. 1
( 7)


This page intentionally left blank

Scienti¬c accounts of existence give chance a central role. At the
smallest level, quantum theory involves uncertainty, and evolution
is driven by chance and necessity. These ideas do not ¬t easily with
theology, in which chance has been seen as the enemy of purpose.
One option is to argue, as proponents of Intelligent Design do, that
chance is not real and can be replaced by the work of a Designer.
Others adhere to a deterministic theology in which God is in total
control. Neither of these views, it is argued, does justice to the
complexity of nature or the greatness of God. The thesis of this book
is that chance is neither unreal nor non-existent but an integral part
of God™s creation. This view is expounded, illustrated and defended
by drawing on the resources of probability theory and numerous
examples from the natural and social worlds.

Davi d J. Ba rt h o lo m e w is Emeritus Professor of Statistics at
the London School of Economics and Political Science. His numer-
ous publications include Measuring Intelligence: Facts and Fallacies
Can God Have It Both Ways?

Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo

Cambridge University Press
The Edinburgh Building, Cambridge CB2 8RU, UK
Published in the United States of America by Cambridge University Press, New York
Information on this title: www.cambridge.org/9780521880855

© David J. Bartholomew 2008

This publication is in copyright. Subject to statutory exception and to the provision of
relevant collective licensing agreements, no reproduction of any part may take place
without the written permission of Cambridge University Press.
First published in print format 2008

ISBN-13 978-0-511-38620-6 eBook (EBL)

ISBN-13 978-0-521-88085-5 hardback

ISBN-13 978-0-521-70708-4 paperback

Cambridge University Press has no responsibility for the persistence or accuracy of urls
for external or third-party internet websites referred to in this publication, and does not
guarantee that any content on such websites is, or will remain, accurate or appropriate.

List of ¬gures page vii
Preface ix

1 What is the problem? 1
2 What is chance? 16
3 Order out of chaos 28
4 Chaos out of order 55
5 What is probability? 67
6 What can very small probabilities tell us? 77
7 Can Intelligent Design be established
scienti¬cally? 97
8 Statistical laws 116
9 God™s action in the quantum world 136
10 The human use of chance 156
11 God™s chance 173
12 The challenge to chance 196

13 Choice and chance 211
14 God and risk 223

References 243
Further reading 248
Index 250

3.1 The form of the exponential frequency
page 35
3.2 The form of the normal frequency
distribution 37
8.1 The frequency distribution of the two
outcomes in a single toss of a fair coin 122
8.2 The frequency distribution of run length in
successive tosses of a fair coin 123
8.3 The binomial distribution of the number of
heads in four tosses of a fair coin 124


Chance has become an integral part of contemporary science
but, for the most part, is still not at home in theology. Theology
speaks of a purposeful God while chance, by very de¬nition,
seems to signify a total lack of purpose. To suggest the very
opposite “ that chance lies within the purposes of God “ may
seem perverse, if not foolhardy, and yet that is precisely what
is argued for in this book.
One might have expected that the slow seepage of evo-
lutionary theory or quantum theory into the public con-
sciousness would at least have softened the hard edges of
the confrontation. But “ to change the metaphor “ the Intelli-
gent Design debate has fanned the dying embers into ¬‚ames.
˜Atheistic evolution™ is now set in stark opposition to the the-
istic design which Intelligent Design sees as responsible for
the wonder of the universe. This, therefore, is an opportune
moment to argue again for the positive bene¬ts which ¬‚ow
to theology from seeing chance as an intended part of the
As is so often the case when matters are hotly disputed, the
stark con¬‚ict between opposites begins to dissolve when we
examine them carefully. Much depends on the ˜level™ at which
we choose to observe the world. Many of the regularities
of nature are built on randomness and much of the seeming
randomness around us is like a shower of sparks thrown off by
the lawfulness of processes on a larger scale. Self-organisation
in apparently disorganised systems occurs on such a scale that
one suspects it does not emerge by accident. It is just possible
that primeval chaos was the precondition of a lawful world.
This is an exciting question which is probed from several
angles in this book.
I make no pretence that this is an easy book, even for those
who are familiar with, if not expert in, the technical material
which lies behind it. Many of the big recurring questions with
which the theological giants have wrestled over the centuries
reappear in these pages. The theology of chance is no magic
solvent to dissolve the problems of yesteryear. What I do claim
is that there is a great deal of misunderstanding which can be
dispelled by rigorously subjecting widely accepted arguments
to the critical eyes of someone trained in the statistical sciences.
These are not, in themselves, intrinsically dif¬cult so much as
unfamiliar but the reader must expect to read slowly and to go
over the ground several times, perhaps. I hope that the use of
familiar, even homely, examples in place of mathematics will
help. As an additional help, each chapter begins with a brief
summary of its argument.
I suspect that chapter 7, refuting Dembski™s claim to have
produced a method for eliminating chance as an explanation,
will be particularly challenging. It is, perhaps, also the most
important chapter. Although I have reduced the technical mat-
ter to a minimum, it is essential to engage with Dembski on his
own ground and in his own language. He has not spared his
lay readers and I have, to some extent, followed his example.
There is, in fact, almost no technical discussion in the book
which requires formulae for its expression and very little use is
made of symbols. This does not really make things any easier
because the economy and clarity of a mathematical argument
makes it, typically, briefer and more precise than the equivalent
Preface xi
verbal version. Its absence however, does make the text more
reader-friendly and that counts for much. This observation
should not lull one into thinking that probabilities, for exam-
ple, can be plucked from thin air by some sort of innate intu-
ition. Probability theory provides the backbone of reasoning
about chance. Although it is not necessary to understand the
theory to grasp the message of the book, it is important to
follow the gist of the argument, and in particular, to be aware
of the pitfalls which await the unwary. For this reason, some
chapters represent a marking time in the progress of the main
argument as I secure the foundations, albeit informally.
This is not the ¬rst time that I have ventured into this ¬eld.
My God of Chance appeared in 1984. It is now out of print and
seriously out-of-date although it is still available and may be
downloaded free of charge at www.godofchance.com. Its pri-
mary aim, appropriate at the time, was to counter the impli-
cation of books such as Monod™s Chance and Necessity that
science had ¬nally banished belief in God to the obscurantist
backwoods. At that time I was not as well informed as I ought
to have been about the late Arthur Peacocke™s thinking in the
same direction. The aim here is more ambitious, namely to
give chance its rightful place in serious theology. My Uncer-
tain Belief, ¬rst published in 1996, discussed reasoning about
theological matters in an uncertain world. The uncertainty
there was in our ˜heads™ rather than in the ˜world™. For the
rest, articles, lectures and chapters in books have provided the
opportunity to develop many of the strands of thought which
have come together in this book.
Chapter 14 is a shortened and updated version of the Gow-
land lecture which I gave to the Christ and the Cosmos Initiative
at Westminster College, Oxford in 1999. It represents a ¬rst
attempt to draw out, on a small front, the kind of theological
thinking that is becoming imperative.
The footnotes serve the usual purpose of leading the reader
into interesting and relevant byways. However, the reader
with access to the Internet can track down a wealth of addi-
tional information by using a search engine such as Google.
Occasionally web addresses are given here but the use of a
search engine is so easy that they are almost super¬‚uous.
As a ˜solitary™ thinker I may not acknowledge, as readily as
I should, the debt I owe to others. Most of those from whom
I have learnt much will recognise their contributions in these
pages. I now ¬nd it impossible to identify and properly appor-
tion credit where it is due. However, the Science and Religion
community in the United Kingdom and internationally is a
constant reminder of the interdependence of all thinking in
this ¬eld.
In a book of this kind a disclaimer is essential. Anyone
attempting to span so many disciplines must, inevitably, echo
St Paul, who asked, in a different context: ˜who is suf¬cient for
these things?™ (2 Cor. 2.15) The short answer, of course, is: no
one. But if the apologetic task is not to go by default someone
must take the risk. My only claim is that I am a statistical
scientist whose work has taken him into many other ¬elds.
As one of the most famous of my colleagues (the late John
Tukey) once said, ˜the best thing about being a statistician is
that you get to play in everyone else™s back yard™.
It is becoming increasingly dif¬cult to know how to thank
my wife adequately for her continual and very practical sup-
port. Indeed, in these gender-sensitive days, it is hard to know
whether these things should be mentioned in public at all!
Whatever the proprieties, I cannot conclude without remark-
ing that Proverbs 31.10“31 gets it about right.
c h a pt e r 1
What is the problem?

