Key message: New ideas don't fall from the sky. They arise from knowledge and practice.
If we want to solve a problem, we need a method to do it. A method is the way to a desired goal. In order to develop a method, we must first have an idea. An idea is a brief mental image of something, a concept that describes the essence (principle) of something. If we have an idea of how a goal can be achieved, then it is not yet a precise description of the way to the goal. Only the method to the idea provides this exact description.
If we want to
choose an optimal solution for our problem from several alternatives, we need to have several ideas. An idea arises from knowledge. (There is no
point in brainstorming with people who have no knowledge of the problem.)
"... 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, p. 39)
With sufficient knowledge, we would easily find or have ideas how to solve our problem or we would realize that it is unsolvable. How can we come to the necessary knowledge? There are two possibilities:
We find ideas that others have used to solve a similar 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:
"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)
If find an idea that someone else has already used to solve our problem, we should still try to improve this idea.
We need to be creative and have new ideas to solve our problem
"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/has value. "Something
new" is useful when it improves our lives and can be implemented to solve a problem.
First Definition: Creativity is the ability to have new ideas that can be used to achieve a goal.
"... in Leo Tolstoy’s novel 'War and Peace', Prince Andrei Bolkonsky explains the concept of war ʹ... 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, p. 7)
The method "trial and error" is the simplest method to fill a knowledge gap with an idea and thus to find a solution for a problem but 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, p. 620)
Artificial intelligence agents (computer programs) can quickly calculate many trials, but they are less creative when asked to fill knowledge gaps.
"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)
A good commander has so much knowledge and experience that he can fill gaps in knowledge through abstraction and logical reasoning and thus come to the right decisions (see below).
Scientists also create new knowledge that is useful. So are all scientists creative? If a scientist researches a question for so long that in the end he can't help but come up with a new idea, that can't be called creative.
Example: Two scientists are looking for the solution to a problem. Nobody knows what the other is doing. One scientist needs 10 years to solve the problem, the other only 2 years. Which of the two is more creative?
Final definition: Creativity is the ability to come up with new ideas that are useful based on little information.
1. Domain specific knowledge
"... 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, p. 40/41)
An expert also knows what knowledge is relevant to the problem at hand.
"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)." (National Research Council. (2000). How people learn: Brain, mind, experience, and school. Washington, DC: National Academy Press, p. 43, www.nap.edu/read/9853/chapter/5)
"Mobilisation of prior knowledge is not sufficient to solve novel problems in many everyday situations. 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. Instead of a straightforward application of previously mastered knowledge, existing knowledge needs to be reorganised and combined with new knowledge using a range of reasoning skills." (Pisa 2012 Field Trial Problem Solving Framework, www.oecd.org/pisa/pisaproducts/46962005.pdf, 01.11.20, p. 15)
Rules are conditional statements (if premise then consequence). When I want to calculate the area of a rectangle, I can use the formula A = L x W (rule: If I multiply the length by the width, then I get the area). But that is only possible if I know the values for L and W (facts).
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, p. 213 - 216)
Logic is important for creativity: If I want to reach a goal, then what do I have to do? I have to fill my knowledge gaps. In order to do that, it is helpful to know or imagine what knowledge I am missing.
Example: 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, p. 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)
Laws are like rules conditional statements (if premise then consequence). When I want to calculate the area of a rectangle, I can use the formula A = L x W (rule: If I multiply the length by the width, then I get the area). 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." (Barr, N. (2014). Reasoned connections: Complex creativity and dual-process theories of cognition. UWSpace, p. 12)
Rules (patterns) often apply to the relationships between the elements of a system. If two systems have analogies, it may be possible to apply the rules of the known system to the unknown system. People with a great general knowledge know the most important rules in many fields and can transfer them from one field to another.
"... 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. 34-38, www.nap.edu/read/9853/chapter/5)
So it is important to know the rules behind the surface properties.
3. Problem-solving knowledge
Become an expert in problem solving. 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 belong together. Both are necessary to solve problems creatively, but we need to know what we are doing and control ourselves. For this we need the problem-solving knowledge.
"Knowledge and skill, then, are necessary elements of understanding, but not sufficient in themselves. Understanding requires more: the ability to thoughtfully and actively 'do' the work with discernment, as well as the ability to self-assess, justify, and critique such 'doings'." (Wiggins, G., & McTighe, J. (1998). Understanding by design. Alexandria, VA: ASCD, www1.ascd.org/publications/books/103055/chapters/Understanding-Understanding.aspx, 10.12.21, p. 6)
Problem-solving knowledge is very helpful for someone who wants to solve problems optimally.
"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 some 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 problem-solving ideas or creating new ones.
Continue with the next step of the problem-solving process: