The schoty (abacus) as the phenomenon of Russian accounting

Abstract

The Russian abacus (the schoty [счёты]) is a unique Russian counting device that has no comparable counterparts anywhere in the world. It was developed when a decimal system was introduced in Russia in the sixteenth century. The Russian abacus took its familiar form in the eighteenth century, and it is still used for arithmetic calculations and for teaching maths at school, as an example of decimal calculations. The widespread use of the Russian abacus in business activities made it an integral part of entrepreneurship and accounting. The Russian abacus became more associated with Russian merchants and accountants than ledgers, and it was depicted in works of fine art. This article describes the history of the schoty, evidence about them from Western historians and mathematicians, the principles for its use as well as its role in accounting, and the descriptions of the schoty in literature and art.

Keywords

Russian abacus accountant decimal system counting devices

Introduction

This article is about a unique Russian counting device – the abacus (schoty) – and about its role in the development of accounting practice and profession, as well as its role in the cultural context of the epoch. Civilisation began with accounting, when writing and counting emerged (Hallo and Simpson, 1971; Sokolov, 1996). Counting devices have been used throughout the history of accounting, improving along with accounting's progress, and largely defining the capabilities of accountants to keep records. For Russian economic life, the schoty was more important than ledgers, since it was widely used. There were manuals on how to use the schoty. As one of these manuals states: ‘The schoty was so essential and important there (in accounting and in shops) that clerical work, bookkeeping and trade would be unfathomable without them, at least here in Russia’ (Bykov, 1902: 3).

The modern history of accounting is written in the international language of science – English. Consequently, many studies in other languages are completely or substantially unknown to accounting historians (Carnegie and Napier, 1996), who are now becoming aware of accounting's long-lasting international scope (Parker, 1971; Samuels and Piper, 1985). Accounting history in Russia represents a gap in this knowledge. Certain issues of theoretical research (Kuter et al., 2019; Kuter and Sokolov, 2012; Lvova and Lvova, 2018) and the development of the profession (Sidorova et al., 2019; Sokolov, 2015) are covered in the literature. Nonetheless, knowledge around the use of accounting records in business history in Russian firms remains terra incognita. This claim also applies to calculations in accounting and the devices used, in particular the schoty. Therefore, the primary aim of this article is to examine one of the issues relating to accounting and business history in Russia – the use of counting devices, one of the constituent changes in accounting (Hopwood, 1987).

This article was written based on a review of available literature and the authors’ personal experience in using this tool. The schoty is so firmly entrenched into Russian life that its descriptions are given not only in scientific literature, but also in fiction and art.

The research analyses the schoty over the nineteenth and twentieth centuries, the period of its greatest spread in Russia. The origin and gradual modification, as well as changes in the economic system, and the emergence of capitalism are briefly described to clarify the reasons for the spread of this counting tool. The methods of the Annales’ School are used as a research methodology. According to them, historical sources are not only documents, but ‘everything that a person says or writes, everything that he makes, everything that he touches, can and should give information about him’ (Bloch, 1949: 40). To understand the historical process, it is necessary to understand the way of thinking of the person in the studied epoch and culture, as this determines his/her individual and collective behaviour. Accounting is ‘primarily a social and organisational practice’ (Colasse, 2007: 106). Accounting history is the social practice of accountants. Currently, there is a lack of research on the behaviour, habits and mentality of accountants.

This article aims to analyse the impact of using the schoty on the social life of society and the organisation of accounting. Thus, accounting appears in its pragmatic everyday life (Lepetit, 1995). For its analysis, multidisciplinary research is necessary, which could cover such aspects as the schoty design and its evolution, the rules of its use and application by different persons, primarily accountants in relation to business development.

This research is the first in which using the schoty in accounting is studied in an economic, social and cultural context. It presents a brief history of the schoty as a counting tool, describes the rules for using them and reveals their role in Russian society, education and art in connection with the development of capitalism in Russia. It refutes the widespread assertion about the borrowing of Russian abacus from China, which has been expressed by scientists since the first half of the nineteenth century (Bykov, 1902; Khvatov, 1924; Kiryushin, 1925; Tikhomirov, 1830). Moreover, the difference in designs of the schoty and their connection with other counting devices are described.

The Russian abacus is an original counting tool that is not related to any Eastern abacus (Japanese and Chinese). We can say that there are the same differences between them as between the alphabet and hieroglyphs. The peak of using the Russian abacus falls on the industrial society (19th–20th centuries in Russia). This is the difference between this wooden instrument and tally sticks, counting boards and other tools of the Middle Ages and Renaissance. The schoty is a sign of Russian life. They are not only a symbol of accounting, but also a symbol of capitalism. The great Russian futurist poet Mayakovsky (1893–1930), who sang of the revolution, wrote: ‘To the arena! Go fight the merchants! It is necessary to learn how to beat with the schoty’ (Mayakovsky, 1957: 10).

Literature review

The main historical sources of using the schoty are publications on counting devices, textbooks on calculations on the schoty, principles for using the schoty by accountants, historical chronicles, works of classics of Russian literature and paintings.

This article contributes to research relating to the application of various nonpaper accounting tools, in this case, the schoty. The most famous nonpaper tools are tallies. Stone (1975) described their origin and use in practice in antiquity, the Middle Ages and the twentieth century. Grandell (1977) identified the types and purposes of the tally stick and reckoning board, which he asked not to be confused with the abacus used by the Romans. Noke (1981), in his article ‘Accounting for Bailiffship in Thirteenth Century England’, discussed the tally recording process. Baxter (1989) published an article on the tally and the checkerboard. Apostolou and Crumbley (2008) reviewed the history of tally sticks in England. Mattessich (1994) substantiated the need to study the history of the accounting development for archaeological artefacts of the preliterate period. Antonelli et al. (2019), describing agricultural accounting in the eighteenth century in Italy, considered additional archival materials – wooden rods as a supplement to the accounting documents. Jones (2009, 2010) demonstrated that the abacus was used as a counting tool in the Exchequer in the twelfth century, and the Exchequer's activities would be practically impossible without it. He wrote that the exact origin of this instrument was unclear. It was widely used by the Romans, but after the fall of the Roman Empire, information about its use was absent until the return of the abacus to Europe in the eleventh century. Tallies were widely used in Russia as well. Their Russian name – birka – indicated Swedish, possibly Hanseatic, origin (björk – birch). However, none of these wooden instruments have been used since the middle of the nineteenth century, while for the Russian abacus this was the time of widespread distribution and use.

