. 5
( 7)


˜Wherever there is randomness, science cannot distinguish between truly
random events, providentially decreed by God, and speci¬c events, selected
by his creative choices™ (p. 197).
˜This suggests some divine guidance of quantum and other random events™
(p. 198).
˜God has plenty of options to providentially and creatively direct (or
override if necessary) both natural events and actions of personal free-will
creatures™ (p. 200).
˜God™s “interference” may even represent a speci¬c probability density
function modifying the natural stochastic one™ (p. 201).
c h a pt e r 1 0
The human use of chance

Chance is no threat to the notion of design as is evident from the fact that
we actually use it to achieve our own purposes. Some of these uses are
long established but the ready availability of massive computing power
has opened the way for a much wider range of applications. We are now
able to generate randomness on a large enough scale to simulate many
complex processes. Applications range from chemistry to music, with
statistical sampling still playing a central role. Competitive situations
call for chance selections in the choice of strategies, and so-called
genetic algorithms attempt to mimic design by random variation and
natural selection. These and other uses of chance are surveyed in this

i s c h an c e u s e f u l to u s ?
So far we have thought of chance as part of the natural order
of things. Whether real or not it pervades the natural world,
where many see its presence as a threat to the sovereignty of
God. Eliminating chance as a possible explanation has been
one of the main objectives of the Intelligent Design movement.
Before I move on to argue that chance is a friend, not a foe, it
will be helpful to prepare the ground by noticing that chance
is often ˜man-made™ with the deliberate intention of achieving
serious objectives or even entertaining us. This consideration
may help to prepare us for the altogether more radical idea
that in so doing we may be imitating God himself.
The human use of chance 157
We begin with the more frivolous end, as some will see
it “ namely games of chance. Games are recreational activities
designed to entertain as much as to educate and they come in
several varieties. There are games of pure chance, where the
outcome is determined solely by the role of a die or the dealing
of cards and where skill plays no part at all. In other games
the outcome may depend on a mixture of chance and skill,
where the role of chance may be minor or major. In many
team games such as cricket, for example, a main role of chance
may be to decide, by the toss of a coin, which side has the
choice of batting ¬rst. In card games, such as bridge, much
more may depend on chance through the dealing of the cards.
Not all games are played against a single, or several, oppo-
nents in a competitive fashion. Playing, as it is rather oddly
called, in a national lottery or on a fruit machine in an amuse-
ment arcade is a solitary activity which involves no skill at
all “ though there are many pundits who purvey advice as if
it did.
Why is game playing such a widespread and, for those who
organise it at least, lucrative activity? There are people who
will not take part in games which involve chance, though few,
if any, carry their scruples so far as to avoid them altogether.
Chance introduces an element of uncertainty into games and
this, in turn, induces surprise, excitement and enjoyment with-
out the attendant risks and costs of real-life risk taking. For
a time players live in an arti¬cial world in which they enjoy
the positive bene¬ts of chance and derive immense satisfac-
tion from it. For some, of course, this is not suf¬cient and
they seek to inject the costs of real life into the action. The
gambling instinct is deep rooted and the extra excitement gen-
erated by the real risk involved may, in moderation, add to the
perceived recreational value. However, the line between the
positive and the negative bene¬ts is hard to draw and it would
God, Chance and Purpose
be foolish to pretend that man-made chance, in this context,
is wholly bene¬cial. This should not be allowed to detract
from the harmless pleasures which many derive from board
games such as Monopoly, and Snakes and Ladders. The point
is simply that man-made chance plays a useful role in society
and adds greatly to the total human experience.
There is another contribution which chance makes in the
world of games. In chapter 8 I considered the tossing of a coin
at the start of a football match, to give a choice of ends. Here
I shall delve a little more deeply into what that implies. It is
not primarily to inject a further modicum of surprise into the
match “ though it may do that. Its prime purpose is to ensure
fairness by eliminating any advantage which the local features
of the pitch or environment might confer on one side. If the
decision were made by any person, that individual could be
accused of bias. If the choice depends on the toss of a coin
there can be no argument. The principle at stake is one of
fairness but it is worth pausing to ask in what sense it achieves
this. For, in the end, one side has the advantage and this may
well contribute materially to the outcome of that particular
match. There are two answers which can be made to this
query. One is by appealing to the ˜long run™. Any particular
side or individual will, in the long run, get the advantage on
about half of the occasions. This could, perhaps, be achieved
by more deterministic methods but only at the price of much
greater organisational demands. Tossing a coin on each occa-
sion achieves much the same end more cheaply and simply.
The second way of justifying the random choice of starting
position is that it eliminates all possible human bias. There
can then be no justi¬ed claim of human interference in the
outcome. Furthermore it is important that the tossing should
be public, with both sides witnessing the event. All of this can
be ensured by the simple tossing of a coin.
The human use of chance 159
There is another aspect to fairness. Games of pure chance
eliminate any disparities there may be between the contestants.
At ¬rst sight this might appear to run counter to the whole
idea of competing but it is a way of bringing children or others
of limited ability into a contest on equal terms. The bene¬ts
conferred by the shared excitement of game playing can thus
be appropriated by a wider spectrum of individuals. Even
when some skill is involved, the weaker partner still has some
chance of winning as a result of ˜the luck of the draw™. Chance
may not level the playing ¬eld entirely but it does help to make
the game more interesting for the less able players.

c h an c e c an h e l p to s o lv e g e o m et r i c a l
p ro b l e m s
Paradoxically, chance can be used to solve problems in math-
ematics which may have nothing to do with uncertainty. As
an example, imagine that we wish to calculate the area of an
irregular land mass such as, for example, the Peloponnisos in
Greece or Newfoundland in Canada. One rather crude way is
to trace the outline onto squared paper and to count the squares
lying inside the outline. If the squares are small enough, this
will be time consuming but will give a reasonably accurate
answer. Another way is to superimpose the map on a square
which is large enough to include the whole area. If we adopt
the side of the square as our unit of length we can choose points
at random within this unit square. (Exactly how we do this is
an important practical matter but for present purposes it can
be ignored: we would choose pairs of random numbers within
the range (0, 1) and each pair would de¬ne a point within the
square. Sticking in a pin with eyes blindfolded is the vernac-
ular equivalent.) The proportion of the square occupied by
the land in question can then be estimated by the proportion
God, Chance and Purpose
of randomly chosen points which fall within the land area.
This is only an estimate, of course, and its precision is deter-
mined by how many points are selected “ the more points, the
more accurate the estimate. The precision can be estimated by
using sampling theory. We can then calculate in advance how
many points we shall need to select to achieve a desired preci-
sion. This can all be automated on a computer and would be
extremely fast in practice. Here we are using chance as a tool
to solve a mathematical problem: there is no uncertainty in
the problem; it all lies in the method of solution. A great merit
of this approach is that it is not con¬ned to two-dimensional
objects but will work in three dimensions, where the squared-
paper method cannot be used. All that we need is a way of
determining whether or not a point lies within the object.
In the above example we are using the fact that what is
random at the level of the individual point creates regularity
when the points are aggregated. The same principle applies in
many other areas. A spray of paint, for example, consists of a
mass of tiny droplets which are distributed more or less ran-
domly throughout the area covered by the spray. A short burst
of spray will produce a spotty effect with unequal amounts of
paint being delivered to different areas. But a longer burst will
produce a much more uniform coverage because the num-
ber of droplets per (small) unit area will now, proportionally
speaking, be more nearly the same. In practice this method
will be much better than what could be achieved by hand.

m on t e c a r lo m et h o d s
This allusion to the Mecca of games of chance may raise unreal
expectations.1 We shall not be concerned here with methods

The name Monte Carlo comes from the Principality, in which the casino is

a centre of randomness. Stanislaw Ulam, a Polish born mathematician, is
The human use of chance 161
of breaking the bank of that Principality but in using chance to
imitate, or simulate, physical or social processes which are too
complicated to study mathematically. Here we move from the
realm of simple and rather contrived examples to processes
which play a major role in almost all branches of science, pure
and applied. To illustrate what is involved I shall use a very
simple queuing example.
Imagine someone serving behind a counter, as in a shop
or post of¬ce, with a line of customers before them in order
of arrival. Uncertainty about what happens subsequently may
arise in two ways: there may be variation in the times taken to
serve each customer and there may be irregularity in the times
at which new customers arrive. This is a dynamic process
and the state of the system will change as time passes. We
may want to know such things as the proportion of time the
server is occupied and the average waiting time of a newly
arrived customer. To answer such questions we may turn
to mathematics2 and, if the uncertainty can be described in
simple enough terms, the theory of queues may enable us
to do just that. Often this is not the case and then we can
turn to Monte Carlo, or simulation methods. These provide
us with a means of generating service and arrival times that
have the same probabilistic patterns as those observed to occur
in the real process. If we do this many times we shall begin

usually credited with inventing the technique in 1946 though, like so many
such inventions, it is easy to trace the essentials of the idea long before
that. Simulation is another term used in almost the same sense, although it
does not necessarily carry the implication that the process involves a chance
Queuing theory was much in vogue in the 1960s as one of the techniques of

operational research. One of its main applications was to studies of traf¬c
intensity in telephone systems, which goes back to the early part of the
twentieth century. Most real queuing systems are much too complicated
to be amenable to mathematical treatment, and resort has to be made to
God, Chance and Purpose
to build up a picture of the distribution of waiting times and
suchlike. Furthermore we can experiment with the system by,
for example, looking at the effect of adding a new server. In
effect we are using chance to imitate the process and so to
learn something about the real world.3
This queuing situation is actually much simpler than most
that occur in real life and its behaviour is fairly well under-
stood. Monte Carlo methods really come into their own when
the system is much more complicated. For example, con-
gestion problems of some complexity are common at air-
ports, on the roads and in many industrial production and
distribution processes. However, it is the principle of the
thing which concerns us here. Without the ability to sim-
ulate complex processes, and to do so rapidly enough to
accumulate information while the problem is still a live one,
ignorance and hunch would still be the only guide in many
Much of the work on networks touched on in chapter 8
has been facilitated by the use of Monte Carlo methods (see
Barab´ si 2003). It is relatively easy to simulate the behaviour
of a network on a computer. The results often give clues as
to what results might be proved mathematically. It is usually
much easier to prove something when you already have a good
idea of what the answer is.
Essentially, it is the speed andcapacity of modern computers
which has revolutionised this ¬eld. For present purposes it
clearly demonstrates how chance can be useful for learning
about the real world and achieving things within it.

A similar kind of example showing how natural selection can generate

novelty is given by Ayala (2003), beginning at the bottom of page 19. This
shows how bacterial cells resistant to streptomycin can be produced by using
natural selection to sift through a vast number of possibilities.
The human use of chance 163

r an d o m c h e m i s t ry
This term seems to have been coined by Stuart Kauffman in the
early 1990s though it is also referred to as combinatorial chem-
istry. It does not, as the name might suggest, refer to chemistry
carried out in a haphazard fashion but to the systematic use
of randomisation to discover complex molecules capable of
combating disease. In the search for effective drugs one needs
to construct molecules capable of binding to invaders to neu-
tralise them. One might imagine doing this constructively by
identifying what sort of shape the molecule needs to have and
then building the required drug to order. This is more easily
said than done. If the basic ingredients (chemicals) are known,
the number of ways in which they can be linked together to
form a possible drug may be truly enormous. This number
may be so large that, even if it were possible, there would not
be suf¬cient time before the end of the world to sort through
them all systematically and ¬nd any that were effective. Some
other strategy has to be found of searching the ˜space™, as it
is called, of possibilities. This can be achieved quite easily
if there is some way of mixing up the ingredients so as to
produce a great many, if not all, of the possible candidates.
In addition, we need to have some means of identifying any
which ˜work™ “ because these will be the potential drugs. The
proposed method works by selecting possible candidates rather
than by constructing them. The role of chance is to generate
a wide range of possibilities. To speak more technically, we
make a random selection from the space of possibilities and
then check whether any can do the job asked of them.
To show how this might work out in practice Kauffman
describes (1995, pp. 145“7) how one might ¬nd a molecule that
mimics the hormone oestrogen. The process starts with about
1,000 molecules which one anticipates will include building
God, Chance and Purpose
blocks for the sought after molecule. These are then mixed
into a solution of about 100 million antibody molecules. If the
mixture is what is called supercritical then, over time, billions
of new kinds of organic molecules will be formed, among
which it is hoped that there will be at least one which will
mimic oestrogen. Some oestrogen is now added to the ˜soup™
which already contains some radioactive oestrogen; this will
have bound itself to any candidate molecules. If there are any
such present, the added oestrogen will displace the radioactive
variety and that occurrence can be detected. At that point it
is known that there is at least one type of molecule present
which can do the same job as oestrogen. The next step is
to identify this molecule. Kauffman describes a method of
repeated separation and dilution at the end of which it is pos-
sible to identify the successful molecule. Once it is identi¬ed,
its structure can be determined and this paves the way for
it to be manufactured in quantity. Chance enters this pro-
cess when the supercritical mixture ˜explodes™ to produce the
vast number of candidate molecules. The larger the number
the greater is the probability that there will be one among
them with the required properties. Chance achieves easily
what it would be virtually impossible to do in any other
way and it does so with an elegance and ease which should
amaze us.

sa m p l i n g
Inference from samples is by far the largest and most important
¬eld for the deployment of chance to serve useful ends. It lies
at the root of modern statistics and represents one of the great
intellectual achievements of the last century. To many, it is not
at all obvious that one can learn very much about the attitudes
or voting intentions of a population of several millions by
The human use of chance 165
questioning only a few hundred people. In general, of course,
one cannot but the possibility all turns on how the individuals
are selected. A simple random sample provides one answer. At
¬rst sight it may appear paradoxical that the way to get hard
information is to go down the uncertain route of chance but
that is how it turns out.
First, we need to know what a simple random sample is or,
more exactly, what a simple random sampling process is. To keep
things on a level where we can easily imagine the sampling
being carried out, imagine a school with 500pupils and suppose
we wish to know what proportion travel more than one mile to
school. Because we do not have time or resources to question
every individual, it is proposed that we base our estimate of this
proportion on the answers given by the members of a sample
of size twenty. Next imagine a listing all possible samples of
this size. This is an enormously large number, 2.67 — 1035 to
be exact, but as all of this is only going on in our imaginations,
there is nothing to prevent us from thinking in terms of such
numbers. We are only going to pick one sample and it must be
one from this list because the list contains all the samples there
could possibly be. So the question is: how shall we make the
selection? The principle of simple random sampling says that
each possible sample should have an equal chance of selection.
The technicalities of how this is done need not detain us. We
certainly do not need a full list from which one sample has
to be selected because there are ready-made samples already
available in tables of random numbers, or their equivalent
which can be generated on a computer.
At ¬rst sight this may seem a rather risky way of trying to
learn about the population of 500 pupils. Some samples will be
very untypical of the population and if one of these happens to
be drawn we shall get a very misleading picture. That is true
but very unlikely, because most samples will be similar to the
God, Chance and Purpose
population as regards the proportion who travel more than a
mile to school. All of this can be quanti¬ed by using the theory
of probability. This shows that as the sample size increases
the sample proportions become ever more closely clustered
around the population value. Inverting this statement, the
distance from the sample value to the population value will
decrease and so our estimate of the latter will become ever
more precise.
There is a lot more to statistical inference than taking fairly
small samples from smallish populations. Much of it, in fact,
concerns what are called in¬nite populations, where there is
no limit to the size of sample which may be taken and where
it makes sense to enquire what happens as the sample size
becomes inde¬nitely large. None of this affects the basic ideas
underlying the use of chance to learn about the world which
is illustrated by the example given above.
The principal points which emerge from this discussion of
inference from samples, echo those already familiar from the
earlier sections of this chapter. One is the notion of fairness
embodied in giving every possible sample an equal chance of
being selected. It is notoriously dif¬cult for an individual to
pick a sample randomly from a small population of objects
laid out before them. Simple random sampling provides a
guarantee that there could not have been any introduction of
bias, witting or unwitting. Secondly, there is the emergence
of order from chaos as outcomes are aggregated. Although
individual samples may show wide divergences from expecta-
tion, the sampling distribution, as it is called, shows a de¬nite
and repeatable pattern. There are near certainties on which
we can base our inferences which emerge in the aggregate and
which ensure that we almost always get things right in the long
run. Although these things could be checked empirically, in
principle at least, probability theory is available to save us the
The human use of chance 167