The problem is to reconcile the central place which chance has in the
scienti¬c account of the world with the theological account of God™s
relationship to the world. Chance suggests lack of purpose; theology
speaks of purpose. This long-running source of tension has come to
the fore again in the claims of the Intelligent Design movement, which
aims to eliminate chance in favour of design. Quantum theory, which
places chance at the heart of matter, poses essentially the same question
for theologians. This chapter sets the scene and, very brie¬‚y, points
the way to a solution which lies in seeing chance within, not outside,
the providence of God.

c h an c e v e r s u s go d
Chance has become a major weapon of those who regard sci-
ence and theology as locked in mortal combat. On the theolog-
ical side there are those like Sproul,1 who signals his intentions
in the title of a book Not a Chance (1994). The subtitle makes

Dr R. C. Sproul is an American theologian in the strict Calvinist tradition.

He is a proli¬c author and the chairman of Ligonier Ministries, which he
founded. The book, from which these quotations come, appears to be his
only excursion into the science and religion ¬eld though his argument is
primarily directed against what he perceives to be the faulty logic used by
mainstream scientists. The quotations used here were chosen because they
express, with great clarity, an extreme position adopted by some Christians.

God, Chance and Purpose
his intentions doubly clear: The Myth of Chance in Modern Sci-
ence and Cosmology. In the preface he goes on to say ˜this book™
may be viewed as a diatribe against chance. ˜It is my purpose
to show that it is logically impossible to ascribe any power to
chance whatever.™ As if that did not make his intentions clear
enough he continues, on page 3, ˜If chance exists in its frailest
possible form, God is ¬nished . . . If chance exists in any size,
shape or form, God cannot exist.™
These are strong words indeed and one can only marvel that
such an annihilation can be accomplished in hardly more than
two hundred pages. Sproul is not alone, of course, though few
other protagonists claim quite so much. Overman2 is another
who has entered the lists with his A Case against Accident
and Self-organization (1997). This is a more sharply focussed
attack and with more technical apparatus, but its intention is
much the same. Those unfamiliar with the probability logic
involved may be easily impressed when he concludes: ˜The
probability of chance causing the formation of a universe
complete with life and the ¬rst forms of living matter is less
than the mathematical impossibility at the accepted standard
of 1 in 1050™ (p. 181). It is not clear where he acquired this
˜accepted standard™ or who accepts it! We shall return to the
matter of very small probabilities later.

Dean L. Overman is a distinguished lawyer based in Washington DC.

The foreword to his book was contributed by Wolfhart Pannenberg and
there is a commendation on the ¬‚yleaf by Alister McGrath. The laudatory
remarks on the dust cover include quotations from Owen Gingerich and
John Polkinghorne. It seems generally agreed that this is a detailed and clear
approach to a very important topic, but endorsement of the conclusions
reached is not so easy to ¬nd. In my judgement the central conclusion, like
many of its kind, is based on a fallacious probability argument as will be
shown later.
What is the problem? 3
From the science side there are equally forceful advocates
for chance. Although it was written more than thirty years
ago, Jacques Monod™s Chance and Necessity remains one of
the most eloquent statements of the contrary view. Although
often quoted, it bears repetition.
We say that these events are accidental, due to chance. And since they
constitute the only possible source of modi¬cations in the genetic text,
itself the sole repository of the organism™s hereditary structures, it nec-
essarily follows that chance alone is at the source of every innovation,
of all creation in the biosphere. Pure chance, absolutely free but blind,
at the very root of the stupendous edi¬ce of evolution: this central con-
cept of modern biology is no longer one among other possible or even
conceivable hypotheses. It is today the sole conceivable hypothesis, the
only one compatible with observed and tested fact. And nothing war-
rants the supposition (or the hope) that conceptions about this should,
or ever could, be revised. (1970, p. 110; trans. Wainhouse 1972)

