The SciFri Book Club Visits 'Flatland'

Mathematician Ian Stewart joins the Science Friday Book Club meeting to discuss Edwin Abbott's classic Flatland. The book, published in 1884 under the pseudonym "A. Square," tells the story of a two-dimensional world where women are straight lines and men are polygons.

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IRA FLATOW, HOST:

Up next, I know you've all been waiting for it. It's time again for our SCIENCE FRIDAY Book Club. This month's pick - what are we reading this month? You did do your homework and read along with us, right? It's "Flatland: A Romance of Many Dimensions" by Edwin Abbott. It was - it's a classic. It was written in 1884, and, as I say, I hope you had time to read it.

Our book club regulars - Flora Lichtman, our multimedia editor, Annette Heist, SCIENCE FRIDAY senior producer - have gathered together here in the studio. I brought in some cheesecake for the club today.

FLORA LICHTMAN, BYLINE: That we'll eat off-mic.

(LAUGHTER)

FLATOW: Let's talk about "Flatland." Now why did we pick that book this week, Annette?

ANNETTE HEIST, BYLINE: Our listeners chose this book. We gave them a choice of four books: "2001: Space Odyssey," "The Andromeda Strain," "Brave New World," and "Flatland." And "Flatland" won. Overwhelming selection by SCIENCE FRIDAY fans.

FLATOW: And if you'd like to talk about it, we welcome you to join us. Our number is 1-800-989-8255. Did you like the book? What did you think about it? You know, talk to us. We're going to schmooze about it a little bit here. You can also tweet us @scifri, @S-C-I-F-R-I. And I'll start out the conversation by saying I was disappointed in the book.

HEIST: Ooh.

LICHTMAN: Ooh.

FLATOW: I thought it was a little dated, you know? And I thought it sort of pounded over my head the same theory of society, over and over and over, again, too many times.

LICHTMAN: Well, it was old. But what do you mean dated?

FLATOW: Well, I just think that if it were rewritten today, it would be edited better.

(LAUGHTER)

LICHTMAN: Ouch.

HEIST: (unintelligible) just a little...

LICHTMAN: Clunky. Right. Yeah.

HEIST: Yeah.

FLATOW: You don't agree, I take it.

LICHTMAN: Yeah. Well, I mean, I feel like I'm in the minority here, but I really liked it. I thought it was sort of comforting, because, to me, this book was about butting up against the limits of your own imagination. You have the square living in two dimensions, and a guy from three dimensions, the sphere, tries to bring - explain what it would be like to live in three dimensions. And it's almost impossible, and I feel like this is true all the time. It's really hard - for me, anyway - to imagine a world that's very different from our own. And so in that sense - I don't know - I liked it.

HEIST: Yeah. I think the message is timeless, but I do think the language was a little cumbersome. And I warmed up to the book. I read it about 10 years ago.

FLATOW: Yeah.

HEIST: I remembered liking it. I didn't really like it for the first, I'm going to say, maybe 30 pages. And then as soon as things get exciting, when they visit the Spaceland and Lineland in our own dimension when we go there.

LICHTMAN: Yeah.

FLATOW: This is SCIENCE FRIDAY from NPR. I'm Ira Flatow, here with Flora Lichtman and Annette Heist. We're talking about "Flatland." It's our Book of the Week. It's Book of the Month Club. And, you know, it was written a long time ago, relatively speaking...

HEIST: Right, right.

FLATOW: ...so sort of around Dickens, that sort of era?

HEIST: Yes, in Victorian England. And this is - I'm horrible at metaphor, so I was glad that you get hit over the head with the metaphors, over and over again, in "Flatland." And it is a satire of life in Victorian England, where women are the very bottom rung of the ladder. In this book, they're straight lines...

LICHTMAN: One-dimensional.

HEIST: ...one-dimensional, straight lines who, if they come at you the wrong way, they can hurt you, though.

FLATOW: They're like needles.

HEIST: Yes.

FLATOW: They get pretty - if you hit them on - they're pointy. So they have to announce themselves all the time, right?

HEIST: Yes, with peace-cries.

FLATOW: We don't know what a peace-cry sounds like, but we can imagine.

HEIST: We can imagine. It's - well, I don't know.

LICHTMAN: You fill in the blank.

HEIST: Yeah.

LICHTMAN: It seems to work...

