Slavic numbers in letters. Numerical meaning of Cyrillic letters
Old Slavonic notation
StoryIn the Middle Ages, in the lands where the Slavs lived, they used the Cyrillic alphabet, and a system of writing numbers based on this alphabet was widespread. Indian numerals appeared in 1611. By that time, Slavic numbering was used, consisting of 27 letters of the Cyrillic alphabet. Above the letters, denoting numbers, a mark was placed - a title. IN early XVIII V. due to the reform introduced by Peter I, Indian figures and Indian system numbers have replaced Slavic numbering from use, although in the Russian Orthodox Church (in books) it is used until today. Cyrillic numerals originate from Greek ones. In form, these are ordinary letters of the alphabet with special marks indicating their numerical reading. The Greek and Old Slavonic ways of writing numbers had much in common, but there were also differences. The first Russian monument of mathematical content is still considered to be the handwritten work of the Novgorod monk Kirik, written by him in 1136. In this work, Kirik showed himself to be a very skillful calculator and a great lover of numbers. The main tasks that Kirik considers are: chronological order: calculation of time, flow between any events. When making calculations, Kirik used a numbering system called a small list and expressed in the following terms:
10000 – darkness
100,000 – legion
In addition to the small list, in Ancient Rus' there was also a large list, which made it possible to operate with very large numbers. In the system of a large list of basic digit units had the same names as in the small one, but the relationship between these units was different, namely:
a thousand thousand is darkness,
darkness to darkness is legion,
legion of legions - leodr,
leodr leodriv - raven,
10 ravens - a log.
About the last of these numbers, that is, about the log, it was said: “And more than this is borne by the human mind.” Units, tens and hundreds were depicted in Slavic letters with a ~ sign placed above them, called “titlo”, to distinguish numbers from letters. Darkness, legion and leodr were depicted with the same letters, but to distinguish them from units, tens, hundreds and thousand, they were circled. With numerous fractions of one hour, Kirik introduced his system of fractional units, and he called the fifth part the second hour, the twenty-fifth - three hours, the one hundred and twenty-fifth - four hours, etc. The smallest fraction he had was seven hours, and he believed that there can no longer be smaller fractions of hours: “This does not happen anymore, there are no seventh fractions, of which there will be 987,500 in days.” When making calculations, Kirik did the operations of addition and multiplication, and distribution, in all likelihood, he carried out shlyakhompidbora, considering successive multiples for a given dividend and divisor. Kirik made the main chronological calculations from the date that was accepted in Ancient Rus' as the date of the creation of the world. Calculating the moment of writing his work in this way, Kirik (with an error of 24 months) claims that 79,728 months have passed since the creation of the world, or 200 unknown and 90 unknown and 1 unknown and 652 hours. By the same kind of calculation, Kirik determines his age, and we learn that he was born in 1110. Operating with fractional hours, Kirik was essentially dealing with a geometric progression with a denominator of 5. In Kirik’s work, space is also given to the issue of calculating Easter, so important for clergy and being one of the most difficult arithmetic questions the ministers of the church had to solve. If Kirik does not give general methods for this kind of calculations, then in any case he shows his ability to do them. Kirik's handwritten work is the only mathematical document that has come down to us from those distant times. However, this does not mean that others mathematical products did not exist in Rus' at that time. It must be assumed that many manuscripts are lost to us due to the fact that they were lost during the troubled years of princely civil strife, perished in fires, and always accompanied the raids of neighboring peoples on Rus'.
Learning to countLet's write the numbers 23 and 444 in the Slavic number system.
We see that the entry is no longer than our decimal. This is because alphabetic systems used at least 27 "digits". But these systems were convenient only for writing numbers up to 1000. True, the Slavs, like the Greeks, knew how to write numbers greater than 1000. For this, new notations were added to the alphabetic system. So, for example, the numbers 1000, 2000, 3000... were written in the same “digits” as 1, 2, 3..., only a special sign was placed in front of the “digit” at the bottom left. The number 10000 was denoted by the same letter as 1, only without a title, it was circled. This number was called “darkness”. This is where the expression “darkness to the people” comes from.
Thus, to denote "topics" ( plural from the word darkness) the first 9 “digits” were circled.
10 topics, or 100,000, was the highest level unit. They called it "legion". 10 legions made up the leord. The largest of the quantities that have their own designation was called “deck”; it was equal to 1050. It was believed that “the human mind cannot comprehend more than this.” This method of writing numbers, as in the alphabetic system, can be considered as the beginnings of a positional system, since in it the same symbols were used to designate units of different digits, to which only special signs were added to determine the value of the digit. Alphabetic number systems were not very suitable for handling large numbers. During development human society these systems gave way to positional systems.
Slavic numbers were used for counting and recording. This counting system used symbols in sequential alphabetical order. In many ways it is similar to the Greek system of writing numerical symbols. Slavic numbers are the designation of numbers using letters of ancient alphabets -
Title - special designation
Many ancient peoples used letters from their alphabets to write numbers. The Slavs were no exception. They denoted Slavic numbers with letters from the Cyrillic alphabet.
In order to distinguish a letter from a number, a special icon was used - a title. All Slavic numbers had it above the letter. The symbol is written at the top and is a wavy line. As an example, the image of the first three numbers in the Old Slavonic notation is given.
This sign is also used in other ancient counting systems. It only changes its shape slightly. Initially, this type of designation came from Cyril and Methodius, since they developed our alphabet based on the Greek. The title was written both with more rounded edges and with sharp ones. Both options were considered correct and were used everywhere.
Features of number designation
The designation of numbers on the letter occurred from left to right. The exception was the numbers from "11" to "19". They were written from right to left. Historically, this has been preserved in the names of modern numerals ( eleven twelve etc., that is, the first is the letter denoting units, the second is tens). Each letter of the alphabet represented numbers from 1 to 9, from 10 to 100 to 900.
Not all letters of the Slavic alphabet were used to represent numbers. Thus, “F” and “B” were not used for numbering. They simply were not in the Greek alphabet, which was adopted as a model). Also, the countdown began from one, and not from the usual zero.
Sometimes a mixed number designation system was used on coins - from the Cyrillic alphabet and most often only lowercase letters were used.
When Slavic symbols numbers from the alphabet represent numbers, some of them change their configuration. For example, the letter "i" in this case is written without a dot with the sign "title" and means 10. The number 400 could be written in two ways, depending on geographical location monastery Thus, in the Old Russian printed chronicles the use of the letter “ika” is typical for this figure, and in the Old Ukrainian ones - “Izhitsy”.
What are Slavic numbers?
Our ancestors used special notations to write dates and necessary numbers in chronicles, documents, coins, and letters. Complex numbers up to 999 were denoted by several letters in a row under common sign"title". For example, 743 on the letter was indicated by the following letters:
- Z (earth) - "7";
- D (good) - "4";
- G (verb) - "3".
All these letters were united under a common icon.
