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Circles Disturbed: The Interplay of Mathematics and Narrative
Circles Disturbed brings together important thinkers in mathematics, history, and philosophy to explore the relationship between mathematics and narrative. The book's title recalls the last words of the great Greek mathematician Archimedes before he was slain by a Roman soldier--"Don't disturb my circles"--words that seem to refer to two radically different concerns: that of the practical person living in the concrete world of reality, and that of the theoretician lost in a world of abstraction. Stories and theorems are, in a sense, the natural languages of these two worlds--stories representing the way we act and interact, and theorems giving us pure thought, distilled from the hustle and bustle of reality. Yet, though the voices of stories and theorems seem totally different, they share profound connections and similarities.
A book unlike any other, Circles Disturbed delves into topics such as the way in which historical and biographical narratives shape our understanding of mathematics and mathematicians, the development of "myths of origins" in mathematics, the structure and importance of mathematical dreams, the role of storytelling in the formation of mathematical intuitions, the ways mathematics helps us organize the way we think about narrative structure, and much more.
In addition to the editors, the contributors are Amir Alexander, David Corfield, Peter Galison, Timothy Gowers, Michael Harris, David Herman, Federica La Nave, G.E.R. Lloyd, Uri Margolin, Colin McLarty, Jan Christoph Meister, Arkady Plotnitsky, and Bernard Teissier.
Apostolos Doxiadis is a writer whose books include Uncle Petros and Goldbach's Conjecture and Logicomix. Barry Mazur is the Gerhard Gade University Professor in the Department of Mathematics at Harvard University. His books include Imagining Numbers and Arithmetic Moduli of Elliptic Curves (Princeton).
Endorsements:
"Circles Disturbed offers a range of possibilities for how narrative can function in mathematics and how narratives themselves show signs of a mathematical structure. An intelligent, exploratory collection of writings by a distinguished group of contributors."--Theodore Porter, University of California, Los Angeles
"This collection is a pioneering effort to trace the hidden connections between mathematics and narrative. It succeeds magnificently, and represents a very significant contribution that will appeal to the professional mathematician as well as the general educated reader. The articles are written by top authorities in their fields."--Doron Zeilberger, Rutgers University
"The idea of a volume devoted to mathematics and narrative is a good one. The strength of the present volume is the breadth of its outlook, and I would imagine a fairly diverse readership from a wide variety of perspectives."--Robert Osserman, professor emeritus, Stanford University
[description taken from Princeton University Press's web site]
A book unlike any other, Circles Disturbed delves into topics such as the way in which historical and biographical narratives shape our understanding of mathematics and mathematicians, the development of "myths of origins" in mathematics, the structure and importance of mathematical dreams, the role of storytelling in the formation of mathematical intuitions, the ways mathematics helps us organize the way we think about narrative structure, and much more.
In addition to the editors, the contributors are Amir Alexander, David Corfield, Peter Galison, Timothy Gowers, Michael Harris, David Herman, Federica La Nave, G.E.R. Lloyd, Uri Margolin, Colin McLarty, Jan Christoph Meister, Arkady Plotnitsky, and Bernard Teissier.
Apostolos Doxiadis is a writer whose books include Uncle Petros and Goldbach's Conjecture and Logicomix. Barry Mazur is the Gerhard Gade University Professor in the Department of Mathematics at Harvard University. His books include Imagining Numbers and Arithmetic Moduli of Elliptic Curves (Princeton).
Endorsements:
"Circles Disturbed offers a range of possibilities for how narrative can function in mathematics and how narratives themselves show signs of a mathematical structure. An intelligent, exploratory collection of writings by a distinguished group of contributors."--Theodore Porter, University of California, Los Angeles
"This collection is a pioneering effort to trace the hidden connections between mathematics and narrative. It succeeds magnificently, and represents a very significant contribution that will appeal to the professional mathematician as well as the general educated reader. The articles are written by top authorities in their fields."--Doron Zeilberger, Rutgers University
"The idea of a volume devoted to mathematics and narrative is a good one. The strength of the present volume is the breadth of its outlook, and I would imagine a fairly diverse readership from a wide variety of perspectives."--Robert Osserman, professor emeritus, Stanford University
[description taken from Princeton University Press's web site]
552 pages, Hardcover
First published January 1, 2012
13 people are currently reading
382 people want to read
About the author
Apostolos Doxiadis
6 books277 followersApostolos Doxiadis (Greek: Απόστολος Δοξιάδης) was born in Brisbane, Australia in 1953, and grew up in Greece.
