You’re hardly alone in disliking report back, but I suspect your feelings arise from a misunderstanding. None of the usage manuals I checked object to report back. The people who do object argue that it’s redundant, because the prefix re- means “back.” But that isn’t the only thing re- means. Consider, for example, reform and resign—or re-form and re-sign, in which re- means “again.” Consider “They released the bobcat back into the wild.” And consider the difference between “They asked me to report to them” and “They asked me to report back to them.” Do you like get back better than report back? If so, say that—but don’t hold it against the rest of us if we say report back. The phrase is useful.
Some usage manuals do call refer back redundant. But back adds meaning when refer means “send”—as in “Let’s refer this back to the committee that drafted it, with suggestions for revision.” I understand the objection when the use is something like “If we refer back to the original sources … ” And yet even here back might be excused as an element that adds emphasis—like different in “five different books” and brand and spanking in “a brand spanking new car.”
With such other re- verbs as refund, return, relapse, and revert, though, back is redundant in every context I can think of. Whether back adds anything to a given sentence is worth considering, but there’s no reason for a blanket prohibition.
I’ll bet you wouldn’t be confused about plug in if people in the computer world hadn’t started using login indiscriminately as a verb, a noun, and an adjective. The grammar of the two expressions is the same. But please don’t write plug-in to—or, worse, plugin to, which is the way some people style it, but which looks as if its first syllable ought to rhyme with loo.
First English had the noun plug, then came the verb plug, and then, a couple of hundred years later, once we began using electricity, came the phrasal verb plug in. That gave rise to plug-in as an adjective (“a plug-in device”) and as a noun: plug-in things became plug-ins, much as write-in votes and candidates have become write-ins. Plug-in is fine as an adjective and a noun, but when you want a verb, good old plug in stands ready. It is appropriate both in the literal sense and in the metaphorical one that you and your grammar police have in mind.
You asked about plug into, though. Since plug in is a recognized phrasal verb, shouldn’t we write plug in to? Some usage guides say that into ordinarily denotes movement from outside to in, whereas in tends to mean “within.” But if that’s the case, what’s with plug in (“plug within”)? How about break in or check in or any number of other phrasal verbs in which in clearly means “into”? Why do we write turn in to in “I turned the report in to my supervisor” and turn into in “I’ve turned into a good do-bee”? Here the in to phrase involves movement from one place to another and the into one doesn’t. Why must into be two words in “I traded my car in to the dealer” when a person who makes a trade-in takes the car into the dealer’s establishment?
Well, never mind—I brought all that up in case anyone thinks you asked an obvious question. Dictionaries give plug into as well as plug in and say the two mean pretty much the same thing. Plug into turns up much more often in edited media than plug in to. Even though the movement suggested by your slogan is only metaphorical—people don’t need to stick their finger into a socket in order to plug into something—into here follows the general rule having to do with movement from outside to in. Plug Into Progressive California” it is.
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