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A Certain Ambiguity: A Mathematical Novel
While taking a class on infinity at Stanford in the late 1980s, Ravi Kapoor discovers that he is confronting the same mathematical and philosophical dilemmas that his mathematician grandfather had faced many decades earlier--and that had landed him in jail. Charged under an obscure blasphemy law in a small New Jersey town in 1919, Vijay Sahni is challenged by a skeptical judge to defend his belief that the certainty of mathematics can be extended to all human knowledge--including religion. Together, the two men discover the power--and the fallibility--of what has long been considered the pinnacle of human certainty, Euclidean geometry.
As grandfather and grandson struggle with the question of whether there can ever be absolute certainty in mathematics or life, they are forced to reconsider their fundamental beliefs and choices. Their stories hinge on their explorations of parallel developments in the study of geometry and infinity--and the mathematics throughout is as rigorous and fascinating as the narrative and characters are compelling and complex.
Moving and enlightening, "A Certain Ambiguity" is a story about what it means to face the extent--and the limits--of human knowledge.
As grandfather and grandson struggle with the question of whether there can ever be absolute certainty in mathematics or life, they are forced to reconsider their fundamental beliefs and choices. Their stories hinge on their explorations of parallel developments in the study of geometry and infinity--and the mathematics throughout is as rigorous and fascinating as the narrative and characters are compelling and complex.
Moving and enlightening, "A Certain Ambiguity" is a story about what it means to face the extent--and the limits--of human knowledge.
304 pages, ebook
First published July 2, 2007
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Displaying 1 - 30 of 78 reviews
June 30, 2018
So Many Stories; So Little Point
A Certain Ambiguity is appropriately titled; it is highly ambiguous in both form and content. It starts as a Bildungsroman of a Stanford University student from India, fades into an Historical Mystery about the student’s mathematician grandfather, lapses occasionally into a rather unromantic Romance, and ends up commenting on the conflicting duties toward self, family and humanity. A substantial portion of the book is concerned with the axiomatic method as applied in mathematics, and a comparison of this method with that of religious faith. It also provides extended tutorials on the rigours of geometry and the mathematics of infinity.
So if you are interested in why Euclid’s fifth postulate is like Cantor’s Continuum Hypothesis, this may be your thing. If not, it doesn’t have the necessary literary qualities to justify either its price or the investment in reading-time. Its observations are trivial where they are not tedious. Its suggestions - particularly about the similarity of religious faith and mathematical commitment - are not only wrong, they are dangerously stupid (See here for a refutation of the contention that scientific and religious faith are analogous: https://www.goodreads.com/review/show...). Page after page of mathematical proofs and faux correspondence by philosophers ancient and modern constitute a travesty of narrative story-telling.
At one point the protagonist has an epiphany: “Maybe it’s because mathematics is not a spectator sport. You have to do it to appreciate it.” Perhaps this insight is worthwhile. Of course it also obviates the point of the book: An axiomatic contradiction which should have prevented its publication. If you have an interest in literary mathematics, I suggest a far superior alternative: https://www.goodreads.com/review/show...
A Certain Ambiguity is appropriately titled; it is highly ambiguous in both form and content. It starts as a Bildungsroman of a Stanford University student from India, fades into an Historical Mystery about the student’s mathematician grandfather, lapses occasionally into a rather unromantic Romance, and ends up commenting on the conflicting duties toward self, family and humanity. A substantial portion of the book is concerned with the axiomatic method as applied in mathematics, and a comparison of this method with that of religious faith. It also provides extended tutorials on the rigours of geometry and the mathematics of infinity.
So if you are interested in why Euclid’s fifth postulate is like Cantor’s Continuum Hypothesis, this may be your thing. If not, it doesn’t have the necessary literary qualities to justify either its price or the investment in reading-time. Its observations are trivial where they are not tedious. Its suggestions - particularly about the similarity of religious faith and mathematical commitment - are not only wrong, they are dangerously stupid (See here for a refutation of the contention that scientific and religious faith are analogous: https://www.goodreads.com/review/show...). Page after page of mathematical proofs and faux correspondence by philosophers ancient and modern constitute a travesty of narrative story-telling.
At one point the protagonist has an epiphany: “Maybe it’s because mathematics is not a spectator sport. You have to do it to appreciate it.” Perhaps this insight is worthwhile. Of course it also obviates the point of the book: An axiomatic contradiction which should have prevented its publication. If you have an interest in literary mathematics, I suggest a far superior alternative: https://www.goodreads.com/review/show...
February 14, 2020
Ενδιαφέρον και καλογραμμένο μυθιστόρημα, αλλά οι υποψήφιοι αναγνώστες καλά θα κάνουν να πάρουν στα σοβαρά τον χαρακτηρισμό "μαθηματικό". Τα μαθηματικά αποτελούν εξαιρετικά μεγάλο μέρος του κειμένου και δε νομίζω ότι είναι απόλυτα κατανοητά από τον μέσο άνθρωπο. Εγώ δεν έχω γνώσεις μαθηματικών (τριτοδεσμίτισσα γαρ), αλλά έχω διαβάσει αρκετά βιβλία με μαθηματικό περιεχόμενο και σε γενικές γραμμές δεν είχα πρόβλημα στην κατανόησή τους. Με το συγκεκριμένο δυσκολεύτηκα πολύ και σε ορισμένα σημεία ήταν αδύνατο να το παρακολουθήσω, αν και αυτό δε με εμπόδισε να απολαύσω τα λιγότερο τεχνικά κομμάτια και δε μετάνιωσα που το ξεκίνησα. Το συνιστώ ανεπιφύλακτα σε όσους γνωρίζουν καλά μαθηματικά, ενώ για τους υπόλοιπους το συνιστώ επίσης, αλλά προειδοποιώ ότι δεν είναι βατό. Caveat emptor.
January 3, 2010
This is quite a unique and enjoyable book. Encapsulated as a novel, the book covers elementary mathematics of infinity, set theory, and Euclidean and non-Euclidean geometry. It covers the history of these topics, as well. And it isn't dry--the subjects are covered in a easily-understood, "Socratic" approach. Nico, the professor of mathematics, knows how to motivate students, cultivate enthusiasm, and lure students into a deeper understanding of the topics of his course. Nico also shows how mathematicians think about their work, and about the world.
