# The World is Small

I start to read the “The Physical Basis of The Direction of Time” by Dieter H. Zeh the 5th edition (!) because I am always more interested by this strange paradox of reversibility: the physics law must be reversible on time , must be symmetric on time .

This physic axiom can not be underestimated in the computer science if this reversibility is true how can inverse problems exist ?

Reversibility in computer science means that for each state St we have a different state St+1 and we have a different state St-1 .

This is a very strong assumption that remove exponential problems I am not sure about that but it seem to me that this reversibility do not allow “inverse problems” and all apparently existing “inverse problems” are only a theoretical construction , they exist because we don’t know enough about the state of the system.

For a practical example we have to sum all value of a list of integer numbers we know that we can have the same result for a lot of different list of elements and this is the reason for the difficulty of its inverse problem ,  given a sum find the lists of values . By the reversibility of physic law we know that this is not an existing problem .

How can we solve the paradox ? A possible explanation is that we have to watch a greater context to see a simple solution for the problem , when we identify an inverse problem probably we are watching in a too small context , a too small state and such state is not uniquely reversible but watching a wide state it become directly reversible .

I don’t know if the world is really reversible and how much is reversible ( what is the minimum size of states at we found reversibility ) but this seem another sign in the direction of small world , the world seem very smaller than combinatorial theoretical possibilities .

In this table I want to summarize the characteristics that limits the world

• Deterministic ( relation cause-effect )
• Discrete
• Finite
• Reversible ( relation cause-effect and effect-cause! )

This is important becouse we need to limit the space where to search a solution for a problem all this characteristics let to limit this research .