Randomness

Author : Deborah J. Bennett
Publisher : Harvard University Press
Page : 260 pages
File Size : 43,7 Mb
Release : 2009-07-01
Category : Philosophy
ISBN : 0674020774

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Randomness by Deborah J. Bennett Pdf

From the ancients' first readings of the innards of birds to your neighbor's last bout with the state lottery, humankind has put itself into the hands of chance. Today life itself may be at stake when probability comes into play--in the chance of a false negative in a medical test, in the reliability of DNA findings as legal evidence, or in the likelihood of passing on a deadly congenital disease--yet as few people as ever understand the odds. This book is aimed at the trouble with trying to learn about probability. A story of the misconceptions and difficulties civilization overcame in progressing toward probabilistic thinking, Randomness is also a skillful account of what makes the science of probability so daunting in our own day. To acquire a (correct) intuition of chance is not easy to begin with, and moving from an intuitive sense to a formal notion of probability presents further problems. Author Deborah Bennett traces the path this process takes in an individual trying to come to grips with concepts of uncertainty and fairness, and also charts the parallel path by which societies have developed ideas about chance. Why, from ancient to modern times, have people resorted to chance in making decisions? Is a decision made by random choice fair? What role has gambling played in our understanding of chance? Why do some individuals and societies refuse to accept randomness at all? If understanding randomness is so important to probabilistic thinking, why do the experts disagree about what it really is? And why are our intuitions about chance almost always dead wrong? Anyone who has puzzled over a probability conundrum is struck by the paradoxes and counterintuitive results that occur at a relatively simple level. Why this should be, and how it has been the case through the ages, for bumblers and brilliant mathematicians alike, is the entertaining and enlightening lesson of Randomness.

Author : Nassim Nicholas Taleb
Publisher : Random House
Page : 369 pages
File Size : 54,8 Mb
Release : 2008-10-14
Category : Business & Economics
ISBN : 9781588367679

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Fooled by Randomness by Nassim Nicholas Taleb Pdf

Fooled by Randomness is a standalone book in Nassim Nicholas Taleb’s landmark Incerto series, an investigation of opacity, luck, uncertainty, probability, human error, risk, and decision-making in a world we don’t understand. The other books in the series are The Black Swan, Antifragile, Skin in the Game, and The Bed of Procrustes. Fooled by Randomness is the word-of-mouth sensation that will change the way you think about business and the world. Nassim Nicholas Taleb–veteran trader, renowned risk expert, polymathic scholar, erudite raconteur, and New York Times bestselling author of The Black Swan–has written a modern classic that turns on its head what we believe about luck and skill. This book is about luck–or more precisely, about how we perceive and deal with luck in life and business. Set against the backdrop of the most conspicuous forum in which luck is mistaken for skill–the world of trading–Fooled by Randomness provides captivating insight into one of the least understood factors in all our lives. Writing in an entertaining narrative style, the author tackles major intellectual issues related to the underestimation of the influence of happenstance on our lives. The book is populated with an array of characters, some of whom have grasped, in their own way, the significance of chance: the baseball legend Yogi Berra; the philosopher of knowledge Karl Popper; the ancient world’s wisest man, Solon; the modern financier George Soros; and the Greek voyager Odysseus. We also meet the fictional Nero, who seems to understand the role of randomness in his professional life but falls victim to his own superstitious foolishness. However, the most recognizable character of all remains unnamed–the lucky fool who happens to be in the right place at the right time–he embodies the “survival of the least fit.” Such individuals attract devoted followers who believe in their guru’s insights and methods. But no one can replicate what is obtained by chance. Are we capable of distinguishing the fortunate charlatan from the genuine visionary? Must we always try to uncover nonexistent messages in random events? It may be impossible to guard ourselves against the vagaries of the goddess Fortuna, but after reading Fooled by Randomness we can be a little better prepared. Named by Fortune One of the Smartest Books of All Time A Financial Times Best Business Book of the Year

Author : André Nies
Publisher : OUP Oxford
Page : 451 pages
File Size : 40,9 Mb
Release : 2009-01-29
Category : Philosophy
ISBN : 9780191552274

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Computability and Randomness by André Nies Pdf

The interplay between computability and randomness has been an active area of research in recent years, reflected by ample funding in the USA, numerous workshops, and publications on the subject. The complexity and the randomness aspect of a set of natural numbers are closely related. Traditionally, computability theory is concerned with the complexity aspect. However, computability theoretic tools can also be used to introduce mathematical counterparts for the intuitive notion of randomness of a set. Recent research shows that, conversely, concepts and methods originating from randomness enrich computability theory. The book covers topics such as lowness and highness properties, Kolmogorov complexity, betting strategies and higher computability. Both the basics and recent research results are desribed, providing a very readable introduction to the exciting interface of computability and randomness for graduates and researchers in computability theory, theoretical computer science, and measure theory.

