This is the first in a planned series of notes on English composition. These notes are intended as a reference for the writing of academic works to be used by ``non-native" physicists and mathematicians. They are specifically designed to help Japanese writers, but hopefully they will be found useful by a wider audience.
In writing these notes, it is not my purpose to create a comprehensive guide to scientific writing. Something of this nature would be both very difficult to write and of little practical use. It is also not my intention to explain standard points of English grammar or elementary rules of English composition, as there are already many textbooks on these subjects. My goal in writing these notes is to create a practical tutorial that addresses specific common mistakes made by non-native (and particularly Japanese) writers. Using examples taken from academic papers, I will consider the most common problems I have encountered and offer my advice on how to correct them. In this way, I hope to help these writers to improve their writing by eliminating mistakes one by one.
I hope that those who read these notes will think of them as not just a guide to scientific writing but as one piece in a more general English education. According to my personal experience, real improvement in one's understanding of a foreign language can only be gained by studying many concrete examples. Abstract speculation on language structure and the formulation of general grammatical rules may be interesting from a linguistics point of view, but they are of little use if the goal is to improve one's communication skills. ``Theoretical" discussion usually becomes only an obstacle to language instruction, and I will therefore try to keep such discussion at a minimum. The ultimate goal for students of a foreign language should be the development of an intuitive understanding, without which writing remains a mechanical operation that can never do justice to the ideas it is used to convey. I believe that the example-based instructional format I will use here is the most effective for the purpose of developing such an understanding. I hope that by contemplating these examples, readers will eventually develop an insight that transcends the set of ``microscopic" lessons they provide.
Over the last four years, I have proofread on the order of 1,000 papers, most of these written by Japanese physicists and mathematicians. During this time, I have found that a large percentage of the mistakes that I see are repeated again and again. Some of them seem almost universal. In many cases, these problems result from the tendency of authors to directly translate Japanese into English, while in other cases they arise from what seems to be some pervasive misinformation existing in Japan with regard to English usage. Most of these problems are fairly simple and are easily corrected. It may be wise to restrict the focus of these notes to such simple problems, and eventually this may be what I decide to do. However, I would also like to make an attempt at addressing some more difficult problems that arise from the complexities of the English language itself.
I consider these notes to be an open-ended project, as I am sure that there is no end to the useful examples that could be added to them. Partly for this reason and partly due to my own lack of organization, the monthly installments to appear on the Progress webpage will consist of collections of very incomplete notes on a variety of perhaps unrelated topics. In addition, their content will undoubtedly reflect my personal writing style, my preferences, and my prejudices. I hope the readers will overlook the shortcomings of my very imperfect presentation. I welcome and will do my best to honor any requests for material to be covered, and I invite comments of all kinds.
The expression ``on the contrary" is used very often in the papers I proofread, and it is almost always used incorrectly. This expression can only be used to introduce a statement that expresses a meaning that is opposite to what has been previously stated or to what is expected. Its use gives emphasis to the statement in which it appears and to the falsity of that which this statement denies. The following sentences demonstrate its proper use:
2. This interaction does not lower the energy of the system. On the contrary, it increases the energy by such a large amount that the approximation used above becomes invalid.
In most of the cases that ``on the contrary" is used in the papers I read, the intended meaning is that expressed by ``contrastingly", ``in contrast", ``by contrast", ``while", ``but", ``however", etc. Consider the following (incorrect) examples:
2. This equation can be easily solved. On the contrary, that derived in Sect. 1 can only be treated numerically.
3. Bose-Einstein statistics describe integer spin particles. On the contrary, the particles in which we are interested are always of half-integer spin.
4. In the case discussed above, t0 > t1. On the contrary, in the present case, t0 < t1.
5. The primitive form of analysis used in the previous section does not allow us to draw any definite conclusions with regard to properties of this solution. On the contrary, with the form of analysis developed in this section we are able to determine upper bounds on the values it assumes in each of the intervals in question.
Note that in none of these cases does the second sentence contradict the first. For this reason, ``on the contrary" is inappropriate. Rather than contradiction, in each case above, the second sentence presents a situation which is in contrast with or in some sense inconsistent with that presented in the first sentence. In 1, the situation in which Anderson investigates the full system and that in which we investigate a simplified system are not mutually exclusive. In 2, since we are considering different equations, there is nothing contradictory about claiming that one of them can be solved easily while the other cannot. The following are some possibilities for corrected versions of the above examples.
2. This equation can be easily solved. Contrastingly, that derived in Sect. 1 can only be treated numerically.
3. Bose-Einstein statistics describe integer spin particles, while the particles in which we are interested are always of half-integer spin.
4. In the case discussed above, t0 > t1. However, in the present case, t0 < t1.
5. The primitive form of analysis used in the previous section does not allow us to draw any definite conclusions with regard to properties of this solution. Contrastingly, with the form of analysis developed in this section we are able to determine upper bounds on the values it assumes in each of the intervals in question.
The word ``keep'' is often mistakenly used by Japanese authors in situations that ``maintain'' or ``preserve'' would be appropriate. In fact, in the papers I read, this word is more often used improperly than properly.
In written English, and in particular scientific writing, it is best to avoid words with very broad meanings and to use in their place more precise expressions: ``perform,'' ``carry out,'' ``undertake,'' or ``execute'' instead of ``do,'' ``take on,'' ``obtain,'' or ``become'' instead of ``get,'' etc. The situation is the same in the case considered presently. Because the word ``keep'' has many meanings, its use can be ambiguous, and it is therefore better to use more narrowly defined (and therefore more precise) words such as ``retain,'' ``maintain,'' ``preserve,'' ``conserve'' and ``prevent.''
1.* The system keeps its symmetry under the transformation ${\cal{T}}$.
2.* The qualitative behavior of the system is kept even when the temperature is raised by as much as 10 Δ T.
3.* The delicate balance of these two opposing terms is kept until the critical temperature, because until this point, the operator P keeps the only relevant quantity, z.
4.* In this way, the system is kept from reaching a global equilibrium.
5.* The integral of this function keeps its value for all time.
6.* This measurement keeps the total angular momentum of the system.
7.* Of course, the system keeps its total energy.
8.* The center-of-mass distances are all kept during the evolution.
9.* The propagator keeps the values of α and β.
10.* The material keeps its structural integrity until the amplitude of the driving force is increased to f0.
