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2. Mathematical Translation of the Calendar Terms of Nominalia
The Nominalia of the Asparuh Bulgars is an excellent field for the application of mathematics. Its information is exclusively numerical - a line of connected one to another numbers.

The previous translation attempts relied on coincidence, the unclear calendar terms were interpreted not by mathematical calculations, but on the basis of a priori considerations about the similarity of the Proto-Bulgarian calendar with Turkic and Mongolian calendars. And these considerations were very arbitrary, i.e. it was assumed that TVIREM means 9, VECHEM - 3, CHITEM - 7, etc. and after that followed the attempts to calculate the periods of rule of the individual princes. That led to contradictory results but nobody knew where (in which term) the errors laid.

Since we know the exact periods of rule of the princes, we must follow to other way round - to calculate the points on the twelve-years cycle corresponding to the calendar expressions. I decided to check whether it was possible to find an unique and logical mathematical solution to that problem. It was shown that such a mathematical solution exists and that it is unique. So we can be convinced that each calendar term of the Proto-Bulgarians is a part of a harmonious system, which forms the basis of Proto-Bulgarian calendar dates. The mathematical solution supplied the following translation of the Proto-Bulgarian calendar terms:

SOMOR - Mouse ALEM - first
SHEGOR - Bull TUTOM - second
CHITEM - third
DVAN - Hare TVIREM - fourth
VER - Dragon VECHEM - fifth
DILOM - Snake SHEHTEM - sixth
TEKU - Horse 
TOH - Cock ELEM - tenth
ETH - Dog ENIALEM - eleventh
DOHS - Wild boar ALTEM -twelfth, literally last

So, the mathematical decoding of the Nominalia detected, for example, that the year DILOM and the month TVIREM correspond to the year of the SNAKE, the fourth month of the cyclic calendar. The procedure was applied successively to all calendar terms, it pointed that TOH ALTOM was the year of the cock, the twelfth month. Likewise, TEKUCHITEM was determined to be the year of the horse, the third month - only this translation satisfied all conditions of the Nominalia.

The scholars working on the Nominalia accused the unknown VIIIth c. writers of being imprecise and having often entered false years and months. By these accusations they tried to excuse their own inaccurate translations. In fact, the authors of the Nominalia were quite precise - both the periods of rule and the years of ascension (or the life span) of all Bulgarian princes were perfectly correct.

The only, and easy to overcome, inaccuracy which crept into the Nominalia was due to later transcribers. The late XV-XVIth c. transcribers had the month ENIELEM, in which Isperih (Asparuh) assumed the throne, written as ENIALEM. They have also inadvertently changed the dates of the successor of Tervel by copying the expression TVIREMAK LET as TVIREM KH LET, but both errors are easily spotted mathematically. In the case of Isperih by the fact that writing his month as ENIELEM we obtain the right correspondence between his first year and Tervel, and in the second case -  by the fact that only the return of the letter K to its place (before L) fits to the other history records about Tervel.

Let us look at one example, which best illustrates the mistakes of the previous investigators. 61 years are entered against the name of Isperih. These 61 years made hard the life of those, who those tried to decipher the name calendar with the help of the Turkic calendar. Assuming that VER - the year of Isperih's ascension, corresponded to the Tatarian word VJORE (wolf), and that the year of ascension of his successor Tervel was the year of the sheep (for a long time the term TEKU was translated in this way), they concluded Isperih ruled for 65 and not for 61 years.

Rarely, the Turcologists shifted the first year of Isperih to the year of the dragon, although the dragon was LUN and not VER in the Turkic calendar. But again, the years did not fit, now they had 63.5 years for the reign of Isperih. Similarly, the shift of the ascension of Tervel to the year of the horse did not help, because between the first month of the dragon and the seventh month of the horse (as TEKU CHITEM was translated) there were 62 years and six months and not 61 years. It seemed as if the authors of the Nominalia were quite ignorant about Isperih - the central figure of their work.

The mathematical deciphering put the guessing to an end. It proved that the month written next to Isperih corresponds to the eleventh month of the year of the dragon, and the month next to Tervel - to the third month of the year of the horse. Counting on the twelve-year cycle, between the eleventh month of the dragon and the third month of the horse we have the whole numbers of 13, 25, 37, 61 etc. years. The authors of the Nominalia did not err writing 61 years next to Isperih - between the eleventh month of the dragon and the third month of the horse there are 61 years and four months.

The determination of exact meaning of the term ELEM (tenth) and its derivation ENIALEM (or ENIELEM) - eleventh, was very important for the solution of another mystery of the Nominalia. The Chatalar inscription from Omurtag says that it was made in the year SIGOR ELEM (written with Greek letters), i.e. in the year of the bull and the month ELEM. The Turkologists mistranslated SIGOR ELEM as the year of the bull, the first month - the first month of the bull corresponded to January of 821 AD; at the same time the inscription in Greek read that it was made in September of 821 (the 15th Byzantine indict began in September 821). The Greek date clearly showed that ELEM was not the first month and the solution of the mystery was quite simple - SIGOR, that is - SHEGOR ELEM, was October 821 and that is exactly the second month of the Byzantine 15th indict.

The mathematical deciphering places all calendar terms on their correct places. Let us examine briefly these so important for the Bulgarian history dates:

AVITOHOL. He assumed the throne in DILOMTVIREM (snake, fourth month). A legendary progenitor of the Bulgars, he lived for 300 years. Counting 300 years from the cyclic calendar we arrive in the year of the snake, fourth month in which, according to the Nominalia, was born Irnik.

IRNIK. The second progenitor. Born in DILOMTVIREM (snake, fourth month). Lived for 150 years. Counting 150 years we arrive in the year of the wild boar.

