Subscribe to RSS
Homeopathic effect: a network perspective
Received08 June 2001
revised06 August 2001
accepted15 October 2001
27 December 2017 (online)
There are two aspects to the problem of describing the homeopathic effect in physical terms: the nature of the therapeutic agent, and the system on which it acts. The latter can be considered as a network, which provides a conceptual framework that throws new light on long-standing questions, based on generic results such as the enhanced susceptibility of networks near critical states. It suggests a characterisation of health and disease in terms of distance from a critical state. The Internet provides a concrete analogy. This predicts a limiting condition on the acceptable loss of highly connected nodes in the system, and suggests a procedure to measure its connectivity and related parameters.
- 1 Endler PC, Schulte J. Ultra High Dilution: Physiology and Physics. Dordrecht: Kluwer Academic Publishers; 1994. p. 99–171.
- 2 Torres J-L, Ruiz G. Stochastic resonance and the homeopathic effect. Br Hom J 1996; 85: 134-140.
- 3 Stevens PS. Patterns in Nature. Boston: Little, Brown and Company; 1974.
- 4 Reichl LE. A Modern Course in Statistical Physics. Austin: University of Texas Press; 1980.
- 5 Binder K, Young AP. Spin glasses: experimental facts, theoretical concepts, and open questions. Rev Mod Phys 1986; 58: 801-976.
- 6 McCulloch WS, Pitts W. A logical calculus of ideas immanent in nervous activity. Bull Math Biophys 1943; 5: 115-133.
- 7 Hertz J, Anders K, Palmer RG. Introduction to the Theory of Neural Computation. Redwood City: Addison-Wesley; 1991.
- 8 Kauffman SA. Metabolic stability and epigenesis in randomly constructed genetic nets. J Theor Biol 1969; 22: 437-467.
- 9 Kauffman SA. The Origins of Order. Oxford: Oxford University Press; 1993.
- 10 Rodriguez-Iturbe I, Rinaldo A. Fractal River Basins. Cambridge: Cambridge University Press; 1997.
- 11 West GB, Brown JH, Enquist BJ. A general model for the origin of allometric scaling laws in biology. Science 1997; 276: 122-126.
- 12 Hopfield JJ. Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci USA 1982; 79: 2554-2558.
- 13 Varela FJ, Coutinho A. Second generation immune networks. Immunol Today 1991; 12: 159-166.
- 14 May RM. Will a large complex system be stable?. Nature 1972; 238: 413-414.
- 15 Strogatz SH. Exploring complex networks. Nature 2001; 410: 268-276.
- 16 Albert R, Jeong H, Bararasi A-L. Error and attack tolerance of complex networks. Nature 2000; 406: 378-382.
- 17 Huang K. Statistical Mechanics. New York: John Wiley and Sons; 1987.
- 18 Callen HB. Thermodynamics. New York: John Wiley and Sons; 1960.
- 19 Dodds PS, Rothman DH, Weitz JS. Re-examination of the ‘3/4-law’ of Metabolism. J Theor Biol 2001; 209: 9-27.
- 20 Torres J-L. Biological power laws and Darwin's principle. J Theor Biol 2001; 209: 223-232.
- 21 Bak P, Tang C, Wiesenfeld K. Self-organized criticality. Phys Rev A 1988; 38: 364-374.
- 22 Cohen R, Erez K, ben-Avraham D, Havlin S. Resilience of the Internet to random breakdowns. Phys Rev Lett 2000; 85: 4626-4628.
- 23 Callaway DS, Newman M EJ, Strogatz SH, Watts DJ. Network robustness and fragility: percolation on random graphs. Phys Rev Lett 2000; 85: 5468-5471.
- 24 Torres J-L. Natural selection and thermodynamic optimality. Il Nuovo Cimento D 1991; 13: 177-185.
- 25 Nicholls JG, Martin AR, Wallace BG. From Neurones to Brain. Sunderland: Sinauer Associates, Inc; 1992. p. 181–182.
- 26 Kandel ER, Schwartz JH, Jessell TM. Principles of Neural Science. Norwalk: Appleton & Lange; 1991.
- 27 Alberts B, Bray D, Lewis J, Raff M, Roberts K, Watson JD. Molecular Biology of the Cell. New York: Garland Publishing, Inc; 1994.
- 28 Cheung VG, Morley M, Aguilar F, Massimi A, Kucherlapati R, Childs G. Making and reading microarrays. Nat Genet Suppl 1999; 21: 15-19.
- 29 Jeong H, Tombor B, Albert R, Oltval ZN, Barabasi A-L. The large-scale organization of metabolic networks. Nature 2000; 407: 651-654.
- 30 Ruiter PC, Neutel A-M, Moore JC. Energetic, patterns of interaction strengths, and stability in real ecosystems. Science 1995; 269: 1257-1260.
- 31 Mills LS, Soulé ME, Doak DF. The keystone-species concept in ecology and conservation. BioScience 1993; 43: 219-224.