Translators and Math:

The case of approximators

Source texts may also contain numerical expressions which are puzzling. Consider this passage from a text I once translated into English.

Translators are language people. As a result, they may not pay much attention to numerical expressions.

The literal English translation seen above is odd in that the approximator word about¹ seems to clash with the specificity of 3047. (Whether the corresponding source-text expression seems odd to native speakers of French is a subject I shall not consider.) A translator who tends to pass quickly over numerals might write about 3047 ships without any thought. Even during revision, the oddness of such expressions might continue to escape notice if the translator is not mentally attuned to mathematical matters.²

There are two questions to be answered here. First, obviously: What should one write in the English translation? But second, a question which may have a bearing on the answer to the first question: Why is the French sentence written the way it is? Let’s begin by considering this second question. Here are some possible explanations that might occur to the translator:

A. 3047 is a calculated rather than an observed quantity; that is, the count of ships for 2002 has not yet been made; instead, the count for 2001 has been adjusted using a formula (for example, one that reflects changes in the cost of shipping and in the number of days in the shipping season).

B. A count has been made for 2002 but it has not been checked, or it is based on partial reports. The preliminary and therefore uncertain nature of the number seems to be supported by another sentence in the same text:

“Un peu plus de 66,366 passagers ont été accueillis selon des informations préliminaires.”

[a little more than 66,366 passengers were accommodated according to preliminary information]

This latter sentence, however, introduces a problem of its own: How does the writer know that the true figure is a little more than the very specific number 66,366? Why not a little less? Perhaps it has been discovered in previous years that the final figure is always a little more than the preliminary one.

C. The true figure is known to the writer, but for the time being it cannot be disclosed.

D. The writer believes that you should always qualify a number with an approximator, even a very specific number like 3047, unless you are very certain that it is accurate (for example, you are certain because you made the count yourself, unlike in the case at hand, where the writer is reporting someone else’s count).

E. The writer did not want to use a nearby round number like 3050 because, being round, it does not look the result of a real count. The writer thought that adding an approximator to a specific number like 3047 would achieve a more realistic effect without being deceptive about accuracy.

Some solutions

Now to the first question: What shall we do with à peu près 3047 navires in English? Let’s assume for the sake of argument that neither the author nor another subject-matter expert is available to confirm or disconfirm our theories about why 3047 is accompanied by an approximator. Here are some possibilities:

i. about 3047 ships

ii. 3047 ships

iii. some 3047 ships

iv. 3050 ships

v. just under 3050 ships

Solution i. may be the ‘let’s play it safe’ or the ‘let’s not think about this’ or the ‘it’s not up to me’ solution. Alternatively, it may stem from any of the first three above-mentioned theories (A, B, C) about why the French is written the way it is. Theories A and B assume that the figure 3047 is an estimate, whether arising from calculation or from a preliminary count. In this case, the estimate is about the year that has just passed, so there is a fact of the matter, but that fact—the real number of ships—is not yet known with certainty. Of course estimates can also be about the future, in which case they are inherently uncertain, since one cannot know how many ships will pass through the Seaway next year until the end of next year. In a database of English-to-French translations, I found a text calling for bids to provide bus service; in a column headed 'estimated usage,' the text refers to a need for approximately 8 buses to make approximately 16 trips. Given uncertainty about the future (those calling for bids do not yet know exactly how many buses will be needed and exactly how many trips will have to be made), there is nothing odd about the presence of approximately next to the specific numbers 8 and 16.

Solution ii arises from theory D about the French wording: the translator decides that the approximator is only present because the source writer did not personally make the count, not because there is any real question about the accuracy of 3047. The French-English translation corpus at www.linguee.com includes a text from the UNAIDS Web site where the approximator environ in des correspondants d'environ 71 pays is simply eliminated in the English translation: respondents in 71 countries, rather than about 71 countries.

Solution iii draws on the approximator word some, which may seem to work better than about, perhaps because it is a word whose main function in the language is not that of signalling approximation; in this respect it is unlike roughly, about or, worst of all, approximately. This is the solution which I used when I translated the text.

Solution iv uses a round number which, the translator believes, readers will take as an approximation.

Solution v arises from theory E. It uses an approximator, but with a round number, so that the oddness is eliminated.

What is a round number?