Slavic numbers that denoted 1000 were written with a special sign ҂. It was placed in front of the desired letter with a title. If it was necessary to write a numeral greater than 10,000, special characters were used:
- "Az" in a circle - 10,000 (darkness);
- "Az" in a circle of dots - 100,000 (legion);
- "Az" in a circle consisting of commas - 1,000,000 (leodr).
A letter with the required digital value is placed in these circles.
Examples of using Slavic numerals
This designation could be found in documentation and on ancient coins. The first such numbers can be seen on Peter's silver coins in 1699. They were minted with this designation for 23 years. These coins are now considered rarities and are highly valued among collectors.
Symbols have been stamped on gold coins for 6 years, since 1701. Copper coins with Slavic numerals were in use from 1700 to 1721.
In ancient times, the church had a huge influence on politics and the life of society as a whole. Church Slavonic numerals were also used to record orders and chronicles. They were designated in writing according to the same principle.
Children were also educated in churches. Therefore, the children learned spelling and counting precisely from publications and chronicles using Church Slavonic letters and numbers. This training was quite difficult, since the designation of large numbers with several letters had to be simply learned by heart.
All sovereign decrees were also written using Slavic numbers. Clerks of that time were required not only to know by heart the entire Glagolitic and Cyrillic alphabet, but also the designation of absolutely all numbers and the rules for writing them. Ordinary residents of the state were often ignorant of this, because literacy was the privilege of very few.
This numbering was created together with the Slavic alphabetic system to translate the sacred biblical books for the Slavs by the Greek monks brothers Cyril and Methodius in the 9th century. This form of writing numbers became widespread due to the fact that it was completely similar to the Greek notation of numbers. Until the 17th century, this form of recording numbers was official in the territory modern Russia, Republic of Belarus, Ukraine, Bulgaria, Hungary, Serbia and Croatia. Until now, Orthodox church books use this numbering.
Numbers were written from digits in the same way from left to right, from large to small. Numbers from 11 to 19 were written in two digits, with the unit coming before the ten:
We read literally “fourteen” - “four and ten”. As we hear, we write: not 10 + 4, but 4 + 10, - four and ten (or for example, 17 - seven-ten). Numbers from 21 and above were written in reverse, with the full tens sign written first.
The number notation used by the Slavs is additive, that is, it only uses addition:
= 800 + 60 + 3
In order not to confuse letters and numbers, titles were used - horizontal lines above the numbers, which we see in our drawing.
To indicate numbers greater than 900, special icons were used that were drawn around the letter. This is how the following large numbers were formed:
| Designation | Name | Meaning |
|---|---|---|
| Thousand | 1000 | |
| Dark | 10 000 | |
| Legion | 100 000 | |
| Leodre | 1 000 000 | |
| Crow | 10 000 000 | |
| Deck | 100 000 000 |
Slavic numbering existed until late XVII centuries, until with the reforms of Peter I, a positional decimal number system - Arabic numbers - came to Russia from Europe.
An interesting fact is that almost the same system was used by the Greeks. This is precisely what explains the fact that for the letter b there was no digital value. Although, there is nothing particularly surprising here: the Cyrillic numbering is completely copied from the Greek. The Goths also had similar numbers:
Year according to the old Russian calendar
Here, too, there is a special calculation algorithm: if the month is from January to August inclusive (according to the old style), then you need to add 5508 to the year (the new year begins on the first of September, according to the old style). After the first of September, you need to add one more, that is, 5509. Here it is enough to remember three numbers: 5508, 5509 and September 1.
At the beginning of the 18th century, a mixed system of recording numbers was sometimes used, consisting of both Cyrillic and Arabic numerals. For example, on some copper kopecks the date 17K1 (1721) is minted, etc.
Convert Cyrillic numbers online
Press all the symbols sequentially in the order they are located on your exhibit:
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The question of the origin and development of the Glagolitic alphabet raised in this material is very complex. And not only because practically very little has survived historical monuments and documentary evidence of the use of this font. Looking through the literature, scientific and popular publications that somehow relate to this issue, it should, unfortunately, be noted that there are practically no works that fully cover this topic. At the same time, M.G. Riznik claims that “no other letter has been written as much as about the Glagolitic alphabet and its origin” (Letter and font. Kyiv: Higher schools", 1978).
G.A. Ilyinsky at one time counted about eighty works devoted to this issue. About 30 hypotheses have been put forward regarding the origin of the Glagolitic alphabet. Today, it’s enough to go online and see that a lot has actually been written about the Glagolitic alphabet. But basically it’s just a rehash of the same information, opinions and views. One gets the impression of a huge “circulation” of the same information.
In our opinion, a lot of interesting things can be found in the design of Glagolitic characters if you try to consider them from the point of view of the artistic and figurative expressiveness of this font. Despite the exceptional graphic originality of Glagolitic letters (not to mention the semantic meaning of each sign), many scientists tried to find prototypes of letter patterns in various alphabets of the world. The basis of the Glagolitic alphabet was most often found in Greek italic. Some see its basis in pre-Christian Cyrillic writing. Others saw its roots in the Iranian-Aramaic script in the East. The emergence of the Glagolitic alphabet was associated with Germanic runes. Safarik P.I. I saw the graphic basis of the Glagolitic alphabet in Hebrew writing. Obolensky M.A. turns to the Khazar script in search of sources of the Glagolitic alphabet. Fortunatov F.F. saw the basis of the Glagolitic alphabet in the Coptic script. Other scientists found the roots of the Glagolitic alphabet in Albanian, Persian, and Latin.
However, the searches listed above by comparing the graphic features of Glagolitic letters with other types were mostly of a formal nature.
The two main types of Slavic writing preserved in history are Glagolitic and Cyrillic. From school course we know that both types of writing existed in parallel for some time. Later, the Cyrillic alphabet replaced the Glagolitic alphabet. Every schoolchild knows these, now elementary, truths. Information has become so firmly ingrained in our consciousness that it is perceived as an axiom. We know the time of the appearance of the official Slavic alphabet - 863, the 9th century after the Nativity of Christ, which began a new era.
We can judge the Cyrillic alphabet based on its name. Probably its creator was Kirill. Although this is not true to this day. Yes, there is historical information that Cyril invented some kind of alphabet for translating Christian liturgical books onto a Slavic basis.
But there is still no consensus on which alphabet exactly. In the chronicle sources of the 9th-10th centuries there are specific indications that Cyril (Constantine) created the Slavic alphabet, but none of these sources provide examples of the letters of this alphabet.
We know the number of letters included in Cyril’s alphabet, and the list of them that Chernorizets Khrabr gives in his work. He also divides the letters of Cyril’s alphabet into those created “according to the order of Greek letters” and into letters “according to Slovenian speech.” But the number of letters in the Glagolitic and Cyrillic alphabet, as well as their sound meaning, were practically the same. The oldest monuments of the Cyrillic and Glagolitic alphabet date back to the end of the 9th - beginning of the 10th century. The name of this alphabet is not proof of the creation of the Cyrillic alphabet by Kirill.
