Editing Problem solving (section)

== Dreaming: problem solving without waking consciousness ==
People can also solve problems while they are asleep. There are many reports of scientists and engineers who solved problems in their [[dream]]s. For example, [[Elias Howe]], inventor of the sewing machine, figured out the structure of the bobbin from a dream.<ref>{{cite book|last=Kaempffert|first=Waldemar B.|year=1924|title=A Popular History of American Invention|volume=2|location=New York|publisher=Charles Scribner's Sons|page=[https://archive.org/details/popularhistoryof02kaem/page/385/mode/1up 385]}}</ref>

The chemist [[August Kekulé]] was considering how benzene arranged its six carbon and hydrogen atoms. Thinking about the problem, he dozed off, and dreamt of dancing atoms that fell into a snakelike pattern, which led him to discover the benzene ring. As Kekulé wrote in his diary,

{{blockquote|One of the snakes seized hold of its own tail, and the form whirled mockingly before my eyes. As if by a flash of lightning I awoke; and this time also I spent the rest of the night in working out the consequences of the hypothesis.<ref>{{multiref2|1={{cite journal | last1 = Kekulé | first1 = August | year = 1890 | title = Benzolfest-Rede. | journal=Berichte der Deutschen Chemischen Gesellschaft|volume=23|pages= 1302–1311 }} 
|2={{cite journal | last1 = Benfey | first1 =  O. | year = 1958 | title = Kekulé and the birth of the structural theory of organic chemistry in 1858 | doi = 10.1021/ed035p21 | journal = Journal of Chemical Education | volume = 35 | issue = 1 | pages = 21–23 | bibcode = 1958JChEd..35...21B}} }}</ref>}}

There also are empirical studies of how people can think consciously about a problem before going to sleep, and then solve the problem with a dream image. Dream researcher [[William C. Dement]] told his undergraduate class of 500 students that he wanted them to think about an infinite series, whose first elements were OTTFF, to see if they could deduce the principle behind it and to say what the next elements of the series would be.<ref name="Dement 1972">{{cite book|last=Dement|first=W.C.|year=1972|title=Some Must Watch While Some Just Sleep|location=New York|publisher=Freeman}}</ref>{{page needed|date=September 2023}} He asked them to think about this problem every night for 15 minutes before going to sleep and to write down any dreams that they then had. They were instructed to think about the problem again for 15 minutes when they awakened in the morning.

The sequence OTTFF is the first letters of the numbers: one, two, three, four, five. The next five elements of the series are SSENT (six, seven, eight, nine, ten). Some of the students solved the puzzle by reflecting on their dreams. One example was a student who reported the following dream:<ref name="Dement 1972"/>{{page needed|date=September 2023}}

{{blockquote|I was standing in an art gallery, looking at the paintings on the wall. As I walked down the hall, I began to count the paintings: one, two, three, four, five. As I came to the sixth and seventh, the paintings had been ripped from their frames. I stared at the empty frames with a peculiar feeling that some mystery was about to be solved. Suddenly I realized that the sixth and seventh spaces were the solution to the problem!}}

With more than 500 undergraduate students, 87 dreams were judged to be related to the problems students were assigned (53 directly related and 34 indirectly related). Yet of the people who had dreams that apparently solved the problem, only seven were actually able to consciously know the solution. The rest (46 out of 53) thought they did not know the solution.

[[Albert Einstein]] believed that much problem solving goes on unconsciously, and the person must then figure out and formulate consciously what the mindbrain{{jargon inline|date=September 2023}} has already solved. He believed this was his process in formulating the theory of relativity: "The creator of the problem possesses the solution."<ref>{{cite journal | last1 = Fromm | first1 = Erika O. | year = 1998 | title = Lost and found half a century later: Letters by Freud and Einstein | journal = American Psychologist | volume = 53 | issue = 11| pages = 1195–1198 | doi = 10.1037/0003-066x.53.11.1195 }}</ref> Einstein said that he did his problem solving without words, mostly in images. "The words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be 'voluntarily' reproduced and combined."<ref>{{cite book|last=Einstein|first=Albert|year=1954|chapter=A Mathematician's Mind|title=Ideas and Opinions|location=New York|publisher=Bonanza Books|page=25}}</ref>