Key message: Creativity builds on knowledge. Solving a problem creatively means closing a knowledge gap with a new idea.
If we want to solve a problem, we first need an idea and then a method that fits the idea: An idea is a concise mental picture of something, an idea that describes the essence (principle) of something. A method is the way to a desired goal (a precise description of this way). To find an optimal solution to the problem, we must have several alternative ideas. Then we can choose the best one and implement it.
"A common misconception about the CPS process is that it is a free-running, unstructured, almost mystical process [CPS = creative problem solving]. This belief is encouraged by anecdotes of creative breakthroughs occurring during periods of unconscious sleep or via an unconscious thought process." (Titus, P. A. (2000). Marketing und der kreative Problemlösungsprozess. Zeitschrift für Marketing-Ausbildung, 22, p. 226)
Ideas arise on the basis of knowledge. But why do many people think that new ideas arise unconsciously, that they "fall from the sky"?
"Our brain is actually not designed to learn and retain knowledge, especially rarely used detailed knowledge. Every human brain is evolutionarily more adapted to skill and the accumulation and generalization of experience that enables survival in its environment." (Rost, F. (2018) Lern- und Arbeitstechniken für das Studium. Springer VS, Wiesbaden, p. 34)
In dangerous situations, we do not have time to think for a long time, which is why our brain tries to intuitively (unconsciously) do the right thing, i.e. what corresponds to our previous experience. Our brain thinks unconsciously in "tracks", i.e. in a predetermined direction. Therefore, if we want to develop new ideas, we have to leave these "tracks".
When we think about a difficult problem for a long time, we intuitively think in such "tracks". It's not until we take a break and restart the thought process that we can leave the old "tracks" and come up with a new idea. Then it seems as if the idea "fell from the sky".
Example: With a difficult problem, it makes no sense to brainstorm with people who know nothing about 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:
1. 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.
2. 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.
Creativity is the ability to have new ideas that can be used to achieve a goal. Is this
the definition of creativity?
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. Neither of them 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?
If you want to evaluate a person's creativity, you have to evaluate not only the quality of his idea,
but also the time it took him to come up with the idea. So a person is particularly creative if he or she can develop new ideas that are very useful in a short time on the basis of very little
information. However, it is also true that difficult problems can rarely be solved in a short time.
Definition: Creativity is the ability to have new and useful ideas based on incomplete information.
"... 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)
A good commander has a lot of knowledge and experience. With his existing knowledge, he can carry out an analysis of the problem and thus identify where there are gaps in knowledge.
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)
"The 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)
When an expert examines a problem, he imagines what knowledge he is missing and what possibilities (what facts and rules) there are to fill his knowledge gaps. He uses his sense of possibility and becomes creative (see below at "abstract thinking and logical reasoning").
"This sense of possibility entails ... being able to construe an unknown whole that could accommodate a known part. The whole has to align ... with the laws of physics and chemistry. Otherwise, the entire venture is ill-founded. A sense of possibility does not aim for the moon but imagines something that might be possible but has not been considered possible or even potentially possible so far." (Dörner, D., & Funke, J. (2017). Complex problem solving: What it is and what it is not. Frontiers in Psychology, 8,1153, p. 7)
(How to recognize the whole of a situation/system, see on Learn-Study-Work "How to analyze situations/systems".)
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).
"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)
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.
"... for all flying animals in nature [apply] the same physical laws [rules] for propulsion and lift ... : Propulsion by the flapping of the wing, lift by the negative pressure on the curved upper surface of the wing (Bernoulli's principle)." (www.planet-schule.de/wissenspool/tierische-flugpioniere/inhalt/hintergrund.html#kap2, 23.04.22)
In the years 1486 - 1513, Leonardo da Vinci was engaged in flying, e.g. he designed a swinging aircraft. However, he lacked the necessary knowledge to put the design into practice.
