Feedback in a system that changes over time is the mechanism
where an action results in an effect, which then in turn influences the
original action. The action literally “feeds back” on itself.
Reinforcing Feedback
For example, if a population grows through births, the more
in the population, the more people are born, thus even more are added to the
population and it grows faster. This is a reinforcing feedback loop; the result
is exponential growth, that is growth
that speeds up [1].
Sometimes church leaders think that churches grow the same
way. The larger the church becomes, the more people are added to the church,
thus the church grows even faster, figure 1. People may be added through births
and through conversion. The rectangle “Church” is called a stock. It is an
accumulation of people. The pipe “add to church” is called a flow and
represents the addition of people in a fixed period of time. Figure 1 is an
example of a system dynamics model.
Fig 1. Reinforcing
feedback (R) applied to church growth
It is true that the early phase of a church’s growth is
often exponential. However, with a bit more thought, not everyone in a church
is engaged in the process of adding people to the church. Some are inactive in
church altogether. Others may be active in church life but may have never
brought anyone new to church. Others may have invited new people in the past
but are no longer doing so. For many of the churches I have studied I have
estimated that at any one time less than 5% of church members are active in
adding people to their church.
Enthusiasts
As an alternative to the hypothesis in figure 1, I have
proposed an alternative feedback hypothesis where only a subset of the church
actively adds people to the church [2]. I call these people enthusiasts, after
the nickname given to the Methodists in the 18th century – people
who were very active in evangelism. Figure 2 expresses this hypothesis as a
reinforcing feedback loop
Fig 2. Reinforcing
feedback (R1) and enthusiasts
Those from outside the church who are made enthusiasts are
also added to the church, and make more enthusiasts – the feedback effect. In
addition, enthusiasts convert others who, although added to the church, are not
enthusiasts themselves, converting no one. This latter mechanism has no
feedback loop. The feedback of figure 2 is weaker than that of figure 1,
however it is the mechanism seen in revival, evangelistic campaigns and courses
such as Alpha, and can result in considerable exponential growth in the church.
Balancing Feedback
Balancing feedback is the process where the effect of an
action attempts to restrain rather than reinforce the action. For example when a population is
declining through deaths, the more deaths, the less people in the population,
thus deaths are reduced. The result is the exponential
decay of the population, decline that
slows down [3].
Limited Enthusiasm
There is good evidence that enthusiasts do not remain so
indefinitely. Some run out of people to invite to church, others get taken up
with other aspects of church life and forget evangelism. John Wesley complained
that his converts went on to become much better people as a result of the Holy
Spirit in their lives, so good they became prosperous, and lost their zeal for
religion! This is often called Wesley’s law of the decline of pure religion [4],
and can be expressed as balancing feedback:
Fig 3. Balancing
feedback (B2) and enthusiasts
Limited Population Size
Of course converting people and making them enthusiasts does
not occur in a population of an unlimited supply of people. Populations are
finite and as people are made enthusiasts, this pool of unbelievers declines,
and it becomes harder to make enthusiasts. This is balancing feedback on
unbelievers:
Fig 4. Balancing
feedback (B3) and unbelievers
Because unbelievers become enthusiasts, then the effect of
the balancing feedback on unbelievers, slowing its decline, is mirrored in its equal and opposite effect on
enthusiasts, slowing their growth. Feedback loops exert forces on the
population, speeding them up or slowing them down, and this mirroring effect is
the equivalent of Newton’s third law of motion. Some readers may remember that
from high school physics.
Balance of Forces
It follows that the stock of enthusiasts is subject to three
forces from the three feedback loops. The action of the enthusiasts themselves,
R1, accelerates their growth; the
decline of unbelievers, B3, slows the
enthusiasts’ growth, turning growth to accelerating decline; the loss of enthusiasts,
B2, eventually slowing their decline
to zero, figure 5. Growth in enthusiast numbers eventually turns to decline
because the effect of the unbelievers reduces the production of enthusiasts to
a level below their losses.
Fig 5. The effects of
feedback on the growth and decline of enthusiasts (percentage of population)
The effect of enthusiasts’ activity is that the total
church, enthusiasts and inactive Christians, follows S-shaped growth, figure
6. The final level of the church
falls short of the total population. The enthusiasts have burnt out before they
reach all people, just under 40% of the population in this example, the result
of the three competing feedback loops.
Fig 6. Church growth
resulting from feedback (percentage of population)
Other Feedback Loops
Over time people leave the church and people die, both
balancing feedback. However new are born into the population, replenishing the
pool of potential converts, a reinforcing loop. Thus enthusiasts never quite go
to zero and a stable balance of church numbers is possible, despite losses and
deaths. Nevertheless if conversions are not sufficient, both enthusiasts and
church can head for extinction, the situation currently faced by many UK
denominations.
Second Order Feedback
This “limited enthusiasm” model described here works well
for a couple of generations, but over longer periods the effectiveness of
churches in conversion changes for other reasons, usually resulting from “second
order” loops.
All the feedback described above is “first order”, that is,
only one stock is involved in the loop, see figures 1-4. First order feedback means that its
effect on increasing or decreasing a population is immediate, and thus
relatively easy to follow. Not so for second order feedback, which involves two
stocks. Its effects are often delayed and counter intuitive.
To give an example of second order feedback, consider the case of loops R1, figure 2, and B3, figure 4, acting
together, figure 7. Although B3 is first
order on unbelievers as only one
stock is involved, figure 4, the combination is second order on enthusiasts, figure 7. As enthusiasts
increase, more people are taken from unbelievers, thus unbelievers falls, thus
less are made enthusiasts and their numbers eventually slow – a balancing
effect with two stocks. The result, with B2
(figure 3) added, is growth of enthusiasts changing to decline, figure 5, a
type of behaviour that cannot occur in a stock that only has first order
feedback.
Fig 7. Combining
feedback loops B3 and R1 is a “second order” effect.
Jay Forrester, the founder of system dynamics, suggested
that our “life and mental processes have been conditioned almost exclusively by
first order negative feedback loops” [5].
By contrast second order feedback takes us by surprise and we tend not
to respond to it effectively. This is so true for church growth and decline –
but that is the next blog!
References
[1] Reinforcing feedback is also called positive feedback.
Martin, LA. 1997. An Introduction to Feedback, Road Maps, MIT System Dynamics in Education Project, D4691.
Also on the Creative Learning Exchange, Road Maps
[2] Hayward J. 1999. Mathematical
Modeling of Church Growth, Journal of Mathematical Sociology.
23(4), 255-292.
Hayward
J. 2005. A General
Model of Church Growth and Decline. Journal of Mathematical
Sociology, 29(3), 177-207.
[3] Balancing feedback is also called negative feedback. See
[1] above.
[4] Kelley D. (1986). Why Conservative Churches are Growing:
A Study in the Sociology of Religion. Mercer University Press.
Wesley's Law of the Decay of Pure Religion
[5] Forrester, JW. 1969. Urban Dynamics, p.109. MIT Press.
No comments:
Post a Comment