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Mathematical Principles: Tales of Tails

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Handbook of Systems and Complexity in Health

Abstract

A mathematical principle is an overarching statement of what will always occur given a prescribed set of circumstances. Such principles are very useful because they can guide us in making decisions about the real-world even though their basis can be quite abstract. For example, in physics, we have the second law of thermodynamics, which is a phenomenological generalization of vast amounts of experimental data. The empirical law is that heat flows from hotter regions to colder regions, but the implied physical principle is that the universe is slowing down and the total entropy of the universe is increasing. The mathematical principle associated with the second law governs how entropy changes under specified conditions. The good news is I will not talk further about the second law, but I thought it essential that you realize at the outset that we will discuss the connection between data, the patterns we identify within data and the theories we construct to understand those patterns, all of which form our view of the world and how the world responds to our interventions.

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References

  1. Gauss CF. Theoria motus corporum coelestrium [Theory of motion of heavenly bodies moving about the sun in conic sections, eng. trans]. New York/Hamburg: Dover; 1809.

    Google Scholar 

  2. Adrian R. Research concerning the probabilities of the errors which happen in making observations, etc. The Analyst; or Mathematical Museum. 1809;1:93–109.

    Google Scholar 

  3. Laplace PS. Analytic theory of probabilities. Paris: Imprimerie Royale; 1810.

    Google Scholar 

  4. Poincare H. The foundations of science. New York: The Science Press; 1913.

    Google Scholar 

  5. Norwich KW. Le Chatelier’s principle in sensation and perception: fractal-like enfolding at different scales. Front Physiol. 2010;1:17.

    Article  PubMed  Google Scholar 

  6. West BJ. The wisdom of the body; a contemporary view. Front Physiol. 2010;1:1.

    PubMed  Google Scholar 

  7. Galton F. The geometric mean in vital and social statistics. Proc R Soc Lond. 1879;29:365.

    Article  Google Scholar 

  8. West BJ. The lure of modern science; fractal thinking. Singapore: World Scientific; 1995.

    Google Scholar 

  9. Pareto V. Cours d’economie politique. Lausanne: Rouge; 1897.

    Google Scholar 

  10. West BJ. Why Six Sigma Health Care is oxymoronic in hospitals. In: Davidson A, editor. Nursing, caring and complexity science. Carlisle: Springer; 2011.

    Google Scholar 

  11. Gupta HM, Campanha JR, Chavorette FR. Power-law distribution in high school education: effect of economical, teaching and study conditions. arXir.0301523v1 (2003).

    Google Scholar 

  12. West BJ. Where medicine went wrong; rediscovering the path to complexity. Singapore: World Scientific; 2006.

    Google Scholar 

  13. Gould SJ. Full house. New York: Harmony Books; 1996.

    Google Scholar 

  14. Mandelbrot BB. Fractals, form, chance and dimension. San Francisco: W.H. Freeman and Co.; 1977.

    Google Scholar 

  15. Bassingthwaighte JB, Liebovitch LS, West BJ. Fractal physiology. New York: Oxford University Press; 1994.

    Google Scholar 

  16. Suki B, Alencar AM, Frey U, Ivanov PC, Buldyrev SV, Majumdar A, Stanley HE, Dawson CA, Krenz GS, Mishima M. Fluctuations, noise and scaling in the cardio-pulmonary system. Fluct Noise Lett. 2003;3: R1–25.

    Article  Google Scholar 

  17. Peng CK, Mistus J, Hausdorff JM, Havlin S, Stanley HE, Goldberger AL. Long-range anti-correlations and non-Gaussian behavior of the heartbeat. Phys Rev Lett. 1993;70:1343–6.

    Article  Google Scholar 

  18. Ivanov PC, Rosenblum MG, Peng C-K, Mietus J, Havlin S, Stanley HE, Goldberger AL. Scaling behavior of heartbeat intervals obtained by wavelet-based time-series analysis. Nature. 1996;383:323–7.

    Article  PubMed  CAS  Google Scholar 

  19. West BJ. Physiology in fractal dimension: error tolerance. Ann Biomed Eng. 1990;18:135–49.

    Article  PubMed  CAS  Google Scholar 

  20. West BJ, Griffin LA, Frederick HJ, Moon RE. The independently fractal nature of respiration and heart rate during exercise under normobaric and hyperbaric conditions. Respir Physiol Neurobiol. 2005;145:219–33.

    Article  PubMed  Google Scholar 

  21. Mutch WAC, Harm SH, Lefevre GH, Graham MR, Girling LG, Kowalski SE. Biologically variable ventilation increases arterial oxygenation over that seen with positive end-expiration pressure alone in a porcine model of acute respiratory distress syndrome. Crit Care Med. 2000;28:2457–64.

    Article  PubMed  CAS  Google Scholar 

  22. Altemeier WA, McKinney S, Glenny RW. Fractal nature of regional ventilation distribution. J Appl Physiol. 2000;88:1551–7.

    PubMed  CAS  Google Scholar 

  23. Peng C-K, Metus J, Li Y, Lee C, Hausdorff JM, Stanley HE, Goldberger AL, Lipsitz LA. Quantifying fractal dynamics of human respiration: age and gender effects. Ann Biomed Eng. 2002;30:683–92.

    Article  PubMed  CAS  Google Scholar 

  24. West BJ, Griffin L. Biodynamics: why the wirewalker doesn’t fall. New York: Wiley; 2004.

    Google Scholar 

  25. Goldberger AL, Rigney DR, West BJ. Chaos, fractals and physiology. Sci Am. 1990;262:42–9.

    Article  PubMed  CAS  Google Scholar 

  26. Mutch WAC, Lefevre GR. Health, ‘small-worlds’, fractals and complex networks: an emerging field. Med Sci Monit. 2003;9:MT19–23.

    PubMed  Google Scholar 

  27. Philippe P, Garcia MR, West BJ. Evidence of “essential uncertainty” in emergency ward length of stay. Fractals. 2004;12(2):197–209.

    Article  Google Scholar 

  28. Buchman TG. Physiologic failure: multiple organ dysfunction syndrome. In: Delsboeck TS, Kresh JY, editors. Complex systems science in biomedicine. Berlin: Springer; 2006.

    Google Scholar 

  29. Chauvet GA. Hierarchical functional organization of formal biological systems: a dynamical approach. I. The increase of complexity by self-association increases the domain of stability of a biological system. Phil Trans R Soc Lond B Biol Sci. 1993;339:425–44.

    Article  CAS  Google Scholar 

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Author information

Authors and Affiliations

  1. Army Research Office, 4300 S. Miami Blvd., Research Triangle Park, 27709, NC, USA

    Bruce J. West

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  1. Bruce J. West
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Correspondence to Bruce J. West .

Editor information

Editors and Affiliations

  1. , Department of General Practice, Monash University, PO Box 3010, Wamberal, 2260, New South Wales, Australia

    Joachim P. Sturmberg

  2. Northern Ontario School of Medicine, Merchandise Mart Plaza, Suite 1212 222, Chicago, 60654, Illinois, USA

    Carmel M. Martin

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West, B.J. (2013). Mathematical Principles: Tales of Tails. In: Sturmberg, J., Martin, C. (eds) Handbook of Systems and Complexity in Health. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4998-0_5

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  • DOI: https://doi.org/10.1007/978-1-4614-4998-0_5

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  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4614-4997-3

  • Online ISBN: 978-1-4614-4998-0

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