What Is Random

In this fascinating book, mathematician Ed Beltrami takes a close enough look at randomness to make it mysteriously disappear.


Author: Edward Beltrami

Publisher: Springer Nature

ISBN: 9781071607992

Category: Mathematics

Page: 192

View: 688

In this fascinating book, mathematician Ed Beltrami takes a close enough look at randomness to make it mysteriously disappear. The results of coin tosses, it turns out, are determined from the start, and only our incomplete knowledge makes them look random. "Random" sequences of numbers are more elusive, but Godels undecidability theorem informs us that we will never know. Those familiar with quantum indeterminacy assert that order is an illusion, and that the world is fundamentally random. Yet randomness is also an illusion. Perhaps order and randomness, like waves and particles, are only two sides of the same (tossed) coin.


Schumer, P. D., “Pascal potpourri”, in Mathematical Journeys (Wiley, Hoboken, 2004) chapter 16. Probability ◦ Beltrami, E., What Is Random? Chance and Order in Mathematics and Life (Copernicus Springer-Verlag, New York, 1999).


Author: Richard Kautz

Publisher: Oxford University Press

ISBN: 9780199594573

Category: Mathematics

Page: 369

View: 535

One CD-ROM disc in pocket.

Cognition and Chance

Bell, P.A., Fisher, J.D., Baum, A., & Greene, T.C. (1990). Environmentalpsychology. Fort Worth, TX: Holt, Rinehart & Winston. Beltrami, E. (1999). What is random? Chance and order in mathematics and life. New York: Springer-Verlag.


Author: Raymond S. Nickerson

Publisher: Psychology Press

ISBN: 9781135614621

Category: Business & Economics

Page: 472

View: 452

Lack of ability to think probabilistically makes one prone to a variety of irrational fears and vulnerable to scams designed to exploit probabilistic naiveté, impairs decision making under uncertainty, facilitates the misinterpretation of statistical information, and precludes critical evaluation of likelihood claims. Cognition and Chance presents an overview of the information needed to avoid such pitfalls and to assess and respond to probabilistic situations in a rational way. Dr. Nickerson investigates such questions as how good individuals are at thinking probabilistically and how consistent their reasoning under uncertainty is with principles of mathematical statistics and probability theory. He reviews evidence that has been produced in researchers' attempts to investigate these and similar types of questions. Seven conceptual chapters address such topics as probability, chance, randomness, coincidences, inverse probability, paradoxes, dilemmas, and statistics. The remaining five chapters focus on empirical studies of individuals' abilities and limitations as probabilistic thinkers. Topics include estimation and prediction, perception of covariation, choice under uncertainty, and people as intuitive probabilists. Cognition and Chance is intended to appeal to researchers and students in the areas of probability, statistics, psychology, business, economics, decision theory, and social dilemmas.

Strategies to Approximate Random Sampling and Assignment

Becker, G. (1991). Alternative methods of reporting research results. American Psychologist, 46,654–655. Beltrami, E. (1999). What is random? Chance and order in mathematics and life. New York: Springer-Verlag. Bennett, D. J. (1998).


Author: Patrick Dattalo

Publisher: Oxford University Press

ISBN: 9780195378351

Category: Social Science

Page: 203

View: 403

This book is a single source of a diverse set of tools that will maximize a study's validity when RS and RA are neither possible nor practical. Readers are guided in selecting and implementing an appropriate strategy, including exemplar sampling, sequential sampling, randomization tests, multiple imputation, and much more.

How Mathematicians Think

Using Ambiguity, Contradiction, and Paradox to Create Mathematics William Byers ... Vintage, Random House, London. Becker, Ernest (1973). The Denial of Death. ... What Is Random? Chance and Order in Mathematics and Life.


Author: William Byers

Publisher: Princeton University Press

ISBN: 9780691145990

Category: Mathematics

Page: 424

View: 934

To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results. Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure. The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory? Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself.

General Theory of Statistics

Beltrami E. What is Random: Chance and Order in Mathematics and Life.- N.Y.: Springer, 1999 172. Brzezniak Z., Zastawniak T. Basic Stochastic Processes.- London: Springer-Verlag, 1999 173. Karatzas I., Shreve S. Methods of Mathematical ...


Author: Victor Aladjev

Publisher: Fultus Corporation

ISBN: 9781596820128

Category: Mathematics

Page: 256

View: 242

Book Description The present book is a statistical course for undergraduate students in all fields of social and economic sciences. The book presents a manual on the course "General Theory of Statistics", including a series of not quite traditional topics. First of all, it concerns the mathematical bases of statistics and use of computer technologies in statistical probing. Thematic choice of the chapters and sections of the book is caused not only by interests and tastes of the authors, but also by modern tendencies in applied statistics and orientation of the given work. The book is based on a course of lectures given by the first author for undergraduates in social and economic sciences along with three books published in Russian and English in Estonia, Lithuania and Byelorussia. This book has been written for a large enough audience of teachers, researchers, statisticians, students, collegians and users of statistics in behavioral and social sciences. Above all, the book is directed to a wide circle of the readers studying statistical disciplines in high schools and colleges; however, it can be useful also to persons independently studying statistics. Author Biography (Aladjev V.Z.) Professor Aladjev V.Z. was born on June 14, 1942 in the town Grodno (Byelorussia). Now, he is the First vice-president of the International Academy of Noosphere and the president of Tallinn Research Group, whose scientific results have received international recognition, first, in the field of mathematical theory of Cellular Automata (CA). He is member of a series of Russian and International Academies. Aladjev V. Z. is the author of more than 330 scientific publications, including 63 books, published in many countries. He participates as a member of the organizing committee and/or a guest lecturer in many international scientific forums in mathematics and cybernetics. Author Biography (Haritonov V.N.) Dr. Haritonov V.N. was born on August 2, 1946 in the town Nizhni Novgorod (Russia). On successful graduation from Tallinn Technical University, he has acquired a profession of economics. Since 1972, Haritonov V.N. has the respectable positions in the Estonian banking system. Now, he is the Chairman of the Board of Tallinn Business Bank. Most considerable methodological projects and practical results of Haritonov V.N. are related to economic sciences, and, above all, to banking field, including automation of banking system, banking statistics, etc. Along with a series of publications, Haritonov V.N. has participated in many scientific and applied forums on banking economics.

Philosophy of Statistics

What is random? Chance and Order in Mathematics and Life. Copernicus (Springer-Verlag), New York, 1999. [Bennett, 1979] C.H. Bennett. On Random and Hard-to-Describe Numbers. Technical Report RC-7483, IBM Watson Research Center, ...



Publisher: Elsevier

ISBN: 0080930964

Category: Philosophy

Page: 1260

View: 962

Statisticians and philosophers of science have many common interests but restricted communication with each other. This volume aims to remedy these shortcomings. It provides state-of-the-art research in the area of philosophy of statistics by encouraging numerous experts to communicate with one another without feeling “restricted by their disciplines or thinking “piecemeal in their treatment of issues. A second goal of this book is to present work in the field without bias toward any particular statistical paradigm. Broadly speaking, the essays in this Handbook are concerned with problems of induction, statistics and probability. For centuries, foundational problems like induction have been among philosophers’ favorite topics; recently, however, non-philosophers have increasingly taken a keen interest in these issues. This volume accordingly contains papers by both philosophers and non-philosophers, including scholars from nine academic disciplines. Provides a bridge between philosophy and current scientific findings Covers theory and applications Encourages multi-disciplinary dialogue

Studia Phaenomenologica VI 2006

What is Random: Chance and Order in Mathematics and Life, New York: Copernicus, 1999, pp. 5-6. 14 G. GIGERENZER, Z. SWIJTINK, T. PORTER, L. DASTON, J. BEATTY, L. KRÜGER, The Empire of Chance: How Probability Changed Science and Everyday ...


