# 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.

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.

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.