The copyright restrictions associated with Wolfram|Alpha (Terms of Use) are not that unusual for reference books (encyclopedias, dictionaries, textbooks, etc.) and even some online reference tools. Thus today most fiction writers need to possess some basic understanding of copyright law in order to know what legally can or cannot be used when conducting research for – and crafting – their works of fiction.
 

A couple of legal questions should be considered when using Wolfram|Alpha (as I proposed in the original article) as a resource for writing science fiction:

1. Is the content found using Wolfram|Alpha being reprinted/reproduced within the author’s work of fiction, or did that content merely serve as an inspiration?

2. If content from Wolfram|Alpha is being incorporated into the work of fiction, is the author adhering to the Terms of Use (i.e., providing attribution, securing a commercial use license when required, etc.)?
 
In my case, when I write science fiction (and I suspect I’m somewhat typical among fiction writers) most of the initial and background research that I gather never makes it directly into the final novel or short story. For example, I initially might research the distances between different star systems where a novel takes place. Thanks to the introduction of Wolfram|Alpha, I now can look up those distances using that tool. The actual chart and data that Wolfram|Alpha provides, however, most likely would never make it into my actual novel. (To include that chart, I would need to create a scene that likely would seem unnaturally contrived in the flow of the story.) Instead I might use the chart and information to map out the novel’s timeline, or to make plot decisions about where characters might realistically travel.
 
In the event that I did wish to reprint/reproduce content verbatim from Wolfram|Alpha (i.e., calculated data, a quote or definition, etc.), the Wolfram|Alpha service does offer a “low-cost or no-cost commercial use license” designed for use in commercial and for-profit situations.
 
As a matter of personal practice, even if I don’t directly reprint content from a specific research source, I still like to provide a “thank you” in print acknowledging that resource. Such acknowledgements can credit everyone from a community historical society (which helped me gain a sense of local flavor and culture) to a friend (who asked a critical question that took a subplot in an entirely new direction). None of this is required under copyright law, but I believe it is appropriate (and helps strengthen those relationships for when I research my next work). And although I haven’t yet published anything written using Wolfram|Alpha as a research tool, for such future works I would include an acknowledgement and attribution for Wolfram|Alpha (even though no actual content from Wolfram|Alpha may appear in the final published work).
 
Finally, in their Terms of Use the Wolfram|Alpha folks invite people to reach out to them with any questions (Contact Wolfram|Alpha), so a writer can contact them directly with any questions about whether – and how – a particular piece of information can be incorporated legally into a story. If you have any doubts about any specific situation, ask them.
 
Copyright Resource:
In the not too distant future, I hope to post an article that examines US copyright law and how it applies to fiction writers. In the meantime, a great resource for US copyright information is the website for the US Copyright Office.

“If you make results from Wolfram|Alpha available to anyone else, or incorporate those results into your own documents or presentations, you must include attribution indicating that the results and/or the presentation of the results came from Wolfram|Alpha.…Failure to properly attribute results from Wolfram|Alpha is not only a violation of these terms, but may also constitute academic plagiarism or a violation of copyright law.”

So while you could find all this great information out, you would not be able to (legally) write fiction to sell / distribute / publish.