Abstract
The paper shows meta-mathematical prerequisites for basic concepts of rigorous science called mathematics. These concepts explore a very simple idea concerning the hypothesis that all surrounding physical processes are basically algorithmic processes - as understandable as well as partially or fully incomprehensible ones. Mathematics is very successful in studying, formal describing and utilizing of such processes, because mathematics is based on similar algorithmic ideas, methods, and structures. These facts allow us to formulate more precisely useful mathematical (meta-scientific) concepts concerning some well-known scientific problems in various rigorous theories, including the theory of object calculus, the theory of automatic cognition, the theory of biological evolution, the theory of heterogeneous electronic systems, the theory of logics in various chemical transformations, the basic architecture of completely programmable universal (multi-purpose) synthesizers-analyzers for various objects, and so on.
Highlights
Idea to use fundamental algorithmic structures to explain the furniture of our world has a very long history - as well as Metaphysics itself
There were no notion of “algorithm” in that times, but we can see in Aristotle’s words an attempt to emphasize the importance of basic algorithmic operations such as synthesis (“combination”) and decomposition (“separation”) of various objects. In his ninth chapter of Metaphysics, Aristotle tried to connect these ideas with the notion of number
In spite of the seeming absurdity, this idea has some signs of truth, especially if we expand a central mathematical concept called “algorithm” to the wider set of objects including numbers and symbols, and real things
Summary
Idea to use fundamental algorithmic structures to explain the furniture of our world has a very long history - as well as Metaphysics itself. There were no notion of “algorithm” in that times, but we can see in Aristotle’s words an attempt to emphasize the importance of basic algorithmic operations such as synthesis (“combination”) and decomposition (“separation”) of various objects. In his ninth chapter of Metaphysics, Aristotle tried to connect these ideas with the notion of number. Explaining the essence of term “operation” she wrote: “...by the word operation, we mean any process which alters the mutual relation of two or more things, be this relation of what kind it may This is the most general definition, and would include all subjects in the universe. In spite of the seeming absurdity, this idea has some signs of truth, especially if we expand a central mathematical concept called “algorithm” to the wider set of objects including numbers and symbols, and real things
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