Although interested in fiction and the arts from his youngest years, a sudden and totally unexpected love affair with mathematics led him to New York's Columbia University at the age of fifteen. He did graduate work in Applied Mathematics at the École Pratique des Hautes Études in Paris, working on mathematical models for the nervous system.
After his studies, Apostolos returned to Greece and his adolescent loves of writing, cinema and the theater. For some years he directed professionally for the theater, and in 1983 made his first film Underground Passage (in Greek). His second film, Terirem (1986) won the prize of the International Center for Artistic Cinema (CICAE) at the 1988 Berlin International Film Festival.
Since the mid-eighties, most of Apostolos' work has been in fiction. He has published four novels in Greek, Parallel Life (1985), Makavettas (1988), Uncle Petros and Goldbach's Conjecture (1992) and Three Little Men (1997). His translation of Uncle Petros was published internationally in 2000, to great critical acclaim, and has since been translated into over thirty languages. Apostolos now writes in both Greek and English.
Apart from his work in fiction, Apostolos has written two plays. In 1999, he wrote and directed the musical shadow puppet play "The Tragical History of Jackson Pollock, Abstract Expressionist", accompanied by a volume of texts and images, Paralipomena. In 2006, his play Seventeenth Night had a year-long run in an Athens theatre. The play is a fictional recreation of the last days in the life of the great logician, and father of the incompleteness theorem, Kurt Gödel.
In autumn 2008, Apostolos, completed the graphic novel Logicomix, co-authored with Christos H. Papadimitriou, with art by Alecos Papadatos and Annie di Donna. The book's story is based on the epic quest for the foundations of mathematics. Logicomix was published in Autumn 2009 by Bloomsbury in the U.S. and the U.K.
Apart from his work in the various modes of storytelling, in the past few years, Apostolos has been studying the relationship between mathematics and narrative. He is currently editing a volume on mathematics and narrative with mathematician Barry Mazur, of Harvard University, due to be published in 2010.
Apostolos lives in Athens with his wife, the novelist Dorina Papaliou, and their children.
Although interested in fiction and the arts from his youngest years, a sudden and totally unexpected love affair with mathematics led him to New York's Columbia University at the age of fifteen. He did graduate work in Applied Mathematics at the École Pratique des Hautes Études in Paris, working on mathematical models for the nervous system.
After his studies, Apostolos returned to Greece and his adolescent loves of writing, cinema and the theater. For some years he directed professionally for the theater, and in 1983 made his first film Underground Passage (in Greek). His second film, Terirem (1986) won the prize of the International Center for Artistic Cinema (CICAE) at the 1988 Berlin International Film Festival.
Since the mid-eighties, most of Apostolos' work has been in fiction. He has published four novels in Greek, Parallel Life (1985), Makavettas (1988), Uncle Petros and Goldbach's Conjecture (1992) and Three Little Men (1997). His translation of Uncle Petros was published internationally in 2000, to great critical acclaim, and has since been translated into over thirty languages. Apostolos now writes in both Greek and English.
Apart from his work in fiction, Apostolos has written two plays. In 1999, he wrote and directed the musical shadow puppet play "The Tragical History of Jackson Pollock, Abstract Expressionist", accompanied by a volume of texts and images, Paralipomena. In 2006, his play Seventeenth Night had a year-long run in an Athens theatre. The play is a fictional recreation of the last days in the life of the great logician, and father of the incompleteness theorem, Kurt Gödel.
In autumn 2008, Apostolos, completed the graphic novel Logicomix, co-authored with Christos H. Papadimitriou, with art by Alecos Papadatos and Annie di Donna. The book's story is based on the epic quest for the foundations of mathematics. Logicomix was published in Autumn 2009 by Bloomsbury in the U.S. and the U.K.
Apart from his work in the various modes of storytelling, in the past few years, Apostolos has been studying the relationship between mathematics and narrative. He is currently editing a volume on mathematics and narrative with mathematician Barry Mazur, of Harvard University, due to be published in 2010.
Apostolos lives in Athens with his wife, the novelist Dorina Papaliou, and their children.
