Derek York’s In Search of Lost Time(IOP, £7.95/$15,
ISBN 0750304758) passes this test. It contains an interesting kernel of novel
material about how we learnt to determine the ages of the oldest things on
Earth—rocks, artefacts and fossils—as well as how we became
comfortable with a world that was not just thousands but billions of years old.
This is not to be found in other popular books on time.

I enjoyed many of the book’s digressions, notably the strange story of Robert
Gentry’s claim to have discovered superheavy elements in the 1970s. I remember
the announcement by his co-worker at a hastily arranged Oxford seminar with many
famous physicists present—I suspected that, by chance, I was the only
person who happened to know about Gentry’s creationist ideas and their need for
superheavy elements. Eventually, the sky fell in on Gentry and the whole chain
of evidence that he used.

The closing chapters of the book are less successful. The author feels the
need to remind us about fashionable topics—chaos, Schrödinger’s cat,
and the cosmological arrow of time. Really, there was no need. Readers are well
served by timelords Davies, Hawking and Penrose.

Laced as it is with nice human stories, the bittiness of the book is
frustrating. We have good evidence that brief histories of time can succeed, but
it was a mistake to conclude that briefer still was better.

The quantum world deviates strongly from those of Newton when things are
very small. By contrast, general relativity only changes Newton’s predictions
when gravitational fields are strong and masses are very large. These
conditions rarely overlap except in the cosmological problem of the Universe’s
first expansive moments.

Over the past thirty years, Stephen Hawking and Roger Penrose have done
more than anyone to further our understanding of the nature of gravitation and
cosmology. Both have developed new approaches to these problems that differ
from the mainstream work by particle physicists (and from each other). The
Nature of Space and Time is the result of their attempt to stage a structured
dialogue about these problems, to isolate points of disagreement, and
stimulate further investigation of these problems. Alternate lectures are
presented by the two protagonists, culminating in a final debate where they
summarise their points of agreement and disagreement. The level of argument is
highly technical, but you can skip the equations and still get a feel for what
is going on.

Generally, great debates in science don’t work. Science is not a democratic
activity in which the idea that gains the most popular votes wins. Politicians
need not apply. Nonetheless, this volume shows that this adversarial style can
be extremely valuable – at least at a textual level. Both authors are well
acquainted with each others’ ideas and write with great clarity. They agree on
much and have to struggle a bit to play up points of disagreement over the
interpretation of quantum mechanics, irreversibility, violation of CPT in
gravitational collapse, the equivalence of black and white holes.

The opening two lectures introduce the minimum collection of ideas from
differential topology needed to understand what a singularity is (an edge of
space-time found, for example in a black hole, where all laws of physics break
down), and the conditions under which it would be inevitable in our past. Then
they move on to quantum effects and gravity with Hawking discussing black hole
thermodynamics and introducing Euclidean methods. Penrose lets the cat out of
the bag (and into a box) introducing the problems of interpreting quantum
measurement, even proposing a simple formula for the time duration of wave
function collapse.

The final pair of lectures is about quantum cosmology. Hawking argues for
the inevitability of the Hartle-Hawking “no-boundary” condition as a way of
describing the initial state of the Universe which uses quantum mechanics to
explain how time originates at the big bang. Penrose, on the other hand,
argues for some measure of gravitational entropy. In this picture the second
law of thermodynamics implies that a low value for gravitational entropy at
the initial state would be natural. So the Universe would be almost isotropic
and homogeneous initially, but chaotically irregular at any final
singularity.

If you cast a critical cosmological eye over the proceedings, then several
things are evident. Neither author is very impressed by superstring theory (to
the exasperation of at least one questioner at the end of the lecture), both
have wonderful geometrical intuitions and their taste in theories is strongly
influenced by that penchant. Neither believes that inflation – the fashionable
idea that the Universe underwent a phase of accelerated expansion in the first
moment of its existence – is the whole answer to the problem of why the
Universe is so isotropic and homogeneous today. And neither adequately
considers the impact of cosmological inflation upon their viewpoint.

Hawking argues that superstring theories make no observable predictions
that are not those of general relativity, to which superstrings reduce when
gravity is weak. By contrast, he also claims that the no-boundary condition of
quantum cosmology makes two successful predictions: the amplitude and spectrum
of fluctuations in the microwave background. This claim is surely a piece of
gamesmanship. These two predictions come from inflation, not from the no-
boundary condition. The no-boundary condition allows inflation to occur but
only by adding extra matter called a scalar field. This leads to the observed
spectral slope of the fluctuations in microwave background radiations, but I
could just as well have inserted a different scalar field into the early
Universe which would give fluctuations in conflict with the observations, even
though the no-boundary condition still holds.

The “correct” fluctuations come in all cases from an arbitrary choice of
the scalar field, rather than from any prediction of the no-boundary condition
itself.

