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plete because it ignores alternative hypotheses. To the second
question the answer is also negative because the calculation
of the key probability is incorrect. The second failure could,
in principle, be put right even though the practicalities are
almost insurmountable. The ¬rst failure seems irredeemable
because, once we introduce alternative hypotheses, a circu-
larity in the argument for the construction of the critical set
becomes apparent. Dembski™s method is not, therefore, a valid
scienti¬c method.
c h a pt e r 8
Statistical laws



Do statistical laws offer space for God to act in the world? It is ¬rst
made clear that such laws are not represented primarily by probability
distributions but by the basic processes underlying them. One possi-
bility is that the laws are illusory in the sense that God is actually acting
in every event in a way that mimics chance. Another possibility is that
God acts only occasionally at particularly signi¬cant junctures. In this
case his purposeful action would be masked by the mass of genuinely
random happenings. It is concluded that neither explanation is satis-
factory and hence that God™s action is more likely to be seen in the
behaviour of chance happenings in the aggregate.



ro o m f o r go d ™ s ac t i on ?
From this point in the book onwards, chance plays a positive
role. It is no longer to be seen as a threat to theistic belief
which has to be ruled out, but as part of the richness of the
creation. In the present chapter I investigate whether so-called
statistical laws, which involve a chance element, offer a degree
of ¬‚exibility which might create the space for God to act
without disturbing the general lawfulness of the world. Having
dipped our toes into the water, so to speak, we shall move on
in the following chapter, to see whether the ideas carry over
onto the broader canvas of the quantum world.

116
Statistical laws 117
God™s possible action in the world is one of the most intrigu-
ing and dif¬cult issues for theologians who wish to pay due
regard to the way the world actually works. The subject has
spawned an enormous literature and it was singled out for
detailed study in the Divine Action Project (DAP), spon-
sored jointly by the Vatican Observatory and the Center for
Theology and Natural Sciences, Berkeley.1 This programme
brought together many of the most distinguished workers
in the ¬eld. It also included a series of conferences and ¬ve
main publications in the period 1988“2003. Its impact has been
assessed by Wesley Wildman in two articles in Theology and
Science (Wildman 2004 and 2005). The ¬rst paper provides
a summary and assessment of the project. The second deals
with a number of responses to the ¬rst article by several key
¬gures in the debate.
If the world were completely deterministic there would be
a rigidity which would require God to break laws in order
to change things. Statistical laws have been seen to offer the-
ologians a lifeline by providing room for God to manoeuvre
without challenging the overall lawfulness of the creation.
This seductive avenue is fraught with hazards and in this
chapter I shall begin to show why, by considering the sim-
plest kind of example. We begin with the question of how
God might keep a statistical law “ because the answer is far
from obvious. Only then shall we see what might be involved

This volume is perhaps the central reference in this ¬eld, including, as it
1

does, chapters by most of the major contributors to this subject (Russell
et al. 1995). Each of the chapters in Sections III and IV deals directly and
authoritatively with different aspects of the problem. The last chapter, by
George Ellis, is not only of interest in its own right, but also because he brings
together, and comments on, many of the earlier contributions, especially
that of Nancey Murphy.
God, Chance and Purpose
118
in breaking one or, more to the point, how one might take
deliberate action within such a law.

w h at, e x ac t ly, i s a s tat i s t i c a l law ?
This is the crucial question which must be answered before the
main issue can be addressed. At ¬rst sight it all seems quite sim-
ple. Ordinary, non-statistical laws are concerned with things
which specify unchanging features of the world. Ohm™s law,
the law of gravity and Newton™s laws of motion are all familiar
to us. For example, the current ¬‚owing through a resistor is
proportional to the drop in potential between the ends. In all
these cases the relationship seems to be the same everywhere
at all times. However, when referring to statistical laws, we
are often thinking of a single quantity “ not the relationship
between quantities. In the universe there are the so-called con-
stants of nature, such as the speed of light, which are all part of
what we mean when we speak of the lawfulness of the world.
A statistical law is then generally thought of as replacing the
¬xed quantity by a probability distribution. This distribution
speci¬es how the quantity varies by telling us how frequently,
relatively speaking, each different outcome occurs. Looking
at it theologically, one might suppose that God chooses the
form of the distribution but not necessarily the particular values
which occur and which, collectively, make up that distribution.
Keeping such a law might seem to be a very straightforward
matter. All one has to do is to continually check that values
are occurring with the correct relative frequencies. If any are
not, then all that is necessary is to top up those values which
are under-represented and to curtail those that are occurring
too frequently. That is evidently what Florence Nightingale
thought, as the following episode shows, but she was
wrong!
Statistical laws 119

f lo r e n c e n i g h t i n ga l e an d
˜ill-driven cabs™
Muddled thinking about the theology of statistical laws is
provided by an example relating to Florence Nightingale. She
was much more than ˜the lady of the lamp™ in the Crimea.
She had a lively interest in statistics and although failing in
her attempt to persuade the University of Oxford to establish
a chair in the subject, she bombarded the powerful of her
day with the ¬gures with which she hoped to persuade them
to make reforms. Her interests were extremely practical. She
thought that there were social laws and that their discovery
would enable them to be used to achieve good ends. If God had
made society lawful, she reasoned, it was up to us to discover
those laws and to use that knowledge for the betterment of
society. She wrote:
. . . of the number of careless women to be crushed in a given quarter
under the wheels of ill-driven cabs: were the number not made up
on the last days of the Quarter, we await (not with coolness, let us
hope) the inexorable law of Fate which “ always supposing the state
of Society not to be changed always ¬lls up its quota. (Diamond and
Stone 1981, p. 77;2 see also p. 337 of Part III)


The article by Diamond and Stone (1981) was entitled ˜Nightingale on
2

Quetelet™ and it was divided into three parts: I The Passionate Statistician,
II The Marginalia, and III Essay in Memoriam. Adolphe Quetelet was
the Astronomer Royal of Belgium who wrote a two-volume work enti-
tled Physique Sociale, published in 1869. This work was based on the idea
that society could be studied scienti¬cally in an analogous way to that in
which the physical world was studied in physics. Florence Nightingale was
passionately concerned with the quantitative study of society and, for her,
Quetelet™s work was vital. The article is based on Nightingale ™s copy of
Physique Sociale, presented to her by the author in 1872, and on a bundle of
her manuscripts tied up with the book in the British Library Department
of Manuscripts. The copy of the book contained extensive marginal notes.
God, Chance and Purpose
120
The ˜inexorable law of Fate™ was, of course, essentially an
example of a statistical law which, in this instance, governed
the number of young ladies falling under cab wheels. In fact,
it is very much the same as the archetypal statistical law gov-
erning the outcomes of coin tossing, to which we shall come
shortly: the correspondence is not exact but near enough for
present purposes. According to the law, the expected number
of such deaths in a quarter should then be approximately con-
stant from one quarter to another. This is the aspect of the
law which caught Florence Nightingale™s attention and which
could be found repeated in many of the tables available in
the publications of National Statistics Of¬ces. However, she
misunderstood the law as an iron rule of fate which demanded
such a number to occur. Thus she imagined that if as the end of
the quarter approached the numbers were falling short, then
more accidents would have to be engineered. Presumably also,
some brake would have to be put on their occurrence if the
numbers were mounting up too rapidly in the course of any
quarter. It is not unknown to ¬nd people thinking in the same
way today. But this is to get things back to front. The near con-
stancy of the numbers from quarter to quarter is a consequence
of an underlying statistical process, not an externally imposed
law. We shall see that if one wanted to in¬‚uence the death
rate, it is the independence between what happens on succes-
sive days and the probability of the happenings that would
have to be altered. If anywhere, God™s involvement must be at
the more fundamental level. This example makes it clear that
the characterisation of a statistical law as a probability distri-
bution may have been too hasty and I should re-trace my steps
and dig a little deeper.