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Displaying 1 - 6 of 6 reviews
June 11, 2022
This collection, which presents the results of a meeting held in 2005, investigates a fascinating interdisciplinary question. If you're a hard scientist, your basic feeling is probably going to be that everything is really mathematics: formal mathematical models are the right way to address almost any question. If you're a soft scientist, your basic feeling is probably going to be that everything is some kind of narrative: when you're talking about how people interact, you need to do it in terms of the narratives they tell each other and themselves. But somewhere, the hard sciences and the soft sciences must meet up. So is it the case that mathematics is really some kind of narrative, or, conversely, that narratives have some kind of mathematical structure?
I had never thought about this, and if nothing else the fifteen essays here will at least convince you that there are a lot of different angles. The long chapter by Doxiadis about the emergence of the notion of "mathematical proof" in Classical Greek culture is particularly thought-provoking. As he says, new ideas don't just suddenly appear, they evolve slowly out of other ideas. So where did "proof" come from? He makes a good case for the claim that it started off as certain structures in Greek poetry; these later became used in legal arguments, which apparently had a fixed form including claims and supporting evidence for those claims, and mathematicians may have taken over the framework from the lawyers when they wanted to make their own arguments for mathematical truths tidy and convincing. If he is right, then a certain kind of narrative gradually turned into what we now call mathematics.
Other chapters look at specific pieces of mathematics and argue that they generally seem to embody some kind of story; if there is no story, we can't understand them, and this is one of the problems with artificial theorem provers. There are yet other chapters which trace the evolution of mathematical ideas which at first seemed counterintuitive: irrational numbers, imaginary numbers, non-Euclidean geometry, quantum mechanics. Initially, people said they made no sense. But after a while, it turned out that there was a good story to tell, and they were accepted; mathematicians are now prepared to consider any kind of consistent story, as long as it offers interesting problems to discuss. I was less impressed by the narratologists and their attempts to show that narratives have mathematical structure, which could be exploited to create stories by formal means. This came across as already very dated: today, I would be curious to see an analysis of how GPT-3 succeeds in (apparently, at least) automatically creating narratives without any human intervention.
If you've read Sapiens, there's a thought here that suggests itself. Harari argues that the unique thing about the human race is our ability to create stories and then act as though they are real: by doing this, they become real. The stories that Harari is most interested in are religion, money and empire. They are "only" stories, but people often experience them as more real than physical objects. I wonder if Harari has considered adding mathematics to his shortlist of the key stories we live by. Maybe a religious person believes in God for essentially the same reason that a mathematician believes in the square root of minus one; the mathematician accepts the existence of i because it's a story that ties together many things in the mathematical world and makes them more coherent, and the religious person accepts the existence of God because it ties together many things in the moral world and makes it more coherent. I don't know whether this is a good story or not! But the book certainly takes you in some interesting directions.
I had never thought about this, and if nothing else the fifteen essays here will at least convince you that there are a lot of different angles. The long chapter by Doxiadis about the emergence of the notion of "mathematical proof" in Classical Greek culture is particularly thought-provoking. As he says, new ideas don't just suddenly appear, they evolve slowly out of other ideas. So where did "proof" come from? He makes a good case for the claim that it started off as certain structures in Greek poetry; these later became used in legal arguments, which apparently had a fixed form including claims and supporting evidence for those claims, and mathematicians may have taken over the framework from the lawyers when they wanted to make their own arguments for mathematical truths tidy and convincing. If he is right, then a certain kind of narrative gradually turned into what we now call mathematics.
Other chapters look at specific pieces of mathematics and argue that they generally seem to embody some kind of story; if there is no story, we can't understand them, and this is one of the problems with artificial theorem provers. There are yet other chapters which trace the evolution of mathematical ideas which at first seemed counterintuitive: irrational numbers, imaginary numbers, non-Euclidean geometry, quantum mechanics. Initially, people said they made no sense. But after a while, it turned out that there was a good story to tell, and they were accepted; mathematicians are now prepared to consider any kind of consistent story, as long as it offers interesting problems to discuss. I was less impressed by the narratologists and their attempts to show that narratives have mathematical structure, which could be exploited to create stories by formal means. This came across as already very dated: today, I would be curious to see an analysis of how GPT-3 succeeds in (apparently, at least) automatically creating narratives without any human intervention.
If you've read Sapiens, there's a thought here that suggests itself. Harari argues that the unique thing about the human race is our ability to create stories and then act as though they are real: by doing this, they become real. The stories that Harari is most interested in are religion, money and empire. They are "only" stories, but people often experience them as more real than physical objects. I wonder if Harari has considered adding mathematics to his shortlist of the key stories we live by. Maybe a religious person believes in God for essentially the same reason that a mathematician believes in the square root of minus one; the mathematician accepts the existence of i because it's a story that ties together many things in the mathematical world and makes them more coherent, and the religious person accepts the existence of God because it ties together many things in the moral world and makes it more coherent. I don't know whether this is a good story or not! But the book certainly takes you in some interesting directions.
February 3, 2015
Truthfully, I didn't finish this book. It was simply over my head. This book was written for the very, very intelligent, and I am merely intelligent.
June 30, 2015
[3.5 stars]
I've been wrestling with whether I want to give this book a higher score simply due to how much I like the concept, and how much I'd like to see more of this. And there's a lot to like in this book. As a math guy I often feel like math straddles the sciences and humanities both more than we'd like to admit, and while math is enshrined in the contemporary STEM quadrinity, it's inroads with the humanities aren't nearly as high up in the public focus (including my own focus, regrettably). And that's part of the reason for the low (and subjective, duh) score for this book: I loved a lot of the math (which was pretty technical) and the basic narrative work done on it, but some of the essays dealing with more involved narratology sailed right over my head. This is definitely one that I'd like to read later once I know more about some of these subjects.
Until then, there's still a kernel of essays in here that can appeal to folks aboard the Ark of STEM. I particularly enjoyed Michael Harris' essay Do Androids Prove Theorems in Their Sleep?, which focused on near-future ideas of automatic theorem provers and how it throws human mathematical goals into sharper focus (i.e. do we care as much that a theorem is proven if its proof is an unreadable pile of primitive statements that can't be adequately understood by a human or group of humans?) Apostolos Doxiadis' contribution A Streetcar Named (among Other Things) Proof: From Storytelling to Geometry, via Poetry and Rhetoric was also quite interesting, if in my opinion a bit long-winded, in tracing the Aristotelian syllogism to language structures common in earlier forms of Greek poetry and rhetoric.
All in all, I found this enjoyable, though I'll most likely enjoy this considerably more when I actually know more about what I'm reading.
I've been wrestling with whether I want to give this book a higher score simply due to how much I like the concept, and how much I'd like to see more of this. And there's a lot to like in this book. As a math guy I often feel like math straddles the sciences and humanities both more than we'd like to admit, and while math is enshrined in the contemporary STEM quadrinity, it's inroads with the humanities aren't nearly as high up in the public focus (including my own focus, regrettably). And that's part of the reason for the low (and subjective, duh) score for this book: I loved a lot of the math (which was pretty technical) and the basic narrative work done on it, but some of the essays dealing with more involved narratology sailed right over my head. This is definitely one that I'd like to read later once I know more about some of these subjects.
Until then, there's still a kernel of essays in here that can appeal to folks aboard the Ark of STEM. I particularly enjoyed Michael Harris' essay Do Androids Prove Theorems in Their Sleep?, which focused on near-future ideas of automatic theorem provers and how it throws human mathematical goals into sharper focus (i.e. do we care as much that a theorem is proven if its proof is an unreadable pile of primitive statements that can't be adequately understood by a human or group of humans?) Apostolos Doxiadis' contribution A Streetcar Named (among Other Things) Proof: From Storytelling to Geometry, via Poetry and Rhetoric was also quite interesting, if in my opinion a bit long-winded, in tracing the Aristotelian syllogism to language structures common in earlier forms of Greek poetry and rhetoric.
All in all, I found this enjoyable, though I'll most likely enjoy this considerably more when I actually know more about what I'm reading.
April 13, 2015
The idea of this collection of short essays is great, but the execution is disappointing. The introduction starts the collection out on a great foot, but the following first chapter, with historical inaccuracies and wild speculation, makes the reader skeptical of the rest of the essays. Arkady Plotnitsky has written the best section of this novel. Though some talk about fictional narrative with mathematics, many of the essays discuss the terms used when describing the actual history of mathematics. This book is more about how we write history with math, rather than with literature or literary theory. I was very much disappointed, and I think if Archimedes were able to read this, his circles would be most disturbed.
Want to read
March 21, 2012As seen in
Nature
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May 31, 2017
The chapter by Doxiadis was very interesting and would have rated around 3.5 stars on its own. The remainder of the book however was merely ok.
Displaying 1 - 6 of 6 reviews