The technique of using the Russian abacus is described in Russian in the following works: Apokin and Maistrov (1990), Emenov (1940), Evtushevsky (1871), Gagin (1960), Guter and Polunov (1981), Kazakova (2011), Khvatov (1924), Kiryushin (1925), Kononenko (1960), Simonov (1975, 1987, 1988, 1990, 1993, 1997), Spassky (1952), Tikhomirov (1830), Vilenchik (1984) and Zorin (1907). In English, the application of the schoty in Russia is considered in articles on the history of computing technology without their use in accounting: Aspray (2000), Carr (1805), Croix (1956), Duus (1998), Ryan (1972, 1991), Shilov and Silantiev (2017), Thompson (1906) and Volkov (2018). The study of abacus in Europe is considered by Du stchote ou machine… (1839), Gouzevitch and Gouzevitch (1998), and Hoppe (1952).

Research on the evolution of counting devices (Apokin and Maistrov, 1990; Guter and Polunov, 1981; Kazakova, 2011; Thompson, 1906), as well as an article by Simonov (2011) on the instrumental count of Ancient Russia, reveals the place of the Russian abacus in the history of the development of mechanical computing instruments, to demonstrate the main changes in time and periods of its development.

The results of the study of Russian abacus by mathematicians (Gnedenko, 1946; Yushkevich, 1968), statements of authors of textbooks on the rules for using the schoty (Bykov, 1902; Khvatov, 1924; Kiryushin, 1925), as well as special works devoted to the origin and history of the schoty (Spassky, 1952; Volkov, 2018) confirm the originality of this counting device, which was not used in practice in other countries and was not familiar to researchers outside of Russia. The idea of the abacus is described by testimonies of foreign travellers of the eighteenth and nineteenth centuries (Carr, 1805; Perry, 1716), and also by Voltaire (1694–1778) (Voltaire, 1829).

Textbooks (Bykov, 1902; Gagin, 1960; Kononenko, 1960; Zorin, 1907) describe the abacus calculation mechanism. The use of the schoty in accounting is described by disclosing information about the teaching in educational institutions of the rules for using the schoty (Emenov, 1940) and according to the guidance of the Soviet Ministry of Trade on the organisation and rationing of accounting labour (Vilensky, 1938). The use of illustrations from the specialised accounting journal ‘Schetovodstvo’ (accounting) and the guidance of the Ministry give clarity to this research area. Memoirs of Soviet accountants on the use of the schoty in practice give a particular validity and persuasiveness to this area (Buryshkin, 1991; Dorofeev, 2007; Yaprintsev, 2018).

The originality of this study lies in the presentation of information about the use of the schoty in the work of accountants by citing the works of the classics of Russian poetry and prose (Cherny, 1960; Tolstoy, 1960; Zoshchenko, 1923), who describe the character of Russian accountants or the organisation of their work. They also serve to substantiate the symbolism of this counting device for the Russian consciousness, associating them during the 1917 revolution with the capitalism hated by the common man (Mayakovsky, 1957) and at other times simply with the merchants and their way of life (Chekhov, 1954).

Research methodology

The study of accounting as a social and organisational phenomenon should complement the more conventional refinement of the craft approach (Burchell et al., 1980). Historical research should not only describe technical advances, but also the circumstances and processes that led to their emergence (Burchell et al., 1980). Hopwood (1983) notes that such studies are ongoing, but they are overly fragmentary in nature and can contribute to the emergence of myths. They are often carried out not by accountants, but by economists, sociologists, and so on. For example, economists study the role of accounting in the construction of modern organisational forms, sociologists think about the role of accounting in calculative practice in modern society, and so on. (Hopwood, 1983). In his later study, Hopwood (1987) writes that the prerequisites and consequences of changes in accounting systems should be studied. He explains this relationship as follows: changes in the market, cause, inter alia, through accounting, cause changes in the production policies of companies, which, in turn, cause organisational changes and changes in information systems, and as a result of their changes, accounting changes (Hopwood, 1987). Thus, accounting is constructively linked and therefore not separable from the organisation. At the same time, in his opinion, accounting is one of the important means of including any organisation in the social sphere. Carnegie and Napier (1996) argue that researchers of the ‘new history of accounting’ emphasise the importance of accounting as a social practice, that is accounting, in their opinion, should be seen in the context in which it operates in different cultural traditions. In their later research, Carnegie and Napier (2012) consider Hopwood to be the first to promote the concept of accounting as a social practice. According to Carnegie (2014), history can provide us with insight into contemporary accounting thought and practice through its ability to connect the past, present and future. Historical knowledge of accountings past provides a unifying force that allows one to more fully understand not only accounting, but also the present of society, and contributes constructively to the design and assessment of its possible future.

The perspective of the ‘anthropological approach’ in the study of the past was first discovered by the Annales School. It set the task of restoring history in its entirety and integrity, and not being limited to one event, economic, or some other, separate side. This historical and anthropological approach became the basis for the works of Bloch, Fevre and Braudel, who defined history as the interaction of demographic, industrial, technical, economic, financial, political, cultural and other processes. The history of everyday life was a part of the macro-context of life in the past, ‘total history’. Ludtke (1998/99) encourages researchers to focus on the common, ordinary and unremarkable ‘microhistory’.

The history of everyday life – as Ludtke noted – justifies itself as the most concise and meaningful formulation, polemically pointed against the historiographical tradition that excluded everyday life from its vision. The most important thing is the study of man in and out of work (Ludtke, 1998/99: 77).

Microhistory in Europe and America is one of the most influential research directions today. Its task is to understand the relationship between individual rationality and collective identity (Revel, 1996). Carnegie and Napier (2017) analyse the application of the Annales’ School methodology to the study of accounting history.

