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1
Discrete Information and Life
Platonic Tetrahedron
Abstract. Information and life are intrinsically related and many challenges for
a deep understanding of life phenomena require analyzing the role of informa-
tion, and its specific mechanisms, in biological systems. In this chapter, the main
kinds of discrete informational structures will be informally presented in many bi-
ological contexts where they occur: sets, sequences, multisets, trees, and graphs,
which are mathematically defined and analyzed in the second part of the topic, are
here seen as fundamental mechanisms of aggregation and organization of biological
components.
1.1
Symbols and Molecules
A univocal and clear definition of information is almost impossible. Information,
as energy, matter, time, space, and life are such pervasive notions that any precise
characterization of them necessarily misses aspects which are crucial for any com-
prehensive understanding of their nature. For this reason, it is useful to start with
an informal idea to which we can anchor our initial intuition. We encounter in-
formation in data, which are physical objects, and can be transformed, stored, and
transmitted. But they are meaningful when seen as containers of some kind of “in-
formation”. This sounds clearly tautological, therefore, we need to add something
to avoid vacuity. Data, recognized by some “agents”, have the capability of direct-
ing and regulating their actions. In other words, they direct actions. When a flag
movement or a trumpet sound is executed, then soldiers attack the enemy. The more
complex are the actions, the more the information system regulating them has to be
 
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