Another important aspect of the picture of an inflationary Universe that
both authors ignore is that observation requires only the “beginning” of the
Universe be uniform over a tiny region. Inflation can enlarge that uniform
region so that now it is almost uniform over a region larger than our entire
visible Universe. Beyond our horizon, however, the Universe could be quite
different. The global structure of the Universe today may be extremely
irregular: parts may be collapsing, rotating or possess huge variations in
density. This possibility arises naturally from general initial
conditions.

The possibility of such initial conditions cuts through many of the
assumptions made by both protagonists in this debate. They both maintain that
current observations require a high level of uniformity in the initial stages
of the Universe, using this to justify their own strong theories about
cosmological initial conditions. But the observations do not require this and
the initial state may have been globally highly irregular, contrary to
Penrose’s claim that the initial Weyl curvature was very small or Hawking’s
claim that the Universe began in a ground state defined by the no-boundary
condition.

Considering this possibility is vital because, if allowed, it changes the
entire nature of the Universe. It removes the evidence for any initial state
of low “gravitational entropy” or the need to distinguish fundamentally
between initial and final singularities. Indeed, there need be neither a
global initial singularity nor any quantum tunnelling of the Universe out of
nothing. It shows how cosmology is unlike any other physical problem: the
causal horizon structure of the Universe forbids us access to the information
that we require to test a theory of cosmological initial conditions.

The debate between Hawking and Penrose is a live one between brilliant
scientists that covers far more ground than their seven cameo lectures can
encompass. This elegant little volume provides a clear account of two
approaches to some of the greatest unsolved problems of gravitation and
cosmology. It is recommended to critical readers who should not forget that
there are other more widely supported views about these cosmological problems.
Which, if any, view is true? At present only God knows – or maybe
not.

In recent years a vigorous political battle has been fought in the US over
the funding of the most expensive piece of scientific equipment ever planned
– the Superconducting Super Collider (SSC). While particle physicists –
Steven Weinberg among them – foresee its funding and construction as a dream
come true, there are other scientists who see it more as a nightmare in
Ellis County. Lobbying has changed the future of the SSC each year in
response to political football and budgetary realities.

But the debate has not just been about money. Scientific opponents of the
SSC see it as symbolic of a skew in the priorities of science funding,
brought about by a widespread association of words like ‘fundamental’,
‘elementary’ and ‘particle’. Nobel laureates such as Philip Anderson have
argued strongly against the accolade ‘fundamental’ being exclusively
accorded to the study of the smallest particles in nature. In an important
sense he is right. We now recognise three frontiers in modern physics: the
traditional realms of the very large and the very small explored by
astronomers and particle physicists have been joined by that of the very
complex.

Studying complex systems that manifest unusual or unpredictable behaviour as
a consequence of the way in which their constituents are organised has
become a fashionable and inexpensive research industry in recent years. Many
physicists would like to see more investment of resources in such areas at
the expense of the vast particle physics projects that produce a small
number of important facts. By contrast, particle physicists like Weinberg
despair of their subject coming to an end if the funding were to dry up for
experiments. There is only one thing to do in such a situation: write a
book.

Weinberg’s aim is to provide a rationale for a project such as the SSC by
explaining some of the key developments in high-energy particle physics and
what it might reveal about the Universe with a few more tesla electron volts
(TeV) of particle acceleration. He also tries to provide a defence of the
ideas that particle physics is the most fundamental of sciences and that
reductionism holds true by setting up suitable definitions of these two
concepts. No doubt complexity theorists could furnish us with suitable
competing definitions.

He takes the reader on a tour of modern physical ideas that motivate and
support the quest for unification of the laws of nature. The result is a
wide-ranging, if slightly disjointed, discussion that moves from the
exposition of parts of physics to contemplations on beauty in physics, the
unreasonable ineffectiveness of philosophy and speculations about an
ultimate formulation of the laws of nature to the case for constructing the
SSC.

I found the most interesting parts of the discussion dealt with the creation
of the theory of the electroweak interaction, for which Weinberg and Abdus
Salam shared the Nobel prize. The most questionable parts deal with the
nature and recognition of an ultimate theory of physics. Here, too much is
claimed. Weinberg stresses the idea that an ultimate theory should be
‘isolated’ in the sense that any small perturbation of it should in turn
produce quite different physics. Quantum mechanics seems isolated among
existing physical theories; general relativity does not. This criterion of
isolation is advocated as an indicator that an ultimate theory has been
reached (admitting that there may be other quite different isolated
theories as well), but this seems fraught with difficulties. Surely, if
there exist separate isolated theories there must exist a deeper principle
that dictates what they may each be like.

There are two hard questions about ultimate theories of the forces of
nature: can theorists find them? If so, can they be checked by experiment?
There is no evolutionary reason why we need to be smart enough to fathom an
ultimate theory. It would be sheer good fortune to find ourselves living in
a Universe whose underlying laws are simple enough for us to unscramble
after such a short period of investigation. Weinberg focuses upon the ways
in which our search could succeed. He even goes so far as to claim that ‘It
may be that experiments at the Super Collider will yield such illuminating
new information that theorists will be able to complete the final theory
without having to study particles at the Planck energy’. I suspect
Weinberg’s different arguments may interfere destructively at times. The
claim that the ultimate theory might be pieced together from observations at
low energy is hard to reconcile with its isolation in the ‘universe’ of
logically consistent theories. If the ultimate theory is isolated, then
small deviations from it are horribly wrong. But if there is an additional
force of nature too weak to produce any observable effects (it would be
anthropocentric to rule this out), then its existence may still be crucial
for the determination of the ultimate symmetry dictating the laws of nature.
Moreover, even if a theory is logically isolated we can never know that it
is not embedded in some larger mathematical structure. We could not show it
to be a synthetic a priori. In fact, Weinberg believes we will have to use
the anthropic principle to incorporate the cosmological constant into the
theory. However, it could be argued that if recent attempts to explain the
cosmological constant probabilistically were extended to explain the values
of other constants of nature then all their explanations would need to be
anthropic as well.

The experimental testing of an ultimate theory is even more problematic. The
Universe is not constructed for our convenience. There is no reason why
decisive testing of any ultimate theory should be within reach of our
technology. Indeed, current theories lead us to expect that the most
dramatic and decisive features of an ultimate theory will be manifest at
energies billions of times higher than those achievable by the SSC.

Weinberg’s discussion is a mixed bag. He explains difficult physics clearly
and incisively and makes a sensible case for the funding of the SSC as the
next step in the process of checking and developing good theories of
high-energy physics. But I did not find the way in which the search for the
Higgs boson and other new TeV physics is set in the context of discovering
the ultimate theory of nature very persuasive. True, it may yield some
information about such a theory but it is not going to tell us the ultimate
theory of everything.

Here and there Weinberg reveals interesting personal views on peripheral
matters that readers will enjoy. He argues, for instance, that the
structure of King Lear is more beautiful than that of the general theory of
relativity. Elsewhere, one finds further examples of Weinberg’s claim to be
a compromising reductionist (having once been accused of being an
uncompromising one). His discussion of the various threads of theological
opinion is intriguing, as is his confession that it is a tribute to the
fundamental importance of elementary particle physics that very bright
students continue to come into the field when so little is going on. It
will be interesting to see whether this case for the SSC is strong enough to
change minds rather than merely confirm opinions already held.

John Barrow is professor of astronomy at the University of Sussex. His most
recent books are Theories of Everything (Vintage) and Pi in the Sky:
Counting, Thinking and Being (Oxford University Press).

The history of the sciences displays two recognisable types: the unifiers
and the intricacists. The unifiers are fascinated by the harmony and simplicity
at the root of complicated sequences of events. Among their ranks one finds
mathematicians and physicists of a theoretical persuasion who ponder the
parts of the world that are little and large. Whereas the unifiers have
tried to synthesise the world out of little pieces, the intricacists have
sought to understand the whole by studying its pieces bit by bit. Among
their ranks one numbers naturalists, psychologists, meteorologists and sociologists,
along with all manner of physicists and chemists dedicated to the study
of exotic materials in every shape and form.

While the second strategy sounds admirable it is liable to descend
into an elaborate form of stamp collecting, gathering fact after fact in
the hope that there is a grand unifying theory to pull them together.
Meanwhile, the unifiers have unravelled simple laws, solved all manner of
mysteries about the world and, above all, developed a masterly facility
for distilling off the simple essence of a situation so that they can describe
its workings approximately. As a result, the unifiers have dominated many
of the scientific disciplines.

This has begun to change with the advent of fast, inexpensive, small
computers, which have added a formidable weapon to the armoury of the intricacist.
Complex systems and sequences of events can now be simulated and watched.
Their evolution can be speeded up by enormous factors. Problems which are
intractable using exact mathematical methods become the focus of experimental
mathematical study, opening a new frontier of fundamental science (see Complexity
Supplements, żìĂš¶ÌÊÓÆ”, 6 and 13 February). What characterises the objects
of study is collective behaviour that amounts to more than the sum of its
parts. A system like the brain does what it does, not because of the nature
of the pieces out of which it is made, but because of the way in which those
pieces are organised.

This book tells the story of some of these searchers after complexity:
how they germinated ideas about the development of organised complexity
and the emergence of transient order in evolving systems far from the simplicities
of equilibrium; how they were pulled together by the dream of the Santa
Fe Institute in New Mexico; and how their vision of a new interdisciplinary
science of evolving complexity has itself evolved in unexpected ways.

Mitchell Waldrop has focused on the interesting personalities that
have played a role in the development of the study of organised complexity.
They are a band of economists, biologists, computer scientists physicists
and mathematicians who thought they had nothing in common until they were
forced into interaction by the interdisciplinary programmes that were initiated
by the Santa Fe Institute. Set up in 1984 to act as a catalyst for research
into complex systems, the institute plays host to a stream of visiting researchers
and as well as building links with other centres of research.

The style of the book is serious journalism with a strong emphasis on
personal conversations to try to convey an inside feel for the concept of
Santa Fe and the style of work it has encouraged. Waldrop describes some
of the scientific projects in great detail, particularly those in the biological
area, but is sketchy on others, especially the economics projects which
seem to be a major part of the institute’s programme. But by focusing on
individuals, the story avoids becoming stuck in the groove of just explaining
the science of complexity. The price to pay is that the book ends up being
rather too long, with repetition of general scientific ideas. Indeed, the
author seems to have begun to weary himself, because the book peters out
into an unmemorable end. But along the way there are some nice lines from
the protagonists: the University of Arizona – ‘a real Ken and Barbie kind
of place’ – or the image of a mountaineer about to descend into a hole in
the ground, ‘because it’s not there’.

A recurring lesson from Waldrop’s story is how complex systems are providing
an interesting antidote for philosophers of science who place too much
emphasis upon falsification and prediction as the hallmarks of science.
When faced with a complex system such as the Earth’s weather system or an
economy, we may have mathematical models of all or part of it. But because
the system will exhibit extreme sensitivity to its starting conditions we
will not be able to predict the future with that model. We can predict
aspects of the weather, but not the detailed whole. However, one can understand
and explain any atmospheric phenomena that are seen by using the ingredients
of the model. The comprehension and explanation of observed trends is more
fundamental to the study of complex systems than the ability to predict
the future.

The students of organised complexity are seeking general principles
that can specify what complexity is and determine how it develops. If such
generalities exist then they would have application across a wide range
of disciplines. At present the search for such principles is pursued through
thorough investigation of subjects which display novel types of complexity.
In this way one builds up a repertoire of examples and ideas which can be
stripped of their specific applications in, say, biology or economics, in
order to isolate the general lessons that underpin them.

Waldrop has done a good job of conveying the intellectual atmosphere
surrounding the emergence of the study of complexity. This is not the book
to read if you want to learn about complexity itself, for while the author
provides quite a lot of background discussion of the problems it tackles,
that is not his primary aim. He has succeeded in showing that the social
organisation associated with a collective intellectual development is
itself a complex system which exhibits many of the vital features of emergence,
modified adaption, random drift and selection that typify many of their
objects of study.

John Barrow is professor of astronomy at the University of Sussex. His
most recent books are Pi in the Sky: Counting, Thinking and Being (Oxford)
and Theories of Everything: The Quest for Ultimate Explanation (Vintage).

A French writer Jacques Bernadin de St Pierre taught people that dogs
were generally of two opposite colours so that we might distinguish them
more easily from the furniture when they were inside the house, and that
fleas jump instinctively on white colours so that we might kill them more
readily. People once believed that everything in the world was designed
solely for their convenience and benefit. One consequence of this belief
is that there can exist no unpleasant by-products to muddy the waters in
a cloud-cuckoo-land where all is for the best in the best of all possible
worlds.

It is evident that Hubert Reeves has been influenced in the writing
of this book by the question ‘Why do scientific popularisers so often write
only about the wonders of the Universe?’ The implication is that there is
so much of the opposite all around us, and not just that created by our
own efforts either, that one might legitimately inquire whether these failings
in human and cosmic affairs are an inevitable side effect of some natural
process.

In fact, it is rather like asking the scientific populariser about the
problem of evil. But to ask popularisers why they dwell on the bright side
reveals a real difference in perspective. For the questioner, it is the
human condition that looms largest. But the populariser, perhaps, sees humanity
as a very small part of an impersonal network of law and order, matter and
motion, that make up the Universe.

Some scientists and writers see science as a means of taking us away
from parochial or subjective matters and into contact with some sort of
ultimate objective reality of which we are but a minuscule consequence.
The questioner may find that tendency related to the growth of a scientific
attitude that can be impervious to human concerns unless they fit technical
goals.

Reeves attempts to sketch the astronomical and biochemical aspects of
the evolution of complexity from molecules to sentience in the Universe.
He sets this seemingly inexorable rise against the vista of imminent self-destruction
that he believes we face by arming ourselves with weapons of mass destruction.
Why does the human species indulge in destructive warfare? How should we
treat animals and the natural environment? How can we guard against human
fanaticism? Is the silence of infinite space simply a witness to the self-destruction
of other advanced civilisations torn apart by the contradictions and conflict
that seems to be the culmination of advanced evolution?

