No, for the first time, we are not going to talk your ears off—or write your eyes out?—about mathematics. Parallelism is a subject you probably covered in a persuasive writing course, or perhaps in a poetry course. Here is a famous example from Charles Dickens’ Two Cities:
“It was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness, it was the epoch of belief, it was the epoch of incredulity, it was the season of Light, it was the season of Darkness, it was the spring of hope, it was the winter of despair.”
Props to anyone who got through that book—or Great Expectations for that matter.
For our purposes, as editors of scientific material, we look at a more formal definition. As The Chicago Manual of Style (CMS, 16th ed.) says, a parallel construction is a “series of like sentence elements” and when “linked elements are not like items, the syntax of the sentence breaks down.”
The CMS also gives us some examples of parallelism in action, and how the syntax is altered with its absence. It’s like playing a game of “one of these things is not like the other”... or, you know, singing it.
In one of the examples in the Chicago Manual, a series is “unparallel” because a verb phrase appears in a list of noun phrases:
IINCORRECT: The candidate is a former country judge, state senator, and served two terms as attorney general.
CORRECT: The candidate is a former country judge, state senator, and two-term attorney general.
In this case, the verb phrase (red) needed to be altered into a noun phrase. Below, the Chicago Manual corrects a series that needs parallel prepositions:
INCORRECT: I looked for my lost keys in the sock drawer, the laundry hamper, the restroom, and under the bed.
CORRECT: I looked for my lost keys in the sock drawer, in the laundry hamper, in the restroom, and under the bed.
(Please retain the reference in reprint: http://www.letpub.com/index.php?page=author_education_parallelism)