V. ``on the other hand"

1. Introduction

In the papers I read, improper use of the expression ``on the other hand" is very common, and in fact its improper use is much more common than its proper use. In general, this expression is (correctly) used to imply some kind of opposition between the discussion appearing before and after it. Its use implies that the assertion which follows presents some sort of contrasting situation, point of view, result, idea, etc., with regard to the topic of discussion. There are two important points concerning its use: The main assertion of the statements appearing before and after ``on the other hand" must have the same topic, and these assertions must present in some sense opposing or different points of view. In other words, these statements must give different perspectives of the same thing.

The most common misuse of this expression is as an indication that the topic of discussion is changing. It cannot be used in this way. On the contrary, in general, its use implies the continuation of the topic of discussion. In particular, use of this expression is generally not appropriate to connect two statements about two different things, even when these things are closely related. Its misuse most frequently appears in connecting two such statements that describe somehow contrasting situations. This use is illustrated by the following.

Note that the topic of discussion of the first sentence in (1*) is the stability of ψ1, and that of the second sentence is the stability of ψ2. The sentences in (2*) contrast two closely related cases, but here too the topic changes: That of the first sentence is the stability below β = 1, and that of the second sentence is the stability above β = 1. In these examples, the assertions of the first and second sentences describe contrasting situations, but they cannot be regarded as presenting opposing views, since the topic of each is different. Depending on the intended implication, ``on the other hand" here should be replaced by ``and," ``but," ``while," or something similar in the following manner: ``The solution ψ1 is stable, and the solution ψ2 is unstable."

The appropriate use of ``on the other hand" is demonstrated by the example below.

Here, while the first sentence discusses the first method and the second sentence the second method, the main topic of discussion of both sentences is the relative utilities of the methods. With regard to this single main topic, these two sentences provide opposing points of view.

Below, I give a number of examples demonstrating the most common types of misuse of ``on the other hand."

2. Some simple examples:
The pattern ``A is/does... On the other hand B is/does..."

When we make two statements about the identity, nature, behavior, etc., of two different things, even if these things are closely related and the statements present some kind of contrast, we generally do not use ``on the other hand." The following are some fairly simple examples of this type of misuse.

In each of the above examples, while the first and second sentences describe some kind of contrasting situations, there is no opposition represented by this contrast because the topics of discussion differ.

3. Some more complicated examples

The following examples are quite similar to those appearing above in that there is no opposition between the first and second assertions. The examples we consider in this section are somewhat more complicated only because of their sentence structure.

There is certainly a contrast expressed here with regard to the type of metric signature considered in different situations. However, the problem with (1*) is that these are different situations. Certainly the fact that the author considered a Lorentzian signature does not oppose the fact that the Euclidean signature is appropriate in other situations. (Even in the case that the intended meaning is that a Euclidean signature is in fact appropriate in the situation considered in the present paper -- and perhaps a Lorentzian signature was inappropriately used -- ``on the other hand" is incorrect. The fact that the Euclidean signature is appropriate and the fact that the author used the Lorentzian signature are not in opposition. Taken together, they simply imply that he used the wrong signature.)

There is clearly no opposing points of view here, since the two sentences consider completely different things.

Again, these sentences do not in any way express opposing points of view.

Note that the two sentences here not only are non-opposing but, in fact, they both support the conclusion that ``our method" is superior.

The contrast presented here is that the defect solution is zero in one case and non-zero in the other. [This is made somewhat unclear by the wording of (2*).] Obviously, these assertions are not in opposition. In the sentence before ``on the other hand," the topic of discussion is the nature of this solution and its implications in the d ≤ 2 case, while in the sentences following this expression, it is the nature of this solution and its implications in the d > 2 case.

The two sentences here express no contrast. In fact their meanings are almost the same.

Here, the second sentence does not present contrasting information but, rather, additional information.

Here the contrast is between the two different things, the distributions in the two cases.

There is nothing even contrasting expressed by the assertions before and after ``on the other hand" in this case.

Again, there is no real contrast presented by the statements before and after ``on the other hand." The topic of discussion simply changes. Of course, the two types of study discussed here are in some sense contrasting, but the assertions of the two sentences themselves express no opposition. Taken together, they simply imply that two different approaches to the investigation of a particular class of physical phenomena have been used.

Here there is contrast between the statements before and after ``on the other hand," but, again, the topic of discussion changes. The first sentence is with regard to the small α regime and the second sentence is with regard to the large α regime. Clearly, assertions regarding the equilibriation time in these two independent regimes cannot be in opposition.

Again there is clearly nothing expressed by the second sentence that opposes the assertions of the first sentence.

Here the ideas expressed by the two sentences are not even contrasting.

4. Unclear opposition

In the following examples there seem to be some opposing views presented by the first and second sentences, but because this opposition is not clear, ``on the other hand" is not appropriate.

There seems to be something of an implied opposition between the first and second sentences in (1*) with regard to the question of whether or not the lift experienced by the insect is symmetric. However, in fact, neither sentence gives clear support for either conclusion, and thus they cannot be regarded as expressing opposing points of view. In (2*), the sentences may be viewed as expressing opposing views with regard to the use of the T-duality group in the treatment of these fields. However, while the first sentence seems to express a merit of its use, the second sentence clearly does not express a demerit.

5. Proper uses of ``on the other hand"

The following are examples demonstrating the proper use of this expression. In all of these cases, the topic of discussion is unchanged, and the two sentences express opposing points of view with regard to this single topic.

The topic of discussion in (1) is the utility of the T$^*$-product. The first sentence clearly expresses a merit of its use, while the second sentence clearly expresses a demerit. The discussion of (2) is with regard to the appropriateness of the treatment in question. The first sentence raises a question concerning its appropriateness, while the second gives reason to disregard this question. (3) regards the advantage of leaving a field fallow. The first sentence states what can be gained by doing this, and the second states what can be lost.