Otto Lilienthal was the "first to systematically investigate and describe aerodynamic principles. His groundbreaking book ʹDer Vogelflug als Grundlage der Fliegekunstʹ ... was used by the Wright brothers, for example, for their aircraft developments: ʹThe most important finding (...) was the discovery that curved wings provided greater lift than flat onesʹ, they noted." (https://aeroreport.de/de/good-to-know/wie-ein-vogel, 05.01.23)
He writes in his book:
"If we now look back at what has been presented in this work, a number of theorems [rules] derived from experiments stand out in it ... The insight of the correctness of these theorems requires only an understanding of the simplest concepts of mechanics ... " (www.luftfahrt-bibliothek.de/datenarchiv/otto-lilienthal-der-vogelflug-als-grundlage-der-fliegekunst.pdf, 25.04.22, S. 182)
In the field of science, the possibilities that are supposed to fill gaps in knowledge are called hypotheses.
"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)
The difficulty lies in imagining the "unknown unknows" as well.
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)
If a person has a good expertise, he knows many rules and facts in the relevant domain and he/she also knows where and how they can be applied to solve problems.
"... expertise in a domain helps people develop a sensitivity to patterns of meaningful information that are not available to novices. ...
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 [rules] that can be applied to solve the problems; novices’ piles are arranged on the basis of the problems’ surface attributes. ...
Experts have not only acquired knowledge, but are also good at retrieving the knowledge that is relevant to a particular task." (National Research Council. (2000). How people learn: Brain, mind, experience, and school. Washington, DC: National Academy Press, p. 33, 38, 43, www.nap.edu/read/9853/chapter/5, 22.07.23)
So it is important to understand the rules behind the surface properties.
2. 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)
If two objects (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.
3. Problem-solving knowledge
A lot of expertise and general knowledge is good, but we also need to know how to apply this knowledge and how to control ourselves. That is why we need problem-solving skills.
"... 'skills' means the ability to apply knowledge and use know-how to complete tasks and solve problems." (https://eur-lex.europa.eu/legal-content/EN/TXT/HTML/?uri=CELEX:32017H0615(01)&from=DE#d1e32-20-1, 14.11.20)
"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, 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)
Creativity techniques can also help to have new ideas. Unfortunately, I don't know much about these techniques. However, if you read my texts here on this web site, you will find that they contain many new ideas.
"One of the challenges facing artificial intelligence research today is designing systems capable of utilizing systematic reasoning to generalize to new tasks. The Abstraction and Reasoning Corpus (ARC) measures such a capability through a set of visual reasoning tasks." (https://link.springer.com/chapter/10.1007/978-3-030-93409-5_54, 02.06.23)
A problem solution has four main elements: the initial situation, the goal, the obstacle that prevents the achievement of the goal and the method that should lead to the goal. If there are
knowledge gaps in one or more of these elements, we cannot solve the problem.
For each knowledge gap, we must use our sense of possibility (see above). That means we have to list all the possibilities that could fill that gap. First, we do this at a high abstract level. Then we concretize each of these abstract possibilities. We need thinking to understand the problem and to imagine possible solutions and we need reasoning to decide which option leads to our goal.
"Reasoning denotes acute and exact mentalizing involving logical deductions. ... Thinking, however, is ... the construction of an initially unknown reality. ... Once our sense of possibility has helped grasping a situation, problem solvers need to call on their reasoning skills. Not every situation requires the same action, and we may want to act this way or another to reach this or that goal. This appears logical, but it is a logic based on constantly shifting grounds: We cannot know whether necessary conditions are met, sometimes the assumptions we have made later turn out to be incorrect, and sometimes we have to revise our assumptions or make completely new ones. It is necessary to constantly switch between our sense of possibility and our sense of reality, that is, to switch between thinking and reasoning." (Dörner, D., & Funke, J. (2017). Complex problem solving: What it is and what it is not. Frontiers in Psychology, 8,1153, p. 7)
"Despite the onslaught of creative machines like generative AI, they won’t conquer human creativity and ingenuity. Just as the advent of photography didn’t kill painting, creating a new art form instead, generative AI enables new avenues of art and creativity." (https://nextconf.eu/2023/05/lets-get-physical/?ct=t(nl_07_23_next23, 08.07.23)
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)
Continue with the next step of the problem-solving process: