Customer Reviews

Flatland/Sphereland (Everyday Handbook)

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If you are not familiar with Edwin Abbott's "Flatland", this is the edition to buy. If you are familiar with it (but presumably do not yet own it), this is still the edition to buy.

You've heard the classic criticism of a story is that it is "two dimensional". Well, Edwin Abbott's tale of an imaginary two-dimensional land adds a whole new twist to that phrase. Flatland, as he describes it, is about as rich as a two-dimensional story can be. And it is marvelously extended by its narrator's encounters with the unknown - the world of 3 dimensions. The challenges that narrator faces as he encounters the incomprehensible, quite closely mirror mine whenever I attempt to think about a 4th (or 5th or 7th) dimension. If you've faced the same struggle, you will be delighted by this book.

If you've ever wondered what a 4th dimension would look like, Flatland provides a lens through which you can imagine that extension of our 3D world. From here you can go on to read Rudy Rucker or Pickover or Hawkins - but this is the place to start your exploration of dimensions beyond experience. Abbot accomplishes this by describing the eye-opening extension of his narrator's 2D world when visited by a 3D apparition, a "sphere". His framing of the foundational issues through the experiences of what you'd expect to be the least interesting character in fiction are really quite engaging. The storyline, however sparse, is as interesting as the mathematics - albeit quite nineteenth-century'ish in tone.

Don't misconstrue Abbott's seemingly misogynist portrayal of women and of his class-stratified society. This element was intended to provide a third layer of sharp, Swiftian satire and critical commentary on the rigid social mores of his era. Abbot succeeds in this (but I, nevertheless, decided not to read it aloud to my 6th grade classes - worrying that they might not be attuned to this subtlety of tone.) Be forewarned.

The neat twist of this edition, the inclusion of Dionys Burger's 1983 "Sphereland", as an upside-down "second book", is quite a nice touch. Although I did not find Burger's stylings quite as engaging as those of Abbott, his extension of the mathematical ideas into non-Euclidian spaces is a nice introduction to that idea for non-mathematicians. Since it was intended as a standalone book, "Sphereland" commences with a detailed review of the "Flatland" story. This can be skipped without loss but is not a substitute for reading the original "Flatland", here, first.

Flatland is a timeless classic; a great book for the mathematician and non-mathematician alike.

I am only 17 and I read both of these books and understood every word of it. Not to say that the things covered in these two books are easy to see or comprehend but the authors did such a beautiful job of making everything easy to understand from life in the 2nd dimention to slightly grasping the 4th dimention through mathmatics and to flipping 3 dimentional objects in the 4th dimention thus reversing them like turning a left shoe into a right shoe. Even if you are not interested in math or science these books let you see the world in another way and will stay with you provoking thought at every turn.

This book introduced me to the amazingly interesting possibilaty of a fourth dimension, or even an infinite number of dimensions, and the way the material was presented (by a story of A Square and A Hexoagon and there adventures with a sphere) is delightfully entertaining. Since the human mind has such a horrid time visualizing the fourth dimension, taking it down one level by having creatures living in a two dimensional world who try to understand the third dimension is an excellent way to help people grasp the possibility of higher dimensions. I was also very interested in the books discussion about a curved space and an expanding universe. This book is great for any teenager interested in theoretic sciences and geometery and it is a great intellectual read.

Flatland and Sphereland are very well written books, but for entirely different reasons. Flatland is a fun story that takes you into the 2nd (and 1st, and 0th) dimensions to see what life is like there with its final goal to make you speculate on what the fourth dimension would be like. Flatland, the first book, excels at making you grasp the concepts and has a very good story to go along with it. The story seems to be the main focus, rather than the other aspects.

Sphereland is entirely the opposite. Sphereland deals with ideas such as the expanding universe theory others. This it explains even clearer then flatland did. But Sphereland's focus was not on the story, but rather on the theories that it tried to convey. This may be a good thing in some people's minds, but I enjoyed the story of flatland and didn't like it pushed aside to explain the theories. I also didn't like the fixing of flatland to make it less backwards (Besides giving equality to women) since flatland to me was backwards.

So If you want to learn complex Ideas simply and with fun, these are the books for you.

Many topics in modern physics and astronomy involve thinking of the universe in more than our customary three dimensions. Super-string theories, for instance, suggest as many as ten dimensions in our universe. Yet the general public is completely unfamiliar with this mode of thinking. Flatland and Sphereland are both stories with the perfect blend of simplicity and sophistication. Their simple, precise language is easy enough for even the casual reader to follow, yet the concepts presented are advanced enough that even experts in the field will be churning it around in their minds for days after. When I ordered these books, I expected an entertaining story that, while intriguing, would contribute little to my education in the long run. What I found, beneath the delightful tale, was a depth of concept that has changed my thinking.

I am 17, and I thought that these books opened doors to a new way of thinking for me. It is very likely that anyone who didn't like these books simply did not understand them. Yes, the language was very wordy compared to modern literature, but no more difficult to understand than *Sherlock Homes* or Charles Dickens. I recomend this book to anyone who is scared of physics or simply wants too expand their mind.

This is a must read for anyone. Its written simply for anyone to understand yet the underlying principles can inspire thought and contemplation on the ideas of relativity and perspective. On the surface this book explores dimensions but it provokes thought about perspective and encourages you to evaluate your own perspectives. You can get anywhere from mild amusement from this book to philosophical life changing perspectives.

In detail, Flatland is a classic story about a two dimensional square that discovers the world of a line, a point, a sphere and beyond. The square contemplates his role in society as a square and realizes that there is something else out there when a sphere comes to visit.