Oddly enough, both sides agree that chance eliminates God.
Sproul™s remedy is to oust chance; Monod™s, to do the same to
The object of this book, roughly speaking, is to bridge the
gap by saving Sproul™s theology and Monod™s science using
chance as the link between them. Sproul was wrong in seeing
chance as a threat to the sovereignty of God and Monod was
wrong in seeing chance as eliminating God. These are strong
claims and their justi¬cation rests, essentially, on the claim that
chance must be seen as lying within the providence of God and
not outside it.
As I pause to draw breath it is pertinent to remark that
whatever chance is, it is certainly not an agent capable of
causing anything, as Overman supposes. Even such a careful
writer as Dowe (2005) falls into this trap when he writes ˜If the
latter is true God does not cause any event caused by chance™
God, Chance and Purpose
(p. 184). But there is a broader ¬eld to survey before we return
to this matter.
The essential problem is how to accommodate within a
single world-view the element of real chance, which science
seems to require, and the existence of a God who is supposed to
be actively involved in creating and in¬‚uencing what happens
in the world.
A good deal clearly hangs on what we mean by chance.
This is not such an easy matter as it may seem and it forms the
subject of chapter 2. A chance event arises when something
happens which we could not predict, but this may be because
we do not have enough information. Chance is then the other
side of the coin to our ignorance; this is sometimes called epis-
temological chance. Alternatively, chance may be ontological.
That is, it is somehow inherent in the nature of things and
there is no knowledge we could possibly have which would
make any difference. This brings us to the crucial issue of
God™s involvement in the world because this depends on what
view we take on the nature of chance.
Nevertheless there are some situations where we do not
need to answer the deep philosophical questions. In particular,
these arise when we come to calculate probabilities. The theory
of probability is not so much about what probability is as
about how to make probability calculations about uncertain
happenings. Any attempt to calculate the probability that life
would appear on earth, for example, depends upon putting
together the probabilities of simpler, constituent events which
were necessary for life to appear. This is where Overman, and
many like him, have gone wrong.
Next there are rather crucial questions about what is implied
by the existence of chance happenings in the world. It is com-
monly assumed to be self-evident that any intrusion of chance
will lead to unpredictability and uncontrollability. This is not
What is the problem? 5
necessarily so and quite the opposite may be true. We shall
discover that there may be extreme constraints which render
the outcome of some chance processes almost certain. There
is also an important matter of levels, to which we come in a
moment, where what is uncertain at one level may be virtually
certain at another level. Dying, for example, is still a highly
unpredictable matter for individuals, but insurance companies
and undertakers make a steady living out of it because what is
individually uncertain is highly predictable in the aggregate.
There are equally weighty questions to be raised on the the-
ological side about the nature of God. It was Sproul™s deter-
mination to defend the sovereignty of God that led him to
conclude that chance was impossible in God™s world. Is it
really true that absolute sovereignty requires that God knows
and controls every one of the trillion upon trillions of events
that occur in the universe every second? Might it not be that
such a view actually diminishes the greatness of God? I shall,
in fact, argue that this is the case.
More important, perhaps, is the effect which uncertainty in
the world has on what God can know “ his omniscience. Can
he know, for example, what is as yet undetermined? Can we be
truly free in a world in which God controls every single thing?
I raise such questions now merely to show that the chance issue
is not peripheral, but goes to the heart of age-old questions
which have become even more pertinent in a scienti¬c age
than they were in the early centuries after Christ, or even in
the Middle Ages.
New questions arise which can only be phrased in the lan-
guage of chance or risk. We have to ask not merely whether
God can cope with chance or even use it to good effect, but
whether it might have a more positive role. After all, we use
chance in large-scale computer modelling to mimic the uncer-
tainty of the world, and to achieve goals which lie beyond
God, Chance and Purpose
our reach without it. If we ¬nd that risk taking can be bene-
¬cial and not always a necessary evil, may this not open new
perspectives for theology? Can we conceive of God as a risk
taker? This is, perhaps, the key theological question and we
return to it in chapter 14.
Chance and providence go together in popular debate
because each seems to be at variance with the other. How
can God act providentially in a world if it is not wholly under
his control? This question is distinct from, but not unrelated
to, the question of whether and how God can act in the lawful
world revealed by science. What kind of a place the world is
also affects what we can know about it. If there is genuine
uncertainty about what we observe, then presumably there is
some uncertainty about what we can infer about it. More espe-
cially, and challenging perhaps, is the question of what we can
know about God and his purposes for us and the whole cre-
ation. Are there any certainties left for the believer or, indeed,
the unbeliever?
Next, there is the relationship between chance and law. The
two seem to be in direct opposition but this is not necessarily
true. In fact some laws have been correctly described as sta-
tistical, or probabilistic. These are laws which relate to large
aggregates and thus operate at what I have called a different
level. The simplest possible example is the tossing of a coin.
The outcome of a single toss is a highly uncertain matter but
the outcome of 10 million tosses is highly predictable in the
sense that we can say that almost exactly 50 per cent of all
tosses will be heads and, furthermore, we can also be precise
about what deviation from that average ¬gure is likely to be.
The constancy of such ratios certainly has the law-like charac-
teristic we expect in dealing with a system of divine origin and
concern. The gas laws are a more interesting example, where
the relationship between the pressure and volume of a gas at
What is the problem? 7
a constant temperature is simply determined by the average
effect of a very large number of gas molecules. Lawfulness at
the higher level of aggregation is thus the direct consequence
of complete randomness at the lower level.
This intimate relationship between levels of aggregation
also works the other way round: lawfulness can give rise to
chaos. The word chaos is used here in its technical sense but, for
present purposes we can think of it as, more or less, equivalent
to chance. Very simple, law-abiding processes can give rise
to chance. The subtlety of these relationships emphasises that
what we see in the world depends on the level at which we enter
it to make our observation. The same is true in the realm of
physics where, as we shall see, the quantum world seems very
different to the everyday world viewed on the human scale.
As we unravel the complexities of these relationships it
will become apparent that Sproul™s and Overman™s categorical
statements are not so much wrong as inapplicable to the world
in which we actually live, or to the God who created and
sustains it.

l e v e ls an d s c a l e s
Before we go any further I must digress to expand on some-
thing which has already cropped up several times and which is
central to the question of God™s sovereignty.3 What we observe
in the world, and how we describe it, depends upon how big
The idea of levels and scales occurs in other contexts. A recent example is

provided by The View from the Centre of the Universe by Primak and Abrams
(2006). The prime object of that book is to argue that, in a certain sense,
we are at the centre of things and that gives us signi¬cance as humans.
For example, humans are at the centre of the scale of size. If length is
measured in orders of magnitude (that is powers of ten) then lengths on the
human scale come somewhere near the middle of the range which extends
from the smallest things we know (the Planck length of 10’33 cm) to the
God, Chance and Purpose
or small a scale we view it on. The world viewed through
a microscope is very different from what we see through a
telescope. On the astronomical scale we simply do not notice
the biological details of nature. The microscopic world has no
place for mountains and trees. They are too big to be viewed
on such a small scale.
If we go to the limits of size, in either direction, the worlds
we ¬nd are beyond our imagining and the best we can do is to
describe them by mathematical equations. On the very large
scale, the Euclidian geometry of the schoolroom lets us down
and we then have to reckon with things moving close to the
speed of light. Space has to be thought of as curved and we ¬nd
ourselves in a world in which Newton™s physics is inadequate
and our imagination fails.
Something similar occurs at the smaller end of the scale
where we get down to the level of atoms and what goes on
inside them. It is an unfamiliar world in which our intuitions
based on the everyday world simply do not work. The mathe-
matics continues to work perfectly and delivers results which
are entirely consistent with the world as we perceive it at our
level, but any attempt to picture it fails.
For practical purposes, we can think of three levels. First,
the everyday world of things that we can see, touch and handle,
where distances are measured in metres or miles “ but not in

