Customer Reviews

Flatterland: Like Flatland, Only More So

5 star:		(11)
4 star:		(5)
3 star:		(6)
2 star:		(8)
1 star:		(7)

 

 

As a high school student, I was tortured into reading this book for Math Analysis. Having previously read Flatland, I was not keen on the idea of reading the sequel. My grade-conscious self got the better of me and I started to read the book. From the first chapter I was enthralled! Ian Stewart knew how to write and keep my attention. My parents had to threaten me so I would put it down so I could eat. (Imagine: a high schooler entranced in a MATH book!) I so totally recommend this book because I would have NEVER understood Mandelblot (er... Mandelbrot) nor would I have read on to discover a plethora of new dimensions (one and a quarter). I would recommend any person, avid mathematician or high schooler, to read this. It was easily understood and Ian Stewart is a fantastic writer! Too bad they didn't have ten stars!

I've used Flatland and Sphereland in my High School Pre-Calculus class. They're both entertaining books, but also ones that are a bit elementary for the class. I would say they are written for entertainment first, enlightenment second. Flatterland is NOT the same type of book. I have never been an Ian Stewart fan, but I do like this book. While the first two books are easy enough for a 7th grade student to understand, the topics in this book will require most high school students to be walked through the material. It's not an easy read. I will use this book with some of my students in the future, but only those that enjoy a challenge. It's true that the book tries to cover too much, but I think you should view it as a survey of modern mathematics. In my opinion, this is some of the best writing I've seen from Stewart, but definitely not up to the literary level set by Flatland and Sphereland.

A little more than a century ago, an English minister named Edwin Abbott Abbott penned a remarkable story called FLATLAND. In it, Abbott laid out his case for the seemingly incomprehensible notion (certainly to his fellow citizens of Victorian England) that the universe might contain spatial dimensions beyond the three we recognize. Abbott built his argument through a form of inductive reasoning, much like a mathematical proof by induction, in which he took his readers on a journey through four dimensions, from Pointland (zero dimensions) and Lineland (one) to Flatland (two), and finally Spaceland (three). Each of these "worlds" could be easily imagined by his readers, and movements from one to another required only moving in an obviously "perpendicular" direction into the next plane. This approach allowed Abbott to pose the rhetorical questions, "Why stop at three dimensions? Why not imagine moving `perpendicularly' into the fourth dimension?" Of course, Riemann, Poincare, Dirichlet, and other mathematicians and physicists had already long been at work on multidimensional and non-Euclidean spaces, and it would only be a few more years after FLATLAND's publication that Einstein would put their ideas to revolutionary use.

In the present day, mathematician and writer Ian Stewart set out to build on FLATLAND and introduce modern readers to the many new worlds of multidimensional mathematics that have evolved since Abbott's time. Dangerously for a writer of any talent, Stewart opted to mimic the structure and style of a literary classic and, to paraphrase Lloyd Bentsen's memorable Vice Presidential debate putdown of Dan Quayle, "Mr. Stewart, you are no Edwin Abbott Abbott."

Mr. Stewart builds his exposition around Victoria Line (no apologies offered to the London Underground authorities), a two-dimensional lineal (ouch) descendant of A. Square, the tragic hero of FLATLAND. Vikki is an inquisitive, modern sort of line (in Flatland, all women are straight lines) who discovers her great-great-grandfather's old manuscript describing his adventures visiting other dimensions a century earlier with his Sphere tour guide. This time around, Vikki is accompanied by Space Hopper, a creature capable of passing through any dimension or space in the known Mathiverse. Vikki and Space Hopper progress from four dimensional space to mathematically multidimensional space (linear programming and optimization), sphere packing and self-correcting codes, fractional dimensional space (fractal geometry), topological (curved) space, finite geometry (graph theory), and non-Euclidean (hyperbolic geometry) space, stopping at each for an exposition by Space Hopper on the mathematical origins and significance of each. These discussions are descriptive in nature, designed as introductions to each topic while avoiding any mathematics whatsoever. Once this array of mathematical spaces has been exhausted, Space Hopper takes Vicky on a tour of quantum and relativistic physics, followed by a jump to the cosmological level to consider Minkowski spacetime, light cones, time travel, Schwarzschild radii, black holes, p-branes, superstring theory, the Big Bang, and the shape of the universe. If all of this seems like too much to cram into a 294-page fairy tale, it is.

