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Science Books Media Book Reviews

Flatterland 42

Posted by timothy from the like-flatland-only-more-so dept.
howardjp writes: "Ian Stewart has penned a fabulous sequel to Edwin A. Abbot's classic geometric classic, Flatland. Mr. Stewart's sequel, Flatterland, discusses the geometric advances over the preceding one hundred years and how these advances have applied in the real world. From the simplest plane geometry to passing through a wormhole, Flatterland describes the mathematics in simple and easily digestible terms." Read the rest of James' review below.

Flatterland: Like Flatland Only More So
author Ian Stewart
pages 294
publisher Perseus Publishing
rating 8
reviewer James Howard
ISBN 0-7382-0442-0
summary A one dimensional line living in a two dimensional world issuddenly thrust into three dimensional space, fractal worlds,and hyperbolicplanes.

Flatterland begins one hundred years after Flatland's end. A. Square's great-great-granddaughter, Victoria Line has found A. Square's ancient text, Flatland: A Romance of Many Dimensions. After causing some trouble with her family, Victoria reads the text and signals the third dimension. She is soon greeted by the Space Hopper, who soon teaches her about three and dimensions, fractal space, perspective, hyperbolic space, topology, time travel, wormholes, and everything else relating to geometry.

Flatland was written to warm the public up to a more complex space than the three dimensions they normally perceived. Shortly after the start of the new century, Albert Einstein proved the relationship between time and space adding a forth dimension. Flatterland is not written the same way. Rather than warming the reader up to physical possibilities, Mr. Stewart pedanticly explains the Universe as it is known today. In those areas where science has no answer, Flatterland simply says there is none and offers several possible answers.

Mr. Stewart went to great lengths to demonstrate Victoria's naivity. All names from the book are spelled as one part and even names are combined. Albert Einstein becomes Albereinstein and Felix Klein becomes Felixklien. Even planet Earth becomes Planiturth whose inhabitants are Planiturthians. First cute, by the end of the book, the nomenclature becomes dreadful and deciphering names can be difficult when the original is unknown to the reader.

Missing most from Flatterland, though, is the social satire. Flatland endlessly mocks Victorian society. The role of women was questioned along with evolutionary theories. Flatland was more of a social satire than it was a text on geometry. Flatterland's social satire is weak and confused. In Mr. Stewart's introduction, Flatland has evolved into a sixties-like era, but modern technology from the nineties has also arrived. What little social criticism there is in Flatterland addresses the women's movement. Unfortunately, the style and discourse would have been more appropriate forty years ago.

These flaws aside, Flatterland's discussion of mathematics and science is amazing. The simplicity of the breadth of material makes Flatterland helpful aid in study. The personification of mathematical concepts includes a five-sided figure with five ninety degree angles from the hyperbolic plane called a squarrel. Viewed from inside the hyperbolic plane, Victoria is confused to see a creature with the wrong measure of angles for five sides until the Space Hopper patiently explains. The personification also includes a cow whose tail flips and joins its nose named Moobius. Victoria takes to washing one side of Moobius only to discover that Moobius has only one side.

Through the Space Hopper, Mr. Stewart explains complex mathematical concepts with explicit detail but very simply and often several times from several angles to ensure the reader understands the topic. Additionally, the book includes ample diagrams from simple grapefruit stacking problems to visions of wormholes. The images are most helpful when discussing perspective.

Ideally, Flatterland would embody the mathematics, science, satire, creativity of Flatland. However, Flatterland usually sacrifices satire and creativity for science and mathematics. The book is still an exceptional read and well worth the time. It does not tarnish the reputation of Flatland, but it is not destined to become the classic that its predecessor is."

You can purchase this book at Fatbrain.
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  • Re:Nits too big to ignore (Score:1)

    by Anonymous Coward
    I feel your argument resembles Zeno's paradox. It seems to revolve around the concept of "one slice at a time" where we already defined time to be that one slice, so what do we mean by "at a time"? [Did I understand you?]