This book is a must have for all bonafide Flatlands fans.

First off, it has the original Flatlands classic by Edwin Abbott Abbott, the mathematician/clergyman would first took us to the world of A Square. And it also has the 1967 followup Sphereland.

It bears noting that Sphereland is but one of many follow up so Abbott's classic and because they're all good and worthy in their own right, I'll repeat them here:

Spaceland...the Rudy Rucker classic which focuses more on following up the story than the science of Abbott's original book;

Plainiverse...the Dewdney work which actually endeavors to thoroughly flesh out the physics and biological issues of what life actually would be like in 2D (for what it's worth philosopher Dan Dennett says that this is favorite take on the Flatlands theme); and

Flatland Annotated and Flatterlands...both by mathematician Ian Stewart. If I wasn't as a big of a fan of this book I probably admittedly would've stopped my collection at just these entries because the annotated version has the original Flatland in it and also because in my opinion at least Flatterlands does the best and most recent job of updating the mathematics of Flatland.

But that being said, Sphereland is a serviceable entry and does faithfully follow the A Square story...albeit two generations later...and like the original Flatland serves as a great metaphor for the desireability of open mindedness and looking past your limitations.

Flatland the book is about many intelligent geometrical creatures who think 2 dimensions is all there is until one day a square starts thinking otherwise. Learn what is would be like to live in 2 dimensions and try to fill in the holes

My appreciation of mathematics came late in life, but it finally came. I have neither the aptitude nor the training to be a professional mathematician, but I like to spend a fair amount of time reading books on mathematics. A handful that I recommend are: Darrell Huff's _How to Lie With Statistics_ (1954); David Salsburg's _The Lady Tasting Tea_ (2001); Simon Singh's _The Code Book_ (1999); Robert Osserman's _Poetry of the Universe_ (1995); Reuben Hersh's _What is Mathematics, Really?_ (1997); Bryan Bunch's _The Kingdom of Infinite Number_ (2000); James Gleick's _Chaos: Making a New Science_ (1987); and Douglas R. Hofstater's _Godel, Escher, Bach: An Eternal Golden Braid_ (1979). The last is fairly stiff reading. But it is beautifully written; and if you read only a fraction of it, your perception of the world is likely to change.

All of which brings us to a Victorian gentleman who gave some attention to the nature of and the limits of our perceptions of the world. Edwin A. Abbott (1836--1926) was a Shakespearean scholar who also took honors in mathematics and theology. In 1884, he published a mathematical fantasy called _Flatland_. It is set largely in a two-dimensional world, populated by sentient lines and shapes. Most denizens appear as lines to one another, though the relative faintness of lines gives a clue to the nature of different shapes. There is a class system built on the relative complexity of shapes: women (Straight Lines), workers and laborers (Isosceles Triangles), the middle class (Equilateral Triangles), professional men and gentlemen (Squares and Pentagons), and the nobility (Hexagons and Many-sided Figures). There is some movement from class to class, but "a woman is always a woman". The houses are also two-dimensional, mostly pentagonal in shape. There is a kind of gravitational pull to the south so that the base of various shapes turn toward the south and their apex angles toward the north. The narrator, "A. Square," has accepted his world at face value. But one day, he encounters a shape that _seems_ to be circular but who _says_ that it is a sphere... And nothing is ever quite the same.

_Flatland_ quickly became a classic. Several sequels and companion stories to the novel were written over the years by other hands, but one of the best is that of Dionys Burger, a Dutch physicist. It was originally published in 1957 as _Bolland_ and was translated as _Sphereland_ in 1965. Burger's novel relates how the natives of Flatland discover that their land is really curved. They then discover the Einsteinian properties that it contains. Burger relates how triangles can become greater than 180 degrees, how mongrel dogs can become pedegreed through three-dimensional trickery, how a brave Line explorer defied the courts to reveal new truths about the nature of space, and what geometric fairy tales can reveal about the nature of the world.

I hear the dry thunder of voices of the Mathematically Challenged rolling across the Waste Land: "We could _never_ understand!" And I say unto you: "Oh, yes you can." You don't need advanced training in math to grasp the concepts-- and they are presented in a painless, charming, and entertaining manner. So read these books and be refreshed by the rain.

Burger's book modernizes _Flatland's_ portrayal of women (Straight Lines). Here is Abbot's treatment in his novel:

Nor must it be for a moment supposed that our Women are destitute of affection. But unfortunately the passion of the moment predominates, in the Frail Sex, over every other consideration. This is, of course, a necessity arising from their unfortunate conformation. For as they have no pretensions to an angle, being inferior in this respect to the very lowest of the Isosceles, they are consequently wholly devoid of brainpower, and have neither reflection, judgement nor forethought, and hardly any memory. (15)

In a foreward to the novel, Isaac Asimov asserts that Abbott "may have participated in these now-antiquated social views" (ix). Perhaps. But I think that Asimov misses an ironic bite in this passage. I suspect that Abbott was less blinded by the prejudices of his day than his narrator, A. Square. In Burger's book, women still are the bottom social class. But they are better educated, more responsible, and less hysterically emotional. The social classes in Burger's novel (which takes place some time after the action in _Flatland_) have become a bit more fluid.

I hesitate to recommend a book because it is good for other people. That sort of praise is the kiss of death as far as most readers are concerned. But sometimes you just can't avoid mentioning that characteristic. These two fantasies are good for you. But they are also great fun. There is not a stuffy bone in either one of these beasts.