I would consider your Mendeleev quotation as an example of a different, though also quite fascinating phenomenon. What is being discussed in the above article relates to processing sensory input during sleep. The Mendeleeev anecdote is related to memory consolidation/restructuring that occurs during sleep and can cause insight (ie "a mental restructuring that leads to a sudden gain of explicit knowledge allowing qualitatively changed behaviour"[0]), independent of sensory input during sleep. Your Mendeleev reference reminds of a fascinating study[0] that examines the capability of sleep to yield insight because they also reference the Mendeleev anecdote in their introduction. I highly recommend reading the article. It's short, easy to understand, and demonstrates the importance of sleep for problem solving.
Comments
I would consider your Mendeleev quotation as an example of a different, though also quite fascinating phenomenon. What is being discussed in the above article relates to processing sensory input during sleep. The Mendeleeev anecdote is related to memory consolidation/restructuring that occurs during sleep and can cause insight (ie "a mental restructuring that leads to a sudden gain of explicit knowledge allowing qualitatively changed behaviour"[0]), independent of sensory input during sleep. Your Mendeleev reference reminds of a fascinating study[0] that examines the capability of sleep to yield insight because they also reference the Mendeleev anecdote in their introduction. I highly recommend reading the article. It's short, easy to understand, and demonstrates the importance of sleep for problem solving.
[0] Original paywalled source: http://www.nature.com/nature/journal/v427/n6972/full/nature0...; free-to-access copy: https://www.msu.edu/course/psy/401/Readings/WK9.PresentA.Wag...