The author freely admits that he has no answers to these great human
problems. He believes that a recognition of their existence is a sufficient
ground for future hope and asks the reader to indulge in some delight at
the nature of the world around us. Even if biologists persuade us that unsavoury
aspects of human and animal behaviour are concomitants of the evolution
of complexity in the Universe, Reeves believes passionately in the importance
of individual conscience and responsibility for what happens in the world.
At root he is attempting to join a rough and ready theory of aesthetics
and ethics to the scientific picture of the evolving Universe. Annie Leclerc
illuminates the sense of the book’s title as she writes of her childhood
experience of coming to know and appreciate the world around her. She discovered
‘that knowing and asserting had to come from the strongest and most forceful
place, that our faculty for what is truly desirable was neither understanding,
nor reasoning, nor intelligence, but solely delight’.

At the core of the book, to which three-quarters of its pages are devoted,
is a description of the hierarchy of structures that are found in nature
from sub-atomic particles, through atom and molecules, up to materials,
planets and people. This discussion is in some ways an outline of the anthropic
principle. They involve the chain of interesting coincidences that have
been exploited by the evolution of matter in the Universe in its path from
simplicity to complexity.

Reeves chooses complexity as the parameter that charts the progress
of the material contents of the Universe. He proposes a ‘complexity principle’
that ‘Since the earliest times accessible to our exploration, the Universe
has possessed the properties required to enable matter to ascend the pyramid
of complexity’. These properties, as we now appreciate, are rather peculiar
and could easily have been avoided. If the Universe had turned out to be
devoid of life, we would have had little trouble in explaining the fact
(an aphorism whose self-referential consistency should not be examined too
closely).

Reeves characterises this complexity only in terms of thermodynamic
entropy. This is unsatisfactory as we now know about other measures of complexity
that go some way to capturing the quality, as well as the quantity of the
information. The lack of any contact with this extensive modern literature
on order and complexity is one of the consequences of the five-year interval
since this book first appeared in French. Indeed, this long gap since the
original writing of the book makes quite a lot of its discussion seem dated.
There can even be progress outside of science. The nuclear equation has
been transformed into a new and less threatening form. In all probability
this was a bigger issue for the French readers of the original edition,
faced as they were by the appalling revelation of state terrorism in the
Rainbow Warrior affair.

This is a thoughtful book that was hugely successful in France where
Reeves is a household name. It is easy to read, has interesting scientific
content and raises great questions which it leaves unanswered. It attempts
to bring together scientific and humane concerns about the evolution of
the Universe and some of its contents. But I don’t believe it will console
the sceptical inquirer who inspired it. The humane considerations do not
emerge naturally enough from the cosmological picture that the author paints.
They are almost artificially attached and not subject to the same careful
discussion as the scientific facts. This uneasy alliance may merely confirm
our sceptic’s worst fears that scientists devote all their talents for systematic
and careful analysis to scientific questions but do little more than think
haphazardly about more pressing problems.

As a cure for the blues it’s never been enough to say with Goethe that
theories are grey, but trees are always green. Things are never quite so
black and white. But maybe we should nonetheless read this book.

John Barrow is professor of astronomy at the Astronomy Centre, University
of Sussex. His newbook Theories of Everything has recently been published
by Oxford University Press.

Christian apologetics, like those of other religions, bend with the
winds of change. As the dominant paradigms that we use to encapsulate the
Universe have evolved so has the emphasis of the apologists’ arguments.
From the beginnings of serious philosophical thought you can extract two
strands of thinking about the world: one that emphasises the unchanging
elements of and behind the physical world as pre-eminent; the other points
to the ephemera of individual events as the over-riding reality.

We see this divide in ancient philosophy where the Platonists tried
to associate the true nature of things with the unchanging forms behind
the world of observation while the earthiness of Heraclitus and Aristotle
heralded the individual outcomes as the vital element. There have been parallel
strands in theology that have set the unchangeableness of God – ‘the same
yesterday, today and forever’ – against the process theologians’ picture
of a continously changing and evolving deity ‘perfecting all things unto
łóŸ±łŸČő±đ±ôŽÚ’.

In physical science there is a similar dichotomy between laws and events.
Laws of change can be represented as invariances of particular ‘conserved’
quantities in nature, which are equivalent to the preservation of some underlying
symmetries in the way of the world. The outcomes of those laws, on the other
hand, need not respect that symmetry and will in general be far more complicated
in form than the laws themselves. Physicists talk endlessly about the symmetry
and simplicity of the laws of nature but invariably fail to impress the
life scientists whose bread and butter is the complicated outcomes of the
laws of nature that result from the higgledy-piggledy of natural selection
where the underlying symmetries are totally hidden.

Science has been dominated by the strand that emphasises the unchanging
laws and symmetries of nature as her most indelible hallmark from the time
of Newton until little more than a decade ago. Religious apologetics followed
this lead, pointing to the harmonious form and unerring logic of the laws
of nature – the ‘laws that never shall be broken. For their guidance hath
He made’ – rather than the peculiar appropriateness of their asymmetrical
outcomes – the eye, the hand, the match between creature and habitat that
natural selection so elegantly explained – as the signature of the author
of nature.