In the intense struggle for religious and political influence between the Roman Catholic and Eastern Byzantine Orthodox Churches, these two alphabet played an extremely important role in the formation of the identity of the Slavs. The Glagolitic alphabet was used in liturgical books in Dalmatia. A modified Cyrillic alphabet was used in Bulgaria.
Letters of the “round Glagolitic” alphabet and their meaning
| symbol | Name | numeric value | note | |
|---|---|---|---|---|
| Ⰰ | Az | 1 | ||
| Ⰱ | Beeches | 2 | ||
| Ⰲ | Lead | 3 | ||
| Ⰳ | Verbs | 4 | ||
| Ⰴ | Good | 5 | ||
| Ⰵ | Eat | 6 | ||
| Ⰶ | live | 7 | ||
| Ⰷ | Zelo | 8 | ||
| Ⰸ | Earth | 9 | ||
| Ⰺ, Ⰹ | Izhe (I) | 10 | Which of these letters is called what and how they correspond to the Cyrillic I and I, researchers do not have a consensus. | |
| Ⰻ | I (Izhe) | 20 | ||
| Ⰼ | Gerv | 30 | ||
| Ⰽ | Kako | 40 | ||
| Ⰾ | People | 50 | ||
| Ⰿ | Myslete | 60 | ||
| Ⱀ | Our | 70 | ||
| Ⱁ | He | 80 | ||
| Ⱂ | Peace | 90 | ||
| Ⱃ | Rtsy | 100 | ||
| Ⱄ | Word | 200 | ||
| Ⱅ | Firmly | 300 | ||
| Ⱛ | Ik | - | ||
| Ⱆ | Uk | 400 | ||
| Ⱇ | Firth | 500 | ||
| Ⱈ | Dick | 600 | ||
| Ⱉ | From | 700 | ||
| Ⱊ | Pѣ (Pe) | 800 | A hypothetical letter, the appearance of which is different. | |
| Ⱌ | Tsy | 900 | ||
| Ⱍ | Worm | 1000 | ||
| Ⱎ | Sha | - | ||
| Ⱋ | State | 800 | ||
| Ⱏ | Er | - | ||
| ⰟⰊ | eras | - | ||
| Ⱐ | Er | - | ||
| Ⱑ | Yat | - | ||
| Ⱖ | Hedgehog | - | A hypothetical letter (with the meaning of iotized E or O), included in the ligature - large iotated yus. | |
| Ⱒ | (Хлъмъ?) “Spider-shaped” sign for the sound [x]. Some researchers believe that it was included in the original Glagolitic alphabet as a separate letter. | |||
| Ⱓ | YU | - | ||
| Ⱔ | small us | - | ||
| Ⱗ | small iotized us | - | ||
| Ⱘ | jus big | - | ||
| Ⱙ | jus big iotized | - | ||
| Ⱚ | Fita | - | ||
There are several points of view on the problem of the formation and development of the Cyrillic and Glagolitic alphabet.
According to one of them, Cyril created the Glagolitic alphabet, and the Cyrillic alphabet arose later as an improvement of the Glagolitic alphabet.
According to another, Cyril created the Glagolitic alphabet, and the Cyrillic alphabet existed among the Slavs earlier, as a modification of the Greek letter.
It is assumed that Cyril created the Cyrillic alphabet, and the Glagolitic alphabet was formed among the Slavs in the pre-Cyrillic period. And it also served as the basis for the construction of the Cyrillic alphabet.
Perhaps Cyril created the Cyrillic alphabet, and the Glagolitic alphabet appeared as a kind of secret writing during the period of persecution of books written in Cyrillic by the Catholic clergy.
There is also a version according to which Glagolitic letters appeared as a result of deliberate complication, adding curls and circles instead of dots in Cyrillic letters, and in some characters due to their inversion.
There is a version that the Cyrillic and Glagolitic alphabet existed among the Slavs even in the pre-Christian period of their development.
All these points of view on the problem of the formation and development of the Glagolitic and Cyrillic alphabet are quite controversial and today have a lot of contradictions and inaccuracies. Modern science and factual material do not yet make it possible to create an accurate picture and chronology of the development of Slavic writing in general.
There are too many doubts and contradictions, and very little factual material on the basis of which these doubts can be dispelled.
Thus, Kirill’s student allegedly improved the alphabet created by the teacher, and thus the Cyrillic alphabet was obtained based on the Glagolitic alphabet and the Greek statutory letter. Most Cyrillic-Glagolic books (palimpsests) have an earlier text - Glagolitic. When rewriting the book, the original text was washed away. This confirms the idea that the Glagolitic alphabet was written before the Cyrillic alphabet.
If we agree that Kirill invented the Glagolitic alphabet, then the question naturally arises: “Why was it necessary to invent complex signs letters in the presence of simple and clear letters of the Greek script, and this despite the fact that it was necessary to strive to ensure Greek influence on the Slavs, which was the political mission of Cyril and Methodius?
Kirill had no need to create a more complex in outline and less perfect alphabet with letter names containing entire concepts, when it would have been enough to give only the sound meaning of the letter.
“First of all, I didn’t have books, but with features and cuts I read and gataahu, the trash that exists... Then, the lover of mankind... sent an ambassador named after St. Constantine the Philosopher, called Cyril, the husband of the righteous and true, and created for them writings (30) and osm, ova wobo according to the order of the Greek letters, but according to the Slovenian speech...” says in “The Legend of the Letters” by Chernorizets Khrabra. Based on this passage, many researchers
tend to believe that Kirill created the Glagolitic alphabet (L.B. Karpenko, V.I. Grigorovich, P.I. Shafarik). But in the “Legend” it is clearly stated “... twenty-four of them are similar to Greek letters ...”, and a list of letters similar to Greek is given, and then fourteen letters “according to Slavic speech ...” are listed. The word “similar” “similar” corresponds to the Russian word “similar”, “similar”, “similar”. And in in this case we can only speak with certainty about the similarity of Cyrillic letters with Greek letters, but not Glagolitic ones. Glagolitic letters are not at all “like” Greek letters. This is the first. Second: the digital values of the Cyrillic letters are more consistent with the digital values of the letters of the Greek alphabet. In the Cyrillic alphabet, the letters B and Z, which are not in the Greek alphabet, lost their digital meaning, and some received a different digital meaning, which precisely indicates that the Cyrillic alphabet was created in the model and likeness of the Greek alphabet. Glagolitic letter styles “according to Slavic speech” were forced to partially change their style, retaining their names. Most likely, this is how two styles of the Slavic alphabet appeared with the same composition and names of letters, but different patterns letters and most importantly - purpose. The Cyrillic alphabet was created on the basis of the Glagolitic alphabet and was intended for the translation of church books into the Slavic language.
“The presence of more ancient linguistic features in Glagolitic monuments in comparison with Cyrillic ones, Glagolitic insertions in the form of individual letters and text segments in Cyrillic manuscripts, the presence of palimpsests (texts on recycled parchment), in which the Cyrillic text is written on the washed-out Glagolitic alphabet, indicate the seniority of the Glagolitic alphabet ... The most ancient Glagolitic monuments are connected by their origin either with the territory where the activity of the Thessaloniki brothers took place, or with the territory of western Bulgaria, where the activity of the disciples took place” (L.B. Karpenko).
The totality of historical and linguistic facts based on a comparative analysis of Glagolitic and Cyrillic sources confirms our opinion about the primacy of the Glagolitic alphabet.
End of 9th century for countries Western Europe- this is the presence not only of writing, but also of a large number of different types of fonts: Greek, Roman capital square, rustic, old and new uncial, half-uncial, Carolingian minuscule. Written great amount books that have survived to our time. There is written evidence of Greek and ancient temples preserved in stone, mosaic, wood and metal. The origin of various types of writing dates back to the 8th-22nd centuries BC. Mesopotamia and Egypt, Byzantium and Greece, Mayans and North American Indians. Pictography and ideography, wampums and shell writing. Everywhere and among many, but not among the Slavs, for for some reason they could not have written language until Saint Constantine was sent.
But it's hard to believe. Everyone needed it Slavic tribes at that time to be blind and deaf, so as not to know and not see how other peoples, with whom the Slavs undoubtedly had various kinds of connections, have been using different types of fonts for centuries. Slavic lands were not an isolated reservation. However, judging by the theory of the development of writing that has developed and exists to this day, the Slavs,
being in close trade, political and cultural contacts with their neighbors, throughout all centuries remained until the 9th century throughout the entire territory of Ancient Rus' a huge “blank spot” on the map of the spread of writing.
This situation is difficult to resolve due to the lack of reliable written sources. This is all the more strange in the presence of an amazing, almost unknown to this day, truly wonderful world those beliefs, customs, and rituals that our ancestors, the Slavs, or, as they called themselves in ancient times, the Rus, completely indulged in for thousands of years. Just take Russian epics and fairy tales as an example. They didn't happen out of nowhere. And in many of them the hero is, if not a fool, then simple peasant son, meets at a crossroads or crossroads a stone with certain information indicating where to go and how the trip may end. But the main thing is not what and how is written on the stone, the main thing is that the hero easily reads it all.
The main thing is that he can read. This is common. And for Ancient Rus' there is nothing surprising in this. But in the fairy tales and legends of European and other “written” peoples there is nothing like this. The Slavs have come a very long and difficult historical path. Many nations and their empires fell, but the Slavs remained. That richest oral folk art, fairy tales, epics, songs, and the language itself, numbering more than two hundred and fifty thousand words, could not have appeared by chance. With all this, what is surprising is the practical absence or ignorance ancient monuments writing. Today there are very few monuments of Glagolitic writing.
In the 19th century there was a Psalter dating back to 1222, copied by the monk Nicholas of Arba under the papacy of Honorius in Glagolitic letters from the old Slavic Psalter, written by order and cost of Theodore, the last archbishop of Salona. Salona was destroyed around 640, so it can be argued that the Slavic Glagolitic original dates back to at least the first half of the 7th century. This proves that the Glagolitic alphabet existed at least 200 years before Cyril.
On the parchment sheets of the famous “Klotsov Codex” there are notes in Old German, indicating that the “Klotsov sheets” were written in Croatian, which is a local dialect of the Slavic language. It is possible that the pages of the Klotsov Codex were written by St. himself. Jerome, who was born in 340 in Stridon - in Dalmatia. Thus, St. Jerome back in the 4th century. used the Glagolitic alphabet, he was even considered the author of this alphabet. He was certainly a Slav and reports that he translated the Bible to his fellow countrymen. The sheets of the Klotsov Codex were later framed in silver and gold and divided among the owner’s relatives as the greatest value.
In the 11th century, the Albanians had an alphabet very similar to the Glagolitic alphabet. It is believed that it was introduced during the Christianization of the Albanians. The history of the Glagolitic alphabet, in any case, is completely different from what it is imagined to be. It is too simplified to the point of primitiveness, especially in Soviet literature on the history of type.
The emergence and development of writing in Rus' is canonically associated with its Christianization. Everything that could have been or was before the 9th century was rejected as having no right to exist. Although, according to Cyril himself, he met a Rusyn who had books written in Russian characters.
And this was even before Rurik was called to Novgorod and almost one hundred and thirty years before the baptism of Rus'! Kirill met “and found a man” who spoke “through that conversation”; that is, in Russian. Kirill met a Rusyn, who had two books - the Gospel and the Psalter - in 860 or 861. These books are very complex in their theological content and archaic style, but they existed and were written in Russian letters. This historical fact is given in all twenty three famous science lists of the Pannonian Life of Constantine, which confirms the authenticity of this event.
The presence of these books is indisputable evidence that Constantine took the script, which was quite developed by the Rusyns, as the basis for his Cyrillic alphabet. He did not create, but only improved (“by arranging the writing”), he streamlined the East Slavic writing that already existed before him.
One of the messages of Pope John VIII, a contemporary of Cyril and Methodius, clearly states that “Slavic writings” were known before Cyril and he “only found them again, rediscovered them.”
These words give reason to seriously think about their meaning. What does “found again” mean? This clearly indicates that they already existed before, were found earlier. They were used, and then somehow forgotten, lost, or stopped being used? When was this, at what time? There is no clear answer to these questions yet. Kirill “rediscovered” these letters. Didn't come up with it, didn't invent it, but just again
opened. It is precisely by improving what someone once created Slavic writing The mission of Cyril and Methodius to create Slavic writing was completed.
Some information about ancient writing in Rus' is available among Arab and European writers and travelers. They testified that the Rus had writings carved on wood, on a “white poplar” pole, “wrote on white tree bark.” The existence of pre-Christian writing in Rus' is also contained in Russian chronicles. There is historical evidence of the Byzantine king and chronicler Constantine VII Porphyrogenitus (912-959), who in the treatise “De administrando imperio” (“On State Administration”) wrote that the Croats of 635, after baptism, swore allegiance to the Roman capital and in a charter written “ in their own letter,” they promised to maintain peace with their neighbors.
Baschanskaya (Boshkanskaya) plate is one of the oldest famous monuments Glagolitic alphabet 11th century, Croatia.
The oldest monuments of Glagolitic writing are several inscriptions from the era of Tsar Simeon (892-927), an inscription of a Slavic priest on a letter of 982, found in the Athos monastery, and a tombstone dating back to 993 in a church in Preslav.
An important monument of the Glagolitic letter of the 10th century is the manuscript known as the “Kyiv Glagolitic sheets”, which at one time arrived at the Kiev Church Archaeological Museum from Archimandrite Antonin Kapustin, head of the Russian Ecclesiastical Mission in Jerusalem, and this document is located in the department of manuscripts of the Central scientific library Academy of Sciences of Ukraine, in Kyiv.
Kievan Glagolitic sheets, 10th century.
