Human beings, since the most remote times, have sought methods to anchor their perennial existence in posterity, to somehow, in one form or another, reach eternity. The forms of manifestation were very varied, and art or science stood out among the most highlighted throughout history. Of course, approaches were not limited to these forms and the means of manifestation had both positive and negative connotations.

Through these forays into the outer and inner world of human existence, successful efforts have spread over time and endured for eternity.

In the theory of dynamical systems, the analysis of the unboundedness of a function is used to determine the state of stability or instability. So any system that evolves naturally or artificially towards infinity, without interfering in any way, becomes uncontrollable, and the results, most of the time, are undesirable.

Examples are countless in all scientific directions, in quantum physics a fission reaction of an atom carried to infinity turns into a nuclear explosion, in geography the extreme interaction of tectonic plates and the exorbitant pressure of terrestrial magma leads to earthquakes and devastating volcanic eruptions, in chemistry a combustion process with high reaction rates becomes detonating, in biology a virus that replicates to infinity leads to the destruction of the organism infected, in the economy the unlimited development of a participant on the capital market pushes the financial market towards a monopoly zone and implicitly the blocking of free competitive mechanisms, in sociology the acute turmoil of people can trigger street conflicts that due to lack of reason escalate and turn into civil or even military wars, in IT technology the mechanisms of closed loop replication of information units saturate and block the storage or processing support, and in the algorithmic form the more complex information, represented by artificial intelligence, the evolution towards infinity of performances and intelligent autonomous systems may escape at a given moment from the ability to maintain the evolutionary step in relation to the human species and not only, and the results may not be exactly what was expected. But to the same extent, many of the current bands and trends led to infinity represent a form of society's development.

Therefore, if such a transformation towards infinity is produced for the benefit of humanity, the human and animal ecosystem, with all intrinsic and extrinsic aspects, desired results can also be produced.

Every longing, tendency, aspiration from the boundless distance, in any direction of inquiry, brings to man the desire for self-transcendence, but if it is unchecked and maliciously directed it will finally materialize in one form or another of destruction.

In order to investigate the various forms of manifestation of evolution towards infinity, in various scientific fields, I invite the reader to discover the approaches on this topic of each co-author in this book.

Mihai Alexandru Barbelian