largest (the distance of the cosmic horizon of 1028 cm). Similarly, if less
convincingly, human life has occurred in the middle of time measured from
the beginning to end of the universe or the life of the earth. The important
thing, from the present perspective, is that according to the authors, certain
questions only have meaning “ and hence meaningful answers “ if posed
at the appropriate level. This idea is applied in many ¬elds including the
nature of God. ˜God™ must therefore mean something different on different
size-scales yet encompass all of them. For example, all-loving, all-knowing,
all-everything-else-we-humans-do-only-partially-well may suggest God-
possibilities on the human size-scale, but what about all the other scales?
What might God mean on the galactic scale, or the atomic?
What is the problem? 9
light years “ where weight is measured in pounds and tonnes,
and so forth. This I shall often refer to as the human level, or
Secondly there is the world of the very small “ too small to
be observed by the naked eye “ the world of cells, molecules,
atoms and electrons. At best we can only see parts of this
world through microscopes but often what is going on has to
be observed indirectly through the observable consequences
of what is happening at the micro level beyond the limits of
our direct observation. This may conveniently be designated
the micro level.
Finally, there is the world of the very large where, for exam-
ple, masses can be so large as to produce observable de¬‚ection
of a beam of light. In this world we encounter incomprehen-
sibly large numbers and unimaginably long periods of time.
This I shall call the macro or cosmic level. We can sometimes
be helped to grasp the signi¬cance of these things if they are
scaled down to something we can understand. For example,
the relative distances between the planets in the solar system
can be represented by where they would appear if they were
laid out on a football pitch with the distances between them in
the same proportions.
The concept of scale or level is central to understanding
the place that chance occupies in the grand scheme of things.
For example, what appears chaotic at one level may reveal a
pattern when viewed on a larger scale.
This phenomenon is familiar to computer users through the
zoom-in and zoom-out facility which many computers offer.
As we zoom in we see more and more of the detail and less
and less of the overall picture. Conversely, when we zoom out
the reverse is true. This is very obvious when viewing a map.
At the lower level we see individual streets, whereas at the
higher level these merge into a blur as the shape and location
of the town becomes the dominant feature. When viewing text
God, Chance and Purpose
at large magni¬cations we lose sight of the words and notice
only the patchiness of the individual letters. When we take
the broader view, the words disappear and we begin to see the
pattern of the layout and so on. Each view shows a different
aspect of reality.
In our world it is natural to think in terms of the human
scale on which we live our lives and form our understandings
and intuitions. It is in this world that we form our concepts. It
is in this world that Christians believe God revealed himself
on a human scale. The truth thus revealed makes sense to us
because it is on our scale. It does not follow, of course, that
God™s actions can be necessarily or exclusively understood at
our level. In fact, as we shall see later, there have been valiant
attempts to account for God™s providential action by reference
to happenings at the micro level.
Since, presumably, God and his creation are not commen-
surable we must be very wary of creating a God in our own
image and on our own scale. The intimate connection between
chance and order at different levels of the creation, which has
been noted above and which I shall explore later, make it very
important to be careful about how we use language. To sup-
pose arbitrarily that God™s main sphere of action is at the level
we can most easily comprehend may be a dangerous and mis-
leading assumption. This is relevant to two issues which are
of great interest in themselves and which have brought chance
to the fore in contemporary debates.

intelligent design
One of the most extraordinary phenomena to have arisen on
the science and religion scene in the last few decades is the
Intelligent Design4 movement. This is largely an American
There is an immense literature on Intelligent Design. In this present book

we are concerned only with the logic of the argument by which, it is claimed,
What is the problem? 11
phenomenon and it is fed by the peculiar mix of fundamen-
talisms which ¬‚ourish there. In a sense it springs from the
acute concerns of those, such as Sproul, who fear that chance
strikes at the root of Christian belief. The great enemy, as its
protagonists see it, is the naturalism of modern science. This
refers to its attempt to explain everything that happens with-
out recourse to any external direction such as is traditionally
supplied by God. Chance and necessity, in Monod™s mem-
orable phrase, account for everything. Even well-meaning
Christians, who see evolution as God™s way of creating things,
are deluding themselves, opponents would argue, and they are
embarked on a path which will inevitably leave no room for
God. Methodological naturalism is also viewed with great
suspicion. This is the strategy of proceeding as if everything
could be explained without reference to any external creator
or designer. For if you really believed that there is clear evi-
dence of design in the world it would be foolish to ignore it,
as a matter of policy, and so have to compete with one hand
tied behind your back!
The search for evidence of Intelligent Design, which I shall
examine in some detail in chapter 7, involves the attempt to
eliminate chance. If this could be done, design would remain as
the only, and obvious, explanation. Intelligent Design assumes

chance can be eliminated as an explanation of evolutionary development.
William Dembski has developed this single handedly and his work, there-
fore, is the focus of our attention. A fuller account would have to take note of
the work of Michael Behe, especially his Darwin™s Black Box: the Biochemical
Challenge to Evolution (1996). Another key ¬gure is Phillip E. Johnson, also
a lawyer. It is pertinent to note that lawyers approach things in a rather
different way to scientists. Lawyers operate in an adversarial context where
their object is to detect and expose the weaknesses in the opponent™s case.
Science is an ongoing activity in which the well established and the provi-
sional often exist side by side. It is not too dif¬cult to ¬nd weak points in
any scienti¬c theory. This is a valuable thing to do but it does not establish
what is true or false in any absolute sense.
God, Chance and Purpose
at the outset that chance and design cannot coexist and this
claim is totally contrary to the thesis advanced in this book.
If the Intelligent Design movement were to be successful, the
ideas to be set out here would be completely undermined. It
is therefore essential to examine the logic of the arguments
of those, such as William Dembski, whose highly technical
treatment of inference under uncertainty underpins the whole
At this and other points on our journey it will therefore be
necessary to examine the logic of inference under uncertainty.
It is to Dembski™s credit that he recognises the need to provide
a rigorous account of what is needed to eliminate chance as an
explanation of any phenomenon. He also recognises that much
of the groundwork has already been done by statisticians and
he cites Sir Ronald Fisher5 as one of those who have paved the
way for his own new developments. Unfortunately for him,
Dembski™s ambitions founder not only on the faulty logic of
his inference procedure but on the calculations necessary to
implement it.

d o e s go d ac t i n t h e wo r l d ?
When we look at the world on the very small scale there is
a whole new territory on which to debate the role of chance.
Oddly, this ¬eld does not appear to have had any serious inter-
action with the evolutionary issues which have so exercised

Sir Ronald Fisher was, perhaps, the leading statistician of the twentieth cen-

tury, though some of his ideas, including those on signi¬cance testing, were
controversial and are not widely accepted today in their entirety. He was,
successively, Galton professor of Eugenics at University College London
and Arthur Balfour professor of Genetics in the University of Cambridge.
A full account of his life will be found in his daughter™s biography: R. A.
Fisher, the Life of a Scientist (Box 1978).
What is the problem? 13
the debaters of Intelligent Design. Classical mechanics has
been very successful in describing the dynamics of the world
of everyday objects such as tables and tennis balls but when
we look at things on the scale of electrons and photons it
breaks down. In that case we need quantum mechanics, which
was specially developed for work at that level. Using quan-
tum theory it is possible to be quite precise about calculations
made relating to quantum phenomena. The trouble is that the
theory provides an incomplete description of reality at that
level. This is of no great inconvenience to physicists, who can
make their calculations regardless, but it poses serious ques-
tions for philosophers and theologians. The latter, especially,
want to know what is really going on, so that they can examine
whether it is an appropriate arena for the action of God. There
are competing interpretations of what the quantum world is
actually like, and it is those that incorporate an element of
chance that fall within our present concerns.
At one extreme are those who prefer a wholly determin-
istic interpretation of the quantum world. This is possible, if
somewhat contrived, and it certainly ¬ts in with the world-
view of theologians such as Sproul. At the other extreme,
what is prescribed are probabilities. According to that view,
the individual events can then occur as God wills provided
that, in aggregate, they conform to the overall probabilities.
One way of describing this situation is to say that we only
know the quantum world through probability distributions.
This enables us to predict where particles are and what they
are doing probabilistically but these distributions do not pro-
vide de¬nitive information about what is actually the case. So
chance is seen as a positive asset because it provides room for
manoeuvre for a God intent on purposeful activity. Chance is
then not the enemy of theism but necessary for it to be cred-
ible. The problem posed by the possibility of God™s acting in
God, Chance and Purpose
quantum events is not essentially different from his action in
relation to any statistical law. This will be a recurring theme
in the following chapters.

