Mathematics of Church Growth References

Papers and Books Using Mathematics and System Dynamics in Church Growth

• Acuua Moreno, N., Cuevas, R. C., Ospina, Y. C., & Valencia, J. P. (2001). Caleb: Microworld of the Christian Church's Membership Dynamics. Paper presented at the The 19th International Conference of the System Dynamics Society, Atlanta, Georgia. Uses system dynamics to model the growth of a specific denomination in Latin America. Organisational rather than diffusion.
• Anderson, Duane. Estimates of the future membership of the Church of Jesus Christ of Latter-day Saints. An attempt to fit church data to the logistic model - thus using the concept of carrying capacity and limited growth.
• Ausloos M. and Petroni F. (2010). On World Religion Adherence Distribution Evolution, appears in "Econophysics Approaches to Large-Scale Business Data and Financial Crisis: Proceedings of the Tokyo Tech-Hitotsubashi Interdiciplnary Conference + APFA7, eds. Takayasu M., Watanabe T. and Takayasu H., 289-312, Springer.
• Ausloos M.R., Vitanov N.K. and Dimitrova Z.I. (2011). Verhulst-Lotka-Volterra (VLV) model of ideological struggles, Arxiv preprint arXiv:1103.5362.
• Bullock J.L. (1999). The Parish Learning Laboratory: A Computer Based Simulation for Exploring the Long-Term Outcome of Policies and Planning. PhD. Thesis. Berkeley, California, Church Divinity School of the Pacific. Uses system dynamics to model the growth and finances of a parish .
• Gaynor A.K., Morrow J. & Georgiou S.N. (1991). Aging, contraction, and cohesion in a religious order: A policy analysis. System Dynamics Review, 7(1): 1-19. Systems dynamics model of a religious order. Organisational rather than diffusion.
• Howells L. (2010). The Dynamics of Religious Revival and Church Growth, 5th Research Student Workshop, University of Glamorgan, March 2010.
• Levy G. and Razin R. (2010). Religious Organizations, Fondazione Eni Enrico Mattei Working Papers. Model using game theory.
• Loomis R.D. Church Growth and the Latter Day Saints. Presented at The Association for the Sociology of Religion August 15-17, 2002 Chicago, IL . Uses statistical modelling to examine the future growth of the Mormon Church. Also see details.
• Mangeloja E. (2007). Preaching to the choir? Economic analysis of church growth. European Network on the Economics of Religion Online, paper 07/03, www.ener-online.org. [Accessed 01/03/2010]. Statistical model of church growth that supports growth through the activity of the most committed.
• Penrose L.S. (1952). On The Objective Study of Crowd Behaviour. This is the first reference found by this project that refers to the use of epistemology to explain the spread of religious behaviour. In addition there are applications to politics, fashion and panic reactions. More descriptive than mathematical however these is the demonstration of the famous Penrose Theorem that is the basis of the square root voting rule of organisations such as the UN. Lionel Penrose was the father of the famous relativist Roger Penrose.
• Ormerod P. & A.P. Roach (2004). The medieval inquisition: Scale-free networks and the suppression of heresy. Physica A 339: 645-652. Not church growth as such, but does model the spread of religious belief which would be an important part of a more sociological approach to church growth within a given social context.
• Schell M. (nd). Using computers to support total church growth. Chapter 18 of Church Growth - State of the Art by Peter Wagner. Although this is computer applications rather than mathematics Mel Schell produce what was an early attempt to model growing and successful churches. Much of these ideas would translate over into a system dynamics model.
• Shy O. (2005). Dynamic Models of Religious Conformity and Conversion: Theory and Calibration. Discussion paper, Social Science Research Centre, Berlin. SP II 2005 – 12. Uses economic modelling to explain changes in numbers of non-believers by differing both rates with believers, and differeing ratios of nonconformity in each group.
• Vitanov N.K., Z.I. Dimitrova & M. Ausloos (2009). A Model of ideological struggle, Arxiv preprint arXiv:0906.4962, arxiv.org. [Accessed 01/03/2010]. A differential equation model of ideological spread with competition, relevant to competing churches.
• Wieder T. (2011). A Simple differential equation system for the description of competition among religions, International Mathematical Forum, 6:35, 1713-1723.

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Papers Using Ideas From Physics to Model Church Growth

Statistical physics looks at how matter behaves in terms of how the individual atoms behave. By analogy a group of people can be understood statistically in terms of how the individuals behave. Although people are not atoms, many ideas from physics carry over.

• Ausloos M. & F. Petroni (2007). Statistical dynamics of religions and adherents. Europhysics Letters, 77: 38002-38006.
• Ausloos M. & F. Petroni (2009). Statistical dynamics of religion evolutions. Physica A: Statistical Mechanics and its Applications, 388(20): 4438-4444.
• Logan P.F. & Dye T.W. (1984). Physics for Anthropologists, Search, 15(1-2), 30-32. Modelling the growth of a church in a developing country using diffusion ideas from gas dynamics. Uses the logistic model and the concept of positive feedback.

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Papers Using Mathematics and System Dynamics in Other Social Diffusion

Mathematics and systems dynamics are used to model various forms of social diffusion. The methods and ideas can be relevant
to modelling church growth.

• Baggs I. & Freedman H.I. (1990). A mathematical model for the dynamics of interactions between a unilingual and a bilingual population: Persistence versus extinction., Journal of Mathematical Sociology, 16(1), 51-75. Uses a predator prey model to examine the spread of bilingualism.
• Wyburn J. & Hayward J. (2008). The Future of Bilingualism: An Application of the Baggs and Freedman Model , Journal of Mathematical Sociology 32(4) Pages: 267-284. An extension to the above using ideas similar to the church growth models.
• Burbeck S.L., Raine W.J. & Stark M.J. (1978). The Dynamics of Riot Growth: An Epidemiological Approach, Journal of Mathematical Sociology, 6, 1-22. Very similar modelling to the original church growth model Hayward (1999).
• Bettencourt L.M.A., Cintron-Arias A., Kaiser D.I., Castillo-Chavez C. (2006). The Power of a good idea: Quantitative modelling of the spread of ideas from epidemiological models, Physica A, 364, pp 513-536. Models the spread of a scientific idea in physics throughout the research community. The model has strong similarities to the long-term limited enthusiasm model of church growth in Hayward (2005).
• Sandell R. (2001). Organisational growth and ecological constraints: The growth of social movements in Sweden, 1881 to 1940. American Sociological Review 66: 672-693. Refers to the growth in the number of Christian congregations.

See also references on Social Diffusion