Among other famous monuments of Glagolitic writing, one should name the “Zograph Gospel” of the 10th-11th centuries, found in the Zograf Monastery on Mount Athos, the “Assemanian Gospel” from the Vatican, dating back to the 11th century, the “Sinaiticus Psalter” from the Monastery of St. Catherine, the “Mariinsky Gospel” from Athos, Klotsov collection (XI century) from the Klots family library (Italy).
There is a lot of debate about the authorship and history of the so-called “Klotsov Code”. There is written evidence that the leaves of the Klotsov Codex were written in Glagolitic alphabet in the own hand of St. Jerome, who was born in 340 in Stridon, in Dalmatia. He was a Slav by origin, as clearly evidenced by his own message that he translated the Bible to his fellow countrymen. In addition, the pages of this codex were at one time the object of religious veneration. They were framed in silver and gold and divided among the relatives of the owner of the codex, so that everyone would receive at least something from this valuable inheritance. Thus, already in the 4th century, Saint Jerome used the Glagolitic alphabet. At one time he was even considered the author of the Glagolitic alphabet, but no historical information no information has been preserved regarding this matter.
In 1766, a book by Klement Grubisich, published in Venice, argued that the Glagolitic alphabet existed long before the birth of Christ. Rafail Lenakovich expressed the same opinion back in 1640. All this indicates that the Glagolitic alphabet is centuries older than the Cyrillic alphabet.
In Rus', the beginning of weather records in the Tale of Bygone Years begins in 852, which makes it possible to assume that the chronicler of the 9th century used some earlier records. The texts of the agreements between the Kyiv princes and Byzantium have also been preserved. The texts of the treaties clearly indicate the developed ethics of written documentation of interstate relations already in the 10th century. Probably, the use of writing in Rus' found wide application in addition to church liturgical literature even before the official baptism of Rus'. This opinion is also supported by the existence of two alphabets in Rus' in the 9th century.
At the first stage of the development of writing there was no particular need for it. When something needed to be conveyed, a messenger was sent. There was no particular need for letters, because... everyone lived together, without going anywhere in particular. All basic laws were kept in the memory of the elders of the clan and passed on from one to another, preserved in customs and rituals. Epics and songs were passed on from mouth to mouth. It is known that human memory
capable of storing several thousand verses.
The recorded information was needed to indicate boundaries, boundary posts, roads, and property allocations. Perhaps that is why each sign had not only a graphic form, but also enormous semantic content.
For example, we can recall the fact that in the vast Vedic literature there is no indication of the existence of writing in early Aryan India. There are often indications that written recording had not yet been practiced, and at the same time, references to the real existence of texts, but their existence only in the memory of those who memorized them by heart, are quite common. As for writing, it is not mentioned anywhere. Although there is evidence of children playing with letters, the Buddhist canonical writings praise lekha - “writing”, and the profession of “scribe” is characterized as very good; There is other evidence that suggests the use of writing. All this suggests that in the 6th century BC. Both adults and children mastered the art of writing in India. As Professor Rhys Davide has rightly pointed out, this is one of those rare cases where the absence of written evidence where there is good reason to expect it is in itself useful evidence. By the way, a very interesting fact. In one of the northwestern variants of the Indian Gurmukhi script, the first letter of the alphabet completely repeats the Slavic Glagolitic letter Az...
Yes, today there is very little actual evidence of pre-Christian Slavic writing, and this can be explained by the following:
1. Written monuments on “white bark”, “white poplar”, and on any other tree they are simply short-lived. If in Greece or Italy at least a small amount of marble products and mosaics saved time, then Ancient Rus' stood among the forests and the fire, raging, did not spare anything - neither human dwellings, nor temples, nor information written on wooden tablets.
2. The Christian dogma of the creation of the Slavic alphabet by Constantine was unshakable for centuries. Could anyone in Orthodox Russia allow themselves to doubt the generally accepted and deeply established version of the acquisition of writing by the Slavs from Saints Cyril and Methodius? The time and circumstances of the creation of the alphabet were known. And for centuries this version was unshakable. In addition, the adoption of Christianity in Rus' was accompanied by the zealous destruction of all traces of pagan, pre-Christian beliefs. And one can only imagine with what zeal all kinds of written sources and even information about them could be destroyed if they did not relate to Christian teaching or, moreover, contradicted
to him.
3. Most of the Slavic scientists of the Soviet era were restricted from traveling abroad, and even if they could go to foreign museums, their limited knowledge of languages, and the temporary timing of their business trips, did not allow them to work fruitfully. In addition, there were practically no specialists who dealt specifically with the emergence and development of Slavic writing, either in Russia or in the USSR. In Russia, everyone specifically adhered to the version of the creation of Slavic writing by Kirill and bowed to the opinion of foreign authorities. And their opinion was unequivocal - the Slavs did not have writing before Cyril. The science in the USSR about the writing and script of the Slavs did not create anything new, copying memorized generally accepted truths from book to book. It is enough to look at the illustrations that wander from book to book to be convinced of this.
4. Foreign scientists practically did not study the issues of Slavic writing. And they didn’t show much interest. If they tried to deal with this issue, then necessary knowledge Russian, and even more so Old Slavonic language, they didn't have it. Pyotr Oreshkin, the author of a book on Slavic writing, rightly writes: “The professors of Slavic languages” to whom I sent my work answered me in French,
in German, in English, being unable to write a simple letter in Russian.”
5. The monuments of early Slavic writing that were encountered were either rejected, or dated no earlier than the 9th century, or were simply not noticed. There is a fairly large number of all kinds of inscriptions on rocks, for example in the Kremnica region of Hungary, which then passed to Slovakia, on utensils located in various museums around the world. These inscriptions undoubtedly have Slavic roots, but this additional historical material has not been used or studied at all, just like the Slavic runic inscriptions. If there is no material, there is no one to specialize in it.
6. The situation is still very well developed among scientists when a recognized authority on any issue expresses its opinion, and others (less recognized) share it, not allowing themselves not only to object, but even to doubt such an authoritative opinion.
7. Many published works are not of a research nature, but of a compilation nature, where the same opinions and facts are copied by one author from another without specific work with factual materials.
8. Future specialists who are preparing at universities barely have time to study what was written before them from session to session. And talk about serious things scientific research in the field of the history of Slavic writing is not yet available in universities.
9. Many researchers simply denied the alphabet of our ancestors the right to an independent path of development. And they can be understood: whoever wants to admit this - after all, the recognition of this situation destroys many pseudo-scientific constructions of scientists of previous centuries, aimed at proving the second-rate and secondary nature of the Slavic alphabet, writing and even language.
Of the two types of Slavic writing that existed together for some time, its further development received Cyrillic. The Glagolitic alphabet moved away as a more complex letter in terms of the characters, as the officially accepted version says. But the Glagolitic alphabet could also fall out of use as a letter that ceased to be used, in connection with the introduction of the Cyrillic alphabet, for writing church books. The Glagolitic alphabet that has survived to this day
The letter has 40 letters, 39 of which represent almost the same sounds as in the Cyrillic alphabet.