The quotation reproduced here is purely illustrative of her views. Much
more could be gleaned from the article.
Statistical laws 121

s tat i s t i c a l laws : a d e e pe r lo o k
I start with a very simple example which is far removed from
the grand ¬nale of the next chapter, which centres on the quan-
tum uncertainties that some see as the prime arena for God™s
action. In a sense, I have already set off in the wrong direction
by referring to statistical laws in chapter 3 as frequency (or
probability) distributions but we can now begin to see that the
matter is more subtle. There we met the idea of a frequency
distribution, with a ¬xed shape, which described an aggregate
property of something like time intervals between radioactive
emissions. For a second pass I take what is, perhaps, the sim-
plest example of all. The main point I wish to make is that
frequency distributions which we may observe are not funda-
mental. What matters is the process by which the distribution
is generated and it is there that the law-like character is to be
found. This is the point which Florence Nightingale failed to
grasp and which is clari¬ed by the following example.
Many contests in sport, and elsewhere, depend on the toss
of a coin at the start to determine which team or competitor has
the initial advantage of going ¬rst, choosing end or whatever.
In the long run this is seen as fair because, on average, the coin
will fall one way half the time and the other way the other half.
In individual cases it may give an unfair advantage to one party
but in the long run such things will ˜average out™ as we say.
Just occasionally one side may get the advantage on several
successive occasions but everyone accepts that this is just ˜the
luck of the draw™ and that no one can be held responsible
for it.
There are actually several probability distributions asso-
ciated with coin tossing. To begin with, and most obviously,
there is that which is composed of the probabilities of heads
and tails respectively. With a fair coin these probabilities are
God, Chance and Purpose
122
equal so we can picture the distribution as consisting of two
˜lumps™ each of size 0.5 located at ˜head™ and ˜tail™ as illustrated
below.
The usual way of explaining God™s involvement in such
a sequence is to say that God chooses the probability, 0.5 in
this case, but leaves open the way in which that proportion
is achieved. This is where space is supposedly created for
particular actions by God without disturbing the overall dis-
tribution. If we were to collect the results of a large number of
tosses we would expect to get proportions close to 0.5 but the
order in which they occurred could be almost anything. The
problem with this statement is that it is not a complete speci-
¬cation of the statistical law involved. There are sequences
of heads and tails which yield a frequency distribution of the
right form but which are clearly not random; for example,
one in which heads and tails alternate. This is not the sort of
thing we see happening in tossing at the start of competitive
games, so something is clearly lacking in this speci¬cation. It
is that in coin tossing any toss is (has to be) totally independent
of all other tosses. A higher being attempting to conform to
such a law has more to do than merely ensure a roughly equal
number of heads and tails; they have to be randomly mixed
up as well.
A second law associated with the coin tossing process is
obtained by looking at runs. To determine the length of a run




Heads
Tails

Fig. 8.1 The frequency distribution of the two outcomes in a single toss of a
fair coin
Statistical laws 123




0 123456
Number of tails between successive heads

Fig. 8.2 The frequency distribution of run length in successive tosses of a
fair coin


of tails we count how many tails occur between successive
heads. In the following sequence:

HTTHTTTHHTTTTHHH . . .

The ¬rst run is two because there are two Ts after the ¬rst head
and before the second head; the next run is three and this is
followed by zero and zero again. The frequency distribution of
runs will look something like that given above with frequencies
declining in geometric progression. This is another statistical
law associated with the coin-tossing process.
These two examples of probability distributions arising
from the sequence do not exhaust the possibilities. Another is
obtained by dividing up the sequence into blocks of, say, four
outcomes each. In that case we could write our sequence as:

HTTH TTTH HTTT THHH . . .

We may then count the number of heads in successive blocks
which gives us the sequence: 2,1,1,3, . . . The frequency distri-
bution of these numbers, known as the binomial distribution,
is a further statistical law associated with the same process.
Such a distribution is illustrated in the ¬gure below.
God, Chance and Purpose
124




01234
Number of heads

Fig. 8.3 The binomial distribution of the number of heads in four tosses of a
fair coin

It should now be clear that these three laws are derivative
in that they are all consequences of the basic probability law by
which the series was generated, namely that successive tosses
are independent and each has an equal probability of produc-
ing a head. If we wish to speculate about how God might be
involved in all of this we have to look at both the probability
and the independence, not at individual distributions.

k e e pi n g an d b r e a k i n g s tat i s t i c a l laws
We may get more insight into what is involved in keeping a
statistical law and of breaking it by attempting to put ourselves
in the position of a deity trying to generate happenings accord-
ing to such a law. There are several possibilities depending on
what powers and objectives you have.
Imagine ¬rst that you are a lesser deity with responsibility
for overseeing the outcomes of sequences of coin tosses. Your
problem is how to decide the outcome of each toss. It is not
enough, as we have just seen, to ensure that heads and tails
occur in equal numbers. You also have to ensure that tosses are
independent. That means, for example, that any occurrence
must not depend on anything that has gone before in the
sequence. For example, the chance of a head must still be 0.5
whether it is preceded by one or a hundred heads “ though this
Statistical laws 125
may seem counterintuitive, that is exactly what independence
implies.
There is one very obvious way to meet this requirement “
by tossing coins or using some equivalent generating method.
Later we shall see how this can be done on computers using
pseudo-random numbers. This method ensures that the sta-
tistical law will be kept but it poses acute problems for the
deity whose job it is to see that other outcomes, consequen-
tial on the toss, are in line with the overall plans of ˜head-
quarters™.
But maybe such sequences are not generated by something
equivalent to coin tossing. It is certainly not how those who
emphasise the sovereignty of God would want to see it. For
them the deity in charge would have to make a decision about
every single outcome and, presumably, this would be done
in the light of its consequences for all other happenings in
the world to which it was connected. This might seem the
easy option as it gives you complete freedom in choosing the
outcomes. All that you have to ensure is that the aggregate
properties of what you have done conform to the requirements
of the random series. But this freedom is illusory and is not
easy to achieve as I now explain.

