Key message: New ideas don't fall from the sky. They arise from knowledge.
It is always good to ask the basic questions first and answer them precisely: What is a solution? A
solution is a way to solve a problem and thereby achieve a desired goal. The way to a goal is a method. To develop a method, we first need an idea. An idea arises from
knowledge. Knowlege consists of facts and rules.
"... hard problems are those for which a solver (human or computer) has insufficient knowledge and resources ..." (Wang, P. (2007). The logic of intelligence. In Artificial General Intelligence eds. B. Goertzel and C. Pennachin. New York, NY: Springer, page 31/39)
If we had sufficient knowledge, we could easily find or have ideas for the solution to our problem or we would know that it is unsolvable. How can we come to the necessary knowledge? There are two possibilities:
We find ideas someone else has used to solve our problem
Nowadays we can find almost everything on the internet. In order to search with the right keywords, it is always good to ask a basic question or to look at the definition of the term we are interested in. I did a search with the sentence "How to find ideas someone else has used to solve our problem" and I found this article:
"Find Someone Else Who Has Solved Your Problem Before ... Before any project, we need to stop and ask ourselves, has somebody already solved this problem. Then we need to genuinely ask ourselves, is there a good reason why our solution needs to be different." (www.producttalk.org/2013/08/find-someone-else-who-has-solved-your-problem-before, 03.10.2020)
We want to find an optimal solution for our problem. If someone else has already used an idea to solve our problem, we should still try to improve that idea. If we want to choose an optimal solution for our problem from several alternatives, we need to have several ideas.
We need to be creative and have new ideas to solve our problem
So what is creativity?
"I define creativity more specifically as the process of having original ideas that have value. ... Creativity is about producing something new. ... It does have to be new to the maker at least and not just a copy or a repetition." (www.interaliamag.org/interviews/ken-robinson, 21.09.20)
"Too often ... “creativity” means having great, original ideas. ... the ideas are often judged more by their novelty than by their potential usefulness ..." (https://hbr.org/2002/08/creativity-is-not-enough, 26.09.20)
Creativity is when someone produces "something new" that is useful. "Something new" is
useful when it improves our lives or helps to solve a problem. Creative ideas are useful when they have a goal.
Definition: Creativity is the ability to have new ideas to achive a goal.
To produce "something new" a person needs to have a new idea. An idea is a brief mental image of something. An idea is only useful if it can be implemented. If an idea is concretized, a plan or a method emerges (a method is the way to a goal, see figure below).
We have a problem when we want to achieve a goal, but our knowledge is insufficient to
find the way to it. We need ideas to fill our knowledge gaps ("blanks") and thus achieve our goal.
"... in Leo Tolstoy’s novel “War and Peace”, Prince Andrei Bolkonsky explains the concept of war ʹ... in war, a battalion is sometimes stronger than a division and sometimes weaker than a company; it all depends on circumstances that can never be known. In war, you do not know the position of your enemy; some things you might be able to observe, some things you have to divine (but that depends on your ability to do so!) and many things cannot even be guessed at. ... If you decide to attack, you cannot know whether the necessary conditions are met for you to succeed.ʹ In essence, war is characterized by a high degree of uncertainty. A good commander ... can add to that what he or she sees, tentatively fill in the blanks ... A bad commander extrapolates from what he sees and thus arrives at improper conclusions." (Dörner, D., & Funke, J. (2017). Complex problem solving: What it is and what it is not. Frontiers in Psychology, 8,1153, page 7)
"Ideally, we would like Artificial intelligence (AI) agents to interact with an arbitrary environment where only partial information is available with uncertainty. ... AI agents are much better at quantitative computation than humans but are less capable of perceiving concepts qualitatively. This is the reason why AI agents can beat human experts in deterministic games such as chess and go but are struggling to complete an everyday task ..." (https://openresearch-repository.anu.edu.au/handle/1885/154259, 11.10.20)
The method "trial and error" is the simplest method to fill a knowledge gap with an idea and thus to find a solution for the problem. The search for solutions consists of trials to reach the goal. Nobody wants to rely on his luck and choose the ideas for the trials randomly.
"If trials are chosen randomly, the probability of arriving at a valuable solution
to a complex, high-interaction problem is very low. More efficient orderings utilize knowledge to direct this search process." (Nickerson, J. a. and Zenger, T.R. (2004) A Knowledge-Based Theory of the Firm—The Problem-Solving Perspective. Organization Science, Vol. 15 No. 6, page 620)
1. Domain specific knowledge
Become an expert in the domain the problem belongs to. Read the domain literature, do experiments and ask other expert about the problem.