Roundness is not a mathematical but a linguistic concept. A round number is one which signals that the writer is not claiming accuracy. However it is not always clear whether a given number will be interpreted by readers as round. Merely ending in a 0 is not sufficient, for no number is inherently round; it depends on what is being counted. If I write There were 100 people at the party, you will take that as an approximation because you think it unlikely that I made a head count, whereas if I write I took $100 out of the bank machine, you will take that to mean exactly $100, because you know that bank machines do not dole out amounts like $98. (If I want you to think that I did make a head count at the party, I must write exactly 100 in order to counteract the default interpretation that 100 people at the party is an approximation.)

Now suppose I write There are 100 Neanderthal sites in Western Europe. This is less clear-cut. It’s the kind of thing that someone may well have counted, so perhaps I should not assume that it will be treated by readers as an approximation. If I want to be more certain that it will be so treated, I could write a hundred, rather than 100 or one hundred; the former is more likely to be taken to be an approximation. Better yet, I could avoid all possible uncertainty about my meaning by writing about a hundred, a hundred or so or roughly a hundred.

Solution iv above thus presents a problem, for it is not clear how 3050 ships will be interpreted. Unlike, say, 3000 ships, it may or may not be taken as round. If it is taken as accurate, then the meaning of the French source text will not have been conveyed.

Accurate counting versus precise measuring

Approximating expressions with specific numbers like 3047 are not inherently odd. They can make perfect sense when precision of measurement rather than accuracy of counting is at issue in a text. Accuracy has to do with correspondence to reality, whereas precision has to do with fineness of measurement. Consider:

· La réduction prévue de GES est d’environ 1 803 tonnes d’ici deux ans.

[It is expected that there will be a decline in greenhouse gases of about 1803 tonnes over the next two years.]

In this text, the actual figure (the result of a calculation, since this is a forecast) was given on an accompanying table: 1,802,792 kg. The author then simply re-expressed this number imprecisely, to the nearest metric tonne (the nearest 1000 kg), perhaps to avoid encumbering the prose passage with lengthy numerals. The phrase about 1803 tonnes makes perfect sense because a tonne is a measuring unit. The word about signals a lesser degree of fineness: 3 tonnes as opposed to 2792 kg. Similarly, there is nothing odd about saying that someone got married about 29 years ago, or that students are to submit papers which are about 9 pages long. In both these cases, the presence of measuring units (years, pages) tells us that precision rather than accuracy is at stake: the marriage is being measured in years rather more finely in terms of years and months; the papers are being measured in pages rather than words. The situation with the ships is completely different. Unlike tonnes, pages and years, ships are not measuring units; they are entities being counted. In about 3047 ships, the word about signals the absence of a claim to accuracy in counting, but this seems incompatible with the specificity of the non-round number 3047.

Lawyers too may be interested in precision: a property might be described on a deed as having 3047 acres more or less, meaning that the writer of the deed is not warranting that the property has an area of exactly 3047 acres. It might turn out to have 3047.1 or 3046.8 acres. Again there is a unit of measurement involved, the acre.

Finally, imprecise expressions may be used when averages or percentages are calculated. Consider this sentence from a text about the cost of operating pilot boats to guide ocean-going ships:

· Le coût moyen par mille piloté est de l’ordre de 12,86 $.

[the average cost per pilot mile is about $12.86]

If the actual prices charged by three boat operators were $12.89, $12.84 and $12.86, the average would be $12.86333, which might then be reported as about $12.86. The word about can be seen as pointing the reader to the imprecision of averaging.

The same applies to percentages:

· Si l’on considère l’ensemble des brevets dans tous les secteurs, les étrangers se sont vus octroyer près de 91.4 % des brevets.

[if we consider all patents in all fields of activity taken together, foreigners were granted nearly 91.4% of them]

Once again, the process of calculation will often result in a figure which the writer will want to express imprecisely. If 7966 patents were granted, and 7279 went to foreigners, then 91.375847 percent went to foreigners. This can be expressed to the nearest tenth of a percent as 91.4% or, with an overt indication of imprecision, as nearly 91.4%.