Author : Rodney G. Downey,Denis R. Hirschfeldt
Publisher : Springer Science & Business Media
Page : 883 pages
File Size : 43,5 Mb
Release : 2010-10-29
Category : Computers
ISBN : 9780387684413

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Algorithmic Randomness and Complexity by Rodney G. Downey,Denis R. Hirschfeldt Pdf

Computability and complexity theory are two central areas of research in theoretical computer science. This book provides a systematic, technical development of "algorithmic randomness" and complexity for scientists from diverse fields.

Author : Cristian S. Calude
Publisher : Springer Science & Business Media
Page : 502 pages
File Size : 44,5 Mb
Release : 2002-09-12
Category : Mathematics
ISBN : 3540434666

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Information and Randomness by Cristian S. Calude Pdf

The first edition of the monograph Information and Randomness: An Algorithmic Perspective by Crist ian Calude was published in 1994. In my Foreword I said: "The research in algorithmic information theory is already some 30 years old. However, only the recent years have witnessed a really vigorous growth in this area. . . . The present book by Calude fits very well in our series. Much original research is presented. . . making the approach richer in consequences than the classical one. Remarkably, however, the text is so self-contained and coherent that the book may also serve as a textbook. All proofs are given in the book and, thus, it is not necessary to consult other sources for classroom instruction. " The vigorous growth in the study of algorithmic information theory has continued during the past few years, which is clearly visible in the present second edition. Many new results, examples, exercises and open prob lems have been added. The additions include two entirely new chapters: "Computably Enumerable Random Reals" and "Randomness and Incom pleteness". The really comprehensive new bibliography makes the book very valuable for a researcher. The new results about the characterization of computably enumerable random reals, as well as the fascinating Omega Numbers, should contribute much to the value of the book as a textbook. The author has been directly involved in these results that have appeared in the prestigious journals Nature, New Scientist and Pour la Science.

Author : Gregory J. Chaitin
Publisher : Springer Science & Business Media
Page : 176 pages
File Size : 51,6 Mb
Release : 2001-07-30
Category : Computers
ISBN : 1852334177

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Exploring RANDOMNESS by Gregory J. Chaitin Pdf

This essential companion to Chaitin's successful books The Unknowable and The Limits of Mathematics, presents the technical core of his theory of program-size complexity. The two previous volumes are more concerned with applications to meta-mathematics. LISP is used to present the key algorithms and to enable computer users to interact with the authors proofs and discover for themselves how they work. The LISP code for this book is available at the author's Web site together with a Java applet LISP interpreter. "No one has looked deeper and farther into the abyss of randomness and its role in mathematics than Greg Chaitin. This book tells you everything hes seen. Don miss it." John Casti, Santa Fe Institute, Author of Goedel: A Life of Logic.'

Author : Andre? I?U?r?evich Khrennikov
Publisher : World Scientific
Page : 299 pages
File Size : 41,9 Mb
Release : 2016
Category : Science
ISBN : 9781783267972

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Probability and Randomness by Andre? I?U?r?evich Khrennikov Pdf

"Creating a rigorous mathematical theory of randomness is far from being complete, even in the classical case. Interrelation of Classical and Quantum Randomness rectifies this and introduces mathematical formalisms of classical and quantum probability and randomness with brief discussion of their interrelation and interpretational and foundational issues. The book presents the essentials of classical approaches to randomness, enlightens their successes and problems, and then proceeds to essentials of quantum randomness. Its wide-ranging and comprehensive scope makes it suitable for researchers in mathematical physics, probability and statistics at any level"--

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 42,6 Mb
Release : 2024-06-28
Category : Electronic
ISBN : 9789814462631

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Randomness Through Computation by Anonim Pdf

Author : Bernd Möller,Michael Beer
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 49,5 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662073582