FLATOW: But don't you think - I mean, we know it's a satire or it's a commentary on life.

HEIST: Right.

FLATOW: But I just thought that was too heavy-handed with the women. I mean, the way they were insulting the women, I thought, after a while it didn't sound much like a satire, but that he really felt that way about the women, you know?

HEIST: Right. And I think it was perceived that way when it came out. Our guest later, Ian Stewart, will talk a little bit more about that. At first, Abbott was criticized for the way that he portrayed women in the book. But he came back later and said, no, no, no. I don't really feel that way. It's a satire, and you guys missed it.

LICHTMAN: Yeah.

FLATOW: All right. Let's go to the phones. Let's go to Michael(ph) in Beltsville, Maryland. Hi, Michael.

MICHAEL: Hello.

FLATOW: Hi there.

MICHAEL: Hi. I'm a mathematics tutor. I travel, and I listen to the podcast. I rarely listen live. And I was listening to last week's podcast and heard next week we're going to be talking about "Flatland." I immediately turned off the podcast and turned on the live show. It happened to be just the right time. I'm so excited because I love "Flatland." And part of it is about the social - the criticism of the social structure that Abbott was making, beyond the math - which I love the math.

But I also wanted - I don't know if you're going to get to this, but there have been a number of books that have been written that are follow-ups to "Flatland," and I've only read one of them, and it was recently. It's called "Sphereland" by Rudy Rucker, and it was absolutely fantastic. I don't know if you're familiar with Rudy Rucker.

HEIST: There have also been movies made about "Flatland" as well.

MICHAEL: Pardon?

FLATOW: There are movies made about "Flatland" as well.

MICHAEL: Oh, yeah. I own them. I own them.

FLATOW: Well, you really did love this book, I can see.

MICHAEL: Oh, I - it - I give it as presents. I give those DVDs of the movies as presents. It's one of my all, you know, the math is - because I'm a math tutor and a - well, I probably read it about 45 years ago, and - the first time I read it. And the math, I think, when I'm telling students about, you know, what one dimension is and what two dimension is, what three dimensions are and then I say - I lead into well, what would four dimensions be? And they just look at me a little startled when I breach that subject and I say, you know, pull out the book "Flatland." And I said, this is what you have to read so you can get a glimpse of what we're trying to accomplish when we're trying to think about a fourth dimension.

FLATOW: All right, Michael, stay tuned because we're going to bring on Ian Stewart, who's an expert in "Flatland," on our next segment after the break. So stay with us. We'll be right back with Annette Heist and Flora Lichtman and our book club reading "Flatland." Get at your copy during the break, and we'll talk about it. Stay with us. I'm Ira Flatow. This is SCIENCE FRIDAY from NPR.

(SOUNDBITE OF MUSIC)

FLATOW: You're listening to SCIENCE FRIDAY. I'm Ira Flatow. We're talking, this hour, about "Flatland: A Romance of Many Dimensions" written by Edwin Abbott. It's our SCIENCE FRIDAY book club discussing it. Our number: 1-800-989-8255 if you've read Flatland and you'd like to talk about it. I'm going to bring on a "Flatland" expert, Ian Stewart. He's emeritus professor of mathematics at the University of Warrick in England. He's author of the book "Flatterland: Like Flatland, Only More So" and "The Annotated Flatland: A Romance of Many Dimensions." Thanks for being with us Dr. Stewart.

DR. IAN STEWART: It's a pleasure. Thanks for having me on the show.

FLATOW: Tell us how women are treated in there, because we're sitting and chatting about it, and that's - the one thing we've all picked out immediately is the harsh treatment women get.

STEWART: Yeah, Edwin Abbott, he had a daughter who was actually very, very bright, and he was a schoolmaster. He was the headmaster of City of London School, which was quite a - it was a school for the well-off middle classes, basically. And in those days, women really - the education of women in Victorian times was aimed at things like sewing and maybe history or might just be something that, you know, they were felt to be capable of. But I mean, the idea that a woman could be an engineer, for example, was just something that the Victorians would've considered completely ludicrous.

But Abbott realized that his daughter was actually very, very bright, and he felt that she was not going to get the education that she deserved. So as well as writing books and things, satirizing this state of affairs, he engaged private tutors, and he made sure that his daughter had the sort of education that he felt she deserved, rather than the sort of education that his society was willing to give her. So he, you know, he took action as well as just writing.