The notion of roundness is used in connection with both accuracy and precision. If a fractional measurement of length (a rod 2.14 cm in diameter) is rounded off to the nearest whole number (2 cm or about 2 cm), that’s a matter of precision. If a big city population count ( 2,256,476 people) is rounded off to the nearest million (2 million people or about 2 million people), that’s a matter of accuracy. Note the difference between the two unrounded numbers when used with approximators: about 2.14 cm in diameter makes perfect sense, since 2.14 could be a rounded-off version of 2.139257, whereas about 2,256,476 people does not make sense in terms of rounding: people are not divisible measuring units, so this number cannot be a rounded-off version of some other number.

A final example

Now consider this sentence:

· Il a aidé différentes confessions religieuses à bâtir, agrandir ou rénover plus de sept églises de Kingston.

[he helped various religious denominations to build, enlarge or renovate more than seven of Kingston’s churches]

Once again, the point of interest will be the impact of the literal English translation, not the impact of the French text on French speakers. The expression more than cannot be taken as signalling imprecision, since churches are not measuring units. A church can be 7.3 km away but you can't renovate 7.3 churches. So what is at stake here is accuracy in counting. To me, if someone writes more than seven churches, it creates one of two impressions: that the writer knows the actual number but for some reason is not revealing it; or that the writer had previously used the expression only seven or less than seven and is now creating a contrast, as in Only seven organizations originally signalled interest in the event, but more than seven are in fact participating. Here, more than seven makes perfect sense, but only because of the preceding only seven.

The problem in our sample sentence can be overcome by writing at least eight churches. This conveys the notion that the writer only knows of eight churches for sure, but believes there may be more. To think of this solution, however, you must first notice the problem with the literal translation. And for that, your math radar needs to be set to ON.

A little more math

The set of expressions a hundred, a thousand, a million etc. and their plurals hundreds, thousands, millions etc. has one very odd member: a dozen and its plural dozens. Dozen first appeared in English, according to the Oxford English Dictionary, around the year 1300, having come into the language through Anglo-Norman French dozeine, which was not an adjective meaning ‘about 12’ but a noun meaning ‘a set of exactly 12 things or people’. A relic of this meaning in modern English is a dozen eggs (occasionally one still finds a dozen of eggs, in which dozen is clearly a noun). In Norman England, where French was the official language of law, dozeine meant, amongst other things, a twelve-man jury. Twelve is an extremely useful number when counting or measuring, especially for commercial purposes, because it is divisible by 6, 4, 3 and 2 (10 is only divisible by 5 and 2). Before metrication, there were 12 inches in a foot and 12 pence in a shilling, with coins for three of the divisors: 2 pence, 3 pence and 6 pence.

Despite its importance as an exact amount, dozens was being used as early as the 15^th century in its modern sense: ‘quite a large number (perhaps more than you might have thought)’, as in There were dozens of people in the room. When it’s used in the singular with anything other than products sold in twelves such as eggs (There were a dozen people in the room), it means ‘somewhere between 10 and 15’. As a result, it can often be used as a translation of French dizaine, which according to the Robert dictionary means ‘a set of 10’ or ‘about 10’, though in practice the latter meaning is by far the most common.

Dizaine is the first of a set of approximative quantity nouns: vingtaine (‘about 20’), trentaine (‘about 30’) and so on through soixantaine (‘about 60’), then centaine (‘about 100’); Belgian and Swiss French also have such nouns for 70, 80 and 90. Then there’s douzaine (dozen), and quinzaine, meaning ‘about 15’, but also ‘a period of 2 weeks’, analogous to the British fortnight, which is a shortened form of fourteen-night. Quinzaine makes sense because the count is inclusive, e.g. Friday July 6 to Friday July 20, including both Fridays, which works out to 15 days rather than 14.

Inclusive versus exclusive counting is another example of a mathematical translation problem. If you translate from a language that usually counts inclusively, then your source text is not wrong when it says On Tuesday, she bought a sweater; three days later, on Thursday, she returned it. With inclusive counting, Thursday is three days after Tuesday, because Tuesday is included in the count. But if your target language tends to count exclusively, you will need to write two days later!

² Sentences like this are not extremely common but they are not rare either. My impression is that I come across a text containing one or more such expressions about 10 times a year. Here’s a small sampling of other such sentences I’ve seen. To save space, I’ve just written the literal English translations:

…a bank of data on levels and flows in Quebec’s lakes and watercourses, from about 214 sites

Border guards have access to more than 16 types of detection technology.

As for Facebook, the company now has nearly 4438 followers.