go d ™ s c h an c e
In chapter 11 we come to the heart of the matter and I argue for
the view that chance is a deliberate part of God™s creation. Not
only is the presence of chance an integral part of the created
order but it actually offers possibilities of variety, ¬‚exibility
and interest which would not be available in a determinis-
tic universe. This contention does not, of course, sweep all
opposition before it. There remains a cogent case to be made
in defence of a more traditional theology. However, this is
not to be found by following Sproul, Overman and others
down the road of anti-science or of pseudo-science. It is more
likely to be found in arguments such as those of Byl (2003),
whose case I answer in chapter 12. But there is also a para-
dox in introducing chance as a way of providing freedom of
choice and then having to reckon with what this does for the
rationality of human choosing. This is the subject of chapter
13. In the ¬nal chapter I deal at greater length with what I see
as one of the most serious theological challenges posed by the
God who works, in part at least, through chance.

c h an g i n g pe r s pe c t i v e s
One can detect a progression as one moves through the debates
which provide a connecting thread throughout this book. First
there is the idea that chance is a problem for theology. Its per-
ceived existence seems to challenge the sovereignty of God and
call for scienti¬c effort to be devoted to its elimination. Only
when this is done will the true nature of reality be revealed.
What is the problem? 15
This was the thrust of much early work designed to show that
the complexity and wonder of the world revealed by science
simply could not be ˜due to chance™. Overman cites many
examples. Some of this work is reviewed in chapter 6 but this
line of thinking ¬nds its culmination in Dembski™s approach
to Intelligent Design treated in chapter 7.
In the second stage chance has a more benign role. It is
seen as playing an essential, but passive, part in providing
the space for God to act without disturbing the lawfulness of
the world. The trouble with the fully deterministic system,
which a rigorous view of God™s sovereignty seems to require,
is that it leaves no room for free action either on God™s part
or our own. If we can create space for free actions, without
disturbing the order in nature or requiring God to contradict
himself, then progress will have been made. Quantum theory,
according to some interpretations, appears to allow just the
¬‚exibility that is called for.
More generally, the widespread occurrence of statistical
laws in nature and society seems to provide further room for
manoeuvre for both God and ourselves.
Neither of these two approaches is satisfactory and a sub-
stantial part of this book is devoted to exposing their weak-
nesses and preparing the ground for what I believe is a
more adequate view. This sees chance in a more positive
light, as something which actually does greater justice to the
sovereignty of God and to his remarkable creativity. Freed
from an excessively ˜mechanical™ way of thinking about God™s
actions, we see an enormously rich tapestry of opportunities
and possibilities in the creative process. In short, chance is to
be seen as within the providence of God rather than outside
it. It is a real part of the creation and not the embarrassing
illusion which much contemporary theology makes it out to
c h a pt e r 2
What is chance?

This chapter aims to clarify the terminology. In a ¬eld where there
are many terms with overlapping meanings, it is important to estab-
lish a common language. The approach is through the familiar notion
of uncertainty, and the chapter continues by dealing with chance in
relation to ignorance, accident, contingency, causation and necessity.
Particular attention is paid to the idea of ˜pure™ chance, and the para-
doxical relationship of choice and chance is touched upon.1

w h y t h e q u e s t i on m at t e r s
to understand why some think that the very idea excludes God.
Sometimes chance is spelt with a capital C as though to accord

Chance is commonly set in opposition to purpose as in the title of this book.

It is therefore important to raise at an early stage the question of what it
means. This is not a straightforward matter, because it is used with so many
variations of meaning, especially when we come to philosophy and theology.
Originally, as in Abram de Moivre™s famous Doctrine of Chances, the ¬rst
edition of which was published in 1718, it had the purely technical purpose
of referring to chance events such as rolling dice or drawing cards. This use
persists in speaking of games of chance and in much of scienti¬c writing.
However, chance has more emotive connotations as in ˜blind™ chance, and
this usage has become a common weapon in the debates on evolution versus
creationism. The prime purpose of this chapter is to draw attention to the
subtleties of the situation and to prepare the ground for the discussion of
probability in chapter 5. This provides a more secure foundation for what

What is chance? 17
it a quasi-metaphysical status. I have already noted, in chapter
1, the hazards of thus personifying chance because to do so
almost inevitably sets it up in opposition to God. It is then but
a short step to speaking of chance as causing things, and once
that happens we are on a very slippery slope indeed. The fact
that we have so many words for chance with an overlapping
meaning in our vocabulary shows the subtlety of the concept.
Random, likelihood, probability, contingency and uncertainty
are all terms which arise and sometimes they are used in con-
junction as when people speak of ˜random chance™ as though
to emphasise the sheer uncertainty of it all! In the following
section I seek to elucidate the meaning of chance by looking at
it in the context of some other terms with which it is commonly

c h an c e an d u n c e rta i n t y
Chance and uncertainty are closely related. In fact I shall
conduct the present discussion, initially at least, in terms of
uncertainty, because this word seems less laden with meta-
physical overtones than chance and thus has the merit of being
something we would never think of personifying. Life is unde-
niably uncertain; we confront uncertainty at every turn, so this
provides a gentle, if somewhat roundabout, route to our ¬nal
goal. What the term lacks in precision is made up for by its

The late Arthur Peacocke wrote extensively on chance and its role in the

world. Much that is relevant to this chapter, and the book as a whole, will be
found in his chapter entitled ˜Chance and law in reversible thermodynamics,
theoretical biology and theology™ in Russell et al. (1995). See especially the
sections on Chance, Two meanings of chance, God and chance, and Living
with chance.
God, Chance and Purpose
To say that some event happens by chance is to say no
more than that we do not know enough about its antecedents
to predict its outcome with certainty. This leaves open the
question of whether our failure to predict is due simply to lack
of knowledge on our part, or whether there is no knowledge
available, even in principle, which could give us a degree of
certainty. In the ¬rst instance all uncertainty arises through
lack of knowledge.
We are uncertain about many things and events because our
knowledge is limited. Certainty is where we arrive when we
have all the knowledge that is relevant, so it is a good idea to
begin with certainty as the end point of the scale of uncertainty.
We are certainthat the sun will rise tomorrow because we know
that ˜tomorrow™ is de¬ned by the rotation of the earth and its
position in relation to the sun. As the earth revolves, the sun
repeatedly comes into view and then sets again. Philosophers,
of course, might dispute the certainty of this, and distinguished
members of that fraternity have questioned, in all seriousness,
whether it really is certain. Here, however, I do not seek
to set up a watertight argument, but to conduct an enquiry
at a commonsense level. Death and taxes are the traditional
certainties but there are many others. If we drop a lead ball
from an unobstructed church tower, we are certain that it will
hit the ground. If we are bitten by a poisonous snake, we are
certain to be very unwell. If we refuse all food and drink for
a suf¬ciently long time, we shall certainly die.
Actually, very few happenings are as certain as that. If we
are exposed to someone with a cold, it is not certain that we,
ourselves, will develop one soon afterwards. If we set out on a
train journey, it is uncertain that we shall arrive on time. If we
plant a hundred pea seeds, the number that will germinate is
uncertain. The difference between the certain events and the
uncertain events is in the degree of knowledge we have in each
What is chance? 19
case. In the ˜certain™ cases we know all about the circumstances
and how the ˜mechanism™ determining the outcome works; in
the uncertain cases our knowledge is incomplete.
There are degrees of uncertainty. We may know some rel-
evant things but not enough to be sure about what is going to
happen. The weather, especially in countries such as Britain, is
a highly uncertain affair. But weather forecasters know a great
deal about what determines the weather and, though they may
not always be right in their forecasts, they usually do a bet-
ter job than untutored amateurs. Weather forecasters do better
than we can because they have more relevant information than
we do and are able to handle it more ef¬ciently. As more knowl-
edge about the atmosphere has become available so, by and
large, the uncertainty in their forecasts has decreased. Thus
there is an inverse relationship between uncertainty and rel-
evant knowledge. Generally speaking, uncertainty decreases
as the accumulation of relevant knowledge increases. The
general drift of this argument so far suggests that if only we
could acquire enough knowledge, we would be able to banish
uncertainty. Whether or not this is so is actually an interesting
and fundamental question. Is it, in fact, true, I ask again, that
uncertainty is solely the result of removable ignorance? Or is
it possible that some events are unpredictable in principle “ at
least to some degree? This would mean that however much
knowledge we had, some things would remain irreducibly
Statisticians often behave as if there were an irreducible
uncertainty about the things they try to predict. When trying
to predict the sales of, say, a new computer they will typically
identify those variables that seem to be important (e.g. number
already sold, performance of the new model, etc.) and put these
into their equations. (It does not matter for present purposes
where these equations come from or what form they take.)
God, Chance and Purpose
These will not be suf¬cient to give perfect predictability, so
statisticians will then add what is variously called an error
term or a residual whose purpose is to capture the effect of
everything else that has been left out. It is a sort of balancing
item because it is what it would be necessary to add to make the
sales fully predictable. In practice, of course, they will never
know the value of this balancing item but there are sometimes
ways of estimating it if we have replications of the data.
In certain very simple situations one can come very close to
perfect predictability with very few predictors, but this is the
exception rather than the rule. In most cases, especially in the
social sciences, the predictability is poor even after the list of
known potential predictors has been exhausted. The question
then arises as to whether, even in principle, it would be possible
to achieve perfect prediction if one had complete knowledge.
If not, then there would seem to be an irreducible degree of
unpredictability. This, in turn, touches on deep questions of
what, if anything, determines outcomes in the absence of any
causal factor. For the moment, we must be content to leave
that question unanswered.

