Information Drives Chance to Order and Organization: Applications to Mathematics, Physics and Biology

Starting from a previous paper, here improved, we show, by didactical examples, how algorithmic information (coded e.g., into a computer program) is required to build the structure of an organized system (either simple or complex). Ordered structures can be obtained as attractors both by some dynamics starting from sequential initial conditions (order from order) and by some dynamics starting from random initial conditions (order from chance) provided that a leading algorithmic information is assigned to govern the evolution of the generating process. In absence of information emergence of some ordered structure, like e.g., an organ of a living system is so highly improbable to be impossible in practice. We start from didactical examples, arising in mathematics and physics, to arrive to propose static models of a human heart. Systems are generated starting either from ordered initial conditions, or from random sparse initial conditions, or more realistically by random cellular automata (so that any mother cell is allowed to generate a daughter cell only in a random contiguous location). Significantly, as it was pointed out by Gregory Chaitin, not all algorithmic information can be compressed into a string shorter than the sequence of its original individual code digits (incompressible information string). A question is still open about the DNA and, more generally, any biological information: is it to be considered as a compressible or an incompressible code string? In our example of anatomic human heart model we have treated the sequence of the co-ordinates of each sphere (roughly modeling a cell) as an uncompressed string, while a compressed program string seems to be able to provide only less realistic models.