These sentences are better written as follows:
1. The system maintains its symmetry under the transformation ${\cal{T}}$.
2. The qualitative behavior of the system is maintained even when the temperature is raised by as much as 10 Δ T.
3. The delicate balance of these two opposing terms is maintained until the critical temperature, because until this point, the operator P preserves the only relevant quantity, z.
4. In this way, the system is prevented from reaching a global equilibrium.
5. The integral of this function is independent of time.
6. This measurement preserves the total angular momentum of the system.
7. Of course, the system maintains its total energy.
8. The center-of-mass distances are all preserved during the evolution.
9. The propagator preserves the values of α and β.
10. The material maintains its structural integrity until the amplitude of the driving force is increased to f0.
``Maintain''
In general, it is better to use ``maintain'' when describing the action of some physical or mathematical object on itself. For example, as in 1 above, it sounds more natural to say ``The system maintains its symmetry'' than ``The system preserves its symmetry.'' While it cannot be said that the latter is wrong, it seems to suggest that ``it'' here is not referring to the ``system'' but to something else.
It is also better to use ``maintain'' when in reference to a general state or condition. This can be seen by considering the following examples.
1. A near-equilibrium state is maintained throughout this process.
1.*A near-equilibrium state is preserved throughout this process.
2. Laminar flow is maintained below R = R0.
2.*Laminar flow is preserved below R = R0.
Finally, it is better to use ``maintained'' to convey the meaning that there is some influence being somehow defended against. For example, while ``The structure was maintained against the constant eroding force of the ocean'' is very natural, ``The structure was preserved against the constant eroding force of the ocean'' is quite unnatural.
``Preserve''
While use of ``maintain'' seems to imply a defending (oneself or something else) against some influence, ``preserve'' implies the somewhat different idea of keeping/leaving unchanged.
There are two cases in which ``maintain'' cannot be used instead of ``preserve.'' First, ``preserve'' should be used when that which is unchanged is some specific quantity or quality. This is demonstrated by the following:
1. The value of the parameter α is preserved in time.
1.* The value of the parameter α is maintained in time.
2. The velocity of the flow in the region between points a and b is preserved when the electric field is applied.
2.*The velocity of the flow in the region between points a and b is maintained when the electric field is applied.
The second situation in which ``preserve'' must be used is that in which there is some action applied to a system that produces some kind of change, but there is some property of the system which is not changed and which is being singled out for discussion. This is a very common situation in mathematics and physics:
1. The operator ${\cal{Z}}$ preserves the rotational symmetry of this state.
1.*The operator ${\cal{Z}}$ maintains the rotational symmetry of this state.
[While such a statement is possible, the meaning is entirely different from that of 1. Here, it would seem that there is some other influence (perhaps some kind of perturbation, etc.) against which ${\cal{Z}}$ is acting in order to keep the rotational symmetry unchanged.]
2. The number of vertex points is preserved under the mapping in question.
2.*The number of vertex points is maintained under the mapping in question.
3. This change of coordinates preserves the total volume of all the regions.
3*This change of coordinates maintains the total volume of all the regions.
4. Only c1 and c2 are preserved under this transformation.
4.*Only c1 and c2 are maintained under this transformation.
5. This perturbation preserves the total energy.
5.*This perturbation maintains the total energy.
(Again, note that 5*is possible, but the implication is that if the perturbation were not applied, the total energy would change. The implication of 5 is much different.)
Proactive vs. Reactive
There is another difference in nuance between ``maintain'' and ``preserve'' that could perhaps be surmised from the above discussion but has not been made explicit. While these nuances are often not present when these words are used in mathematical discussion, I think it is helpful to gain a more intuitive understanding to make this difference clear.
When describing some object or property that is being either ``preserved'' or ``maintained'' in the presence of some perturbing influence, use of ``maintain'' implies stabilizing action in response to this influence, while use of ``preserve'' implies action in anticipation of it.
The word ``maintain'' is more appropriate than ``preserve'' in the following situations:
1. The dog stood on top of a fence and maintained her balance in the windstorm.
2. The woman managed to maintain her sanity during a very difficult time.
In the situations here, the dog and the woman are acting in response to some destabilizing forces.
Now consider the following:
4. During the processing of the food, certain chemicals are added to it to preserve its flavor.
5. The quality of the book has been preserved against aging by placing it in an ultra-clean environment.
In both cases here, some action is taken in anticipation of the effect of aging.
Now, let us see how the meanings of the above sentences change if we switch ``maintain'' and ``preserve'':
1.*The dog stood on top of a fence and preserved her balance in the windstorm.
2.*The woman managed to preserve her sanity during a very difficult time.
These both sound quite unnatural. It seems that perhaps the ``windstorm'' and the ``difficult time'' are not the perturbing forces whose effect is to be prevented by the ``preservation'' in question.
4.*During the processing of the food, certain chemicals are added to it to maintain its flavor.
This does not sound unnatural. In fact, the meaning changes little when replacing ``preserve'' by ``maintain''. However, in the former, the adding of chemicals seems to be part of the processing, while in the latter case, it seems to be something separate from the processing, perhaps something done only after it was discovered that the flavor of the food had changed.
5.*The quality of the book has been maintained against aging by placing it in an ultra-clean environment.
This sounds quite strange, because placing the book in the ultra-clean environment is clearly something done in anticipation of the influence of aging, while use of ``maintain'' seems to imply that this is done in response to this influence.
The following examples demonstrate the appropriate use of ``order'' in the present context.
2. This state has an energy on the order of 50 eV.
3. The characteristic timescale of the phase separation process is on the order of hours.
4. The average velocity of the particles is on the order of .1 c.
5. This energy scale is on the order of the Planck mass.
6. The overestimate is on the order of the size of the system.
7. There are on the order of 100 particles in the reaction chamber.
9. This quantity is of order ε, the small parameter in terms of which we are expanding.
10. The size of the system is of order Nα, where N is the total number of particles.
11. The dimensionless velocity of the front is of order z3/2, which in the system described by Fig. 1 is approximately 1.5. This corresponds to a velocity on the order of .2 mm/sec. in the `typical' physical system considered in the previous section.
