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Mathematics and Humor
John Allen Paulos cleverly scrutinizes the mathematical structures of jokes, puns, paradoxes, spoonerisms, riddles, and other forms of humor, drawing examples from such sources as Rabelais, Shakespeare, James Beattie, René Thom, Lewis Carroll, Arthur Koestler, W. C. Fields, and Woody Allen.
"Jokes, paradoxes, riddles, and the art of non-sequitur are revealed with great perception and insight in this illuminating account of the relationship between humor and mathematics."—Joseph Williams, New York Times
"'Leave your mind alone,' said a Thurber cartoon, and a really complete and convincing analysis of what humour is might spoil all jokes forever. This book avoids that danger. What it does. . .is describe broadly several kinds of mathematical theory and apply them to throw sidelights on how many kinds of jokes work."— New Scientist
"Many scholars nowadays write seriously about the ludicrous. Some merely manage to be dull. A few—like Paulos—are brilliant in an odd endeavor."— Los Angeles Times Book Review
"Jokes, paradoxes, riddles, and the art of non-sequitur are revealed with great perception and insight in this illuminating account of the relationship between humor and mathematics."—Joseph Williams, New York Times
"'Leave your mind alone,' said a Thurber cartoon, and a really complete and convincing analysis of what humour is might spoil all jokes forever. This book avoids that danger. What it does. . .is describe broadly several kinds of mathematical theory and apply them to throw sidelights on how many kinds of jokes work."— New Scientist
"Many scholars nowadays write seriously about the ludicrous. Some merely manage to be dull. A few—like Paulos—are brilliant in an odd endeavor."— Los Angeles Times Book Review
124 pages, Paperback
First published January 1, 1980
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Displaying 1 - 28 of 28 reviews
October 8, 2010
I've always felt that one of the really big philosophical questions concerns the nature of humour. What is humour? What purpose, if any, does it serve? Why are some things funny, and others not? I've thought about this stuff, on and off, for ages. The other day, I was poking around on Google and stumbled over this little book, which I immediately ordered from Amazon. It arrived yesterday and only took an evening to read.
Well... if you've got a mathematical background and you're as interested as I am in these issues, I strongly recommend it. The author starts by giving you a quick tour through various theories of humour, from antiquity to the present day. Lots of eminent thinkers have had something to say here: Plato, Hobbes, Kant, Hazlitt, Schopenhauer and Bergson all get quoted. There is a great deal of diversity, but one theme that keeps coming back is incongruity. Humour arises when two radically different ways of looking at something are juxtaposed. Though, as the author immediately notes, incongruity isn't enough on its own. There needs to be a point, and timing is very important. This is all lead-up to his own theory, whose immediate predecessor is Koestler, in The Act of Creation. Koestler argues that humour and creativity are closely linked: the patterns of thought are similar in both cases, though the end result is different.
The next few chapters build up the necessary mathematical and logical background, and if you know a little about logic you'll find them straightforward. He tells you about formal theories and models, and how a formal theory can have models that are very different. He also talks about self-reference and grammar, though I found this part a bit of a detour. The grammar is necessary though when he wants to discuss puns and plays on words.
Finally, he gets to the point, and a very imaginative one it is too! He suggests that catastrophe theory might give you a mathematical tool that lets you understand humour. The idea isn't as far-fetched as it may sound. Catastrophe theory, which he introduces in a simple and non-technical way, is about discontinuous change in dynamic systems, where the system suddenly flips over to a new state as a result of a small change in the input parameters. The effect is irreversible: moving the input parameter back to where it was doesn't get you back to the previous state. The fundamental theorem of catastrophe theory states that, surprisingly, there are only a very small number of ways in which the discontinuous change can happen.
He thinks this is what happens when we find something funny. We have two potential models for our theory, and as we acquire information we initially consider one of the models to be the plausible one. In most cases, we don't even think of the other candidate. Suddenly, we get an extra piece of information: that pushes us over the edge of the cusp, after which the second model immediately becomes the preferred one. Now we see the story differently, and we can't go back to our earlier way of seeing it. He argues, reasonably persuasively, that this explains many of the things we notice about humour, including the importance of timing. If the information is presented in the wrong way, you give away the joke by revealing the second model too soon, and there is no discontinuity.
The book is cooler than you may imagine from reading the above description. He illustrates his ideas with plenty of jokes; also, he is well aware of all the things that might be wrong with his account, and of the fundamental absurdity inherent in trying to reduce humour to mathematics. Indeed, he suggests that you should should think of the book itself as a kind of joke. So read it as a Zen koan whose purpose is to awaken you to a new view of the world which you hadn't previously even considered. It worked on me.