"... experts do not possess better general cognitive skills than novices – such as better memory capacity – but rather experts have better domain knowledge based on their experience ..." (Pisa 2012 Field Trial Problem Solving Framework, www.oecd.org/pisa/pisaproducts/46962005.pdf, 01.11.20)
The knowledge gap of experts concerning the problem is smaller than that of other individuals. Because they know all the facts and rules in their field, they can use them to create ideas
that overcome obstacles and solve the problem.
"Gaps in knowledge must be filled by observation and exploration of the problem situation. This often involves interaction with a new system to discover rules that in turn must be applied to solve the problem." (Pisa 2012 Field Trial Problem Solving Framework, www.oecd.org/pisa/pisaproducts/46962005.pdf, 01.11.20)
Example: If I want to fly I can use the rule that hot air has a lower density than cold air and I can build myself a hot air balloon.
"In the broadest sense, a rule could be any statement which says that a certain conclusion must be valid whenever a certain premise is satisfied, i.e. any statement that could be read as a sentence of the form “if ... then ...” ... it should be noted that there are a number of rather different interpretations of the term “rule” outside of first-order logic." (Hitzler P., Krötzsch M., Rudolph, S. (2009). Foundations of Semantic Web Technologies. Chapman & Hall/CRC, page 213 - 216)
Logic is important for creativity: If I want to reach a goal, then what do I have to do? I have to look for facts and rules that I can use to fill my knowledge gaps. In order to do that, it is helpful to know or imagine what knowledge I am missing.
If I want to fly I should study all things that go up: hot air, some gases, birds, leaves in the wind, etc. When I understand the rules why these things go up, then maybe I can use these rules to fly myself. Birds can fly. It is possible that they can fly because their wings have a special shape. So I should examine the shape of their wings.
"A sense of possibility ... imagines something that might be possible but has not been considered possible or even potentially possible so far. (... sense of
possibility is often used synonymously with imagination even though imagination is not the same as sense of possibility, for imagination also encapsulates the impossible)." (Dörner, D., & Funke, J. (2017). Complex problem solving: What it is and what it is not. Frontiers in Psychology, 8,1153, page 7)
The difficulty lies in imagining the unknown unknows as well.
"In February 2002, Donald
Rumsfeld ... stated at a Defence Department
briefing: ‘There are known unknowns. That is to say, there are things that we now know we don’t know. But there are also unknown unknowns. There are things we do not know we don’t know.’ ... Much scientific research is based on investigating known unknowns. In other words, scientists develop a hypothesis to be tested, and then in an ideal situation experiments are best designed to test the null hypothesis. ... it is common for the researcher to believe that the result that will be obtained will be within a range of known possibilities. Occasionally, however, the result is completely unexpected—it was an unknown unknown." (Logan, D. C. (2009). Known knowns, known unknowns, unknown unknowns and the propagation of scientific enquiry. Journal of Experimental Botany, 60(3), p. 712)
Another difficulty is to find the knowledge that is relevant to the problem at hand.
"... chess masters described above considered only a subset of possible chess moves, but those moves were generally superior to the ones considered by the lesser ranked players. Experts have not only acquired knowledge, but are also good at retrieving the knowledge that is relevant to a particular task. In the language of cognitive scientists, experts’ knowledge is “conditionalized”—it includes a specification of the contexts in which it is useful (Simon, 1980; Glaser, 1992). Knowledge that is not conditionalized is often “inert” because it is not activated, even though it is relevant (Whitehead, 1929). ... “Textbooks are much more explicit in enunciating the laws of mathematics or of nature than in saying anything about when these laws may be useful in solving problems” (Simon, 1980:92)." (National Research Council. (2000) How people learn: Brain, mind, experience, and school. Washington, DC: National Academy Press, p. 43)
Laws (rules) are conditional statements. If I want to calculate the area of a rectangle, I can use the formula A = L x W (rule). But that is only possible if I know the values for L and W (facts).
"An expert system is a modular program consisting of a knowledge base, an inference engine and a user interface ... The knowledge base contains human expertise, which is often expressed in terms of rules and facts. Rules are conditional statements that state what action occurs if a specific condition is satisfied. ... An "inference engine" applies a reasoning strategy and generates solutions based on the rules in the knowledge base and data collected by the expert system." (Taylor, T. and Lubkeman, D. (1989). Applications of Knowledge-Based Programming to Power Engineering Problems. IEEE Transactions on Power Systems, Vol. 4, No. 1, p. 345)
2. General knowledge
Become an "expert" in general knowledge. We need general knowledge to be able to find analogies that inspire us to have new ideas.
