Relativity, Uncertainty, Incompleteness and Undecidability

Carlos Castillo, a postdoc at the University of Pompeu Fabra presents the four principles of Relativity, Uncertainty, Incompleteness and Undecidability.

I am especially in:

Uncertainty
Measure implies interacting, and interacting implies a certain alteration. At our scale, that alteration does not matters, but when we go to the very small, this alteration is a very important part of the rules.

Incompleteness
Classical mathematical logic deductive system, and actually any logical system consistent and expressive enough, is not complete, has “holes” full of expressions that are not logically true nor false.

Undecidability
If we want to write a “perfect” program, that never hangs, then one way is to test it to try all different inputs, but this is often impractical as there are too many combinations; besides this, there is a deeper problem and that’s that even if a long time has passed, we can never know for certain if the program is still doing something useful or if it has “hung”.

A Blind Spot
These fundamental principles should not be taken as limitations to science, and they do not exclude the existence of an objective reality. They are rather limitations to some operations, such as making a measurement or working with formal logic, that have to be taken into account to understand natural phenomena. Uncertainty and undecidability govern our capacity of making predictions, while relativity and incompleteness are related to the fact that references are necessary, but prevent us from doing certain operations.