The Annales’ School established an expanded understanding of the historical source by supplementing written sources with artefacts. A new method of working with a source emerged by asking him/her questions and penetrating into his/her ideological background. The initial premise of this approach is the conviction that a person and his/her psyche are changeable, that is, the way to perceive the world and arrange your life in it in different eras and in different cultures are different. Consequently, it is necessary first to understand the way of thinking and actions of a person of the studied era and culture in order to understand the historical process. The main merit of the ‘annalists’ is that they see in history not only socio-economic schemes, but a living person with his/her thoughts and feelings, and began to explain the history by explaining the motivation of a person's actions.

Artefacts are a rich source of historical information as they provide a better understanding of the lives of individuals and organisations (Francis and Samkin, 2014). Knowledge can be embedded or encoded into the physical properties of artefacts and subsequently successfully transferred from the artefact to the user. The value of the physical properties of artefacts lies precisely in the transfer of knowledge within the framework of social processes (Rooke et al., 2009). The study of artefacts complements the picture of the historical era when they were applied. Accounting artefacts are a useful source of information about the history of accounting methods. Accounting artefacts include ledgers, tallies or technical tools such as abacus (the schoty), for example. This article describes the historical and social context: how the schoty influenced changes in accounting practice and the perception of the accounting profession in society. Thus, the importance and necessity of studying the schoty as a phenomenon of Russian accounting, as a unique artefact, are undeniable.

Even though the schoty is not related to the way social production is organised, their widespread use and availability to all social groups of population greatly contributed to the development of capitalism in Russia.

What is the schoty?

The schoty is a traditional Russian mechanical counting tool; it was often called ‘the Russian abacus’. It is used to perform all basic arithmetic operations: addition, subtraction, multiplication and division. An ordinary schoty was a frame with twelve wires, with beads sliding on the wires. There are two types of the schoty: the soviet-time schoty and pre-revolutionary one. They are different due to a change in the system of measures and currency units. In a classic Russian abacus, the first and the fourth wires from the bottom had only four beads (Figure 1). The lower row had only four beads because the smallest coin was 1/4 of a kopeck (polushka), and the fourth reflected different weight measures. The main measure of weight was a pound (funt [фунт]) – a little over 400 grams, and almost 50 grams less than an English pound, 40 pounds made a pood (пуд), and then the measures were decimal: 10 poods equal one berkovets (берковец), which was used to measure grain and other commodities. In 1918, Russia switched to a metric system, and in the new Soviet schoty, the lowest wire carried 10 beads (Figure 2). Thus, in the new schoty, all three lower wires were used to count kopecks (second and third wires) and grams (all three). The fourth wire with four beads became a separator between integer numbers (roubles and kilograms) and their parts (kopecks and grams) and was not used for calculations. For the user's convenience, two beads in the middle (fifth and sixth beads) on each wire have a different colour, usually black. In some models, the same colour is used for the first bead in the fourth row to mark the order of thousands.

Figure 1.

Сlassic Russian schoty (photo taken by the authors).

Figure 2.

Soviet-time Schoty (Kazakova, 2011: 16).

Russian abacus among similar counting devices

The schoty was very popular in Russia, while nothing similar was used in other countries. Even to translate the name of this counting device is a challenge (abacus, comptoir, Rechentafel, Rechenbrett, counting-board, boulier). The word closest in meaning is ‘abacus’ or ‘counting board’. The origin of the term ‘abacus’ is not established. Most historians derive it from the Semitic root; according to this interpretation, abacus means a board covered with a layer of dust (Guter and Polunov, 1981). Abacus in its original form is simply a board covered with a layer of sand or dust, on which lines were drawn, pebbles were laid out and geometric figures were built (Apokin and Maistrov, 1990). In other countries, this word means different things. In Ancient Greece and Rome, it was a counting board with lines or grooves for pebbles. The first mention of the abacus can be found in Herodotus (484–425 BC). Phoenician merchants introduced the abacus to ancient Greece. The first drawing of the abacus still available dates to the 3rd century BC. It depicts the Persian king and his treasurer, who performs calculations on the counting board (Apokin and Maistrov, 1990). In Europe, instead of pebbles, people used jetton with numbers, Roman numerals or special symbols drawn on them. An abacus in the Ancient East and Europe was a counting board with counting pieces that had to be moved across the board. The peoples of the Western Europe never used an abacus with beads on wires (Spassky, 1952).

Chinese Suanpan (Figure 3) and Japanese Soroban are the most similar to Russian abacus. A comparison of Russian schoty with Chinese Suanpan and Japanese Soroban reveals two main differences: (a) the location of the wires with beads (horizontal – in Russian schoty, vertical – in Chinese and Japanese devices) and (b) the decimal (rather than the fivefold) number system (Kazakova, 2011; Spassky, 1952).

Figure 3.

Suanpan and using it (Thompson, 1906).

A Russian historian Spassky (1904–1990) analysed the idioms and written sources (fiction, research articles and training materials) in Russian, texts of Russian laws, tax rules and the operating rules for the schoty and the counting devices of other nations, and proved the authentic origin of the schoty and lack of any connection with Chinese and Japanese devices (Spassky, 1952). Moreover, he demonstrated the interrelation of the schoty with the coin system in Russia (Spassky, 1962).

The fact that the Russian abacus is a tool primarily for business and accounting is emphasised by its name in Russian, in which this word denotes three key terms of business and accounting: invoice, account and calculation.

History of the Russian schoty

Modern schoty evolved dramatically. Computing technology researchers (Apokin and Maistrov, 1990) identified four stages of the invention and development of the Russian abacus. The first stage preceded its invention and was a method of pebble counting similar to the Western European counting system on lines (Figure 4).

Six or seven horizontal lines were drawn with a chalk on a specially adapted board. Then one or more vertical lines, depending on what arithmetic operations should be performed, intersected these lines. Counting on this device was carried out using ‘bones’ (plaques), deposited both on horizontal lines and in the spaces between them … All four arithmetic operations were performed with ‘bones’ (Kononenko, 1960).

Figure 4.

English abacus, line board or counting on lines (Kazakova, 2011: 14).

The second stage was a counting board (doschanoy schot) developed in the sixteenth to eighteenth centuries. Originally, the counting board (Figure 5) was a rather bulky contraption containing four counting fields made of wooden frames with wires fixed inside the frames and counting beads sliding on the wires – for monetary calculations, fiscal settlements, volume and weight calculations. Unlike the modern schoty, the wires in the lower part of counting boards were used to count fractions (quarters and thirds with their halves), as required for taxation (Simonov, 2011). Fractional units were widely used in taxation; sokha fractions constructed after the type of sequential halving: halve in the one-third, halve in halve in the one-third and next halve in quarter, halve in halve in quarter, and so on. It was needed to transfer fractions from one to another to calculate taxes constantly. For example, in modern designation it can be expressed by the following equation: 1/4 + 1/8 + 1/12 + 1/24 = 1/3 + 1/6. The transfer was carried out to rationalise the calculations when collecting taxes from the land, consisting of sections of possessions of various sizes and values (arable land, forests and meadows) (Simonov, 2011). A special device was used for such calculations. It consisted of several groups of wires with beads – a counting board. This device was also required to convert natural units of measurement into monetary ones. The counting board became the basis for the invention of Russian schoty, that is, their predecessor. At some stage, the Russian schoty was invented. The decimal organisation of the schoty is a strong reason to affirm that this device was invented in the sixteenth century, when the decimal system was first applied in the Russian monetary policy. In the 1530s, the Moscow Government under Elena Glinskaya (1508–1538, regency 1533–1538), the mother of young Ivan the Terrible (1530–1584, years of reign 1547–1584), conducted a monetary reform, uniting the Moscow and Novgorod monetary systems. The Moscow denga was at that time equal to 1/100 of the Moscow rouble. A half of denga was called polushka. Denga and polushka became a half and a quarter of the new main monetary unit named kopeika. After kopeika was introduced, the rouble could be divided into 100 basic units.

Figure 5.

A counting board. A model of the device described in Counting Wisdom (Schotnaya Mudrost) in 1691 (Kazakova, 2011: 15).

The word schoty was first found in the Register of the house coffers of patriarch Nikon, 1658. According to archaeologists and historians, it was already manufactured for sale in the seventeenth century (Guter and Polunov, 1981). The schoty of that period looked different from the modern schoty, and instead of one counting field, it first had four, and then two counting fields (Figure 6). At this time, the decimal positional number system was only beginning to spread in Russia. However, many foreigners noticed the wide use of this counting tool in trade in the seventeenth and eighteenth centuries, a device never seen in the West. An English captain, John Perry (1669–1733), who was in Russia in 1698–1712, published a book on his return to his home country entitled The State of Russia under the Present Czar, where he wrote,

There never has been any school before to teach arithmetic, nor did they know the use of figures, I believe, not twenty men in the whole country, but they made use of a kind of bead … which they set upon wires in a frame, like that which our women in England use to set their smoothing irons on, … by crossing of which beads together and again, they could multiply and divide any sum after a very tedious way and liable to gross mistakes, which method they yet use (Perry, 1716: 211).

Figure 6.

Russian schoty with four fields (Apokin and Maistrov, 1990: 43).

Voltaire (1694–1778) had the same opinion. To substantiate his statement that before Peter the Great (1672–1725, years of reign 1682–1725), ‘Muscovites were less civilised than the Mexicans when they were discovered by Cortes’, Voltaire wrote: ‘They don't even recognise numbers, and they use small beads strung on a copper wire to perform calculations’ (Voltaire, 1829: 51, 52).

The third stage covers the eighteenth and early nineteenth centuries. The schoty takes on its classic shape (Figure 7) and is later improved only in terms of looks, to make it easier to operate. The schoty evolved, and so did the attitude towards it in the world. If Captain Perry's comment was rather pejorative and sarcastic, the review written by Sir John Carr (1772–1832), a barrister who came to Russia in the beginning of the nineteenth century, was quite enthusiastic. On the intelligence of the Russian merchants, in general, John Carr remarked in 1804:

The consummate knowledge which the Russian shopkeeper possesses of the most complicated calculation, and the entangled caprices of that chameleon-coloured goddess who presides over the exchange, is absolutely astonishing. If he cannot write, he has recourse to a small wooden frame, containing rows of beans, or little wooden balls, strung upon stretched wires, and with this simple machine he would set the spirit of Necker at defiance (Carr, 1805: 163).

Figure 7.

Russian schoty in a box, 18th century (Spassky, 1952: 358).

French authors also exonerated the schoty. Magasin pittoresque published an article in 1839 (Du stchote ou machine…, 1839) and included a picture of the schoty and short instructions for using it. The Du stchote article refuted Voltaire's statement that Peter the Great replaced the schoty with numbers.

The fourth development stage of the Russian abacus covers the period from the early nineteenth to the early twentieth century. The growing need to mechanise calculations gave rise to numerous attempts to modernise the schoty.

One of the last attempts to modernise the schoty was made by F. Ezersky (1835–1915), the creator of the triple-entry form of bookkeeping, who patented his model in the USA in 1873 (Figure 8). For multiplication and division, mechanical devices replaced the schoty, mostly by arithmometers invented by V. Odhner (1845–1905), a Swedish engineer that served in Russia under Nobel and obtained a patent for an original machine based on Pascal's calculator (Apokin and Maistrov, 1990). However, different so-called advanced schoty did not meet the requirements of practice (Zorin, 1907), that's why ‘attempts to further improve the schoty, sometimes very witty, were not particularly successful’ (Kononenko, 1960: 8).

Figure 8.

The schoty of F. Ezersky, patented in 1873 (Spassky, 1952: 14).

Around 1820, the schoty travelled from Russia to Western Europe, though not as a counting device, but as a teaching aid for primary schools. This idea was an initiative of Jean–Victor Poncelet (1788–1867), an outstanding French mathematician and associate member of the Russian Academy of Science. As a lieutenant in Napoleon's army's engineering troops, he participated in the campaign in 1812 and was taken captive. In captivity, in Saratov, he saw the schoty, and on his return to France he created a teaching aid based on it for a school in Metz. Then this teaching aid became widely used in France and was later utilised in other Western European countries (Evtushevsky, 1871). Western mathematicians described the schoty many times including Georgi (1790) and Von Humboldt (1829). It is interesting to note that Humboldt compared the schoty to the rosary – a ritual counting tool. After the Second World War, the schoty was brought to the Soviet bloc countries. It was seen as a convenient device; several manuals were published on how to use it. Even so, it never took root (Hoppe, 1952).