12. This quantity is of order ρv/ρh, where ρv and ρh, are the vertical and horizontal dimensions of the apparatus.
13. All quantities appearing on the right-hand side of this equation are of order unity.
14. The number of particles in the reaction chamber is of order 100.
Several of these examples deserve some discussion. First, in 6, since we may be thinking of the size of the system as a dimensionless quantity, it may seem that this could also be written as follows:
However, in fact this sentence is very problematic. The reason for this is that even in the case that we are thinking of the size of the system as a pure number, ``the size of the system'' is not. This points out that often the distinction between the two cases considered here is more a matter of English semantics than mathematical meaning. To make this point more explicit, if we change this sentence to read something like
Next, let us consider examples 7 and 14. These seem to be making precisely the same statement, and it may thus seem strange that we use ``on the order of'' in one case and ``of order'' in the other. Again, this is a problem of linguistics rather than mathematics or physics. In 7, ``order'' is used in reference to ``100 particles,'' while in 14 it is used in reference to ``100.'' This difference is also reflected in the fact that in 7 the verb is plural (``are''), while in 14 it is singular (``is'').
2. The values σ and θ are of the same order.
3. The temperatures T1 and T2 are on the same order.
4. A and B are of vastly different orders.
There are a number of similar expressions that are often confused. Here I discuss the most common of these.
If we were to use ``as far as" here, the implication would be that the relation α < αc can be satisfied to varying degrees. In this case, perhaps the interpretation would be that the assumption becomes more valid as the difference between α and αc increases, but this is quite unnatural and in fact a misuse of the mathematical expression ``α < αc."
Here, using ``as far as" would yield a sentence whose implication is that to ``consider only..." is something that can be done to different degrees. This, however, is incompatible with the word ``only." If ``only" were deleted, ``as far as" would be possible, and the meaning would be that the effect of the perturbation becomes smaller as the time over which we average this behavior increases. However, if this were the intended meaning, it would be better to express this idea in this more direct manner.
Here, replacing ``as long as" with ``as far as" would result in the meaning that exceeding 50 K is something that can be partially realized. Note that the resulting sentence could not be interpreted as meaning that the reliability of the data increases as the temperature of the chamber decreases.
This phrase is used to express a relationship characterized by some variable degree or extent. The examples below demonstrate its correct usage.
Here, the implication is that the quality of the overall description provided by the model is determined essentially by the quality of the description near the sink: As the latter improves the former also improves. Thus in this case, the ``properness" of the description near the sink is interpreted as a matter of degree. In this sentence, we could replace ``as far as" by ``as long as." If we did, however, the implication of the resulting sentence would be that we have some criterion to define what is meant by ``properly describe the behavior near the sink," and that this criterion is something that is either satisfied (completely) or not satisfied (completely).
In this sentence, the implication is that the ``simplicity" of the type of systems in question is considered a matter of degree, and that the agreement between the predictions of these models increases as the system in question becomes simpler. Again, we could use ``as long as" here, but the implication would then be that a system of the type in question is considered as being either ``simple" or ``not simple" (that is, that we have some objective criterion defining ``simpleness.")
The meaning of this sentence is that the model provides a good qualitative description of some physical phenomena, but not necessarily a good quantitative description. Further, it is implied that our interest can be to a varying degree in quantitative predictions, but that the usefulness of our model decreases with the degree to which we are so interested. If we use ``as long as" here, the implication is that there are only two possibilities, that we are interested in qualitative behavior or that we are not. In fact the resulting sentence is quite natural.
The statement here is clearly with regard to a time, and thus ``instance" cannot be used. If we changed ``At" to ``In," the meaning of the prepositional phrase ``In the instance...potential" would be ``In the case that..." This, however, would result in a very strange sentence, as the meaning of main clause (and the verb ``begin") would not be compatible with that of the prepositional phrase.
Clearly this is with regard to a situation, rather than a time. Here, in fact, ``case" seems more natural than ``instance," as the latter usually carries with it the implication that the situation in question is in some sense an example. However, ``instance" would also be natural if we were considering several previously mentioned examples and in one of these we ignored the external field.
(i) ``such as" is used to introduce examples:
While ``such as" and ``for example" are very similar in meaning, there is a slight difference in nuance. More than simply indicating that those things which follow are examples, the former also includes the implication that they are somehow representative of a certain class of things that share some characteristic by virtue of which they are all examples.
(ii) ``so as" means ``for the purpose of" or ``in such a manner that":
Note that this expression is almost always used in front of an infinitive verb form (here ``to minimize"). [Grammatically, in general a phrase ``so as + (infinitive clause)" acts as an adverb (a so-called adverbial phrase. Here the infinitive clause can consist of an infinitive verb alone or something more complicated.] In the present case ``so as to minimize" modifies the verb ``wrapped." Usually, the meaning of such a sentence is changed little if ``so as" is deleted, but in general it serves to express the idea that the action in question was carried out in a particular manner chosen to bring about the desired result.
(iii) ``such that" is used in the modification of nouns. It is usually used to mean something like ``of a type that":
Here note that ``such that..." modifies the noun ``manner." [More precisely, ``such" is an adjective modifying ``manner," and it is joined to the complementary subordinate clause ``the loss of..." by the conjunction ``that."] The implication is that this manner in which the insulating material was wrapped is of some particular type specifically designed to minimize heat loss. In the above sentence, it is important to note that ``such that..." does not modify ``wrapped." This is a common misconception, and it results in some very strange sentences, such as the following:
Here, the intended meaning is that this term was ignored to allow for determination of the behavior in question, but since grammatically ``such that..." modifies ``term," the actual meaning of the sentence is quite strange. The simplest way to fix this sentence is to replace ``such that" by ``so that." If this is done, the phrase ``so that we..." acts correctly as an adverb, modifying ``ignored."
(iv) ``so that" is usually used to express a meaning similar to ``for the purpose of," ``therefore" or ``with the consequence that":
Here, the meaning of ``so that" is quite similar to `` and therefore," but there is also an implication of purposefulness; that is, the insulating material was wrapped around the tube with the purpose of obtaining the stated result. Note that the meanings of ``so as" and ``so that" are similar, but grammatically they are not interchangeable. [The expression ``so as" is used to introduce a to-infinitive adverbial clause, while ``so that" introduces a finite adverbial clause.]
Here, the object of the preposition ``to" is ``rotor problem," and it represents the target application of the adaptation. Contrastingly, ``adopt" is never used with the preposition ``to." Thus, sentences like the following are incorrect:
In general, it is not possible to adopt something to something else. To rewrite this sentence, ``adopt" could be replaced by ``adapt." In this case, the implication would be that the perturbation procedure was appropriately modified for application to the treatment of non-linear differential equations. This sentence could also be rewritten as follows:
In this case, there is no implication that the treatment was modified for this particular application (although this possibility is not ruled out).
