Simple Electric Circuit

Simple Electric Circuit. Photo Credit Wikimedia Commons

Some people think that complex problems require simple solutions. This is very far from reality. Complex problems usually require complex solutions. This is the reason why complexity grows in a natural way in most systems. This can be analyzed understanding well the meaning of complexity. Complexity can be seen as the amount of the most probable states in a system. The higher the number of agents in a system is the higher the number of possible states is. And the higher the number of restrictions between agents, the lower the number of possible states. Complexity is then related to functionality.

I am going to show you this fact. A system with a single status variable has only a single degree of freedom. In a physical system its value can be determined by the interaction with the environment.

Imagine that you want to illuminate a room with an electric bulb connected to a power supply. The value of the energy dissipated would depend only on the voltage of the power supply and the resistance of the bulb.

If we want to illuminate two rooms, in that case, we will need and additional bulb. In this case, the energy dissipated depends on the connection of the devices too. The energy dissipated will depend on the disposition of the circuit (serial or parallel). In the parallel disposition the energy dissipated by every bulb will depend only on the voltage and the own resistance of the bulb, however, in the serial disposition the energy dissipated will depend on the other resistance too.

At this point, most of the readers will not find where the complexity of this problem is; because the problem can be easily solved connecting always the bulb in parallel. Yes, it is a solution, but it does not seem to be the solution of an engineer that usually work searching for efficiency. A power supply has a limit for the current that it can provide, if we begin to add rooms we could finally reach the maximum energy and the voltage could go down reducing the illumination level of all rooms. If we require that some rooms preserve the level of illumination we can connect some dependencies in a serial disposition in order to reduce the total current from the power supply without reduce the voltage in the main dependencies. Then, increasing complexity it is possible to preserve the level of the illumination on the main rooms reducing the total consumption of energy. As we have seen, in order to solve a more complex problem with limited resources we have used a more complex disposition.

Politicians usually say that austerity means to reduce retirement payments and healthcare services and public treasurers only are able to see the solution of increasing taxes (having a larger power supply); however, this is only a simple vision of a complex problem that requires a much more complex solution. Austerity can be made preserving retirement payments and healthcare services without increasing taxes, reducing the salary of some public officials that can be very high for the real value that they providing for the society in a certain time due to economic conditions, for instance, and other not critical expenses.

Why must complexity be managed? The reason is precisely the opposite one: Simple problems require simple solutions. In the previous example we have found that it is possible to preserve the illumination level in some rooms and reducing it in other ones. Imagine that you are the manager of a hotel, and you want that illumination conditions for the clients depend on what they are paying every month. It would not be a proper solution to rewire all the facility every month, it should be better to have lighting with variable resistance in every room and link the value of this resistance proportionally to the paid bill.

Politicians usually say to us that it is impossible to change fast the expenditure of the State. This can be true but it is only showing that the design of the State was done in complex way. A simpler solution could be that services were provided by private organizations that can be opened or closed in accordance with the requirements of the society and the environmental situation. Adaptability to temporal changes can be easily implemented in a not hazardous way when the permanent structure of the organization is not huge and rigid.

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