Randomness 1st Edition by Deborah J. Bennett (PDF)

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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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Introductory texts on scientific and mathematical subjects are important.They will be responsible for giving basic understanding on a given subject for the general public, and maybe that will be important in everyday life in many situations, like detecting charlatans, avoiding bad politicians, defending one’s rights and neutralizing fallacious arguments.An introductory book may also be taken by someone just before pursuing a more serious course on the subject addressed by the text. Mistakes and confusions in such a book may have deleterious long lasting repercussions in the academic and professional life of the reader.Unfortunately, “Randomness”, by Deborah Bennett, is not a very good introduction to the subject of probability and randomness.In fact, it is just a repetition of fallacious arguments about the centrality of the concept of “randomness” in probability theory.There will never be a satisfactory definition of randomness if it is taken as a property of physical systems, but that is exactly the path taken by the book.It is, in itself, a demonstration that not even a vague concept of “randomness” is possible in this mindset, because despite the title, after reading Bennett’s text no clear idea of what “randomness” is emerges. The last part of chapter 9, “Criteria for Randomness”, p. 161-173, shows that eloquently.The reason for that is simple: “randomness” and probability are not ontological, but epistemological concepts. They are not “embedded” in reality, they are tools rational beings use to approach reality and draw conclusions applicable to empirical and hypothetical systems.For those interested in capturing a coherent and useful understanding of probability, I highly recommend “Probability Theory: The Logic of Science”, by E. T. Jaynes, which is, in my opinion, a superb discussion of the basic concepts of probability, including randomness. Jaynes’ book has many technical passages that will only be of interest for advanced readers, but being myself not such a reader, I can assure that anyone who could read “Randomness” will also have no difficult in reading the conceptual discussions in “Probability Theory: The Logic of Science”. Simply jump over its more technical sections and stick to the very enlightening arguments.The following specific observations can be made about the book “Randomness”:1. probability can, in fact, be viewed as a formalization of logic (something not even mentioned in the other introductory text by D. J. Bennett, “Logic made easy”);2. there is no fundamental difference between deduction and induction. Deduction is no more than a limiting form of induction. Bennett’s book does not recognize that. On the contrary, chapter 6 of “Randomness” shows the author got stuck on this false dichotomy. Her argument to refuse the view of probability as the tool to approach problems where we have uncertainty is that it would lead to mysticism (“a Grand Designer must exist”, p. 88). What is embedded in her error is the false notion that rational thinking is related only to deduction, not to induction.The book takes determinism as a necessary scientific conclusion of putting uncertainty, not randomness, in the center of probability theory. That is incorrect. From a scientific point of view, absolute determinism is foolish. It may be a hypothesis from the metaphysical perspective, but from the physical perspective it is a meaningless question, because to compute every single aspect of the universe in any given coordinate of space-time it would be necessary to build a computing machine that would need to use more than what is available in the whole universe.What is really a mystical position is seeing a “mysterious”, undefinable, unmeasurable entity – randomness – as the root of probability.3. “randomness” is just a way to refer to systems where the observer cannot predict the outcome with certainty.Bennett’s book has a paragraph claiming randomness can be measured by probability distribution functions (chapter 7, p. 131), but not even that is true (one can generate pseudorandom, deterministic sequences obeying a given probability function, as shown in chapter 8 of the book).About that, I strongly recommend reading chapter 10, “Physics of ‘random experiments'”, in Jaynes’ book.Diaconis, Holmes and Montgomery studied coin tossing in the paper “Dynamical bias in the coin toss” (2007). This paper is an excellent illustration of what Jaynes discusses in that chapter 10.Unfortunately, Jaynes died in 1998. He would certainly be very happy to read Diaconis paper.There is also a 2013 presentation by Diaconis where he addresses randomness as an epistemological, not ontological, concept, although in a much more “soft” way than Jaynes.After all, Diaconis is a statistician. Jaynes was a physicist who had no professional concerns to openly show his criticism about the way induction in real situations was made the sole domain of the so called “statistical inference” and the statisticians.One can find this 50 minute presentation in the University of Washington’s Youtube channel. The title of the video is “The search for randomness with Persi Diaconis”.4. As randomness, “probabilistic independence” is also a logical concept, not an ontological feature of empirical systems.Trying to directly tie probabilistic independence to causal/physical independence is foolish.Doing that will result in false paradoxes.One of them is the “gambler’s fallacy”, which can be found, for instance, in https://en.wikipedia.org/wiki/Gambler%27s_fallacy, in the YouTube Numberphile channel video “Randomness is Random”, and also in D. Bennett’s book (e.g., ch. 5, p. 79-80).All these sources wrongly say something like the following: when tossing a coin or die, the independence between successive tosses means that you can have an endless stream of the same result and “four heads in a row do not make a tail more likely on the next throw” (p. 14 of “Randomness”).But intuition says just the opposite, which is an apparent paradox.Bennett’s book does not even remotely addresses the subtleties of this frequentist dead end.Four paragraphs of Jaynes’ book (ch. 4, p. 91-2 of “Probability Theory: The Logic of Science”) are enough to make things clear.In the case of coin tossing, seeing a very large stream of heads will make a rational observer, from a bayesian perspective, draw valid inference about the next result, contrary to what Bennett says. It may make you suspect the tossing process is not fair, and that tail is less (not more) likely in the next toss. Or, if you are certain that the tossing process is fair, to believe that a tail is about to occur. In any case, it may give you empirical data that will correct a previous estimation about the probability of heads and tails. For instance, from 1/2 for the probability of heads to something higher than 1/2.The lesson is: probabilistic independence is a logical concept. The same events in the same physical system can be taken as logically independent or logically dependent, according to the objectives of the analysis undertaken.This false paradox is in fact an illustration of the artificial (and confusing) distinction between probability, on the one hand, and statistical inference, on the other, in orthodox literature, something lenghtily discussed in ch. 16 and 17 of Jaynes’ book.For a practical coin tossing example, I recommend reading ch. 2, p. 14-20 of D. S. Sivia and J. Skilling book “Data analysis: a bayesian tutorial”, 2.ed.5. As a last observation, it is worth addressing the so called “counter-intuitive aspects of probability” (p. 188, last paragraph of “Randomness”).Probability theory is not easy. In a passage of Jaynes’ book about infinite sets and measure theory, he replies to a remark from the father of all current college textbooks on probability, William Feller, by saying: “in this field [probability] we are all beginners” (appendix B.3, p. 664).When assessing how regular people think about problems, it is necessary to have the adequate theoretical tools to reasonably interpret the results.Kahneman & Tversky works are normally taken as a definitive demonstration of our brains inability to reason about probability.”Randomness” takes their conclusions for granted: at the end of the first chapter, one of the questions the book puts to itself is “why is probability so counter-intuitive?” (p. 9).But then, how can it be that intuitive elementary plausible reasoning principles are the basis for R. T. Cox derivation of the two fundamental “laws” of probability in his seminal 1946 paper “Probability, frequency and reasonable expectation”?Jaynes addresses the “intuition problem” on p. 126-32, item 5.3 of ch. 5. Based on his insights, I would say that:a) interpretation of the results of psychological tests normally does not take into account different prior information. What ends being reflected in the conclusions of the authors are their prior information, not their understanding of the inductive process they intend to assess;b) equivalently complex deductive problems would show the same “error rate”.By the way, “Randomness” has an example of that: the last “paradox” of ch. 10, the “Simpson’s Paradox”, p. 184-5, is a purely deductive problem related to fractions. In current frequentist jargon, it is a descriptive, not inferential, statistical problem;c) “intuitiveness” cannot be separated from what is the ideological mind-set of a society. And formal education cannot be taken out of the ideology equation.Given the fact the logical formalization of induction, probability theory, is a relatively new field, and most of the literature available today has so many mistakes, it is no wonder so many people get confused after being exposed to “explanations” that confront basic common sense instead of building up solid knowledge from intuitive notions.Bennett’s book “Randomness” is an example of the current somewhat deplorable state of affairs.

⭐Overall, Randomness by Deborah J. Bennett is very easy to read and understand. She has picked the perfect pace for the book. It was not hard to understand her examples, but I still did not find myself growing bored of reading. The quotes at the beginning of each chapter offer an appreciated mixture of comic relief (but sometimes drama) and anticipation. She knew exactly when it was appropriate to change topics, and did so subtlety so that the book did not become predictable, but noticeable enough so that the reader did not become disoriented. Bennett was also able to cover the major aspects of probability that I know of in a short book.A major aspect of Bennett’s book is the detail of history that is included. Clearly, she has researched the history of the development of the mathematical study of probability very thoroughly: from country to country, from the major time periods, and includes more than just the major figure involved in each process along with a short summary of their biography. This is very interesting for much of the book, but at times, the amount of detail that she provides becomes overdone.The most notable area in which Bennett shines is perhaps her ability to understand probability through the eyes of the everyday person. After studying a discipline for so many years, it can be easy to forget what it is like for a beginner. In addition, probability is one of the most difficult subjects to teach because of its lack of intuitiveness. For example, I never understood the classic problem that is along the lines of: a family has two children, one is known to be a particular gender, so what is the probability that the other child is of the same gender? Bennett was able to clearly identify nearly all of the concepts that I had trouble understanding, summarize what was probably going on in my head (which was accurate), point out the source of error in this way of thinking, and explain why the correct reasoning was different. Bennett’s step-by-step and careful way of clarifying possible pitfalls was incredibly helpful in clearing up the confusions that I had.

⭐I decided to give this otherwise good book 3 rather than 4 stars because I think it somewhat misses the mark for any of the possible audiences I could imagine for it. It fails to give complete enough explanations for the mathematically illiterate to be comfortably introduced to basic concepts (for instance, the initial coin-tossing and dice-throwing examples should have included more of the standard diagrams and figures found in any basic book to help the reader visualize the combinations). It begins discussing some advanced concepts such as the standard distribution without adequate definition or introduction, making it more suitable for an undergraduate with background knowledge; and it probably doesn’t satisfy readers with advanced mathematical training unless they are unfamiliar with the historical development of concepts, which seems unlikely as most textbooks cover that rather well. As a reader with modest prior background I found it a good review, but perhaps not as smooth an exposition as I could have hoped for. It’s a book that will benefit some and frustrate others, but it is worth reading…

⭐I am I openly admit not gifted with a great mathmetical mind so was pleasantly surprised at how skilful and adept this book is at portraying the history of “probability theory and problems” and how the world’s approach and knowledge has developed over the centuries. It is a very accessible read and despite covering very complicated mathematical concepts delivers it in a very easy style and with many simple examples that did not leave me struggling.The basic premise that we are not very inclined to understand or intuitively accept the inevitable outcomes of probability, partly because of how our knowledge has developed over the ages so our brains are wired to think a certain way on mathematical problems but more critically our continual holding on to basic beliefs in good fortune, bad luck and God is very lucidly portrayed.My main criticism of the book as a non-mathematician is that like reading about economic theories, understanding the concepts is half the battle and the other is the applying of them. While there is endless coverage of the growing interest in the theory of randomness and “gambling concepts” over the centuries, only rarely do you get some idea or insight of the potential benefit and application of such probability theories in the real world e.g. the drawing of lots for military service candidates in the US; usage by Guinness in improving the production of their beer and the development of how atoms behave under nuclear bomb research experiments.Sadly this results in a well written book being a good intellectual read but lacking in how to develop a wider understanding of what it can all be used for in everyday life.

⭐In this charming little book, the author discusses various aspects of randomness. From ancient perspectives on chance events to modern thought on whether randomness truly exists, the author guides the reader through a subject matter that has perplexed humankind for millennia. In addition, various probability problems are discussed, as are results of research in this fascinating discipline.The author writes well, in a prose that is friendly, lively and engaging. I did find, however, that some of the technical discussions could have been explained a bit more clearly. This book can be enjoyed by any interested reader.

⭐I think this is a good book to read if you are learning about statistics or research.

⭐It’s OK. Not nearly as good as I expected. The best book on the role of randomness in life and finance is Fooled By Randomness, by far the best book written by Nassim Nicholas Taleb. Read that rather than this. If you have not read it, read that rather than this, and if you have read it, well read it again rather than bothering with this.

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