Well... if you've got a mathematical background and you're as interested as I am in these issues, I strongly recommend it. The author starts by giving you a quick tour through various theories of humour, from antiquity to the present day. Lots of eminent thinkers have had something to say here: Plato, Hobbes, Kant, Hazlitt, Schopenhauer and Bergson all get quoted. There is a great deal of diversity, but one theme that keeps coming back is incongruity. Humour arises when two radically different ways of looking at something are juxtaposed. Though, as the author immediately notes, incongruity isn't enough on its own. There needs to be a point, and timing is very important. This is all lead-up to his own theory, whose immediate predecessor is Koestler, in The Act of Creation. Koestler argues that humour and creativity are closely linked: the patterns of thought are similar in both cases, though the end result is different.
The next few chapters build up the necessary mathematical and logical background, and if you know a little about logic you'll find them straightforward. He tells you about formal theories and models, and how a formal theory can have models that are very different. He also talks about self-reference and grammar, though I found this part a bit of a detour. The grammar is necessary though when he wants to discuss puns and plays on words.
Finally, he gets to the point, and a very imaginative one it is too! He suggests that catastrophe theory might give you a mathematical tool that lets you understand humour. The idea isn't as far-fetched as it may sound. Catastrophe theory, which he introduces in a simple and non-technical way, is about discontinuous change in dynamic systems, where the system suddenly flips over to a new state as a result of a small change in the input parameters. The effect is irreversible: moving the input parameter back to where it was doesn't get you back to the previous state. The fundamental theorem of catastrophe theory states that, surprisingly, there are only a very small number of ways in which the discontinuous change can happen.
He thinks this is what happens when we find something funny. We have two potential models for our theory, and as we acquire information we initially consider one of the models to be the plausible one. In most cases, we don't even think of the other candidate. Suddenly, we get an extra piece of information: that pushes us over the edge of the cusp, after which the second model immediately becomes the preferred one. Now we see the story differently, and we can't go back to our earlier way of seeing it. He argues, reasonably persuasively, that this explains many of the things we notice about humour, including the importance of timing. If the information is presented in the wrong way, you give away the joke by revealing the second model too soon, and there is no discontinuity.
The book is cooler than you may imagine from reading the above description. He illustrates his ideas with plenty of jokes; also, he is well aware of all the things that might be wrong with his account, and of the fundamental absurdity inherent in trying to reduce humour to mathematics. Indeed, he suggests that you should should think of the book itself as a kind of joke. So read it as a Zen koan whose purpose is to awaken you to a new view of the world which you hadn't previously even considered. It worked on me.
Read
November 4, 2010I'm moving on. Call this read. Maybe nobody will notice that it isn't.
But it has made me discuss humour with people and I've been given some great ideas along the way. And I would like to preserve bits and pieces here.
My mother said that when we were little we were really funny but that other kids aren't. My first thought was that's what all mothers think. But actually, we were raised to think that laughing at life and ourselves is so important.
My family was experimental and this somewhat bothered friends of my parents who thought we were being brainwashed. Once when my brother was seven one of these friends asked him if he was allowed to think for himself. Quick as a flash in his best robot voice Chris said 'I am not programmed to answer that question'.
I can't imagine a more brilliant put down and from a little boy. I think we'd been allowed to watch an episode of Dr Who and it had greatly influenced us. I was a year older. So, when I say robot, I mean Dalek, of course.
---------------
Pardon my putting down some things as we go along.
(1) ‘both mathematics and humor are economical and explicit'. Well, that simply isn't true even as a generalisation for humour. Any particular piece of humour may or may not rely on economy and explicitness.
(2) I have been asking this today: why is it that jokes from the past - let's say the 1930s - aren't funny for us. I want to know this partly because it is an aspect of how impossible it is to generalise about humour. It could be all sorts of things: social, political, cultural changes that prevent one being able to associate with a joke. It may be in the writing - perhaps if it was rewritten in a modern idiom it would be funnier.
But I do very much like this idea: that it is related to the Flynn effect. Ie, as our capacity for abstract thought increases maybe our humour becomes more abstract and we might define this as more sophisticated.
(3) This happened tonight. I was playing bridge and was introduced to my opponent as being 'the writer'. So slightly smug wanker says he is a writer too...he's written a book on squeezes and he didn't need to add that this makes him somewhat superior as it is technically advanced stuff. You know. Boy's stuff. AND he's played for England. Oh...so this was such a pleasure. I'm playing 3NT, his partner at some point shifts to a suit he has the ace of. He ducks the ace and then is subsequently squeezed out of it. Then he blamed his partner. Honestly. It was such fun.
