Lietuviškos matematinės terminologijos istorijai

LIETUVIŲ KALBOS LEKSIKOS RAIDA LIETUVOS TSR MOKSLŲ AKADEMIJA TOWARD A HISTORY OF LITHUANIAN MATHEMATICAL TERMINOLOGY Z. ŽEMAITIS Lithuanian mathematical literature is young, and its terminology is young as well. Nevertheless, it has its own history, with certain notable periods, brief though they may be. The first period—from E. Mainionis’s (according to the “Lithuanian Bibliography,” S. Gimžauskas’s) “Pradžomokslio Lietuwiszko spaudraszczio ir rankraszczio su pridėjimu skatmanio” (Warsaw, 1862) to the First World War—was a period of searching for terminology. E. Mainionis sometimes used very strange terms, of unknown formation, such as skaitmanys “calculation, arithmetic,” pražas “digit,” skaitlis “number,” vienalakė “unit,” pridendis “plus sign, plus,” išžembis “minus sign, minus,” užmatas “problem,” and so on. Nor did the other authors of that period (S. Skačkauskas, J. Gailutis—P. Matulionis, Petras Nėris—V. Vileišis, A. Vėgelė—the translator of Thoma’s arithmetic, P. Mikolainis—the author of a beautifully illustrated arithmetic book, P. Mašiotas, J. Damijonaitis, and others) have a common, unified terminology. The mathematics textbooks published by the Lithuanian Scientific Society during the First World War for Lithuanian primary and secondary schools likewise did not adhere to a unified terminology. During the First World War, the revolutionary movement against the tsar and the reactionary government that served him grew and spread rapidly in Russia. It began to become clear that the defeat of tsarism would give the peoples within the Russian Empire, including Lithuanians, the freedom to develop their own culture and establish their own schools. Encouraged by such hopes, Lithuanian mathematicians P. Mašiotas, M. Šikšnys, and the author of this article, who at the time were working in Lithuanian schools for war refugees in Voronezh, became concerned with preparing Lithuanian mathematics textbooks and resolved first to establish a unified mathematical terminology. Our eminent linguist and cultivator of the Lithuanian literary language, J. Jablonskis, who taught at the same schools, readily agreed to help them with this work. He set aside a regular time (Thursday evenings) when the aforementioned mathematicians could come to him and consult on questions concerning the creation of mathematical terminology. P. Mašiotas attended those meetings only occasionally, since, having become director of both gymnasiums (boys’ and girls’) and being deeply involved in writing children’s literature, he had no time for the discussions. K. Šakenis, who was writing a physics textbook for secondary schools, sometimes came to consult on questions of physics terminology. The author of these memoirs attended the consultations most regularly; J. Jablonskis assigned him 195 most of the work: reporting on the meaning and origin of terms in other languages, suggesting Lithuanian equivalents, and so on. The question of what to call a number was examined in depth. Until then, the terms skaitlis, skaitlinė, skaitlius had been used, as well as the verb derived from the last of these, skaitliuoti. We mathematicians found skaitlius quite acceptable, since living speech also had words of similar structure: derlius, drėblius, dieglius, perteklius. J. Jablonskis did not object strongly to that word, but he would not agree under any circumstances to forming the word skaitliuoti from it: he maintained that a noun could be formed from a verb, but forming a verb in turn from such an artificial noun was impermissible; on that occasion he angrily denounced the already fairly widespread neologisms mokytojauti, gydytojauti and the like. J. Jablonskis proposed using the words skaičius, skaičiuoti, and it was clear to all of us that these would be the best terms. There was also considerable discussion about what to call a unit. The terms used earlier—vienaląkė, vienutė, vienukė—were disliked by all of us; vienata had also begun to be used, especially by non-mathematicians, but we disliked this word because it sounded archaic (cf. gyvatą in old Lithuanian writings). It was pointed out that small numbers of objects, or units in general, are called in Lithuanian dvejetas, trejetas…, so the term vienetas would not conflict with the spirit of the Lithuanian language. J. Jablonskis strongly supported this, but some participants in the discussion accepted it with reservations. Apparently, some mathematicians were influenced by the practice of other languages, in which a unit is invariably called by a feminine noun (cf. jedinica, jedynka, Einheit, unitas). Nevertheless, J. Jablonskis’s support for using the term vienetas proved decisive. K. Šakenis was advised to use in physics the analogously formed word visetas (вселенная, universum) rather than visata, which also sounds archaic. J. Jablonskis agreed with this too, as far as I recall, but the term was not included in the glossaries of terms that we later published, and to this day visata is used. I reported on the names of mathematical operations that in other languages the name of a mathematical operation itself is generally not distinguished from the name of the process by which it is actually performed, whereas logically they ought to be distinguished—and in Lithuanian this is easy to do. Everyone agreed, and