# 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.