up tofifteen percent. At higher conversion-rates or at lower numbers of
itinerants, the effect becomes minimal. This can be understood if we consider
the learning strategy selected: the movement can spread from any household
to its neighbor in one day. In the model, an apostle covers exactly the same
distance in one way, moving to the next patch in some direction. Theoretically,
we could change the model to speed up the travel of the apostles. However,
there is no reason to build into the model the assumption that the itinerants
of the Christ movement traveled faster than anyone else did. Indeed, Paul’s
example shows that some itinerants could take fast sea routes; yet other
followers, such as merchants or other mobile people, could do the same.
There are two conditions, in particular, under which the presence of apostles
makes significant difference.
When we adjust the conversion-rate to values between 0.1 and 1, we assume
extremely high chances of transmission. It is very unlikely, that one,five, or
even ten encounters with a neighbor will result in successful recruitment to a
new religion on the average. Indeed, if that were the case, the entire population
of an ancient city would have been converted to Christianity in a matter of a
couple of days (given the parameters of our model). If we now test the model
with a different conversion-rate, assuming that one in a hundred encounters
result in conversion, the spread of the movement slows down considerably, to
about 1500 days until every household is converted. In this scenario, however,
the presence offive itinerants already reduces the number of days by almost 30
percent (as shown in the rightmost column of Table 9.1).
A further important detail is the effect of the apostles at different stages of
the growth of the movement. If we repeat the experiments and stop the spread
of the movement at earlier stages, we can observe a very important trend: the
earlier we stop the simulation, the greater the impact of the apostles will be.
For example, if we take a look at the spread of the movement when it reaches
ten percent of the population (see Table 9.2), even at the relatively high
conversion-rate of 0.1 (see our discussion of conversion-rates above), the
presence of one apostle decreases the number of days needed for such pene-
tration from about 30 to about 25 days. Two tofive apostles make a difference
of almost ten days. If we choose the more realistic conversion-rate of one
percent, the number of days needed for the movement to reach ten percent of
the households drops from around 300 to around 150 after adding as few as
two or three itinerants, meaning that the movement now spreads twice as fast
as before in thefirst stage of its expansion even with a modest involvement of
itinerancy.^14 Let us put this observation into historical context: in thefirst and
second centuries, the size of the Christ movement was negligible as compared
to the total population of the Roman empire, which the movement eventually
(^14) Note that in the beginning the proportion of itinerants relative to the entire size of the
movement is very high, a problem that is not examined further in this simple model.
200 Cognitive Science and the New Testament