Skip to main content
Log in

Lyapunov Stability as a Metric for Meaning in Biological Systems

  • Short communications
  • Published:
Biosemiotics Aims and scope Submit manuscript

Abstract

The physical and relational structure of the biologic continuum (both internal and external to the organism) creates the information signature that is the basis for the origination of meaning in the living system. A meaning metric can be grounded in the significance of that information to the stability of the system during the process of adaptive reconciliation of divergences from the steady state condition. From this perspective, an information-theoretic formulation of the process for translating incident information into adaptive action is proposed that can be practically used in defining and quantifying the meaning of that information for the living system.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3

References

  • Abou Al-Ola, O. M., Fujimoto, K., & Yoshinaga, T. (2011). “Common Lyapunov function based on Kullback-Leibler divergence for a switched nonlinear system.“ Mathematical Problems in Engineering. Vol. 2011, ID 723509, 1–12. London, UK: Hindawi Publishing Corporation, https:doi:https://doi.org/10.1155/2011/723509

  • Amari, S., & Nagaoka, H. (1993). Methods of Information Geometry, Volume 191 of Translations of Mathematical Monographs. Oxford, England: Oxford University Press

    Google Scholar 

  • Astakhov, K. (2009). Chapter 6: Methods of Information Geometry in Computational System Biology (Consistency between Chemical and Biological Evolution). Biomedical Informatics. Methods in Molecular Biology No, 569, 115–127. doi:https://doi.org/10.1007/978-1-59745-524-4_6. Humana Press https:

    Article  Google Scholar 

  • Baez, J. C., & Pollard, B. S. (2016). Relative Entropy in Biological Systems. Entropy, 18(2), 46–52

    Article  Google Scholar 

  • Bateson, G. (1972). Steps to an Ecology of Mind. New York, New York: Ballantine Books

    Google Scholar 

  • Benish, W. A. (1999). Relative Entropy as a Measure of Diagnostic Information. Medical Decision Making No, 19, 202–206

    Article  CAS  Google Scholar 

  • Boden, G., Chen, X., & Stein, T. P. (2001). Gluconeogenesis in moderately and severely hyperglycemic patients with type 2 diabetes mellitus. Am J Physiol Endocrinol Metab 280:E23–E30,200.

  • Cafaro, C. (2008). The Information Geometry of Chaos. Riga. Latvia:VDM Verlag Dr. Mueller

  • Cárdenas-García, J. F. (2020). The Process of Info-Autopoiesis—The Source of all Information. Biosemiotics, 13, 199–221. https://doi.org/10.1007/s12304-020-09384-x

    Article  Google Scholar 

  • Caticha, A. (2015).Entropic Dynamics. Entropy17,6110–6128

    Google Scholar 

  • Chevalier, S., Burgess, S., Malloy, C., Gougeon, R., Marliss, Errol, & Morais, J. (2006). The Greater Contribution of Gluconeogenesis to Glucose Production in Obesity Is Related to Increased Whole-Body Protein Catabolism. Diabetes, 55, 675–681. https://doi.org/10.2337/diabetes.55.03.06.db05-1117

    Article  CAS  PubMed  Google Scholar 

  • Fisher, R. (1930). The Genetical Theory of Natural Selection. Oxford,UK: Clarendon Press

    Book  Google Scholar 

  • Friston, K. (2010). The free-energy principle: a unified brain theory? Nature Reviews Neuro, 11, 12738

    Google Scholar 

  • Gastaldelli, A., Baldi, S., Pettiti, M., Toschi, E., Camastra, S., Natali, A., Landau, B. R., & Ferrannini, E. (2000). Influence of obesity and type 2 diabetes on gluconeogenesis and glucose output in humans: a quantitative study. Diabetes 49:1367–1373.

  • Hall, J. E., Summers, R. L., Brands, M. W., Keen, K., & Alonso-Galacis, M. (1994). Resistance to metabolic actions of insulin and its role in hypertension. Am J of Hypertension, 7, 772–788

    Article  CAS  Google Scholar 

  • Harper, M. (2009a). The replicator equation as an inference dynamic. arXiv:0911.1763

  • Harper, M. (2009b). Information geometry and evolutionary game theory. arXiv:0911.1383

  • Jaynes, E. T., & Rosenkrantz, R. D. (Eds.). 1983 Papers on Probability, Statistics and Statistical Physics,Reidel Publishing Company, Dordrecht

  • Juarrero, A. (1999). Dynamics in Action: Intentional Behavior as a Complex System. Cambridge, MA: MIT Press

    Book  Google Scholar 

  • Karev, G. (2010). Replicator Equations and the Principle of Minimal Production of Information.Bulletin of Mathematical Biology.72:1124–42. https://doi.org/10.1007/s11538-009-9484-9

  • Kullback, S. (1968). Information Theory and Statistics. New York: Dover

    Google Scholar 

  • Lyapunov, A. 1892(1992). The General Problem of Stability of Motion. International Journal of Control No, 55(3), 531–773. Transl. Davaux, E., Fuller, A.T