Mr. Stewart's goal is a worthy one, and he does indeed manage to convey at least some sense of the mathematics and physics he seeks to explain. However, where Edwin Abbott wrote for an audience he knew had little formal mathematical background, Mr. Stewart seems far less sure of his audience. His discussion of mathematical worlds in the first half of the book are likely to leave a novice confused about where these ideas come from (what exactly is a hyperbolic plane, and how exactly do you generate a fractal fern?) and a knowledgeable reader bored and bemused. In the latter half of the book, Mr. Stewart seems to have abandoned his novice readers, writing at confusing length about Penrose maps, quantum spin, quantum infinities, mathematically feasible time machines, and "some kind of p-braned topological hypersurface in a higher-dimensional space."

As if not writing to a clearly-defined audience wasn't problematic enough, Mr. Stewart compounds the deficiency by insisting on the use of endlessly cloying puns throughout. Readers are forced to tolerate such "gems" as "the catenary was out of the bag," "there will be convex hull to pay," "I'm certain as Squares fit [bears s--t] in the Woods," "they'd just get you segment [pregnant] and dump you," "a used cardiod dealer," "Queens i Way," a bag marked "Doughnut Disturb," a cow named Moobius, projective lions, edgehogs, and squarrels, the Space Girls (Curvy, Bendy, Pushy, and Squarey), "crisp moose [Christmas] cards," and too painfully many others. Late in the book, Mr. Stewart adds a chapter about time travel through wormholes that inexplicably and ungraciously represents Stephen Hawking as the "Hawk King," a greedy and imperious wretch whose Domain is "right next to the Public Domain." They are forced to bribe their way into an audience with "His Majesty," who sits at the far end of a vast audience room on a splendid throne (an unfortunate choice, given the general tone and Mr. Hawking's actual physical condition). The Hawk King closes their meeting with a disdainful, "You are dismissed." No other human in the book is referenced in such misplaced and disparaging terms, and the entire scene comes across as mean-spirited and petty sniping.

One of Edwin Abbott's remarkable accomplishments in FLATLAND was to combine his mathematical/philosophical ponderings of multidimensional space with a biting satire of Victorian society worthy of Jonathan Swift. As if in faint recognition of Abbott's social commentary, Stewart occasionally tosses in a less-than-heartfelt comment about Vicky's incipient feminism, even going so far as to suggest that Flatland's straight line females (considered the lowest level of Flatland society because they have only one side) are in fact pentagons in an unseen, other-dimensional "shadow world." These silly efforts at social relevance only serve to amplify the shortcomings of FLATTERLAND relative to its renowned progenitor.

Ian Stewart's FLATTERLAND does offer some introductory explication of multidimensional and non-Euclidean mathematics and physics in a format suited to entertain teenagers. However, I believe it will leave them at least as confused as informed, as well as groaning over the incessant bad punning. In the end, this book is neither a worthy successor to FLATLAND nor an effective introduction to its mathematics and physics content. Better to read Abbott's original FLATLAND followed by Michiko Kaku's HYPERSPACE and/or Brian Greene's THE ELEGANT UNIVERSE.

The heroine Vikki Line is a great-great-granddaughter of the narrator A. Square of Edwin Abbott's classic book, "Flatland." The teenaged Flatlander heroine goes to a tour to higher dimensional worlds guided by a Space Hopper. She visits the Fractal Forest, Topologica, Platterland, Cat Country, the Domain of Hawk King, etc., and learns, together with the reader, about many concepts of modern mathematics and physics. The author Ian Stewart, a winner of the Royal Society's Michael Faraday Medal for furthering the public understanding of science, writes the story in the style of "Alice in Wonderland" by using enjoyable wordplay and putting exotic and cute creatures he invented to familiarize the difficult concepts.