“The ability to perceive similarities and analogies is one of the most fundamental aspects of human cognition. It is crucial for recognition, classification, and learning and it plays an
important role in scientific discovery and creativity. ... analogical reasoning involves the identification and transfer of structural information from a known system (the source) to a new and
relatively unknown system (the target).” (Vosniadou, S. and Ortony,
A. (1989). Similarity and analogical reasoning, Cambridge: Cambridge University Press, p. 1)
"An analogy is said to exist when the pattern of relations amongst one set of elements ... is shared with that of another set." (Nathaniel Barr (2014). Reasoned connections: Complex creativity and dual-process theories of cognition. UWSpace., p. 12)
The relations between the elements of a system are determined by rules (patterns). When two systems have analogies, it may be possible to apply the rules of the known system to the new unknown system.
"... expertise in a domain helps people develop a sensitivity to patterns of meaningful information that are not available to novices. ... experts and competent beginners (college students) were asked to describe verbally the approach they would use to solve physics problems. Experts usually mentioned the major principle(s) or law(s) that were applicable to the problem, together with a rationale for why those laws applied to the problem and how one could apply them (Chi et al., 1981). ... Differences in how physics experts and novices approach problems can also be seen when they are asked to sort problems, written on index cards, according to the approach that could be used to solve them (Chi et al., 1981). Experts’ problem piles are arranged on the basis of the principles that can be applied to solve the problems; novices’ piles are arranged on the basis of the problems’ surface attributes." (National Research Council. (2000) How people learn: Brain, mind, experience, and school. Washington, DC: National Academy Press, p. 34, 37, 38)
So it is not important just to accumulate a large amount of general knowledge, but rather to try to recognize the rules behind the information.
"Many ways of teaching science ... overemphasize facts (American Association for the Advancement of Science, 1989; National Research Council, 1996). The Third International Mathematics and Science Survey (TIMSS) (Schmidt et al., 1997) criticized curricula that were “a mile wide and an inch deep”... (National Research Council. (2000) How people learn: Brain, mind, experience, and school. Washington, DC: National Academy Press, p. 42)
3. Problem-solving knowledge
Become an expert in problem solving. Problem solving is a skill. So what is a skill?
Knowledge has two meanings: We use the word knowledge for things we know and for things we understand. We know all the things that we have memorized in our brain and can recall. Understanding means something different.
"Making matters worse is our tendency to use the terms know, know how, and understand interchangeably in everyday speech. ... Understanding is about transfer ... The ability to transfer our knowledge ... effectively involves the capacity to take what we know and use it creatively, flexibly, fluently, in different settings or problems, on our own." (Wiggins, G. P., & McTighe, J. (2005). Understanding by design (Expanded 2nd ed.). Alexandia, VA: Association for Supervision and Curriculum Development)
"... ‘skills’ means the ability to apply knowledge and use know-how to complete tasks and solve problems. ... ‘competence’ means the proven ability to use knowledge, skills and personal, social and/or methodological abilities, in work or study situations and in professional and personal development" (https://eur-lex.europa.eu/legal-content/EN/TXT/HTML/?uri=CELEX:32017H0615(01)&from=DE#d1e32-20-1, 14.11.20)
For me understanding and skill/competence are the same. Understanding/skills/competence can only be acquired through practice. Problem-solving knowledge is only helpful for someone who practices problem solving.
"The reason the executive so often rejects new ideas is that he is a busy man whose chief day-in, day-out task is to handle an ongoing stream of problems. He receives an unending flow of questions on which decisions must be made. Constantly he is forced to deal with problems to which solutions are more or less urgent and the answers to which are far from clear-cut. It may seem splendid to a subordinate to supply his boss with a lot of brilliant new ideas to help him in his job. But advocates of creativity must once and for all understand the pressing facts of the executive’s life: Every time an idea is submitted to him, it creates more problems for him—and he already has enough." (https://hbr.org/2002/08/creativity-is-not-enough, 26.09.20)
Many people think problem-solving knowledge and creativity is only for big problems. They think they don't have time to optimise the solutions of their daily live problems. They see that they have to invest time, but they do not understand that they can also save a lot of time by solving problems optimally. Learning starts with small steps. First solve many small problems optimally, then you can try to solve a larger problem optimally.
(1995) described that, for any organization to keep pace with the
fast-changing environment, it needs to take full advantage of both CI [continuous improvement] and breakthrough improvement. Organizations which are just starting their improvement process activities should first direct their efforts to CI, establishing a working base. Then they should expand their improvement effort to include breakthrough improvement." (Singh, J., and Singh, H. (2015), “Continuous improvement philosophy–literature review and directions”, Benchmarking: An International Journal, Vol. 22 No. 1, p. 95)
The third obstacle we may encounter on our way to solving a problem is a lack of knowledge, which prevents us from finding existing ideas or creating new ones for the solution.
Continue with the next step of the problem-solving process: