Integral Biomathics (Simeonov, 2010a/b, Simeonov et al., 2012a/b, Simeonov et al., 2013a/b, Simeonov et al., 2015) is a cross-disciplinary approach, involving both internalist and externalist mathematical biology and biological mathematics based on advanced biocomputation, such as e.g. the Wandering Logic Intelligence (Simeonov, 2002) and Memory Evolutive Systems (Ehresmann & Vanbremeersch, 2007), an evolutionary dynamic category theory, aimed at integrating Turing oracle machines (Turing, 1939) and related mathematical and computational theories and abstractions, as well as heuristics and a broad range of simulation, visualization and other creative support techniques capable of dealing with phenomena and data that cannot be handled by formalisms only. It allows interrogation marks/interfaces between its constituents and builds bridges to other disciplines.
The operative framework of Integral Biomathics is defined as a multi-perspective approach to knowledge production: observation of new phenomena / incorporation of new forms of entailment generating- technology (e.g. scanning methodologies) as well as modeling approaches → articulate convergent theoretical synthesis across divergent fields → integrate multiple mathematical formalisms under one relational umbrella → develop integrated mathematical models accounting for multi-scale structures and multi-temporal dynamics → study the dynamic relation between emergent phenomena and predictive phenomena → justify initial theoretical approaches via computational modeling → develop empirical demonstration and verification → articulate a falsifiable theoretical foundation for practical applications.
This gives us a panoramic view of the system with all its structures, dynamics and functionality:
Integral Biomathics can be regarded as a new branch of Theoretical Biology. Its aim to devise a research program with the following foci:
- development of a theoretical and computational framework that incorporates both oracles and mechanisms whereby real-life complexity can be captured to an extent that other contemporary approaches (e.g. systems biology) do not;
- stepwise elimination of oracles by the generalizing the theory (or theories) underlying the framework; i.e. the oracles will gradually be replaced by statements/models that lie within the mathematical and computational theories being generalized;
- clear definition of milestones that include the following:
- conceptualization and elaboration of the computational framework that includes, but also separates meta-level oracles from mechanisms;
- construction of experimental and validation protocols to verify the legitimacy of the oracles (or classes thereof) and their interactions with the modeled mechanisms;
- search of statements/models within existing theories that will eventually replace a subset (if not all) of the oracles;
- discover/unveil new/neglected theories in an attempt to obtain a single “unified theory”.
- physical or hardware implementations of oracles.