Author: Cristian Ciocan

Publisher: Romanian Society for Phenomenology

ISBN: 9789735014162

Category: Phenomenology

Page: 487

View: 573

Spatial Complexity

What is random? Chance and order in mathematics and life. New York: Springer-Verlag. Brugger, P. (1997). Variables that influence the generation of random sequences: An update. Perception and Motor Skills, 84, 627–661.


Author: Fivos Papadimitriou

Publisher: Springer Nature

ISBN: 9783030596712

Category: Mathematics

Page: 298

View: 905

This book delivers stimulating input for a broad range of researchers, from geographers and ecologists to psychologists interested in spatial perception and physicists researching in complex systems. How can one decide whether one surface or spatial object is more complex than another? What does it require to measure the spatial complexity of small maps, and why does this matter for nature, science and technology? Drawing from algorithmics, geometry, topology, probability and informatics, and with examples from everyday life, the reader is invited to cross the borders into the bewildering realm of spatial complexity, as it emerges from the study of geographic maps, landscapes, surfaces, knots, 3D and 4D objects. The mathematical and cartographic experiments described in this book lead to hypotheses and enigmas with ramifications in aesthetics and epistemology.

Digital And The Real World The Computational Foundations Of Mathematics Science Technology And Philosophy

In: Mathematical Proceedings of the Cambridge Philosophical Society 146(1), 45–55. Awodey, S. (2012): Type theory and homotopy. ... Beltrami, E. (1999): What is Random? Chance and Order in Mathematics and Life. Copernicus: New York.


Author: Mainzer Klaus

Publisher: World Scientific

ISBN: 9789813225503

Category: Mathematics

Page: 472

View: 490

In the 21st century, digitalization is a global challenge of mankind. Even for the public, it is obvious that our world is increasingly dominated by powerful algorithms and big data. But, how computable is our world? Some people believe that successful problem solving in science, technology, and economies only depends on fast algorithms and data mining. Chances and risks are often not understood, because the foundations of algorithms and information systems are not studied rigorously. Actually, they are deeply rooted in logics, mathematics, computer science and philosophy. Therefore, this book studies the foundations of mathematics, computer science, and philosophy, in order to guarantee security and reliability of the knowledge by constructive proofs, proof mining and program extraction. We start with the basics of computability theory, proof theory, and information theory. In a second step, we introduce new concepts of information and computing systems, in order to overcome the gap between the digital world of logical programming and the analog world of real computing in mathematics and science. The book also considers consequences for digital and analog physics, computational neuroscience, financial mathematics, and the Internet of Things (IoT). Contents: Introduction Basics of Computability Hierarchies of Computability Constructive Proof Theory Computational Mathematics and Digital Information Systems Intuitionistic Mathematics and Human Creativity Proof Mining bridging Logic, Mathematics, and Computer Science Reverse Mathematics Bridging Logic, Mathematics, and Computer Science From Intuitionistic to Homotopy Type Theory — Bridging Logic, Mathematics, and Computer Science Real Computability and Real Analysis Complexity Theory of Real Computing Real Computing and Neural Networks Complexity of Algorithmic Information Complexity of Information Dynamics Digital and Real Physics Digital and Real Computing in the Social World Philosophical Outlook Readership: Undergraduate and graduate students, scientists and readers who are interested in foundational, interdisciplinary, and philosophical questions of mathematics, computer science, and science in general. Keywords: Computability;Complexity;Constructive Mathematics;Proof Mining;Real Computing;Analog Networks;Information System;Digital PhysicsReview: Key Features: Compact introduction into the foundations of modern mathematics and computer science Bridging the gap between digital, real and analog computing by new concepts of information systems Consequences in natural and social sciences with respect to scientific computing