the proposal was adopted to call the operations sudėtis, atimtis, daugyba, dalyba, while retaining the previously used terms sudėjimas, dauginimas… to denote the carrying out of specific operations (e.g., trupmeninių skaičių dauginimas). It was proposed that the further operations—raising to a power and extracting a root—be called laipsniuote and šakniaute. The first proposal was approved; the second met with considerable reservations. For in other languages (probably by tradition), the name of the operation was associated with a physical process—the pulling up of a plant’s root. In a mathematical operation, however, certain numbers are simply sought, perhaps rather ineptly called šaknimis (cf. the different meaning of root in equations). The term under discussion did not take hold later, and the path taken was the one already well trodden by other languages. An important area of mathematical terminology concerns the names of the numbers involved in operations and of their results. The report on the practice of other languages showed that, through tradition or perhaps a kind of inertia, even very illogical usages had survived in them. For example, the result of multiplication is called Produkt in German, произведение in Russian, and iloczyn in Polish; fundamentally, these terms say nothing about which operation’s result they refer to, since the same name could be given to the result of multiplication or of any other 196 consequences of the operation. The result of division is called Quotient in German, a word of Latin origin that tells a German speaker nothing about which operation produced that number; in Polish, the quotient is called iloraz, but that name could also be given to the multiplier, which likewise indicates how many times (ile razy) the given number must be multiplied (or taken). In those languages, the multiplier and divisor are called as they were in earlier Lithuanian publications: daugintojas, dalytojas (meaning not a particular number, but a person performing multiplication or division). We had resolved to avoid such illogicalities strictly, to call the numbers involved in operations by the shortest possible noun forms (e.g., dėmuo, dėmenys rather than dedamieji, sudedamieji); to treat the numbers by which one multiplies or divides as special kinds of instruments and form their names according to living-language patterns (e.g., adiklis, kabiklis), namely: daugiklis, daliklis and, analogously, in the shorter forms—skaitiklis, vardiklis. It was therefore also decided to call the result of multiplication sandauga. The question of preposition use in describing multiplication and division operations caused us considerable concern. Previously, people had said: dauginti, dalyti ant 5 or dauginti, dalyti penkiais. It was clear that the first construction was wholly unsuitable for Lithuanian. The second construction is correct and could be used when the multiplier or divisor is a specific positive integer, but in more general cases and in operations with literal numbers it is inconvenient, since one would have to add “...skaičiumi” each time, and so on. J. Jablonskis recalled the expressions of everyday speech padalyti, išmatuoti iš akies: ji moka išvirti pietus iš knygos, that is, “as the eye indicates,” “as the books indicate.” Hence the preferred construction was padauginti iš daugiklio, that is, “as the multiplier indicates.” We were all delighted with this proposal. J. Jablonskis’s proposal to use the preposition iš (“from”) in the case of division as well did not arouse enthusiasm among mathematicians. I pointed out that using the preposition iš in three different operations would be inconvenient not only stylistically, but would also make mathematical language harder to understand; one would often have to say dalytis iš skaičiaus (“divide from a number”), and so on. Attention was drawn to the fact that division encompasses two cases that differ considerably in how the operation is interpreted and performed: (a) division into equal parts and (b) division by capacity (measurement division). In the first case (a), it is natural to use the preposition į (“into”) (e.g., dalyti į 5 dalis, “divide into 5 parts”), while in the second (b), the preposition po (“each”) (e.g., 35 kg padalyti, išdalyti po 5 kg, “divide, distribute 35 kg into portions of 5 kg each”). With concrete numbers, especially numbers expressed in words, one must use one preposition or the other according to the nature of the operation; with general, literal numbers, however, the preposition po (“each”) is more suitable. I therefore proposed using the preposition po (“each”) in such general cases, rather than iš (“from”). J. Jablonskis’s authority prevailed, but even now it seems to me that it would have been better to retain the preposition po. The new Lithuanian algebra terms (teigiamieji, neigiamieji skaičiai ir kt., “positive, negative numbers, etc.”), as far as I remember, were proposed by M. Šikšnys and quickly accepted by all of us. Much thought, and even some argument, went into the term lygties (“equation”). This term had not appeared in earlier Lithuanian writings. Following the example of other languages, the terms lygybė, lyginys (“equality, equalizer”) suggested themselves; the terms lygmė, lygmuo (“equivalence, level”) had also been proposed. It seemed that the most