Kostas UŠPALIS

AFTER THE ARRIVAL OF THE DICTIONARY OF MATHEMATICAL TERMS

In order for Lithuanian to be on an equal footing with the languages of modern, cultured and civilized nations, it is not enough for us to have only a correct, well-regulated standard language—which may have sufficed at the beginning of this century—but also a correct language of science. The language of science, after all, is the same standard language plus scientific terminology. Therefore, to preserve the vitality and prestige of our language (not only among linguistics specialists), we need to work more rapidly to organize and standardize terminology, and, where it is lacking, to create Lithuanian scientific terminology. I emphasize Lithuanian, not international, because some people think there is no need to create or standardize Lithuanian terms. It is enough to take international terms (or, more simply, terms from other languages) and add Lithuanian endings and suffixes to them. That would be simpler and more scientific (we might add: and get us to the West faster). For us to have a Lithuanian language of science, as many terms as possible must be genuinely Lithuanian. Therefore, every article or publication on scientific terminology, and especially a terminology dictionary, arouses great interest—we are curious to see what new contribution it has made to the development of our scientific language.

We have long been eagerly awaiting the publication of the “Dictionary of Mathematical Terms” (MTŽ). Although the “Dictionary of Physics Terms” (FTŽ), printed 15 years ago, includes some of the most essential mathematical terms for physicists, they are not enough. We know that the mathematics terminology commission has created many new Lithuanian terms or replaced those used previously, so we were eager to become acquainted with them as soon as possible. I do not intend to write a review of that dictionary—I did not feel competent to do so. I only want to discuss some terms common or closely related to mathematics and physics, and to consider their similarities and differences in usage.

Sometimes one hears the objection that physicists and mathematicians use different terms for the same concepts meaning and value (see FTŽ and MTŽ). Surely they can agree on one common term. I want to answer that these different terms are used deliberately and that there is no disagreement here. A single term should be used only when

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the concepts are identical (that is, there is one and the same concept). In this case, the terms meaning and value are used to denote different concepts. Mathematicians use the term meaning to say what number (or other mathematical quantity), or what kind of number, something denotes, or how large it is. Physicists use the term value to say how much or to what extent a physical quantity is measured in a chosen (usually international) system of units. For example, a physicist will say: “In the formula for free fall, the meaning of the quantity g is the acceleration due to free fall, and its value is 9.81 m/s²,” or “The meaning of Planck’s constant h in physics is very great, while its value is quite tiny (6.6·10⁻³⁴ J.s).” Both quantities are measured experimentally. Many physical quantities can also be evaluated theoretically—calculated using mathematical formulas or models.

Sometimes, indeed, the same concepts in neighboring scientific disciplines are expressed by different terms. It is then difficult to avoid confusion. An example is the use in Lithuanian of the terms komponentas and komponentė. Both derive from the same Latin word componens (genitive componentis). But it is doubtful that they can be considered international. The English use only component, the Germans only Komponente, the French use neither, while the Russians use both. Both mean a constituent part of something (a device, piece of equipment, chemical compound, or mixture). The former is most often used by engineers and chemists, and the latter by mathematicians. Physicists often have to use both terms in the same text. For example, in electromagnetic theory, the field strength is described by the electromagnetic field tensor, whose komponentai (constituent parts) are the electric field strength and the magnetic field strength. The komponentės of that tensor (also its constituent parts) are the komponentės of the electric- and magnetic-field-strength vectors (MTŽ). Thus one has to say komponentų komponentės or komponentai yra komponentės. To avoid confusion, we often used the Lithuanian term dedamoji instead of both terms; mathematicians used it earlier alongside komponentė as well. Now the new MTŽ has dropped dedamosios, retaining only komponentė. Perhaps with good reason. The Physics Terminology Commission, when considering these matters, noted that all Lithuanian dictionaries (even school dictionaries) include a good, sonorous Lithuanian word sąn-

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das, which means precisely a constituent part of something, and therefore proposes using it as a term for engineers, chemists, physicists, and mathematicians instead of komponento ir komponentės (or at least alongside them as a Lithuanian equivalent). Such a short, sonorous term is easily adopted and quickly spreads.