In this sense, this word has a somewhat relative implication. In the example here, there is the implication that although this simplicity assures us of the equation's usefulness, it may not assure other people in the same way. Thus ``assure" is most naturally used with regard to a person's opinion or state of mind regarding some matter. By contrast, the implication of ``insure," ``ensure" and ``guarantee" is quite certain and absolute. They are not used with regard to a person's opinion or state of mind, but rather with regard to objective facts. Also, these three words are used in the situation in which there is a direct cause-effect relation, while ``assure" is used in situations that are less direct.
Consider the following.
The first sentence here could be made grammatically correct by simply changing ``assures" to ``assures us." The resulting meaning, however, would be somewhat strange. Its implication would be that the relation between using this more valid approach and correctly taking account of the swelling behavior is somewhat indirect -- that using this more valid approach somehow provides evidence that we will correctly account for the swelling behavior, but that we cannot be entirely sure. Here, the more direct implication of ``insures/ensures/guarantees" is appropriate. [Note that the main problem here with ``assure us" is not its somewhat tentative implication, but the indirect relation it expresses. Thus it is not appropriate here even in the case that there is some doubt about whether this approach will have the stated result. In such a situation, this could be written as ``We believe that by using this more generally valid approach, we will correctly account for the swelling behavior.] The situation is quite different with the second example. Here, note that the actual relation between the agreement of these two sets of results and our belief in the validity of ``our results" is somewhat indirect and subjective. In particular, it involves our state of mind.
Consider the following correct uses of these two expressions:
The implication here is that as a first step in our treatment of the equation in question, we ignore the perturbation. Note that if we change ``for the moment" to ``for a moment," the meaning is very strange. In this case, it would seem as if we simply ignore the perturbation for a short time, although this does not necessarily have anything to do with how we treat the equation.
Here, clearly the intended meaning is ``for a short time," and thus ``for the moment" is not possible.
Here, ``result" refers to the situation that we now possess this intuitive understanding. (Note that the meaning is essentially unchanged if we replace ``as a result of" by ``owing to.") In this case, ``as the result" would be quite unnatural, because that which constitutes ``the result" does not explicitly appear here. Now, consider the following:
Here, ``result" refers to the relation g = a23. Note that, as exemplified by this sentence, usually the expression ``as the result" can be replaced by ``constituting the result," and in this expression ``result" refers to some clearly defined quantity, expression, data, etc. Note that if we changed ``the" to ``a" here, the resulting sentence would be somewhat unnatural. In this case, ``result" would somehow seem to refer to our obtaining the relation rather than the relation itself. (Note that in the case that there are several concrete results and that g = a2/3 is one of them, it is better to write ``We thus obtain the relation g = a2/3 as one result of our analysis.")
When referring to previous work in an abstract, the same rules apply as when referring to previous work in the main text.
1. Galileo studied the motion of the planets.
2. This topic was the studied extensively in the mid-1800's.
3. Many authors made the mistake of ignoring elastic effects in the early years of this field.
1. Smith has studied this system with much success.
2. This topic has been the focus of a great deal of study in recent years.
3. Many people have made the mistake of ignoring the effect of non-linear terms.
The implication of 1 is that this is study of a current topic, and allows the possibility that Smith is still studying this system (or perhaps something related). However, it is clear that she has obtained some results and carried some aspect of the work to completion. The implication of 2 is that this topic is still the focus of a great deal of study. The implication of 3 is that at least some people are (probably) still making this mistake.
1. Thompson computed these coefficients systematically.
2. These measurements were made at 1.2 K.
3. We proved this result with the help of Theorem 1 above.
In 1, the present perfect tense is also possible: ``Thompson has computed these coefficients systematically." The difference between this and the sentence above is a matter of time. If Thompson did this, for example, several years ago, and the result is well known, the past tense is best. If, however, Thompson just published results on this, and these are perhaps not yet well known, the present perfect tense is better. Now, suppose the tense of 2 is changed to present perfect: ``These measurements have been made at 1.2 K." In this case, the meaning is that these measurements have been made a number of times (perhaps by several different people), while the meaning of the original sentence is that the measurements were probably done just once and perhaps by only one person (or group). In contrast to 1 and 2, the meaning of 3 is almost completely unchanged when the past tense is replaced by the present perfect: ``We have proven this result with the help of Theorem 1 above." However, in the case that this proof was done some time ago (and perhaps is well known), the past tense is better.
1. Simpson has been studying this system numerically.
2. We have been calculating these terms analytically.
The implication of 1 is that Simpson is not yet done studying this system. The implication of 2 is that we are not yet done calculating these terms, and therefore that there are probably many of them and that calculating them takes a great deal of time. The second situation is that in which the work has not yet been taking place over a long time, or that work on it has just begun. In this case, we use the present progressive tense:
3. We are presently studying this system in the deep quench regime.
4. Experiments on such systems are now being performed.
1. Our results are in agreement with those of Stevens.
2. The results of our experiment show that the electronic structure of the system is not as simple as is generally believed.
3. The proof we have given in Sec. 1 implies that the set S is dense in D.
However, it should be kept in mind that when referring to the actual act of obtaining these results (calculating, measuring, proving...), rather than their meaning or implication, one must use the past tense or the present perfect tense:
4. According to the results obtained in Section 3, we can conclude that the equation in question is structurally unstable.
Here, in referring to the act of deriving the results, ``obtained" is used, since this was done in the past, but in referring to the implications, which are timeless, we use present tense.
5. We calculated the value of the exponent β using the method described above.
6. In this paper, we have shown that the instability of the system cannot be described using the simple linear analysis introduced in Ref. [2].
7. In Sect. III, we present the results of numerical simulations of this gel system carried out using this model.
1. As shown by Sato, these solutions diverge in the t → ∞ limit.
2. The behavior of the system we presented in the previous section is common to a large class of reaction-diffusion equations.
3. In the experiments we performed on these systems, we found that they are quite insensitive to temperature changes in the range in question.
Contrast the above examples with the following:
4. In Sato's numerical study of these equations, he discovered that the solutions in question diverge in the long time limit.
5. The behavior of the system presented in the previous section was found to be common to a large class of reaction-diffusion equations.