In many books, articles and publications, Glagolitic letters are described as graphically more complex, “pretentious”, “contrived”. Some even characterize the Glagolitic alphabet as a “chimeric” and artificial alphabet, not similar to any of the currently existing alphabetic systems.
Many researchers looked for the graphic basis of the Glagolitic alphabet in the Cyrillic alphabet, in the Syriac and Palmyra alphabets, in the Khazar script, in the Byzantine cursive script, in the Albanian script, in the Iranian script of the Sassanid era, in Arabic script, in the Armenian and Georgian alphabets, in the Hebrew and Coptic alphabets , in Latin italics, in Greek musical notations, in Greek “spectacled writing”, in
cuneiform, in Greek astronomical, medical and other symbols, in Cypriot syllabary, in magical Greek writing, etc. Philologist G.M. Prokhorov showed the similarities in graphic terms between the letters of the Glagolitic alphabet and the signs of other writing systems.
And no one allowed the idea that the Glagolitic alphabet could have arisen independently, and not as a letter borrowed from someone. There is an opinion that the Glagolitic alphabet is the result of an artificial individual work. And the origin of the very name of this alphabet is not entirely clear. Traditionally, the Glagolitic alphabet is understood as a derivative of the word glagoliti - to speak. But there is another version, set out by I. Ganush in a book with characteristic
for its time the name: “On the issue of runes among the Slavs with a special review of the runic antiquities of the Obodrites, as well as the Glagolitic and Cyrillic alphabet. As a contribution to comparative Germanic-Slavic archaeology, the creation of Dr. Ignaz J. Hanusch, full member and librarian of the Imperial Czech Scientific Society in Prague". Ganush offers the following explanation for the Glagolitic name: “It may be that, according to the mass, the singing (reading) Dalmatian priests are called “verbalists,” just like their writings (books) from which they read. The word “verb” even now in Dalmatia serves as a designation for the Slavic liturgy, but the words “verb” and “glagolati” are already alien to today’s Serbo-Slavic dialects.” The Glagolitic alphabet has another name - the initial letter, which “in age surpasses all other names of alphabets,” and it is associated with the idea of “the Glagolitic letter, the beech, the beech line.”
Both types of Glagolitic - rounded (Bulgarian) and angular (Croatian, Ilirian or Dalmatian) - really differ in a certain intricacy of characters in comparison with the Cyrillic alphabet.
It is this intricacy of the Glagolitic signs, together with their names, that forces us to look more carefully and in detail at each sign, its design and try to understand the meaning inherent in it.
The names of the alphabetic characters of the Glagolitic alphabet, later transferred to the Cyrillic alphabet, cause not only surprise, but also admiration. In Chernorizets Khrabra’s essay “On Letters” there is a clear description of the creation of the alphabet and the first letter: “And he created for them thirty-eight letters, some in the order of Greek letters, and others in accordance with Slavic speech. In the likeness of the Greek alphabet, he began his alphabet, they began with alpha, and
he put Az at the beginning. And just as the Greeks followed the Hebrew letter, so he followed the Greek... and following them, Saint Cyril created the first letter Az. But because Az was the first letter given from God to the Slavic race in order to open the letters of the mouth to the knowledge of those who learn, it is proclaimed by a wide parting of the lips, and other letters are pronounced by a smaller parting of the lips.” In the tale of Brave, not all letter names have
description.
The most interesting thing is that no other people and no other writing system have such or even similar letter names. It is very characteristic that not only the names of the Glagolitic alphabetic characters themselves cause surprise, but also their numerical meaning up to and including the letter “Worm”. This letter meant 1000, and the remaining letters of the Glagolitic alphabet no longer had a digital meaning.
Time and many layers and changes today have significantly distorted the original meaning and meaning laid down by the creators of the Slavic alphabet, but even today this alphabet represents something more than a simple letter series.
The greatness of our Glagolitic alphabet lies in the fact that the very shape of the letters, their order and organization, their numerical value, their names are not a random, meaningless set of signs. The Glagolitic alphabet is a unique sign system based on the specific experience of the worldview and worldview of the Slavs. Creators Slavic system the letters, as many researchers note, undoubtedly came from a religious reflection of the world, from the idea of the sacredness of the alphabet.
In this regard, another question arises: “If Kirill created the Slavic alphabet, then why not end it with omega, following the example of the Greek alphabet?”
“Alpha and Omega” - the Lord calls himself, as the first and last, as the beginning and end of all things. Why shouldn’t Kirill use this expression, which was known at that time, and put omega at the end of the alphabet, thereby emphasizing the religious meaning of the alphabet he created?
The point is probably that he simply gave a different design to the letters, while preserving their existing structure and the established names of the letter styles of the Glagolitic alphabet used centuries before.
And the names of all the signs of the Slavic Glagolitic, and even the Cyrillic alphabet, when read carefully, not only indicate sound, but are also arranged into clearly meaningful phrases and sentences. To denote the letters of the Glagolitic alphabet, Old Church Slavonic words and word forms were used, which today have already lost a lot, but still retained their original meaning. The verbal meaning of the Glagolitic letters up to and including the letter “Worm” is especially pronounced.
Translated into modern Russian, the names of the letters sound like this: az (ya), beeches (letter, letters, literacy), vedi (I know, realize, know), verb (I say, speak), dobro (good, good), is ( exists, exists, is), live (live, live), zelo (very, completely, extremely), earth (world, planet), kako (how), people (children of men, people), think (meditate, think , think), he (one, otherworldly, unearthly), peace (peace, refuge, tranquility), rtsi (speak, say), word (speech, commandment), tvrdo (solid, immutable, true), ouk (teaching, teaching ), fert (elected, selective).
The meaning of the letters “Hera” and “Cherva” is still not resolved. The Cyrillic name of the letter “Khera” in the Orthodox interpretation is an abbreviation of the word “cherub”, borrowed from Greek language. In principle, this is the only abbreviated name for the letter in the entire Slavic alphabet. Why on earth did Kirill, if he composed it, need to abbreviate this one word, and even with such a meaning? The worm, in the Orthodox interpretation, is a symbol of the most insignificant creation of the Creator. But whether this was their meaning in the Glagolitic alphabet remains a mystery to this day.
When reading the names of the letters of the Glagolitic alphabet, there is a clear, logical connection between the names of all letters and their combinations, up to the letter “Cherv”. When transferring to modern language the names of the letters form the following phrases and sentences: “I know the letters (letter)”, “I say (say) good is (exists)”, “live perfectly”, “the earth thinks like people”, “our (unearthly) peace ( calm)", "I say
The word (commandment) is firm (true)”, “teaching is chosen”.
There remain four letters with names: “Her”, “Omega”, “Qi”, “Cherv”. If we accept the Orthodox interpretation of these letters, then we can compose and obtain the phrase: “Cherub, or worm.” But then, naturally, questions arise with the letter “Omega”. Why it was included in this series and what it means will probably remain a mystery to us.