t h e a rts
The element of surprise and unpredictability inherent in ran-
Abstract creations in either ¬eld may, sometimes at least, take
us beyond the conventional limits of imagination to explore
unknown territory. To put it rather more grandly, chance
enables us to explore the space of possibilities more thor-
oughly by opening up to us obscure corners which might
otherwise be missed. One famous example of random com-
position goes back to Mozart.4 In his Musikalisches W¨ rfelspiel
(K.516f, 1787) he wrote a piece for piano consisting of
32 bars “ a 16-bar minuet and a 16-bar trio. Mozart composed
176 bars altogether from which the bars of the pieces were
to be selected randomly. The original idea was that the bars
would be selected by rolling dice. Today this can be done by
drawing random numbers. In practice one can do this by vis-
iting the web site http://sunsite.univie.ac.at/Mozart/dice/
and clicking on a button to play the piece. There are also
options to choose instruments, one for each hand, and to make
one™s own random selection of bars. The number of possible
musical pieces which can be constructed by this means is enor-
mous “ about 1.5 — 1015 for the minuet alone “ so the chance
of all the possibilities ever being heard is remote! The interest
of the exercise is that pleasing and unexpected results can be
obtained from an uncertain process.

s e r i o u s ga m e s
At the outset I reviewed the place of chance in games of the
kind we play for amusement. There are more serious ˜games™

The material about Mozart was obtained from a note by David Bellhouse

in the International Statistical Newsletter 30 (2006): 19“20.
God, Chance and Purpose
in the worlds of economics, politics and management gener-
ally.5 The word game in this context is apt to hint at a lack of
seriousness which may divert the reader from its real impor-
tance. A game in this more general sense is a decision-making
situation in the face of uncertainty, though here I shall inter-
pret it more narrowly. For our present purpose a game is a
situation where two or more parties, with con¬‚icting goals,
compete with one another for some desirable end. Compe-
tition between ¬rms for customers in the marketplace is an
obvious example; candidates seeking the support of voters in
an election is another. In the simplest case there are just two
players with each trying to outwit the other. The uncertainty
in such games arises mainly from lack of knowledge about
what the opponent will do. Each player must therefore seek
to see the game from their opponent™s point of view, to try to
anticipate what the other will do and to respond accordingly.
Each player will have a number of strategies available to them
and will have to guess what are available to the opponent. For
each combination of strategies chosen by the contestants there
is what is known as a payoff. This may not be monetary and
its value may not be the same for the two players.
An extremely simple game, so simple that it would be rather
boring to play, illustrates how it may be advantageous for a
player to resort to chance in selecting a strategy. Each player “
call them Bill and Ben “ has a coin and has to choose which
face to display. If they choose the same face, Bill wins and

Although traces of the ideas go back to the early 1700s the mathematician

John von Neumann created the ¬eld in a series of papers in 1928. His
book with Oskar Morgenstern, entitled The Theory of Games and Economic
Behaviour and published in 1944, was a landmark in the subject. However,
in the early days it was dif¬cult to ¬nd good applications in subjects such
as economics to convince people of the theory™s usefulness. More recently
there has been a surge of interest extending into other ¬elds such as biology.
The human use of chance 169
pockets both coins. If they make different choices, Ben wins.
There are thus four possible outcomes which may be set out
in a table as follows:
+1 ’1
’1 +1
The entries show the game from Bill™s point of view; so
a negative entry shows what Bill loses. If Bill and Ben both
choose heads the gain to Bill is 1 and this appears in the top
left position. If Ben chooses heads and Bill chooses tails the
rules say that Ben wins, which means that Bill loses 1 as the
bottom left entry in the table shows. If the game is played only
once, each player will either lose or gain one unit and there
is no way of telling, short of mind reading, which way it will
go. The most that Bill or Ben can say is that their loss, in a
single play, cannot be bigger than 1. However, if the game is
played repeatedly, things become more interesting. There is
now a strategy which ensures that either player can do better
in the long run. Suppose Bill simply tosses the coin. When Ben
chooses heads, Bill will gain 1 on half the time, when his coin
falls heads, and lose 1 on the other half. These will balance out
in the long run. The same will be true whenever Ben chooses
tails. So Ben™s choice is irrelevant to Bill because whatever it
is, his gains and losses will balance out in the long run. Bill
thus does better by ensuring that his gains never fall below an
average of zero per play. It also turns out that he cannot do
better than this whatever strategy he chooses.
The intriguing thing about this is that Bill does best by
choosing heads or tails at random! Use of chance will yield
more in the long run than can be achieved by long and careful
thought. This seems paradoxical but it is not. The point is
God, Chance and Purpose
that if Bill did use some non-random choice strategy, then
Ben would be able to observe his choices and, in principle,
learn something about how Bill was making his choices. He
could put this knowledge to good use by trying to predict Bill™s
choices. Knowing what Bill is likely to do enables Ben to take
advantage of that knowledge. For example, if Ben thinks that
Bill is likely to choose heads, he will counter by choosing tails
and so win. The only way that Bill can ensure that Ben cannot
predict his choice is to make his own sequence of choices
unpredictable. And the only way he can be absolutely sure of
this is by not knowing, himself, what he is going to do “ by
tossing the coin. Simple though it is, this example conveys the
essential point I wish to make, namely that in a competitive
situation it is important to deny information to the enemy.
The sure way of doing this is to blind the enemy with chance.

g e n et i c a lgo r i t h m s
Not only do humans use chance; ˜nature™ uses it also and on
a grand scale. The whole evolutionary process has created
living things exquisitely adapted to their environments. The
combination of chance variation and natural selection has been
a powerful creative force, fashioning the world as we know
it. It is not surprising, therefore, to ¬nd that humans can be
creative, albeit on a smaller scale, by imitating nature.
Genetic algorithms6 are attempts to imitate nature by creat-
ing variation and selecting those products best ¬tted to survive.

