Results of the Limited Enthusiasm Model with Spiritual Life

In the Spiritual Life model, enthusiasts generate the spiritual life of the church, as well as make converts. In addition, the effectiveness of the enthusiasts in conversion improves with more spiritual life. The model captures the feedback loop: more life gives more growth and thus gives more life. The Spiritual Life model is an extension of the Limited Enthusiasm model.

The model is applied to the membership data for Welsh churches from 1902 to 1906 to show how a buildup of spiritual life in the churches prior to the 1904/5 revival tipped those churches into revival growth. Consequently, spiritual life decreased as the revival subsided, as there were insufficient enthusiasts to maintain it.

Data Fitting & Calibration

The total membership numbers in the Welsh churches are taken from Williams (1985) with estimates of the Anglican church, see Explanatory Notes on “Mathematical Modeling of Church Growth”, section 5.6. The combined membership is compared with the Spiritual Life model to give an optimum fit, figure 1. The numbers on the horizontal axis refer to the END of each year, following the method of data collection.

Figure 1

Figure 1 shows the churches growing slowly from 1902 through most of 1904. After that year, the effects of the revival on membership accelerated, giving a massive increase by the end of 1905. Subsequently, there was a moderate fall. The data fit is achieved with a natural reproduction potential of 1.915 enthusiasts per enthusiast and a duration enthusiastic of around 1 week. This short timescale may be because many revival meetings were on consecutive nights. Thus, the influence of a revived Christian might have fallen once they went into a second week. The enthusiastic period can also appear artificially short as the “week of enthusiasm” may be spread over many weeks of nonconsecutive periods.

The natural reproduction potential is insufficient for revival growth. Instead, the actual reproduction of enthusiasts is influenced by a rise in the spiritual life of the churches, allowing it to rise above the natural level. That is, church growth is like a disease with increasing infectiousness. The effect of spiritual life on conversion was 1.176, the maximum number of extra converts per enthusiast possible. The effect of church enthusiasts on spiritual life was 7.54, the maximum fractional increase in spiritual life possible per year. Spiritual life would decay at a rate of 70% a year if there were no attempts to maintain it.

Revival and Spiritual Life

The church’s growth is driven by enthusiasts who make converts, some of whom also become enthusiasts. The reviving work of the Holy Spirit is passed on from person to person as they are converted. The simulation shows that during 1902, the number of enthusiasts in the church fell, as shown in Figure 2. However, the level of spiritual life of the enthusiasts was increasing. This increase reflects the renewing work of the Holy Spirit in the increasing number of prayer meetings. These meetings were for the specific purpose of seeking a deeper life. Spiritual life rose steadily from 1902-4 and ultimately enhanced the ability of enthusiasts to make converts. Hence, the rise in enthusiasts.

Figure 2

Halfway through 1904, the number of enthusiasts explodes, figure 2. The result was a rapid increase in the church due to conversion in 1905, figure 1. Note the rise in spiritual life precedes the rise in enthusiasts, which in turn precedes the growth of the church. Revivals start with an increase in the work of the Holy Spirit and its effect on existing believers and the church.

Revival and Church Growth

The enthusiasts peaked halfway through 1905, well before the church peaked in early 1906, figure 2. However, spiritual life kept growing until late in 1905. The peak in spiritual life is a good marker of the end of the revival, as most of the growth in the church has taken place, figure 3. After this point, the life in the church, and thus the effectiveness of individual enthusiasts, starts to fall quite significantly. By 1906, there were no enthusiasts left, figure 2. Although many people still felt the effects of the revival, their enthusiasm was no longer channelled into making converts. Maybe they had lost influential contacts with unbelievers.

Figure 3

A significant level of spiritual life remains well after the growth phase of the revival. Post-revival churches are undoubtedly much livelier, with more works of the Holy Spirit taking place than in the beginning. These are spiritual churches but with few conversions. Thus, the continuing presence of spiritual life is not a predictor that a revival is coming to an end. By the time spiritual life falls, it is too late. The early predictor for the end of revival is the number of enthusiasts, not the liveliness of the church. Revival growth could be extended by ensuring revived Christians and new converts are committed to evangelism and witness.

Revival Threshold

At the end of 1902, the reproduction potential of the enthusiasts was still below the threshold for revival growth, indicating the inadequate reproduction of enthusiasts to give revival growth, figure 4. However, early in 1903, the reproduction potential rose due to the effects of the increasing spiritual life in the churches. The enhanced enthusiasts are able to make sufficient enthusiasts to more than replace themselves. Thus giving the revival growth in the church.

Figure 4

Figure 4 shows the revival growth threshold (line 2) rising. It rises because the enthusiasts find it harder to find fresh unbelievers as their pool shrinks due to conversion. Halfway through 1905, the threshold rises above the reproduction potential. Thus, enthusiasts decrease, and church growth slows.

Conclusions

The original limited enthusiasm model did not explain Welsh Revival data when the simulation started in 1902. The reproduction potential was higher during the revival than before, a feature outside the scope of the original mode. Adding the variable spiritual life provides a mechanism for explaining why the reproduction potential increases in terms of the action of a small number of church members seeking and receiving more of the Holy Spirit. This extended model gives an excellent fit to the data over that period, figure 1.

One drawback is that a value for spiritual life of zero in 1902 is unrealistic. Clearly, there are model elements missing, such as enthusiasts making new enthusiasts out of existing church members. Such a further extension is possible, but the extra number of parameters may make data fitting complex. The results presented above are sufficient to drive home the importance of seeking the work of the Holy Spirit to help tip a church into revival.

This work was part of an M.Phil project pursued by L. Howells at the University of South Wales, thesis Dynamics of Church Growth and Spiritual Life, 2015.