But it has made me discuss humour with people and I've been given some great ideas along the way. And I would like to preserve bits and pieces here.
My mother said that when we were little we were really funny but that other kids aren't. My first thought was that's what all mothers think. But actually, we were raised to think that laughing at life and ourselves is so important.
My family was experimental and this somewhat bothered friends of my parents who thought we were being brainwashed. Once when my brother was seven one of these friends asked him if he was allowed to think for himself. Quick as a flash in his best robot voice Chris said 'I am not programmed to answer that question'.
I can't imagine a more brilliant put down and from a little boy. I think we'd been allowed to watch an episode of Dr Who and it had greatly influenced us. I was a year older. So, when I say robot, I mean Dalek, of course.
---------------
Pardon my putting down some things as we go along.
(1) ‘both mathematics and humor are economical and explicit'. Well, that simply isn't true even as a generalisation for humour. Any particular piece of humour may or may not rely on economy and explicitness.
(2) I have been asking this today: why is it that jokes from the past - let's say the 1930s - aren't funny for us. I want to know this partly because it is an aspect of how impossible it is to generalise about humour. It could be all sorts of things: social, political, cultural changes that prevent one being able to associate with a joke. It may be in the writing - perhaps if it was rewritten in a modern idiom it would be funnier.
But I do very much like this idea: that it is related to the Flynn effect. Ie, as our capacity for abstract thought increases maybe our humour becomes more abstract and we might define this as more sophisticated.
(3) This happened tonight. I was playing bridge and was introduced to my opponent as being 'the writer'. So slightly smug wanker says he is a writer too...he's written a book on squeezes and he didn't need to add that this makes him somewhat superior as it is technically advanced stuff. You know. Boy's stuff. AND he's played for England. Oh...so this was such a pleasure. I'm playing 3NT, his partner at some point shifts to a suit he has the ace of. He ducks the ace and then is subsequently squeezed out of it. Then he blamed his partner. Honestly. It was such fun.
January 8, 2009
If you are looking for an in depth look at the logical structure and psychology of humor, this is it. I've seen other attempts at a book like this and this definitely takes the cake.
The book finds solid explanations for various kinds of humor, cultural differences, uses logical / cognitive theories used in other fields and applies them to humor, all the while providing insight into what is funny, what isn't, comedians, culture, etc.
Highly recommend
The book finds solid explanations for various kinds of humor, cultural differences, uses logical / cognitive theories used in other fields and applies them to humor, all the while providing insight into what is funny, what isn't, comedians, culture, etc.
Highly recommend
August 25, 2022
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March 19, 2021
'Comedy is serious business.' Few people get that, because like social and emotional intelligence, humor is not a teachable skill; if you get it, you get it. This book is definitely not to teach humor, but aptly grasps the philosophy and structure behind humor. Many authors have grasped and explained the psychology behind humor, including but not limited to Freud, but few have attempted at a structure behind it, and this comes very close - focusing on intellectual play, detachment, incongruity, following a play to the point of absurdity, but the most important contribution of the book, I would say is very accurately capturing the mental oscillation involved in the paradoxes, leading to the catastrophe form of humor - that which we call punchlines. As an aside, I do think building and punchline is a masculine interpretation of a joke, and a feminine interpretation involves multiple punchlines and observations, interleaving each other. Make of that what you will, and I don't mention masculine and feminine to indicate gender, but more to indicate two types of humorous constructs - order and chaos. Humor for humor's sake and why is it necessary, for a person and a society, is the layman's takeaway from the book and you don't have to be a mathematician to appreciate this.
September 4, 2008
I thought this was going to be some mildly interesting collection of math-themed humor, but it's much better than that. It's an absolutely fascinating application of mathematics to model how humor works. That might sound ridiculous, but I thought a lot of it made sense, especially the example of using catastrophe theory to model how punchlines work.
December 26, 2019
John Allen Paulos, in my humble opinion, has a beautiful mind. If you're a math+philosophy+humor (must be all 3) nerd, you'll enjoy this. The mathematical perspective on humor is both satisfying and amusing. I'll read anything this guy writes.