    Nothing is "wrong" here, you're just confusing a metaphor with the actuality. The metaphor breaks down when you realize that you cannot extricate the time dimension from such an explanation - NO explanation in human terms can omit the time dimension.

    Of course it is meaningless to say one "travels" along the time dimension, because "to travel" implies a rate of change w.r.t. time. But true space-time geometry does not use this concept. Only the lame explanations do.

    Let go of your conception of time, if you want to understand time as a dimension. That's the challenge. It's too easy to say "this is all bollocks".

  • If you are interested in this sort of stuff, look for books by Lillian Lieber. She wrote:

    • The Einstein Theory of Relativity some of which is online here [ship.edu]
    • Non-Euclidean Geometry
    • Galois and the Theory of Groups
    • The Education of T. C. Mits
    • Mathematics for the Two Billion
    • Mits, Wits, and Logic
    • Infinity

    I really loved her books as a kid and I find that they still hold up today. Mrs. Lieber, wherever you are today, thank you!


    OpenSourcerers [opensourcerers.com]
  • Another book by Ian Stewart that I really liked is "Does God Play Dice", which explains chaos theory very nicely.

    ...richie

  • Ignoring the misspelling and poor grammar, this is just plain wrong.

    Grammar: The comma is optional.
    Spelling: The spelling is correct.
  • It's not a review, it is a link to the New York Times.
  • But which one seems simpler. I know how to stack grapefruits but have no idea how to construct a wormhole. :)
  • Ack! I thought Einstein did that. But I disagree on the statement that you cannot prove a relationship.

  • Charles H. Hinton's "An Episode of Flatland [mediaone.net]"

  • When used in the context of science (as opposed to math), the verb "to prove" has a very loose meaning. It can even mean "to suggest" or "to imply". And while SR doesn't have all the wacky geometry of GR, even SR is easier to understand if you think of time as being as flexible as the other dimensions. Thus Einstein 1905 "proves" (as abhorrant as that usage may be) that time is a dimension.

    So cut 'im some slack. "Prove" was raped and murdered a long time ago, and the body was cold long before James got there.


    ---
  • That would be professor Stewart, or just Ian Stewart if you don't like titles.
  • No, its just a translatlantic difference in language. In the UK (where Ian Stewart is from) not every university teacher is a professor. This term is reserved for the head of department, and is in fact a title.
  • No, it's just that much of a classic.

  • One [mediaone.net]
    Two [sunet.se]
    Three [upenn.edu]
    Four [upenn.edu]

    The last two seem to have links to other download sites. Courtesy of ipl [ipl.org]. BTW, the review above really stinks.

    -rt
    ======
    Now, I think it would be GOOD to buy FIVE or SIX STUDEBAKERS

  • Time as the fourth dimension doesn't make any sense. It's usually explained in a Flatland-like manner; space-time is like a loaf of bread, we travel through and experience once "slice" at a time.

    While this might be reassuring to determinists, it's also plain wrong. If we are moving through the loaf of bread, experiencing once slice at a time, then time is not a dimension of the bread, because time is still external to the bread (and you looking at the bread). I'll leave it as an excercise to the reader to determine *what*, in this metaphor, is supposed to be moving through the bread.

    Think about it. And please stop that "time is the fourth dimension" thing.

    Boss of nothin. Big deal.
    Son, go get daddy's hard plastic eyes.

  • Flatland is social sattire (Score:3)