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Fuzzy Randomness by Bernd Möller,Michael Beer Pdf

sections dealing with fuzzy functions and fuzzy random functions are certain to be of special interest. The reader is expected to be in command of the knowledge gained in a basic university mathematics course, with the inclusion of stochastic elements. A specification of uncertainty in any particular case is often difficult. For this reason Chaps. 3 and 4 are devoted solely to this problem. The derivation of fuzzy variables for representing informal and lexical uncertainty reflects the subjective assessment of objective conditions in the form of a membership function. Techniques for modeling fuzzy random variables are presented for data that simultaneously exhibit stochastic and nonstochastic properties. The application of fuzzy randomness is demonstrated in three fields of civil engineering and computational mechanics: structural analysis, safety assessment, and design. The methods of fuzzy structural analysis and fuzzy probabilistic structural analysis developed in Chap. 5 are applicable without restriction to arbitrary geometrically and physically nonlinear problems. The most important forms of the latter are the Fuzzy Finite Element Method (FFEM) and the Fuzzy Stochastic Finite Element Method (FSFEM).

Author : Anatoly Ruvinsky
Publisher : CRC Press
Page : 186 pages
File Size : 53,8 Mb
Release : 2009-07-28
Category : Mathematics
ISBN : 9781420078879

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Genetics and Randomness by Anatoly Ruvinsky Pdf

Analyzes Randomness in Major Genetic Processes and EventsNo matter how far science advances, the proportion of what is knowable to what is random will remain unchanged, and attempts to ignore this critical threshold are futile at best. With the revolutionary explosion in genetic information discovery, it is crucially important to recognize the unde

Author : Lena Zuchowski
Publisher : Cambridge University Press
Page : 82 pages
File Size : 54,6 Mb
Release : 2024-03-06
Category : Philosophy
ISBN : 9781009217316

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From Randomness and Entropy to the Arrow of Time by Lena Zuchowski Pdf

The Element reconstructs, analyses and compares different derivational routes to a grounding of the Arrow of Time in entropy. It also evaluates the link between entropy and visible disorder, and the related claim of an alignment of the Arrow of Time with a development from order to visible disorder. The Element identifies three different entropy-groundings for the Arrow of Time: (i) the Empirical Arrow of Time, (ii) the Universal Statistical Arrow of Time, and (iii) the Local Statistical Arrow of Time. The Element will also demonstrate that it is unlikely that high entropy states will always coincide with visible disorder. Therefore, it will dispute that there is a strong link between the Arrow of Time and visible disorder.

Author : Anastasios A Tsonis
Publisher : World Scientific
Page : 204 pages
File Size : 51,7 Mb
Release : 2008-09-18
Category : Science
ISBN : 9781908978882

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Randomnicity by Anastasios A Tsonis Pdf

This unique book explores the definition, sources and role of randomness. A joyful discussion with many non-mathematical and mathematical examples leads to the identification of three sources of randomness: randomness due to irreversibility which inhibits us from extracting whatever rules may underlie a process, randomness due to our inability to have infinite power (chaos), and randomness due to many interacting systems. Here, all sources are found to have something in common: infinity. The discussion then moves to the physical system (our universe). Through the quantum mechanical character of small scales, the second law of thermodynamics and chaos, randomness is shown to be an intrinsic property of nature — this is consistent with the three sources of randomness identified above. Finally, an explanation is given as to why rules and randomness cannot exist by themselves, but instead have to coexist. Many examples are presented, ranging from pure mathematical to natural and social processes, that clearly demonstrate how the combination of rules and randomness produces the world we live in. Contents: The Three Parts of EverythingSources of RandomnessRandomness in the UniverseThe Emergence of Real WorldThe Role of Randomness Readership: Academic and general public. Keywords:Randomness;Chaos;Fractals;Determinism;Natural ProcessesKey Features:Differs from other books on this subject in that it treats randomness from a complex systems point of view rather than from a solely probabilistic oneSuitable for the general public with an interest in scienceUseful for scientists in all areasReviews:“Reading the book is like visiting a museum, and as the reader goes successively through the chapters he (or she) encounters beautiful ideas and interesting comments. Although the book is not a book on the history of mathematics, it contains interesting historical facts.”Zentralblatt MATH “I recommend reading it to those who want a quick introduction to ideas about randomness and those whose exposure to these ideas has been piecemeal, as mine was. The book may spark the imaginations of readers and advance our science through innovative application of the concepts. Someone might just find life-changing inspiration.”Vadose Zone Journal “As a contribution to popular science this book is welcome. Tsonis explains randomness as it enters into mathematics, science and everyday life.”Mathematical Reviews