The phrase “The earth thinks like people” seems a little strange at first. However, if we take into account the achievements of modern science, we can only be amazed at the knowledge of our ancestors. Only in the middle of the twentieth century did scientists make a grand discovery - fungal mycorrhiza unites the root systems of all plants into a single network. Conventionally, this can be imagined as a huge web that connects the entire vegetation cover of the earth. This is also similar to the Internet that has taken over the entire world today. Due to this mycorrhiza, information is transmitted from plant to plant. All this has been proven by the experiments of modern scientists. But how did the Slavs know about this two thousand years ago, speaking in their alphabet,
that “the earth thinks like people”?
In any case, even what we have seen and already understood suggests that the Slavic Glagolitic alphabet is a unique example of an alphabet that has no analogue on our planet in terms of the conceptual meaning of the signs. It is now difficult to establish by whom and when it was compiled, but the creators of the Glagolitic alphabet undoubtedly had extensive knowledge and sought to reflect this knowledge even in the alphabet, putting into each sign not only conceptual, but also figurative, visual figurative information content. Each sign of the Glagolitic alphabet contains a huge amount of information. But many people need to point this out and decipher it, then everything immediately becomes clear.
Therefore, probably, many easily see in the first letter a hieroglyphic image of a cross, especially if they adhere to the opinion that Kirill developed this alphabet to translate liturgical books onto a Slavic basis. If we accept this version, then it would be possible to come up with many letters with Christian symbolism. However, this is not observed. But in the Glagolitic alphabet, almost every letter graphically reveals its meaning. Majority modern systems letters convey only the sound from which the reader extracts meaning. At the same time, the sign itself, its graphic drawing has practically no significance, performing only the nominal function of the generally accepted, symbol sound. In the Glagolitic alphabet, almost every sign carries a meaning. This is always typical for early forms writing, when first of all they tried to express in each sign the meaning of the message. Below we will try to consider all the letters of the angular and round Glagolitic alphabet from the point of view of the artistic and figurative expressiveness of the sign.
A.V. Platov, N.N. Taranov
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Hello. In this episode of the TranslatorsCafe.com channel we will talk about numbers. We will look at different number systems and classifications of numbers, and also discuss interesting facts about numbers. A number is an abstract mathematical concept denoting quantity. Numbers have been used by humans for counting since ancient times. At first, numbers were indicated by counting sticks, or notches, or lines on wood or bone. Later, numbers began to be used in more abstract systems. There are many ways to express and work with numbers; We'll look at some of them a little later in this video. Number systems have evolved over many centuries. Some ancient systems have been replaced by others that are more convenient to use. Some systems, which we will talk about below, are no longer used. Scientists believe that the concept of number arose independently in different cultures. Symbols for representing numbers in writing also arose separately in each culture. Gradually, with the development of trade, people began to exchange ideas and borrow from each other the principles of counting or writing numbers. Therefore, the number systems that we now use were created by many peoples. The Arabic number system is one of the most widely used systems. It was borrowed from India and refined by Persian and Arab mathematicians. During the Middle Ages, this system spread to Europe through trade and replaced Roman numerals. European colonization also influenced the spread of Arabic numerals. In Europe, Arabic numerals were first used in monasteries and later in secular society. The Arabic system is decimal, that is, with a base of 10. It uses ten symbols that can express all possible numbers. Ten is one of the most widely used numbers in counting systems, and the decimal system is common in many countries. This is due to the fact that since ancient times people have used ten fingers on their hands to count. To this day, people who learn to count or want to illustrate an example related to counting use their fingers. There are even such expressions as “counting on your fingers.” Some cultures also used their toes, knuckles, and even the space between their fingers to count. Interestingly, in many languages word, denoting fingers and numbers are the same thing. For example, in English, this word is “digit”. Roman numerals were used in Ancient Rome and Europe until about the 14th century. They are still used in some cases, such as on watch dials. You can also find them in the names of the Pope. Roman numerals are also often used in the names of recurring events, such as the Olympic Games. The Roman numeral system uses the seven letters of the Roman alphabet to represent all possible combinations of numbers: The order in which the numbers are written in the Roman numeral system matters. A larger number to the left of a smaller one means that both numbers must be added. On the other hand, the smaller number to the left of the larger one should be subtracted from the larger number. For example, this number is eleven, and this is 9. This rule is not universal and only applies to numbers of type: IV (4), IX (9), XL (40), XC (90), CD (400) and CM (900). In some cases these rules are not followed and the numbers are written in a row, such as this number meaning 50. The inscription in Latin using Roman numerals on Admiralty Arch in London reads: In the tenth year of the reign of King Edward VII to Queen Victoria from grateful citizens, 1910 Many cultures used number systems similar to Roman and Arabic. For example, in the Cyrillic number system, numbers from one to nine, ten, and multiples of one hundred were written in Cyrillic letters. There were also signs for larger numbers. There was also a special sign, similar to a tilde, which was written above such numbers to show that these were not letters. There was a similar system using the Glagolitic alphabet. In the Hebrew number system, the letters of the Hebrew alphabet were used to write numbers from one to ten, multiples of ten, as well as one hundred, two hundred, three hundred, and four hundred. The remaining numbers were written as the sum or product of these numbers. The Greek number system is also similar to the systems above. Some cultures had simpler number systems. For example, Babylonian numerals could be written using just two cuneiform signs, representing one and ten. The sign for one looks like a large letter "T", and ten looks like the letter "C". So, for example, 32 can be written like this, using the appropriate cuneiform characters. The Egyptian number system is similar, only it also had symbols for zero, hundred, thousand, ten thousand, one hundred thousand and million, and also had special signs for writing fractions. Mayan numbers were written using the symbols for zero, one and five. Numbers above nineteen also had a unique spelling. They used the signs for one and five, but with a different arrangement to show that the meaning of these numbers was different. In the unit or unary number system, only one sign is used to indicate one. Each number is written using such signs, the number of which is equal to this number. For example, if such a sign is the letter “A”, then the number five can be written as five letters A in a row. The unary system is often used by teachers who teach children to count because it helps children understand the relationship between the number of objects, such as counting sticks or pencils, and the more abstract concept of number. Often the unary system is used during games to record the points scored by teams or to count days or items. In addition to simple counting and accounting, the unary system is also used in computer technology and electronics. Moreover, the recording method differs in different cultures. For example, in many countries of Europe and America, they usually write four vertical lines one after another, which on the count of “five” are crossed out with a horizontal or diagonal line, and continue counting with a new group of lines. Here the count reaches four, after which these lines are crossed out with a fifth. Then add five more lines, and again start a new row. In countries where Chinese characters are or have been used in the language, for example in China, Japan and Korea, people usually draw not four lines crossed out by a fifth, but a special character, but also made of five strokes. The sequence of these strokes is not arbitrary, but is established by the rules of spelling hieroglyphs. In our