Genetic algorithms are an example of what are called computer-intensive

techniques and for that reason did not become widely used until the dramatic
increase in the power of desktop computing in the 1980s. They take their
name from their analogy with genetic reproduction but, viewed mathemat-
ically, they are optimisation techniques which, to borrow a topographical
metaphor, exploit the ability of computers to search systematically for a
route to a summit.
The human use of chance 171
The essentials are as follows. In nature the genome contains the
code for reproduction. In successive generations the genome is
modi¬ed by mutation and crossover. At each generation those
most ¬tted to survive are best placed to breed and so form the
next generation. Over a long period, the organism becomes
better adapted to its environment by the accumulation of small
bene¬cial changes.
The key idea which readily translates into engineering
design, say, is to let chance generate a large number of varia-
tions on the current design from which the best can be selected.
To do this we need some way of selecting the most success-
ful examples to carry forward into the next generation. This
is achieved by what is called an objective function. This pro-
vides a measure of how good a particular design is and so
enables the best to be selected. The genome in this case is
the design speci¬cation which lists every variable under the
designer™s control; it is the blueprint which would enable the
design to be constructed. Typically this will be a list of, per-
haps, hundreds or thousands of components, all of which could
be varied. Adjusting them all in a systematic fashion to dis-
cover the optimum solution would be prohibitively expensive
in time and resources. The speed and capacity of modern
computers enables chance to step in and facilitate the explo-
ration of a vast number of alternatives. Each is evaluated by
the objective function and the best is selected as the start-
ing point for the next round in the search for the optimum.
Blind chance, as it is sometimes called, thus enables the opti-
misation process to see its way to a good solution. The true
location of the design is in the mind of the creator of the
algorithm who could not “ and did not need to “ see the
details of the path which the process would follow. A human
designer who took the alternative course of laboriously and
systematically searching for the optimum would be quickly left
God, Chance and Purpose
This chapter may have appeared to be something of a
digression with no immediate theological implications. How-
ever, its purpose has been to show that chance is not necessarily
the enemy of all that is rational and that it is certainly not the
antithesis of planning and design. Chance, in the shape of
deliberate randomisation, has found an increasing range of
applications in human activity both serious and recreational.
This has been nourished and developed enormously by the
fact that modern computers are good at performing large num-
bers of simple repetitive operations very quickly. If there are
so many advantages in deploying chance in our own affairs,
it is natural to ask whether there may not be bene¬t to God in
achieving his own purposes in the wider creation. That is the
subject of the next chapter.
c h a pt e r 1 1
God™s chance

In chapter 3 we saw that chance and order are not incompatible; many
of the regularities in the world are the aggregate effects of chance
happenings at a lower level. In chapter 10 we saw that such regularities
enable us to use the lawfulness which they introduce for our own
purposes. God, of course, created these possibilities in the ¬rst place,
so it is natural to suppose that he would use the order which results to
achieve his own ends.
In this chapter I show how this might have happened in three exam-
ples where the presence of a chance element has often seemed to rule
out divine involvement. These are: the origin of a life-bearing planet,
the evolution of life through natural selection, and the social order.

w h y m i g h t go d u s e c h an c e ?
Is chance a real feature of our world and, if so, how can
we reconcile its presence with belief in the God of Chris-
tian theology? That question was raised at the outset and it
has overshadowed all that I have said since. I have already
rejected the idea that what we see is only the appearance of
chance “ that in reality every single thing that happens is as a
result of the direct and immediate action of God. This is logi-
cally possible, of course, but we have seen that, in practice, it is
extremely dif¬cult to mimic chance. Indeed, the only sure way
of getting it right is to resort to a chance process itself. I have
also rejected the idea that what appears to be chance mostly is
God, Chance and Purpose
chance, but that every now and again God intervenes at crit-
ical junctures to achieve his particular purposes. This view is
equally impossible to reject solely on logical grounds, because
such interventions need not be empirically detectable. There
are also signi¬cant theological objections, to which we shall
come later, but the central purpose of this book is to argue for
the third view that God uses chance. In other words, that the
chance we observe in nature is there because God intended it
to be so. It serves his ends and furthermore, when properly
interpreted, is conformable to a rational and biblical theology.
A clue as to the way we should proceed to establish this
thesis will be to recall the advantages which the use of chance
offered in some of the various human activities looked at in
the last chapter. These may be listed under four headings as

(1) Some random processes have outcomes which can be pre-
dicted with near certainty. In particular, their aggregate
properties often obey simple laws which make things
effectively deterministic at that level. If it is only the
aggregate behaviour which matters, then the fact that
there is a random substructure is of no signi¬cance.
(2) There is a principle of fairness, or equality, which is sat-
is¬ed when selections are made at random. We saw this
particularly in relation to random sampling but it is also
prominent in random searches to ensure that ˜no stone is
left unturned™.
(3) A chance element in a system introduces a ¬‚exibility and
resilience which makes it robust in the face of the uncer-
tainties of the world.
(4) Randomisation often introduces the elements of surprise,
novelty, ¬‚exibility and variety, which add immensely to
the enjoyment of life and which develop a capacity to deal
with the unexpected.
God™s chance 175
To the common way of thinking, chance, as I have already
had occasion to point out, is synonymous with lack of purpose
or direction and therefore hostile to belief in a God whose
will and purpose is supposed to be expressed in the created
order. My aim is to argue that this view is based on a total
I aim to substantiate this claim by focussing, in turn, on
three major issues where the apparent con¬‚ict between God
and chance is most acute and where the theological impli-
cations seem to be most far-reaching: ¬rst, the existence in
the universe of a habitable planet on which life has appeared;
secondly, an evolutionary process in which chance plays an
integral part, leading to the rich diversity of life on this planet
including the production of sentient beings capable, for exam-
ple, of writing and reading books; thirdly, the growth of human
society in which a measure of genuine individual freedom
seems to con¬‚ict with any overall divine purpose.

life in the universe
Here the gulf between what theology requires and science
tells us seems to be wide and deep. The early picture was of
the earth at the centre of things with humanity at the pinnacle
of creation. The sun went inexorably round the earth, only
stopping when it was commanded to do so by its Creator!
Incarnation and redemption were comprehensible in terms
of a small-scale universe with heaven above and earth below.
Then the picture gradually changed. Copernicus placed the
sun at the centre of the solar system and humankind was
thus relegated to one of the smaller planets. Worse was to
come in the discovery that our sun was one of a vast number
of stars in a galaxy which seemed in no way special. The
galaxies themselves were more numerous than the stars had
once seemed and, furthermore, were receding at a rate that
God, Chance and Purpose
was hardly imaginable. From being a big ¬sh in a small pond,
humanity had become a mere speck located well off centre in
a vast universe which seemed much too large to even notice
it. It was hard to go on believing that humanity was as central
to the meaning of things as the Bible seemed to suggest.1
This argument can, of course, be disputed on its own terms
by asking why size, measured in light years or whatever,
should be the relevant metric for judging these things. Or,
why insigni¬cance should be attributed to any particular loca-
tion in a universe in which there is no natural point of ref-
erence.2 If sheer complexity were the criterion for judging
importance then the human brain, of which there are cur-
rently over 6 billion functioning on this planet, would provide
good grounds for keeping the inhabitants of the earth in a cen-
tral place. However, when we add to mere size the extremely
hostile environment in which life had to gain a toehold, with
extreme temperatures and bombardments from outer space,
the last nail seems to be hammered in the cof¬n of the well-
ordered, God-controlled earth which, in the pre-science era,
had seemed so natural and credible.
The sheer size of the universe revealed by science has nat-
urally encouraged speculation about the possibility of life on
other planets. After all, we know for certain that life can occur,
as our presence on earth proves without doubt. Why should
there not be many other civilisations dotted around this vast
universe? And what would that imply for doctrines such as