6. In our experiment, the system was quite insensitive to temperature changes in the range in question.
The difference between 1 and 4 is that in 1, the main clause is discussing the behavior of the solutions -- the fact that they diverge for large t. This is true at any time, past, present or future. In 4, however, we are discussing the discovery made by Sato. This discovery was made in the past. Similarly, 2 and 3 are relating the nature of the behavior of the respective systems, while 5 and 6 are describing what was found and what was measured, respectively.
In this note, I discuss several verbs that are to various degrees synonymous with ``do''. These verbs are, of course, very common, and because they are often misused by Japanese authors, I consider their treatment to be quite important.
The verb ``do'' itself is quite nondescript. Its meaning is very broad, and therefore imprecise. For this reason, it is best avoided when there are more descriptive words that can be used in its place. In particular, I suggest making more use of verbs like ``perform'', ``conduct'', ``carry out'', ``execute'', ``undertake'', etc., when these are appropriate. In this note, I discuss the appropriate and inappropriate use of these verbs.
I should point out that the verbs considered here certainly do not constitute a complete set of alternatives to ``do'' and that the example sentences appearing below in no way exhaust the possible ways of using these verbs.
1. The experiment was performed at room temperature.
2. We performed the calculation in two regimes.
3. Numerical computations were performed for a variety of systems.
4. We performed a set of manipulations on the equations in question and obtained the following result.
The following are all inappropriate ways in which to use ``perform'':
5. We perform an approximation of the equation in question.
6. The measurement was performed at a scattering angle of 12.5°.
7. We perform a proof of this theorem in the next section.
8. Discussion is performed in Sec. II.
9. We perform research on systems of this type.
The sentences 5 and 6 are not good because in each case, the action being ``performed'' does not consist of a set of steps (at least in most natural situations).
The situation with 7, 8 and 9 is perhaps somewhat more subtle, as we now discuss. To ``perform'' usually implies the following of some prescription or previously devised plan. An experiment is performed according to some plan. A calculation is performed following some prescription or set of predefined rules. (Note that ``perform'' also is used with regard to actors, who, in fact, follow some predetermined script.) A proof, discussion, and research on the other hand, do not follow some predesigned set of rules (in most meaningful cases, anyway). Thus ``perform'' is not appropriate.
The above sentences are better rewritten as follows:
5. We make an approximation of the equation in question.
5'. We approximate the equation in question.
6. The measurement was taken at a scattering angle of 12.5°.
6'. The measurement was made at a scattering angle of 12.5°.
7. We construct a proof of this in the next section.
7'. We give a proof of this in the next section.
7''. We prove this in the next section.
7'''.This is proven in the next section.
8. Discussion is given in Section II.
8'. Discussion appears in Section II.
9. We conduct research on systems of this type.
1. We conduct research on spin systems.
2. The experiment was conducted at temperatures just below the phase transition.
3. We conducted a survey of all the presently available experimental results.
4. We conducted a series of numerical simulations.
The following are inappropriate ways to use ``conduct'':
5'. The calculation was conducted.
6'. A simulation of the systems was conducted.
7'. We conduct a proof of this property in the following section.
8'. Measurements were conducted for a range of field strengths.
The verb ``conduct'' is used almost exclusively in reference to experiments and research, or, more generally, activities that require the coordination of many sub-activities. (Note that the conductor of an orchestra is responsible for coordinating the activities of all of the members of the orchestra.) Thus, for example, 4 above is feasible because each of the series of numerical simulations can be thought of as such a sub-activity. The problem with 5'-8' is that, although each of the activities in question can be thought of as consisting of sub-activities, these sub-activities are more naturally thought of as (perhaps somewhat mechanical) steps that do not necessarily require some kind of overall coordination. The following represent some appropriate ways to rewrite the above:
5. The calculation was carried out.
5'. The calculation was performed.
6. A simulation of the system was carried out.
6'. A simulation of the system was performed.
7. We give a proof of this property in the following section.
8. Measurements were taken for a range of field strengths.
1. Study of this system was undertaken with the hope of settling the remaining unanswered questions.
2. We undertook this research knowing little about the difficulty inherent in its experimental observation.
The following are inappropriate ways to use ``undertake'':
3*. We undertook an experiment on this system.
4*. Calculation of these exponents was undertaken numerically.
Use of the verb ``undertake'' implies that the thing which is being undertaken is in some sense of grand scope. It usually is reserved for very large projects requiring years of effort. It is also best used in reference to more abstract activities (e.g., ``studies'', ``research''), as opposed to more concrete activities (e.g., ``calculations'', ``experiments'').
3* and 4* can be better rewritten as:
3. We performed an experiment on the system.
3'. We conducted an experiment on the system.
3''. We undertook an experimental study of the system. (This is most appropriate for a set of a large number of experiments.)
4. Calculation of the these exponents was performed numerically.
4'. These exponents were calculated numerically.
1. The authors carried out a calculation and obtained the following results.
2. We carried out a series of experiments that confirm the theoretical predictions made in Ref. [1]
3. Analysis of this system is carried out below.
This term is usually used in reference to some activity consisting of a set of (at least to some extent) clearly defined steps. It is similar to ``perform''. (Note that ``perform'' could be used in all three of the examples above.) There is a slight difference in nuance, however, as ``carry out'' seems to imply a slightly more mechanical following of well-defined steps. Also note that for 2, ``carried out'' could be replaced by ``conducted'' with little change in meaning. Again, the difference here is that use of ``carried out'' seems to imply that there perhaps has not been an effort to coordinate the various experiments or their results. For example, if the results of this series of experiments must be used together to obtain some result, ``conduct'' is better. However, if the ``theoretical predictions'' referred to here can be ``confirmed'' independently from the results of a series of independent experiments, ``carried out'' is better. The following are inappropriate uses of ``carry out'':
4*. We carry out discussion of this point in the following section.
5*. Research has been carried out on this topic for the last ten years.
6*. We have carried out a study of hadron systems ignoring the effect described above.
7*. In this paper a confirmation of the results obtained previously is carried out.
8*. Measurements were carried out near the critical point.
9*. Let us carry out an approximation of this interaction.
10*. In this paper, predictions are carried out concerning the nature of crystal growth under such extreme conditions.
