Integral Biomathics

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:

Enable the use of information from different areas of discourse to examine how low level processes “percolate up” and relate to higher levels, and how human scale behavioural processes may enable 1st and 3rd person comparative relations.
Define concrete approaches to discrete computational methodologies (functioning at different scales) to capture change over time from a series of different multi-modal observational perspectives. Define systems that can also present coherent integrated high level processes that relate to the lower level processes. This is about an integration of the computational aspect and its material underpinning.

As a first step towards realizing this goal is a follow-up project of the INBIOSA initiative that will devise a research framework combining object-level mechanisms with Turing oracles (Chaitin, 2011). This is going to be a step stone towards a “unified theory” of living systems, both “natural” and “artificial” ones. Therefore, our longer-range objective will be to step-wise replace the oracles by a more general theory of life. Our approach is mathematics-based and biology-driven.

Integral Biomathics can be regarded as a new branch of Theoretical Biology. We 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.

Life and mind have been escaping all effective complete theories to this moment. Therefore, we require that Integral Biomathics be an incomplete theoretical and computational framework. It uses oracle machines, but it remains always incomplete and extendible. Without (halting) oracles, theories can only be "more incomplete". With (halting) oracles we obtain a research program hyper-computer or super-Turing machine (Siegelmann, 1995).

Current theories about life do not use oracle machines to model living systems in their full complexity. By involving oracles in our Integral Biomathics research framework we create a methodology, which leads us stepwise closer to reality.

References

Chaitin, G. J. 2011. Life as Evolving Software. http://vixra.org/pdf/1202.0076v1.pdf.

Ehresmann, A. C., Vanbremeersch, J.-P. 2007. Memory Evolutive Systems: Hierarchy, Emergence, Cognition. Elsevier Science. ISBN-10: 0444522441; ISBN-13: 978-0444522443.

Siegelmann, H. 1995. Computation Beyond the Turing Limit. Science 268 (5210): 545–548.

Simeonov, P. L., Rosen, S. M., Gare, A. (Eds.) 2015. Life Sciences, Mathematics and Phenomenological Philosophy. Special Theme Issue on Integral Biomathics. Journal Progress of Biophysics and Molecular Biology. (in preparation; CFP: http://ibiomath.org/2015-cfp/) Elsevier. ISSN: 0079-6107.

Simeonov, P. L., Gomez-Ramirez, J., Siregar, P. 2013a. On Some Recent Insights in Integral Biomathics. J. Progress in Biophysics and Molecular Biology. Vol. 113, Issue 1 (Sept. 2013). Special Theme Issue on Integral Biomathics: Can Biology Create a Profoundly New Mathematics and Computation? Elsevier. ISSN: 0079-6107. DOI: 10.1016/j.pbiomolbio.2013.06.001. (also in http://arxiv.org/abs/1306.2843. 216-228.)

Simeonov, P. L., Matsuno, K., Root-Bernstein, R. S. (Eds.) 2013b. Can Biology Create a Profoundly New Mathematics and Computation? Special Theme Issue on Integral Biomathics. Journal Progress of Biophysics and Molecular Biology. Vol. 113, Issue 1 (September 2013). Elsevier. ISSN: 0079-6107.

Simeonov, P. L., Brezina, E., Cottam, Ehresmann, A. C., Gare, A., Goranson, T., Gomez-Ramirez, J., Josephson, B. D., Marchal, B., Matsuno, K., Root-Bernstein, R. S., Rössler, O. E., Salthe, Schroeder, M., S. N., Seaman, Siregar, P., B., Smith, L. S. 2012a. Stepping Beyond the Newtonian Paradigm in Biology. Towards an Integrable Computational Model of Life: Accelerating Discovery in the Biological Foundations of Science. INBIOSA White Paper. In: Integral Biomathics: Tracing the Road to Reality, Proc. of iBioMath 2011, Paris and ACIB '11, Stirling UK, P. L. Simeonov, L. S. Smith, A. C. Ehresmann (Eds.), Springer-Verlag, Heidelberg, ISBN-10: 3642281109; ISBN-13: 978-3642281105. http://www.inbiosa.eu (download INBIOSA White Paper)

Simeonov, P. L., Smith, L., S., Ehresmann, A. C. (Eds.), 2012b. Integral Biomathics: Tracing the Road to Reality, Proceedings of iBioMath 2011, Paris and ACIB '11, Stirling UK. Springer-Verlag, Heidelberg. ISBN-10: 3642281109; ISBN-13: 978-3642281105. OCLC WorldCat Number: 800365119.

Simeonov, P. L. 2010a. Integral Biomathics: A New Era of Biological Computation. Part I. CONTRIBUTIONS to the online FET FLAGSHIP CONSULTATION. Status 30. April 2010. Future and Emerging Technologies Unit. 100-105. http://cordis.europa.eu/fp7/ict/fet-proactive/docs/flagshipcons09-01_en.pdf.

Simeonov, P. L. 2010b. Integral Biomathics: A Post-Newtonian View into the Logos of Bio. J. Progress in Biophysics and Molecular Biology, Elsevier, ISSN: 0079-6107, Vol. 102, Issues 2/3, June/July 2010, 85-121. Available online: 8 February 2010. DOI: 10.1016/j.pbiomolbio.2010.01.005. http://dx.doi.org/10.1016/j.pbiomolbio.2010.01.005. also in: arXiv.org, http://arxiv.org/abs/cs.NE/0703002.

Simeonov, P. L. 2002. The Wandering Logic Intelligence, A Hyperactive Approach to Network Evolution and Its Application to Adaptive Mobile Multimedia Communications, Dissertation, Technische Universität Ilmenau, Faculty for Computer Science and Automation, Dec. 2002. Die Deutsche Bibliothek, urn:nbn:de:gbv:ilm1-2002000030. http://d-nb.info/974936766/34.

Turing, A. 1939. Systems of Logic based on Ordinals. Proc. London Math. Soc. Ser. 2, Vol. 45. 158-226. http://www.turingarchive.org/browse.php/B/15.