Physicists and mathematicians have not agreed on the use of the terms vaizdas ir atvaizdas. In everyday language there is no strict boundary between these concepts. In physics, vaizdas is generally used to describe the object itself, and atvaizdas its counterpart, formed when light is reflected or passes through an optical instrument (a lens, binoculars, camera, etc.). When preparing FTŽ, after consulting representatives of the Mathematics Terminology Commission, atvaizdais was also chosen for the concepts in group theory describing certain representations of groups (Russian представление, English representation). But that was nearly 20 years ago. In preparing MTŽ, mathematicians’ opinion of that term apparently changed. MTŽ now distinguishes these group “images” from other atvaizdžiai (Russian отображение, English mapping). This is a fairly logical step both in terms of content and the unambiguity of terminology. It is only a pity this was not done earlier, before FTŽ was published. Now considerable effort will be needed before physicists adopt those terms. It remains unclear what to call Tourier and Laplace transforms (transformantes), which physicists need very much but which are absent from MTŽ.

The distinction between atvaizdų and vaizdų (Russian образ, English image) is also welcome. But not everything here is open to approval. For example, if an object's reflection in a mirror is called a veidrodiniu vaizdu, it is quite unclear what atvaizdas then means. In physics, a veidrodinis atvaizdas is the primary example of atvaizdų. It is doubtful that the term can have a different meaning in mathematics.

There are words that, when used as terms in different scientific disciplines, have different meanings. For example, modulis is used in physics to describe (or measure) some kind of deformation; in engineering it means a particular part of a device or structure, whereas in mathematics (as appears from MTŽ) it has still other meanings. One of them is the absolute magnitude of a number or another quantity. It is simply unclear why the terms skaičiaus absoliutusis didumas ir skaičiaus modulis are given separately as two

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in those nests, without a link from one to another. To avoid the ambiguity of the term modulus, physicists use only absolute value of a number or absolute value of a quantity when referring to a dimensional quantity expressed in physical units.

A few more minor ambiguities or inconsistencies could be mentioned, especially concerning new terms. Here are some examples. What is the difference between an estimate and a value, a relation and connectivity, a residue and a resid(u)e, mathematicians’ image and physicists’ consumption (especially when the equivalents in other languages are the same)? Why weight coefficient, but the center of gravity of a function (or curve)? (In physics, the weight of a body is the force with which the Earth attracts that body.) Why is the Lithuanian postūmis (not used by physicists) compared with Russian перенос (physics: переноса) and English translation (physics: displacement?

To eliminate the inconsistencies mentioned and not mentioned here, or to clarify the ambiguities, one would need to know the definitions of all those terms, which is a matter for explanatory dictionaries. For now, it would be desirable for at least the definitions of the most ambiguous terms, especially new ones, to be published in some mathematics or Lithuanian-language publication. I think it would be useful to discuss common or closely related terms in physics and mathematics, and their usage, at joint meetings of the physics and mathematics terminology commissions, or at least to invite representatives of the other commission to their meetings.

It seems that the terminology commissions of mathematicians and physicists differ somewhat in their stance toward the use of international and Lithuanian terms. Although mathematicians, in compiling MTŽ, created and proposed more new Lithuanian terms than physicists did when preparing FTŽ, they nevertheless give preference to Lithuanian terms less often than physicists do over international ones. This is particularly true of compound (specifying) terms. In many cases, only an international term is proposed, even though a perfectly good Lithuanian equivalent exists, perhaps one that is already in use. For example, the international adjectives (specifying modifiers) effective, equivalent, global, homogeneous, horizontal, local, maximal, minimal, specific, stationary, vertical, etc., are given without also including Lithuanian equivalents (synonyms) effective, equivalent, universal (or global), homogeneous, horizontal, local, minimal, vertical, and so on. Some inter-

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national words in Lithuanian have come to play a parasitic role—they push, or have already pushed, good native words out of our language. For example, one could say that the international terms horizontal, vertical have already displaced the Lithuanian horizontal, upright. The younger generation no longer even knows their meaning and confuses them with oblique, perpendicular, although before the war and for quite some time afterward those Lithuanian words were widely used both in society and in schools. Some international terms are used with multiple meanings, although unambiguity is the most important quality of a good term. For example, optimal is used to mean “best,” “most favorable,” “most suitable,” “most convenient,” and so on; structure is used (at least by physicists) to mean “structure,” “formation,” “compound,” “specimen,” although in all dictionaries it is listed only as a synonym of the Lithuanian word structure.

The Physics Terminology Commission maintains that when there is a good Lithuanian term, it should be preferred over an international one (or at least used alongside it), especially in popular and school texts. We recommend that mathematicians and terminology editors and users in other fields of science follow this approach everywhere.

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