The book by Primack and Abrams (2006) aims to tackle the seeming insignif-

icance of humankind in the universe from a largely scienti¬c point of view.
Their main point has been noted in note 3 of chapter 1, but without ade-
quate theological backing it does little to make the universe more ˜human-
Paul Davies explains why the universe has no centre. See the section ˜Where

is the centre of the universe?™ on page 27 of Davies (2006).
God™s chance 177
original sin and the need for redemption? It makes the whole
Christian enterprise seem so parochial that one might scarcely
credit that belief still exists among some, even, of the intelli-
Scienti¬c opinion is divided on whether we are alone, and
there is precious little hard evidence to go on. If there were
other advanced civilisations extant at the present time one
might expect them to be indicating their presence, and large
sums of money are being spent ˜listening™ for them “ so far
without hearing anything. In so far as probability arguments
have been brought into play, the crudest goes somewhat as
follows.3 Given the size of the universe, there must be many
stars with planets and some of them must have, or have had,
or will have, conditions suitable for intelligent life to appear
and evolve. The probability of life emerging at any location
cannot be zero, because it has already occurred at least once,
but given all that we know about the hazards involved the
probability must be very small indeed. The expected number
of such civilisations would then be obtained by multiplying
the number of locations by the probability of life occurring
at any one of them. (This assumes the probability is the same
at all locations, but this assumption can be relaxed without
affecting the point of the argument “ see later.) This is where
the trouble starts. The answer you get when multiplying a very

There is a serious scienti¬c side to the search for extraterrestrial life, and

a growing subject called astrobiology. Another major interest is in how
one would recognise alien messages were they to be directed towards our
planet from living beings elsewhere in the universe. Conversely there is the
question of what information should be transmitted from earth into space
so that any recipients would recognise what they were receiving as coming
from intelligent beings. The acronym SETI (Search for Extraterrestrial
Intelligence) is often used to describe the community working in this ¬eld.
The public imagination goes much further, and many people, in America
especially, will testify to having been abducted by visiting aliens.
God, Chance and Purpose
small number, the probability of life, by a very large number,
the number of planets, can be almost anything; it depends on
knowing the magnitudes of the two numbers fairly precisely.
Yet, if the approach is to be of any use, we need to know
whether the answer is much less than one, in which case life
elsewhere is unlikely, or much larger than one, in which case
the opposite is true.
Conway Morris (2003, pp. 229ff.) quotes a number of exam-
ples of this kind.4 He refers to Gaylord Simpson, for example,
who agreed that there were many locations at which life might
have occurred and that the probability at any one must have
been very small. From this he claims that ˜the Universe is a
big place, so however uncommon life was, the total number
of planets with life must be quite large™ (p. 229). There is no
must about it. Everything depends on just how many planets
there are and what the probability actually is. George Beadle
(p. 230) was another whose arguments appear to depend on
the fact that numbers may be very large and probabilities very
small without an adequate logic for relating the two.
A slightly more sophisticated attempt to solve the prob-
lem is embodied in Drake™s formula.5 All this does is to
break the problem down into smaller components, without
The page references in this paragraph are to the beginning of his chapter 9

entitled ˜The non-prevalence of humanoids™. George Gaylord Simpson was
a notable evolutionary biologist of the last century. In the notes to chapter
9 Conway Morris gives more information about his work. George Wells
Beadle was an American geneticist who shared the Nobel prize in 1958 with
Edward Lawrie Tatum for work showing that genes act by regulating the
chemical events within the cell.
Frank Drake, an American astronomer, formulated what is known as

Drake™s formula, or equation, in 1961. It exists in more elaborate forms
than that implied by the discussion here but, in any version, it is essentially
a tautology. Its purpose is to break down the problem of ¬nding the proba-
bility into more manageable parts. It tells us something about the structure
of the probability but nothing about its value.
God™s chance 179
materially contributing to its solution. In fact it has been
shrewdly remarked that it is merely ˜a way of compressing
a large amount of ignorance into a small space™. This quota-
tion is reproduced in a paper by Lineweaver and Davis (2002,
p. 11) which does take matters a little further. Drake™s formula
represents the proportion of stars in our galaxy orbited by
planets that have had independent biogenesis as the product
of three proportions. These are: the proportion of stars in
our galaxy with planetary systems; the proportion of those
planetary systems that have a terrestrial planet suitable for
life in the same way as the earth; and the proportion of these
suitable planets on which biogenesis has occurred. We do
not know any of these proportions, but progress might be
made if some estimates could be made of one or other of the
components. Lineweaver and Davis claim that they have a
method which tells us something about the last of the three
The idea is quite simple. On an earth-like planet there will
be a ˜window of opportunity™ when conditions are propitious
for the emergence of life. If it is easy for life to emerge it is more
likely to do so early in that period than if it is hard. By estab-
lishing that life appeared on earth at a relatively early stage,
we can conclude that the Earth™s environment is in the easy
category, and hence that life will have arisen quite frequently
on other, ˜similar™ planets. By this means, and by making fur-
ther assumptions, the authors claim that the probability of life
arising under these conditions is likely to be greater than 13
per cent. Hence there is a fair chance that biogenesis will have
arisen once a suitable planet occurs. This interesting result still
leaves us a long way short of an estimate of the proportion of
life-bearing planets in the galaxy.
There is, in fact, a more relevant calculation which can
be made which shows the whole issue in a totally different
God, Chance and Purpose
light. Its novelty lies not in that it replaces the naturalism
of the approach just discussed by a theological perspective,
but rather that it retains all of that without excluding God.
We shall consider how God might use these same natural
processes to achieve a life-bearing planet. In pursuing this
strategy we shall adopt what may seem to be a presumptu-
ous usurping of God™s place by asking what God might do.
However, we often do this unconsciously and it is better to
be open about it than to adopt a false deference. Essentially
we are using our imaginations to contemplate a set of possible

on e wo r l d o r at l e as t on e wo r l d ?
In this chapter I am asking how God might use chance, and
at this point, how he might use it to bring planets into being
capable of supporting intelligent life. The deity would begin
by recognising that, in the sort of universe brought into being
by the ˜big bang™, the chance that such life might arise at
any location was bound to be extremely small. The uni-
verse, therefore, would have to be very large for there to
be any chance of its happening. But how large? Large enough
for there to be a very high chance of its happening at least
once. At this point a part of probability theory becomes rele-
vant. However big the universe is, the actual number of life-
supporting planets will not be certain but it will have a proba-
bility distribution. Furthermore, and surprisingly perhaps, we
can deduce what the form of that probability distribution will
be. If we have an exceedingly large number of locations and
an exceedingly small chance that any of them will produce
life, then we know that the distribution will have the Pois-
son form, a distribution we have already met in chapter 3.
This does not require the probabilities to be equal “ just
God™s chance 181
small.6 There is one further assumption which is that there
will be independence between what happens in one part of
a galaxy from what happens in another. Given the size of
the universe, with such immense distances between stars and
galaxies, there seems to be no problem about that. The form
of the Poisson distribution depends solely on the (unknown)
average number of life-supporting planets. Taking all this into
consideration, we can easily determine what this mean num-
ber has to be in order to ensure that life occurs at least once.
This means that once God has decided what the probability of
getting at least one occurrence should be, the average number
of occurrences and the distribution of occurrences is deter-
mined. Let us put some numbers on these abstract statements
to see just what is involved.
Suppose that the Deity would be satis¬ed with a probability
of achieving at least one ˜success™ equal to 999/1000. A simple
calculation shows that this can be achieved with an average
number of 5.9 life-bearing planets. Interestingly, this makes
the chance of getting exactly one occurrence a mere 0.016,
so our ensuring that we get at least one means we shall very
likely have a lot more than one. A more risk-averse Deity
who wanted to raise the chance to 999,999/1,000,000 would
get an average of about fourteen. These simple calculations
have far-reaching consequences. It appears that the number
of inhabited planets would be relatively small if such a method
of creation were used. Furthermore, since any given planet
would only be able to support intelligent life for a relatively
short time, and given the fact that the appearance of life would