For 4*-7*, the activities in question do not follow a sequence of clearly defined steps. The situation for 7*-10* is somewhat more subtle. The ``measurements'' referred to in 8* could be considered as resulting from a sequence of well-defined steps, and thus it may seem that ``carry out'' is appropriate. The problem, however, is that while a measurement may involve a set of well-defined steps, it is not equivalent to such a set. Rather, it is most natural to consider a measurement as the culmination of a set of steps. Thus, while the sentence
The steps necessary to make the measurements near the critical point were carried out.
sounds quite natural, 8* is somewhat unnatural. The problems with 9* and 10* are similar: In both cases, while it is natural to think of ``carrying out'' the steps through which the approximation or prediction is obtained (if indeed it consists of a set of well-defined steps), the approximation or prediction itself is not equivalent to these steps. (Note, by contrast, that a calculation is most naturally thought of as being equivalent to the steps it involves.)
The following are appropriate ways to rewrite the above sentences:
4. We give discussion of this point in the following section.
4'. We discuss this point in the following section.
5. Research has been conducted on this topic for the last ten years.
6. We have undertaken a study of hadron systems ignoring the effect described above.
6'. We have studied hadron systems ignoring the effect described above.
7. In this paper a confirmation of the results obtained previously is given.
8. Measurements were made near the critical point.
9. Let us make an approximation of this interaction.
9'. Let us approximate this interaction.
10. In this paper, predictions are made concerning the nature of crystal growth under such extreme conditions.
1. We carried out an experiment on this system.
2. We carried out the steps of this experiment.
are quite natural, only 4 below represents an appropriate use of ``execute'':
3*. We executed an experiment on this system.
4. We executed the steps of this experiment.
The following are appropriate uses of ``execute'':
5. The steps in the experiment were executed in the following order.
6. The computer program executed commands as shown in the diagram given in Fig. 1.
7. Though there seems to be some ambiguity in this regard, the steps in the calculation must in fact be executed in a particular order.
The following are inappropriate uses of ``execute'':
8*. This integration can be easily executed after applying the transformation discussed above.
9*. This proof is executed in the following section.
10*. Analysis of this spin system has been executed by a number of people.
11*. We execute a similar argument in the present paper and reach a similar conclusion.
12*. A transformation into a more convenient coordinate system is executed below.
These sentences are better rewritten as follows:
8. This integration can be easily performed after applying the transformation discussed above.
9. This proof is given in the following section.
10. Analysis of this spin system has been carried out by a number of people.
11. We make a similar argument in the present paper and reach a similar conclusion.
12. A transformation into a more convenient coordinate system is performed below.
The limited use of abbreviations for well-known and commonly used terms is obviously desirable for the purpose of conciseness, but their overuse only leads to confusion. While the employment of a large number of abbreviated terms can be timesaving and convenient for the author, it is anything but convenient for readers. In addition, this practice is stylistically very poor.
I believe that in many cases, people are simply unaware of the great number of abbreviations they introduce into their papers and the problems that this often presents to readers. In general, I think it is best for authors to limit themselves to ``standard'' abbreviations (PDE, RG, UV, QED, WKB, etc.) and avoid creating their own. Of course, there is no problem in introducing one or two non-standard abbreviations, but one should be alerted when sentences like ``The solution of WKE found by UIJA loses meaning in the IAH limit.'' begin to appear. There is a second type of problem involving the use of abbreviated expressions that I would like to briefly mention, although this is perhaps somewhat outside the expressed scope of these notes. When proofreading papers, I often come across such abbreviated mathematical expressions as the following:
2. ``ti,k > tj,l'' in place of ``ti > tj and tk > tl''
3. ``We assume that γa,b becomes negligible as t approaches t0,1.'' in place of ``We assume that γa and γb become negligible as t approaches t0 and t1, respectively.''
I strongly recommend that such abbreviated expressions be strictly avoided. They are stylistically very poor and can be quite misleading.
Consider the following sentences:
2. We thus obtain
The first problem here is that in English, use of ``'s'' implies possession, not plurality. Of course in the present case, the reason for the appearance of the apostrophe is simply that if we change ``ai's'' to ``ais,'' there is the possibility that the ``s'' will be misinterpreted as being a part of the mathematical expression. In any case, this type of usage is syntactically awkward at best. (Perhaps the conclusion regarding this point is simply that we should avoid mixing mathematical and English symbols.)
The second (and more important) reason the above usage should be avoided is the following. Let us suppose we wish to think of the ai as ``coefficients.'' We could make this explicit by rewriting example 1 as perhaps something like, ``...where the coefficients ai are positive integers.'' Here it is obvious that ``ai'' is a collective (plural) noun. Note that this fact does not depend on the explicit presence of the word ``coefficients'' before ``ai,'' as is easily seen if we simply change the position of this word, for example as follows: ``...where the ai are positive integer coefficients.'' Here again, it is clear that ``ai'' represents a collective noun. In fact, it is not necessary for ``coefficients'' to appear at all, as the meaning of the following is clear: ``...where the ai are positive integers.'' In this case, it is natural to think of there being an implied ``coefficients'' appearing in front of ``ai.'' Of course, the same can be said for the original sentence in example 1 above. But if we make this explicit, we obtain, ``...where the coefficients ai's are...,'' or perhaps, ``...where the coefficient ai's...'' However, it is obvious that neither of these makes sense, and thus the problem with this example becomes clear.
For example 1 some of the alternatives are the following:
2. ...where the ai are... (This more concise. Note that there is no danger of misinterpreting ``the ai'' as being singular.)
3. ...where the ai (i = 1$\cdots$N) are...
4. ...where the ai (i = 1$\cdots$∞) are...
For example 2, the best expression is clearly, ``...where σ1 and σ2 are...'' (Note that it is best to avoid something like ``...where σ1,2 are...'' This is very misleading.)
Pronouns are used in place of nouns. They are useful for the purpose of conciseness, but their ambiguous use can create great problems for the reader. In this note, I discuss several points concerning pronoun usage. Further notes will appear in the future.
The topics to be covered in my discussion of pronouns include problems with the general use of pronouns, problems with relative pronouns, and problems with the pronoun one. I briefly consider all of these in this note.
The most common problems involving the use of pronouns is exemplified by the following:
When we transform this function by applying the operator ${\cal{T}}$, we obtain a solution to a certain class of equations that possesses the important property we discuss in the following section. It was studied by James and Chu [1].
This example is actually very typical. I believe one reason that sentences like this appear is that their authors are too familiar with the material they are discussing, and for this reason the ambiguity of their statements is not apparent to them.