c h an c e an d i g n o r an c e
It is now time to move away from the focus on uncertainty and
link uncertainty more speci¬cally with the technical terms of
chance and probability. Both are clearly related to uncertainty
through the fact that there are degrees of uncertainty. But
uncertainty and probability are not identical and part of the
price I must pay for the opening digression through the more
familiar territory of uncertainty is a partial retracing of my
We now return to the subject of epistemological chance
mentioned earlier. Even if everything were perfectly
What is chance? 21
predictable it does not follow that the study of uncertainty
would be redundant. Complete knowledge may be practically
unobtainable, so the world appears much as it would if it were
unpredictable in principle. In other words, we may be igno-
rant. There are a great many situations in which we know
that there is further information available, at a price, which
would improve our predictions “ weather forecasting is a case
in point. In the social sciences this situation is the norm. In
practice, therefore, we are usually working with chance as
re¬‚ecting a degree of ignorance. These degrees of ignorance,
or knowledge for that matter, are measured by probability, to
which we come in chapter 5 but, for the moment, I note that the
calculus of probability takes no cognisance of how the proba-
bilities with which it works are de¬ned. Uncertainties, whether
they are irreducible or simply descriptions of our ignorance,
are all grist to its mill. Probability, as we shall see, is a measure
of uncertainty which conventionally ranges between zero and
one. A value of one denotes certainty and zero indicates impos-
sibility. Uncertainty diminishes as we approach either extreme.
For example, we may be almost certain that our friend will
keep a promise to keep an appointment with us. This amounts
to saying that there is a high probability of the appointment
being kept. Equally, we may be practically certain that it will
not snow on Midsummer™s Day, for which the probability is
almost zero. Very high and very low probabilities thus corre-
spond to low uncertainty and vice versa.

c h an c e an d ac c i d e n t
Accidents happen when two or more causal chains coincide.
An accident is, therefore, a coincidence. Coincidences are
not usually predictable, by us at any rate, because we do not
have suf¬cient knowledge to foresee what is certainly going
God, Chance and Purpose
to happen. An all-seeing and all-knowing being, like God,
would be able to see the whole situation as it developed and for
him there would be no chance involved. Chance and accident
could, therefore, have been subsumed under the general head-
ing of ˜Chance and ignorance™ but accidents involve the lack
of a special kind of knowledge, namely about the antecedent
causal factors. It is in the apparent independence of the causal
chains that the source of the uncertainty lies.

c h an c e an d c on t i n g e n c y
Contingency is a philosophical term referring to the fact that
some happenings are not determined “ that things could have
turned out otherwise. It is sometimes used as a synonym for
uncertainty, accident or chance, but in the present context it
is liable to be ambiguous. It might mean determined by God
or accidental in the sense de¬ned in the last section and that
distinction can be very important. In her book Divine Will and
the Mechanical Philosophy, Osler (1994) explores the attempts
of philosophers and theologians of the seventeenth century
to get to grips with the way that God related to the created
world. The subtitle, Gassendi and Descartes on Contingency
and Necessity in the Created World, shows us that their efforts
crystallised around contingency and necessity. This resonates
with the chance and necessity which has come to epitomise the
essence of evolutionary theory, but the similarity of language
conceals a major difference. Both sides in the earlier debate
accepted that God was responsible for everything. The point at
issue was whether some things happened of necessity because
God had planned the world to work that way or whether, as
Pierre Gassendi thought, God had complete freedom to act
as he willed on every occasion. Chance (and fortune) in their
understanding was more in the nature of accidents which are
What is chance? 23
only uncertain to us because we do not have full informa-
tion. As we shall see, contingency in that earlier sense is still
an option canvassed by many theologians but it is radically
different, in the view of most scientists, from the chance that
drives evolution.

p u r e c h an c e
The pure in pure chance suggests a lack of contamination which
is a fair way of describing the absence of any predictive factors.
Pure chance is what we get when there is nothing at all which
has any predictive value. We can, therefore, never be sure that
a chance event is pure, in that sense, because we can never
be sure that there is not some elusive and unobserved factor
which might help us to predict and so remove some of the
uncertainty. The archetypal example of pure chance appears
to be provided by radioactive decay. The word ˜appears™ is
crucial in this sentence because we can never know for certain
that there is no possible predictor lurking somewhere in the
universe that we have failed to notice, but it is the best example
we have. Nothing is known which helps us to predict when the
next emission from a radioactive source will occur. The term
pure chance is sometimes used as a synonym for ontological
chance, which distinguishes it from epistemological chance.
Must every event have a cause? If so, we have to ¬nd some
causal agent for those happenings where pure chance has been
invoked; otherwise we must abandon the idea that every event
must have a cause. Paradoxical though it may sound, such
events must be caused by whatever, or whoever, it is that causes
apparently uncaused events! It is at this juncture that theolo-
gians have often felt they can save causality by introducing
God as the suf¬cient cause of anything lacking a detectable
cause in the physical universe. If we seek to avoid this dilemma
God, Chance and Purpose
by denying that all events have causes, we have to allow that
there are some things that simply cannot be explained and
leave it at that.