    by divec ( 48748 ) on Wednesday May 30, 2001 @05:51AM (#188924) Homepage
    For example, colours are banned in Flatland. Why?
    Some private individual [...] having casually discovered the constituents of the simpler colours and a rudimentary method of painting, is said to have begun decorating first his house, then his slaves, then his Father, his Sons, and Grandsons, lastly himself. The convenience as well as the beauty of the results commended themselves to all. [...] The fashion spread like wildfire. within two generations no one in all Flatland was colourless except the Women and the Priests. The Art of Sight Recognition [which is difficult in a monochrome 2D world] was no longer practised [...] Year by year the Soldiers and Artisans began more vehemently to assert -- and with increasing truth -- that there was no great difference between them and the very highest class of Polygons, now that they were [...] enabled to grapple with all the difficulties and solve all the problems of life, by the simple process of Colour Recognition. [...] Soon, they began to insist that the Law should follow in the same path, and [...] all individuals and all classes should be recognized as absolutely equal and entitled to equal rights.
    [...] The Circles hastily convened an extraordinary Assembly of the States; [...] the Chief Circle Pantocyclus arose to find himself hissed and hooted by a hundred and twenty thousand Isosceles. But he secured silence by declaring that henceforth the Circles would enter on a policy of Concession; yielding to the wishes of the majority, they would accept the Colour Bill. The uproar being at once converted to applause, he invited Chromatistes, the leader of the Sedition, into the centre of the hall. [...] Then followed a speech, a masterpiece of rhetoric, which occupied nearly a dayin the delivery, and to which no summary can do justice.
    [...]With a grave appearance of impartiality he declared that [...] it was desirable that they should take one last view of the perimeter of the whole subject, its defects as well as its advantages. [...] Turning now to the Workmen he asserted that their interests must not be neglected. [...] Many of them, he said, were on the point of being admitted to the class of the Regular Triangles; others anticipated for their children a distinction they could not hope for themselves. [...] With the universal adoption of Colour, all distinctions would cease; [...] the Workman would in a few generations be degraded to the level of the Military, or even the Convict Class; political power would be in the hands of the greatest number, that is to say the Criminal Classes. [...] "Sooner than this," he cried, "Come death."
    At these words, the Regular Classes [attacked supporters of the revolution]. The Artisans, imitating the example of their betters, also opened their ranks. [...] The battle, or rather carnage, was of short duration. [...] the rabble of the Isosceles did the rest of the business for themselves. Surprised, leader-less, attacked, [they] raised the cry of "treachery". This sealed their fate. Every Isosceles now saw and felt a foe in every other. In half an hour not one of that vast multitude was living; and the fragments of seven score thousand of the Criminal Class slain by one another's angles attested the triumph of Order.
    The Circles delayed not to push their victory to the uttermost. The Working Men they spared but decimated. [...] every town, village, and hamlet was systematically purged of that excess of the lower orders. [...] Henceforth the use of Colour was abolished, and its possession prohibited. Even the utterance of any word denoting Colour, except by the Circles or by qualified scientific teachers, was punished by a severe penalty. Only at our University in some of the very highest and most esoteric classes it is understood that the sparing use of Colour is still sanctioned for the purpose of illustrating some of the deeper problems of mathematics. [...] Elsewhere in Flatland, Colour is now non-existent. The art of making it is known to only one living person, the Chief Circle for the time being; and by him it is handed down on his death-bed to none but his Successor. [...] So great is the terror with which even now our Aristocracy looks back to the far-distant days of the agitation for the Universal Colour Bill.
    The whole of the book is social commentary such as this. That's what makes its 40000 words interesting to read, more so than any mathematical insight it might lend. Of course, Stewart's book is aiming at different goals from this; and Stewart is an excellent expositor of Mathematics. But the original is well worth reading even if you aren't at all interested in geometry. Take a look at it for free [upenn.edu], thanks to Project Gutenberg.

  • For more Flatland antics... (Score:3)

    by nicky_d ( 92174 ) on Wednesday May 30, 2001 @06:10AM (#188925) Homepage
    Check out Rudy Rucker's great book, "The Fourth Dimension and How to Get There". It discusses Flatland and related dimensional realms at length, covering questions such as "how does a 2d creature's digestive system work?" along the way. A Very Good Book. Rucker also revisited Flatland in his short story, Message Found in a Copy of Flatland - that can be found in his recent short fiction anthology, "Gnarl!"

    Well, long post short, just buy all his books.
  • by A.K. Dewdney is also very good.

