An Unabridged, Digitally Enlarged Printing: The Meaning Of Probability - Probability In Relation To The Theory Of Knowledge - The Measurement Of Probabilities - The Principle Of Indifference - Other Methods Of Determining Probabilities - The Weight Of Arguments - Historical Retrospect - The Frequency Theory Of Probability - The Theory Of Groups, With Special Reference To Logical Consistence, Inference, And Logical Priority - The Definitions And Axioms Of Inference And Probability - The Fundamental Theorems Of Necessary Inference - The Fundamental Theorems Of Probable Inference - Numerical Measurement And Approximation Of Probabilities - Some Problems In Inverse Probability, Including Averages - The Nature Of Argument By Analogy - The Value Of Multiplication Of Instances, Or Pure Induction - Some Historical Notes On Induction - The Meanings Of Objective Chance, And Of Randomness - Some Problems Arising Out Of The Discussion Of Chance - The Application Of Probability To Conduct - The Nature Of Statistical Inference - The Law Of Great Numbers - The Theorems Of Bernoulli, Poisson, And Tchebycheff, etc., etc. - Bibliography And Comprehensive Index

"...a blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) ...and the illustrations include many superb examples of computer graphics that are works of art in their own right." Nature

A fascinating memoir from the man who revitalized visual geometry, and whose ideas about fractals have changed how we look at both the natural world and the financial world.
Benoit Mandelbrot, the creator of fractal geometry, has significantly improved our understanding of, among other things, financial variability and erratic physical phenomena. In The Fractalist, Mandelbrot recounts the high points of his life with exuberance and an eloquent fluency, deepening our understanding of the evolution of his extraordinary mind. We begin with his early years: born in Warsaw in 1924 to a Lithuanian Jewish family, Mandelbrot moved with his family to Paris in the 1930s, where he was mentored by an eminent mathematician uncle. During World War II, as he stayed barely one step ahead of the Nazis until France was liberated, he studied geometry on his own and dreamed of using it to solve fresh, real-world problems. We observe his unusually broad education in Europe, and later at Caltech, Princeton, and MIT. We learn about his thirty-five-year affiliation with IBM’s Thomas J. Watson Research Center and his association with Harvard and Yale. An outsider to mainstream scientific research, he managed to do what others had thought impossible: develop a new geometry that combines revelatory beauty with a radical way of unfolding formerly hidden laws governing utter roughness, turbulence, and chaos.
Here is a remarkable story of both the man’s life and his unparalleled contributions to science, mathematics, and the arts.

