From Cosmos to Chaos: The Science of Unpredictability

225 Pages·2010·3.195 MB·English

by  Peter Coles

FROM COSMOS TO CHAOS
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FROM
COSMOS TO
CHAOS
The Science of Unpredictability
Peter Coles
AC
AC
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Coles,Peter.
Fromcosmostochaos:thescienceofunpredictability/PeterColes.
p.cm.
ISBN-13:978–0–19–856762–2(alk.paper)
ISBN-10:0–19–856762–6(alk.paper)
1. Science—Methodology. 2. Science—Forecasting. 3. Probabilities. I. Title.
Q175.C61552006
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ISBN0–19–856762–6 978–0–19–856762–2
1 3 5 7 9 10 8 6 4 2
‘The Essence of Cosmology is Statistics’
George Mcvittie
Acknowledgements
IamverygratefultoAnthonyGarrettforintroducingmetoBayesian
probabilityanditsdeeperramifications.Ialsothankhimforpermission
to use material from a paper we wrote together in 1992.
Various astronomers have commented variously on the various
ideas contained in this book. I am particularly grateful to Bernard
Carr and John Barrow for helping me come to terms with the
Anthropic Principle and related matters.
I also wish to thank the publisher for the patience over the
ridiculously long time I took to produce the manuscript.
Finally, I wish to thank the Newcastle United defence for helping
me understand the true meaning of the word ‘random’.
Contents
List of Figures viii
1. Probable Nature 1
2. The Logic of Uncertainty 7
3. Lies, Damned Lies, and Astronomy 31
4. Bayesians versus Frequentists 48
5. Randomness 71
6. From Engines to Entropy 95
7. Quantum Roulette 115
8. Believing the Big Bang 138
9. Cosmos and its Discontents 161
10. Life, the Universe and Everything 180
11. Summing Up 199
Index 213
List of Figures
1 Venn diagrams and probabilities 12
2 The Normal distribution 29
3 The Hertzprung-Russell diagram 33
4 A scatter plot 34
5 Statistical correlation 40
6 Fitting a line to data 41
7 Pierre Simon, Marquis de Laplace 43
8 The likelihood for the distribution of arrival times 57
9 Inductive versus deductive logic 62
10 Correlation between height and mass for humans 74
11 Lissajous figures 82
12 The transition to chaos shown by the
He´non-Heiles system 84
13 Transition from laminar to turbulent flow 85
14 The first-digit phenomenon 88
15 Randomness versus structure in point processes 91
16 A computer-generated example of a random walk 93
17 Using a piston to compress gas 97
18 The set of final microstates is never smaller than the
initial set 112
19 The ultraviolet catastrophe 117
20 A classic ‘two slit’ experiment 124
21 Closed, open, and flat universes 141
22 A map of the sky in microwaves revealed by WMAP 155
23 The cosmological flatness problem 167
24 The Strong Anthropic Principle may actually be Weak 176
N O
1
Probable Nature
The true logic of this world is the calculus of probabilities.
James Clerk Maxwell
This is a book about probability and its role in our understanding of
the world around us. ‘Probability’ is used by many people in many
differentsituations,oftenwithoutmuchthoughtbeinggiventowhat
the word actually means. One of the reasons I wanted to write this
book was to offer my own perspective on this issue, which may be
peculiar because of my own background and prejudices, but which
may nevertheless be of interest to a wide variety of people.
My own field of scientific research is cosmology, the study of the
Universeasawhole.Inrecentyearsthisfieldhasbeenrevolutionized
by great advances in observational technology that have sparked a
‘data explosion’. When I started out as an ignorant young research
student20yearsagotherewasvirtuallynorelevantdata,thefieldwas
dominatedby theoreticalspeculation andit waswidely regardedas a
branch of metaphysics. New surveys of galaxies, such as the Anglo-
Australian Two-degree Field Galaxy Redshift Survey (2dFGRS) and
the (American) Sloan Digital Sky Survey (SDSS), together with
exquisite maps of the cosmic microwave background, have revealed
the Universe to us in unprecedented detail. The era of ‘precision
cosmology’hasnowarrived,andcosmologistsarenowrealizingthat
sophisticatedstatisticalmethodsareneededtounderstandwhatthese
new observations are telling us. Cosmologists have become glorified
statisticians.
Thiswasmyoriginalmotivationforthinkingaboutwritingabook,
but thinking about it a bit further, I realized that it is not really
correct to think that there is anything new about cosmology being
a statistic subject. The quote at the start of this book, by the dis-
tinguishedBritishmathematicianGeorgeMcVittieactuallydatesfrom
the 1960s, long before the modern era of rapid data-driven progress.