c h an c e an d c au sat i on
As just noted, the existence of chance events raises fundamen-
tal questions about causation. In the last chapter I introduced
the idea of levels of reality. Appealing to the notion, made
familiar to computer enthusiasts, of zooming in and zooming
out, I noted that descriptions of the world at one level may
appear quite different to those at another level. This applies
especially to what I have said about uncertainty. We may be
uncertain about a particular outcome of some event but have
little uncertainty, at a higher level, relating to a larger aggre-
gate of which the single event forms a part. The drawing,
at random, of a card from a well-shuf¬‚ed standard pack is a
highly uncertain event and is, as near as makes no difference,
a purely chance happening. But if we draw, with replacement
a thousand times, the number of hearts will be very close to
250, or 25 per cent. There is thus no inconsistency in having
a great uncertainty at one level and near certainty at the next
higher level. It is, therefore, important to be speci¬c about the
level we are describing.
In order to give a ¬rmer grasp of these important ideas it will
be useful to relate them to a number of familiar situations in
which uncertainty arises and which are germane to the present
discussion. This I do in the next chapter.

c h an c e an d n e c e s s i t y
In the titles of the other sections of this chapter so far chance has
been paired with one of its synonyms to illustrate the diversity
What is chance? 25
of usage and meaning. It may seem perverse, therefore, to
pair it with its opposite. However, chance and necessity have
become indissolubly linked by Jacques Monod™s use of them as
the title of his ground-breaking book. From that point onwards
they have become part of the currency of the debate between
evolutionists and creationists, usually in the form of chance
versus necessity. In effect this has implicitly de¬ned chance as
that part of the evolutionary account which makes it anathema
to anti-evolutionists.
But the chance referred to here is not the pure chance just
de¬ned but is much closer to accident. It arises in the evo-
lutionary story where mistakes occur in the copying of the
DNA. In practice the copying process is extremely accurate
but very occasionally errors occur for a variety of reasons.
When such changes occur they are described as mutations.
Cosmic rays or other damaging effects, such as chemicals,
can introduce such errors. There are causes for these errors
which can be explained in physical terms, so it cannot be said
that they are without cause. The justi¬cation for using the
word ˜chance™ is that their effects are quite independent of
the resulting change in the phenotype. In practice this lack of
linkage makes it impossible to predict the consequences of the
mutations. Mutations introduce uncertainty, and uncertainty
spells chance.
Because of the fervour with which the role of chance, in
this sense, is condemned as blind chance and therefore as anti-
purpose, it may help to introduce an illustration. Children
play a game known as Chinese Whispers. A number of chil-
dren sit in a row. The child at one end whispers something
to their immediate neighbour. The neighbour repeats what
they think they have heard to their neighbour, and so on
down the line until the message reaches the other end. In
most cases the message will have become so distorted in the
God, Chance and Purpose
course of its being passed from one to another that the ¬nal
result will cause much hilarity. It is dif¬cult to obtain a bet-
ter example than the, no doubt, apocryphal story (from pre-
decimalisation days!) of the British general who sent the fol-
lowing message to headquarters: ˜Send reinforcements; we™re
going to advance.™ After it had passed through several hands
HQ received it as: ˜Send three and four pence; we™re going
to a dance.™ The amusement of the game results from copy-
ing errors, or mutations. Each person in the line attempts to
copy the sequence of sounds received from their neighbour
and errors will inevitably occur. The analogy is not exact, of
course, and one should not press it too far, but the point is
that any errors should be independent of meaning. Changes
of meaning are therefore, not predictable and the outcomes
may be legitimately described as chance effects. Necessity is
thus the opposite of chance because the former is precisely
predictable and the latter is not.

free will
There is another realm where the existence of causal links
is in serious question: the ¬eld of human choice. Are all our
choices predictable? This would be so if, having observed
enough things about the person™s brain, their immediate envi-
ronment and the universe in general, we could say with cer-
tainty what choice that person would make. Thus would free
will be banished. Note that it is not enough to say that we
can predict a decision in some situations, for there might be
others where we could not, and that would save free will in
some circumstances at least. So whether or not free will exists
depends on whether our decisions and actions are always, in
principle at least, predictable. There is then no uncertainty
about the outcome of what goes on in the process of making
What is chance? 27
up our minds. In practice, of course, we are likely to be in the
˜in-between™, state where we can observe things which reduce
the uncertainty but do not eliminate it.
If free will exists in this sense, it must be impossible to
obtain enough knowledge to predict, with certainty, what we
shall do in every circumstance.
The de¬nition of free will that I have just given bears a
remarkable similarity to that proposed for pure chance. How
something which seems to be the very epitome of rationality
and purpose can be so similar to its antithesis is an intriguing
question which will have to wait for a fuller treatment.
For a second time then, we see that asking simple questions
about uncertainty touches on the most fundamental issues
which have exercised philosophers and theologians down the
centuries. The free-will versus determinism debate brings
choice and chance together and in doing so creates a para-
dox which I shall not attempt to resolve until chapter 13.
c h a pt e r 3
Order out of chaos

Much of the order in the world is built on disorder. This fact makes
it dif¬cult to speak unambiguously about whether or not it expresses
purpose. For when many chance events are aggregated, order often
appears. This chapter substantiates the claim that haphazard happen-
ings at one level may lead to lawfulness at a higher level of aggre-
gation. It begins with simple processes such as sex determination
and moves on to the regularities which appear in networks of many