But the emergence of the sciences of complexity has changed the course
of the river to change. There exist complex phenomena whose evolution through
time cannot be represented by any abbreviated formula, so that the most
succinct representation of their information content is nothing less than
their complete history. There exists no briefer encapsulation: no invariant
whose preservation is equivalent to their ever-novel behaviour.

The focus upon these complex and chaotic processes has urged us to regard
‘becoming’ as irreducible to mere ‘being’: we cannot expunge the concept
of time from all of the everyday phenomena that we encounter by restating
them as abbreviated statements of invariance. Professor John Polkinghorne
takes this change of focus within science very seriously and attempts to
extract from it some new theological lessons. His short book is based upon
a series of lectures delivered in Oxford in 1987, which was probably a little
too early to take on board the most striking developments in the study of
complexity. Although the author writes eloquently upon topics from the problem
of evil to miracles, from prayer to time and providence, he has been greatly
impressed by these developments. He repeatedly uses them in his attempts
to create a new theological perspective.

So Polkinghorne claims that, because chaotic systems possess so strong
a dependence upon their initial states that they are unpredictable, there
is scope for the deity to make his presence felt in an otherwise deterministic
world. This idea spreads its influence through the discussion of providence
and miracles.

He argues: ‘The generation of weather is a much more complex process,
within which it is conceivable that small triggers could generate large
effects. Thus prayer for rain does not seem totally ruled out of court.
In this way one can gain some rough comprehension of the range of imminent
action. It will always lie hidden in those complexes whose precarious balance
makes them insusceptible to prediction. The recently gained understanding
of the distinction between physical systems which exhibit being and those
which exhibit becoming may be seen as a pale reflection of the theological
dialectic of God’s transcendence and God’s imminence .. If God acts in
the world through influencing the evolution of complex systems, he does
not do so by the creative input of energy’. The author sees this breach
of traditional determinism as the new gap through which God can slip.

While I believe that this change of emphasis in the scientific view
of the world should have important consequences for theological and philosophical
ideas about the nature of things, I think one might be sceptical as to whether
Polkinghorne has picked a fruitful point to exploit. If one restricts attention
to the Newtonian, deterministic view of the world, and ignores quantum mechanics
for a moment, then while it is true that there exist complex and chaotic
phenomena whose behaviour depends with exponential sensitivity upon their
starting state, this means simply that they are indeterministic in practice
(for us), not that they are indeterministic in principle. There is no logical
gap for God to sneak through and direct events without doing violence to
the observed laws of nature unless the deterministic laws are temporarily
suspended. If we go along that road we are simply back with the same old
choice that existed long before any apologist ever thought of chaos.

If we introduce the quantum nature of reality then the game does change
because the starting conditions of a complex chaotic system are now indeterminate
in principle, not just in practice. Moreover, this irreducible quantum uncertainty
can be amplified to a significant level on the scale of everyday experience
very easily and quickly. So there do exist some aspects of things that are
indeterminate and through which a deity could apparently intervene without
doing violence to the invariant laws of nature.

But there does not seem to be anything in this that has not been said
by religious apologists ever since they appreciated the implications of
quantum theory. There is a finite probability that jars of water will quantum-mechanically
tunnel into jars of wine: that is, change between two states. No laws of
nature need be violated. But I wonder how persuasive such apologetics really
are with the audience at whom they are aimed: those who understand quantum
mechanics.

Moreover, as the scientists of the 18th and 19th century fully appreciated,
when you consider ‘random’ processes, as they would have called them, it
is important to explain why there exist stable long-term averages. Florence
Nightingale, who in her spare time was a keen student of the fast-growing
subject of statistics, regarded the emergence of such long-term stability
out of a concatenation of independent random events as a hallmark of divine
guidance. Polkinghorne ignores this emergence of orderly large-scale phenomena
out of microscopic chaos in his discussion but it would be interesting to
see him attempt to incorporate it into his view.

This is an interesting although not entirely persuasive attempt to draw
together some modern ideas in science and theology. All those interested
in the interaction between science and religion should read it. It is less
than 100 pages long, clearly written, and delightfully free of unnecessary
verbiage and semantic obfuscation. Whether the result is a theology of chaos
or a chaotic theology, I must leave discerning readers to decide for themselves.

John Barrow is professor of astronomy at the University of Sussex. His
most recent book, The World Within The World, is published in paperback
by Oxford.

The Big Bang theory of the expanding Universe is the central paradigm
within which we make sense of the observations that accrue from the instruments
of modern astronomy. Whereas the ancients could see no more than a few thousand
stars in the heavens, we have come to witness not only billions of stars
and galaxies beyond our own, but also a faint glimmer of microwaves all
around us. This is the echo of the Big Bang, the fallout of radiation from
the once hot Universe. As the Universe has expanded and aged so this radiation
has cooled and rarefied until it has become only a minor player besides
the other forms of matter in the Universe.