FLATOW: But he - Flora?

LICHTMAN: Well, you were saying that you thought it was too much, and it's funny because when I read it, I didn't feel that way. And maybe we have a difference of opinion because we, you know, I'm a woman, and so, for me, I felt sort of like, oh, I have a friend here in this author, who, you know, who really is blasting this point home.

STEWART: Yeah, I think...

LICHTMAN: I think - go ahead, Dr. Stewart.

STEWART: Sorry. Yeah. I think that's right, but I think the audience at the time was rather polarized, because some people got this. Some people realized that this man is - he's writing satire. He doesn't actually believe this himself. In fact, he believes the exact opposite of this. Quite a lot of people took it rather at face value and felt that because he was making this point, over and over and over again, during the course of the book in various ways, that actually this - he was saying just how things should be.

And he went to some lengths in the second edition, which is published a year later in 1885. In the presses, he added a new section saying, in fairly gentle terms, basically, pointing out that he was acting in this fictional setup, that he was acting as a historian of the events that has happened in Flatland. And a historian's job is to report events. It is not to advance his own opinions. So in a gentle way, he was saying, come on, guys, haven't you noticed? You know, this is satire, I don't mean this.

I think people who knew Abbott would have realized, because they knew what his attitude - I mean, in general terms, he was fairly enlightened socially. But the people who didn't know and just picked up the book and started reading it, you can imagine somebody reading and thinking, what's this man doing? I mean why are the women so completely - I mean, they're totally brainless is the point. They're not just one dimensional. They really are - as far as the story goes, they are completely inferior to the men folk.

And for the men folk, it's a question of how many sides do you have. If you're a square, you're higher up the rank than a triangle. A pentagon is better than a square. A six-sided figure is even better. And the most perfect beings, which are the priesthood, are circles.

LICHTMAN: But he does give the women some qualities, being - having feelings, being merciful and more loving than the men. I think that comes in at the end when he's talking to the seer.

STEWART: That's right. And, OK, now - again, you can read that two ways because you can say, well, women are not great at intellectual activity, but they're fantastic at emotional things. He wasn't really quite trying to say that, but this was the prevailing view in Victorian times. And so he set up Flatland so that it reflected the state of affairs but - I think, particularly since he's putting it near the end when everything's coming to a climax. He's sort of finally revealing to you what the women of Flatland are really like, and you realize that actually there are more dimensions to them than the physical.

STEWART: But I think, particularly since he's putting it near the end, when everything's coming to a climax, he's sort of finally revealing to you what the women of Flatland are really like. And you realize that, actually, there are more dimensions to them than the physical dimension, that is only one. And I think - you know, I mean, when I read it, I was about 16, and it took a little while to kind of figure out - I had to reread it several times to start to see the depth of the thing. But I - he's actually very, very sympathetic to the - to Flatland's women and to Flatland's lower classes.

FLATOW: Hmm. Let's go to the phones, 1-800-989-8255. Wanda in Oakland. Hi, Wanda. Did you like the book?

WANDA: Yes, very much. I read it in 1970 and - with my partner. And, actually, we saw the satire in it. And you have to remember when it was written. I think it's pretty obvious that he's trying to show the treatment of women. I think he's doing everything he can to show how everyone's treated, not just women, but the caste system in England and the monarch being a character.

FLATOW: How did it affect you? Did it make you stop and think about things?

WANDA: Yes. We actually did a lot of thinking about - it was hard, I think, to perceive, from our point of view, a visualization of it. You know, you - when you start reading it, you go, well, those little, you know, pictures on the page, so to speak, dots and lines and things, but - at least in the one we read. But it was really difficult for the mind to perceive it, and you had to really stop and ask yourself: What do they mean? How can there be no other dimension? And it's thought-provoking, and I sincerely believe he was trying to show how women were being treated, by satire.

LICHTMAN: You know, the - that was an interesting part to me, how he actually went through and explained how to think about Flatland, that you could bring your nose down to the table...

FLATOW: Thanks, Wanda.

LICHTMAN: ...and look at a shape and see that it would appear as a sort of straight line if you looked at, you know, a square in front of you, for example. I don't know. It was sort of a masterful translation, actually.

FLATOW: He did go out of his way for the details. He really did...

