We (hereafter we, our, us mean humans) continuously meet problems, solve them and reencounter new ones. As long as the laws of physics govern us, and we shall survive individually and collectively in this universe, as we have experienced, various problems occur because we need resources to overcome and survive. Usually, problems are termed by where they break out: military, affection, production, diplomatic, financial or health problem. These are solved by their own presumed specific problem-solving process in their fields. If so, literally, we have uncountable problems and problem-solving methods. However, if we can overlook the problems in the bigger picture by their nature, not by their fields, it will be easier to gain insight and control them. This is the ultimate goal of the study: to define the problem, classify them by their nature and find a generalised problem-solving principle. The authors found that the problems can be classified into five groups and solved by their problem-solving principles. These characteristics lead us to the metaproperties of the problem. In this argument, authors use generally acceptable assumptions with which we have experienced and recognised.
Definition of Problem
The authors define the problem in a simple way via inductive reasoning. The details can be found in the Definition of Problem in Method. It is concluded that the problem is a situation where a difference exists between a current state and a target state, shown geometrically in Figure 1. The current state is the state where/when we recognise something imperfect exists, and the target state is the state we aim to clear of it. Thus, if there is no difference, the problem is either not existing or solved.
Group of problems and Problem-solving
Countless problems exist worldwide, and we have solved them individually in the field where the problem belongs. As we already have experienced, nature can be described in a simple and beautiful way. The same is applied to the problems. It is like finding the nature of a gravitational wave in the ocean, which is not described by the molecular motion of water. By describing in a simple way, authors like to recognise the metaphysics of problems. Furthermore, we can handle them more straightforwardly if we classify them by their nature. In Figure 2, we can see that there are three approaches to problem-solving from Figure 1.
- C→T: Current state C approaches target state T to eliminate the difference. It covers all practical and realistic problems we encounter in time and space.
- T→C: Target state T approaches current state C to eliminate the difference. These problems are related to religion or highly sophisticated theories where we cannot understand the process to the conclusion they made. The best strategy is to forget the theory they made and simply satisfy or “do the best” in the present, current state. This approach is problem-solving through persuasion or minimising risk by giving up.
- C→←T: Current and target approach each other to eliminate the difference in-between them. This approach is a combination of the above two approaches.
In this article, the authors describe the approach C→T because this approach is problem-solving against physical and visible problems such that, authors believe, the consequences of this approach are the culture and civilisation we have achieved.
Now, to classify the problems, authors assume causal principle1 and compare it with the definition of problem as shown in Figure 3.a. In other words, if there is a difference, there shall be a cause for it. When the cause of the difference is found, we may establish the problem-solving principle to eliminate the cause and difference. Then the process of eliminating a cause becomes a problem-solving principle. With this principle, we can reach a consequence which finally leads us to a new current state. Figure 3.a. is a microcosm of this process, and the detail is shown in Figure 3.b. Here authors select the cause as the classification criteria. We may choose the problem-solving principle for classification criteria, but the principle is determined by its cause – they are the two sides of a coin.
From Figure 2.a. and Figure 3.a., authors can extract some causes of the difference (we also imagine the corresponding behaviour of the arrow in Figure 2.a.) such that,
- Cause 1: Suppose a conflict element exits and hinders (cause) the approach to the target state. Then problem-solving is stagnant. In this case, the problem is solvable by lifting the governing restriction, which provokes conflict.
- Cause 2: Contrawise to Cause 1, if an adverse element exists and pushes away (cause) the current state from the target state, the problem is solvable via elimination or keeping away the adverse element.
- Cause 3: Suppose the target state is vague (cause). If we can design the target state by our own will and switch the current state with it, problem-solving is possible.
- Cause 4: On the other hand, if we cannot design the target, we try trial and error to reach the target. Designing the target state is the fastest way to the target, and trial and error is the slowest and most risky one in problem-solving.
- Cause 5: Suppose two out of cause, rule of relation(problem-solving principle) and consequence are found (cause) in a difference. In this case, we can infer an unknown one out of two.
Now classify five groups of problems from the above cases ① to ⑤ such that,
- If the problem involves cause, rule of relation and consequence, it is the "logical inference group". The well-known deduction, induction and estimation are the problem-solving principles of this group. Known cause and rule lead us to consequence by deduction; known cause and consequence give us to rule by induction; With rule and consequence, the cause can be found by estimation. Inference can be the fundamental problem-solving principle in all groups in common, and at the same time, it itself is one problem-solving principle.
- If the target state is definable at the current state, in other words, the purpose and fundamental functions of the target state can be specified, it is the "(target state) design group". If the purpose and fundamental functions are specified, we can design the state with the “structure of functions” combination. On the other hand, if we need to direct people to the designer’s target state, there are “direct control” and “game” where the measure is “controllability” of people. An adequate “baiting" strategy is needed to allure people to reach to designer’s target state.
- If the current state is pushed away from the target, the difference becomes more extensive and is in the "adverse element group". We can physically eliminate the adverse element, but it is possible to weaken or incapacitate its effect when it inevitably exists. When weakening or incapacitating the effect, the “baiting" strategy is needed to remove the adverse element.
- If the problem is about hindrance or stagnance in front of the target state, it belongs to the "conflict element group". Conflict occurs at nodes where different functions, demands or restrictions are met. To resolve the conflicts and thus the problem, we can change the governance of the conflict such as law. New technology is also possible if the technology changes the governing fundamental function, which changes the whole system. Meanwhile, we can imagine accommodating all conflicts. It can be realised by trade-off or new material. At last, conflicts can also be separated and allocated in different frames and resolved one by one, which is called separation.
- If the problem does not belong to the above four groups, the rest is the "trial and error group". When we have no choice but to reach a target in the middle of nowhere, we try random choices. However, there is a step-by-step, systematic "trial and error" process to reach the target state. If we systematically change the control factor in the current state, the consequence of the current state shall change correspondingly, and we can observe and control it to reach a target state. The typical examples of this group are parametric study and the "if-then” process.