Analysis of the evolution of the schoty in Russia shows that it is difficult to establish its origin. However, it is still more likely that its predecessor was European models of the counting device rather than Chinese ones. Moreover, an analysis of the opinions of English and French travellers about the schoty unambiguously proves the Russian identity of this counting device.

How to use the schoty

The Russian abacus uses a positional decimal counting system with non-positional unary coding for each digit. Each row of beads represents a digit, from the wire with four beads up increasing the order from ones to hundreds of thousands, and down decreasing from tenths to thousandths (Figure 9). The maximum value for each row is ten multiplied by the row's weight (for the row of ones the maximum number is 10 if all beads are on the left, for the row of tens – 100, and so on). To form a number on the schoty, the user should slide the beads along the wire from right to left (Gagin, 1960). After the tenth bead in the row is added to the other nine on the left, a unit is carried to another row, an operation which involves three steps: (a) sliding the 10th bead to the left to the other nine beads; (b) sliding all 10 beads to the right to empty the whole row; and (c) sliding left one bead in the next row up to record the carried unit.

Figure 9.

Scheme of Russian abacus (Sokolov et al., 2018: 8).

When sliding the number, it is recommended to use three fingers – the middle, index and ring fingers, and for dropping the beads – the large finger (Kononenko, 1960). According to the recommendation of V. Bykov, ‘everyone who wants to work well on the schoty needs to exercise for about two hours daily during a week’ (Bykov, 1902: 24). To work well means the ability to ‘put numbers correctly, distinctly and quickly on the schoty’, as well as ‘so that the schoty do not rattle’ (Bykov, 1902: 24). A number of practical exercises for fingers existed.

The schoty performed addition, subtraction, multiplication and division.

Addition on the schoty is performed upwards (from lower rows to higher rows). The user begins by forming the first addend on the schoty and follows the steps below from the lower row upwards. On the respective wire, one slides left the number of beads corresponding to the number of units in the respective digit of the second addend. If there are insufficient beads for step one, then they slide to the left as many beads as are missing to complete the operation on the required wire, and slide left one bead on the wire above. If after a slide (first or second or next) all 10 beads have been moved to the left, then all the beads on this wire are moved to the right, and one bead is slid to the left on the next wire up. After these steps are completed for each row, the beads remaining in the left-hand column will represent the resulting sum.

Subtraction on the schoty is performed in reverse order – downwards, from the higher rows to lower rows. Since the schoty is not designed to handle negative numbers, one should always deduct the smaller positive number from the bigger positive number. If one needs to deduct a bigger number from the smaller number, they should switch them and keep the minus in mind.

Multiplication by a one-digit number is performed by adding the multiplier to itself the number of times corresponding to the multiplicand. Integer multi-digit numbers are multiplied by value positions. Using simplifying techniques reduces the complexity of calculations. To multiply a number by 10, they move the number on the schoty one wire up. Multiplication by four is replaced with double multiplication by two, multiplication by five – with multiplication by 10 and division by two, multiplication by six – with multiplication by five and addition of the original number, multiplication by seven – with three times multiplication by two and subtraction of the original number, multiplication by eight – with three times multiplication by two, and multiplication by nine – with multiplication by 10 and subtraction of the original number.

Division is generally replaced by subtracting the divisor from the dividend.¹ Division on the schoty, as well as on paper, is a difficult task; it is practised with convenience by no means in all cases. The dividend is formed in the lower part of the schoty. In the upper digits of the dividend, they select a group of such size that the number it makes is bigger than the divisor but smaller than the divisor multiplied by 10. The divisor is subtracted from the number formed on the schoty until the minuend² becomes smaller than the divisor. As in multiplication, simplifying techniques can be applied. Division by two is performed upwards, starting from the lower wires. On each wire, they slide right half of the beads on the left-hand side. If the number of beads on the left is not divisible by two, the ‘extra’ bead is also slid right, and another five beads are moved left on the lower wire (one digit down). Division by three is replaced with multiplying the original number by three and then adding the product of multiplication to itself while shifting down (by forming the addend a wire down) for each addition, as many times as there should be digits in the quotient. Division by four is replaced with two times dividing by two, division by five is replaced with division by 10 and multiplication by two, division by six is replaced with division by two followed by division by three, division by eight is replaced with three times dividing by two, division by nine is replaced with adding the number to itself by shifting a wire down as many times as there should be digits in the quotient. Then, they divide the sum by 10. To divide a number by 10, you should move the number one wire down.

Often simple manipulations help to reduce an operation to a combination of multiplications and divisions. However, the range of such tricks depends on the operator's skills. The art of counting on the schoty essentially boils down to the user's ability to reduce any required calculation to a combination of easier operations. The methods of calculating on the schoty are diverse, and this allows you to choose the best solution, makes you think (Zorin, 1907) and develops the accountant's intelligence.

Russian abacus (schoty) as a driver of social and economic development

Modern research (Carnegie and Napier, 2012) shows that accounting is primarily a social practice, which is based on relationships between people. Therefore, accounting techniques, including counting tools, significantly affect the organisation of business, and through it, society as a whole (Burchell et al., 1980). Within the framework of Annales’ School, Russian abacus as the main counting device in Russia in the nineteenth and twentieth centuries is the very artefact that complements the written sources of historical studies. Accounting history requires a contextual analysis of its impact on organisational and social development in addition to detailed description of the artefact itself (Burchell et al., 1980).

