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.
(1^{*}) The solution ψ_{1} is stable.
On the other hand the solution ψ_{2} is unstable.
(2^{*}) The solution ψ_{1} is stable for
β < 1. On the other hand, it is unstable for β > 1.
Note that the topic of discussion of the first sentence in (1^{*})
is the stability of ψ_{1}, and that of the second sentence
is the stability of ψ_{2}. 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 ψ_{1} is stable, and
the solution ψ_{2} is unstable."
The appropriate use of ``on the other hand" is demonstrated by the example
below.
(3) The first method does not involve such a complicated integration, and
for this reason it is usually
more practical. On the other hand, the second method never produces
unphysical solutions, and therefore it is more reliable.
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.
(1^{*}) Here s_{mn} is the traceless part of
h_{mn}.
On the other hand t_{mn} is the remaining part,
h_{mn} - s_{mn}.
(1) Here s_{mn} is the traceless part of
h_{mn}, and
t_{mn} is the remaining part,
h_{mn} - s_{mn}.
(2^{*}) Here, F^{L}_{μ ν} and
F^{R}_{μ ν} are local field strengths;
on the other hand, F_{η η} and
F_{μ η} are bi-local field strengths.
(2) Here, F^{L}_{μ ν} and
F^{R}_{μ ν} are local field strengths,
and F_{η η} and
F_{μ η} are bi-local field strengths.
(3^{*}) It is thus obvious that by taking the limit χ →
χ _{μ},
the extended derivative operator D^{R}+_{μ}
tends to the local operator
∂^{+}_{μ}. On the other hand,
D^{R}-_{μ} tends to
-ig∂^{-}_{μ}.
(3) It is thus obvious that by taking the limit χ →
χ _{μ},
the extended derivative operator D^{R}+_{μ}
tends to the local operator
∂^{+}_{μ}, while
D^{R}-_{μ} tends to
-ig∂^{-}_{μ}.
(4^{*}) Player 1 succeeded in constructing a productive game
environment, while player 2 failed to do so.
(4) Player 1 succeeded in constructing a productive game environment, while player 2 failed to do so.
(4^{'}) Player 1 succeeded in constructing a productive game environment, but player 2 failed to do so.
(5^{*}) Under this extension, the Higgs-like fields in this model
become bi-local. On the other hand, the gauge fields
and the matter fields remain local, existing in either the left or right
world.
(5) Under this extension, the Higgs-like fields in this model become bi-local,
/although/while/but/ the gauge fields
and the matter fields remain local, existing in either the left or right world.
(5^{'}) Under this extension, the Higgs-like fields in this model
become bi-local. /However/By contrast/,
the gauge fields and the matter fields remain local, existing in either
the left or right world.
(6^{*}) In (a), the average value only with respect to the periodic
part is plotted.
On the other hand, the average value including the transient part
is plotted in (b).
(6) In (a), the average value only with respect to the periodic part is
plotted, whereas
in (b), the average value including the transient part
is plotted.
(7^{*}) Here, the subscript denotes
the multiplicity of the spin states, 2 for a spin-doublet and 4
for a spin-quartet.
On the other hand, the superscript denotes the
degeneracy of the SU(3) flavor state, 8 for a flavor-octet and
10 for a flavor-decuplet.
(7) Here, the subscript denotes
the multiplicity of the spin states, 2 for a spin-doublet and 4
for a spin-quartet, and the superscript denotes the
degeneracy of the SU(3) flavor state, 8 for a flavor-octet and
10 for a flavor-decuplet.
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.
(1^{*}) Since this theorem
concerns an analytic function defined on a Riemannian surface,
the metric signature appropriate for this manifold is
Euclidean. On the other hand, the background manifold which
we have considered in this paper has Lorentzian signature.
(1) Since this theorem
concerns an analytic function defined on a Riemannian surface,
the metric signature appropriate for this manifold is
Euclidean. However, the background manifold which
we have considered in this paper has Lorentzian signature.
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.)
(2^{*}) We thus see that the irreversible work associated with
both the loose
regime and the tight regime can be made as small as we wish by
allotting a large enough time for the operation.
On the other hand, the quasi-static work associated with
the change of ν within
the region χ_{α 0} < χ_{α}
< χ_{α 1}
can be evaluated by Eq. (3.1).
(2) We thus see that the irreversible work associated with both the loose
regime and the tight regime can be made as small as we wish by
allotting a large enough time for the operation.
The quasi-static work associated with
the change of ν within
the region χ_{α 0} < χ_{α}
< χ_{α 1}
can be evaluated by Eq. (3.1).
There is clearly no opposing points of view here, since the two sentences
consider completely different things.
(3^{*}) The player of this species usually cuts tree 1 for several
successive rounds, and as a result this tree becomes shorter and shorter,
as the amount of lumber the player acquires each round becomes less and less.
On the other hand, tree 2 becomes taller and taller.
(3)The player of this species usually cuts tree 1 for several successive
rounds, and as a result this tree becomes shorter and shorter, as the amount
of lumber the player acquires each round becomes less and less.
Meanwhile, tree 2 becomes taller and taller.
Again, these sentences do not in any way express opposing points of view.
(4^{*}) Using the conventional method, the evolution of the decision
making function itself cannot be investigated.
On the other hand, this evolution is systematically investigated using
the S diagram in our method.
(4) Using the conventional method, the evolution of the decision making
function itself cannot be investigated.
Using our method, by contrast, this evolution can be systematically
investigated, and this is done using the S diagram.
Note that the two sentences here not only are non-opposing but, in fact,
they both support the conclusion that ``our method" is superior.
(5^{*}) The solution ξ_{+}(φ) is the only defect
solution that satisfies the boundary conditions.
