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Once Upon A Number: The Hidden Mathematical Logic Of Stories
What two things could be more different than numbers and stories? Numbers are abstract, certain, and eternal, but to most of us somewhat dry and bloodless. Good stories are full of they engage our emotions and have subtlety and nuance, but they lack rigor and the truths they tell are elusive and subject to debate. As ways of understanding the world around us, numbers and stories seem almost completely incompatible. Once Upon a Number shows that stories and numbers aren't as different as you might imagine, and in fact they have surprising and fascinating connections. The concepts of logic and probability both grew out of intuitive ideas about how certain situations would play out. Now, logicians are inventing ways to deal with real world situations by mathematical means -- by acknowledging, for instance, that items that are mathematically interchangeable may not be interchangeable in a story. And complexity theory looks at both number strings and narrative strings in remarkably similar terms. Throughout, renowned author John Paulos mixes numbers and narratives in his own delightful style. Along with lucid accounts of cutting-edge information theory we get hilarious anecdotes and jokes; instructions for running a truly impressive pyramid scam; a freewheeling conversation between Groucho Marx and Bertrand Russell (while they're stuck in an elevator together); explanations of why the statistical evidence against OJ Simpson was overwhelming beyond doubt and how the Unabomber's thinking shows signs of mathematical training; and dozens of other treats. This is another winner from America's favorite mathematician.
224 pages, Paperback
First published January 1, 1998
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Displaying 1 - 25 of 25 reviews
April 18, 2019
In this book John Allen Paulos applies a meta narrative to the subjective experiences of interpreting language and numbers. His approach shows in the chapter titles: Between Stories and Statistics, Between Subjective Viewpoint and Impersonal Probability, Between Informal Discourse and Logic, Between Meaning and Information, Bridging the Gap Between Narrative and Data. When I scanned the chapter headings before reading the book I assumed that Paulos was going to apply a Thesis/Antithesis/Synthesis model to these areas, but he was aiming for something more comprehensive, and while he makes some insightful points, I didn’t feel he was wholly successful.
For one thing, the book is choppy, jumping from one observation to the next, sometimes with connections so tangential the reader is forced to stop and think about how these topics are related. In some places the writing seems like a collection of notes, and sometimes it is a recapitulation of ideas he presented in previous works.
And yet, when he is on target he is brilliant and insightful. He discusses Bayesian analysis at several points, and expanded my understanding of how subjective interpretations of probability can both exacerbate cognitive bias and help combat it.
I found myself smiling at his recounting of the Bible Code travesty; it reminded me of the famous quote by H.L. Mencken that “No one ever went broke underestimating the intelligence of the American public.” The fact it became a best seller, that so many were taken in by it, speaks to the pathetic lack of analytical ability in many people. I guess I shouldn’t have been too surprised though, considering that astrology is a huge business and millions plan their days around what they read in their horoscopes.
Each of the chapters presents a different take on the intersection of stories and statistics, and the author discusses wide ranging aspects of the subjective experience of meaning, such as chaos theory and cryptanalysis. Each digression is interesting in its own way, but some of them seem peripheral to the main topic. I wonder if whoever edited the book was too intimidated by the author’s reputation to demand better organization and a greater effort at showing how the various threads are related.
I picked up the book because I had read Paulos’ Innumeracy, which I liked very much. This one has some interesting ideas, and some brilliant observations, but it doesn’t hang together well. It reads like the first draft of a different book.
For one thing, the book is choppy, jumping from one observation to the next, sometimes with connections so tangential the reader is forced to stop and think about how these topics are related. In some places the writing seems like a collection of notes, and sometimes it is a recapitulation of ideas he presented in previous works.
And yet, when he is on target he is brilliant and insightful. He discusses Bayesian analysis at several points, and expanded my understanding of how subjective interpretations of probability can both exacerbate cognitive bias and help combat it.
I found myself smiling at his recounting of the Bible Code travesty; it reminded me of the famous quote by H.L. Mencken that “No one ever went broke underestimating the intelligence of the American public.” The fact it became a best seller, that so many were taken in by it, speaks to the pathetic lack of analytical ability in many people. I guess I shouldn’t have been too surprised though, considering that astrology is a huge business and millions plan their days around what they read in their horoscopes.
Each of the chapters presents a different take on the intersection of stories and statistics, and the author discusses wide ranging aspects of the subjective experience of meaning, such as chaos theory and cryptanalysis. Each digression is interesting in its own way, but some of them seem peripheral to the main topic. I wonder if whoever edited the book was too intimidated by the author’s reputation to demand better organization and a greater effort at showing how the various threads are related.
I picked up the book because I had read Paulos’ Innumeracy, which I liked very much. This one has some interesting ideas, and some brilliant observations, but it doesn’t hang together well. It reads like the first draft of a different book.
November 15, 2008
My statistics teacher, knowing that I was more literary- than mathematically-minded, asked me to read this book for a final project. I can't thank her enough for bridging the gap between math and my interests. A good read indeed!
August 21, 2022
A bit alien view on life and stories vs math and stats. If I ever meet an alien (not the illegal but the SF kind of one) I will be severely disappointed if they don't share this type of viewpoints. (Kidding but so true!)
Q:
How can all these parochial posters and self-conceptions be reconciled with accurate maps, external complexities, and the disembodied view from nowhere? (c)
Q:
There are a number of vaguely similar “obstetric” relationships: particular versus general, subjective versus universal, intuition versus proof, drama versus the timeless, first person versus third person, special versus standard. The first element in each pairing, while it may be held in lower regard, gives rise to or provides the ground for the second. Thus, a feeling of subjectivity is a necessary preliminary for an appreciation of universality, and dramatic immersion in the moment gradually leads to an awareness of the timeless. (c)
Q:
I began to point out the literal interpretation of street signs (VIOLATORS WILL BE TOWED should be VIOLATORS’ CARS WILL BE TOWED; and KEEP LITTER IN ITS PLACE counsels us to leave it on the ground else it lose its status as litter— placed in a garbage can, it’s no longer litter, but garbage) and was considered strange for my efforts. (c)
Q:
Murphy’s Law aptly illustrates an aspect of this nexus among stories, selves, and statistics. (c)
Q;
Very intelligent people, for example, can be expected to have intelligent offspring, but their offspring usually will not be quite as intelligent. (Why, since the point would be the same, does substituting stupid for intelligent in the last sentence seem offensive, a regression to meanness as well as to the mean?) (c)
Q:
We’ve moved too far away from Victorian novelists, who regularly inserted outlandish coincidences into their works. If Charlotte Bronte stretched the long arm of coincidence to the breaking point, as was once remarked, most modern writers have reduced it to an unnatural stub incapable of reaching out to a larger world. Coincidences are the ubiquitous stuff of life and leaving them out of a novel or movie makes plot and character development necessarily more deterministic and less lifelike.
Some Modernist forms of literature make a conscious attempt to reflect the aleatoric nature of life, and these stream-of-consciousness, fragmented, collage-like works do, like newspapers, contain many coincidences. (c)
Q:
How can all these parochial posters and self-conceptions be reconciled with accurate maps, external complexities, and the disembodied view from nowhere? (c)
Q:
There are a number of vaguely similar “obstetric” relationships: particular versus general, subjective versus universal, intuition versus proof, drama versus the timeless, first person versus third person, special versus standard. The first element in each pairing, while it may be held in lower regard, gives rise to or provides the ground for the second. Thus, a feeling of subjectivity is a necessary preliminary for an appreciation of universality, and dramatic immersion in the moment gradually leads to an awareness of the timeless. (c)
Q:
I began to point out the literal interpretation of street signs (VIOLATORS WILL BE TOWED should be VIOLATORS’ CARS WILL BE TOWED; and KEEP LITTER IN ITS PLACE counsels us to leave it on the ground else it lose its status as litter— placed in a garbage can, it’s no longer litter, but garbage) and was considered strange for my efforts. (c)
Q:
Murphy’s Law aptly illustrates an aspect of this nexus among stories, selves, and statistics. (c)
Q;
Very intelligent people, for example, can be expected to have intelligent offspring, but their offspring usually will not be quite as intelligent. (Why, since the point would be the same, does substituting stupid for intelligent in the last sentence seem offensive, a regression to meanness as well as to the mean?) (c)
Q:
We’ve moved too far away from Victorian novelists, who regularly inserted outlandish coincidences into their works. If Charlotte Bronte stretched the long arm of coincidence to the breaking point, as was once remarked, most modern writers have reduced it to an unnatural stub incapable of reaching out to a larger world. Coincidences are the ubiquitous stuff of life and leaving them out of a novel or movie makes plot and character development necessarily more deterministic and less lifelike.
Some Modernist forms of literature make a conscious attempt to reflect the aleatoric nature of life, and these stream-of-consciousness, fragmented, collage-like works do, like newspapers, contain many coincidences. (c)
November 7, 2012
Paulos introduces a number of new and insightful ways of thinking about the world, which will surely raise the consciousness of most readers. On the other hand, he isn't the most engaging writer in the world, and is almost intolerably smug, but never mind.
August 12, 2020
Math has never been my strong suit. In the fall of my senior year of high school, I took a math class at a community college, and have never studied math since. I married a man who majored in applied mathematics, but his affinity for infinity hasn't really rubbed off on me. So, when I found a book about math and stories, I leapt at the chance to read it.
Paulos limits most of his discussion to probability and statistics. Rather than being about literature, Once Upon a Number is about everyday life: coincidences, likelihood, and so forth. Written in the 1990s, Paulos discusses the Unabomber's math background (the anti-Charlie from Numb3rs) and the statistical background to evidence in the O. J. Simpson trials. Paulos mentions literature in passing, but never lingers. I did have a bit of a revelation, however, when he mentioned Alice in Wonderland. Written by Charles Dodgson, the mathematician also known as Lewis Carroll, its humor is built on mathematical logic. Perhaps that's why I've never connected with it.
Paulos used the phrase "personal complexity horizon" to express one's intellectual limits. This phrase has already nestled into my vocabulary. Higher math is far, far beyond my personal complexity horizon.
A weakness of this book is Paulos's cavalier attitude toward religion. Had he looked at the statistics of religious vs. non-religious people in the world, he'd know that most potential readers might be annoyed by his triumphant materialism. Also, this book is over 20 years old and shows its age. Surprisingly, the sections on computing didn't age so badly, but other aspects (casual racism, misogyny) aged worse.
I think my husband, being the computer scientist-chemical engineer-mathematician that he is, will enjoy this more than I did. It's definitely within his personal complexity horizon, and perhaps he can explain things better to my humanities brain.
Paulos limits most of his discussion to probability and statistics. Rather than being about literature, Once Upon a Number is about everyday life: coincidences, likelihood, and so forth. Written in the 1990s, Paulos discusses the Unabomber's math background (the anti-Charlie from Numb3rs) and the statistical background to evidence in the O. J. Simpson trials. Paulos mentions literature in passing, but never lingers. I did have a bit of a revelation, however, when he mentioned Alice in Wonderland. Written by Charles Dodgson, the mathematician also known as Lewis Carroll, its humor is built on mathematical logic. Perhaps that's why I've never connected with it.
Paulos used the phrase "personal complexity horizon" to express one's intellectual limits. This phrase has already nestled into my vocabulary. Higher math is far, far beyond my personal complexity horizon.
A weakness of this book is Paulos's cavalier attitude toward religion. Had he looked at the statistics of religious vs. non-religious people in the world, he'd know that most potential readers might be annoyed by his triumphant materialism. Also, this book is over 20 years old and shows its age. Surprisingly, the sections on computing didn't age so badly, but other aspects (casual racism, misogyny) aged worse.
I think my husband, being the computer scientist-chemical engineer-mathematician that he is, will enjoy this more than I did. It's definitely within his personal complexity horizon, and perhaps he can explain things better to my humanities brain.
August 16, 2023
Paulos includes some interesting, if recycled, ideas that could have been summarized in an extended essay rather than (what feels like) a bloated monograph. The discourse also wanders and offers a bit too much handholding. Readers who would be interested in Once Upon a Number (OUAN) aren't likely to suffer from an abject aversion to at least some mathematical hieroglyphics, and the book would have benefitted from even a slightly deeper dive into some of the technicalities. Worse, OUAN falters at the points that hold the most interest, offering allusions to connections between mathematics and both philosophy and sociology only to admit that sometimes the number of variables involved precludes a quantifiable approach. Right, well, tell that to the economists.
Unfortunately, OUAN should be indicted on more serious charges. The dismissive discussion on ELS probabilities (i.e., the "Bible codes") involves straw-man constructions on several fronts, all of which are wholly unworthy of Paulos's perspicacity. A few points need greater explication:
First, there's currently no consensus on how to calculate the probability of ELS tables. Programs like CodeFinder give tentative p-values for custom matrices, but those values are generally considered controversial. Determining these p-values isn't merely an issue of letter frequency; it's also about the distance of the terms within the table, a point Paulos completely ignores. A few terms spread out over hundreds of pages should be considered a trivial result. A table that has many terms packed together in a single passage or a page of surface text seems far less likely to occur by chance. Thus, letter frequency is insufficient as a metric for conjuring likelihoods. One can't treat letters as independent events based solely on frequency probabilities. Example: You're probably more likely to find the letters K, B, I, and L in books on serial killers and Bill Clinton than one on, say, noncommutative group theory, but Paulos blithely submits the nonsequitur of letter frequency as evidence to discredit ELS theory. (It's worth noting most modern code studies have revealed entire sentences as ELS strings, constructions that are far less likely to occur by chance than single terms.)
Second, serious researchers of ELS strings have long since acknowledged the fact that such sequences exist, by their design, in all texts, and Brenden McKay has done a fine job of elucidating the obvious counterpoints. You'll find "Kennedy," "assassination," and "Dallas" in Moby Dick, for example—though the ELS table might involve a large portion of surface text covering many pages—so the fact that simple ELS strings exist in other texts is hardly the "gotcha" moment Paulos thinks it is. What distinguishes a Torah ELS from, say, McKay's findings, however, is that it contains far more relevant terms than what we find in "dummy" texts (e.g., "Kennedy," "assassination," "Dallas," "November 22, 1963," "Lee Harvey Oswald," "shot," "conspiracy," "grassy knoll," "president," "rifle," etc.), all occurring within a small area of surface text. We might not be able to quantify the probability of that table happening by chance, but one cannot suppress the feeling these tables represent palpably different outcomes. The Torah also includes significant tables (i.e., at least 5 related terms) for a nearly transfinite number of historical events (e.g., the Holocaust, 9/11, U.S. presidential elections, the assassination of Yitzhak Rabin, the Apollo moon landing, Covid-19, etc.), and arguing that all these intricate tables exist within a single, coherent surface text of moderate length as some function of stochastic serendipity begins to strain the bounds of reasonableness.
Third, search variability is a benign product of the commonality of ELS strings; yes, you could search for "John," "Johnathan," "Jonathan," and "Johnny," but only one search term will be associated with the principal table. This should not surprise you if you believe ELS strings are tantamount to astrological star chasing. But it does not follow that ELS tables are trivial because single-term ELS strings are trivial and admit spelling variations. Failing to make this logical connection would be bad enough, but Paulos doesn't even understand how ELS searches are conducted. He derisively refers to "diagonal" searches, intimating they are yet another way of admitting bias and diminishing the results, but that is surely the result of Paulos looking at finished ELS tables, which often include terms that are positioned "diagonally" on the page. These "diagonal" (as well as "vertical") terms are the result of breaking the single, horizontal string of letters into blocks of text so the terms fit into a single table (or matrix).
Whatever one might think of the ELS tables, Paulos fails to provide all the relevant details. He certainly doesn't need to come to the conclusion the tables are supernaturally inspired—and neither does the reader—but he should be required to understand the specifics of what he's criticizing if only to steel-man the opposing view and present readers with accurate, unbiased information. He bears at least that responsibility, and on that charge he is guilty.
The second, and more serious, problem with OUAN is the misunderstanding of the One-Time Pad (OTP). What Paulos describes is a simple substitution cipher (e.g., A for H, G for L, etc.), not an OTP. An OTP transforms the clear text into an unbreakable ciphertext by using a true random number generator (TRNG) to create a key that is at least as long as the message (it can be longer). One then implements modular arithmetic to build the encrypted message. Example: We want to encrypt the word "tunnel." The letter positions are 20, 21, 14, 14, 5, and 12. A TRNG creates the following random key: 5, 13, 8, 9, 18, and 1. The ciphertext is then (20 + 5), (21 + 13), (14 + 8), (14 + 9), (5 + 18), (12 +1) with all sums calculated mod 26: "Z H W X X M." Of course, this is not at all what Paulos describes in his book. The OPT has been mathematically proven (by Claude Shannon) to be unbreakable if the key (1) is truly random, (2) has a length at least as long as the clear text, and (3) is used only once—thus the "one-time" designation. The idea is that there exists an infinite number of possible messages derived from the ciphertext, and it's impossible to know which message is the correct one because they are all equally likely from a probability perspective. How Paulos bungled the mathematical details of such an important cryptographic system lies beyond all my cognitive powers.
In summary, OUAN enjoys a few isolated moments, but it suffers from serious flaws and doesn't provide much of a payoff for the effort. The substantive and technical errors are significant enough to prevent me from recommending it in any serious way.
Unfortunately, OUAN should be indicted on more serious charges. The dismissive discussion on ELS probabilities (i.e., the "Bible codes") involves straw-man constructions on several fronts, all of which are wholly unworthy of Paulos's perspicacity. A few points need greater explication:
First, there's currently no consensus on how to calculate the probability of ELS tables. Programs like CodeFinder give tentative p-values for custom matrices, but those values are generally considered controversial. Determining these p-values isn't merely an issue of letter frequency; it's also about the distance of the terms within the table, a point Paulos completely ignores. A few terms spread out over hundreds of pages should be considered a trivial result. A table that has many terms packed together in a single passage or a page of surface text seems far less likely to occur by chance. Thus, letter frequency is insufficient as a metric for conjuring likelihoods. One can't treat letters as independent events based solely on frequency probabilities. Example: You're probably more likely to find the letters K, B, I, and L in books on serial killers and Bill Clinton than one on, say, noncommutative group theory, but Paulos blithely submits the nonsequitur of letter frequency as evidence to discredit ELS theory. (It's worth noting most modern code studies have revealed entire sentences as ELS strings, constructions that are far less likely to occur by chance than single terms.)
Second, serious researchers of ELS strings have long since acknowledged the fact that such sequences exist, by their design, in all texts, and Brenden McKay has done a fine job of elucidating the obvious counterpoints. You'll find "Kennedy," "assassination," and "Dallas" in Moby Dick, for example—though the ELS table might involve a large portion of surface text covering many pages—so the fact that simple ELS strings exist in other texts is hardly the "gotcha" moment Paulos thinks it is. What distinguishes a Torah ELS from, say, McKay's findings, however, is that it contains far more relevant terms than what we find in "dummy" texts (e.g., "Kennedy," "assassination," "Dallas," "November 22, 1963," "Lee Harvey Oswald," "shot," "conspiracy," "grassy knoll," "president," "rifle," etc.), all occurring within a small area of surface text. We might not be able to quantify the probability of that table happening by chance, but one cannot suppress the feeling these tables represent palpably different outcomes. The Torah also includes significant tables (i.e., at least 5 related terms) for a nearly transfinite number of historical events (e.g., the Holocaust, 9/11, U.S. presidential elections, the assassination of Yitzhak Rabin, the Apollo moon landing, Covid-19, etc.), and arguing that all these intricate tables exist within a single, coherent surface text of moderate length as some function of stochastic serendipity begins to strain the bounds of reasonableness.
Third, search variability is a benign product of the commonality of ELS strings; yes, you could search for "John," "Johnathan," "Jonathan," and "Johnny," but only one search term will be associated with the principal table. This should not surprise you if you believe ELS strings are tantamount to astrological star chasing. But it does not follow that ELS tables are trivial because single-term ELS strings are trivial and admit spelling variations. Failing to make this logical connection would be bad enough, but Paulos doesn't even understand how ELS searches are conducted. He derisively refers to "diagonal" searches, intimating they are yet another way of admitting bias and diminishing the results, but that is surely the result of Paulos looking at finished ELS tables, which often include terms that are positioned "diagonally" on the page. These "diagonal" (as well as "vertical") terms are the result of breaking the single, horizontal string of letters into blocks of text so the terms fit into a single table (or matrix).
Whatever one might think of the ELS tables, Paulos fails to provide all the relevant details. He certainly doesn't need to come to the conclusion the tables are supernaturally inspired—and neither does the reader—but he should be required to understand the specifics of what he's criticizing if only to steel-man the opposing view and present readers with accurate, unbiased information. He bears at least that responsibility, and on that charge he is guilty.
The second, and more serious, problem with OUAN is the misunderstanding of the One-Time Pad (OTP). What Paulos describes is a simple substitution cipher (e.g., A for H, G for L, etc.), not an OTP. An OTP transforms the clear text into an unbreakable ciphertext by using a true random number generator (TRNG) to create a key that is at least as long as the message (it can be longer). One then implements modular arithmetic to build the encrypted message. Example: We want to encrypt the word "tunnel." The letter positions are 20, 21, 14, 14, 5, and 12. A TRNG creates the following random key: 5, 13, 8, 9, 18, and 1. The ciphertext is then (20 + 5), (21 + 13), (14 + 8), (14 + 9), (5 + 18), (12 +1) with all sums calculated mod 26: "Z H W X X M." Of course, this is not at all what Paulos describes in his book. The OPT has been mathematically proven (by Claude Shannon) to be unbreakable if the key (1) is truly random, (2) has a length at least as long as the clear text, and (3) is used only once—thus the "one-time" designation. The idea is that there exists an infinite number of possible messages derived from the ciphertext, and it's impossible to know which message is the correct one because they are all equally likely from a probability perspective. How Paulos bungled the mathematical details of such an important cryptographic system lies beyond all my cognitive powers.
In summary, OUAN enjoys a few isolated moments, but it suffers from serious flaws and doesn't provide much of a payoff for the effort. The substantive and technical errors are significant enough to prevent me from recommending it in any serious way.
February 19, 2010
This is my least favorite of the three Paulos books I have read; Innumeracy and Irreligion are both great. I was expecting something more interesting, since the comparisons and contrasts between mathematics and stories should have been fun to read.
I got the feeling that he wrote this too fast, not really spending a lot of time making sure what he was writing and what he was thinking made sense to the reader. At times it felt like I was immersed in his stream of consciousness, without any effort on his part to make sure I followed the point he was trying to make. I found myself re-reading a lot of passages, thinking I must have missed something interesting. Sometimes I did, but as I got further into the book my disappointments exceeded any insights I gained, so I just plugged away and was kind of happy to finish. That has never been the case with Paulos before. I’ve always wanted more. Don’t get me wrong, there were some great insights in this book. But there was just too much regular stuff.
I’m hoping this is the worst of his books. I was looking forward to reading the others. I’ve read some rave reviews of this book, so it’s probably my fault for not spending greater effort to enjoy it.
I got the feeling that he wrote this too fast, not really spending a lot of time making sure what he was writing and what he was thinking made sense to the reader. At times it felt like I was immersed in his stream of consciousness, without any effort on his part to make sure I followed the point he was trying to make. I found myself re-reading a lot of passages, thinking I must have missed something interesting. Sometimes I did, but as I got further into the book my disappointments exceeded any insights I gained, so I just plugged away and was kind of happy to finish. That has never been the case with Paulos before. I’ve always wanted more. Don’t get me wrong, there were some great insights in this book. But there was just too much regular stuff.
I’m hoping this is the worst of his books. I was looking forward to reading the others. I’ve read some rave reviews of this book, so it’s probably my fault for not spending greater effort to enjoy it.
October 28, 2013
I was interested in this book because I heard the author on the radio show "In Our Time." He did not get many points across and I expected that his book would better illustrate his ideas. I was wrong.
As someone very interested in math, science, and stories, I thought that the book would look at all three in an interrelated manner. Again, I was wrong. The entire book reads like an episode of "Bullshit!" and, while this isn't bad in and of itself, I expected an episode of "In Our Time."
Having said that, the book is a lovely introduction to the analysis of probability in a manner that is not so widely spread.
If you are about to make the same mistake I did, please just listen to the radio episode instead of reading the book. Here's the link: http://www.bbc.co.uk/iplayer/episode/... The episode is more informative and interdisciplinary than the book by far.
As someone very interested in math, science, and stories, I thought that the book would look at all three in an interrelated manner. Again, I was wrong. The entire book reads like an episode of "Bullshit!" and, while this isn't bad in and of itself, I expected an episode of "In Our Time."
Having said that, the book is a lovely introduction to the analysis of probability in a manner that is not so widely spread.
If you are about to make the same mistake I did, please just listen to the radio episode instead of reading the book. Here's the link: http://www.bbc.co.uk/iplayer/episode/... The episode is more informative and interdisciplinary than the book by far.
January 7, 2014
One upon a number is an important book that attempts to bring understanding to the proliferation of everyday common discourse, especially that which fuses narrative and statistics to give an impression of authoritative truth. The author Paulus commands the pen in a highly stylistic manner that in some cases adds to confusion where a little more grounding in simple language would have benefited the clarity and meaning of critical passages. Literary style aside, this book is a fascinating excursion into the significance and sense underlying neo-factual communications in today's world. Topics covered include: Between stories and statistics, Between subjective viewpoint and impersonal probability, Between Informal discourse and Logic, Between Meaning and information, Bridging the gap between narrative and data. Once Upon a Number is a stimulating and thought-provoking read on a much neglected yet valuable subject for decoding society's news.
August 26, 2013
Paulos versucht den Brückenschlag zwischen naturwissenschaftlichem Denken und erzählerischem Erfahren zu überbrücken und zeigt auf, wie beide teilweise wechselwirken oder sich sogar bedingen können.
Das führt manchmal zu etwas gezwungenen Aussagen, bietet aber auch eine Menge interessanter Ansätze und spannender Erläuterungen.
Das führt manchmal zu etwas gezwungenen Aussagen, bietet aber auch eine Menge interessanter Ansätze und spannender Erläuterungen.
March 15, 2015
Ironically the author has chosen to use a rather "narrative" approach to bring his point across. As a result you sometimes feel a bit lost as to where the story is going. There are enough surprises and funny facts to keep you continuing reading however.
February 18, 2018
I'm afraid Paulos was experimenting with one of the principles from his own book a bit too much: if you just assemble enough words, someone is bound to find a pattern and make sense of them.
I'm not that person however.
I enjoyed the premise of the book (bridging the gap between two intellectual cultures), and the first two chapters were actually very interesting. But the third one couldn't hold my attention, the fourth one didn't seem well researched at all and the fifth one was completely superfluous.
I'm not that person however.
I enjoyed the premise of the book (bridging the gap between two intellectual cultures), and the first two chapters were actually very interesting. But the third one couldn't hold my attention, the fourth one didn't seem well researched at all and the fifth one was completely superfluous.
July 19, 2019
Either I am too dumb to understand this book or this book was not intended for an average schmuck such as myself. While it does have some interesting ideas, it failed to make me excited to pick up the book and keep reading it. In fact, I was kind of dreading it.
Anyway, I'll leave it to smarter book reviewer to give this book a proper review it needs. For now, know that I am disappointed...for whatever that is worth.
Anyway, I'll leave it to smarter book reviewer to give this book a proper review it needs. For now, know that I am disappointed...for whatever that is worth.
April 23, 2025
Self- important gibberish. I read it out of spite once I got started. Overly verbose, a scattered miasma of nonsensical philosophicesque cornucopae, belabored by unnecessarily obtuse vocabulary, obscure references to mundane minutiae. It comes nowhere near unifying mathematical thinking with logic nor stories. I love books with mathematical premises and bases which are inquisitive, well-constructed, and witty, but thus delivers none of that. I cannot figure if this was just a “paycheck” book, or if procrastination led to an unmeetable deadline causing this goulashy ratatouille. Read something else.
January 2, 2026
Ongelofelijk veel kennis, inzichten, en mooie verhalen. Maar de bewering van Paulos op blz. 168 is ook waar - en bemoeilijkt het lezen soms: “Isaiah Berlin zou (via Archilochus) zeggen dat we meer lijken op vossen die veel kleine dingetjes weten dan op egels die één groot ding weten. En inderdaad heeft de episodische hap-snapstructuur van het boek dat u nu leest, te maken met een zelfde soort ongeduld als het gaat om pompeuze beweringen en simplistische theorieën.”
August 7, 2020
Con diferencia el más flojo de Paulos. Ensayo sobre los puentes que se pueden tender entre las matemáticas/ciencias y las historias/narrativas. Tiene ideas que creo que el autor no refinó y quedan muy indefinidas. No es fácil de seguir, no engancha, no es engaging, como lo llaman allá.
May 31, 2017
The author applies mathematics to storytelling, sort of. A lot of cute & counter-intuitive things here.
January 24, 2018
It's terrible. Don't waste your time with this book. The entire book has no logical flow to it. The writing is so disjointed that it's impossible to figure out what the author is talking about.
March 7, 2018
I liked the title. But unfortunately, there is not that much in it. Certainly "the hidden mathematical logic of stories" is not revealed.
June 4, 2021
DNF
I rather enjoyed two other books by this author, but this one just didn't grab me.
I rather enjoyed two other books by this author, but this one just didn't grab me.
December 18, 2021
Mientras que su libro Un matematico lee el periodico me encantó, este lo sentí mucho menos cercano. No lo recomiendo mucho
November 14, 2016
Lots of good insights about the relationship between statistics and stories but it wasn't as tightly written as his first book on the mathematics of humor. So, if you're expecting actual mathematical analyses of various plots or how character traits interact with each other to build an inner world, you won't be getting much of that here.
June 24, 2009
I had to give up on this book, not something I do often. I have been trying to read it for a couple of months now, and just can't get into it. I have read one other of John Paulos' books and found it enjoyable, so maybe I need to try this when I'm in a different frame of mind...
April 8, 2013
Decent book. It was ok as far as math books go.
February 15, 2014
Neat little book, a bit too basic and obvious (for me) at points though.
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