suitable term would be lygtis. J. Jablonskis strongly opposed the singular form and proposed lygtis. He explained that this concerns the necessary interaction of two parts, equality, and balance; in such cases, plural nouns are used in everyday speech, such as rogės, žirklės, žio- 197 tys. I had to do a great deal of persuading to convince J. Jablonskis that mathematicians needed to express the concept in the singular, so that it would be clear that we were dealing not with several equations but with one. J. Jablonskis yielded, and the term lygtis. was adopted. Other terms in arithmetic and algebra (e.g., trupmenos, jų bendravardinimas, proporcijos, logaritmai, “fractions, reducing them to a common denominator, proportions, logarithms,” etc.) caused no major difficulties or disputes. M. Šikšnys undertook to prepare the results of this work for publication1. The author of these memoirs also had to do a great deal of work on the terminology of geometry and trigonometry. One of the first questions concerned the names for lines. It was clear that retaining the terms tiesioji, kreivoji, statmenoji (“straight [line], curved [line], perpendicular [line]”) would create many linguistic inconveniences and mathematical ambiguities. There was a perceived need to name these objects not with adjectival forms but with shorter nouns. I proposed kreivė, tiesė, statmuo (“curve, straight line, perpendicular”). Everyone agreed, although these words were not taken from everyday speech. There was debate over the name for a tangent. The adjectival form of the name for this line could lead to considerable ambiguity and even confusion: is it a line that touches something, or one that is touched by something? Following the pattern of tiesę, kreivę (“straight line, curve”), I proposed naming the tangent liesne, as everyday speech uses words such as rėksnė, dėsnė (višta) (“shrill one, laying hen”). Having examined the nature of the line (it touches, rather than being touched by something), J. Jablonskis decided that the most suitable name would be lietėja, thereby emphasizing a certain activity on its part. By analogy, the secant was named kirtėja. Until then, the words ratas (“wheel”) and stipinas (“spoke”) had been used for the circle and its radius; A. Jakštas-Dambrauskas used the term ratilas. The terms apskritimas (“circle”) and spindulys (“radius”), apparently proposed by J. Jablonskis, were quickly adopted, though radiusas was also allowed. At J. Jablonskis’s suggestion, the term skritulys (“disk”) was also adopted for the “figure bounded by a circle4”. As far as I remember, the term plokštuma (“plane”) caused no disputes. From the outset, it did not seem entirely suitable to me. Plokštuma ought to mean the flat part of any surface (e.g., a particular bounded plain in mountainous terrain, the flat section—a landing—of a folded roof, and so on). Calling an infinite flat surface plokštuma is just as imprecise as calling a straight line tiesuma (“straightness”) or a curve kreivuma (“curvedness”). It seemed to me that a term was needed that would denote not a surface’s property or character, but the infinite surface itself; such a technical term could be plokšmė, plokštis. Everyday language, too, contains many words of this formation that express certain generalized concepts, for example: tėkmė, gelmė, kilmė (“flow, depth, origin”), and so on. Some mathematicians still use the term plokšmę; it readily forms the adjective plokšminis (“planar”), instead of plokštuminis, and this causes no ambiguity. The ordering of trigonometric terminology caused no major difficulties. International terms were used as a basis; differing opinions concerned only their Lithuanian endings and declension. It was proposed that the words sinus, cosinus be treated as nominative forms in Lithuanian as well and declined accordingly: sinus, sinaus, sinui, and so forth. Apparently, J. Jablonskis determined that their nominative forms should be Lithuanianized, that is, written sinusas, cosinusas. It was then suggested that tangens, cotangens, sekans should be called tangensas, contangensas, rather than tangentas, cotangentas..., as J. Jablonskis required, invoking the rule that Lithuanian nominative endings should be attached to the stem of a foreign-language word’s genitive. Even examples from everyday speech did not help, 1 Žr. M. Šikšnys, Aritmetikos ir algebros terminų žodynėlis, Kaunas, 1919, 47 p. 198 where foreign-origin names Felix, Clemens, Alphons were Lithuanianized (cf. Feliksas, Alfonsas, Klemensas), no attention was paid either to the fact that, according to the rule applied to tangentui, cotangentui, perhaps the terms sinus, cosinus should also be used. The terminology of geometry and trigonometry was entrusted to the author of this article for preparation for publication, and it was printed soon afterward2. K. Šakenis had also attended the meetings at J. Jablonskis’s a time or two, specifically to discuss questions of physics terminology, and we would consider them. I remember that the term he proposed, švytuoklė (Russian маятник), prompted considerable debate. Attention was drawn to the fact that the name švytuoklės evokes certain phenomena of light and images of glowing (cf. the word švyturys). The oscillating device of pure mechanics would be most aptly called svyruokle. Nevertheless, as far as I