Some topics are treated in a manner to give the reader good understanding, but others are described only superficially. There are simple errors in giving a number for fractal dimension and describing the behavior of the decoherence time. (I leave it to the reader as exercises to spot them.) The author explains the particle nature of the photon by the uncommon use of the process of electron-impact photon emission, while the orthodox explanation uses the inverse process, i.e., the photoelectric effect.

In spite of these minor defects, this is a joyous read for holidays. The heroine is depicted as such a clever, adventurous and charming linear being (near the end of the story she comes to know that she is something superior to a line) that I think how I would have been happy if I had had a girlfriend like her in my youth. Her guide and tutor, the Space Hopper, often shows a big grin, reminding us of the popular physicist and good lecturer Richard Feynman. In the short last chapter, the reader feels it important that more of us, "Planiturthians," become aware of the possible ten-dimensional reality of our physical universe, which Vikki learned at the final stage of her tour. Thus, I would like to recommend this book to every curious mind.

This book is a sequel to Edwin Abbott's "Flatland" and makes its heroine a granddaughter of the hero of Abbott's book. Some people may find his playing with words excessive (his heroine is named "Victoria Line," combining the fact that she is literally a geometric "line" with the name of a subway line in London) but the book manages to cover a lot of territory in an amusing manner. I can't say I _learned_ a lot from the book, because I already knew most of its subject matter, but I'd certainly encourage someone who wanted to learn about curved spaces and higher dimensions to read it. The ultimate accolade: _After_ I had read it from cover to cover, I bought a copy, just so I'd have it in my own library.

"Flatterland" is a very thought-provoking book by Ian Stewart. It is the sequel to "Flatland". I would call it a mathematical fiction book. It is about a girl from Flatland, a 2D world. She is called Victoria Line (all women on Flatland are lines). She goes on a journey through many different dimensions and universes with a being called the Space Hopper. She learns much about math on the way.
One of my favorite universes was Platterland, a 2D hyperbolic universe. While in Platterland she learns many things about hyperbolic geometry, including that straight lines appear to be curved, squares can have five sides and five right angles, and things shrink as they get closer to the edge of the universe!
Another one of my favorite universes was Topologica, a 3D topologic universe. While there Victoria learns about topology and how two-holed doughnuts can turn into coffee cups! She also meets Moobius, a cow shaped like a Möbius strip (a 2D shape with only one side), who gives milk in Klein bottles! Klein bottles are bottles in which the top curves around and goes back into the bottle!
Throughout the book there are many funny puns, right down to the name of the main character. Victoria Line is a subway line in London! The puns go very deep. One pun is about two people called Twindledum and Twindledumber. They are named after Tweedledum and Tweedledee from Lewis Carroll's "Through the Looking-Glass"! Another character is called the Hawk King, named after Stephen William Hawking!
I really enjoyed reading this book. I highly recommend it to anyone who likes math and knows a little bit about it or just enjoys reading funny books! It helps if you have read "Alice in Wonderland" and "Through the Looking-Glass". Many of the puns come from them. This book is definitely not for young kids though, some parts were way over my head. All in all, I understood most of it-and it was great!

When I first read Flatland (the original) I was deeply inspired and fasinated by the 4th dimensional ideas it brought up. When I picked up a copy of Flatterland, I had hoped for an interesting read with maybe a few new concepts at best, but I certainly got more than I bargained for. Flatterland takes you on a journey through much more than just the 4th dimension (which is interesting enough already.) He takes you through non-Eucludean dimensions, the world of 1.25 dimensions, theoretical dimensions, and even a world of infinite dimension. Ian Stewart brilliantly plays on words and makes you laugh at every step of the way. The ideas brought up are so fasinating and cutting edge, that it definately deserves more than one reading, and better still, they are explained in detail so that even the most complex concepts are easily understood. This book is clever, amusing, and perhaps even brilliant. I highly recommend it.