  • Maturana, H. R., & Varela, F. J. (1991). Autopoiesis and Cognition: The Realization of the Living. New York, NY: Springer Science & Business Media

    Google Scholar 

  • MacKay, D. M. (1972). Information, Mechanism and Meaning. Cambridge, MA: MIT Press

    Google Scholar 

  • Menant, C. (2003). Information and meaning. Entropy, 2003, 5, 193–204

  • Newby, G. B. (2001). Cognitive space and information space. Journal of the American Society for Information Science and Technology No, 52, 12

    Google Scholar 

  • Peirce, C. S. (1931–1935). Collected Papers, Vol 1–6. Cambridge, MA:Harvard University Press

  • Rovelli, C. (2015). Relative information at the foundation of physics. In A. Aguirre, B Foster and, & Z. Merali (Eds.), “It from Bit or Bit from It? On Physics and information” (pp. 79–86). Springer

  • Rutkowski, L. (2010). Computational Intelligence. Methods and Techniques. New York, NY: Springer. ISBN 978-3-540-76287-4

  • Shannon, C. (1948). A Mathematical Theory of Communication. Bell System Tech J, 27, 379–423

    Article  Google Scholar 

  • Skarda, C. (1999). The Perceptual Form of Life” in Reclaiming Cognition”: The Primacy of Action, Intention, and Emotion”. Journal of Consciousness Studies, 6, 11–12

    Google Scholar 

  • Stonier, T. (1997). Information and Meaning: An Evolutionary Perspective. New York, NY: Springer Verlag

    Book  Google Scholar 

  • Summers, R. L. (2020). ; Experiences in the Biocontinuum: A New Foundation for Living Systems. Cambridge Scholars Publishing. Newcastle upon Tyne, UK, ISBN (10): 1-5275-5547-X, ISBN (13): 978-1-5275-5547-1

  • Summers, R. L. (2021). An Action Principle for Biological Systems. J Phys: Conf. Ser. 2090 012109

  • Summers, R. L. (2022). Quantifying the Meaning of Information in Living Systems. Academia Letters, Article 4874. https://doi.org/10.20935/AL4874. 1

  • Summers, R. L., Woodward, L. H., Sanders, D. Y., & Hall, J. E. (1996). Graphic analysis for the study of metabolic states. American Journal Of Physiology, 270(15), S81–S87

    CAS  PubMed  Google Scholar 

  • Summers, R. L., Montani, J. P., Coleman, T. G., & Hall, J. E. (1997). Theoretical analysis of the mechanisms of chronic hyperinsulinemia. Computers in Biology and Medicine, 27(3), 1–7

    Article  Google Scholar 

  • Summers, R. L., & Montani, J. P. (1989). Mathematical model of glucose homeostasis for the study of metabolic states. J Miss Acad of Sci, 34, 15–24

    Google Scholar 

  • Summers, R. L., Kevin Ward, K., Witten, T., Convertino, V., Ryan, K., Coleman, T. G., & Hester, R. L. (2009). Validation of a Computational Platform for the Analysis of the Physiologic Mechanisms of a Human Experimental Model of Hemorrhage. Resuscitation, 80, 1405–1410

    Article  PubMed  PubMed Central  Google Scholar 

  • Summers, R. L. (1998). Computer simulation studies and the scientific method. J Applied Animal Welfare Sci, 1(2), 119–131

    Article  CAS  Google Scholar 

  • Summers, R. L., Coleman, T. G., & Meck, J. V. (2008). Development of the digital astronaut program for the analysis of the mechanisms of physiologic adaptation to microgravity: Validation of the Cardiovascular Module. Acta Astronautica, 63, 758–762

    Article  Google Scholar 

  • Unger, R. H. (1971). Glucagon and the insulin:glucagon ratio in diabetes and other catabolic illnesses. Diabetes, 20, 834–838

    Article  CAS  PubMed  Google Scholar 

  • Volkenstein, M. V. (1994). Physical Approaches to Biological Evolution. Berlin, Heidelberg, Germany: Springer-Verlag

    Book  Google Scholar 

  • Wolpert, D. H., & Kolchinsky, A. (2016). Observers as systems that acquire information to stay out of equilibrium, in The physics of the observer Conference. Banff, 2016

  • Yalow, R. S., & Berson, S. A. (1960). Immunoassay of endogenous plasma insulin in man. J Clin Invest, 39(7), 1157–1175. doi:https://doi.org/10.1172/JCI104130

    Article  CAS  PubMed  PubMed Central  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Richard L. Summers.

Ethics declarations

Funding and/or Conflicts of interests/Competing interests

The work is unfunded and there are no conflicts of interest or competing interests to disclose.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Summers, R.L. Lyapunov Stability as a Metric for Meaning in Biological Systems. Biosemiotics 16, 153–166 (2023). https://doi.org/10.1007/s12304-022-09508-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12304-022-09508-5

Keywords

Navigation