  • Nits too big to ignore (Score:3)

    by VSarkiss ( 173815 ) on Wednesday May 30, 2001 @05:59AM (#188927)
    I hate to nitpick, but this one's a whopper. My hackles hit the ceiling when I read it.
    Shortly after the start of the new century, Albert Einstein proved the relationship between time and space adding a forth dimension.
    Ignoring the misspelling and poor grammar, this is just plain wrong.

    If the reviewer is referring to Einstein's "On the electrodynamics of moving bodies" paper of 1905, that one has no references to geometry at all. It was Minkowski's 1907 lecture entitled "Time and space" that showed that considering time (as clarified by Einstein's formulation) to be a fourth coordinate axis simplifies and unifies many calculations greatly. But it did not prove the relationship--you can't prove a relationship.

    You could make a case that the reviewer is referring to Einstein's 1915 "Foundations of general relativity" paper, since that one does make an advance in geometry by constructing what is now known as the Einstein tensor. But though it's solidly grounded in geometry, the true impact of that paper is Einstein's demonstration of the significance of that tensor in physics.

    However you cut it, nothing in that sentence holds up.

  • Yes, it seems that every time somebody wants to use geometry to make a point (pardon the pun), or wants to make a point about geometry, they write a "sequel" to Flatland.

    Every attempt to do so that I have seen has been really shitty. The original story was creative and entertaining, if a little dated.

    People should try to write works inspired by their own imagination, instead of sponging off the populatity of a more creative mind.

  • to say that using "living" characters and story twists to successfully explain complex spatial concepts isn't creative, is selling Ian Stewart short.

    It was creative when it was done in Flatland. When Ian Stewart did it, it was not.

    If I were to write a "sequel" to The Screwtape Letters, would I be praised for my creativity in my decision to write ironic satire from the perspective of a demon? Only by rubes who did not read Lewis's original stories first.

  • That was a fairly astute and insightful analysis of Flatland, and how it differs from the recent "Sequel". The social and theological subtext of Flatland is part of what made it such an interesting piece of literature.

    It looks as though somebody moderated the comment down as "off-topic" as a knee-jerk reaction. "It mentions religion, so he must be... uh... trolling... or something."

    I liked the AC's comment so much, that I am posting here with my +1 Bonus to call attention to it. If you do not see it, click on "parent" at the bottom of this post.

    (Should the parent be moderated up to 2 or higher, I suppose this comment should be marked down as "redundant".)

  • Actually, Chapters.ca [chapters.ca] (if you're in Canada) and Amazon.com [amazon.com] (if you're elsewhere) both list Planiverse as "usually shipping in 24 hours".

    I did see a copy of it on the shelf at the local Chapters, so it seems to still be available.

  • Perhaps I phrased that badly. The original idea wasn't Stewart's creation, but the story and character usage were. There isn't a simple "translation" he could have done to automatically generate Flatterland from Flatland - writing the book required creativity.

    Your idea to write satire from the perspective of a demon would not be considered "creative". If you wrote the book well and expressed new ideas using the characters having used Lewis's ideas as a starting point, then your work could be praised as "creative".

  • Rather:

    If you wrote the book well and expressed new ideas having used Lewis's ideas as a starting point, then your work could be praised as "creative".

  • I'd agree with basically the last part of the review - Flatterland is an excellent introduction to mathematical and cosmological ideas like multi-dimensional space, wormholes, the possibility of time travel, and string theory.

    On the subject of creativity, I'd disagree. I would say that Flatterland is a creatively written book on physics. Perhaps not original in it's use of allegory, but to say that using "living" characters and story twists to successfully explain complex spatial concepts isn't creative, is selling Ian Stewart short.

    Regarding social satire, the reviewer is right - there isn't any (or at least very little). But then, I didn't pick up Flatterland in the "social satire" section of the book store (if such a section exists); I picked it up in the "Mathematics" section (incidentally, Flatland was in the literature section). To critisize the book for poor social commentary seems to miss the point of the book entirely. Flatterland does claim to be a sequel to Flatland in that it's an expansion on the spacial ideas presented in the original book. At no point does it claim to also be a clever satire of modern society. Quite honestly, Flatterland gave me enough to think about - adding any significant amount of satire would only serve to clutter the book and confuse the reader.