This is a standard result in probability theory which will be found in most

texts on the subject. The more elementary version, which supposes that the
probabilities are both small and equal, is usually found as a limiting case
of the binomial distribution, but the generalisation to small and unequal
probabilities is straightforward.
God, Chance and Purpose
be spread over a long period, it would seem unlikely that there
would be more than a very few civilisations extant at any one
time. It is reasonable then, that a planet such as ours has had
no communication from elsewhere in the universe. Although
this is a very slender thread to hang anything by, we do at least
note that our experience is consistent with this theory.
It is also clear that there is no way one could expect to get
exactly one world. This method of creation, if it is to yield at
least one, must almost certainly yield several. It is also clear
that there is no need to have more than a handful if the aim is
to get at least one. What we observe is thus consistent with the
hypothesis that all God had to do was to make the universe
large enough and then leave things to chance. This line of
argument might seem to have pushed God to the sidelines and
accorded him a marginal and unskilled role, which is surely
inconsistent with the power and majesty of the Christian God.
Should he not be at the centre of a detailed and carefully
constructed planning enterprise and in close control of the
whole process? By no means. If there is a simple and elegant
route to the creation of life-bearing planets ought not God to
know about it, and is it not a mark of his greatness if he chooses
to use it? His thoughts are not our thoughts, and perhaps this
analysis gives us a hint of how his ways might not be those
which immediately occur to us.

c h an c e i n e vo lut i on
Nowhere is the possible role of chance more hotly contested
than in evolution.7 Darwin™s theory of evolution by natural
selection, in which random mutations provide the variation on
The perceived con¬‚ict between evolution and creation rears its head at many

junctures, in this book as elsewhere. A good treatment from a scienti¬c
and Christian point of view is provided by K. B. Miller (2003); this is an
edited volume which is particularly suitable for students and others from
God™s chance 183
which selection works, is seen by some as the very antithesis of
the purposeful direction which seems to be the very essence of
Christian theology. The battle lines8 are drawn most sharply
in the United States of America, where evolution is often seen

a more conservative Christian background. A gentler attempt to woo a
similar audience is given in the ¬rst part of Colling (2004). Another very
useful source is K. R. Miller (1999). In an entirely different vein, those
who wish to explore the phenomenon of creationism will ¬nd Coleman and
Carlin (2004) very informative. I know of no work comparable to these
treatments which provides a convincing case for the creationist side of the
The lines are not as sharply drawn as this rather bald statement might

