Complexity, Information and Biological Organisation

Regarding the widespread confusion about the concept and nature of complexity, information and biological organization, we look for some coordinated conceptual considerations corresponding to quantitative measures suitable to grasp the main characteristics of biological complexity. Quantitative measures of algorithmic complexity of supercomputers like Blue Gene/L are compared with the complexity of the brain. We show that both the computer and the brain have a more fundamental, dynamic complexity measure corresponding to the number of operations per second. Recent insights suggest that the origin of complexity may go back to simplicity at a deeper level, corresponding to algorithmic complexity. We point out that for physical systems Ashby's Law, Kahre's Law and causal closure of the physical exclude the generation of information, and since genetic information corresponds to instructions, we are faced with a controversy telling that the algorithmic complexity of physics is much lower than the instructions' complexity of the human DNA: I_algorithmic(physics) ~ 10^3 bit << I_instructions(DNA) ~ 10^9 bit. Analyzing the genetic complexity we obtain that actually the genetic information corresponds to a deeper than algorithmic level of complexity, putting an even greater emphasis to the information paradox. We show that the resolution of the fundamental information paradox may lie either in the chemical evolution of inheritance in abiogenesis, or in the existence of an autonomous biological principle allowing the production of information beyond physics.