The first schoty, which did not yet have a modern look, was used in the Muscovy in the state economy and for taxation. They were restricted to officials use; the rest of the population was mostly illiterate. Peter the Great's (1672–1725) reforms that provided the basis for Russian entrepreneurship led to the expansion of schoty use. This was also when the first books on accounting appeared in Russia. At the end of the eighteenth century, teaching of accounting in schools began (Kuter and Sokolov, 2012). On December 12, 1801, Alexander I (1777–1825, years of reign 1801–1825) issued a decree, according to which persons of non-noble estates could buy land. This was the beginning of the elimination of the monopoly of the state and the nobility on the main means of production. Earlier, in 1800, the Bankruptcy Charter was adopted, which introduced the compulsory keeping of accounting books. The new design of the schoty, which had developed by this time, stayed the same. Abacus made it possible even for illiterate and unaccountable former peasants and small traders to easily perform complex calculations (Spassky, 1962). Russian merchants famously used the schoty without understanding mathematics. This fact is perfectly described by A. Chekhov (1860–1904):

The teacher takes the textbook and dictates: ‘The merchant bought 138 arshin of black and blue cloth for 540 roubles. The question is how many arshins did he buy both, if the blue cost 5 roubles per arshin, and the black cost 3 roubles?’ … ‘It is possible to solve it without algebra’, says Udodov, holding out his hand to the schoty and sighing. – ‘That's so good to see’… – He clicks on the schoty, and he gets 75 and 63, which is what he needed. – In our way, unlearned’ (Chekhov, 1954: 293).

In this way, the schoty became a tool for transforming small-scale commodity production into a capitalist one.

The facts clearly show that the main tendency of small-scale commodity production consists in the development of capitalism, in particular, in the formation of manufactory, and before our very eyes, manufacture is developing into a large-scale machine industry with tremendous speed. Perhaps one of the most striking manifestations of the close and direct connection between successive forms of industry is the fact that a number of large and largest manufacturers were themselves the smallest of the small industrialists and went through all the stages from ‘popular production’ to ‘capitalism’ (Lenin, 1971: 348).

It is noteworthy that in confirmation of this statement by Lenin, V. Ulyanov (1870–1924) refers to the founder of the first Russian journal on accounting, Belov (Lenin, 1971: 487).

The formation of capitalist production brought about the great reforms of Alexander II (1818–1881, years of reign 1855–1881) in the middle of the nineteenth century. The rapid development of the Russian economy began. It required many qualified personnel, including accountants, and caused an explosive growth in the application and production of the schoty. A new type of trader appeared – a seller of the schoty (Figure 10). In the commercial educational institutions, accounting courses introduced the compulsory study of the schoty.

Figure 10.

A seller of the schoty (1860) (Guter and Polunov, 1981: 10).

The ability to count quickly using the schoty was an essential requirement for accountants seeking employment:

The commercial world and trade organisations were somewhat suspicious of young people who had graduated from institutions, thinking that in Russian conditions familiarity with a long range of theoretical disciplines was less required than basic knowledge of accounting or even just the ability to count using the schoty, and undoubtedly it could be noted that until very recently, even in such large centres as Moscow or Kharkov, it was easier for young people who graduated from lower commercial schools to be hired in trade enterprises’ (Buryshkin, 1991: 107).

Furthermore, L. Tolstoy (1828–1910) taught counting to village children and compiled a textbook of arithmetic for them, the tasks in which involved counting using the schoty.

The schoty gave rise to a whole class of low–skilled business clerks, most of whose work consisted of calculations on this device. Their working day lasted from 10 to 18 h. Receiving a low salary (from 50 to 75 roubles – 10 times less than senior management), they formed a new proletariat. In 1900, there were 27,660 clerks in St Petersburg. The result was the formation of a trade union of clerks and accountants, which was headed by the famous Trotskyist D. Sverchkov (1822–1938). Lenin was present at one of the meetings (Sokolov, 2015).

The revolution in Russia did not lead to the abandonment of using the schoty as the main counting tool. On the contrary, the nationalisation of the economy, which provided a sharp decrease in its efficiency and the enormous growth of the state apparatus, led to the almost universal use of the schoty in everyday and economic activities. Curiously, the quality of the schoty became worse. They began to be mass-produced from cheaper materials: poor wood, copper wires were replaced with steel ones, and after the Second World War, wooden beads were replaced by plastic ones. The transition to socialist production was accompanied by the introduction of centralised regulation of everything and everyone. The ministries began not only to teach, but also to establish the rules for using the schoty: their place on the table, the procedure for sliding beads with fingers, and so on. Only the information revolution of the late twentieth century led to a complete ousting of the schoty from the economy. However, the authors of this article often continue to count using them, as it is faster than opening a computer, brings more pleasure and trains memory.

Using the schoty in accounting

The study of the use of computing technology is one of the seven factors in the analysis of comparative international accounting history (Carnegie and Napier, 2002). Accounting historians do not just search for evidence of the physical recording of transactions, and they also seek to understand ‘how those who prepared and used the accounts regarded (or perhaps ignored) them’ (Carnegie and Napier, 1996: 18). Russian abacus became not just a part, but also a symbol of Russian accounting in the eighteenth and up to the early twentieth century (Figure 11), and it would remain significant practically until the end of the twentieth century.

Figure 11.

Exemplary workplace of an accountant. Illustration from the Schetovodstvo journal (Russian Abacus in the Educational Process, 2013).

Back in the 1980s future accountants studied how to use the Russian (trade) abacus in educational institutions. All pupils studied counting using the so-called classroom abacus that was a

wooden frame on the legs, in which 10 wires with 10 beads on each are horizontally installed. 10 wires are vertically inserted into the upper plank of the frames, onto which a whole cylinder and cylinders divided into fractions are strung. Also there was a table version of such abacus, which differed in height and the availability of devices for hanging on a wall or board (Emenov, 1940: 1).

In practice, until the early 2000s, one could meet old school accountants who distrusted electronic calculators and used the Russian abacus to sum up columns in accounting ledgers. The usage of the schoty is also described in special accounting manuals. Guidelines issued by the Soviet Ministry of Trade read:

The productivity of counting using the schoty is especially affected by the factors listed below, however, they are often neglected by accountants. It is well known that the schoty with bent wires reduces productivity and irritates accountants, while straightening the wires is an easy and cheap operation that can be performed in any handicraft workshop. Meanwhile, the schoty in good repair is still rather rare. The two beads in the middle and the first beads on the eighth and eleventh wires should be painted black. This essentially guarantees that the calculations will be correct and more mechanised (the beads will be easier to see), which improves work quality and productivity. In reality, in most cases, the black beads on the schoty were often missing or were in a wrong place, because the beads have scattered and were reassembled carelessly. Many operators checked if addition was correct by subtracting all addends.

Many junior clerks, who performed continuous calculations, used a smaller abacus with smaller beads. Senior employees that need to perform individual calculations had the largest abacus. Of course it would be better if everyone had a larger abacus; however if there were few of them, bigger devices should be given to those who were using them continuously. It's a key to the clerks’ productivity. The schoty was not always correctly positioned on the desk. For continuous calculations, it should be at the clerk's right shoulder. Some accountants performed calculations using only their index finger. It was a bad habit. Experienced clerks used all the fingers on the right hand to perform calculations; most people slid the beads to the left using the middle finger, and to the right with the right thumb. The counting device [the schoty] should be placed on the right hand side. One must ensured that beads [from different rows] on the schoty didn't touch each other. Broken schoty should be turned in for repair’ (Vilensky, 1938: 24–25).

The schoty have become an integral element, a sign of the accounting department, here is its description in the late nineteenth century by a famous Russian writer who served as a tax auditor: ‘The largest room was filled with tables and cabinets, and dozens of people were sitting at these tables. All these people were engaged in writing and clicking on the schoty’ (Salov, 1886: 199). ‘Around the dry bony, fractional crackle – like fingers of the dead, rattle the schoty’ – wrote the famous poet of the twentieth century (Cherny, 1960: 105).

The schoty formed rules for processing accounting data. Transactions were registered in accounting books, the results of which were calculated using the schoty. Their rechecking by senior accountants was also carried out with the schoty.

Calculations of indicators were often made directly using the schoty without intermediate entries and subtotals:

Suddenly he got up, took the schoty and began, without haste, to slide the beads, saying aloud: ‘I’ll give him the papers for the mortgage on the house for five thousand roubles at a nominal price, that is a thousand roubles per each one; I bought them at 660 roubles per each one, this is the best use for each thousand 340 roubles, and the percentages for each thousand – 120 roubles; in total a net profit is 460 roubles – good use – almost a hundred to a hundred’ – he said to himself in thought (Shkulev, 1910: 5).

Similar scenes were shown in the theatre. In the play by the most famous Russian playwright and creator of the classical theatre, A. Ostrovsky (1823–1886), whose main subject was a description of the life of Russian businessmen:

Vasilkov: Vasily! Bring the schoty from the office table. (Vasily brings the schoty and leaves. Vasilkov sits down at the table and begins to calculate the invoices...). Vasilkov: I’ve finished. There are thirty-two thousand five hundred forty-seven roubles ninety-eight kopecks’ (Ostrovsky, 1950: 306–307).

The schoty also showed the result of calculations when making payments with the client, and often a paper document was not drawn up:

Prokhor says nothing; he even more casually takes a tool from the wall, that is the schoty, and hands it to the master, while he stands at a distance with one foot forward and his hands clasped behind him. ‘How much?’ – asks the master, preparing to use the schoty. ‘Last week seventy oats were released to the city…’ – I want to say – five quarters. ‘Seventy-nine’ – the master finishes and puts it on the schoty (Goncharov, 1912: 73).

During conversations, the numbers were often not named or recorded, but shown on the schoty:

He put three thousand on the schoty and was silent for a minute, looking at the schoty, then in the eyes of the father, with this expression: ‘You can see how small it is! It is not profitable to sell hay now, you know…’ (Tolstoy, 1960: 27).

This technique was often used for fraudulent purposes. In the memoirs of a famous Soviet accountant, you can read:

A person buys five items of goods, the cashier gives him five checks. But all the wise sense of the old technique was that the total of five checks the cash register did not count, and the cashier manually summed up the cost of the purchase using the schoty. It is clear that she cheated many people and created self-supporting income for her and people (Dorofeev, 2007: 53).

The representation of numbers is not on the paper, their non-naming, but as a set of beads has become a distinctive feature of the mentality of the Russian accountant. This feature was illustrated by a prominent Soviet writer M. Zoshchenko (1894–1958). The hero of his story, the accountant Zabezhkin, leaving the office, ended the working day on the schoty: ‘At four o’clock exactly Zabezhkin moved his chair and spoke loudly: “Four”, slide four beads on the schoty and went home’ (Zoshchenko, 1923: 137). Zoshchenko knew what he was writing about: before becoming a professional writer, he worked as an accountant at the Leningrad military port.

When processing mass transactions and calculating totals, the practice became widespread when the accountant, making a record, dictated the recorded amount to his assistant, who slides it on the schoty, adding to the previous total. This procedure was described by F. Dostoevsky (1821–1881): ‘He taps on the schoty, and I sit and record into accounting books’ (Dostoevsky, 1958: 432). This practice greatly facilitated the introduction of electric punching machines, such as the machine invented by H. Hollerith (1860–1929). The tabulating machine was an electro-mechanical machine designed to assist in summarising information stored on punched cards. Arrays of homogeneous data were typed on punched cards, loaded into a tabulator, which folded them. Until the advent of electronic machines and calculators, the speed of addition operations using the schoty was higher than the speed of the same operations on mechanical devices.

The schoty ‘programmed’ their owners to work as an accountant. From the memoirs of a Soviet accountant of the second half of the twentieth century:

My father taught me how to use the schoty when I was still at school. I guess that's why I chose my profession. I also worked at Verkhnelupinsk forestry since 1979, first as a cashier, and then, after graduating from the economic college, as an accountant (Yaprintsev, 2018).

In all commercial educational institutions, the rules of using the schoty were taught. For this purpose, special classes were arranged (Figures 12 and 13). The poet M. Roizman (1896–1973), checking the accounts of the most famous literary cafe of the 1920s, the Pegasus Stall, recalled:

When I was in high school at the Moscow commercial school, the students went to the enterprises with our teacher Reinson, who wrote more than one textbook on accounting and commercial correspondence. In trading firms and factories we were familiar with accounting books, and knew very well that any figure can be verified with the help of exculpatory documents. I took the schoty, slid the beads, checking the debit and credit (Alive Yesenin, 2018).