This solution becomes identically zero for d ≤ 2,
and thus no defects
exist in in this case. On the other hand, this solution represents a defect
for d > 2.
(5) The solution ξ_{+}(φ) is the only defect solution
that satisfies the boundary conditions.
This solution becomes identically zero for d ≤ 2,
and thus no defects
exist in this case. For d > 2, however, this solution is non-zero.
Thus in this regime the system possesses a defect.
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.
(6^{*}) It should be noted that only symmetric fluctuations exist
initially.
On the other hand, the inflaton itself generates asymmetric
fluctuations.
(6) It should be noted that only symmetric fluctuations exist initially.
The asymmetric fluctuations are entirely generated by the inflaton itself.
The two sentences here express no contrast. In fact their meanings are
almost the same.
(7^{*}) This relation yields α < 2 γ.
On the other hand, from (3.4), we have α < 2 π.
(7) This relation yields α < 2 γ. In addition, from (3.4),
we have α < 2 π.
Here, the second sentence does not present contrasting information but,
rather, additional information.
(8^{*}) The distribution of the average scores is quite smooth
if we consider only the attractor part of the dynamics.
On the other hand, if we included transient behavior in calculating
the average score, when the number of rounds is small
this distribution is quite irregular.
(8) The distribution of the average scores is quite smooth
if we consider only the attractor part of the dynamics.
However, if we included transient behavior in calculating
the average score, when the number of rounds is small
this distribution is quite irregular.
Here the contrast is between the two different things,
the distributions in the two cases.
(9^{*}) In this way an attractor can be defined topologically.
On the other hand, Milnor (1985) defined an attractor from another viewpoint
in which both topological and measure-theoretic concepts are taken into
account.
(9) In this way an attractor can be defined topologically.
However, there are other ways to define attractors. For example,
employing another point of view, Milnor (1985) defined an attractor
in terms of both topological and measure-theoretic concepts.
There is nothing even contrasting expressed by the assertions before and
after ``on the other hand" in this case.
(10^{*}) Thermodynamics, which is the study of heat, has been
studied for many years, and a number of relations have been derived
concerning the flow of heat and its conversion into other forms of energy.
On the other hand, Brownian motion has also been studied for many years,
and projection methods developed in this study have allowed for the
derivation of Langevin dynamics from microscopic Hamiltonian mechanics.
(10) Thermodynamics, which is the study of heat, has been investigated
for many years, and a number of relations have been derived concerning the
flow of heat and its conversion into other forms of energy.
Brownian motion has also been studied for many years,
and projection methods developed in this study have allowed for the
derivation of Langevin dynamics from microscopic Hamiltonian mechanics.
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.
(11^{*}) When 0 < α < α_{0}, the equilibration
time is sufficiently long that the change in the small system can be
thought of as quasi-static. On the other hand,
the regime α_{1} < α < 1
corresponds to the case in which the equilibration time is much shorter
than what can be discerned experimentally.
(11) For 0 < α < α_{0}, the equilibration time is
sufficiently long that the change in the small system can be thought of
as quasi-static. As the other extreme,
for α_{1} < α < 1 the equilibration time is much
shorter than what can be discerned experimentally.
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.
(12^{*}) Since the late 1940s, there have been many theoretical and
experimental investigations of
such systems at very low temperatures, and their behavior in this regime
is fairly well understood. On the other hand, in 1992, employing a novel
calculational technique,
Allison and Carew carried out the first systematic investigation of their
`high-temperature' behavior.
(12) Since the late 1940s, there have been many theoretical and experimental
investigations of
such systems at very low temperatures, and their behavior in this regime
is fairly well understood. Then, in 1992, employing a novel calculational
technique,
Allison and Carew carried out the first systematic investigation of their
`high-temperature' behavior.
Again there is clearly nothing expressed by the second sentence that
opposes the assertions of the first sentence.
(13^{*}) The work required to change the parameter a
during the quasi-static adiabatic process A → B
is less than W_{h}.
On the other hand, we can also consider the process B → A.
(13) The work required to change the parameter a during the
quasi-static adiabatic process A → B
is less than W_{h}.
Of course, we can also consider the process B → A.
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.
(1^{*}) Since the interaction between a vortex and the insect's
wing is simple,
the lift generated by a single vortex is essentially symmetric.
On the other hand, the long lifetime of vortices implies that
vortices produced in different downstrokes may interact.
(1) Since the interaction between a vortex and the insect's wing is simple,
the lift generated by a single vortex is essentially symmetric.
However, the long lifetime of vortices implies that
vortices produced in different downstrokes may interact.
(2^{*}) Because the T-duality group G is a subgroup of
the U-duality group
it has a special property:
It is the maximum subgroup which consists of the elements
that transform H-S and Q-Y fields into themselves.
On the other hand, we often encounter situations in which H-S
and Q-Y fields are better treated in a different way.
(2) Because the T-duality group G is a subgroup of the U-duality group
it has a special property:
It is the maximum subgroup which consists of the elements
that transform H-S and Q-Y fields into themselves.
However, while this property is convenient in some situations, we often
encounter situations in which H-S
and Q-Y fields are better treated in a different way.
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.
(1) The T^{*}-product is certainly very convenient, because we need
not be concerned with the order of operation, even for field operators
that are separated in a time-like manner. On the other hand, as emphasized
in the present paper, the T^{*}-product can also create serious
problems involving the explicit violation of the field equations.
(2) This treatment ignores the difference in symmetry of the two systems.
On the other hand, our main interest here is in certain aspects of the
macroscopic behavior that are independent of the symmetry.
(3) When an unproductive wheat field is left fallow for a sufficiently
long time, there is a possibility that it will regain its productivity.
On the other hand, if the field is left fallow for too long, long-range
productivity will inevitably decrease.
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.