(LAUGHTER)

LICHTMAN: Yeah.

FLATOW: ...talk about them.

LICHTMAN: Are his equations accurate, Dr. Stewart, when you look at the diagrams? Are they mathematically sound?

STEWART: He - most of what he says is pretty sound. He's - what he's doing is he's taking something he was familiar with, which was Euclidian geometry. It was the kind of geometry that was taught to all Victorian schoolboys - not the girls, only to the boys. The girls weren't capable of studying geometry, of course.

And so he modeled his world on the flat plane of Euclid and the triangles and squares and circles and the kind of thing that you see in the geometry book. And most of what he says about them is actually pretty accurate. And when he starts doing his - the kind of scientific heart of the book is a dimensional analogy.

What he's really trying to explain to the Victorians - who were very interested, actually, in - the idea of the fourth dimension was floating around Victorian times, both in science and in various aspects of culture. And they were quite intrigued by this, in a way that we still are, as well, I think, the idea that space might have extra dimensions, or at least that a space with more dimensions might be possible.

And so Abbott is saying - really what he's saying to his readers is we three-dimensional creatures, trying to contemplate this mysterious fourth dimension, can learn a lot by putting ourselves in the place of a two-dimensional creature trying to comprehend the third dimension. We are familiar with that, but the two-dimensional creature would not be. What kind of arguments would they advance to prove it doesn't exist? What kind of ways of thinking could they come up with to convince themselves that maybe it's possible?

And if you have this analogy running, you start to see the bigger picture in the math. And that's very powerful, and it - this is a very good way of approaching the whole business of how many dimensions do things have, because mathematicians now are very happy to have as many dimensions as you'd like.

(LAUGHTER)

FLATOW: Whatever works.

STEWART: It's no big deal anymore.

LICHTMAN: I feel like a Flatlander trying to understand them.

(LAUGHTER)

FLATOW: Did he know Dickens? Were they contemporaries, or - I mean, Dickens wrote social commentary at the same time in some of his novels. Was that what's going on at that time, that period in history?

STEWART: He knew George Eliot, the novelist who, despite her name, was actually - that was a pseudonym for a woman novelist. And there is documented evidence that he knew and moved in the same society as George Eliot. I don't think there is any - I've not come across contact with Dickens, as such. He was also a Shakespearian scholar and a theologian. And he wasn't actually terribly good at math.

(LAUGHTER)

STEWART: He, you know, he approved of it, in some sense, but it wasn't his thing. And it - I mean, it's extraordinary that suddenly, this little book comes into being. You know, where did he get the idea from? Why did he want to write that book? What on Earth motivated the man? Actually, we don't know. There's no useful documentary evidence, or very, very little. You have to infer and guess. And it's all a little bit mysterious.

FLATOW: Let's go to David in Huntsville, Alabama.

Hi, David.

DAVID: Hello.

FLATOW: Hi, there. Go ahead.

DAVID: I just wanted to say that, you know, issues of satire aside or, you know, the stodginess of language, when I recently reread this, the climax, for me was in chapter 19 when the square has this transcendent realization that there are worlds beyond measure, that there are dimensions beyond measure. And, you know, basically, he is dissed by the sphere, who can't see this. The student has exceeded the master, and he has this intellectual, transcendent moment. And that's, you know, that's - makes the whole book for me.

STEWART: I think that's a wonderful point, and I'm glad you brought that up, because, yeah, the sphere has been very, very carefully explaining to him that three dimensions are, in fact, possible. And - but then the sphere turns out not to have an imagination that goes beyond the familiar space that he lives in. And, of course, Abbott there is saying, you know, we're really like the sphere. You see, we can see that Mr. Square has a limited view of the world, but we haven't realized that we also have a limited view of our own world. And, as you say, the student has transcended the instructor, here.

FLATOW: 1-800-989-8255 is our number. We're talking about "Flatland." That's our Book Club of this month on SCIENCE FRIDAY, from NPR. Flora?

LICHTMAN: Yeah, one - well, related to this, one little point that I loved in this book was how the kid, the hexagonal grandson, I think, kind of alludes to the third dimension. They're sitting in the study, and A Square is like, oh, rubbish. What are you talking about? And then - but, you know, we hear this all the time from scientists. I remember Sylvia Earle in an interview a few months ago said to me, you know, what makes a good scientist? You stay a kid. You never grow up. And, you know, it made me think, like, should all our string theorists be consulting with eight-year-olds? Just to expand your mind enough to think about these wild possibilities.