o r d e r b y agg r e gat i on
Much of the debate about whether chance and God are com-
patible centres around the alleged inconsistency of believing
that God™s purposes are constant and in recognising the uncer-
tain behaviour which characterises much of the world we live
in. The former speaks of God™s presence and the latter of
his absence. We thus seem to be presented with the stark
choice: God or chance. Sproul, and those who think like him,
cannot conceive of a world in which the two could coexist.
The purpose of this chapter is to show that things are not as
simple as this crude dichotomy suggests. Order and disor-
der are closely connected and one may be a precondition of
the other. This and the following chapter explore this rela-
tionship and so prepare the ground for a positive role for
Order out of chaos 29
The essence of the point I wish to make in this chapter is
contained in the simple example of coin tossing that was used in
chapter 1. A single toss of a coin is a highly uncertain matter yet
the collective tossing of a million coins is a highly predictable
event. Chance at the level of the single toss is replaced by near
certainty at the aggregate level. The way the world looks and
the randomness, or otherwise, of its processes depend very
much on the level at which we choose to observe it.
The idea is not con¬ned, of course, to the arti¬cial world
of coin tossing but is all-pervasive. The motion of a single
molecule inside an in¬‚ated balloon is chaotic as it collides
with other molecules but the combined effect of the motion of
the billions of molecules inside the balloon is highly regular,
maintaining the shape over a long period. This idea extends
to the stability of the whole universe. At the lowest level,
quantum theory describes what is going on in probabilistic
terms, but at the macro level, at which we observe it all,
much of that randomness merges into the lawfulness on which
our science and engineering are built. For that reason laws
are sometimes described as statistical and it has even been
speculated that all laws may have that character.
Lawfulness is claimed to be a key characteristic of our uni-
verse. The stars remain in their courses and cannonballs con-
tinue to fall from high towers with a constant acceleration.
Because we can rely on the way nature behaves, science is
possible and so, in the more mundane affairs of everyday life,
we can go about our business in a rational way. This all speaks,
theologians tell us, of the faithfulness and constancy of God.
It is all part of the doctrine of creation, but it should already
be clear that it is a very partial view showing us what the
universe looks like from our particular vantage point. For a
God, who has other vantage points, the description may not
be so simple.
God, Chance and Purpose
There are different ways of regarding laws. The laws of
nature can be viewed as descriptive, not prescriptive. Accord-
ing to this view, they do not tell us what must happen but what
does, as a matter of fact, happen. Their very constancy then
warns us of what we can expect to happen when, for example,
we jump off a cliff, but they do not tell us that this must neces-
sarily happen. Another way of looking at laws is as constraints
imposed on what can happen. Water has a different chemical
composition to wine and the conversion of the former to the
latter is not in line with how the world normally works. But
does it have to be like that?
Our view on these matters affects how we think about
other aspects of Christian belief. For example, it does cre-
ate some problems, especially in relation to miracles, as I
have just implied in referring to water and wine. When we
move into this realm there is often a subtle change in the way
we regard laws. We begin to think of them as similar to laws
enacted by parliaments or the governing bodies of sports.
These prescribe how the governing bodies wish people, or
players, to conduct themselves. Incentives and sanctions may
be introduced to induce the desired behaviour, but they in no
way determine the choices of citizens or players. Such laws
can be broken and, in spite of the sanctions or incentives, they
often are. If we think of God™s laws in this way, instead of as
saying what, necessarily, must be so, the whole discussion of
God™s action moves into a different realm. These preliminary
remarks are intended in a cautionary sense to alert us to the
need to be careful about how we regard statistical laws and
the inadvisability of jumping to premature conclusions.
The introduction of chance into our world-view produces
a radical change for both science and theology. Lawfulness
of a certain kind arises from randomness and, indeed, is built
upon it. This requires a reassessment of what such laws tell us
about God, and how he might act in the world.
Order out of chaos 31
In this chapter we shall meet some examples of how order
may arise out of chaos1 and that will provide the backdrop for
a reconsideration of God™s relation to the world and his inter-
action with it. To make the discussion clearer it will be helpful
to designate the two levels with which we are concerned as
the individual level and the collective or aggregate level. These
are to be thought of as relative levels rather than the absolute
levels for which I used the designations micro, human and
macro earlier.

t h e h u m an s e x r at i o
A female child receives an X chromosome from each parent;
a male child receives an X chromosome from the mother and
a Y chromosome from the father. At birth there are about 105
males born to every 100 females. The matching of chromo-
somes at any one conception is quite independent of any other
mating “ whether between the same or different parents. This
corresponds almost exactly to what happens when we toss
coins, where heads might represent male and tails represent
female. The only slight difference is between the proportion
of heads and the proportion of males. What I have to say is
true for sex determination and for coin tossing, but the sex
determination example is more interesting.
The outcome of any particular birth, male or female, is
completely unpredictable “ in the absence of prenatal scans or
other checks. In that sense births might be described as chance
events. The individual birth is an event at the individual level.
On the assumptions I have made there is nothing we can
observe prior to the event which can help us to predict the
The word chaos has an everyday meaning which is virtually synonymous

with disorder. It is in that sense that it is used in this chapter. It also has a
technical meaning, as in mathematical chaos, to which we come in the next
God, Chance and Purpose
outcome. However, if we observe a large number of births in
a town over the space of a year, for example, the proportion of
males will be very close to 51.2 per cent [(105/205)—100 per
cent] and this is something we can con¬dently predict. In the
second case we have an example of a collective event and it
exhibits a lawful character “ something which occurs always
and everywhere. It is a law of human society that the sex ratio
is about 51 per cent. At the aggregate level it is almost the
same as if alternate births were female. But at the level of the
individual family of two or three children, the lack of variation
in the latter case would have implications, of course!
We have moved a little beyond arti¬cial things like coin
tossing, to what is, perhaps, the simplest example that shows
how a particular kind of effect can be both chaotic and lawful at
the same time. Which type of behaviour we observe depends
upon the level at which we choose to make our observation.
Lawfulness emerges from chaos in all sorts of interest-
ing ways and I now supplement this simple example about
sex determination with others which are not quite so simple.
Together they provide the necessary backdrop to the discus-
sion of how God might act in the world. Also, and paradox-
ically it might seem, this movement between the individual
and collective levels is a two-way process. Chaos can emerge
from order as well as order from chaos. This makes it very
dif¬cult to talk about the ˜lawfulness™ and ˜unlawfulness™ in
absolute and unquali¬ed terms.

po i s s on ™ s laws
Sim´ on-Denis Poisson (1781“1840) had humble origins but
became a leading ¬gure in the French scienti¬c establishment.
He lived in turbulent times and it was said of him that he
was one ˜whose political ¬‚exibility was as remarkable as the
Order out of chaos 33
rigidity of his scienti¬c convictions™.2 His original researches
ranged widely, well beyond probability theory, to which he
was a considerable contributor. It is ironic, therefore, that the
law, or distribution, which bears his name, should have been a
fairly insigni¬cant part of his work “ and not entirely original.
It was known to Abram de Moivre more than a century earlier
and has become part of every statistics student™s introduction
to the law through the efforts of Ladislaus von Bortkiewicz a
century later. It was von Bortkiewicz who noted that the deaths
from horse kicks in the Prussian army varied in precisely the
manner required by the law.
For present purposes the Poisson process, as we may call it,
and law are so intertwined as to reduce much of the theological
debate to nonsense. To see this we shall take a step back
and then bypass much of the historical and contemporary
discussion of this topic.
Suppose we begin by asking what it means to say that events
are occurring ˜completely at random™ in time. This is, surely,
a fundamental notion if we are to think about how God might
be involved in such happenings. There are plenty of things,
even within our own experience, on which we can draw to get
to grips with the concept of randomness in time.
Standing at a bus stop, especially in a large city, often seems
to prompt the thought that the arrival of buses is random. The
timetable may say that they should arrive at regular intervals
but the vagaries of traf¬c and other hazards produce marked
irregularities. This experience indicates a way in which we
might begin to characterise randomness in time. If, on arrival

This quotation comes from Bernard Bru™s biography in Statisticians of the

Centuries (Heyde and Seneta, 2001, p. 124). The same publication contains
a wealth of other material about this remarkable man.
God, Chance and Purpose
at the bus stop, we ask other passengers how long they have
been waiting, their answers should give us some clue about
how long we might have to wait. The longer the gap since
the last bus, the less time we should expect to wait before the
next one. If the buses are keeping to the timetable, information
on recent arrivals should tell us a good deal. If, for example,
we arrive as a departing bus recedes into the distance we can
expect a long wait.
Maybe we can approach the idea of randomness in time by
thinking about what we would need to know in order to make
some prediction about when the next event will occur. Any
information about when buses have arrived in the recent past
should provide some useful data. The less the information, the
closer we seem to be to randomness. Perhaps, then, we should
de¬ne randomness in time as a state of affairs in which all such
information would be useless. This is entirely consistent with
my earlier de¬nition of a pure-chance event as one where there
is nothing we can observe which will help in its prediction. Put
another way, there is no discernible reason for what happens.
Roughly speaking we can formalise this by saying that the

. 1
( 7)