May 9, 2017
thoroughly enjoyed. clever, meta, a bit of math history, humor theory, what is not to like? read in the midst of a binge on standup comedy
October 11, 2019
Very interesting book. What I found most compelling was the author's adaptation of "Catastrophe Theory Model" to explaining humor. Complex math has a unique way of being adaptable to day to day events and vice-versa, and this book explores how math principles and structures are similar to those of humor although the exploration is not exhaustive. This book is very detailed and the mathematical theories as well as philosophies are explained adequately. Great read.
October 24, 2016
It's small, well-written, and the math behind the concepts is also presented well. I'm not great at math, but was able to follow along. The diagrams help too. Overall, a VERY compelling read for anyone interested in linguistics and the construction of narrative. Definitely motivated to keep reading this author's other books to see what sort of insights he has regarding storytelling, etc.
October 5, 2019
If you want to know how catastrophe theory makes punch lines work this book is for you. It's more of an essay than a book. A wonderful, unexpected read.
December 9, 2020
Extraordinarily eye-opening and absolutely brilliant. Comedic structure explained through Euclidean geometry, math logic, catastrophe theory, and so much more! Dope AF. Yes yes yes.
April 19, 2022
The bit at the start of dead poets society where there is a page that over analyses poems and they rip it out and put it in the bin. This is the same thing but for jokes.
May 31, 2020
A short interesting read to understand how mathematics plays a role in construction of a joke. Paulos talks about the history of humor and then goes on to explain how mathematical paradoxes and theories can be used to understand jokes! Its a graphical book so makes it easy for readers to grasp the mathematical concepts discussed in the book.
Check 3 ideas from the book I liked which will hopefully make you want to read this book. I discuss these 3 ideas in my monthly podcast on books called Books 'n Brew.
Link to podcast episode: https://www.youtube.com/watch?v=pOGK9...
Check 3 ideas from the book I liked which will hopefully make you want to read this book. I discuss these 3 ideas in my monthly podcast on books called Books 'n Brew.
Link to podcast episode: https://www.youtube.com/watch?v=pOGK9...
July 1, 2012
John Allen Paulos has written a number of books on Mathematics, and “Mathematics and Humor” was his first, published originally in 1980. It is a short book, at just a little over 100 pages, and that is with plenty of drawings and graphs. I had high hopes going into it of an interesting read, but it just didn’t deliver. Paulos has some interesting thoughts and ideas, but the writing was a detriment to the communication of his points to the reader.
In the introduction, Paulos looks at various definitions of humor from history, which usually involves a formula (non-mathematical formulas or ingredients for what is considered humorous). He then moves to look at some examples of mathematical proofs which are clever, and involve ingenuity, before looking at what he considers to be “a bridge between humor and mathematics” which is “brain teasers”, trick problems, riddles, etc.
The next few chapters deal with looking at mathematical concepts and then looking at what types of humor fit into those categories. This includes applications of axioms and iteration, self-reference and paradox, grammar and philosophy. While some of those don’t specifically sound like mathematical concepts, Paulos does demonstrate how they do relate to mathematical areas.
Paulos then introduces talks about a “Catastrophe Theory Model of Jokes and Humor”, and this is the longest chapter in the book. Paulos discusses how humor, similar to the behavior of an animal, depends on how the situation is presented to the subject. Just as a animal might respond with fear or rage, depending on the circumstances surrounding an event, a person might find something humorous depending on the same.
Paulos finishes with a short wrap-up of the subject, and I think that this book is going to face its own Catastrophe Theory, in that how it is perceived by the reader is going to be based on the circumstances surrounding the event of reading it. I think it will depend largely on the background of the reader on whether they enjoy the book, or find it not very interesting. Paulos has failed to find a way to level-set the subject for the reader so that it delivers a consistent response to the book. I believe he has solved this problem, given the success of his later works.
In the introduction, Paulos looks at various definitions of humor from history, which usually involves a formula (non-mathematical formulas or ingredients for what is considered humorous). He then moves to look at some examples of mathematical proofs which are clever, and involve ingenuity, before looking at what he considers to be “a bridge between humor and mathematics” which is “brain teasers”, trick problems, riddles, etc.
The next few chapters deal with looking at mathematical concepts and then looking at what types of humor fit into those categories. This includes applications of axioms and iteration, self-reference and paradox, grammar and philosophy. While some of those don’t specifically sound like mathematical concepts, Paulos does demonstrate how they do relate to mathematical areas.
Paulos then introduces talks about a “Catastrophe Theory Model of Jokes and Humor”, and this is the longest chapter in the book. Paulos discusses how humor, similar to the behavior of an animal, depends on how the situation is presented to the subject. Just as a animal might respond with fear or rage, depending on the circumstances surrounding an event, a person might find something humorous depending on the same.