recall, J. Jablonskis sided with Šakenis, and the term became established in textbooks. The questions raised by K. Šakenis concerning the names of chemical elements were discussed vigorously. He tried to Lithuanianize many of them, but it was decided to base the names on widely used international terms, making an exception only for one or another element whose name, for practical reasons (technology, physiology, hygiene), ought to become widely popularized. The first exception was the element O (oxygenium). K. Šakenis listed previously used names: rūgštadarys, rūgštagamys, rūgštinys. K. Šakenis himself, if I am not mistaken, proposed calling it rūgdariu or something similar. J. Jablonskis asked what the element’s most characteristic chemical properties were. Knowing at least a little about the principal chemical compounds, I explained that the element’s presence in acids was not essential, since there are acids in whose composition it does not occur (e.g., HCl); the element’s most characteristic property is that other elements burn in it, and therefore its name would most aptly be linked to the word for burning. J. Jablonskis quickly grasped the point, recalled the examples geluonis—that which stings—and gyvuonis—a certain part of the body with which one senses most—and so said that the element O (oxygenium) would most aptly be named deguonimi. It was clear to all of us that this would be the most suitable term. Apparently the same K. Šakenis proposed, by analogy, calling nitrogen gesuonimi, because it extinguishes combustion. This was not approved, since nitrogen does not extinguish every kind of combustion. For the other common element, H (hydrogenium), J. Jablonskis coined the name vandenilio, which soon caught on. Questions of mathematical terminology arose again after returning from Voronezh to Lithuania. At our first institution of higher education—the Higher Courses—advanced mathematics was taught extensively, requiring many new mathematical terms. For the first three or four years, I had to attend to these matters almost entirely on my own, consulting with J. Jablonskis. In questions concerning the Lithuanianization of any scientific terminology, he approved two fundamental principles: a) to base the names of related concepts on one form of a foreign-language word (e.g., a noun) and derive all the other forms from it according to the rules of our language; for example, taking the Greek word analizis, to form analizinis, analiziškas, but not analitinis, analitiškas, which would instead be derived from an adjective form; b) to adopt a foreign-language term in its original form if it does not conflict with the pronunciation of our language. For example, Greek terms that sound entirely Lithuanian, such as ana- 2 Žr. Z. Žemaitis, Geometrijos ir trigonometrijos terminų rinkinėlis, Kaunas, 1920, 99 p. 193 There is no reason to claim the forms *lizis, sintezis*, already twice distorted (in French and German), as one’s own (cf. analizė, sintezė), and to decline them in this way: analizė, analizės, analizei…, when the word can be declined perfectly well according to its original basic form, preserving the Greek stress as well, e.g.: analizis, analizío…; or, in order to preserve the Greek gender of the word too, declined according to the Lithuanian word pilnatis: analizis, analizies, analiziai, and so on. The same should have been done with the words minuta, sekunda, tertia, kvarta, kvinta, etc., rather than changing them to minutė, sekundė, tercė, kvartė, etc. We can also recall another example of the distortion of Latin terms, one that was widespread and accepted by our linguists facitu consensu. In the Middle Ages and at the beginning of the modern era, European scholars widely used sexagesimal fractions, called philosophical fractions (fractiones philosophicae), which had come from Assyria-Babylonia. In these, the first fraction (1/60) was called prima pars minuta (the first diminished part), abbreviated as — minuta; the second fraction (1/60) — secunda; the subsequent ones: tertia, quarta, quinta, and so on. These names for fractions have survived to our days and are still used in measuring angles. Therefore, it would have been better to retain the original forms minuta, sekunda… rather than the secondary forms borrowed from German, minutė, sekundė, and so on. And if this had already been done, then the forms tercija, kvartė, kvintė,… oktavė… should also have been used consistently. On matters concerning mathematical terminology, I also had occasion to approach the State Terminology Commission, which was established in 1921 and included a subcommittee on mathematical terms. Its members included Pranas Mašiotas, A. Jakštas-Dambrauskas, the artist Adomas Varnas, Antanas Kaunas and, I believe, two young linguists as well. Around 1923–1924, I approached P. Mašiotas at least twice, asking that the subcommittee express its opinion on terms used at the university and those being newly coined. P. Mašiotas organized meetings. At these, P. Mašiotas himself remained passive, while A. Jakštas-Dambrauskas proposed his own terms, sometimes even strange ones. The linguists had not delved into mathematical subjects and could offer little help when the terms were being considered. Therefore, almost nothing was accomplished in the field of mathematical terminology under bourgeois