Hermeneutics and metaphorics of numbers

The book is devoted to the genesis of the contemporary understanding of the concept of number, which is multifaceted. The axis is the progression from natural numbers to quaternions and octonions, which is structured as a concatenation of hermeneutic cycles both within mathematics and between mathematics and physics. Natural and rational numbers are closely related to our being in the world, they are more or less part of our natural world. It is different with negative, irrational and complex (imaginary) numbers. These were created in a formal way out of the internal needs of mathematics, often against the will and with the resistance of the mathematicians themselves. However, only with negative and irrational numbers was it possible to build differential and integral calculus. The theory of differential equations then enabled the formulation of universally valid physical laws from Newtonian dynamics through thermodynamics, electromagnetic field theory to relativity theory and quantum mechanics. Complex numbers play a fundamental role in it, entering directly into its foundations - and it was mathematical formalism that motivated the introduction of the imaginary unit into the Schrödinger equation, the dynamic principle of the microworld. In addition to this main line, attention is paid to three important modifications of the concept of number: from natural numbers to transfinite numbers, ordinal and cardinal numbers, from rational numbers to algebraic and algorithmic numbers and finally from "ordinary" numbers to non-standard numbers.