t h e d et e r m i n i s t i c o pt i on
The view that every single outcome is determined by the
deity poses very serious problems because it implies that God™s
determinate actions successfully mimic chance and at the same
time achieve other desired objectives. To give an idea of just
how dif¬cult this might be in practice, let us think through
the process of trying to construct a sequence of heads and
tails which had all the appearance of being random. Imagine
the deity considering the options in advance with the aid of
God, Chance and Purpose
126
a set of black and white counters strung out in a line (black
representing heads and white, tails, say).
To begin with there needs to be roughly the same number
of black and white counters “ out of several hundreds or thou-
sands, perhaps. They must not be laid out in any recognisable
pattern of course, because, if they were, the sequence would
certainly not be random. However, we know that having the
same number of black and white counters in an order which
appears random is not the whole story. Randomness implies
that what happens on any outcome has no effect on other
outcomes. In particular this means that every black counter
should be followed, equally often, by black or white. Similarly,
every time we ¬nd two blacks in succession there should be an
equal chance that the next outcome will be black. (There is a
marked tendency for people to think that the longer a run of
blacks, for example, the greater the probability that the next
counter will be white. Sometimes it is said that the ˜law of
averages™ requires it. It requires nothing of the kind.) So far I
have considered two blacks in succession but it is already clear
that it is quite hard to construct a series which has the charac-
teristics of a truly random series “ the reader who doubts this
is invited to try!
The real problem emerges when we recall that the object is
not merely to produce the appearance of randomness, which
is dif¬cult enough, but that each occurrence also has to trigger
intended happenings in the complex web of the world. Imagine
again that the deity surveys the sequence of black and white
counters he has laid out and then considers what events they
will trigger in the world at large. The second toss, maybe, leads
to some undesirable consequence, so he changes its colour
and ¬nds, perhaps, that the consequential outcomes are more
acceptable. But after he has done this a few times it begins to
appear that the original randomness has been compromised, so
Statistical laws 127
he goes back to the beginning and starts juggling the members
of the sequence to get a better overall ¬t. It is far from clear
whether this exercise of the deity™s considerable powers of
foresight will converge on an acceptable solution. To make
matters worse he realises that each choice creates a whole web
of consequences, some of which are desirable and intended
and others not. To show just how complicated things can
become, remember that this exercise began by contemplating
a series of coin tosses to decide, let us say, the choice of end in
a football match. All sorts of things depend on the outcomes
of football matches, outcomes which may be in¬‚uenced by the
winning of the toss. If they did not we would not be having this
discussion. For example, a disgruntled spectator might leave
the ground early in one case and be killed by a passing car
whereas in the other he would arrive home safely. These two
very different outcomes depend on the toss of a coin because
which team kicks off leads to two different games. The death
of that individual in the ¬rst game will have consequences for
his family. A child who would otherwise have been born will
not now be born and all the things that child might have done
will not now be done. A neighbour might be so affected by
the death that they turn to drink, or religion, with tremendous
consequences for their families, including such trivial things
as their decision to buy new shoes and the consequences that
might have for the commission earned by a shop assistant . . .
and so on. The rami¬cations are beyond our comprehension
in number and scope. The ripples from that simple toss extend
across the world and, maybe, to future generations. All of these
have to be taken into account by the deity, along with all the
consequences of the thousands of other tosses which fall within
his responsibility. Steven Strogatz (2003, p. 189) re¬‚ects in a
similar manner about the potentially profound consequences
of the order in which we do up our shirt buttons. He also notes
God, Chance and Purpose
128
that the imaginative possibilities have not been lost on ¬lm
makers, quoting the case of the ¬lm Sliding Doors,3 in which
there are radically different consequences for a woman™s life
depending on whether she gets through the sliding doors of a
departing underground train before they close.
The response that only God is big enough to encompass
all this and to choose the outcomes is too glib. The profound
theological question is not so much whether God could handle
the enormous complexity of the scenarios I have hinted at but
whether it is a God-like enough thing for him to be doing. We
return to the issue later and I do no more now than observe
that the deterministic option I have been considering poses
enormous complications which are often overlooked by those
who so easily adopt it.
The whole situation can, of course, be looked at the other
way round. Perhaps the sequence of heads and tails would have
to be a consequence of decisions taken on other grounds. Thus,
suppose that the decision of head or tail was based solely on
the desirability of the consequences which that choice would
initiate and that it just happened to turn out that the resulting
sequence was indistinguishable from random. What we would
have then would be something very close to the generation
of pseudo-random numbers which we have already met in
chapter 4. This possibility is certainly plausible but it does
not avoid the problem of the immense complexity of trains of
events triggered as the ripples spread outwards through the

This is not the only example of the use of randomness as a literary device.
3

The use can be more explicit as when the roll of the die is actually supposed
to determine future outcomes. Luke Rhinehart wrote his novel The Dice
Man in the 1970s and has followed it up with other works in the same
vein, including plays and television adaptations. The English opera singer
Lesley Garrett claimed that reading The Dice Man changed her life (The
Independent, 18 November 2006).
Statistical laws 129
web of possibilities. But even if this were the case, the statistical
law in question would be the indirect consequence of all these
other decisions and not the primary law.
It is worth pausing to re¬‚ect for a moment on the situation
into which we shall have argued ourselves if we adopt this
position. In effect we are saying that the outcome of the toss
in a football match may be determined by the effects, long
term and short term, which that insigni¬cant happening will
have on the future of the world. Is that really credible? It
has to be, if we follow the logic of supposing the world to
be determined, in every detail, by an all-powerful and all-
knowing deity. Before committing ourselves to such seeming
absurdities, perhaps we should examine another option.

o c c as i ona l i n t e rv e n t i on
This is, in fact, the third strategy to consider. The ¬rst, remem-
ber was to leave it all to chance, which seemed to leave little
opportunity for God to act at all. The second, the determin-
istic option, seemed almost to strangle God in the complexity
of his own creation. The third seeks to obtain the best of both
worlds by combining a modest amount of direct action with
a large dose of genuine randomness. In this third scenario
there are many genuinely random happenings and, most of
the time, the deity in charge has no more to do than to sit back
and delight in the variety of the creation. On the rare occa-
sions when intervention is necessary there will be nothing to
give away the fact that intervention has occurred. Any actions
are obscured by chance. This is because there is always some
variation in the aggregate results of random processes such
as coin tossing. Although about 50 per cent of all tosses are
heads, the actual number will vary. It is this variation which
conceals any intervention. Since the law of coin tossing does
God, Chance and Purpose
130
not specify exactly how many heads will occur, there is no way
of detecting the intervention provided that that action is a rare
occurrence. One might note, cynically perhaps, that this strat-
egy escapes all criticism on strictly scienti¬c grounds because it
is empirically undetectable. The occasions of intervention are
suf¬ciently rare for them not to disturb the regularity required
by the statistical laws governing them.
However, this strategy is not without its problems, over and
above that of wondering whether acting somewhat furtively
under cover of randomness is a God-like thing to do. It still
has to be possible for God to determine the points at which
to intervene in the light of the consequences. These, as the
illustrations used above showed, are extremely complicated
and may not be universally bene¬cial. The real point at issue
is whether it is actually possible to achieve suf¬cient control
by intermittent intervention. Again, the glib answer that an
all-seeing, all-knowing God can take such things in his stride,
whereas mere mortals see only impossibilities, must reckon
with the fact that even God cannot do what is logically impos-
sible. And in this case we have no idea what can be achieved by
occasional interventions in vastly complicated systems. Nev-
ertheless we must allow this third strategy as a possibility,
since it cannot, as yet, be categorically ruled out.
None of these three strategies offers a clear view of how
God might act in the world in the space created by statistical
laws. His total involvement in a deterministic world offers
theological attractions to some but it is far from clear whether
it would work. The same objections apply if the coin tosses
are made purely in the light of their consequences. Occasional
intervention is a possibility, but again, it is not clear whether
or not it would work. Leaving it all to chance, as in the ¬rst
strategy, deliberately rules out action in individual cases and
so offers no help. I tentatively conclude, therefore, that the
Statistical laws 131
original hope that statistical laws would provide an opening
for God™s action was ill-founded.

