era was created, in which the beginning of the year was postponed to March 1!

    But back to the "Teaching".The traditional beginning of the Byzantine era is September 1.However, Kirik points to the counting of the circles of the Sun from October 1.And this is not accidental. Such a beginning was convenient for calculating the days of the week for the given numbers of calendar months: the fact that in the last, 28th, circle of the Sun on October 1 was accounted for on Saturday. Recall that here in the calculations, the "leading" numbering of days in the week was used. The days were designated by numbers in this order: Sunday-1, Monday-2, Tuesday-3, Wednesday-4, Thursday -5, Friday-6, Saturday- 7.

    So, the last 28th round of the Sun began on Saturday, this yearwas a leap year( with the March-style leap year is the third year of the cycle, then the 7th, 11th, etc., but since the beginning of the year was shifted five months ago, the leap-axes moved and the leap-marks were 4th, 8th,..., the 28th year of the cycle).This means that in the 1st year of the October 1 cycle falls on Monday, the 2nd on Tuesday, the 3rd on Wednesday, the 4th on Thursday, and since this last year is a leap year, then October 1 5th year of the cycle is already on Saturday.

    Apparently, for his calendar calculations, Kirik Novgorodskiy used solar regulators( RS) and solar epakttes, calculated, possibly, for the Byzantine circle of the Sun, as follows from formula XI-2).Let's see specifically how he could determine that in 6644 from the "creation of the world" "Annunciation( March 25) was on Wednesday."Dividing the number of the year by 28, we find its circle of the sun Q = 8. The number of shifts of the days of the week due to leaks [Q / 4] = 2. From the table we find the solar regular for March RS = 5, D = 25. As a result,that in the leading account system q = 4, that is, on March 25, 1136, it really happened on Wednesday.

    So, Kirik: 1) calculated the circle of the Sun for the year of interest to him,

    2) determined how many times there was an additional displacement of days by the number of months due to leap-outs,

    3) found in the table( it should have it at hand)monthly coefficient - solar regular for March,

    4) summed up all these numbers with the date for which it conducted the calculation, and

    5) determined the remainder of the division by 7 received amount;this remainder and showed him the day of the week.

    Actually, Kirik used the scheme of calculations, which came to Russia from Byzantium. This is how it is described in the so-called "Parisian Anonym" - a Greek manuscript dated 6587 from the "Creation of the World"( -5508 = 1079 CE): "Define the circle of the Sun, adding to it its fourth part. Further go from October, adding at the expense of all the months that have 31 days, three days, and those who have 30 days - two days. And from that month, which accounts for [the interesting date], take all the days. The sum is divided by seven, and if the balance is two, then the day is Monday.

    And again the sunny effects. Let us now turn to the two other calendar monuments of the 13th-14th centuries mentioned aboveOn the wall of the St. Sophia Cathedral in Kiev was found a table - graffiti, the reconstruction of which is shown in Fig.

    Fig. The calendar table-graffiti, found on the wall of the St. Sophia Cathedral in Kiev( RA Simonov, Kirik Novgorod-M.: Nauka, 1980)

    As can be seen, these are numbers from 1( "az") to 7( "land"),.Their total number is 28, which corresponds to a 28-year solar cycle. Therefore, the table is made up for certain calendar calculations. But what and how?

    The only logical way to read the table is from left to right and from bottom to top. Let us write the letters and the series: A, B, D, D, S, 3, A, B, D, E, S, 3, B, D, E, 3, A, B, D, E, S, 3, A, D, E, E, S and compare it with Table. It's a liar. It is not difficult to see that the order of "exclusion" of letters from the series is different here. Consequently, on the wall of the cathedral are not given a vest. What then?

    We write down the same series, giving the letters their numerical values: 1, 2, 3, 4, 6, 7, 1, 2, 4, 5, 6, 7, 2, 3, 4, 5, 7, 1,2,3, 5, 6, 7, 1, 3, 4, 5, 6. .. We have received solar epics( competitors) exactly in the same sequence in which they are given in Table.9, i.e. the first number is related to 1 year of the "Western European" solar cycle.

    "Set" of the calendar values ​​mentioned above - solar epic and solar regulators - and placed on top and right of the first sheet of the Norov Psalter( fig.).

    Fig. The calendar table of the Norov Psalter

    The upper plate is the same solar epicentas as on the wall of the St. Sophia Cathedral( in the Psalter, the third digit 3, ie the letter G, is erroneously omitted, in the figure it is restored and placed somewhat higher than the others).To the right of the sheet are solar regulators in this order:

    March -5, July -1, November -5,

    April-1, August-4, December-7,

    May-3, September-7, January-3,

    June - 6, October - 2, February - 6.

