Barrow - Impossibility - Limits Of Science.pdf - Science and Philosophy - michalszasz121

The meaning of the world is the separation of wish and fact.

KURT GÖDEL

In memory of

Roger Tayler

Impossibility

The Limits of Science and

the Science of Limits

JOHN D. BARROW

Astronomy Centre

University of Sussex

OXFORD UNIVERSITY PRESS • OXFORD

1998

Preface

The Preface is the most important part

of the book. Even reviewers read a preface.

PHILIP GUEDALLA

Both scientists and philosophers are much concerned with impossibilities.

Scientists like to show that things widely held to be impossible are in fact entire-

ly possible; philosophers, by contrast, are more inclined to demonstrate that

things widely regarded as perfectly feasible are in fact impossible. Yet, para-

doxically, science is only possible because some things are impossible.

The incontrovertible evidence that Nature is governed by reliable 'laws' allows

us to separate the possible from the impossible. Only those cultures for whom

there existed a belief that there was a distinction between the possible and the

impossible provided natural breeding grounds for scientific progress. But

'impossibility' is not only about science. In the pages that follow we shall look at

some of the ways in which the impossible in art, literature, politics, theology,

and logic has stimulated the human mind to take unexpected steps: revealing

how the concept of the impossible sheds new light on the nature and content of

the actual.

The idea of the impossible rings alarm bells in the minds of many. To some,

any suggestion that there might be limits to the scope of human understanding

of the Universe or to scientific progress is a dangerous meme that undermines

confidence in the scientific enterprise. Equally uncritical, are those who enthu-

siastically embrace any suggestion that science might be limited because they

suspect the motives and fear the dangers of unbridled investigation of the

unknown.

At the end of each century there seems to arise a stock-taking in science. We

shall see that at the end of the last century the issue of the limits of science

became a live one and attempts were made to pick out problems that could

never be solved. These problems still make interesting reading. But what will

people say about our concerns in a hundred years time? As we near the end of

the twentieth century we look back on an extraordinary century of progress. Yet

it is progress that possesses some extraordinary characteristics. A pattern has

emerged in many spheres of inquiry in which a scientific theory becomes so

successful in the quantity and quality of its accurate predictions that its practi-

VIII PREFACE

tioners start to wonder whether the end is in sight—whether their theory might

be able to explain everything within its encompass. But then something strange

happens. The theory predicts that it cannot predict. It turns out to be not simply

limited in scope, but self-limiting. This pattern is so strikingly recurrent that

it suggests to us that we can recognize mature scientific theories by their self-

limiting character. Such limits arise not merely because theories are inadequate,

inaccurate, or inappropriate: they tell us something profound about the nature

of knowledge and the implications of investigating the Universe from within.

Our study of the limits of science and the science of limits will take us from

the consideration of practical limits of cost, computability, and complexity to

the restrictions imposed on what we can know by our location in the middle of

the Nature's spectra of size, age, and complexity. We shall speculate about our

possible technological futures and locate our current abilities on the spectrum

of possibilities for the manipulation of Nature in the realms of the large, the

small, and the complex. But practicalities are not the only limits we face. There

may be limits imposed by the nature of our humanity. The human brain was not

evolved with science in mind. Scientific investigation, like our artistic senses, are

by-products of a mixed bag of attributes that survived preferentially because

they were better adapted to survive in the environments they faced in the far

distant past. Perhaps those ambiguous origins will compromise our quest for

an understanding of the Universe? Next, we shall start to pick at the edges of

possible knowledge. We shall learn that many of the great cosmological

questions about the beginning, the end, and the structure of our Universe are

unanswerable. Despite the confident exposition of the modern view of the

Universe by astronomers, these expositions are invariably simplified in ways

that disguise the reasons why we cannot know whether or not the Universe is

finite or infinite, open or closed, of finite age or eternal. Finally, we delve into

the mysteries of the famous theorems of Godel concerning the limitations of

mathematics. We know that there must exist statements of arithmetic whose

truth we can never confirm or deny. What does this really mean? What is the

fine print on this theorem? What are its implications for science? Does it mean

that there are scientific questions that we can never answer? We shall see that the

answers are unexpected and lead us to consider the possible meaning of incon-

sistency in Nature, of the paradoxes of time travel, the nature of freewill and the

workings of the mind. Finally, we shall explore some of the strange implications

of trying to pass from the consideration of individual choices to collective

choices. Whether it is the outcome of an election or the making up of one's

mind in the face of the brain's competing options, we find a deep impossibility

that may have ramifications throughout the domain of complex systems.

Here, in this strange world of fundamental limits we learn that worlds that are

complex enough for certain individualities to be manifest necessarily display an

PREFACE

open-endedness that defies capture within the confines of a single logical sys-

tem. Universes that are complex enough to give rise to consciousness impose

limits on what can be known about them from within.

By the end of our journey, I hope the reader will have come to see that there is

more to impossibility than first meets the eye. Its role in our understanding of

things is far from negative. Indeed, I believe that we will gradually come to

appreciate that the things that cannot be known, that cannot be done, and can-

not be seen, define our Universe more clearly, more completely, and more

sharply than those that can.

This book is dedicated to the memory of Roger Tayler, who sadly did not live

to see it finished. His selfless service to his colleagues at Sussex and to the wider

community of astronomers in Britain and around the world won him the

respect, admiration, and friendship ,of scientists everywhere. He is greatly

missed.

I would like to thank many people who helped me by their comments or

advice, or who provided pictures and references, especially David Bailin, Per

Bak, Margaret Boden, Michael Burt, Bernard Carr, John Casti, Greg Chaitin,

John Conway, Norman Dombey, George Ellis, Mike Hardiman, Susan Harrison,

Jim Hartle, Piet Hut, Janna Levin, Andrew Liddle, Andre Linde, Seth Lloyd,

Harold Morowitz, David Pringle, Martin Rees, Nicholas Rescher, Mark Ridley,

David Ruelle, John Maynard Smith, Lee Smolin, Debbie Sutcliffe, Karl Svozil,

Frank Tipler, Joseph Traub, and Wes Williams. My wife Elizabeth helped in

many practical ways, and accommodated innumerable new pieces of paper in

the house with surprising good humour, whilst the subject of this book merely

provoked our children, David, Roger, and Louise, to worry that there might

indeed be fundamental limits on the use of the telephone.

Brighton

November 1997

J.D.B.

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