r a d i oac t i v e e m i s s i on s r e vi s i t e d
The reader may feel that a great deal has been built on this sin-
gle coin-tossing example, so, to reinforce the main message, we
return to the case of radioactive emissions striking a Geiger
counter. This will underline the importance of the primary
process rather than any frequency distributions derived from
it. Remember that the process involves the occasional emis-
sion of particles from a radioactive source. A record of such
a process could be made in several ways but one of the most
obvious is to record the times at which emissions occur. There
are several probability distributions associated with such pro-
cesses, each of which might be described, inaccurately as we
now know, as a statistical law.
Another way is to construct the frequency distribution of
time intervals between events. As noted above, this follows
what is known as an exponential distribution, whose shape
was illustrated in ¬gure 3.1 (see p. 35). This exponential law
does not fully determine the process as we can see if we try to
use it to reconstruct the process. How would we do it and how
might God do it? One way which might occur to us is to take
a set of intervals whose distribution has the exponential form.
We could place the intervals end to end and we would then
have a series which conforms to the statistical law in the sense
that it has the right frequency distribution. But a moment™s
thought shows that the distribution does not capture all that
is implied by having a random series. Suppose, for example,
that we began the series by starting with the shortest interval
and then followed it with the next shortest, and so on. Clearly
the result would not be a random series. In a truly random
God, Chance and Purpose
132
series the lengths would be all mixed up. This is because it is an
essential feature of the random process that its future devel-
opment does not depend upon its history. Given the proposed
series we would be able to predict, at any stage, that the next
interval in the series would be larger than all its predecessors.
No such prediction should be possible. We might, therefore,
go back and arrange the intervals in a random order to capture
that particular aspect of the basic idea, which would certainly
give us something much nearer to the truly random series.
However, there would be more subtle differences even after
both of these steps had been taken. For example, no ¬nite set
of frequencies would conform exactly to any distributional
form. If the correspondence were too close, suspicions would
be raised about whether it was too random. But this seems
a complicated way of producing something which was sup-
posed to be without any law or pattern. The similarities with
the coin-tossing example are clear, even though one process
is taking place continuously in time and the other discretely.
The exponential distribution reveals one aspect of the pro-
cess. Other aspects are revealed, for example by the Poisson
distribution as we saw in chapter 3.

laws o f g e n e r at i on
I have concluded that the lawfulness which is exhibited in what
are widely, but somewhat misleadingly, called statistical laws
is actually a manifestation of the underlying processes which
generate the distributions. In the two examples considered
above, these processes are best described by the constancy
of a probability, or a rate, and by independence. These two
aspects speak of a ˜hands-off™ approach to control rather than
the expression of purposeful activity. If that is so, any purpose
which they express must be via the aggregate properties of
Statistical laws 133
the system. In that case one only has to ask how a deity might
generate something which bears all the signs of being left to its
own devices. By far the easiest way to construct a truly random
process is to use some kind of pseudo-random generator which
is available on most computers. Although this would not be
strictly random, it would be as close as makes no difference.
In an important sense this is the simplest possible method.
It does involve a constant striving to come as close to some
ideal as possible. It follows that if there is a method so simple
and elegant, it is surely the method God would use. There is
nothing to be gained by imagining that even God, by taking
thought about the timing of the occurrence of each event,
could do any better. If there are to be random processes in
the world to serve useful purposes, the creation of them needs
to be in God™s repertoire. There is then no need for him to
be concerned with happenings at the individual level. All that
matters is their behaviour in the aggregate.

m o r e on laws
Theologians often speak as though God decided upon the
laws of nature, meaning that he decreed, for example, that
the attraction between two bodies should vary inversely as
the square of the distance between them. Each body in the
universe is thus thought of as being endowed with properties
which ensure that it obeys the prescribed law for ever. It
is this lawfulness which is often claimed as a sign of God™s
involvement.
But, as was observed in chapter 3, there is another way in
which people think about ˜laws™ according to which God is
thought of as enacting laws, which have to be obeyed. It is
worth noting, in passing, that miracles present no insuperable
problem if we think of laws in this way. If God can make laws
God, Chance and Purpose
134
in the ¬rst place he can surely alter them, or even suspend
them, for his own purposes. It is not at all obvious that this is
the way to think about laws of nature. It certainly does not sit
well with our focus on the basic underlying processes which
generate the so-called statistical laws. We know that these laws
emerge at the aggregate level out of lawlessness at the lower
level.
To pursue the matter a little further, suppose that ˜in the
beginning™ there was total chaos (a formless void as the book
of Genesis puts it) at the micro level. Is it then conceivable
that all laws, which we experience at a much higher level,
are basically statistical? A positive answer could be viewed
theistically or atheistically. The atheist might say ˜I told you
so. It needs absolutely nothing to create a lawful universe. It
just could not be any other way. There is always order in chaos
if only we look at the right level. It is not necessary to invoke
a God as everything we observe could happen without one.™
The theist might counter by saying ˜what could be more
elegant than to conceive and get going such a simple and
beautiful system? A universe which makes itself. A universe
burgeoning with potential. Surely God could have done no
other.™
It certainly does not seem to me that all laws have this
statistical character, but there may be an inevitability about
them which we have failed to detect. There may be some-
thing necessary about them so that not even God could have
decreed them otherwise. Perhaps the laws with which we are
so impressed are inevitable consequences of the very nature of
things and that to expect them to be otherwise would involve
a logical contradiction somewhere.
The manner in which order can arise out of chaos is a many-
sided thing and it has already been explored in some detail in
chapter 3. In chapter 4 it was noted that it is also true that most
Statistical laws 135
chaos, in the technical sense, is generated deterministically;
that is according to some rule or formula. It would be unwise
to conclude prematurely that, at bottom, the world is either
random or deterministic. What we do know is that we are
in a situation in which random behaviour at the micro level
produces order at the macro level and where determinism at
the micro level generates apparent randomness at the macro
level.
In this chapter I have only scratched the surface of how
God might control, or in¬‚uence, things through the ¬‚exibility
which chance offers. The world is full of probability distribu-
tions and I have considered the possibilities offered by only
one. Quantum theory sees things on the grand scale and it is
on this stage that most participants in the science“theology
debate wish to play their parts. In the following chapter we
shall see how far the ideas developed here carry over to that
wider arena.
c h a pt e r 9
God™s action in the quantum world



Quantum theory provides the most fundamental account of the phys-
ical world and it is at that level, one might suppose, that the roots of
God™s action would be found. The fact that the theory is probabilistic
leads to the hope that the uncertainties present will provide enough
room for God to manoeuvre. The conclusion of this chapter is that this
hope is too optimistic for very much the same reasons as those used
in the simpler cases treated in chapter 8. It is argued that the transi-
tion from the superimposed states of the theory to the single observed
states is most naturally explained by expressing the problem in terms
of conditional probabilities.1

a s tat i s t i c a l a p p roac h
How God acts in the world, I repeat, has become one of the
most discussed questions in the science and religion ¬eld “ and
beyond. As yet, there is no satisfactory answer to that question.
This conclusion has been illustrated in the last chapter, on
the small scale and on a restricted front. Now we view the

My disclaimer in the preface applies with particular force in this chapter.
1

Quantum theory is a highly technical subject and an area where a ˜little
learning™ may be a particularly dangerous thing. Nevertheless if God does
act at that level, it is important that non-specialists try to understand what
is going on. Some theologians, notably Keith Ward and Nancey Murphy,
have attempted to engage with quantum physics, and this contribution is
offered in the same spirit. Quantum theory is probabilistic and that provides
the point of entry for a statistician.