Author : Mieko Tanaka-Yamawaki,Yumihiko Ikura
Publisher : Springer Nature
Page : 153 pages
File Size : 45,6 Mb
Release : 2023-05-23
Category : Business & Economics
ISBN : 9789811939679

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Principal Component Analysis and Randomness Test for Big Data Analysis by Mieko Tanaka-Yamawaki,Yumihiko Ikura Pdf

This book presents the novel approach of analyzing large-sized rectangular-shaped numerical data (so-called big data). The essence of this approach is to grasp the "meaning" of the data instantly, without getting into the details of individual data. Unlike conventional approaches of principal component analysis, randomness tests, and visualization methods, the authors' approach has the benefits of universality and simplicity of data analysis, regardless of data types, structures, or specific field of science. First, mathematical preparation is described. The RMT-PCA and the RMT-test utilize the cross-correlation matrix of time series, C = XXT, where X represents a rectangular matrix of N rows and L columns and XT represents the transverse matrix of X. Because C is symmetric, namely, C = CT, it can be converted to a diagonal matrix of eigenvalues by a similarity transformation SCS-1 = SCST using an orthogonal matrix S. When N is significantly large, the histogram of the eigenvalue distribution can be compared to the theoretical formula derived in the context of the random matrix theory (RMT, in abbreviation). Then the RMT-PCA applied to high-frequency stock prices in Japanese and American markets is dealt with. This approach proves its effectiveness in extracting "trendy" business sectors of the financial market over the prescribed time scale. In this case, X consists of N stock- prices of length L, and the correlation matrix C is an N by N square matrix, whose element at the i-th row and j-th column is the inner product of the price time series of the length L of the i-th stock and the j-th stock of the equal length L. Next, the RMT-test is applied to measure randomness of various random number generators, including algorithmically generated random numbers and physically generated random numbers. The book concludes by demonstrating two applications of the RMT-test: (1) a comparison of hash functions, and (2) stock prediction by means of randomness, including a new index of off-randomness related to market decline.

Author : Arlin Stoltzfus
Publisher : Oxford University Press
Page : 283 pages
File Size : 51,5 Mb
Release : 2021
Category : Science
ISBN : 9780198844457

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Mutation, Randomness, and Evolution by Arlin Stoltzfus Pdf

What does it mean to say that mutation is random? How does mutation influence evolution? Are mutations merely the raw material for selection to shape adaptations? The author draws on a detailed knowledge of mutational mechanisms to argue that the randomness doctrine is best understood, not as a fact-based conclusion, but as the premise of a neo-Darwinian research program focused on selection. The successes of this research program created a blind spot - in mathematical models and verbal theories of causation - that has stymied efforts to re-think the role of variation. However, recent theoretical and empirical work shows that mutational biases can and do influence the course of evolution, including adaptive evolution, through a first come, first served mechanism. This thought-provoking book cuts through the conceptual tangle at the intersection of mutation, randomness, and evolution, offering a fresh, far-reaching, and testable view of the role of variation as a dispositional evolutionary factor. The arguments will be accessible to philosophers and historians with a serious interest in evolution, as well as to researchers and advanced students of evolution focused on molecules, microbes, evo-devo, and population genetics.

Author : A. Shen,V. A. Uspensky,N. Vereshchagin
Publisher : American Mathematical Society
Page : 511 pages
File Size : 42,8 Mb
Release : 2022-05-18
Category : Mathematics
ISBN : 9781470470647

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Kolmogorov Complexity and Algorithmic Randomness by A. Shen,V. A. Uspensky,N. Vereshchagin Pdf

Looking at a sequence of zeros and ones, we often feel that it is not random, that is, it is not plausible as an outcome of fair coin tossing. Why? The answer is provided by algorithmic information theory: because the sequence is compressible, that is, it has small complexity or, equivalently, can be produced by a short program. This idea, going back to Solomonoff, Kolmogorov, Chaitin, Levin, and others, is now the starting point of algorithmic information theory. The first part of this book is a textbook-style exposition of the basic notions of complexity and randomness; the second part covers some recent work done by participants of the “Kolmogorov seminar” in Moscow (started by Kolmogorov himself in the 1980s) and their colleagues. This book contains numerous exercises (embedded in the text) that will help readers to grasp the material.