HEIST: But they get to the kid, by the end.

LICHTMAN: Yeah, that was depressing.

(LAUGHTER)

HEIST: Keep that mind.

(LAUGHTER)

STEWART: A dose of realism came into the story at that point. Yeah.

FLATOW: How young do you think somebody - what age could you start to read "Flatland" and appreciate it, do you think?

STEWART: I think that even at the age of 10 or 12, it might be that the mathematical side of it, the scientific side is actually - that's the easy part of the book, in a sense. That's the part that - it may be an area of human activity that only some of us feel comfortable with. But it's not - it doesn't require the sort of sophistication that social satire does. So the first time a young person reads the book, the social side of things might go - they might not be terribly aware of it, or they might feel it's just sort of part of the story to make things go.

But I think, certainly, you know, there is no reason why a 10 or 12-year-old shouldn't read it. By the time you're 13 or 14, it's entirely suitable. I mean, I read it when I was about that sort of age, and maybe slightly older, and could've read it earlier. If someone had given it to me when I was about 10, I would have loved it.

(LAUGHTER)

FLATOW: Let's go to Jim in New York. Hi, Jim. Welcome to SCIENCE FRIDAY.

JIM: Hi. Thanks. I just wanted to mention the sort of follow-up piece by Rudolf Rucker, called "Geometry, Relativity and the Fourth Dimension," which picks up sort of with the same arguments as "Flatland." Then also, to give an example of how the two-dimensional to three-dimensional allegory can be used to imagine a model of expanding space, if you imagine the three-dimensional sphere passing through the two-dimensional plane of Flatland, and then just imagine the space inside the sphere without the sphere, then imagine that happening at every point in that two-dimensional space, then convert that allegory to the same thing happening with four-dimensional space entering our three-dimensional universe, you get a pretty good way to picture expanding space.

FLATOW: Well, I think we'd have to see a picture of that, Jim.

(LAUGHTER)

LICHTMAN: Like A Square, I'm getting angry. I can't see past my perspective.

(LAUGHTER)

FLATOW: Thanks for the call. It's hard to - you know, and that's why he puts diagrams in the book.

LICHTMAN: Yeah.

FLATOW: It's hard to just describe these things, right?

LICHTMAN: Yeah, it is. It is. And I think that's one of the points of the book, is that when you're challenged in that way, people get mad. The point gets mad. The line gets mad whenever someone introduces the idea that there's an extra dimension. And the narrator himself gets mad, until he finally accepts.

FLATOW: Is there any final message, Ian, to you in this book? Is there any over-encapsulating message that you could sum up simply, here?

STEWART: I think it is the message of realizing that your own particular parochial little bit of universe is not necessarily everything there is, and that you really should keep an open mind, but not so open that your brains fall out.

(LAUGHTER)

FLATOW: Great message for the weekend.

(LAUGHTER)

FLATOW: All right. I think we're going to end it right there. I'm going to gavel our Book Club closed for this month. We'll be having another selection next month.

LICHTMAN: Yes. And you can join the chat at sciencefriday.com/bookchat and also write us at - I'm going to get it wrong, scifri...

FLATOW: Go to our website and click.

LICHTMAN: ...at bookclub@sciencefriday.com and tell us what we should read next.

FLATOW: Oh, so we'll take a vote again on what book to read for next month.

LICHTMAN: Yes.

FLATOW: Thank you. Thank you. I adjourn this meeting...

(LAUGHTER)

FLATOW: ...of the Book Club.

LICHTMAN: Thank you.

FLATOW: Thank you to Dr. Stewart. Ian Stewart, the emeritus professor of mathematics, University of Warwick in England, author of the "The Annotated Flatland: A Romance of Many Dimensions." If you are a Flatland person, you want this book, because it really is very well-done. Thank you, Dr. Stewart, for joining us today.

STEWART: It's a pleasure. Thank you.

FLATOW: And thank you, Flora. Thank you, Annette.

LICHTMAN: Thank you.

HEIST: Thank you.

FLATOW: And thank you all on the phones for taking time to be with us today. And as I say, send your suggestions to bookclub@sciencefriday.com.

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