I have to disagree with the two other reviews. I've always had problems understanding some of the idea of modern mathematics. But after readingflatterland I get it. Flatterland puts it in an easily digestible form. Yes, some of the names (the Hawk king and Moobius, for example) are too cute for my sensibilities, but it clears up the mathematics. I found Victoria Line and the space hopper fun characters and the diagrams really helped bring the math down to my level. I rememeber the profound affect that Flatland had on me and trying to see things grow and shrink in this dimension. And not I've been equally caught up in thinking about fractals and time. Platterland was also a really mind-blowing chapter.

Though =Flatland=, by Edwin Abbott^2 100 years ago, was exclusively about 2 things: satirizing Victorian English society and explaining a 4th Euclidean dimension, Ian Stewart's =Flatterland= is about all sorts of geometries that mathematicians play in: finite projective geometries, in which there are a finite number of points and lines, interacting in specific ways; discrete binary geometries, which described digital encoding and the error-correcting codes used in things such as CDs and DVDs; hyperbolic geometry, in which there are and infinite number of line parallel to a particular line, all going through the same point (as opposed to the usual one parallel line); and on and on and on.

However, as a math grad student, I found the treatment too shallow, the puns too egregious (especially when I saw them coming) and too unrelenting (though now I've got plenty of math jokes to add to my arsenal), and some of the descriptions are somewhat confusing -- the only reason I knew what was going on is that =I knew= all these subjects from mathematics before. And, being a physics major in my undergrad life, I wasn't thrown off by the veering into modern physics topics.

This book is more like a travel brochure - letting you know what exciting sights are to be found in the strange lands of Geometry - but not giving you much of an experience of what's there. I think this book would be a great gift for a child who's interested in math - sure, they won't understand alot of it (and they'll miss many of the puns), but then my favorite math book, =Godel, Escher, Bach=, was given to me when I was 12, and I grew into it over the years through rereading it and learning more stuff in school. I can see this book as inspiring kids to learn more about strange concepts in math, but it would be nice to have a list of followup books for doing some =real= exploring as opposed to this travel guide. (I recommend Rudy Rucker's book =The 4th Dimension= for those who want to do more thinking about the 4th dimension).

If you're a math teacher, this book can come in handy in providing was to visualize some very odd concepts in math. And, again, there's the puns that you can try out on your class.

For those interested in getting a feel for what math is about, there's actually a great secret revealed inside the book - just what makes something a geometry. The answer doesn't seem evident when one compares the odd spaces and places visited by Victoria Line and the Spacehopper, but it does become clear. I will not give that secret away, but I will give another secret away that is also shown by the book - yes, mathematicians love to play with their math.

I enjoyed Flatland and Sphereland, so I received this book as a gift. It will be for sale, in mint condition, momentarily. The second half of the book will remain unseen by me, because I simply could not bring myself to continue.

Flatland was interesting and entertaining both mathematically and for its social satire. Sphereland was also interesting and entertaining. But Flatterland tries too hard. In the inroduction the author says he had the idea for explaining multiple dimensions using a similar approach to the earlier books, and then developed those ideas into this book. Sounds like a good idea, but the book lacks the wit to keep it interesting. And in some places lacks adequate explanations of concepts. I can imagine that somoene already familar with the concepts and enamored of the topic might think the author did a clever job of explaining someting that they have had difficulty explaining themselves. But, for someone who doesn't work in the field and hasn't had the challenges of explaining the concepts this book is nether fascinating nor interesting and only sometimes achieves the goal of explaining. It is mostly boring, although the introduction is interesting and explains a possible satirical reference to the origin of A. Square's name that would have probably eluded anyone not from London.

On page 32 there is the assertion that a cube of side 1.06 can fit through a cube of side 1. There is an illustration to demonstrate that. The illustration is not clear and I believe it has errors in it. Unfortunately there is no information to find other sources that explain this obscure factoid. On page 72, in the chapter explaining fractals he makes the assertion that if you take one segment of a snowflake and fit together four copies you will have an area three times the size. This turns out to be an important assertion for his example, but it sure ins't obvious and there is no explanation of why that assertion might be true.

But, by now these comments are probably as boring and of diminishing interest as the book itself. You and I both have better ways to spend our time.