"A writer cannot do too much research... though sometimes it is a mistake to try and cram too much of what you learned into your novel. Research gives you a foundation to build on, but in the end it's only the story that matters."
Although many talents in fictional media show they Did Not Do the Research, some actually did. In fact, sometimes they learned so much and worked so hard to learn it that it would hardly seem fitting to just not show it off.
The Shown Their Work trope comes in when the creators tweak their stories to show the viewer/reader what they have learned. The trick is to do it so this advances the story instead of stopping it cold. When it's done right in a well made work, awards for its educational value can be just as nifty as the artistic awards.
This often happens in older, harder Sci Fi books, wherein the authors try to keep the science as consistent as possible with currently-understood scientific theories. Of course, since Science Marches On, this may date the book badly.
Note that this does not include explicitly educational productions, since they obviously have to be both accurate and explanatory to be effective.
Compare Write What You Know (where the writer doesn't need to research because he already knows the topic inside-out), Doing It for the Art, Narrative Filigree (both also about going above and beyond in regards to production quality), Lampshaded the Obscure Reference.
Note that this is only as good as the writer makes it. Just because you did the research, doesn't mean it adds to the story. Likewise, sometimes it's better just to make things up. Remember that one of the reasons why the Sci Fi Ghetto existed in the first place was because Authors of old (and some still do) overused this trope, creating walls of Info Dump instead of stories. If people wanted to have a lecture in Science, they would grab scientific essays in the first place.
Also keep in mind that referencing things doesn't by default make a work smarter than one that doesn't.
Try to keep this page from becoming Gushing About Shows You Like.
If the work is simply using real locations as backgrounds, consider using Real Place Background. If the work contains both real backgrounds and other research, then by all means include it here as well.
Comparing Shown Their Work and Write What You Know: Shown Their Work is for the times when the writer did the research on a subject and let the results appear in the work, while Write What You Know is for the times when the writer knew the subject from previous experience. As an example, somebody who researched a particular small town would know where the only diner is, while somebody who grew up in that town would know what to order because it's the cook's specialty.
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