Problem solving: Difference between revisions

Revision as of 17:56, 11 October 2024

Latest revision as of 05:09, 2 August 2025

(28 intermediate revisions by 22 users not shown)

Line 6:

{{Puzzles}}

'''Problem solving''' is the process of achieving a [[goal]] by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from simple personal tasks (e.g. how to turn on an appliance) to complex issues in business and technical fields. The former is an example of '''simple problem solving''' ('''SPS''') addressing one issue, whereas the latter is '''complex problem solving''' ('''CPS''') with multiple interrelated obstacles.<ref name="Complex Problem Solving">{{Cite book|date=2014-04-04|editor-last=Frensch|editor-first=Peter A.|editor2-last=Funke|editor2-first=Joachim|title=Complex Problem Solving|publisher=Psychology Press |doi=10.4324/9781315806723|isbn=978-1-315-80672-3}}</ref> Another classification of problem-solving tasks is into well-defined problems with specific obstacles and goals, and ill-defined problems in which the current situation is troublesome but it is not clear what kind of resolution to aim for.<ref name=":0" /> Similarly, one may distinguish formal or fact-based problems requiring [[G factor (psychometrics)|psychometric intelligence]], versus socio-emotional problems which depend on the changeable emotions of individuals or groups, such as [[Emotional intelligence|tactful]] behavior, fashion, or gift choices.<ref name="Blanchard-Fields">{{cite journal |author=[[Fredda Blanchard-Fields|Blanchard-Fields, F.]] |year=2007 |title=Everyday problem solving and emotion: An adult developmental perspective |journal=Current Directions in Psychological Science |volume=16 |issue=1 |pages=26–31 |doi=10.1111/j.1467-8721.2007.00469.x |ref=Reference-Blanchard |s2cid=145645352}}</ref>

Solutions require sufficient resources and knowledge to attain the goal. Professionals such as lawyers, doctors, programmers, and consultants are largely problem solvers for issues that require technical skills and knowledge beyond general competence. Many businesses have found profitable markets by recognizing a problem and creating a solution: the more widespread and inconvenient the problem, the greater the opportunity to develop a [[Scalability|scalable]] solution.

There are many specialized problem-solving techniques and methods in fields such as [[science]], [[engineering]], [[business]], [[medicine]], [[mathematics]], [[computer science]], [[philosophy]], and [[societies|social organization]]. The mental techniques to identify, analyze, and solve problems are studied in [[psychology]] and [[cognitive science]]s. Also widely researched are the mental obstacles that prevent people from finding solutions; problem-solving impediments include [[confirmation bias]], [[mental set]], and [[functional fixedness]].

== Definition ==

Line 64:

[[Forensic engineering]] is an important technique of [[failure analysis]] that involves tracing product defects and flaws. Corrective action can then be taken to prevent further failures.

Reverse engineering attempts to discover the original problem-solving logic used in developing a product by disassembling the product and developing a plausible pathway to creating and assembling its parts.<ref>{{Cite web |url=https://litemind.com/problem-definition/|archive-url=https://web.archive.org/web/20170621145314/https://litemind.com/problem-definition/|archive-date=2017-06-21|title=Einstein's Secret to Amazing Problem Solving (and 10 Specific Ways You Can Use It)|website=Litemind|language=en-US|access-date=2017-06-11|date=2008-11-04 |last1=Passuello |first1=Luciano }}</ref>

=== Military science ===

Line 157:

===Unnecessary constraints===

Unnecessary constraints are arbitrary boundaries imposed unconsciously on the task at hand, which foreclose a productive avenue of solution. The solver may become fixated on only one type of solution, as if it were an inevitable requirement of the problem.<ref>{{Cite web |date=2023-08-24 |title=How Your Subconscious Solves Complex Problems at Work - WorkforceWise |url=https://workforcewise.org/how-your-subconscious-solves-complex-problems-at-work/ |access-date=2024-10-11 |website=workforcewise.org |language=en-US}}</ref> Typically, this combines with mental set—clinging to a previously successful method.<ref name="Kellogg, R. T. 2003">{{cite book|last=Kellogg|first=R. T.|year=2003|title=Cognitive psychology|edition=2nd|___location=California|publisher=Sage Publications, Inc.}}</ref>{{page needed|date=September 2023}}

Visual problems can also produce mentally invented constraints.<ref>{{cite book|last=Meloy|first=J. R.|year=1998|title=The Psychology of Stalking, Clinical and Forensic Perspectives|edition=2nd|___location=London, England|publisher=Academic Press}}</ref>{{page needed|date=September 2023}} A famous example is the dot problem: nine dots arranged in a three-by-three grid pattern must be connected by drawing four straight line segments, without lifting pen from paper or backtracking along a line. The subject typically assumes the pen must stay within the outer square of dots, but the solution requires lines continuing beyond this frame, and researchers have found a 0% solution rate within a brief allotted time.<ref>{{cite journal|last2=Ormerod|first2=T.C.|last3=Chronicle|first3=E.P.|year=2001|title=Information-processing and insight: A process model of performance on the nine-dot and related problems|journal=Journal of Experimental Psychology: Learning, Memory, and Cognition|volume=27|issue=1|pages=176–201|doi=10.1037/0278-7393.27.1.176|last1=MacGregor|first1=J.N.|pmid=11204097}}</ref>

Line 179:

