The Digitality of Digital Transformation

The chapter contains an extended definition of the concept of transformation, the starting point of which is a description of the meaning of the words that make up this concept: transformation and digitization. This analysis follows two paths. First of all, it shows its unknown and deep mathematical background. The history of the idea of number, beginning around the fourth century BC, leads to an extremely turbulent period in mathematics at the turn of the nineteenth and twentieth centuries, from which the idea of a machine emerged, which was a conceptual model for the computer, i.e. the Turing machine. During this period, very basic questions about number and mathematics were asked, and novel approaches were proposed, like Peano and Hilbert, that liberated mathematics and its sister, geometry, from the obligation to represent reality. They became purely speculative and probably therefore extremely rich fields of thought that led to philosophical questions. Such questions about ontology of mathematical entities like number were asked, for example, by Alain Badiou. This part is complemented and developed by a description of the contemporary digitization process as a key element of digital transformation into social reality. This process concerns both economic phenomena and deeper anthropological processes, described i.a. by Luciano Floridi.