136
God™s action in the quantum world 137
problem on a larger canvas to see how the conclusions reached
there survive when they are translated to global, or even,
cosmic dimensions. If we ¬nd that the conclusions of the last
chapter carry over, there is little more to be said. However,
the transition from the simple and idealised world of the last
chapter is not automatic, because it is not clear whether the
quantum world is probabilistic in the way that I have been
supposing hitherto.
As noted in the last chapter, the most sustained treatment
of the subject at a general level has been made by the Divine
Action Project (DAP), which enabled many of the most dis-
tinguished workers in the ¬eld to collaborate over the period
1988“2003. In contrast to this collective contribution and, in
some respects, in opposition to it, there is the major contribu-
tion of Nicholas Saunders in Divine Action and Modern Science
(Saunders 2002).
This present contribution cannot be easily located within
the framework established by the DAP and its aims are very
much more limited. Our course has been set by our approach
through the treatment of statistical laws in the last chapter,
where I emphasised the importance of the underlying process
which generates the laws. We approach the subject using the
distinctive (possibly distorting) lens provided by the statisti-
cal/probabilistic way of viewing the world.

q uan t u m t h e o ry
The most fundamental account of nature is provided by quan-
tum theory, which deals with the behaviour of matter at the
level of electrons and other basic particles. The theory involves
uncertainties and these seem to offer a way of seeing how
God might act, out of our sight so to speak, to control what
happens in the world. It is the fact that there appear to be
God, Chance and Purpose
138
irreducible uncertainties at the heart of nature which gives
the subject its place in this book. If nature were determinis-
tic to its very roots, it would be very dif¬cult to ¬nd a place
for what Saunders (2002) and others call special divine action
(SDA). Particular acts of God, such as miracles and speci¬c
answers to prayer, would then require something quite dras-
tic, for example the suspension or alteration of laws of nature.
In such a deterministic world everything is pre-programmed
and things work themselves out according to the inexorable
logic of the machine. But in a world of uncertainties there may
be some room for manoeuvre. Perhaps there is more hope of
¬nding room for God to act if we allow for the probabilistic
character of nature as described by quantum theory.
I must begin by saying something about quantum theory
itself and why it might seem to be the arena, in part at least,
for God™s action. Classical mechanics is concerned with how
things work on the human scale “ with projectiles, cars and
billiard balls, for example. It has been very successful in under-
pinning modern engineering and owes a great debt to Isaac
Newton, with whose name it is often linked. However, if we
move to things which are very small it is found that the world at
that level does not conform to the prescriptions of the classical
methods. Attempts to describe electrons and other entities at
that level by classical methods do not work. This means that
what happens at that level does not ¬t in with our intuition,
which is based on the macro world in which our understanding
is formed.
Quantum mechanics provides the mathematical machin-
ery to handle what goes on at the atomic level. It was one
of the great intellectual achievements of the twentieth cen-
tury and has proved remarkably successful in dealing with the
world as it is when observed at what I shall loosely call the
micro level. Readers who wish to learn more might well begin
God™s action in the quantum world 139
with John Polkinghorne™s The Quantum World (Polkinghorne
1984) or with the introductory articles available on the World
Wide Web. For example, Wikipedia, the online encyclopaedia,
has several relevant articles at http://en.wikipedia.org/wiki/
Quantummechanics, which links to other similar articles
including one on the ˜Interpretation of quantum mechanics™.
The interest of quantum mechanics, for present purposes,
lies in the fact that it is a probabilistic theory and it is this fact
which offers a toehold for the theologian. If certain happenings
are unpredictable they may provide scope for God™s action.
Some theologians, in fact, think that all of those (potential)
happenings must be within God™s immediate control.
It is necessary to emphasise that quantum theory is deter-
ministic in one important sense. A quantum system is repre-
sented in the theory by something called the wave function. In
relation to a particle this enables the probability of its being
found at any particular location to be determined. In other
words, it does not tell us exactly where the particle is, but how
likely it is to be found at any location. Its position is, essen-
tially, described by a probability distribution. A basic equation
of quantum theory tells us how this probability distribution
changes over time. There is nothing uncertain about this. It is
a deterministic differential equation not so very dissimilar to
those differential equations which chart the development of
deterministic systems at the macro level. If all we want to do
is map the future of a system in terms of probability distribu-
tions of the quantities of interest, chance does not come into
the picture.
Quantum systems include things which are called ˜observ-
ables™, which, as their name indicates, can be observed, indi-
rectly at least. This means that they can be made to trigger
an observable event such as the clicking of a Geiger counter.
What we observe is not the probability distribution but a value
God, Chance and Purpose
140
sampled at random from the probability distribution. That is
a statistician™s way of putting it. In the language of quantum
physics it is spoken of as the collapse of the wave function or
wave packet. (The precise meaning of this is important and
we shall come back to it later.) What we actually observe is
something which tells us, for example, whether the spin of an
electron is ˜up™ or ˜down™. The underlying theory will only
tell us that it is up with a certain probability and down with the
complementary probability. This is described by physicists as
the ˜superposition™ of the two states; in statistical parlance it is
a mixture. The act of observation selects one of these options
with the speci¬ed probability.
It is only at this ¬nal stage that chance enters. The selection
appears to be entirely at random. That is, there is nothing that
we could possibly observe which would help us to predict the
outcome. If God acts at all at this level, the argument goes, he
must determine, or at least in¬‚uence, these outcomes.

go d ™ s ac t i on at t h e q uan t u m l e v e l
Many theologians and sympathetic scientists have seen the
attractiveness of locating God™s action in the world at the quan-
tum level. This may be due partly, at least, to the dif¬culty of
seeing how God could act on any larger scale in the physical
world. But more important, perhaps, is that a comprehensive
theology requires an account in which God is not excluded
from any part of his creation. Since what happens at this level
is not entirely predictable it is natural to ¬ll the causal gap
with the action of God. Although this is an attractive propo-
sition, its explication is fraught with dif¬culty, as we shall see
shortly.
The general problems of assuming that God acts at the
quantum level have been clearly documented by Saunders
God™s action in the quantum world 141
(2002)2 among others. Brecha (2002), in particular, writing as
a practising scientist, thinks that the room for God™s action at
the quantum level is less than some theologians believe. The
tendency of some to treat quantum theory as a metaphor fails to
come to grips with the realities of the situation. The crux of the
problem, as I hinted above, is that there are several competing
interpretations of quantum theory. Polkinghorne (1984) dis-
cusses four interpretations and Saunders seven. These inter-
pretations are all consistent with the scienti¬c evidence, so
there is no means by which we can know how things ˜really
are™. And if we do not know that, it is hard to see how a sin-
gle theological account can cover all possibilities. The issue
is sometimes prejudged by speaking of ˜quantum events™ as
though they were realisations of laws expressed by proba-
bility distributions. It is not even known whether the real-
ity which quantum theory describes is, in fact, probabilistic;
some accounts are deterministic and thus offer no foothold
for theistic involvement. Among those on the deterministic
side, Einstein was very reluctant to accept that chance is a
real element of the world at this level. Others, such as David
Bohm,3 have also sought to ¬nd deterministic explanations of
the formalism. These often seem rather contrived but, if they
are correct, there would be no place for God™s action under
the guise of chance.

