How to solve problems

Key message: A problem is solved by a method. A method is the way to a goal.


How to solve problems? The process of problem solving -


I have a problem when I am dissatisfied with an initial situation (the current situation), but at the moment I am not able to achieve a desired target situation (the goal). It may be that I do not know what the goal looks like or the means to achieve the goal are unknown or an obstacle must be overcome on the way to the goal (e.g. the required means may be known but not available). So a problem has four main elements: the initial situation, the obstacle, the goal (the target situation) and the method to achieve the goal.


"A problem occurs when a problem solver has a goal but initially does not know how to achieve the goal. This definition has three parts: (1) the current state - the problems begins in a given state; (2) the goal state - the problem solver wants the problem to be in a different state, and problem solving is required to transform the problem from the current (or given) state into the goal state, and (3) obstacles - the problem solver does not know the correct solution and an effective solution method is not obvious to the problem solver." (, 24.01.20)


In order to solve a problem, three main steps must always be carried out:

  1. analyze the problem (analyze the unsatisfactory situation, the obstacle and the goal)
  2. generate several alternative solution ideas (methods)
  3. make a decision (select a method).

(Lindemann, U.(2009). Methodische Entwicklung technischer Produkte. Heidelberg: Springer, S. 46, my translation)


"If I had an hour to solve a problem I'd spend 55 minutes thinking about the problem and 5 minutes thinking about solutions." (Albert Einstein)


"A problem properly stated is half solved." (John Dewey)


How to analyze situations? How to analyze systems?

A situation describes the relations between several elements (persons or things) at a point in time. (I cannot imagine a situation that consists of only one element.) So a situation is a system at a certain point in time. When I analyze a situation, it means that I am analyzing a system.


A system is a set of interrelated elements. The viewer can decide where to place the system boundary, but the boundary should make sense.


 A situation analysis is a system analysis -


When I say: “I want to analyze this system (situation)” then I really mean: “I want to understand this system.” Why is it not possible to understand a system just by analyzing it? Because “A whole is greater than the sum of its parts.”


Not only must the individual elements be examined, but also their interaction. Analysis breaks a system down into its constituent elements (into its parts). Synthesis combines the relations between the elements to come to an understanding of the whole.

Watch this video:, 15.02.20. In contrast to the video I believe that analysis and synthesis belong together and that it is impossible to understand a system without doing both.


"Analysis and synthesis, as scientific methods, always go hand in hand; they complement one another. Every synthesis is built upon the results of a preceding analysis, and every analysis requires a subsequent synthesis in order to verify and correct its results." ( , 26.02.20, page 1)


In another video the authors say that 3 cups on a table are not a system because they exist independently from each other. I also don't agree. I analyze: there are three cups on the table. Their function is to take up liquid. I synthesize: I can invite two friends to drink a coffee with me (or I can do somthing else with the cups). (, 15.02.20)


"In very general terms, a system is any (circumscribed) object which consists of a number of "parts" or "components" which, in some way or another, work together in order to produce an overall effect or behavior. ... We can only concede to the obvious: that just about everything in the world would seem to be some sort of "system". ( , 26.02.20, page 6)


Three cups on a table are a simple system. Complex systems have many elements and many relations exist between them (high interconnectivity). In addition complex systems may be intransparent (some information about the system is missing) and they may be dynamic (the system changes over time). Complex systems are much harder to understand than simple systems.


When I break down a complex system to its constituent elements I get a large amount of them. Therefore it makes sense to arrange the elements in groups. The groups can be seen as subsystems of the whole system. The continuation of this approach results in a hierarchical representation showing the structure of the system. Only if all elements are equal, they cannot be categorized.


system analysis, sytem synthesis, how to understand / develop / design systems,  -


The figure above shows the hierarchical structure of a complex system. It gives us an overview of the system elements and also a first indication of their relationship to each other, because we can see which elements belong together. Non-fiction books are systems of statements and their table of contents shows the hierarchical arrangement of these statements. Therefore the table of contents of a book is an example for the figure above.


In order to decide whether to start with an analysis or a synthesis to study the system, we need a second overview: what knowledge about the system is available to us.


"... the choice of a suitable method for the study of a given system depends, to a large extent, on the type of knowledge that is empirically accessicble to us ..." ( , 26.02.20, page 7)


We can start with an investigation of the whole or with an investigation of the parts (the elements).


"We regard a system as a primary unit [a functioning unit, "the whole"] when we treat it as a black box and ask about its overall behavior - i.e. what it does or accomplishes. For example, we may submit our black box to various inputs and observe the resulting outputs.
As a set of parts or components (which somehow work together to produce the system's overall behavior) we can examine the system's construction - i.e. its [elements,] internal structure and processes. ... and the specific relationships between its parts ..." ( , 26.02.20, page 6)


Sometimes it is useful to start an analysis and a synthesis at the same time. For example, when the police are looking for a serial killer, they investigate all the crime evidence (the elements) and hire a profiler to describe the killer's criminal profile ("the whole").


"The whole is more than the sum of its parts." So what is "the whole" of a system?

There are many different types of systems and you can look at each system from different angles. "The whole" of a system is the most useful for the viewer of the system. It is the answer to the main question the viewer poses to the system. Therefore "the whole" of a system depends on the observer.


If we put all the parts of a car in a box, then we have the sum of its parts. If we assemble all of these parts, we have a functional unit (the car) as "the whole".
The main question to the system is here: "Can I use it as means of transport?" As means of transport the parts in the box are useless.


Here are some examples for "the whole":

"The whole" as knowledge/conclusion: The "whole" is the conclusion which is drawn from the examination of a system. The police analyze a crime because they want to know the offender. Another police department analyses the same crime from a different angle because they want to know how such crimes can be prevented.

"The Whole" as a function: A customer says to a product developer: "Please develop me a product with these main functions."

"The whole" as a key message: Every text has a key message (Literature often has a moral.)

"The whole" as the main characteristic: Two people talk about a car. The first says, "This is a nice car." The other says, "This car uses a lot of gas." They look at the car from different angles.

"The wole" as the main rule: You organize a meeting. The last meeting was very controversial. For the coming meeting you set the rule: everyone respects the other's point of view.

"The whole" as an idea: A scientist sees that many people have the same problem. He has an idea to solve this problem and starts a research project.


How to analyze and set goals?

A goal is a desired future result, which is precisely determined in terms of content, time and scope.


... to be continued



How to solve the climate change problem?

LEARN-STUDY-WORK is not a political website. Therefore this is just an example how to apply the first and the second step of the problems solving process shown in the image above.


First step: Analyse the unsatisfactory situation, the obstacle and the goal. Think of several solutions to overcome the obstacle.


The climate of our world changes. This is an unsatisfactory situation because as a result glaciers and sea ice melt, the sea level rises, more flooding and droughts occur, hurricanes and other storms become stronger, species become extinct and some diseases can spread due to migration.


The goal is to stop the climate change by reducing the amount of CO2 and other greenhouse gases in the atmosphere.


Unfortunately this is not easy to do because there are two obstacles:

1. To stop the climate change, many people would have to change their lifestyles considerably but not enough people agree.

2. To stop the climate change without changing the lifestyle would cost a huge amount of money but not enough countries are able or agree to invest this amount of money.


Second step: After the analysis of the situation, the obstacles and the goal I list all conceivable strategies (a strategie is a long-term plan):


How to solve the climate change problem? -


*) "Use economic power" means buying green products and services and investing in "green" business.


Everyone must decide for himself which of these alternative strategies is effective and is in line with his values.