=== Other barriers for individuals ===

People who are engaged in problem solving tend to overlook subtractive changes, even those that are critical elements of efficient solutions.{{ For example, a city planner may decide that the solution to decrease traffic congestion would be to add another lane to a highway, rather than finding ways to reduce the need for the highway in the needed|date=Septemberfirst 2023}}place. This tendency to solve by first, only, or mostly creating or adding elements, rather than by subtracting elements or processes is shown to intensify with higher [[cognitive load]]s such as [[information overload]].<ref>{{multiref2

|1={{cite news |first=Sujata |last=Gupta |title=People add by default even when subtraction makes more sense |url=https://www.sciencenews.org/article/psychology-numbers-people-add-default-subtract-better |access-date=10 May 2021 |work=Science News |date=7 April 2021 |archive-date=21 May 2021 |archive-url=https://web.archive.org/web/20210521134851/https://www.sciencenews.org/article/psychology-numbers-people-add-default-subtract-better |url-status=live }}

|2={{cite journal |last1=Adams |first1=Gabrielle S. |last2=Converse |first2=Benjamin A. |last3=Hales |first3=Andrew H. |last4=Klotz |first4=Leidy E. |title=People systematically overlook subtractive changes |journal=Nature |date=April 2021 |volume=592 |issue=7853 |pages=258–261 |doi=10.1038/s41586-021-03380-y |pmid=33828317 |bibcode=2021Natur.592..258A |s2cid=233185662 |url=https://www.nature.com/articles/s41586-021-03380-y |url-access=subscription |access-date=10 May 2021 |language=en |issn=1476-4687 |archive-date=10 May 2021 |archive-url=https://web.archive.org/web/20210510130853/https://www.nature.com/articles/s41586-021-03380-y |url-status=live }}

Line 199:

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.

Mark Blechner conducted this experiment and obtained results similar to Dement's.<ref name="Blechner 2018">{{cite book|last=Blechner|first=Mark J.|year=2018|title=The Mindbrain and Dreams: An Exploration of Dreaming, Thinking, and Artistic Creation|___location=New York|publisher=Routledge}}</ref>{{page needed|date=September 2023}} He found that while trying to solve the problem, people had dreams in which the solution appeared to be obvious from the dream, but it was rare for the dreamers to realize how their dreams had solved the puzzle. Coaxing or hints did not get them to realize it, although once they heard the solution, they recognized how their dream had solved it. For example, one person in that OTTFF experiment dreamed:<ref name="Blechner 2018"/>{{page needed|date=September 2023}}

{{blockquote|There is a big clock. You can see the movement. The big hand of the clock was on the number six. You could see it move up, number by number, six, seven, eight, nine, ten, eleven, twelve. The dream focused on the small parts of the machinery. You could see the gears inside.}}

In the dream, the person counted out the next elements of the series—six, seven, eight, nine, ten, eleven, twelve—yet he did not realize that this was the solution of the problem. His sleeping mindbrain{{jargon inline|date=September 2023}} solved the problem, but his waking mindbrain was not aware how.

[[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>

Line 264 ⟶ 258:

** temporal sensitivity{{clarify|reason=how does this differ from "temporal constraints"?|date=September 2023}}

** phase effects{{Definition needed|date=September 2023}}

** dynamic [[Predictability|unpredictability]]{{Specify|reason=of what?|date=September 2023}}

* intransparency (lack of clarity of the situation)

** commencement opacity{{Definition needed|date=September 2023}}

Line 296 ⟶ 290:

[[Crowdsourcing]] is a process of accumulating ideas, thoughts, or information from many independent participants, with aim of finding the best solution for a given challenge. Modern [[information technologies]] allow for many people to be involved and facilitate managing their suggestions in ways that provide good results.<ref>{{multiref2

|1={{cite journal|last1=Guazzini|first1=Andrea|last2=Vilone|first2=Daniele|last3=Donati|first3=Camillo|last4=Nardi|first4=Annalisa|last5=Levnajić|first5=Zoran|title=Modeling crowdsourcing as collective problem solving|journal=Scientific Reports|date=10 November 2015|volume=5|pagearticle-number=16557|doi=10.1038/srep16557 |pmid=26552943 |pmc=4639727 |bibcode=2015NatSR...516557G|arxiv=1506.09155}}

|2={{cite journal|last1=Boroomand|first1=A.|last2=Smaldino|first2=P.E.|year=2021|title=Hard Work, Risk-Taking, and Diversity in a Model of Collective Problem Solving|journal=Journal of Artificial Societies and Social Simulation|volume=24|number=4|article-number=10 |doi=10.18564/jasss.4704 |s2cid=240483312 |doi-access=free}}

}}</ref> The [[Internet]] allows for a new capacity of collective (including planetary-scale) problem solving.<ref>{{cite journal|last1=Stefanovitch|first1=Nicolas|last2=Alshamsi |first2=Aamena |last3=Cebrian |first3=Manuel |last4=Rahwan|first4=Iyad|title=Error and attack tolerance of collective problem solving: The DARPA Shredder Challenge|journal=EPJ Data Science |date=30 September 2014|volume=3|issue=1|article-number=13 |doi=10.1140/epjds/s13688-014-0013-1|doi-access=free|hdl=21.11116/0000-0002-D39F-D|hdl-access=free}}</ref>

==See also==

Line 363 ⟶ 357:

{{Footer Neuropsychology}}

{{Virtues}}

{{Education}}

{{Authority control}}