We build our picture of the expanding Universe upon this and other fossil
evidence that has endured since the first few seconds of its history. During
those early moments, the Universe resembled a vast nuclear reactor burning
hydrogen into helium, deuterium and lithium. We can predict the abundances
of each of these nuclear by-products with great accuracy, and they are found
to be in agreement with the amounts that now exist.

Despite these great successes, there are a multitude of unanswered
questions in modern cosmology. Where do galaxies come from? Is the Universe
infinite or finite? Why is the Universe expanding at a rate so close to
the great divide that separates a future of indefinite expansion from one
of eventual contraction towards a ‘Big Crunch’ of ever-increasing heat and
density? The absence of answers indicates that there is a fundamental incompleteness
to the simple picture of an expanding Big Bang Universe.

Prior to 1980 there was little consensus in the search for the answers
to such questions. They are all conundrums about the present state of the
Universe whose solutions are ultimately hidden in the miasma surrounding
the first instants of its expansion. A reconstruction of those events has
been possible only since the mid 1970s when researchers presented a successful
new picture of how elementary particles interact at high energy. Whereas
previously, we believed that elementary particles would interact more strongly
at higher energies, so making their study less tractable, the new picture
of ‘asymptotic freedom’ predicted just the opposite; as energies rise interactions
get weaker.

The idea of the ‘inflationary universe’ was proposed by Alan Guth in
1980. It is a minor gloss on the standard picture of the expanding Universe
that has a wealth of interesting consequences which promise to resolve some
of the unanswered questions about the properties of the Universe.

The traditional Bang Bang Universe decelerates for ever after its expansion
begins, slowed by the ubiquitous pull of gravity. But elementary particles
can create states of matter that produce a brief period of cosmic history
during which the Universe accelerates, or ‘inflates’. If this inflationary
surge lasts long enough then we may arrive at an understanding of why the
Universe has got so large.

Andrei Linde has played an important role in unveiling many of the details
of the inflationary universe and has attempted to show that a period of
inflation during the first instants of the Universe’s history is a strong
possibility. This work has led him to propose new approaches to the problem
of describing the Universe as a quantum-mechanical entity. He is also a
strong supporter of the view that the use of the anthropic principle is
absolutely essential for the correct interpretation of the inflationary
universe and the comparison of tis predictions with observation. In reality,
it has been employed in many cosmological models that possess some intrinsically
random element in their early history, creating cosmic conditions that differ
from place to place.

This volume pulls together and amplifies a collection of Linde’s articles.
Some are research papers; others are talks or less accessible expository
articles from scattered collections. Also included is a collection of Linde’s
cartoons with cosmological morals. Responses to these illustrations are
likely to be mixed; cute but the draughtsmanship is often messy.

Students of inflation will find it valuable to have all this material
together although they will find the author’s expository powers somewhat
lacking. Linde has put too little effort into the opening chapter introducing
the problems that his model of the inflationary universe aims to resolve.
The synthetic aspect of the book’s composition also makes it easy to omit
the necessary introductory discussion of theoretical cosmology and fails
to identify many of the notations being used. This considerably reduces
the potential audience.

Another defect is the inevitable repetition of identical material in
different chapters, which arouses the suspicion that it is indeed possible
to write a book one has never read. Linde often appears to ignore the breadth
of earlier cosmological ideas in order to boost the apparent novelty of
the inflationary model. The strong points of the exposition are the way
in which the same basic model for inflation is employed repeatedly to explain
a number of different features of the scheme.

Linde also offers interesting teatments of the quantum cosmological
problem and how it should be interpreted, together with his intriguing proposal
for explaining why the cosmological constant appears to have a numerical
value indistinguishable from zero in our Universe. His detailed model of
a number of different universes interacting together was the precursor of
the currently popular conception of the early Universe as a many-handled
space connected to itself and other ‘baby universes’ by tubes, or ‘worm-holes.’
Here, and in the last third of the book, the author’s fertile imagination
comes fully into play and there is much for any cosmologist to learn from
its pages.

This is a book for the serious student of cosmology. Parts of it will
be of interest to graduate students engaged in final year projects devoted
to aspects of the inflationary universe. Prospective research students in
cosmology would also do well to have a copy.

John Barrow is Professor of Astronomy at the University of Sussex.

THE big bang theory of the expanding Universe is the central paradigm
within which cosmologists make sense of the observations that accrue from
the instruments of modern astronomy. The ancients could see no more than
a few thousand stars in the heavens. Today, we can witness not only billions
of stars and galaxies beyond our own, but also a faint glimmer of microwaves
all around us.

The microwaves are the echo of the big bang; the radiation fallout from
the once-hot Universe. As the Universe has expanded and aged, so this radiation
cooled and rarified until it became only a minor player besides the other
forms of matter in the Universe.