    Thus, in the Norov Psalter there are solar epaktas and regulars. Thus, determining the day of the week for any calendar date must be provided: after all, the "recipe" itself - the formula - is absolutely obvious. This is how the method of the Norov Psalter RA Simonov was deciphered: "By dividing the year by 28, the number of the solar circle was obtained. .. Counting according to the table corresponding to a working unfolding of the upper part of the Norovy tables, or according to the graffiti table from Sofia Kiev,of the solar circle, they found a numerical sign, which we conditionally denote by n. From the right table of the Norov Psalter( or its equivalent), the monthly coefficient y( solar regular) was taken as the third term. Next, the sum a = x + y + z was compiled, where z is the date, for example, of the spring full moon. Finally, they divided the amount received by 7, "if the year was a leap year, or a-1 difference, if the year was simple. We conclude the remainder of the day of the week of the date. "

    A few "why" and the author's suggestions. Calculation of this scheme gives the correct result. And yet there are several questions. After all, if the tables "take as is", then in three out of every four cases one has to make an amendment, to reduce the amount received by a factor of 1. Why is this so? And is it not possible to compile tables in such a way that there is no need for these amendments? Maybe these tables are "wrong" or "not quite those"?

    Earlier than to find out the situation, we note that the same way was calculated and the date of Easter( in any case, the control of the already existing Easter eggs was being carried out).Therefore, on the left in the calendar table of the Norov Psalter, the dates of the spring full moons are given. Comparing them with the data of the table, we find that they are arranged in the usual order as the number of the lunar circle increases from 1 to 19.

    We emphasize once more: the solar epocs placed on the wall of the St. Sophia Cathedral correspond to the eastern solar cycle, onlystarting with the circle of the Sun Q = 12, whereas to the west - from the first number of the solar cycle CS = 1.

    What does the calculator do? He, in the words of RA Simonov, defines first the eastern circle of the Sun Q and "counting so many signs, according to the table-graffiti, what the number of the solar circle", shifts the real distribution of the epatic in the 28-year cycle by 11 positions back. In other words, the calculator uses the epoch of the year R not interested in it, but the year R-11, going 11 years ahead!

    Both cycles begin with ES = 1, and if their beginnings are combined, then the discrepancy by 1 due to the discrepancy of the leap-outs is revealed in the 4th, 8th, etc. years of the cycle. For example, for CS = 4, we have ES = 4, whereas for Q = 4, the formula implies ES = 5. The calculator calculates the above-mentioned sum a, uses not the eastern but the western epak-tu whose numerical value in the leap year by 1less. On the other hand, although the monthly coefficient( RS) is calculated with the inclusion of the first day of the month, the calculator, determining the value of a, does not reduce the date by 1. This is why only in a leap year the result is correct, whereas in the next three years of the cyclethe eastern and western epatic forms coincide in magnitude, and this 1st day of the month( counted once again on the date z) must be excluded from the account, that is, dividing by 7 not the value of a, but a = 1.

    Which conclusions follow fromall that's said here?

    First of all, the graffiti table from the St. Sophia Cathedral and the Norov Psalter is an additional( to the chronicles) evidence that the year of Ancient Rus began in March. Otherwise, in the tables of solar effects for each leap year( seven times in the 28-year cycle), two epakttes would be indicated, which in fact is not present.

    Further, in both of the sources considered here, solar epaktts are recorded for the western cycle, although the schedule for the spring full moons is given according to the Byzantine account( and not by the golden numbers!).To carry out the recalculation of solar effects for the eastern solar cycle, as we have seen, it is elementary simple. It, however, was not held. We can assume that the scribes in Russia consciously combined for their calculations the eastern lunar cycle( for calculation of Easter full moon) with the western solar( for calculating the days of the week).But such calculations would be convenient only if the cycles themselves are counted from one common point. Therefore it is interesting to check: do not these cycles have a common reference point? It turns out there is. In 971 the next 19-year lunar cycle( the Moon circle L = 19) and simultaneously - the solar( western) cycle( CS = 28) came to an end. For 972 year we find: L = 1, CS = 1. This coincidence happens once in 532 years. But how could 971 or 972 be noticeable?(Of course, from the point of view of a scientist or church figure of Ancient Rus, who decided to start from him a countdown for calendar calculations.)

    Perhaps the only suitable event could be the death in 972 of Prince Svyatoslav Igorevich. His son Vladimir became the Prince of Kiev in 978 and ten years later he was baptized himself and made Christianity in Russia a state religion. Perhaps using this combination of the Byzantine lunar and western European solar cycles, the scribes in Russia thereby, as it were, tried to demonstrate their some independence from the influence of Byzantium, their desire to maintain a certain distance from both centers of spiritual culture of that time - Constantinople and Rome.