example, the count reaches five and the person writes the first two strokes of the next hieroglyph, ending the count at seven. Now we will look at positional number systems. In positional number systems, the meaning of each sign denoting a digit depends on its position in the number. The position is usually called rank. This value also depends on the base of the number system. For example, the number 101 in binary is not equal to one hundred and one in decimal. Let's consider the positional number system using the decimal example: The first digit is for units, that is, numbers from zero to nine. The first digit is multiplied by ten to the zero power, that is, by one. The second digit is for tens and the digit in the second digit is multiplied by ten to the first power, that is, 10. The third digit is for hundreds and the digit in the third digit is multiplied by ten to the second power, and so on until the digits run out. To get the value of a number, we add up all the numbers obtained above, that is, the values of the numbers in each digit. This way of writing numbers allows you to work with large numbers. Numbers do not take up as much space in the text compared to numbers in non-positional number systems. The binary system is widely used in mathematics and computer science. All possible numbers are represented in it using just two digits, “0” and “1”, although in some cases other signs are used, for example “+”, “–”. Numbers in the binary system are represented as binary zeros and ones. To represent numbers greater than one, addition rules are used. Addition in the binary system is based on the same principle as in the decimal system. To add one to a number, use the following rule: For numbers ending in zero, this last zero is replaced by one. For example, let's add 1-0-0, that is, 4 in the decimal system, and 1, that is, 1 in the decimal system. We get 1-0-1, that is, 5. Here and below, for comparison, examples are given with the same numbers in the decimal system. In a number ending in one, but not consisting only of ones, replace the first zero on the right with one. All ones following it, that is, to the right of it, are replaced with zeros. Let's add 1-0-1-1, that is, 11 and 1, that is, 1 in decimal. We get 1-1-0-0. In a number consisting of only ones, all the ones are replaced with zeros, and a one is added at the beginning, that is, to the left. For example, let's add 1-1-1, that is, 7 and 1. We get 1-0-0-0, that is, 8. It should be noted that arithmetic operations in the binary system are done in exactly the same way as the usual operations in a column in decimal system the only difference is that instead of 10 they use 2. When adding, both numbers are written one under the other, as in decimal addition. The rules are as follows: 0+0=0 1+0=1 1+1=10. In this case, 0 is written in the right digit and 1 is transferred to the next digit. Now let's try adding 1-1-1-1-1 and 1-0-1-1. When adding in a column from right to left, we get: 1+1=0, and the unit is transferred to the next digit 1+1+1=1, and the unit is transferred to the next digit 1+1=0, the unit is transferred to the next digit 1+1+1 =1, and again we transfer the unit to the next digit 1+1=10 That is, we get 1-0-1-0-1-0. Subtraction is similar to addition, but instead of carrying, on the contrary, they “take” one from the higher digits. Multiplication is also similar to decimal. The result of multiplying two units is one, and multiplying by zero gives zero. If you look closely, you can see that all operations come down to addition and shifts. This feature of the binary system is widely used in computer systems. Dividing and taking square roots is also not much different from working with decimals. Numbers are grouped into classes, and some numbers can be in more than one class at the same time. Negative numbers indicate a negative value. They are preceded by a minus sign to distinguish them from positive ones. For example, if a person owes the bank that issued the credit card fifty thousand rubles, then he has −50,000 rubles. Here –50000 is a negative number. Integers these are zero and positive integers. For example, 7 and 86,766 are natural numbers. Whole numbers are zero, negative and positive numbers that are not fractions. For example, −65 and 11,223 are integers. Rational numbers are those numbers that can be expressed as a fraction where the denominator is a positive natural number and the numerator is a whole number. For example, 3/4 or −10/5, that is, −2, are rational numbers. Complex numbers are obtained by adding a real, that is, not a complex number, and another real number multiplied by an imaginary unit i, for which the equality i^2 = –1 holds. That is, a complex number is a number of the form a + bi. Here a is the real part of the complex number and b is its imaginary part. It is worth noting here that in electrical engineering the letter j is used instead of i, since the letter I denotes current - to avoid confusion. Prime numbers are natural numbers, greater than one, that are divisible without remainder only by one and by themselves. Examples of prime numbers are 3, 5 and 11. 2^57,885,161−1 is the largest prime number known as of February 2013. It contains 17,425,170 digits. Prime numbers are used in public key cryptosystems. This type of coding is used in encrypting electronic information in cases where it is necessary to ensure information security, for example, on the websites of online stores, electronic wallets and banks. Now let's talk about some interesting features of numbers. In China, they use a separate form of recording numbers for business and financial transactions. The usual hieroglyphs used to name numbers are too simple. They are easy to counterfeit or alter, changing their denomination if you add just a few touches to them. Therefore, special, more complex hieroglyphs are usually used on bank checks and other financial documents. In the languages of countries where the decimal number system is adopted, words are still preserved that indicate that a system with a different base was previously used there. For example, in English the word “dozen” is still used to mean twelve. In many English-speaking countries, eggs, flour products, wine and flowers are counted and sold in dozens. And in the Khmer language there are words for counting fruits based on the base-20 system. In the West, as well as in many countries where Christianity is practiced, 13 is considered an unlucky number. Historians believe it is related to Christianity and Judaism. According to the Bible, exactly thirteen disciples of Jesus were present at the Last Supper, and the thirteenth, Judas, later betrayed Christ. The Vikings also had a belief that when thirteen people get together, one of them will definitely die in the next year. In countries where Russian is spoken, even numbers are considered unlucky. It probably has to do with beliefs. ancient Slavs who believed that even numbers are static, motionless, and therefore dead. The odd ones, on the contrary, are mobile, looking for additions, changing, and therefore alive. That's why even number Flowers are brought only to funerals, but not given to living people. IN Western world On the contrary, it is quite normal to give an even number, and flowers are often counted in dozens. In China, Korea and Japan they do not like the number 4 because it is consonant with the word “death”. Often, not only the number four itself is avoided, but also the numbers containing it. For example, often 4, 14, 24, and other similar numbers are missed in the numbering of floors and apartments. In China they also don't like the number 7, due to the fact that the seventh month in the Chinese calendar is the month of spirits. It is believed that during this month the border between the human world and the spirit world disappears, and spirits come to visit people. The number 9 is considered unlucky in Japan because it connotes the word "suffering." Unlucky number in Italy it is 17 because its spelling in Roman numerals can be rewritten as "VIXI" by reversing the order of the letters. Often this phrase was written on the graves of the ancient Romans and meant “I lived”, therefore it is associated with the end of life and with death. 666 is a well-known unlucky number, also called the “number of the beast” in the Bible. Some believe that the actual number of the beast is 616, but references to 666 are more common. Many believe that this number will designate the Antichrist, that is, the deputy of the devil. Therefore, this number is sometimes associated with the devil himself. The origin of this number is unknown, but some are convinced that 666 and 616 are the encrypted names of the Roman Emperor Nero in Hebrew and Latin languages respectively, expressed in numbers. This possibility does exist, since Nero is known for his persecution of Christians and his bloody reign. Some historians even believe that it was Nero who initiated the great fire of Rome, although many historians do not agree with this interpretation of events. Thank you for your attention! If you liked this video, please don't forget to subscribe to our channel!