There are two problems with these sentences. The most obvious problem involves the use of ``It'' in the second sentence. We discuss this sentence in the present section. The second problem is addressed in the next section.
The possible interpretations of the second sentence in the above example are the following:
(i) James and Chu studied ``this function''.
(ii) James and Chu studied the operator ${\cal{T}}$.
(iii) James and Chu studied this ``solution''.
(iv) James and Chu studied this class of equations.
(v) James and Chu studied this ``important property''.
(vi) James and Chu studied the transformation of the function in question under ${\cal{T}}$.
In fact, a good case could be made for any of these interpretations, although the most natural are (i), (iii) and (v). The resolution of this ambiguity is simple: ``It'' should simply be replaced by ``This operator'', ``This function'', ``This solution'', ``This class of equations'', ``This property'', or ``This transformation'', as the case may be.
I believe that the single example considered here is sufficient to demonstrate the most common problem that occurs with the general use of pronouns. The important point to keep in mind is simply whether there is any ambiguity with regard to the noun to which a pronoun refers.
Consider the following sentence:
The ${\cal{O}}$(ε2) calculation is not straightforward. In this case, the standard procedure yields useless results: Although application of this procedure produces a valid description of the system, this description is no simpler than that provided by the original equation. It necessitates a reevaluation of the standard procedure and the construction of a more general method.
In this case, ``It'' appearing at the beginning of the third sentence refers to nothing. There is no word or words appearing in the previous sentences for which ``It'' is acting as a substitute. Of course, one could argue that the meaning of the last sentence is not completely unclear, as we can guess that ``It'' is being used in reference to the situation described in these sentences. However, it is not a good practice to force the reader to guess in this way. In addition, this is an example of very poor style. In general, pronouns should only be used in place of nouns that appear explicitly in the preceding sentence or sentences. The best way to remedy this problem is to replace ``It'' with something like ``The complication presented by the ${\cal{O}}$(ε2) calculation''.
1. When we transform this function by applying the operator ${\cal{T}}$,
we obtain a solution
to a certain class of equations. This solution/class possesses the
important property
we discuss in the following section, which was studied by James and
Chu [1].
(solution/class, property)
2. When we transform this function by applying the operator ${\cal{T}}$, we obtain a solution
to a certain class of equations. This solution/class possesses the important property
we discuss in the following section and was studied by James and Chu [1].
(solution/class, solution/class)
3. This function was studied by James and Chu. When we transform it by applying the operator ${\cal{T}}$, we obtain a solution
to a certain class of equations. This solution/class possesses the
important property
we discuss in the following section.
(solution/class, function)
4. When we transform this function by applying the operator ${\cal{T}}$
(studied by
James and Chu [1]), we obtain a solution
to a certain class of equations. This solution/class possesses the important
property
we discuss in the following section.
(solution/class, operator)
5. When we transform this function by applying the operator ${\cal{T}}$,
we obtain a solution
to a certain class of equations studied by James and Chu [1].
This solution/class possesses the important property
we discuss in the following section.
(solution/class, class)
6. When we transform this function by applying the operator ${\cal{T}}$,
we obtain a solution
to a certain class of equations. This transformation was studied by James
and Chu [1]. The
solution it produces possesses the important property we discuss in the
following section.
(solution, transformation)
7. When we transform this function by applying the operator ${\cal{T}}$,
we obtain a solution
to a certain class of equations. This transformation was studied by James
and Chu [1]. This
class of equations possesses the important property we discuss in the
following section.
(class, transformation)
We treat the first term in this equation as a perturbation, which can be interpreted in the following manner.
The problem here involves the relative pronoun ``which''. It is not clear whether this refers to ``perturbation'' or to our treatment of the term in question as a perturbation. Of course one may argue that the interpretations of these two would be essentially the same thing, and therefore that there is really no ambiguity here. This may be true, but even in this case, this sentence is an example of sloppy writing that should be avoided. It should be rewritten as one of the following:
1. We treat the first term in this equation as a perturbation. This term can be interpreted in the following manner.
2. We treat the first term in this equation as a perturbation. This treatment can be interpreted in the following manner.
In the nonconserved case, the result of the computation is in good agreement with experimental results, but in the conserved case, there is strong disagreement, which supports the conclusions stated in Ref. [2].
In this case, it is not clear whether (i) the fact that there is agreement in the nonconserved case but not in the conserved case, (ii) the fact that there is disagreement in the conserved case, or (iii) the type of disagreement in the conserved case supports these conclusions. Both (i) and (ii) are quite natural interpretations. The third interpretation is somewhat unnatural, because in order for this sentence to possess this meaning, the comma appearing after ``disagreement'' would have to be removed (and, strictly speaking, ``which'' should be changed to ``that''). However, a reader confronted by such a sentence would probably doubt the author's knowledge of such fine points of grammar. In any case, the two most natural interpretations are more clearly expressed by the following:
1. In the nonconserved case, the result of the computation is in good agreement with experimental results, but in the conserved case, there is strong disagreement. These results support the conclusions stated in Ref. [2].
2. In the nonconserved case, the result of the computation is in good agreement with experimental results, but in the conserved case, there is strong disagreement. This disagreement supports the conclusions stated in Ref. [2].
The following are all proper uses of this pronoun:
1. Consider two Riemannian manifolds, one that is conformally flat and one that is only locally conformally flat.
2. Each strictly positive, monotonic steady state solution corresponds to physically realizable behavior for the θ > 0 system, while each strictly negative one corresponds to physically realizable behavior for the θ < 0 system.
3. It is important to note that the type of local solution in question is one in which slow motion and fast motion are formally distinguished.
4. An energy relation for Ψ1 together with one for Ψ2 can be derived quite easily.
In each of these cases, the use of ``one'' in place of that to which it refers leads to a more concise sentence. Also note that there is no ambiguity with regard to this use.
The following represent inappropriate use of ``one'':
5*. We consider an equation that contains a locally acting operator and a globally acting one.
6*. In the simplest case these methods give a consistent result, but in more realistic cases they give an inconsistent one.
7*. It is known that the a posteriori estimate is, in general, much better than the a priori one.
8*. We discuss both the hydrogen atom and the helium one.
9*. In the graphs displayed in Fig. 2, y is the vertical axis and K is the horizontal one.
10*. The functions φ+ and φ- correspond to the non-stationary states localized near the minima of the double well potential on the positive side and the negative one of x, respectively.