  • Spelling: The spelling is correct.
    Not unless you meant that Einstein founded FIG's journal. [forth.org]
  • Isn't the topic intersting enough, that he's has to go to this lenght to try and make it funny and readable( and fail at that too)?

    "Mr. Stewart went to great lengths to demonstrate Victoria's naivity. All names from the book are spelled as one part and even names are combined. Albert Einstein becomes Albereinstein and Felix Klein becomes Felixklien. Even planet Earth becomes Planiturth whose inhabitants are Planiturthians. First cute, by the end of the book, the nomenclature becomes dreadful and deciphering names can be difficult when the original is unknown to the reader."

    I got tired of it in this short para and can only imagine the plight of tthe poor readers. But as the review itself says we can ignore the bad and concentrate on the good.

    Everything has a price you see.

  • Mathematician AK Dewdney published a book back in 1984 entitled "The Planiverse" which was a very entertaining, but thorough, examination of what 2D existence could be like. I think it's currently out of print, but is worth a look if one can find it. A further description is here [csd.uwo.ca].

  • http://www.amazon.com/exec/obidos/ASIN/0486234002/ qid=991301064/sr=1-46/ref=sc_b_46/103-1898435-2554 242 Always from Rudy Rucker. Small book, to read on the bus to school/work/home.
  • Another nitpicky comment regarding the delivery...

    Albert Einstein proved

    Nothing in science is "proved", science is the negating of existing theories and finding support for new ones. Another pet pieve of mine is Newton's Laws. These too are theories that have been negatated by such people as Einstein and Stephen Hawking.

  • Ian Stewart is currently a professor at the Institute of Mathamatics, University Of Warwick. Even if he wasn't he still has a PhD so he would be Dr. Stewart not Me. Srewart. He may be a professor but I would hardly call him a university lecturer - while I did my degree at Warwick I think could have done at most one lecture course by him - over four years! His role at Warwick seems to be writing books, giving public lectures, and promoting Warwick. Next in line would be maths research, and finally teaching students. I might be exagerating, but I was dissapointed that he didn't teach much...
  • ...written by someone who can't spell, use conjunctions, or construct one decent sentence out of three. I mean, what are the chances this guy can *read* well enough to even *think* of a constructive review??

    Say what you like about Mr. Stewart's writing; my money says it beats the phuck out of yours.

    S.T.
  • Interested in wormholes? [howstuffworks.com]
  • I've read Flatterland and I don't really like it as much as the original. In Flatland, Mr. A. Square lived on a 2D plane and was suddenly lifed into the third dimension. In Flatterland, however, this perspective of the universe is not preserved. The author invents a device called a VUE that can do everything. If the author is describing the complex number plane, then the VUE transports the main character to it. Poof! Thats it. Not much fun. Overall, I think the book does a good job of explaining scientific ideas in simple terms, but it doesn't keep with the theme and tone of the original.
  • I knew that... [wups] =)

    My .02,

  • Hemos did a review of this [slashdot.org] on April 21st [440int.com]. Not complaining, just pointing it out for those who tend to find themselves more similar to certain reviewers.

    My .02,

  • Good to hear a sequel is out, although I was pretty sure that there already was a "sequel" that had been published. Ah well... I guess I can shift my mind into a lower gear instead of trying to understand Godel, Escher, Bach. :)
  • I have a copy of Alice in Quantumland, and I can say without hyperbole that it should replace most high school freshman physics texts.

  • "Message Found in a Copy of Flatland" was a decent enough short story, but the geometry was rather messy. The flatlanders had a small amount of depth, for Pete's sake!

  • The 2D animal digestive system thingny, and other dimensional fun, are also in the last chapter(s) of Stephen Hawking's Brief History of Time. A book that's very readable too, say with high school physics completed.

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