In addition to his book, Saunders wrote an article entitled ˜Does God cheat
2

at dice: divine action and quantum possibilities™ (2000). This anticipated the
publication of the book referred to in the text. It was followed, in the same
journal, by the paper by Brecha (2002) and a direct response from Ward
(2000) taking issue with Saunders™ interpretation of what he had said in his
book Divine Action (Ward 1990).
David Bohm (1917“92) was a distinguished, if unusual, physicist who chal-
3

lenged the conventional understanding of quantum theory. He proposed a
non-local deterministic theory to account for quantum behaviour. Hodgson
(2005) also favours interpretations of a deterministic kind.
God, Chance and Purpose
142
Two questions now arise, one theological and the other
scienti¬c. Is it reasonable to suppose that God could act at
the quantum level? And secondly, if he could, would this be
an effective way of in¬‚uencing what happens in the macro
world? The two questions are closely bound up together and
the second is critical because it is hard to see why God would
want to use an approach which was not effective. Roughly
speaking, happenings at the quantum level can make them-
selves felt at the macro level in one of two ways. First, and
predominantly, they contribute to the average effects of the
large ensembles of particles. Secondly, a micro event might
trigger a sequence of causally linked events which produces
something detectable at the macro level. Furthermore, we
know of one way, at least, in which this can be done. Chaos
theory shows how the outcome of a deterministic, non-linear
process may depend critically on the initial conditions. In this
way, a micro happening may be suf¬cient to produce macro-
scopic changes. In principle, therefore, it might be possible to
˜steer™ things in the way the Designer wished.4 It is, however,
far from clear whether this would actually work in practice,
given the enormous complexity of the world.
One of the most puzzling things about quantum theory is
the seemingly paradoxical effect of making an observation.
Before observation, the situation is described by what physi-
cists call the superposition of several events. After the obser-
vation is made, one of those events is realised. How does this
come about? The story of Schr¨ dinger™s5 cat was constructed
o

It is too readily assumed that any gap which is revealed in the causal nexus
4

at the quantum level could be exploited by the Deity to achieve any desired
outcome in the world. I am not aware of any attempt to map out the
possibilities.
Erwin Schr¨ dinger (1887“1961) shared the Nobel prize for Physics with Paul
o
5

Dirac in 1933. He succeeded Max Planck in Berlin in 1927. He left Germany
God™s action in the quantum world 143
to highlight the paradox. Looking at it from a statistical per-
spective, it does not seem quite so paradoxical after all.

¨
a s tat i s t i c i an ™ s vi e w o f s c h r o d i n g e r ™ s c at
Quantum mechanics, as I have noted, provides an excellent
means of calculating the behaviour of systems at the level
of elementary particles. The problem of interpretation is con-
cerned with what reality is actually like at that level. As already
noted, it is impossible to picture it in terms of the macro world
with which classical mechanics deals. This does not matter if
all we wish to do is make calculations, but if we wish to see
how God might act at the micro level, it becomes of central
importance. Quantum theory describes the micro world in
terms of what are called superpositions, that is, mixtures of
states, but when an observation is made only one component
is actually observed. How the process of observation reduces
the mixture to a single component has been something of a
conundrum. The story of Schr¨ dinger™s cat was invented to
o
help to elucidate the problem.
Probability is central to quantum theory and this provides
the point of entry for a statistician. Statisticians regularly han-
dle situations where the formalism is much the same, and it is
interesting to see how the switch to another language alters
the perspective if not the substance.
The state of affairs in the micro world is given by the
wave function. As Max Born showed, this can be interpreted
in probabilistic terms by telling us, for example, how likely
a particle is to be found at different locations. In contrast

on Hitler™s rise to power and subsequently held various appointments until
taking up his ¬nal post at the Institute for Advanced Studies in Dublin, from
which he retired in 1955.
God, Chance and Purpose
144
to classical mechanics, we can thus only make probabilistic
statements about location. Shr¨ dinger™s equation describes
o
how this wave function changes over time. The way that the
probability distributions change over time is thus entirely pre-
dictable. Thus far in the argument, there is no unpredictability
in which God™s action might be cloaked.
Chance enters at the point where observations are made. I
have already noted that it is possible to observe things at the
macro level which indicate what is going on at the micro level.
As an example, I took the case of an electron passing through
a magnetic ¬eld so that its path will be diverted in one of two
directions according to whether its spin is up or down and the
new path of the electron can be detected by placing a Geiger
counter so as to intercept the particle. We do not actually
observe the spin itself but some consequences of it which are
detectable at the macro level. It is here that the nub of the
matter lies. All that quantum theory tells us is that the spin is
equally likely to be up or down. The state of the electron is
then said to be a superposition of the two states “ up and down
but we can only observe one of them. But how and where does
this happen? This is where Schr¨ dinger™s cat comes into the
o
picture “ not to solve the problem but to highlight what it is. In
the quantum world superpositions (mixtures) can exist; in the
world of observables they cannot. In some mysterious way, it
seems, the act of measurement turns the mixture into one of
its components. Let me restate the problem, as Schr¨ dinger
o
did, in terms of the cat.
One can even set up quite ridiculous cases. A cat is penned up in a
steel chamber, along with the following diabolical device (which must
be secured against direct interference by the cat): in a Geiger counter
there is a tiny bit of radioactive substance, so small that perhaps in
the course of one hour one of the atoms decays, but also, with equal
probability, perhaps none; if it happens, the counter tube discharges
God™s action in the quantum world 145
and through a relay releases a hammer which shatters a small ¬‚ask of
hydrocyanic acid. If one has left this entire system to itself for an hour,
one would say that the cat still lives if meanwhile no atom has decayed.
The ¬rst atomic decay would have poisoned it. The psi function for the
entire system would express this by having in it the living and the dead
cat (pardon the expression) mixed or smeared out in equal parts. It is
typical of these cases that an indeterminacy originally restricted to the
atomic domain becomes transformed into macroscopic indeterminacy,
which can then be resolved by direct observation. That prevents us
from so naively accepting as valid a ˜blurred model™ for representing
reality. In itself it would not embody anything unclear or contradictory.
There is a difference between a shaky or out-of-focus photograph and a
snapshot of clouds and fog banks. (Schr¨ dinger 1935, trans. Trimmer)
o