suggest. Many who are theologically conservative are fully committed evo-
lutionists. In the preface to the book edited by K. B. Miller (2003) for
example, Miller writes that ˜having become deeply frustrated with the often
fruitless and divisive nature of the “creation/evolution debate” within the
evangelical Christian community, I hope to move the conversation in a
more positive direction™. The tendency within this collection is to regard
chance as due to ignorance. Miller speaks approvingly of ˜some theologians
who see God™s action exercised through determining the indeterminacies
of natural processes™ (p. 9). The tension becomes acute for those like Terry
Gray, who expresses it in his section on theological musings on pages
385“6. He concludes that ˜while we may not be able to resolve the appar-
ent contradiction, using human reason, we readily af¬rm both truths™. One
cannot help wondering whether part of his trouble arises from regarding the
Westminster Shorter Catechism as the de¬nitive interpretation of scripture.
There are others, such as Morton and Simons (2003), who do believe
that God uses chance and who ¬nd biblical support for the idea. However,
they also believe that God controls chance, but in what sense is not clear.
There is a similar lack of clarity in Garon (2006). In chapter 19, entitled
˜Does chance have dignity?™, he comes close to the idea of seeing chance
as being within rather than outside God™s will. He recognises that disorder
can serve a purpose as when mixing fruit into a cake “ we want it dis-
ordered. However, he still seems to be saying that God knows it all. On
page 14 he says, ˜And, being in¬nite, the Creator knows the outcome of all
things for all time. Nothing can be accidental in the sight of the Lord. What
we call “Accidental outcome” is accidental only to ourselves, not to God.™
In a very recent article Woolley (2006) has argued that the Anglican
theologian Leonard Hodgson (1889“1960) anticipated the idea that chance
is used by God. This is a matter which, clearly, needs to be pursued.
God, Chance and Purpose
as necessarily atheistic by ruling out the notion of design, and
hence, of a Designer. The idea advocated here, that chance
is part of the creative process, is not even entertained. One
gets the impression from Denyse O™Leary™s Design or Chance
(2004) that the real battle lines are drawn between atheistic
Darwinians on the one hand and Intelligent Design advocates
on the other, with theistic evolutionists and young-earth Cre-
ationists playing a secondary role. Theistic evolutionists are
seen by her as being ˜Darwinists with a slight glow of faith™
(p. 240), their problem being to distinguish themselves from
the atheistic Darwinians.
I have discussed and dismissed Intelligent Design, which
seeks to eliminate chance altogether, in chapter 7 and that
leaves us with evolution in some form as the only credi-
ble alternative. The issue to be considered here is whether
chance-driven evolution can be seen as part of God™s creative
process, expressing his purpose, or whether, as some Darwini-
ans believe, it is a blind and undirected process.
Richard Dawkins is prominent among the latter and he
would certainly not see chance in evolution as expressing any
purpose whatsoever. But, oddly enough, his argument does
support God™s involvement but at a different level. Dawkins™
belief that chance is suf¬cient is a continuing theme in his
writings. His invention of computer-generated biomorphs
to illustrate the idea was discussed in Bartholomew (1996,
p. 177). However, a more recent book (Dawkins 2006 [1996])
has introduced the metaphor of climbing Mount Improbable
to illustrate the point. The mountain has one precipitous face
which is extremely dif¬cult to climb and a reverse side which
has an easier gradient. Ascents on this side may be longer and
more winding but are less arduous. Constructing complicated
organisms is like climbing the mountain to reach a summit.
The chance of doing it by the steep face is extremely small but
God™s chance 185
by using the easier route there is a much higher probability of
To see how this works out, let us recapitulate the essen-
tials of Dawkins™ case. He starts by pointing to examples in
nature of extremely complicated constructions which seem
to demand design as part of their explanation. The eye and
the haemoglobin molecule are just two examples. He even
quotes, to their disadvantage, distinguished scientists who
have declared publicly that they could not believe that such
things could have arisen by chance. Dawkins agrees that they
would certainly not have arisen if their creation was merely by
collecting the parts and assembling them ˜at random™. But, he
goes on to say that that is not how they came about. Chance
did, indeed, produce the variation on which natural selection
operated but, instead of climbing the impossibly steep cliff of
Mount Improbable, evolution took the roundabout route on
the easier slopes on the other side of the mountain. In short,
the extraordinarily small probabilities which are quoted are
irrelevant; the true probabilities are much larger and hence
the evolution of complex organisms and molecules was not so
unlikely after all.
By correctly challenging the very small probabilities which
so many, du No¨ y and Overman among them, have seen
as providing incontrovertible evidence for design, Dawkins
supposes that he has demolished the case for a designer God
behind the process. On the contrary, he has helped to make
credible an evolutionary process which is capable of producing
the complexity in the world and hence, as I have argued, that
it could be the God-chosen way of creating things. I also have
been arguing that the inferences to God based on very small
probabilities are often invalid. Only by ¬rst doing that, is the
way clear for a much deeper and more subtle account of what
has been going on.
God, Chance and Purpose
Dawkins, it should be noted, establishes that there may be a
way to the peaks which makes the evolution of complex things
possible. He does not actually show whether a route exists in
particular cases. Is there a route, for example, which leads to
human-like creatures? In attempting to decide this issue, it is
relevant to note that there is a difference, among scientists,
about how evolution develops, and one view is very much
more friendly to theism than the other.
The alternative positions are set out in Gould™s Wonder-
ful Life (1989) and Conway Morris™ Life™s Solution (2003).
Gould created many metaphors to convey scienti¬c ideas to
his readers. One of the best of these, and often quoted, is that
of rerunning the ¬lm of evolution. According to Gould this
would never end up at the same place twice. This seemed
so obvious, and at the same time, so threatening to religious
belief, that if the destination reached is the result of a ˜random
walk™, how can it possibly express any purpose? Conway Mor-
ris, an evolutionary palaeobiologist who also worked on the
Burgess shales from which Gould drew so much of his mate-
rial, reached a different conclusion. Their opposing conclu-
sions are best summarised in their own words, beginning with
Gould. Thus: ˜This book is about the nature of history and
the overwhelming improbability of human evolution under
themes of contingency and the metaphor of replaying life™s
tape™ (1989, p. 51) and ˜Rerun the tape of life as often as you
like, and the end result will be much the same™ (p. 282). Gould
thought that, in the reruns, evolutionary history would never
repeat itself because chance was brought into play at every
Conway Morris, on the other hand, built his case around the
notion of convergence, according to which evolution is liable
to produce similar solutions to similar problems wherever
and whenever they occur. Towards the end of Life™s Solution
God™s chance 187
he says: ˜The principal aim of this book has been to show
that the constraints of evolution and the ubiquity of conver-
gence make the emergence of something like ourselves a near-
inevitability. Contrary to received wisdom and the prevailing
ethos of despair, the contingencies of biological history will
make no long term difference to the outcome™ (2003, p. 328).
Their interpretations imply radically different probabilities
for much the same outcomes. One or other of them must be
mistaken. If Conway Morris is nearer to the truth it is per-
fectly credible to suppose the chance and necessity of classical
Darwinism is suf¬cient to produce human life. If that is so, it
makes sense to suppose that God designed it that way. It makes
sense, also, to see God using chance to achieve a desired end.
We do not have to choose between equally well-supported
scienti¬c cases because, as noted in chapter 5, there is a fal-
lacy in the probability reasoning which Gould and others have
employed. Let us remind ourselves of Gould™s argument. He
begins Wonderful Life by debunking the idea that evolution has
been an inevitable progression by what he calls either a ladder
or a tree. In opposition to both of these pictures he wishes to
give full priority to chance, or contingency as he often calls
it. If we think of evolutionary paths as being possible routes
along which life might have proceeded, there will be a very
large number of branch points at which the path could have
taken one course or another. The probability of completing
any particular path is obtained by multiplying together the
probabilities associated with each junction, and if the choices
are independent, the product will be extremely small, so one
could assert that any repetition would almost certainly yield
a different route. I argued that the assumption of indepen-
dence was false and so the conclusion does not follow. Nev-
ertheless, there is one further thing which should have given
Gould pause for thought. If all the choices are indeed taken at
God, Chance and Purpose
random, perhaps Gould should have noted that the particular
path which was realised is the one which leads precisely to the
end-point which we occupy as sentient beings able to ask these
questions. If an event having an exceedingly small probability
actually occurs, we should at least ask whether that puts us
in a position to reject the hypothesis “ namely of random-
ness “ on which it was calculated. I have already discussed
in chapter 6 the logic of rejecting hypotheses that have very
small probability but shall not pursue it here because Conway
Morris™ objection to Gould™s argument is more fundamental.
Gould does not appear to have considered the matter of inde-
pendence at all, but Conway Morris did notice the problem by
recognising the ubiquity of convergence in evolution. Conver-
gence refers to the coming together of different evolutionary
paths. Gould supposed that this did not happen and that each
path reached an end-point which was distinct from all oth-
ers. Conway Morris™ book contains an extensive catalogue of
examples showing that this is not actually the case.
Before going into this I need to be a little more explicit
about what is meant by an evolutionary path. Such a path is a
full description of the biosphere as it has developed over time,
with any point on that path representing its state at a particular
time. Convergence occurs if several possible paths have things
in common. For example, small mammals living underground
live in similar environments and these exert selective pressures
to evolve similar characteristics “ for communicating, say.
Thus paths which hitherto had been quite separate, at a later
point may converge in this respect. Convergence may refer to
things as diverse as anatomical structure or social organisation.
The important thing is that the environment in which they live
poses challenges for the organism which are met in much the
same way. Usually we think of natural selection as favouring
the ¬ttest in terms of their ability to survive and thrive. In
God™s chance 189
bringing convergence into the picture we are recognising the
fact that the physical environment, including the presence of
other creatures, also plays an important part in who survives.
What matters, of course, is that humans or some similar
creatures should have recognisably human characteristics and
functions. According to Gould, and those who think like him,
the various paths will be so different that the appearance of
humans in our particular path would be purely fortuitous.
Conway Morris claims that the empirical evidence points in
the other direction. He thinks that the evidence shows that
the physical and other constraints are such that humans, of
some kind, are very likely to have turned up in our world or
in virtually any other universe, for that matter.
The suspicions raised by Gould™s assumption that pure ran-
domness determines the path of evolution have been amply
con¬rmed by Conway Morris™ impressive empirical evidence.
Things are very much more complicated than Gould sup-
posed. Conway Morris has not produced a tested probability
model to show that human life is an almost inevitable con-
sequence of a universe such as ours, but at any rate he has
demolished once and for all the attractive but ¬‚awed model of
contingent evolution.
It is possible to take a different line and to argue that evo-
lution by mutation and natural selection is God-guided, with-
out invoking the empirical support provided by evolutionary
convergence, and Keith Ward has done so in God, Chance and
Necessity (1996). Starting from essentially the same point as
Gould, Ward recognises that natural selection alone would
make the emergence of human life extremely improbable but,
as a theist, he sees no problem in supposing that God ˜weights
the probabilities™ in some way to ensure that evolution reaches
the desired destination. This might be by guiding the selection
of mutations in some way, though it must be remembered that
God, Chance and Purpose
most mutations are harmful, in any case. The logic of Ward™s
argument is unexceptional. If there is a God and if he desires a
human outcome to evolution and if he has power to in¬‚uence
natural processes in the world, as Ward claims he must, and if
chance and necessity are insuf¬cient by themselves then God
will surely act to do what is necessary. Ward puts it as follows:

It would be entirely reasonable to conclude that the hypothesis of
God “ of a cosmic mind which sets up the processes of mutation
so that they will lead to the existence of communities of conscious
agents “ is a much better hypothesis than that of natural selection.
For on the God hypothesis, the development of sentient life-forms
from simple organic molecules is very highly probable; whereas on
the natural selection hypothesis, such development is very highly
It is open to a theist to argue that natural selection plus the basic laws
of physics does make the development of sentient life-forms probable.
In that case, one could hold that God has designed the basic laws so
that, in the long run, in one way or another, conscious beings would
come to exist. One would see natural selection as the way in which
God works, without interference in the laws of nature, to realise the
divine purposes in creation. God would not be needed to explain why
natural selection moves in the direction it does, when it could easily
have moved in some other direction (or in no direction at all). But
God would still have an explanatory role, in providing a reason why
this set of physical laws exists, and in assigning a goal (of conscious
relationship to God) to the process of evolution.
For such a view, God and natural selection would not be competing
hypotheses. God would be the ultimate cause of the ¬nite causal pro-
cesses embodied in natural selection, but would not interfere in those
¬nite causal processes, as an additional cause. I am not happy with
accepting this otherwise attractive view. I am not convinced that the
principle of natural selection alone makes the emergence of rational
beings probable. (1996, p. 76)

Ward was writing without taking account of convergence
which, according to Conway Morris, makes the evolution of
God™s chance 191
sentient beings very much more likely. It is thus not necessary
to invoke the direct action of God at all.
Gregerson (1998)9 is another theologian who has looked
in a constructive way at the role of chance in the creative
process. He has introduced the term autopoietic process to
describe the way in which physical processes may develop
using a God-given propensity to move towards a God-
determined end. This is conceived as something less than full
self-determination but it still retains a role for God™s ongo-
ing involvement. This is conceived of as an in¬‚uencing of
the probabilities rather than the outcomes themselves. God
thus sustains and directs the process without its requiring his
detailed involvement. As with Ward, this view presupposes
that chance alone is not suf¬cient to achieve the desired end.
To some this indirect participation by God might seem
like a step backwards and to play into the hands of those
Darwinians who see no need for divine involvement at all.
This is just what advocates of Intelligent Design fear, and what
they are concerned to exclude by insisting on the necessity of
a Designer. However, evolutionary theists have a powerful
riposte to this move which is to agree that the natural world
does, indeed, show evidence of design but that its explanation
is much more remarkable. The God whom they worship not
only designed things the way they are but also designed and
brought into being the ˜machinery™ for making them! There
is no need to leave a glaring gap between the conception in
the mind of God and its execution in the world. The act of
creation is an elegant and, relatively speaking, simple way of
doing it all at once.

There were responses to Gregerson™s article by Rudolf Brun, by Richard

McClelland and Robert J. Deltet, and by Langdon Gilkey in Zygon 34 (1999):
93“115. Gregerson replied in the same issue of the journal (pp. 117“38).
God, Chance and Purpose
Ward is thus half right when he says:
There is no physical mechanism that produces such a bias. Yet it is not
left entirely to chance. It is the being of God, which alone sustains the
universe, that exercises a constant causal ˜top-down™ in¬‚uence on the
processes of mutation and natural selection, and guides them towards
generating sentience and the creation and apprehension of intrinsic
value. (1996, p. 83)

There is no physical mechanism “ there does not need to be “
but chance and necessity alone are suf¬cient to do the job in
exactly the way God intended.

the social order
Here I make an abrupt turn into the social world, not made
up of mindless elementary particles, but of sentient beings
with minds of their own. How can chance possibly arise in this
world, and if it could, what use could God possibly make of it?
The relationship of choice and chance is the subject of chapter
13. My intention here is to make a link between the ˜order out
of chaos™ of chapter 3 and the ˜choice and chance™ of chapter
13 which falls into the present discussion of how chance can be
used to attain desired ends. There is, in fact, an important link
between systems of particles behaving randomly and systems
of people exercising free choices. This link is the lack of control
of what is going on at the individual level.
In the ¬rst section of this chapter, where we were looking
at the generation of life-bearing planets, we did not assume
any immediate divine control over the natural processes out of
which planets arose. In the second section the focus moved to
the process of natural selection driven by random mutations
which, considered individually, expressed no purpose. Here
God™s chance 193
we have collections of people expressing their own individ-
ual purposes independently of any overall direction. What all
these systems have in common is that there is no control at the
micro or individual level in the case of human society. The
fundamental question is then whether the overall Designer
of those systems, having no detailed control, can neverthe-
less still achieve global purposes. If so, and we have seen that
it is so, there are enormous advantages to be gained. In the
evolution, whether of planets or people, there is an econ-
omy and elegance in the ˜production process™ which speaks
eloquently of the character of the Creator. In human affairs,
global purposes can be achieved at the same time as allowing
individuals their freedom. This is a truly remarkable situation,
the signi¬cance of which seems to have been largely lost on
We now come down to particulars. In chapter 3 we had a
hint of how collections of people acting independently might
exhibit some of the aggregate regularities we might other-
wise associate with collections of particles. When we move
on to choice and chance, in chapter 13, the similarities will
become more pronounced. Florence Nightingale was inter-
ested in aggregate social laws though, as we saw, she thought
they were divinely decreed in a very direct manner. There are,
however, many regularities in aggregate human behaviour
which result from something very like chance at the individ-
ual level. If that is so it follows that God would know that free
will at the individual level led to predictable consequences at
a higher level. Allowing free will into the scheme of things is
not, therefore, as risky as it might seem. Individual free will
may have bene¬ts to the individual “ valuable in themselves “
but also have secondary bene¬ts by achieving God™s will at a
higher level of organisation in society.
God, Chance and Purpose
An example10 may help to make the point. In many soci-
eties a person is free to leave their employment whenever they
wish, subject, perhaps, to giving appropriate notice. This is
one way in which individuals can exercise their personal free-
dom, yet a remarkable pattern emerges when we look at the
frequency distribution of lengths of service of many people in
the same type of job. The form of that distribution is not the
main point here but its shape is known as lognormal. Typically
there are a large number of relatively short lengths of service
and fewer longer lengths, with the frequencies tailing off into
the very long lengths of service. This means that it is possible
to plan recruitment and suchlike on the large scale with con-
siderable con¬dence. There is thus no reason to suppose that
God would not take account of such regularities in consider-
ing the global characteristics of social affairs. It is tempting
to go on and speculate on whether history, which is the sum
total of human activity, is determined rather as the gas laws
are, for example. Is it true that the free choices of individuals
acting at the individual level determine the general course of
history? Doubtless there are some broad features such as the
relationship between decisions to leave a job, and the general
characteristics of the labour market, which may indeed seem to
support that conclusion. However, such a conclusion would be
premature because there is one very big difference between
physical systems and social systems.11 This is the matter of
size. In any of the physical systems we have considered there
This is one of the oldest and best-known examples of a law-like phenomenon

in the social sciences. It goes back at least to 1955 and has been widely used
since in what is now called human-resource planning. See also the following
Adolphe Quetelet was the pioneer in the ¬eld of the scienti¬c study of

aggregate social phenomena (see above, chapter 8, note 2). The author™s
own contribution to this ¬eld is contained in Bartholomew 1982. Quetelet
coined the term ˜Social Physics™ and the similarity between the aggregate
God™s chance 195
may be billions or trillions of particles and it is in the regu-
larities they display that the aggregate order is to be found.
Social systems, on the other hand, may sometimes consist of
millions of people but thousands or, even hundreds are more
common. In such relatively small systems the emerging regu-
larities will be clouded by the uncertainties resulting from
the smaller numbers. There will, therefore, be a less clear-cut
boundary between the micro and macro aspects of the system.
Nevertheless, enough order may be retained over the global


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