Lesson 9

(1)Present vs. past tense in mathematical expressions
(2)Tenses when describing scenarios, modeling processes, projections, etc.

(3)Some informal expressions that should be avoided in scientific writing

Lesson 9の解答

Dear Participants,

The correct use of tenses is a problem that researchers often encounter when writing papers in English. In the Autumn 2010 edition of Quarterly Review, we looked at the tenses normally used with the expressions paper and study, noting that a study should generally be referred to in the past tense (e.g., “In this study, we investigated . . . .”), whereas a paper should generally be referred to in the present tense (e.g., “In this paper, we report . . . .”). Then, in the Autumn 2011 edition, we examined tense usage in expressions such as “the results show/showed that X increases/increased.” In this case, the decision as to whether to use the present or past tense depends on various factors. For more detailed explanations, please refer to the relevant edition.

In this edition, we continue our exploration of this subject by examining the use of tenses in mathematical expressions. We then move on to a related topic: the use of tenses when writing about scenarios, modeling processes, projections, and so on. We conclude with some advice on several commonly used informal expressions that should be avoided in scientific writing.

(1) Present vs. past tense in mathematical expressions

Texts containing mathematical expressions can basically be divided into two categories: (a) the “present-tense type,” in which the authors are giving a step-by-step description (as though in real time) of a process of calculations in the paper itself; and (b) the “past-tense type,” in which the emphasis is on reporting how the overall study was conducted.

In papers of the present-tense type, you will often find a real-time expression such as “Let us assume that x is . . . .” or “Let x be . . . .” at the beginning of a set of calculations, followed by an equation or series of equations. After each equation, the terms will usually be defined by a present-tense expression such as “where x is . . . , p is . . . , and w is . . . .”

In papers of the past-tense type, on the other hand, in which the emphasis is on how the study was conducted, assumption-type expressions will be in the past tense; e.g., “We assumed that x was . . . .” Similarly, definitions will also usually be in the past tense; e.g., “where x was . . . .”

It is also possible for a paper to contain a combination of both types of expressions. That is, a paper in which the authors are reporting how their study was conducted (past tense) might switch to a step-by-step description of a process of calculations (present tense), then revert to the past tense again. Here is an example of a case like this:

“We used [= past tense] the following procedure to calculate the value of M:
Let x be p * q, where p is . . . .” [= present tense]
We then replaced [= past tense] N with M to determine the mean value.”

To summarize, use the present tense when describing a process of calculations step-by-step (as though making the calculations in real time together with the reader), and use the past tense if your emphasis is on reporting how your overall study was conducted (i.e., the conventional style).

(2) Tenses when describing scenarios, modeling processes, projections, etc.

Very often, we can use either the present tense or the past tense (or even the present perfect tense) when describing scenarios, modeling processes, estimations, projections, and so on. The key point in deciding which tense to use is, again, to determine what you wish to place emphasis on. For example:

Past tense: If your description mainly focuses on something that was completed in the past (for example, a scenario that was fully developed before the present study was conducted), then the past tense is usually the best choice; e.g., “Scenario X was developed in order to determine Y.”

Present tense: If the development or refinement of the scenario, etc. is still ongoing, or the present paper is describing the results of using the scenario, etc. step-by-step in real time, then the present tense is usually preferable; e.g., “Scenario X shows that Y increases when Z occurs,” or “Scenario X is found to be superior to Scenario Y when Z increases beyond a certain level.”

Present perfect tense: This is not so common, but sometimes the present perfect tense (e.g., “. . . has been developed”) is used when you wish to emphasize the linkage between the past development of the scenario, etc. and its present applicability; e.g., “Scenario X has been developed in order to simplify calculations of Y.”

(3) Some informal expressions that should be avoided in scientific writing

The Summer 2011 edition described certain types of informal expressions that are not appropriate in scientific writing. Here are some additional examples of expressions that should be avoided, with suggested alternatives.

Made: Alternative expressions that could be used include prepared (general contexts), constructed (e.g., in the case of a building or other structure, or a system), fabricated (e.g., a device or product), formulated (e.g., a plan or proposal), devised (e.g., a scheme or mechanism), etc.

Happened: Alternative expressions include occurred, took place, appeared, arose, emerged, etc. Another alternative is an expression such as was found.

Done: This very informal word should definitely be avoided in scientific writing. Use an alternative expression such as performed, conducted, carried out, implemented, etc.

Thank you very much for your dedicated efforts. See you next time!

Sincerely yours,

Bob Gavey
For World Translation Services, Inc.

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