Immediately before the box is opened we do not know
whether the cat is alive or dead. It is equally likely to be in
either state. In quantum terms its state is a superposition of the
two states alive and dead but when the box is opened, it is only
possible to observe one of the constituents. How does the act of
observation resolve the mixture into one of its components?
The wave-function description is, in this case, a mixture of
two states with probability one half associated with alive and
the other half with dead. After observation it is reduced to a
single point “ all of the probability is loaded onto one state.
This is referred to as the ˜collapse of the wave function™ or the
wave packet. The wave function has been changed in form, it
appears, by the act of observation. How can this be, and does
God have any hand in it?
At this point I shall retrace my steps and recast what has
been said in terms more familiar to a probabilist or statistician
as set out in chapter 5. The crucial point to remind ourselves
of is that, in technical terms, a probability is a function of two
arguments. In non-technical terms this means that the proba-
bility in question depends on something that we already know.
An example will illustrate what is meant. The probability of
God, Chance and Purpose
146
throwing a six with a fair die is 1/6. But if you are given
a doctored die, on which the one has been changed into a
six, the probability will be raised to 1/3. If you tossed this
die without bothering to inspect it you would, justi¬ably, say
that the chance of a six is 1/6. But if, after inspecting it, you
see that there are two faces showing six, this new informa-
tion would lead you to revise your probability. The proba-
bility thus depends upon what you already know. Again, a
life table will give the probability that a ¬fty-year-old man
will be dead before reaching the age of sixty, and insurance
companies base their policies on such information. However,
if a medical examination reveals that the man has cancer of
the liver, the probability will be changed because of that extra
information.
Ideally the notation we use for a probability should include
a statement of what is assumed to be known. In practice this is
often omitted because it is assumed to be understood. Things
which are ˜understood™ are easily overlooked, but here we
must make them explicit. The probability of the up and down
alternatives is understood to be a half in each case. This can
be empirically veri¬ed by making a large number of obser-
vations and verifying that the two alternatives occur equally
often. This equality is something which applies to electrons in
general and must be presumed to apply to those we are about
to observe, in particular. When we pass the electron through
a magnetic ¬eld, we acquire some new information “ in which
direction it is diverted. The probability that its spin is up or
down is changed by having this extra information. It becomes
one for up, if up is what we observe. The collapse of the
wave packet is thus marked by the transition in the probability
resulting from the acquisition of extra information.
In general, the acquisition of any relevant information
changes the probability distribution. But how and when does
God™s action in the quantum world 147
this happen? This is the problem the cat example is designed
to clarify.
So to answer these questions let us return to Schr¨ dinger™s
o
cat. Just prior to the box being opened our state of knowl-
edge about the cat is the mixed probability distribution which
assigns equal probabilities to each state. When the box is
opened we discover whether or not the poison was released.
If it was, the cat will be dead. Our initial two-point distribu-
tion (dead or alive) collapses onto one of them. The relevant
probabilities now become those conditional on our knowing
what has happened while the box was shut. In general a total
or partial collapse of the wave function is caused by the acqui-
sition of new information. Where, then, is the wave function
and where does its collapse take place? The answer is “ in
our heads. The wave function is a mental construct embody-
ing what we know about the system. This explanation is not
new of course; in fact it was the explanation that Max Born
favoured and it follows simply and obviously from interpret-
ing what is going on in probabilistic terms. It is also the ¬rst
of the four possible interpretations which Polkinghorne gives
in The Quantum World (1984, p. 63). However, he promptly
dismisses it (noting in passing Max Born™s adherence to it) on
the grounds that it reduces the august and objective science of
physics to a branch of psychology. Presumably this is because
a mental construct in an individual™s head does not seem to
have the hard reality of a feature of the real world. This view is
based upon a misunderstanding of what is intended. The fur-
ther knowledge provided by the viewing of the contents of the
box is not a private subjective thing; it is publicly available. It is
part of what is given to anyone who chooses to make the obser-
vation. The idea is not unfamiliar in other ¬elds of application.
For example, calculation shows that the conditional probabil-
ity that a person immunised against in¬‚uenza will succumb is
God, Chance and Purpose
148
smaller than the unconditional probability that someone not
immunised will contract the disease. The incorporation of the
knowledge that immunisation has taken place does not make
epidemiology a branch of psychology. Conditioning may, of
course, introduce a subjective element into scienti¬c report-
ing. For example, if the results of the cat experiment are not
directly observed but reported by an intermediary, there will
be two bits of information to be incorporated into the col-
lapsed probability calculation. First, there will be the factual
report that the cat is alive, say. Secondly, there will be the
intermediary™s reputation for telling the truth. The latter part
is a subjective matter which may mean that different reporting
will lead the wave function to collapse on different values. But
if the evidence of the cat™s state is open to general observation,
the subjective element becomes swamped by the common core
of truth.
This leaves the question of when the actual collapse takes
place. For any individual it must happen when the information
is received and processed. There is, therefore, no unique time.
It cannot, however, be earlier than the event which triggers
the death of the cat. If there is a radioactive emission, then
the time of its occurrence determines everything. This will be
either when the emission takes place, or when it fails to happen
(that is, at the end of the period). In the standard discussion
of these things, the making of the observation is spoken of as
the act of measurement. Since measurement takes place in the
macro world, it can only take one of the two superimposed
values. In the case of the cat, the opening of the box is the act
of measurement which yields one of the observations alive or
dead. A statistician would use different terminology “ which
does not change anything “ but it does somewhat modify the
strangeness of saying that the act of measurement brings about
the collapse.
God™s action in the quantum world 149
Prior to observation our state of knowledge is summarised
in a probability distribution. Afterwards, we have a value from
that distribution. It is as though, at that moment, we draw a
sampleatrandom.Inthisperspectivethecrucialactistherefore
one of random sampling. In the jargon of probability theory
the characteristics of an electron, say, before observation, are
described by random variables.6 Such a variable is not regarded
as a single number but consists of a set of numbers, each having
a probability associated with it. Drawing a sample is thus a
matter of selecting one of those values with the associated
probability.
What is going on may be looked at in a slightly different
way, of which Einstein evidently approved. According to this
view, what quantum theory describes is not a single process
but an aggregate, or ensemble, of processes. It does not tell us
which one is the case at the moment we choose to observe it.
Because we can only observe one particular value of anything
we set out to observe, rather than a mixture, our sampling
mechanism is a method of making a random selection. The
act of measurement is an act of sampling.
If this interpretation is correct, the best account we have of
the micro world is no better than a probability representation.

The notion of a random variable is fundamental in probability theory. In
6

algebra, letters or other symbols are used to represent numbers. We are
used to the idea of replacing symbols by numbers in a formula in order to
obtain the numerical value of some quantity. For example, there is a formula
which tells us what temperature on the Fahrenheit scale corresponds to a
given temperature on the Celsius scale. Knowing the Celsius temperature
enables us to calculate the corresponding Fahrenheit value. Probability
theory deals with quantities which do not have a single value but may take
different values, each with known probability. When a symbol representing
a random variable appears, it does not represent a single value but a set of
values. It may help to think of an associated probability mass ˜smeared™ over
the set of values giving different weights to each.
God, Chance and Purpose
150
Whatever might be involved in the selection of these partic-
ular observed values, this does not affect the description of
the world at large, provided by the wave function. In statis-
tical terms, therefore, nothing is changed. The macro world
goes on just as before on the back of the micro-level pro-
cesses. Making observations breaks through the probabilistic
fog at one particular point but it does not change the world. A
few observations by a few people on this particular planet do
not change how the world was “ and is. Measurement does,
however, increase our knowledge of little bits of the world.