Preface
It is 2050, and you are watching Who Wants to be a Billionaire? The contestant is one question away from the jackpot. Up comes his
question: “What is the name of the theory that scientists started developing at the beginning of the twenty-first century, and
which helped the world overcome traffic congestion, financial market crashes, terrorist attacks, pandemic viruses, and cancer?” The contestant cannot believe his luck. What an easy question! But he is so nervous that his mind temporarily goes blank. He starts to consider option A: “They are all still unsolved problems” – but then quickly realizes that this is a dumb answer. Instead, he uses his last lifeline to ask the audience. The audience responds unanimously and instantaneously with option B: “The Theory of Complexity”. Without hesitation, he goes with option B. The host hands him the cheque, and the world has yet another billionaire.
Pure fantasy? Maybe not.
In this book, we will go on a journey to the heart of Complexity, an emerging science which looks set to trigger the next great wave of advances in everything from medicine and biology through to economics and sociology. Complexity Science also comes with the
prospect of solving a wide range of important problems which face us as individuals and as a Society. Consequently, it is set to permeate through every aspect of our lives.
There is, however, one problem. We don’t yet have a fullyfledged “theory” of Complexity. Instead, I will use this book to assemble all the likely ingredients of such a theory within a common framework, and then analyze a wide range of real-world applications within this same common framework. It will then require someone from the future – perhaps one of the younger readers of this book – to finally put all these pieces into place.
Complexity Science is a double-edged sword in the best possible sense. It is truly “big science” in that it embodies some of the hardest, most fundamental and most challenging open problems in academia. Yet it also manages to encapsulate the major practical issues which face us every day from our personal lives and health, through to global security. Making a pizza is complicated, but not complex. The same holds for filling out your tax return, or mending a bicycle puncture. Just follow the instructions step by step, and you will eventually be able to go from start to finish without too much trouble. But imagine trying to do all three at the same time. Worse still, suppose that the sequence of steps that you follow in one task actually depends on how things are progressing with the other two. Difficult? Well, you now have an indication of what Complexity is all about. With that in mind, now substitute those three interconnected tasks for a situation in which three interconnected people each try to follow their own instincts and strategies while reacting to the actions of the others. This then gives an idea of just how Complexity
might arise all around us in our daily lives.
While I was writing this book, I had the following “wish-list” in my head concerning its goals:
1. To provide a book which a wide cross-section of people would want to read and would enjoy reading – regardless of age,
background or level of scientific knowledge.
2. To introduce readers to the exciting range of real-world scenarios in which Complexity Science can prove its worth.
3. To provide the book on Complexity that “I never had but always needed”. In other words, to provide an easily readable yet thorough guide to this important scientific revolution.
4. To provide a book that my kids could read – or rather, a book that they would actually choose to read all by themselves. This is a very important goal, since Complexity will likely become the science of interest for future generations.
5. To provide a book which is just as readable on a plane or bus as in a library. As such, it should also make sense when read in short chunks.
6. To provide a book which provides professional scientists,economists, and policy-makers with a new perspective on
open problems in their field, and to help stimulate new Complexity-based interdisciplinary research projects.
However, as I finish the book and offer it up to potential readers,I realize that the above wish-list can essentially be reduced to just
one item: I would wish that you enjoy reading this book, and that it might provide you with fresh thoughts and insights for dealing
with the complex world in which we live, and which our children will inherit.
There are some practicalities concerning the book’s content and layout which I would like to explain. The language, examples and
analogies are kept simple since the focus of the book is to explain what Complexity Science is all about, and why it is so important for
us all. I therefore avoid delving into too much detail in the main text. Instead, the Appendix describes how to access the technical
research papers upon which the discussions in the book are based, and gives a list of Internet websites containing additional information about Complexity research around the world. Having said this, I won’t pull any punches in the sense that I tackle all the topics
which I believe to be relevant. Part 1 of the book takes us through the theoretical underpinnings of Complexity, while Part 2
delves into its real-world applications. Some of the territory is only just beginning to be explored, with very few answers available
for the questions being posed. From the perspective of other scientific revolutions throughout history this might seem to be par
for the course. However we are not talking about history here –instead, we are looking at work which is emerging at the forefront
of a new discipline. For this reason we will be highlighting where such research is heading, rather than where it has been.
But why should you believe what I write about Complexity? This is a crucially important question given that Complexity Science is still being developed and its potential applications explored. Unfortunately many accounts of Complexity in the popular press are second-hand, i.e. they are typically written by people who have done little, if any, research on Complexity themselves and are instead reporting on their interpretation of
other people’s work. Given the relatively immature nature of the field, I believe that such indirect interpretations are potentially
dangerous. For this reason, I will base the book’s content around my own research group’s experience in Complexity. This has
various advantages: (i) it reflects my own understanding of the Complexity field; (ii) it represents what I believe to be the most
relevant and important topics; (iii) it will hopefully give the reader a sense of what it is like to be at the “pit-face” in such a
challenging area of research; and (iv) it ensures that any reader can challenge me directly on any claims that I make, and can
demand an informed answer. To facilitate this process of public scrutiny, a complete list of the relevant scientific research reports
is presented in the latter part of the Appendix. I also encourage any readers who wish to email me with questions, to do so at
n.johnson@physics.ox.ac.uk

This is the only book to chart the history and development of modern probability theory. It shows how in the first thirty years of this century probability theory became a mathematical science. The author also traces the development of probabilistic concepts and theories in statistical and quantum physics. There are chapters dealing with chance phenomena, as well as the main mathematical theories of today, together with their foundational and philosophical problems. Among the theorists whose work is treated at some length are Kolmogorov, von Mises and de Finetti. The principal audience for the book comprises philosophers and historians of science, mathematicians concerned with probability and statistics, and physicists. The book will also interest anyone fascinated by twentieth-century scientific developments because the birth of modern probability is closely tied to the change from a determinist to an indeterminist world-view.

Now available in paperback, this celebrated book has been prepared with readers' needs in mind, remaining a systematic guide to a large part of the modern theory of Probability, whilst retaining its vitality. The authors' aim is to present the subject of Brownian motion not as a dry part of mathematical analysis, but to convey its real meaning and fascination. The opening, heuristic chapter does just this, and it is followed by a comprehensive and self-contained account of the foundations of theory of stochastic processes. Chapter 3 is a lively and readable account of the theory of Markov processes. Together with its companion volume, this book helps equip graduate students for research into a subject of great intrinsic interest and wide application in physics, biology, engineering, finance and computer science.

This comprehensive study of probability, its relation to statistics, and its truth-finding value considers the approaches of Pascal, Laplace, Poisson, and others. It also discusses Laws of Large Numbers, the theory of errors, and other relevant topics. Numerous examples complement the text.

It is Shackle's view that human conduct is chosen with a view to its consequences. But these are in the future, which cannot be directly known. Expectation will confine itself to what is deemed possible, but this leaves it free to entertain widely diverse and rival hypotheses. How can such skeins of mutually conflicting ideas serve the formation of individual or institutional policy? This is the chief question this book examines.