rule. During the years of the Soviet system, terminological work was greatly expanded and intensified. Scientific institutions turned their attention to compiling and publishing terminological dictionaries for individual fields of science, technology and other areas. Dictionaries of legal, geological-geographical, chemical, physical, land-reclamation, textile and sports terminology have already been published. Dictionaries of botany, economics, forestry, medicine and other fields have been prepared or are being prepared for publication. In 1954, consideration of mathematical terms also began, with the participation of the Terminology Commission of the Institute of the Lithuanian Language and Literature (J. Kruopas, V. Bartusevičius, B. Vosilytė) and mathematicians from Vilnius State V. Kapsukas University: Z. Žemaitis, J. Kubilius, P. Katilius, G. Žilinskas, V. Statulevičius, V. Paulauskas, K. Grincevičius. The terms used in elementary mathematics textbooks were considered and adopted at the meetings. The terms tangent (lietėja…), plane (plokštmė…), synthesis (sintezė…) and others sparked the most disagreement. The mathematicians undertook to continue compiling a card index of higher-mathematics terms so that a large dictionary of mathematical terminology covering all branches of mathematics could be prepared in the future. This work continues intensively to this day. 200 As we can see, during the years of the Soviet system serious attention was paid to our mathematical terminology, and much was done to standardize it in textbooks and other mathematical literature intended for a broad readership. At present, greater concern is prompted by terminology associated with new and very rapidly developing mathematical sciences. It would be good if the Terminology Commission of the Institute of the Lithuanian Language and Literature and the republic’s mathematicians continued their terminological work and developed mathematical terminology that: a) would help students of modern mathematical sciences to understand new, sometimes very complex concepts and ideas as accurately as possible; b) would also enable people in at least somewhat related fields to gain a correct understanding of the essence and achievements of the most advanced branches of mathematics. At the same time, the terms already in use should be reviewed once again, and those that do not meet the requirements of logic, precision or consistency, or have other shortcomings, should be replaced with better ones. ON THE HISTORY OF LITHUANIAN MATHEMATICAL TERMINOLOGY 3. Žemaitis Summary Comparatively young Lithuanian mathematical literature was for a long time greatly in need of uniform, generally accepted terminology. Lithuanian mathematicians M. Šikšnys and Z. Žemaitis, and to some extent P. Mašiotas, undertook to remedy this shortcoming while working in Lithuanian refugee schools in the city of Voronezh during the First World War. They set themselves the goal of critically reviewing the highly imperfect terminology then in use and, as far as possible, creating terminology that was logically grounded and in keeping with the spirit of the Lithuanian language. The outstanding Lithuanian linguist I. Jablonskis provided the group with substantial assistance in this work. The group had to put in considerable effort to establish correct names for mathematical operations, the numbers involved in them, and the results of those operations. Earlier terms had for the most part been created by literal translation from other languages, where they had often developed historically through tradition but were not always logically grounded. For example: a) the result of multiplication is called Produkt in German, iloczyn in Polish, and произведение in Russian. These names are not essentially connected with the name of the operation itself: they could just as well designate the results of any other completed, performed operation; b) in other languages, the logical definition of an operation is expressed in the same way as the name of the process of carrying it out in a particular instance; c) the names in other languages for the numbers by which other numbers are multiplied or divided coincide with the names of the agents performing the operations, whereas in essence they ought to bear names characteristic of the instruments of the operations, and so on. With the authoritative assistance of I. Jablonskis, the mathematicians named above established mathematical terminology free from the shortcomings mentioned. A physics teacher also consulted the group on questions of terminology in physics and chemistry, and these were discussed thoroughly. For example, the question was raised of what would be a suitable name for the chemical element O (oxygenium). In other European languages, its name is associated with the idea of acid. It was pointed out, however, that oxygen is not an essential ingredient of every acid (for example, HCl contains no O). Its characteristic property, rather, is that other bodies burn in it, and therefore its name (in Lithuanian, deguonis) was formed from the word degti, “to burn.” The results of the group’s work were published in 1920 by its members M. Šikšnys and Z. Žemaitis in the form of two terminology dictionaries. The terminology they established came into general use in Lithuanian mathematical literature. 201