Our picture of the expanding Universe is built upon this and other fossil
evidence that has remained since the first few seconds of its history. During
those early moments, the Universe resembled a vast nuclear reactor burning
hydrogen into helium, deuterium and lithium. Cos mologists can predict,
with great accuracy, the abundances of each of these nuclear by-products,
and the abundances are in agreement with the amounts of elements that now
exist in the Universe.

Yet, despite these successes, there are a multitude of unanswered questions
in modern cosmology: Where do galaxies come from? Is the Universe infinite
or finite? Why is the Universe so old? Why is the Universe expanding at
a rate so close to the great divide which separates a future of indefinite
expansion from one of eventual contraction leading to a big crunch of ever-increasing
heat and density? The absence of answers to such questions indicates that
there is a fundamental incompleteness to the simple picture of an expanding
big-bang Universe.

Prior to 1980, there was little consensus in the search for the answers
to such questions. They are all conundrums about the present state of the
Universe whose solutions are hidden in the miasma surrounding the first
instants of its expansion.

A plausible reconstruction was not even possible until the mid-1970s,
when physicists conceived a new picture of how elementary particles interact
at high energy. Until then, they believed that elementary particles would
interact more strongly at higher energies, so making their study less tractable.
The new picture of ‘asymptotic freedom’ predicted just the opposite: as
energies rise, interactions become weak er. As a result, the study of the
first moments of the big bang be came a challengeable problem in high-energy
physics.

In 1980, Alan Guth, a physicist at the Massachusetts Institute of Technology
in the US, put forward the idea of the ‘inflationary universe’. It is a
minor gloss on the standard picture of the expanding Universe, but has a
wealth of consequences that promise to resolve some of the unanswered questions
about the properties of the Universe.

The traditional big-bang Universe forever decelerates after its expansion
begins – slowed by the ubiquitous pull of gravity. But elementary particles
can create states of matter which produce a brief period of cosmic history
during which the Universe accelerates, or ‘inflates’. If this inflationary
surge lasts long enough, then we may arrive at an understanding of why the
Universe has got so large, why it hoves so close to the divide that separates
an ever-expanding future from a recollapsing one, and how the seeds from
which the galaxies have grown first originated.

Andrei Linde has played an important role in unveiling many of the details
of the inflationary universe, and he has attempted to show that a period
of inflation during the first instants of the Universe’s history is a strong
possibility. This work has led him to propose a number of new approaches
to the problem of describing the Universe as a quantum mechanical entity.

He is also a strong supporter of the view that the anthropic principle
is absolutely essential for the correct interpretation of the inflationary
universe and the comparisons of its predictions with observation. But in
Inflation and Quantum Cosmology it becomes clear that he mistakenly believes
the weak anthropic principle to be important only in the context of the
inflationary universe model. In reality, it has been employed in many cos
mological models that possess some intrinsically random element in their
early history which creates cosmic conditions that differ from place to
place.

This volume pulls together and amplifies a collection of Linde’s articles
from a variety of sources. Some are research papers, others are talks or
less accessible explanatory articles from scattered collections.

Included as an appendix is a collection of cartoons with cosmological
morals which he has prepared over the years. Responses to these illustrations
are likely to be mixed: the idea behind them is often cute but the draughtsmanship
can be distractingly messy.

A strong point of the book is the way it employs the same basic model
for inflation to explain a number of different features of the scheme. There
are also interesting treatments of the quantum cosmological problem and
how it should be interpreted, together with Linde’s intriguing proposal
for explaining why the cosmological constant appears to have a numerical
value indistinguishable from zero in our Universe.

His detailed model of a number of different universes interacting together
was the precursor of the currently popular conception of the early Universe
as a many-handled space connected to itself and other ‘baby universes’ by
tubes, or ‘wormholes’. Here, and in other sections throughout the last third
of the book, the author’s fertile imagination comes fully into play and
there is much for any cosmologist to learn from its pages.

Students of inflation will find it valuable to have all this material
together, although they may find the author’s expository powers lacking
in some respects. In particular, he expended too little effort upon the
opening chapter which introduces the problems that the inflationary universe
aims to resolve.

Linde also tends to adopt the position of a missionary who is convinced
of the truth of his message. As a result, he oversells some of the features
of the inflationary model. Moreover, he appears often to ignore the breadth
of early cosmological ideas in order to boost the apparent novelty of the
inflationary model.

Irritating defects include a synthetic composition that makes it easy
to omit the necessary introductory discussion of the oretical cosmology,
and to fail to identify much of the notation being used. The repet ition
of identical material in different chapters also arouses the suspicion that
it is indeed possible to write a book which one has never read.

Despite these criticisms, the serious student of cosmology will find
Inflation and Quantum Cosmology useful. Parts of it will be of interest
to undergraduates engaged in final-year projects devoted to aspects of the
inflationary Universe. Prospective research students in cosmology spending
some of their summer vacation at airports would do well to have a copy in
their rucksacks.

John Barrow is professor of astronomy at the University of Sussex. His
latest book is The World Within The World (Oxford UP).