Figure 12.

Lesson on accounting at the Moscow commercial school, photo from the anniversary edition dated 1904. The schoty are on the teacher's desk (Russian Abacus in the Educational process, 2013).

Figure 13.

Special classroom with the schoty (Medvedev, 2013).

The schoty in fine arts

The schoty was the symbol that in the theory of the Annales School constructs the historical period, determining the actions of people. This symbol is visualised in Russia, especially in the fine arts.

Yamey (1989) considered the visualisation of accounting in pictures. He analysed only one picture that contains a counting tool The Parable of the Unjust Steward (woodcut from Das Plenariumorder Ewagelybuoch, 1514) by Hans Schaufelein (ca. 1480/1485 – ca. 1538 or 1540) (Figure 14) – a German painter, engraver and illustrator. It's an illustration within the letter ‘O’ at the top of the page. It represents a wealthy man sitting at a table with two ledgers in front of him, and the man is pointing at the chart with some calculations (Yamey, 1989). In his book, Yamey offered no comments regarding the counting device, since the main focus of his research were accounting books.

Figure 14.

Woodcut by Hans Schaufelein (1480–1538) (Yamey, 1989: 83).

The schoty became the central element of Boris Kustodiev's (1878–1927) The Merchant, or an Old Man Counting Money (Figure 15). The model for A Man with the Schoty, a sketch in lead pencil on paper made one year before the painting, was the husband of his sister, an accountant, V. Kastalsky (Figure 16).

Figure 15.

Kustodiev B. The Merchant, or an Old Man Counting Money. 1918 (Tolstova, 2003: 49).

Figure 16.

Kustodiev B. A Man with the Schoty. 1917.

In addition to Kustodiev's painting, there is another one – Workday Count – where the schoty is in the centre of the composition. It was painted by A. Moravov (1878–1951), an artist who lived at the same time as B. Kustodiev (Figure 17). In the picture, a young girl uses the schoty. The artist is accurate, because the girl slides the beads with the middle finger, the thumb is ready to reset the calculations, and she works correctly, as per the above-mentioned accounting instructions. In the picture by S. Gribkov (1822–1893), At a Small Shop, a Russian abacus is in the centre – on the counter at the merchant's right hand, and ready for application (Figure 18).

Figure 17.

Moravov A. Workday Count. 1934.

Figure 18.

Gribkov S. At a Small Shop. 1882.

The schoty is also the centrepiece of An Accountant's Morning, a still-life painting by G. Valkhvadze (1949–2016), a Georgian painter (Figure 19). It was painted in 2004, which indicates that the schoty still remains a symbol of accounting in Russia.

Figure 19.

Valkhvadze G. An Accountant's Morning. 2004.

Conclusion

In our study, we proceeded from the need to expand the traditional approach to accounting history by analysing its artefacts, which are an important source of historical information. We chose the Russian abacus as the object of our research. This tool, which is very important for Russian accounting, is not well represented in the international literature. The article first includes this object in the international discourse of accounting history. To do this, we examined the physical characteristics of the schoty, their significance for Russian society, economics and accounting. Second, to analyse the social aspects of the application of this tool, we followed the Annales School. It shifts the focus of studying history from describing sources to analysing them from the point of view of knowledge, ideas and mentality of people of the epoch. This ‘New History’ actively studies the development of technology, the memories of individuals, draws on literary sources and objects of art. According to the founder of the school M. Bloch, ‘In our writings, one word reigns and illuminates everything – understand’ (Bloch, 1986: 39).

The analysis of the history, design, rules of using the schoty in the social context and ways of applying them in accounting, as illustrated by examples from literature and art, showed that in the nineteenth and twentieth centuries the schoty became a special phenomenon of Russian life. They were used for calculations, explanations of calculations, teaching numeracy and visual presentation of numbers and were used as a tool for fraud. The schoty was strongly associated in the public mind with accounting and business. This was facilitated by the convenience and extreme simplicity of this device; as a result, we can assume that the Russian abacus was a unique tool. All Russian accountants used the schoty to perform calculations until the twenty-first century. The most famous Russian accountant of late twentieth and early twenty-first centuries, Ya. Sokolov (1938–2010), never used a calculator according to his relatives and students and preferred the schoty until his dying day. The schoty, like arithmetic, is not related to the way social production is organised. However, their simplicity and accessibility to illiterate people, who were the majority in Russia up to the twentieth century, allowed the construction of capitalism to accelerate (Lenin, 1971). Their widespread use thus greatly contributed to the development of capitalism in Russia. The simplicity, low cost and efficiency of the use of the schoty greatly facilitated the functioning of the centralised Soviet economy and made it possible to process large amounts of data.

The interpretation of the counting device as a cause of accounting change follows from Hopwood (1987), the need to include a national (non-English language) narrative in the historical discourse from Carnegie and Napier (1996, 2002), and the consideration of the social and economic aspects of using the schoty adds to the studies of Hopwood (1983, 1987).

Our research is limited in period. It covers only the nineteenth and twentieth centuries. Undoubtedly, the schoty in the Muscovy and the Russian Empire in the eighteenth century needs a separate detailed study. Also, just a few aspects of the schoty application were studied. The relationship between the schoty and other counting devices, the most common of which is Odner's adding machine, remains outside the scope of this research. Descriptions of the schoty in literature and art cannot be considered exhaustive since this was time-based and the analysis of the development of capitalism in Russia was not complete.

This research needs further development. Detailed descriptions of the history of learning how to use the schoty, and their use by other people, not accountants, managers, cashiers, clerks and officials, are required. Their inner life should be considered in this research. We believe that the language of such research may be stylistically different from the usual scientific works of indifference that lack empathy for the story. Ideally, such research should be written in a different language, in which the researcher can also invest their own emotional perception of the object world surrounding the people in the past.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship and/or publication of this article.

ORCID iD

Ekaterina Zuga

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