GOSTUN. A deputy. Reigned for 2 years staring in DOHS TVIREM (wild boar, fourth month). Continuing for two more years, we correctly reach KOURT (Kubrat).

KOURT (Kubrat). The renovator of Old Great Bulgaria. Starts in SHEGOR VECHEM (bull, fifth month), 60 years. Counting these 60 years we again arrive at the starting point, which is the beginning of the next ruler - BEZMER.

BEZMER. Governed for 3 years, starting from the bull, fifth month (SCHEGOR VECHEM).

ISPERIH. Founder of a new state and therefore entered in the Nominalia with his whole life span of 61 years, as the legendary AVITOHOL and the renovator KUBRAT. Ascended the throne in VERENIELEM (dragon, eleventh month).

TERVEL. Started in TEKU CHITEM (horse, third month) and ruled for 21 years.

TVIREMIK (or Tvirelik). He was mentioned in History of Paisij as as Trivelius. Ascended the throne in the year of the DVAN (hare) in the sixth month (SHEHTEM) and ruled for 6 years. Late transcribers introduced an error here.

SEVAR. The last of the clan DULO. He mounted the throne in TOH ALTOM (the year of the cock, twelfth month). Ruled for 15 years.

KORMISOSH. His first year of rule was SHEGOR TVIREM (bull, fourth month), and he ruled for 17 years.

VINEH. Ascended the throne in IMENSHEGOR ALEM (horse, first month). A second name for the year of the horse is not uncommon - many peoples had two or even three names for the same year of the cyclic calendar. Thus, the Tadjiks near Pamir have three different names for the year of the dog - SAK, VAFODOR and KUCHUK, and for the year of the wild boar - two (HUG and HUBON).

TELEC. Assumed the throne in SOMOR ALTEM (mouse, eleventh month) and governed for three years. In June 763 he suffered a catastrophic defeat and soon thereafter, not later than August, he was dethroned and probably murdered. From SOMORALTEM, which corresponds to the eleventh month of the year 760 AD, to August 763 there are two years and nine months, rounded by the authors of the Nominalia to three years.

INTERREGNUM. This period is inferred indirectly. The first year of the next ruler UMOR is DILOM TUTOM (snake, second month) which corresponds to February 765 AD. That is, since the deposition of TELEC (August 763) Bulgaria was governed for one year by a temporarily appointed person, or by an unpopular ruler, whose name was omitted by the authors Nominalia. Exactly in this period the Byzantines mention the unpopular SABIN, who saved his life by taking refuge in Constantinople. Obviously, his name was intentionally omitted after his infamous betrayal.

UMOR. This last ruler of Nominalia ascended the throne in DILOM TUTOM (snake, second month) and governed for 40 days. That fits exactly the information of the Byzantine sources, as in the summer of 765 AD the Byzantine emperor mounted a campaign against Bulgaria because of the deposition of Umor.

The data, arranged in table look thus:
Ruler Year of 
Given in the Nominalia Duration Our 
Avitohol 153 Snake, 4th month 300 300
Irnik 453 Snake, 4th month 150 150
Gostun 603 Boar, 4th month 2 2
Kourt 605 Bull, 5th month 60 60
Bezmer 665 Bull, 5th month 3 3
Isperih 633 Dragon, 11th month 61 61
Tervel 694 Horse, 3rd month 21 21
Tviremik 715 Hare, 6th month 6 6
Sevar 721 Cock, 12th month 15 15
Kormisosh 737 Bull, 4th month 17 17
Vineh 754 Horse, 1st month 7 7
Telec 760 Mouse, 11th month 3 3

It was already said the that mathematical solution is unique. Let us then examine the particularity of this translation and have a closer look at the mysteries of the Proto-Bulgarian calendar.

Let us compare this and the previous attempts for translation of the calendar terms of the Nominalia.
Name of the Month  Mathematical translation Previous translation 
ALEM  first first
TUTOM second fourth
CHITEM third seventh
TVIREM fourth ninth
VECHEM fifth third
SHEHTEM sixth eighth
ELEM tenth first
ENIALEM eleventh
ALTEM twelfth sixth

The previously assumed names of the months were particularly incorrect. All months, except the first one - ALEM, were mistaken. The reason for that was the false belief of the previous translators that the Proto-Bulgarians were Turkic people. They unconditionally tried to find the Turkic prototype behind each Proto-Bulgarian name of the months - behind VECHEM - JUCHINCHI, behind CHITEM - ETINCHI, behind TVIREM - TAHAREMASH, etc. This play with the months undermined the mathematical base of the Proto-Bulgarian calendar.

The names of the months were the weakest and, perhaps, fatal point of the past translations, their translations were much more erroneous than the translations of the names of cyclic years. It can be easily explained - the cyclic years were very helpful, it sufficed to guess the name of the first year of the Nominalia - DILOM (snake), in order to proceed correctly, almost automatically with the next records. Counting 150 years from DILOM (snake) they arrived to the year of the wild boar. Thus, it was correctly assumed DOHS is a wild boar, two more years led to SHEGOR (bull), etc. And although nowhere in the Turkic calendars names such as SOMOR, DVAN, VER, TEKU (as a horse) or IMENSCHEGOR were to be found, the translators obtained their correct meaning on a purely logical way, if even still believing in the Turkic origin of the Proto-Bulgarian calendar.

In the case of the translation of the months, however, the situation was completely different, there were no additional clues to the correct interpretation and it produced a complete chaos. The large inconsistencies in the Turkic translations, were a very valuable symptom to us. The Bulgarian names of the months are not Turkic in origin, they come from a different numerical system.

     (See also --> An alternative "pan-Slavic" reading of the Nominalia by G. Nosovskij and A. Fomenko. Text in Russian )

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