t h e o lo g i c a l i s s u e s
Where does God come into all of this?7 Does he observe
everything and thus sample everything that is going on in
the whole universe? If he did, he would simply have the total
aggregate picture of the world, which would be the statistical
version of what we describe in terms of random variables and
probabilities. A simple example may make the matter clearer.
If we measure the lives of a few dozen electric light bulbs we
may notice that the frequency distribution of their lifetimes
has a shape close to the normal, bell-shaped, curve which we
met in chapter 3. An examination of the mechanisms of failure
might con¬rm this view and lead us to determine a guarantee
period on the basis of this assumption. If observation by God of
all such potential experiments led him to an aggregate normal
distribution, he would have, in aggregate statistical terms,
what our random variable model described. God™s complete
knowledge of what is going on does not, essentially, alter the
Those who wish to pursue the theological interpretations which may be
7

put on quantum theory may ¬nd the article by Roger Paul and the response
from Rodney Holder useful (Science and Christian Belief 17 (October 2005):
155“85).
God™s action in the quantum world 151
reality of the universe. God™s existence does not, therefore,
make any difference to our physical account of the system.
Many physicists are not very concerned with these philo-
sophical and theological issues but use the theory in a purely
instrumental fashion. Theologians and theologically minded
scientists, on the other hand, have, perhaps, been over-eager to
see scope for God™s acting in the uncertainties of the quantum
world. One of the earliest was William Pollard whose book
Chance and Providence (Pollard 1958) has been very in¬‚uen-
tial. More recently Robert John Russell and Nancey Murphy
have been prominent among those who have argued that God
acts in the uncertainties of the quantum world “ but not only
there.
I have concluded that quantum theory describes the world
in probabilistic terms. In principle, therefore, it is not essen-
tially different from the simpler situation considered in the
last chapter. There we were concerned with one probabil-
ity distribution with a single observable outcome; here we
have an immensely complicated probability structure invol-
ving incomprehensibly many variables. But in both cases the
theological question is much the same: how can God be under-
stood to act in such an environment to achieve particular
purposes in the world? Once again there are the same three
directions which an explanation might take:

(a) In reality there is no uncertainty. All is determined by
God and what we see merely appears random to us. If
we could comprehend God™s thoughts we would see that
everything that was going on served some determinate
purpose.
(b) In reality, what appears random to us is exactly what it
appears to be. A vestige of determinism might be pre-
served by allowing that all of this randomness might be
God, Chance and Purpose
152
generated deterministically as are pseudo-random num-
bers.
(c) While (b) might explain most of what happens, God has
the ability to monitor what is going on and, very occa-
sionally, to intervene to steer the cosmos in some desired
direction.

Here, as in the last chapter, there are serious objections to each
of these possibilities, which I take in turn.
On (a) I have noted that the triggering event at the micro
level and the consequent happenings along the way will also
act as triggers for countless other causal paths, each having
consequences in the macro world. Some of these outcomes
may be harmless but others might have effects which can-
cel out, or work against, the intended outcome. All of these
possibilities would have to be contemplated and allowed for.
Further, we are not thinking of one macro outcome but untold
trillions over aeons of time. The bizarre picture of God seated
in front of a celestial control panel watching microscopic
happenings throughout the universe and reacting to them
almost instantaneously may be logically possible but it hardly
¬ts with the notion of the loving heavenly Father of orthodox
Christian belief, neither does it accord with our idea of how
high-level control should take place. The analogy of the man-
agement of a large company might be more helpful here. The
chief executive is not concerned with the day-to-day details
of of¬ce and shop-¬‚oor activity. They are left to subordinates
with more limited responsibilities. The chief executive ™s job is
to focus on the big questions of policy and the strategic issues.
There is a simplicity and elegance about the management
structure of the ¬rm which is lacking in the picture of a celes-
tial manager with a ¬nger on every button. One would surely
expect the God-directed activity of steering the universe to be
no less impressive than those devised by mere mortals for their
God™s action in the quantum world 153
own organisational creations. The picture of a world in which
the details take care of themselves, leaving the big issues to the
Creator, is more appealing and more worthy of directing our
worship. This, perhaps, is a case where we are too prone to
see God in the image of man as someone who thinks control
depends on overseeing every detail.
On (b) Stephen Hawking (quoted in Saunders 2002, p. 128)
makes a very shrewd point with which I conclude the discus-
sion of whether what appears to be random is really random.
˜If one likes one could ascribe this randomness to God, but
it would be a very strange kind of intervention: there is no
evidence that it was directed towards any purpose. Indeed if
it were, it would, by de¬nition not be random.™ It is part of
the last sentence of the quotation that touches the nub of the
matter. Randomness is what we have when all purpose and
direction is excluded. We cannot, therefore, smuggle purpose
in by the back door under cover of randomness.
If, on the other hand, the equations of quantum theory
do describe genuine randomness, there is no room for action
by God mediated through individual events at the quantum
level. This leaves open the central question of this book which
is whether other things are achieved by this very randomness
which are equally expressive of God™s intentions.
It is because (b) has rarely been seen as an option that the
third of the earlier alternatives has proved so attractive. After
all, perhaps all that is needed is for God to give a nudge from
time to time, at critical junctures, to keep things on course. If
these interventions are suf¬ciently rare there is no chance of
them being detected, and it seems that we have the best of both
worlds. The lawfulness of nature is preserved and space has
been created for God to act. The objections to this supposition
are essentially the same as those advanced in the last chapter
for the much simpler situation considered there. First, it is
far from clear that suf¬cient control can be exercised in this
God, Chance and Purpose
154
manner. If anything, the problem is compounded here by the
much greater complexity in the world at the quantum level.
Secondly, there is the theological question of the furtiveness
of this manner of acting, which promptly raises the question
of why God could not have got it right the ¬rst time. Finally,
if the notion of special divine action (SDA) is to be located
in the uncertainty of quantum processes, it is clear that this is
neither easy nor likely to be very effective.
Another interesting theological question arises at the point
of sampling, or measurement. The account I have given says
nothing about how the sampling is done or how the random
variable is turned into an observed numerical value. This is
essentially the same problem as in chapter 3 with reference to
radioactive emissions. It is also the problem which the story
of Schr¨ dinger™s cat was designed to illustrate. In chapter 3
o
we saw that there was nothing observable which would help
us to predict the outcome. Could it be God, therefore, who
decides what we shall see? Is it God who determines, at each
point of measurement, what value is actually observed? Maybe
he does and maybe he does not, but it is worth asking what
theological bene¬ts are to be had by an answer to that ques-
tion. If he does not determine what happens, then clearly
he is not acting at such points. If he does, what purpose
could be achieved thereby? We have already noted Hawk-
ing™s remark that chance rules out purpose and vice versa.
If chance enters only on those occasions where we make a
measurement, our knowledge will be affected but the overall
effect on the progress of events in the world will be negli-
gible. It is true that the knowledge gained by us might in¬‚u-
ence our future actions and this could, conceivably, be how
God interacts with us, but this seems a somewhat cumber-
some way of going about things. For the present, the conclu-
sion has to be that it is very doubtful whether there are any
quantum events which God could in¬‚uence whose outcomes
God™s action in the quantum world 155
might signi¬cantly determine what happens at the macro
level.
Moving on from this point, we come again to the problem
of saying how genuinely random events can be caused if they
are truly random. Humans clearly can make choices and, as a
result, affect what happens in the world. Can God do the same,
and if so, how does he do it? As noted before, such events must
either be caused, in some sense, by God or be without any cause
at all. So the question really boils down to one of whether God
acts from within by upholding and directing everything that
happens or whether he somehow acts on the creation from
outside by choosing from the myriad possibilities on offer.
These two possible modes of action are often described as
bottom-up and top-down. They are not mutually exclusive,
of course, though how they might be brought together is not
as straightforward as it might seem. Some clues might be
obtained by looking more closely at how we use chance and
this we shall do in the next chapter.8

One of the most sustained and detailed discussions of God™s action at the
8

quantum level is given by R¨ st (2005). There is no space here to give a full
u
summary and critique but the following quotations will give an indication
of the author™s position “ which differs fundamentally from that advanced
in this book:
˜God occasionally uses a selection of speci¬c outcomes in quantum and
other random events, in order to guide natural processes in the desired
direction™ (p. 197).

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