The singularities occurring in any sort of ordering are known in physics as defects. In an organized fluid defects may occur both at microscopic (molecular) and at macroscopic scales when hydrodynamic ordered structures are developed. Such a fluid system serves as a model for the study of the evolution towards a strong disorder (chaos) and it is found that the singularities play an important role in the nature of the chaos. Moreover both types of defects become coupled at the onset of turbulence. Besides this specificity, the results can be generalized to any structured physical system. They tend to demonstrate that the full knowledge of the system is "contained inside the surroundings of the singularity". It is also shown that such defects play a crucial role in all types of transitions between homogeneously ordered states from the rest state up to chaos.