GENERAL PRINCIPLES OF PROBLEM SOLVING

INTRODUCTION

Living things with brain/mind apparatus of varying capability are engaged in generating a variety of thoughts concerning views, beliefs, calculations, emotions [Johnson-Laird, 1988]. Thoughts are produced by imagination or arise as a result of input from the sense organs, when they concern : 1. Maintenance of current states of affairs including self or survival or homeostasis, or 2. Achievement of a not yet existing state of affairs we speak of problem solving.

Problem solving activity is innate and universal in living things and consists of : a. Identification of a problematic issue (pi) and an envisaged, consistent, desirable, or not, state of affairs (sa), b. The means of transformation from pi to sa referred to as appropriate interrelation, and c. The means of creation of the interrelation by chance or design referred to as system or structure producing a product so as to enable it to exert the interrelation.

Living things predominantly humans, are incessantly and instinctively engaged in problem solving activity otherwise they would die or would not create novel states of affairs. According to A. Einstein 'Life is like a bicycle : if you stop pedalling you fall off'. However, living things when performing innate problem solving make use of points a., b. and c. Humans rarely if ever apply the three components in a systematic, comprehensive manner. People often suggest means when they hear a problematic issue without being aware of the appropriate interrelation hoping for an envisaged state of affairs. For example, people in public offices are prone to this kind of activity or hearing of an ailment of a friend a person may suggest a remedy. Experience and professional knowledge can alleviate this situation. Currently there are suggestions for envisaged, comprehensive improvements of the life of people in societies with vaguely anticipated means of accomplishment and without detailed investigation [Schwab, 2018]. The inadequate thinking happens because the support by instinctive innate problem solving is not sufficient and current methods in problem solving are vague, fragmented and without agreed analytical support. This paper intends to initiate discussion of a more comprehensive, 'systems theory' which integrates the three components of problem solving giving a framework for more systematic thinking subject to peer scrutiny, further development, availability of software for working out the dynamics of scenarios and applications [Korn, 2022[Korn, , 2023.

BASIC CONCEPTS

The intention is to express the preliminary notions described in the INTRODUCTION in more precise form. In the first instance it is suggested that we perceive things or parts of the world or objects or agents in their entirety resulting in images in the brain/mind and we react to or ignore them. When inquiring into the nature of things, this activity may be followed by making comments using defining characteristics or properties to arrive at a classification :

A. Natural inanimate things ranging from subatomic particles to galaxies created by chance or fortuitously or accidentally in nested hierarchy of increasing complexity B. Natural animate things ranging from cells to humans evolved in nested hierarchy of increasing complexity C. Artificial objects ranging from structures or static to dynamic systems or products created according to purpose in a nested hierarchy of increasing complexity or found in an environment by chance. The term 'nested' means that an entity at one stage of hierarchy is transferred to the next stage of higher complexity as a building block or whole leading to cumulative rather than one-off change. This type of entity was called holon by [Koestler, 1967].

The proposed principles lead to the symbolic structure or model of the 'systems theory' [Korn, 2022[Korn, , 2023.

Principle of equilibrium

It is claimed that a part of the totality of A., B., C. or a thing selected by interest represents our experience aspects of which can be interpreted by arrangements of contingent properties into symbolic structures. Such structures can be seen to change from an initial equilibrium state to a final equilibrium state. Thus, we observe an incessantly evolving, developing or deteriorating world in direction of increasing or decreasing complexity as can be assessed by contingent properties of holons or wholes of which a particular thing is seen to consist. This kind of conclusion had been reached by Heraclitus in ancient Greece who asserted that 'you cannot step into the same river twice [Levene, 2010].

Principle of means of change of equilibrium

Change of equilibrium state of a part of the world cannot change by itself, it needs an agent called system as expressed by Newton's 1 st law of motion with reference to objects with mass. States of defined entities and agents are expressed in terms of properties and changes are seen in terms of these. This notion is shown diagrammatically in Figures 1. and 2. by the lines attached to contours.

Principle of emergence of functional structures

Our perception of the world is that it is structural and there is no alternative. The elements of the symbolic structure of natural language for the representation of such a world are the smallest declarative, meaningful, context free sentences defined as ordered pairs. They can be directly expressed as logical conditionals in accordance with linguistic modelling and are called semi-holons because they cannot be broken down further. They are the elementary, structural properties of which increasingly complex, interacting structures or nested hierarchies can be constructed to model or to design a part of the world. Any such structure is viewed a holon or whole when a function can or cannot be assigned to it [Lipschutz, 1982, Korn, 2022, 2023.

A sentence consists of noun phrases or images and a stative or dynamic main verb organised into a subject-predicate structure. Noun phrases and verbs are qualified by adjectives and adverbs which make a sentence context dependent or falsifiable and called qualitative or quantitative properties [Popper, 1972].

Design thinking proceeds by selecting or constructing holons as qualified, static or dynamic structural units to form functional structures according to requirements generated by PART A. in Figure 2.

'Story' of the problematic situation

The Prime Minister [PM] must return to 'basic values' to win the election, senior members of the political party warned. He was told tax cuts and house building would lure the many voters who stayed away from the polls resulting in recent defeats. The PM was also told to axe the 2030 ban on nonelectric cars. OPI [6] in the 3 rd STEP is the only acceptable state for FS of User/consumer [8] to happen 5 th STEP Selecting product [3] from a 'store of available products' judged and evaluated to be capable of exerting the kind of interrelation with suitable properties to accomplish the change of state from OPI [5] to OPI [6] Interrelation : 'Affecting the mental state of the electorate so as to cast their vote for the candidate of the political party'

The 'material objects' possessing the appropriate qualities and quantities or product [3] capable of producing the interrelation are : 1. The political party is to recall and to act according to 'basic values', 2. The chancellor is to cut taxes, 3. The construction companies are to build houses, 4. The government is to drop the ban on non-electric cars by 2030 which are suggested from the ''Story' of the problematic situation', otherwise to be found by creative imagination or investigation, invention. 6 th STEP Suggesting the pertinent static and dynamic properties of the objects and agents involved in a problematic situation and using the Entailment Relation to generate the REQUIREMENTS for product [3] to cater for these properties. The objects and agents are Interrelation (I) OPI (O) User/consumer (U) Objects external but relevant and interested in Part A. such as the physical and social environments (E) which lead to 'product specifications'. I -Interrelation, 1. The form of interrelation is 'information' to persuade. It needs to be designed and constructed so as to be of interest to the electorate [Korn, 2022]. In addition, information is to be delivered tactfully. O -Electorate, 2. An electorate is usually a group of heterogenous people, here we assume that they are homogenous. They are elderly people preferring solid, time proven values, like tax cuts but not enthusiastic, live in their own houses, do not drive cars. U -All members of the political party, 3. They are a mixture of elderly with a significant proportion of young people preferring new ideas, interested in tax cuts and house building, drive cars. E -Opposition party, 4. Denies basic values, supports tax cuts and house building and preservation of the physical environment. 7 th STEP Matching the properties obtained in the 6 th STEP to those of product [3] obtained in the 5 th STEP using the Entailment Relation followed by the Object Selector Matrix [Korn, 2022]. The Entailment Relation is constructed as follows with the numerals referring to the properties of objects and agents in the 6 th STEP.

Problem solving activity in the INTRODUCTION Figure 1. Change of equilibrium states of inanimate thingsProblem solving activity in the INTRODUCTION