Paulos finishes with a short wrap-up of the subject, and I think that this book is going to face its own Catastrophe Theory, in that how it is perceived by the reader is going to be based on the circumstances surrounding the event of reading it. I think it will depend largely on the background of the reader on whether they enjoy the book, or find it not very interesting. Paulos has failed to find a way to level-set the subject for the reader so that it delivers a consistent response to the book. I believe he has solved this problem, given the success of his later works.
October 17, 2009
I was a little disappointed in this, but then again, I tend to form unreasonably high expectations. I've read a lot of Paulos' stuff, so I was already beyond being impressed by the fact that here is a mathematician who can actually write well and express detailed technical material in something very close to English.
I was initially intrigued by the use of Rene Thom's catastrophe theory to model the logic of humor in another book, the title of which escapes me at the moment. Its reference to the subject was fleeting, but provided enough detail to whet my appetite for more. I ordered this to further explore the subject, but I don't feel that this added much to it. It was not without merit, however, and still offered some food for thought. Just not as much as I'd hoped for, and most of it was reheated leftovers, I'm afraid.
I was initially intrigued by the use of Rene Thom's catastrophe theory to model the logic of humor in another book, the title of which escapes me at the moment. Its reference to the subject was fleeting, but provided enough detail to whet my appetite for more. I ordered this to further explore the subject, but I don't feel that this added much to it. It was not without merit, however, and still offered some food for thought. Just not as much as I'd hoped for, and most of it was reheated leftovers, I'm afraid.
August 10, 2011
Very short; more an essay than a book. It's a strong and powerful essay, an attempt to model humor mathematically. It does this through the tools of catastrophe theory (which I'd never heard of, but Paulos does a great job of explaining it) and brings together modern topology with the classic literary analyses of humor to provide a compelling baseline for future mathematical/comedic study. I know I must be making this sound terribly dull, but it was actually riveting. Paulos wrote the fantastic Innumeracy several years after he wrote this, and I really think he should hit the talk show circuit; he may be able to help break people of their fear of math.
December 13, 2014
Interesting, but the book seems unsure of its audience: is it for a mathematician or for a lay reader. On the one hand, the lay reader will have to muddle through some ideas expressed in logical symbolism that it seems could have been as easily expressed in simple sentences. On the other hand, it doesn't look like there is enough math here to engage someone with a more comprehensive maths background. I am a lay reader, so maybe I just missed something.
Still, the chapter on jokes and their relation to catastrophe theory is fun, although I found the figures in this chapter did not contribute much to my understanding of the material, and in a few cases were very confusing.
Still, the chapter on jokes and their relation to catastrophe theory is fun, although I found the figures in this chapter did not contribute much to my understanding of the material, and in a few cases were very confusing.
April 21, 2013
I just finished reading this book. It starts with a brief summary of the most famous theories on humor. But the second and the third chapters are very vague full of mathematical equations. Quite boring. That's ironic, since this book supposed to be the art of laughter. Anyway, this book still have some greats insights about the psychology of humor, wordplay and paradoxes. But for his attempt to try to explain humor with mathematics, Allen Paulos deserve a smile and a nod.
January 29, 2012
This book is all over the place. While I liked Innumeracy this is just a weird jumbling of "hey this is humor at an algorithmic layer" and then "hey here is some geometry".
Also, most jokes are horrible.
Also, most jokes are horrible.
September 12, 2021
If you really like math more than humor this book will be great for you. If you like humor more than math then you'll probably be lost for 50 percent of the book because of all the math words. Either way, it still offers lots of little insights.
January 24, 2018
Was this book my introduction to Gödel? Perhaps, it was so very long ago...
July 13, 2010
A bit outdated now and sometimes far fetched. I did like his link to catastrophy analysis.
July 4, 2015
Does a surprisingly good job of pointing out non-trivial isomorphisms between mathematics and humour.
May 24, 2012
not as funny as i imagined it. sometimes even dull
May 19, 2016
Strains to explain not why humor is mathematical, but why math is humorous. Fail.
July 22, 2016
It contains interesting ideas and is (as expected from Dr. Paulos) well-written, erudite and witty ... but there's just not very much of it.
October 20, 2017
Definitely not a book for everyone, and not groundbreaking, but it provides an interesting mathematical correlation to how/why things are funny, and accounts for most theories of humor with many examples. Mostly avoids getting into too much math, and even without understanding the math one could appreciate the points he is making. Solid book
Displaying 1 - 28 of 28 reviews