A major theme in the book is the hierarchy of provable theorems, built upon fundamental axioms that are unprovable, but "self-evidently true".
The main character is an Indian student, Ravi, who is enrolled as an economics major at Stanford University. He learns that his late grandfather, who he had adored as a child, had spent some time in a jail in New Jersey! It takes some time for Ravi to unfold the story of his grandfather, who had been a mathematician and an atheist. It seems that his grandfather had been arrested under an obscure law in New Jersey against blasphemy. Of course, this law is in contradiction with the freedom of speech clause in the Bill of Rights. A central question is whether mathematics is built on firmer foundations than religions.
While the story in the novel isn't really believable, it is a fun read if you enjoy mathematics, and highly educational at the same time.
A major theme in the book is the hierarchy of provable theorems, built upon fundamental axioms that are unprovable, but "self-evidently true".
The main character is an Indian student, Ravi, who is enrolled as an economics major at Stanford University. He learns that his late grandfather, who he had adored as a child, had spent some time in a jail in New Jersey! It takes some time for Ravi to unfold the story of his grandfather, who had been a mathematician and an atheist. It seems that his grandfather had been arrested under an obscure law in New Jersey against blasphemy. Of course, this law is in contradiction with the freedom of speech clause in the Bill of Rights. A central question is whether mathematics is built on firmer foundations than religions.
While the story in the novel isn't really believable, it is a fun read if you enjoy mathematics, and highly educational at the same time.
April 6, 2015
The two main topics in this novel are set theory and geometry. The mathematics that is presented here is the usual and well known theorems. In Set theory, starting from Zeno’s paradoxes, infinite series, to the theory of sets and the continuum hypothesis. And in geometry, starting from the Pythagoras theorem, Euclid’s axioms and to the development of Non-Euclidean geometry. They are developed parallelly (and in two parallel story lines, one taking place in contemporary times and the other in 1919) showing the independence of continuum hypothesis and Euclid's fifth postulate.
The main goal of the novel seems to be the epistemological implications of the development of theory of infinite sets and Non-Euclidean geometry. It raises some very important questions about mathematical truth but the writers only give a casual overview of mathematics and they do not go deep enough to better understand their implicationson the nature of truth.
For a beginner, this could be a fascinating tour of the basis of mathematics. It does a pretty good job of introducing continuum hypothesis and Non-Euclidean geometry in elementary terms. For someone already familiar with the mathematics and philosophy dealt with in this book and its historical basis, there isn't much here as the story itself isn't very fascinating.
But i did like the last part of the book, the journal entry of the judge where he and Vijay Sahni come to terms with the lack of certainity.
The main goal of the novel seems to be the epistemological implications of the development of theory of infinite sets and Non-Euclidean geometry. It raises some very important questions about mathematical truth but the writers only give a casual overview of mathematics and they do not go deep enough to better understand their implicationson the nature of truth.
For a beginner, this could be a fascinating tour of the basis of mathematics. It does a pretty good job of introducing continuum hypothesis and Non-Euclidean geometry in elementary terms. For someone already familiar with the mathematics and philosophy dealt with in this book and its historical basis, there isn't much here as the story itself isn't very fascinating.
But i did like the last part of the book, the journal entry of the judge where he and Vijay Sahni come to terms with the lack of certainity.
March 9, 2021
A Certain Ambiguity is the story of certain young man spending some time in college, feeling confused about his future prospects, torn between pragmatism and passion. He listens to some jazz, he finds a young miss, he takes a course on Set Theory, and he reads old correspondence from mathematicians, including the court transcripts in which his grandfather argued with a Christian judge about the nature of certainty.
The narrative is whatever, it’s just a vehicle to explore certain math and philosophy topics.
Basically, the book has some Set Theory (the math of infinity) and also some geometry, particularly the evolution from Euclidean to non-Euclidean geometry and all the angsty uncertainty along the way.
Your average human being doesn’t know a postulate from a pustule, so the book will have a limited audience.
However, I - who love and teach math - am among that audience, so the math side of this book was both business and pleasure. I taught myself tensor calculus one summer, so I’ve explored certain topics of non-Euclidean geometry. But I really only did so in order to learn General Relativity. I didn’t bother with its historical development. So I quite enjoyed doing so now, and, if nothing else, knowing the history shows me how my occasional uncertainty and doubt in understanding the math were mirrored by the very creators of that math.
As for the philosophy… meh. It’s all about certainty. It’s all about Rene Descartes’ motivation in penning his famous, “Cogito ergo sum”: I am thinking, therefore I exist.
Don’t get me wrong, this is an important topic. Before I conceded the impossibility of the task, my original review was a much lengthier mini-primer on the topic.
It’s just, honestly, the topic bores me now. I’ve studied Hume’s Problem of Induction; Godel’s Incompleteness Theorem; the many forms of Heisenberg’s Uncertainty Principle; the No-Cloning Theorem; etc. The heuristic nature of human decision making and the distinction between possibility and probability are important topics that not nearly enough people know appreciate.
But, again I, personally, find it boring. Childish actually. So this facet of the book was a bit aggravating. I mean, the book’s philosophical exploration ends with the concession that absolute certainty is impossible. So… the first and easiest step on a much longer, more interesting philosophical journey.
In short, The good: math. The bad: philosophy. The neutral: narrative. And never forget, God hates idiots, also.
The narrative is whatever, it’s just a vehicle to explore certain math and philosophy topics.
Basically, the book has some Set Theory (the math of infinity) and also some geometry, particularly the evolution from Euclidean to non-Euclidean geometry and all the angsty uncertainty along the way.
Your average human being doesn’t know a postulate from a pustule, so the book will have a limited audience.
However, I - who love and teach math - am among that audience, so the math side of this book was both business and pleasure. I taught myself tensor calculus one summer, so I’ve explored certain topics of non-Euclidean geometry. But I really only did so in order to learn General Relativity. I didn’t bother with its historical development. So I quite enjoyed doing so now, and, if nothing else, knowing the history shows me how my occasional uncertainty and doubt in understanding the math were mirrored by the very creators of that math.
As for the philosophy… meh. It’s all about certainty. It’s all about Rene Descartes’ motivation in penning his famous, “Cogito ergo sum”: I am thinking, therefore I exist.
Don’t get me wrong, this is an important topic. Before I conceded the impossibility of the task, my original review was a much lengthier mini-primer on the topic.
It’s just, honestly, the topic bores me now. I’ve studied Hume’s Problem of Induction; Godel’s Incompleteness Theorem; the many forms of Heisenberg’s Uncertainty Principle; the No-Cloning Theorem; etc. The heuristic nature of human decision making and the distinction between possibility and probability are important topics that not nearly enough people know appreciate.
But, again I, personally, find it boring. Childish actually. So this facet of the book was a bit aggravating. I mean, the book’s philosophical exploration ends with the concession that absolute certainty is impossible. So… the first and easiest step on a much longer, more interesting philosophical journey.
In short, The good: math. The bad: philosophy. The neutral: narrative. And never forget, God hates idiots, also.
August 6, 2010
Good math book. Very bad novel.
February 7, 2014
This is another book I had high hopes for, based on the blurb and the recommendation of a friend. It has math. It has philosophy. Since those subjects both interest me, it sounded full of potential. But I wound up disappointed. I was so disappointed, I almost didn't finish the book.
My main disappointment is with the plot, which was paper-thin and obvious from the beginning. There's this guy and he, through a few quickly dispensed situations, winds up in college with graduation day approaching. A series of unconvincing events puts him in a class that is part math class, part philosophy discussion. He makes new friends. He meets a girl. Already you know that they will discuss math. They will discuss philosophy. He might get involved with the girl.
So they do all that. The author tries to make things more interesting by adding the sudden discovery that the guy's beloved grandfather spent time in jail and so he has to research that, too. But all that plot description makes it sound more interesting than it really is, because that takes up about 25% of the words in the book. The other 75% is taken up with endless dialogs about math and philosophy, either presented in the classroom, or a jail cell (while a judge and the grandfather work through the motivations for the grandfathers 'objectionable' behavior), or at various contrived situations around campus.
At various points the endless dialog, which is always in language far to lofty to come out of ordinary, human mouths, is broken up by fictionalized letters and journal entries from historical mathematicians and philosophers. These are also written in language either too lofty or too modern to be based in reality. The contrived and awkward situations, discussions and documents all kept me from connecting with the story and characters and really enjoying the ride.
This book would be improved by either ditching the 'novel' portion or making it stronger. As it is, the math exposition, while interesting and central to the theme, overwhelm the fiction.
The only reason this gets 3 stars, rather than 2, is because of the intriguing subjects. It did get me to thinking deep thoughts, which I believe was the point of it. But the lack of personal connection and the awkwardly scholarly language kept it from approaching 4 stars. Only recommended if you like math (or are unoffended by it) and are likewise unoffended by flowery dialog and thoughts that do not reflect the way real people behave.
My main disappointment is with the plot, which was paper-thin and obvious from the beginning. There's this guy and he, through a few quickly dispensed situations, winds up in college with graduation day approaching. A series of unconvincing events puts him in a class that is part math class, part philosophy discussion. He makes new friends. He meets a girl. Already you know that they will discuss math. They will discuss philosophy. He might get involved with the girl.
So they do all that. The author tries to make things more interesting by adding the sudden discovery that the guy's beloved grandfather spent time in jail and so he has to research that, too. But all that plot description makes it sound more interesting than it really is, because that takes up about 25% of the words in the book. The other 75% is taken up with endless dialogs about math and philosophy, either presented in the classroom, or a jail cell (while a judge and the grandfather work through the motivations for the grandfathers 'objectionable' behavior), or at various contrived situations around campus.
At various points the endless dialog, which is always in language far to lofty to come out of ordinary, human mouths, is broken up by fictionalized letters and journal entries from historical mathematicians and philosophers. These are also written in language either too lofty or too modern to be based in reality. The contrived and awkward situations, discussions and documents all kept me from connecting with the story and characters and really enjoying the ride.
This book would be improved by either ditching the 'novel' portion or making it stronger. As it is, the math exposition, while interesting and central to the theme, overwhelm the fiction.
The only reason this gets 3 stars, rather than 2, is because of the intriguing subjects. It did get me to thinking deep thoughts, which I believe was the point of it. But the lack of personal connection and the awkwardly scholarly language kept it from approaching 4 stars. Only recommended if you like math (or are unoffended by it) and are likewise unoffended by flowery dialog and thoughts that do not reflect the way real people behave.
March 4, 2010
Ever wondered if there is any connection between mathematics and God? What if I say, the existence of God can be proved or disproved mathematically? The book ‘A Certain Ambiguity’ explores something similar.
The book follows the life of an Indian mathematician and tries to draw parallels between maths and faith and life, in general. While the story and the characters are fictional, the intriguing mathematical proofs are as real as you and I are. The famous Pythagorean theorem, the Euclidean geometry find a place in this book. What occupies the most part of the book is infinity. I had never thought of infinity in terms of an infinity being bigger or smaller than another infinity. The book taught me a lot about infinity and maths in general, which I didn’t know. Was I sleeping through my math class when my teacher covered these?
When I picked up this book, I never expected it to be a page-tuner. For the readers who have forgotten basic math, the authors have thankfully included an introduction to all basic concepts wherever necessary. Anybody having any inclination towards mathematics will love this book. The proofs are beautiful. Even for those who hated maths in school, that non-mathematical part of the book will be interesting. Characters, story, style of writing don’t matter, atleast didn’t matter to me. The very question of ‘Can you prove or disprove mathematically that God exists?’ is intriguing enough for anybody to pick up the book, what say?
Does the book answer that question? Well, that is for you to find out. It might not give you a page of equations which leads to the proof, but it does answer in some way. Only if you think so. You will know what I mean when you read the book.
This book reminds me of another book The God Delusion by Richard Dawkins, in which the author apparently proves that God does not exist. Has anyone read that book?
The book follows the life of an Indian mathematician and tries to draw parallels between maths and faith and life, in general. While the story and the characters are fictional, the intriguing mathematical proofs are as real as you and I are. The famous Pythagorean theorem, the Euclidean geometry find a place in this book. What occupies the most part of the book is infinity. I had never thought of infinity in terms of an infinity being bigger or smaller than another infinity. The book taught me a lot about infinity and maths in general, which I didn’t know. Was I sleeping through my math class when my teacher covered these?
When I picked up this book, I never expected it to be a page-tuner. For the readers who have forgotten basic math, the authors have thankfully included an introduction to all basic concepts wherever necessary. Anybody having any inclination towards mathematics will love this book. The proofs are beautiful. Even for those who hated maths in school, that non-mathematical part of the book will be interesting. Characters, story, style of writing don’t matter, atleast didn’t matter to me. The very question of ‘Can you prove or disprove mathematically that God exists?’ is intriguing enough for anybody to pick up the book, what say?
Does the book answer that question? Well, that is for you to find out. It might not give you a page of equations which leads to the proof, but it does answer in some way. Only if you think so. You will know what I mean when you read the book.
This book reminds me of another book The God Delusion by Richard Dawkins, in which the author apparently proves that God does not exist. Has anyone read that book?
December 19, 2017
This book is unique in it's theme of presenting mathematical concepts in the form of a story. It might not be a literary gem in plot and character development but it is nevertheless refreshing and engaging especially if you have a liking for logic and reasoning. We are introduced to interesting mathematical techniques we learnt in high school but forgot along the way and we rediscover this thrill along with the characters of the story. There are inspired ideas in the book like the journal entries which lend it an emotional connect and give a human feel to the abstract world of maths. The conversations between 2 main characters in the book especially inspire us to think more in our daily lives. A must read for all.
April 4, 2013
This may end up being my favorite book of this semester. Since the book is written by a mathematician whose second language is English, I don’t hold the bad writing against him. Actually, it’s bad in all the right ways. Watching people flirt by discussing Cantor’s theory of infinity is as amusing as it sounds, and the fact that the guru math-prof has a ponytail is just icing on that cake. Beyond that, the author does a great job of mixing math and philosophy into the wonderful, hot mess that it is. So when all’s said and done, the book is hilarious (unintentionally) and profound at the same time. If you think algebra 2 is pointless, you really need to read this book.
March 25, 2008
Who knew mathematics could be the basis for a great novel? This book really got me interesting in math especially Euclid's work in geometry and Cantor's work in set theory. The similarities among the stories of each is fascinating along with the ultimate limits of human knowledge. Also, I learned that a member of the Pythagoreans was killed for discovering and proving irrational numbers. Sometime people can get really passionate about math... (well I'm not sure if that's just a myth or not, but it makes a good story!)
March 19, 2013
I revise my earlier judgment: this isn't crap. It's actually a fascinating journey through the history of mathematics.
It's not well-written.
The characters are not interesting.
The dialogue is sometimes anachronistic and laughable.
But the thinking underpinning this book is great. Awesome, humbling conclusions about mathematical certainty.
It's not well-written.
The characters are not interesting.
The dialogue is sometimes anachronistic and laughable.
But the thinking underpinning this book is great. Awesome, humbling conclusions about mathematical certainty.
October 19, 2014
I really love this book. I leads you from Euclid to Cantor on a quest for certainty and proof (and even faith). Besides that it is also a novel ,an adventure story (sort of) and there is even a hint of a romance. Sometimes I did have to reread a page or two (I've only done high school). That's also part of the charm of this book. Probably the best book I've read so far.
January 6, 2017
I really wanted to give this one 4 stars; the problem is that it doesn't hold up nearly so well as a novel as an introduction to mathematical philosophy. That said, it was an enjoyable read and I'd certainly recommend it.
April 2, 2022
Despite the 3 star rating, I really enjoyed the experience of reading this book. I'll start with the negatives and then move to the positives. My big issue: I didn't find the characters all that realistic - save perhaps the modern day math professor (which is not surprising considering who wrote the book as well as who is writing this review :) ). I also didn't like the fake journals/letters from historical scientists, but that might be a reaction to "When we cease to understand the world."
But the plus side: The characters are dealing with issues that many of us deal with; and I think the book pulls off something very challenging about as well as one could hope for: injecting some of these mathematical ideas about the infinite and certainty in axiomatic systems into a narrative form. And I was not expecting the very fair treatment of religious faith that the story ended with.
But the plus side: The characters are dealing with issues that many of us deal with; and I think the book pulls off something very challenging about as well as one could hope for: injecting some of these mathematical ideas about the infinite and certainty in axiomatic systems into a narrative form. And I was not expecting the very fair treatment of religious faith that the story ended with.
April 9, 2022
Read it for the love of maths! This book beautifully addresses complex mathematical axioms against faith of God in a complex fictional setup consisting of two different timelines..and asks, is there anything absolute truth or it is important to have a certain ambiguity
March 2, 2019
the idea of incorporating mathematics as a big plot point in the story is interesting. As a scientist myself, I find this intriguing and motivating enough to not lose the enjoyment of reading a good novel.
September 4, 2019
Anlatımı muhteşem idi.
June 19, 2021
This novel is truly unique. It is well blended mixture of both mathematics and fiction. If you had the feeling that either maths is boring or its diffcult then this book will definitely change your perspective and may be even develop a great interest towards maths.
March 2, 2011
"Eine gewisse Ungewissheit" ist ein Roman, der sich in Form zweier Handlungsstränge – Student an der Uni sowie Großvater im Gefängnis – mit der Betrachtung der Unendlichkeit auseinandersetzt.
Er handelt von dem jungen Inder Ravi, der in Amerika Wirtschaftswissenschaften studiert. Als Kind entwickelte er durch seinen Großvater Vijay, der ihn mit mathematischen Rätseln herausforderte, eine große Begeisterung für Mathematik, doch nach dessen Tod verlief sich diese Faszination. Als er nun an der Universität den Dozenten Nico kennenlernt und dieser ihn zu seinem mathematischen Seminar zum Thema Unendlichkeit einlädt, wird seine Neugier geweckt. Im Gespräch mit Nico stolpert er zufällig über ein Dokument, das besagt, dass sein Großvater, als dieser in Amerika an einer Kleinstadtuniversität unterrichtete, für einige Zeit wegen Verstoßes gegen das Blasphemiegesetz im Gefängnis saß. Ravi und einige seiner Freunde aus dem Seminar für Unendlichkeit setzen nun alles daran herauszufinden, wie es dazu kam, und stoßen auf die Gesprächsprotokolle zwischen dem für den Fall zuständigen Richter Taylor und Ravis Großvater. Verknüpft werden diese beiden Handlungsstränge durch fiktive Tagebucheinträge und Briefe der Wissenschaftler, die sich mit den jeweils im Seminar oder in den Gerichtsprotokollen behandelten Themen befasst haben.
"Eine gewisse Ungewissheit" ist – gewissermaßen – ein mathematischer Roman. Aber, liebe potentiellen Leser, habt keine Angst davor! Man muss kein mathematisches Genie sein, um der Handlung folgen zu können. Ein gewisses Interesse an Naturwissenschaften sowie die Grundlagen der Mathematik sollten immerhin schon Vorraussetzung sein. Die im Buch aufgeführten Beweise nachvollziehen zu können ist für die Spannung des Buches jedoch keineswegs erforderlich, allerdings habe ich festgestellt – ja, ich, die ich Mathe im Abi abgewählt hatte! – dass der Aha-Effekt im Moment des Verstehens ein echtes Erfolgserlebnis ist.
Dieses Buch erhält von mir vier Sterne; einen Stern Abzug gibt es dafür, dass sich einige Fehler eingeschlichen haben, wie zum Beispiel die Abbildung eines falschen Diagramms, das eine Seite vorher schon gezeigt wurde, oder falsche Benennungen, wenn eine „einsame Menge“ zuerst „L“ (wohl für lonely) und dann „E“ (für einsam) genannt wird. Diese Fehler hätten durch ein wissenschaftliches Lektorat wohl vermieden werden können. Der gesamten Spannung der Geschichte und dem Lesespaß, den es bietet, tun sie jedoch keinen großen Abbruch. Daher von mir eine Empfehlung für alle naturwissenschaftlich interessierten Leser… und auch für alle Nerds, die mal etwas anderes als Fachbücher lesen wollen!
Er handelt von dem jungen Inder Ravi, der in Amerika Wirtschaftswissenschaften studiert. Als Kind entwickelte er durch seinen Großvater Vijay, der ihn mit mathematischen Rätseln herausforderte, eine große Begeisterung für Mathematik, doch nach dessen Tod verlief sich diese Faszination. Als er nun an der Universität den Dozenten Nico kennenlernt und dieser ihn zu seinem mathematischen Seminar zum Thema Unendlichkeit einlädt, wird seine Neugier geweckt. Im Gespräch mit Nico stolpert er zufällig über ein Dokument, das besagt, dass sein Großvater, als dieser in Amerika an einer Kleinstadtuniversität unterrichtete, für einige Zeit wegen Verstoßes gegen das Blasphemiegesetz im Gefängnis saß. Ravi und einige seiner Freunde aus dem Seminar für Unendlichkeit setzen nun alles daran herauszufinden, wie es dazu kam, und stoßen auf die Gesprächsprotokolle zwischen dem für den Fall zuständigen Richter Taylor und Ravis Großvater. Verknüpft werden diese beiden Handlungsstränge durch fiktive Tagebucheinträge und Briefe der Wissenschaftler, die sich mit den jeweils im Seminar oder in den Gerichtsprotokollen behandelten Themen befasst haben.
"Eine gewisse Ungewissheit" ist – gewissermaßen – ein mathematischer Roman. Aber, liebe potentiellen Leser, habt keine Angst davor! Man muss kein mathematisches Genie sein, um der Handlung folgen zu können. Ein gewisses Interesse an Naturwissenschaften sowie die Grundlagen der Mathematik sollten immerhin schon Vorraussetzung sein. Die im Buch aufgeführten Beweise nachvollziehen zu können ist für die Spannung des Buches jedoch keineswegs erforderlich, allerdings habe ich festgestellt – ja, ich, die ich Mathe im Abi abgewählt hatte! – dass der Aha-Effekt im Moment des Verstehens ein echtes Erfolgserlebnis ist.
Dieses Buch erhält von mir vier Sterne; einen Stern Abzug gibt es dafür, dass sich einige Fehler eingeschlichen haben, wie zum Beispiel die Abbildung eines falschen Diagramms, das eine Seite vorher schon gezeigt wurde, oder falsche Benennungen, wenn eine „einsame Menge“ zuerst „L“ (wohl für lonely) und dann „E“ (für einsam) genannt wird. Diese Fehler hätten durch ein wissenschaftliches Lektorat wohl vermieden werden können. Der gesamten Spannung der Geschichte und dem Lesespaß, den es bietet, tun sie jedoch keinen großen Abbruch. Daher von mir eine Empfehlung für alle naturwissenschaftlich interessierten Leser… und auch für alle Nerds, die mal etwas anderes als Fachbücher lesen wollen!
April 23, 2011
This book was such a pleasure to read.
It is about an undergraduate student with a former interest in mathematics. He decides to take a mathematics course on infinity as an elective in hope of rekindling his passion for math. Through his professor, he discovers a paper that his mathematician grandfather wrote, and here the story begins...
The storyline will have to be discovered by the reader through another source. However, I will say that the form of this story is mostly narrated as a dialogue combining mathematics, religion and philosophy. There are easy-to-follow proofs and theories here and there, and a few diagrams, all of which explain the nature of the axiomatic theory to the reader. Most of the mathematical debates concern work done by Euclid in geometry and Cantor in set theory. I found it to be a very enjoyable introduction to the continuum hypothesis.
I was actually quite surprised at how much of a page turner this book turned out to be. It was inspiring, though provoking and good fun! I believe that the authors achieved what they set out to do as they described in the Authors’ Note:
"Our principal purpose in writing A Certain Ambiguity is to show that mathematics is beautiful. Furthermore, we seek to show that mathematics has profound things to say about what it means for humans to truly know something. We believe that both these objectives are best achieved in the medium of a novel. After all it is human beings who feel beauty and it is human beings who feel the immediacy of philosophical questions. And the only way to get human beings into the picture is to tell a story."
Mathematics is truly beautiful! Both numbers and words can attest to that.
And as a final philosophical note, I will directly quote this statement from the book:
“Some may argue that our individual choices are already made for us and the idea of “free will” is an illusion. To them I merely reply that even if choice is an illusion, our perception of being able to choose is not. So our freedom is real- at least as real as anything else we live by.”
It is about an undergraduate student with a former interest in mathematics. He decides to take a mathematics course on infinity as an elective in hope of rekindling his passion for math. Through his professor, he discovers a paper that his mathematician grandfather wrote, and here the story begins...
The storyline will have to be discovered by the reader through another source. However, I will say that the form of this story is mostly narrated as a dialogue combining mathematics, religion and philosophy. There are easy-to-follow proofs and theories here and there, and a few diagrams, all of which explain the nature of the axiomatic theory to the reader. Most of the mathematical debates concern work done by Euclid in geometry and Cantor in set theory. I found it to be a very enjoyable introduction to the continuum hypothesis.
I was actually quite surprised at how much of a page turner this book turned out to be. It was inspiring, though provoking and good fun! I believe that the authors achieved what they set out to do as they described in the Authors’ Note:
"Our principal purpose in writing A Certain Ambiguity is to show that mathematics is beautiful. Furthermore, we seek to show that mathematics has profound things to say about what it means for humans to truly know something. We believe that both these objectives are best achieved in the medium of a novel. After all it is human beings who feel beauty and it is human beings who feel the immediacy of philosophical questions. And the only way to get human beings into the picture is to tell a story."
Mathematics is truly beautiful! Both numbers and words can attest to that.
And as a final philosophical note, I will directly quote this statement from the book:
“Some may argue that our individual choices are already made for us and the idea of “free will” is an illusion. To them I merely reply that even if choice is an illusion, our perception of being able to choose is not. So our freedom is real- at least as real as anything else we live by.”
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January 20, 2016
The math is certainly interesting in this novel and it's presented in a way that makes it accessible to people like me who do not have much of a background in math.
That being said, the prose lets the entire concept down. It feels like there was so much interest in the mathematical side of things that when the plot comes about or when there are long sections detailing something that happened in the past, I found myself bored. I would have enjoyed this book more if it were nonfiction and explaining mathematical concepts than the novel that I read. It seems almost as if the mathematical concepts were decided first and everything else is forced to bend around them.
There are interesting ideas here which just aren't put together well. The novel combines present day prose, mathematical diagrams, journal entries from older mathematicians, court interview transcripts, newspaper articles, university lectures, emails, and regular notes. The transitions between these are jarring to say the least and all the excitement that I felt while first reading the book drained away the further I got into it.
The characters and the plot are completely overshadowed by the math and the potential for beauty in this book was overshadowed entirely by its lack of focus on the narrative itself. I had expected beautiful prose and beautiful math which elevated each other, but I feel like I was left short. The more I read, the more it sounded like the characters were simply there to prove more of the math side of the story than to actually be people. As a nonfiction book with the plot, characters, and jarring set-up left out, I think that I would have put this up there in my favourites. As a novel though...
I sadly can't give a recommendation.
That being said, the prose lets the entire concept down. It feels like there was so much interest in the mathematical side of things that when the plot comes about or when there are long sections detailing something that happened in the past, I found myself bored. I would have enjoyed this book more if it were nonfiction and explaining mathematical concepts than the novel that I read. It seems almost as if the mathematical concepts were decided first and everything else is forced to bend around them.
There are interesting ideas here which just aren't put together well. The novel combines present day prose, mathematical diagrams, journal entries from older mathematicians, court interview transcripts, newspaper articles, university lectures, emails, and regular notes. The transitions between these are jarring to say the least and all the excitement that I felt while first reading the book drained away the further I got into it.
The characters and the plot are completely overshadowed by the math and the potential for beauty in this book was overshadowed entirely by its lack of focus on the narrative itself. I had expected beautiful prose and beautiful math which elevated each other, but I feel like I was left short. The more I read, the more it sounded like the characters were simply there to prove more of the math side of the story than to actually be people. As a nonfiction book with the plot, characters, and jarring set-up left out, I think that I would have put this up there in my favourites. As a novel though...
I sadly can't give a recommendation.
January 19, 2010
The main narrative of this book is, itself, nothing of any great interest: it is the story of a young man, Ravi, in the final year of his undergraduate studies. During this year, at the suggestion of a friend, he decides to case a mathematical course on infinity that is being offered to non-math majors.
Ravi's grandfather had been a mathematician, and while pursuing his studies in this course on infinity, he discovers a paper that his grandfather had written, and the paper makes mention that it was written while his grandfather was in jail. Ravi later learns that his grandfather, Bauji, was in jail because he had violated an archaic law in New Jersey that prohibited blasphemy.
The best parts of the novel focus on Bauji and the reasons for his incarceration and on what Ravi learns about infinity in his math course. I really enjoyed this novel because of what I, as a liberal arts person, was able to learn about mathematics. Prior to reading this novel, I had read about Georg Cantor and his continuum hypothesis, but I never really understood the importance of Cantor's contributions to mathematics despite spending some time researching the issue on line. Amazingly, this work of fiction brought to life and made understandable to me, for the first time, Cantor's Aleph numbers in his set theory as well as his continuum hypothesis.
This novel was a true delight not because of its narrative quality but because I came to understand fully something truly new and interesting. I now see why and how there are different types of infinities and why and how some infinities are actually larger than others. And I came to appreciate what a true genius Cantor really was.
Ravi's grandfather had been a mathematician, and while pursuing his studies in this course on infinity, he discovers a paper that his grandfather had written, and the paper makes mention that it was written while his grandfather was in jail. Ravi later learns that his grandfather, Bauji, was in jail because he had violated an archaic law in New Jersey that prohibited blasphemy.
The best parts of the novel focus on Bauji and the reasons for his incarceration and on what Ravi learns about infinity in his math course. I really enjoyed this novel because of what I, as a liberal arts person, was able to learn about mathematics. Prior to reading this novel, I had read about Georg Cantor and his continuum hypothesis, but I never really understood the importance of Cantor's contributions to mathematics despite spending some time researching the issue on line. Amazingly, this work of fiction brought to life and made understandable to me, for the first time, Cantor's Aleph numbers in his set theory as well as his continuum hypothesis.
This novel was a true delight not because of its narrative quality but because I came to understand fully something truly new and interesting. I now see why and how there are different types of infinities and why and how some infinities are actually larger than others. And I came to appreciate what a true genius Cantor really was.
February 17, 2013
Wow is the only word to describe this book:
First, (to get it out of the way) the bad,
* Plot is not the greatest
* 'Leap of Faith' Relativism
* Difficult Mathematical Equations restricting its ideas to only a few
* The Sexual Tension (Or Lack Thereof)
These are pretty bad and detract from making this book a classic. However, some parts transcend anything I have ever read before and scratch a lot of itches that I have had for a long time. Unlike many secular books promising deep answers to deep questions, this story deals honestly and painstakingly with the philosophy of math from Euclid to Einstein with an open-mindedness that makes for fascination. And, while much of the sub-plot is contrived, giving the protagonist a choice that depended on the whole conversation, not for emotional security like Adin, but for what to do with one's life. I am also impressed by the way they handled faith: even though the Grandfather remained an unbeliever and the Judge should have smacked down, it is an accomplishment that they did not present the false dichotomy of faith v. reason, but allowed the Christian a real dignity and allowed both characters to challenge each other; debates these days are so often more about the public aspect and rarely about people changing like this. Very refreshing. The best thing about it is the way it handled our finitude. Despite its quasi-existential leap of faith, I thought it was very fitting for them to quote Ecclesiastes and the black Pastor's words at the end are quite close to the truth in some very important ways.
There's more but, that's what I think. So, I confess to having liked it.
First, (to get it out of the way) the bad,
* Plot is not the greatest
* 'Leap of Faith' Relativism
* Difficult Mathematical Equations restricting its ideas to only a few
* The Sexual Tension (Or Lack Thereof)
These are pretty bad and detract from making this book a classic. However, some parts transcend anything I have ever read before and scratch a lot of itches that I have had for a long time. Unlike many secular books promising deep answers to deep questions, this story deals honestly and painstakingly with the philosophy of math from Euclid to Einstein with an open-mindedness that makes for fascination. And, while much of the sub-plot is contrived, giving the protagonist a choice that depended on the whole conversation, not for emotional security like Adin, but for what to do with one's life. I am also impressed by the way they handled faith: even though the Grandfather remained an unbeliever and the Judge should have smacked down, it is an accomplishment that they did not present the false dichotomy of faith v. reason, but allowed the Christian a real dignity and allowed both characters to challenge each other; debates these days are so often more about the public aspect and rarely about people changing like this. Very refreshing. The best thing about it is the way it handled our finitude. Despite its quasi-existential leap of faith, I thought it was very fitting for them to quote Ecclesiastes and the black Pastor's words at the end are quite close to the truth in some very important ways.
There's more but, that's what I think. So, I confess to having liked it.
November 25, 2013
What is faith? why do u believe in something- what is true, what can be true, is truth relative?
No, this book does not answer any of these questions, but it does take u on a journey- a journey which is about revelations;and this journey is made more beautiful by using mathematics as a tool.
The author has questioned certain paradigms believed to be true by using the simplicity of Eucladian Mathematics.He tries to establish a line of thought which says that just like mathematical theorems are based on axioms which are inevitably true, religion and faith in god, infact faith in anything is also based on the simple axiom that everything was created by someone!
Though astounded one might be by this reasoning, the beauty lies in the simplicity of it - that everything ultimately is based on
one starting point, and that starting point can be different for different people.
The most delightful aspect about this book was that how intricately the authors have woven a piece of fiction, around non-fiction.
The book takes you back in time - when mathematics was evolving; (not that it isnt now) but the likes of Einstein and Ramanjunam
were still formutaling theories and refuting various hypotheses, but even back to the time of the Greek mathematicians and philosophers.
And amidst all this, the authors have also highlighted the dilemma faced by Gen Y today(passion or money), and have also been successful in bringing out the contrast between the clear-headed and the confused.
thus, to conclude there is no ambiguity about the fact that this book will keep you hooked till you finish it!
No, this book does not answer any of these questions, but it does take u on a journey- a journey which is about revelations;and this journey is made more beautiful by using mathematics as a tool.
The author has questioned certain paradigms believed to be true by using the simplicity of Eucladian Mathematics.He tries to establish a line of thought which says that just like mathematical theorems are based on axioms which are inevitably true, religion and faith in god, infact faith in anything is also based on the simple axiom that everything was created by someone!
Though astounded one might be by this reasoning, the beauty lies in the simplicity of it - that everything ultimately is based on
one starting point, and that starting point can be different for different people.
The most delightful aspect about this book was that how intricately the authors have woven a piece of fiction, around non-fiction.
The book takes you back in time - when mathematics was evolving; (not that it isnt now) but the likes of Einstein and Ramanjunam
were still formutaling theories and refuting various hypotheses, but even back to the time of the Greek mathematicians and philosophers.
And amidst all this, the authors have also highlighted the dilemma faced by Gen Y today(passion or money), and have also been successful in bringing out the contrast between the clear-headed and the confused.
thus, to conclude there is no ambiguity about the fact that this book will keep you hooked till you finish it!
November 23, 2011
Si possono mettere dimostrazioni matematiche in un romanzo? Leggendo questo libro si direbbe di sì. I temi matematici trattati sono abbastanza classici nel pensiero contemporaneo: l'infinito cantoriano e le geometrie non euclidee. La storia intorno si snoda tra il presente e il 1919, e mostra da un lato un professore che ama davvero la matematica da riciclare le dimostrazioni maieutiche - anche se oggettivamente la parte sulla geometria non euclidea mi sembra un po' troppo tirata - e dall'altro una lotta tra due fedi distinte che termina in maniera inaspettata. Forse il fatto che gli autori siano indiani, e quindi abbiano una concezione della matematica (e della fede...) diversa da quella occidentale a cui siamo abituati contribuisce alla riuscita del testo. Molto piacevoli gli estratti apocrifi dei diari dei matematici dell'antichità, insieme con le spiegazioni relative messe in un'appendice: anche questo è un modo diverso dal solito per spiegare il progresso matematico. Purtroppo la traduzione non è sempre all'altezza. L'editore ringrazia Luca Umena per la consulenza matematica, e in effetti la parte più strettamente matematica è spiegata correttamente e in modo direi comprensibile anche per chi matematico non è. Ma nelle parti immagino tradotte direttamente da Alessandro Peroni ci sono almeno un paio di punti in cui il testo italiano è indubbiamente sbagliato e incomprensibile, il che non è bello. (C'è anche almeno un punto in cui l'errore sta già nel testo originale, quando nella lettera a Riemann si parla di iperbole e non di sella; ma quello non viene considerato...)
May 25, 2008
In the first sentences of the author's note, the authors write:
"Our principal purpose in writing A Certain Ambiguity is to show that mathematics is beautiful. Furthermore, we seek to show that mathematics has profound things to say about what it means for humans to truly know something. We believe that both these objectives are best achieved in the medium of a novel. After all it is human beings who feel beauty and it is human beings who feel the immediacy of philosophical questions. And the only way to get human beings into the picture is to tell a story."
In my completely unbiased opinion, the first two sentences are obvious; the remainder of the paragraph is perhaps less obvious. But where the authors follow the vision of this first paragraph in its entirety, I enjoyed the book immensely. The main flaw, to my mind, is the places in the story where the authors can't decide between dialogue and exposition, and end up sacrificing the voice of the characters to the voice of the authors talking about something they think is really cool. The reverse is also true: the strongest points in the story come in the discussions and actions between characters I have known myself in other guises.
A lot in this book reminds me of Turing: A Novel About Computation by Christos Papadimitriou, which had much the same flaw and much the same strength.
"Our principal purpose in writing A Certain Ambiguity is to show that mathematics is beautiful. Furthermore, we seek to show that mathematics has profound things to say about what it means for humans to truly know something. We believe that both these objectives are best achieved in the medium of a novel. After all it is human beings who feel beauty and it is human beings who feel the immediacy of philosophical questions. And the only way to get human beings into the picture is to tell a story."
In my completely unbiased opinion, the first two sentences are obvious; the remainder of the paragraph is perhaps less obvious. But where the authors follow the vision of this first paragraph in its entirety, I enjoyed the book immensely. The main flaw, to my mind, is the places in the story where the authors can't decide between dialogue and exposition, and end up sacrificing the voice of the characters to the voice of the authors talking about something they think is really cool. The reverse is also true: the strongest points in the story come in the discussions and actions between characters I have known myself in other guises.
A lot in this book reminds me of Turing: A Novel About Computation by Christos Papadimitriou, which had much the same flaw and much the same strength.
February 1, 2008
The authors are two mathematicians who make it clear in the introduction and end notes that they are mathematicians first and writers second. It is a very interesting story and not poorly written, but it doesn't exactly sing. Their intent was to translate the beauty of mathematics into a narrative form, and they did a good job, but there are some strained metaphors and the characters and plotting are quite predictable. The main thrust of the novel deals with the human need for certainty and how that is sought through mathematics and religion, and also the concept of infinity. While it does seem that they were inspired by the enthusiasm of very good teachers, the lessons in the book often fall short of their goal of clarity. Half of the "aha" moments that the characters, some of whom supposedly have little mathematical background, did not come to me. I admit that I do not have a naturally mathematical mind, but I am very interested in the theories, so it was a bit frustrating. That said, I'd still recommend it to anyone interested in reading fiction about mathematics and the lives of people who are obsessed with it. I'm on a mathematics-in-fiction binge right now though, so...
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December 6, 2016Öklid'in 5.aksiyomunun (paralellik) ne doğruluğu ne de yanlışlığı ispatlanabiliyor, yanlış olduğu varsayıldığında bambaşka bir geometri ortaya çıkmış. Öklid dışı geometriler. Kitapta, Hakim ile Hintli Matematikçinin felsefe muhabbetleri de mahkeme tutanakları olarak okuyucuya sunulmuş. Her ikisi de 1919 yılında Eddington'un Einstein'ı doğrulamasının ardından, dağılmış durumdalar. Hintli Matematikçi Ateist olup, Öklid Geometrisi ile kafasındaki Tanrısızlık fikrini savunmaya çalışıyor, Matematik sever Hakim Taylor da, tam tersini yani Tanrı fikrinin aynı Öklid'in kabulleri gibi bir kabul olarak farz edilebileceğine inanıyor. Sonuç, her ikisi de Öklid dışı geometrinin Einstein tarafından doğrulanması sonucu, fikirlerinden şüphe duymaya başlıyorlar. "Mutlak Kesinlik" yoktur. Hakim Taylor'a göre, eğer Öklid Geometrisi bazı yerlerde geçerliliğini yitiriyorsa, neden Tanrı aksiyomu da yanlış olmasın ki? Hintli Matematikçi'nin Tanrısızlık savunması da aynı nedenle çöküyor.
Hintli Matematikçi bütün bunların sonunda Ateist olmayı bırakmıyor, haliyle Taylor'da dinine inanmayı sürdürüyor.
Açıkçası bana, Tanrısızlık fikrini Geometriye dayanarak açıklamaya çalışmak saçma geldi.
Hintli Matematikçi bütün bunların sonunda Ateist olmayı bırakmıyor, haliyle Taylor'da dinine inanmayı sürdürüyor.
Açıkçası bana, Tanrısızlık fikrini Geometriye dayanarak açıklamaya çalışmak saçma geldi.
March 13, 2010
This is a charming way to become introduced to formalism in mathematics, as the authors have very cleverly inserted a lot of math theory into a light narrative around a Stanford University student's life.
Past some simple and pleasing proofs (pythagoras, no-greatest-prime-number, etc.) The book dives into Georg Cantor's work in set theory and his continuum hypothesis, the discovery of non-Euclidean geometry, and how these discoveries challenged our understanding of mathematical proofs based on axiomatic theory.
Things never get too complicated, so if you're interested in getting a taste for these mathematical ideas, I think this is probably the best place to start.
I was disappointed that Kurt Godel wasn't mentioned until the final 2 pages of the book. He probably made the most significant contributions in this field, and he was certainly relevant, and perhaps entirely conclusive, this narrative. and I think the authors probably had to cut him out because they couldn't find enough time to fit him into the story.
Past some simple and pleasing proofs (pythagoras, no-greatest-prime-number, etc.) The book dives into Georg Cantor's work in set theory and his continuum hypothesis, the discovery of non-Euclidean geometry, and how these discoveries challenged our understanding of mathematical proofs based on axiomatic theory.
Things never get too complicated, so if you're interested in getting a taste for these mathematical ideas, I think this is probably the best place to start.
I was disappointed that Kurt Godel wasn't mentioned until the final 2 pages of the book. He probably made the most significant contributions in this field, and he was certainly relevant, and perhaps entirely conclusive, this narrative. and I think the authors probably had to cut him out because they couldn't find enough time to fit him into the story.
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