What are real-world problems?

Important features -- complexity and openness

Real-world problems are problems that reflect the nature of real-world systems. Real-world systems are complex and open to other real-world systems. The complexity and the openness of the real world systems are explained here.

Complexity of real-world problems

We believe the most important meaning of complexity is undividability, or irreducibility. If a real-world systems is divided into isolated subsystems, the summation of the functions of these subsystems are quite different from the original undivided system as Bertalanffy pointed out.

Non-modularity as discrete complexity

In the case of systems that are modeled by discrete mathematics, dividability means modularity. Thus, real-world discrete systems are not very modular. Even a human-made systems, such as a banking system, seems to be very modular, the functions of the subsystems deeply depend each other, and they cannot be thus isolated easily.

Nonlinearity as continuous compleity

In the case of systems that are modeled by continuous mathematics, dividability means linearity. Thus, Real-world continuous systems are nonlinear. Nonlinear systems cannot be designed by adding subsystems.

Openness of real-world problems

Real-world systems are open to other real-world systems. For example, a banking system is open to human society, which is another real-world system. Human cannot know every thing about every system. Thus, unexpected phenomena can always occur in any real-world system because it is open to and affected by unknown systems. Thus, complete and global infomation is usually impossible to obtain in real-world problem solving. This fact is called ``partiallity of information'' by Hasida.

Y. Kanada (yasusi @ kanadas.com)
Created: 11/21/95, Modified: 5/6/2002.