11*. Noting that ψ00 and ψ01 are an even function and an odd one of x, respectively, we can carry out the proof in two parts.
12*. In the analysis of this system, the extra differential one-form χ in Z2 is introduced in addition to the usual one-form dxμ in M4, and therefore our formulation is very similar to that using ordinary differential geometry. Contrastingly, in Martin's original one the Dirac matrices γμ and γ5 are used to describe the generalized gauge field.
In these examples, the main reason that ``one'' should not be used is simply that there is no reason to do so. The purpose of pronouns is to provide brevity and simplicity. However, in all the cases above, ``one'' is used in place of a single word. In these examples, its use does not lead to more concise statements, and for this reason there is nothing to be gained by this use. In situations like this, use of this word sounds forced and quite artificial. In addition, its use often creates writing that is difficult to follow. For example, in 11*, upon encountering the phrase ``Martin's original one'', the reader will likely be forced to return to the previous sentence to determine that ``one'' here is used to mean ``formulation''.
In 6*. and 8*-11*, it is best to simply replace ``one'' with the noun to which it refers. The remaining sentences are best rewritten as follows:
4. We consider an equation that contains both a locally acting and a globally acting operator.
5. In the simplest case these methods give a consistent result, but in more realistic cases this is not true.
7. We discuss both the hydrogen and helium atoms.
For non-native speakers, the proper use of articles is quite difficult to understand. For native speakers, it is difficult to explain. There are certain general rules governing the use of articles, but it is often unclear how these apply in specific cases. For this reason, I think it is best to explain their use through examples.
One of the general guiding principles involved in the use of articles is that the definite article, ``the," should be used when the noun in question is unique or in some sense singled out, and its nature as such is known by the reader. Thus, the sentence ``I ate the apple" is appropriate only if the reader has some preexisting knowledge of this particular apple. A situation that gives non-native speakers a great deal of trouble, however, is that in which the information that defines or singles out a noun is given within the sentence in which this noun first appears. In this note, I consider such sentences.
When defining information about a noun appears within the sentence in which the noun appears (a situation I refer to as ``presently defined"), the definite article should be used. In general, this information consists of some definition, identification or description that uniquely identifies the noun in question. It can appear in several forms that modify this noun (in particular, as an adjective, a noun, a prepositional phrase, or a relative clause).
Below I give a number of examples demonstrating the use of articles in such situations. The first sentence (demonstrating incorrect use) for each example was taken (in modified form) from a paper I have proofread.
1. Our model is not applicable to the k $\sim$ 0 case.
2*. This occurs in a following manner.
2. This occurs in the following manner.
3*. This behavior is described by a following equation:
3. This behavior is described by the following equation:
In the first example, ``k $\sim$ 0" is an adjective defining the case in question. Thus this example would seem to be clear. The second example is somewhat more interesting. Here, one might think that because the information actually defining this ``manner" appears after this sentence, ``the" should not be used. However, this is not the case. In fact, mistakes of this kind are quite common -- probably because of this type of reasoning. The important point here is not whether the information given actually allows us to obtain a full understanding of this ``manner," but whether it uniquely identifies it. In the present case, the adjective ``following" certainly does this. The situation for the third example is similar. This sentence was used to introduce a single equation that appeared directly below it. Thus uniquely identifying information is provided by the ``following," the definite article must be used.
1. We thereby obtain the configuration in Fig. 3.
1.' We thereby obtain the configuration depicted in Fig. 3.
Clearly the prepositional phrase identifies the configuration in question. Note that if there were multiple configurations displayed in Fig. 3, grammatically ``a" would be possible. However, in this case the meaning of the sentence as it stands would be quite strange, and something like ``We thereby obtain one of the configurations in Fig. 3" would be more natural.
The following are examples of defining relative clauses that do provide uniquely defining information.
1. This is in contradiction with the fact that τ > 0.
2*. This is known to be true by a fact that γ vanishes beyond the bifurcation point.
2. This is known to be true from the fact that γ vanishes beyond the bifurcation point.
3*. In a sense that we can choose these values freely, this does not present a problem.
3. In the sense that we can choose these values freely, this does not present a problem.
4*. In a sense that the action of each of these operators is largely confined to a particular, isolated region, we can think of the system as being separable.
4. In the sense that the action of each of these operators is largely confined to a particular unique and isolated region, we can think of the system as being separable.
5*. With a value of V = 1.21 that we derived.
5. With the value of V = 1.21 that we derived.
6*. A solution that we derive in the next section exhibits similar behavior.
6. The solution that we derive in the next section exhibits similar behavior.
7*. A person who first introduced this idea is not known.
7. The person who first introduced this idea is not known.
In examples 1 - 4, it is quite clear that the information provided uniquely defines the noun in question. The situation is perhaps not as clear for example 5, but here, the situation in which ``a" would be correct is very strange. For example 6, in the case that there are multiple solutions obtained in the section referred to, ``a" would be grammatically correct, but in this case, the sentence would be better written as ``One of the solutions we derive in the next section exhibits similar behavior." In the paper in which this sentence appeared, however, there was a unique solution derived in the section in question. In such a situation, ``the" must be used. Here, despite the fact that the reader has not yet seen this solution, the information provided here uniquely identifies it. In 7, though we do not know the identity of this person, it is clear that there can be just one, and the information provided here uniquely identifies him or her.
1. There are two solutions to this equation. The solution moving to the right has velocity vr, and the solution moving to the left has velocity vl = vr / 2.
2*. A form of this equation resulting from the transformation T is much simpler than the original.
2. The form of this equation resulting from the transformation T is much simpler than the original.
3*. A function defined by these constraints appears in Fig. 1.
3. The function defined by these constraints appears in Fig. 1.
In example 1, despite the fact that we do not know the nature of these solutions, each is uniquely identified by indicating the direction in which it is moving. The original in example 2 would only be possible in the case that there are multiple forms of the equation produced by the transformation T. Such a situation may be possible, but it would indeed be quite unusual. In the paper in which this sentence appeared, this form was unique. For example 3, the indefinite article is not possible. Grammatically, it could only be used in the case that there are multiple solutions defined by the constraints. However, if this were the case, it would be incorrect to say that such a solution is ``defined."
1. The solution to be chosen is that which first assumes a negative value at x = x0.
Here it is clear that there is only one solution of the kind in question, and though we do not yet know what this solution is, the information provided here uniquely identifies it.