Φλάτερλαντ: η περιπέτεια των πολλών διαστάσεων

by Ian Stewart, Νάσος Κυριαζόπουλος (Translator)

Η περιπέτεια ξεκινά όταν η ηρωίδα, Βικτώρια Λάιν (Γραμμή), ανακαλύπτει στη σοφίτα του σπιτιού της, το σκοροφαγωμένο ημερολόγιο του προ-προπάππου της, Άλμπερτ Σκουέαρ (Τετράγωνου). Η Βίκι προσβάλλεται από τον ιό της Τρίτης Διάστασης -προς μεγάλη απόγνωση τνω γονέων της. Χωρίς αυτοί να γνωρίζουν, ακολουθεί τα βήματα του προγόνου της στο εκτεταμένο σύμπαν της Τρίτης Διάστασης...
Βρίσκει έναν ευτραφή κύριο (έμοιαζε με λαστιχένια φούσκα), εξοικειωμένο με πλήθος μαθηματικούς και φυσικούς χώρους και, κρατώντας τον γερά, «πηδάει» από τον ένα μαθηματικό χώρο στον άλλο, μέχρι που φτάνει στις... δέκα διαστάσεις.
[...]
Το «Φλάτερλαντ» κλονίζει ακόμη και την πιο ευφάνταστη θεώρηση για την έννοια της «διάστασης».
Προσδεθείτε! Η βόλτα θα είναι ιλιγγιώδης

Genres: Science, Mathematics, Nonfiction, Physics, Philosophy, Literature, Humor

376 pages, Paperback

First published January 1, 2001

About the author

Ian Nicholas Stewart is an Emeritus Professor and Digital Media Fellow in the Mathematics Department at Warwick University, with special responsibility for public awareness of mathematics and science. He is best known for his popular science writing on mathematical themes.
--from the author's website

Librarian Note: There is more than one author in the GoodReads database with this name. See other authors with similar names.

Reviews

[Paul Sánchez Keighley · Rating 2 out of 5]

Alas, a decent follow-up to Flatland: A Romance of Many Dimensions, it is not. I know I shouldn’t be comparing it to the original, I know, but I just can’t help it. Every time I picked up this book, all it did was make me feel like reading Flatland again. Flatterland presents itself as a sequel while still managing to pretty much be its own thing. And yet, it lacked that bottled-lightning quality that made Flatland timeless and unique.

Flatland wasn’t really about the math; it was an overly-elaborate way of poking fun at the rigidity of Victorian society. It was the perfect marriage of science and literature, insofar as the science (or math) was always at the service of the story. The fact that the math was solid made it all the better. In a way, it’s something like a hard mathpunk masterpiece.

In Flatterland, the comedy of manners is present, targeting late-20th-century quirks and tropes, but is quaint to the point of being harmless, a very safe nudge-nudge-wink-wink kind of humour which has little to do with Flatland’s subtle satire of Victorian mores. Then again, Flatterland's heart isn't set on social satire. What this book really comes down to is little more than a humorous exposition of abstract geometry.

The tone feels confused. Its ceaseless referring to humans as 'Peoples' (or worse, 'Planiturthians'… ugh), not separating mathematician’s names (e.g., Isaacnewton, Euclidthegreek...), and other such baffling choices all feel like the kind of thing you’d expect to find in a book intended to get kids or (oy) teenagers into math by making it look hip and cool.

And at first, the concepts explored are innocent enough. So much so that about 30 pages in I decided I was reading a children's book and went to make myself a glass of chocolate milk. But when I picked it up again, the level of abstraction had cranked up to eleven and the characters were expounding heady theories on hyperspheres, n-dimensionality and (oh no) binary codes.

I spurted out my milk faster than you can say ‘null’.

And all the while, while tackling these abstract monstrosities, the book kept employing the ludicrous goofy tone of a sex-ed video. It’s enough to make you lay the book down on your lap, stare silently into the middle-distance, and reconsider every life choice you made that lead up to your purchasing of Flatterland.

When I saw that this was neither going to be Engaging or Enlightening but merely Mildly Entertaining, I relegated it to the bathroom reading basket and it continues there still.

[Andrew Breslin · Rating 3 out of 5]

This was entertaining and educational, but it wasn't really a work of fiction. It was a long parable illustrating fascinating ideas about geometry. Very well-written and thought provoking, but there was no actual story.

I've always loved Kurt Vonnegut's succinct and brilliant advice to would-be crafters of fiction: "All your characters must want something, even if it's only a glass of water." The characters here don't want much of anything, other than to be used as tools by the author to illustrate mathematical ideas. And they get what they wish without having to even try.

The characters didn't desire something and face obstacles to the realization of their respective desiderata, with the level of tension steadily increasing as we the readers are swept along in the story, feeling that tension rising, observing those characters as they ultimately either succeed or fail but are, nevertheless changed in some way by their struggle. That's what fiction is all about.

Also: there are puns. But most of these British, so you might not get them. Even more disturbing: you might be British and you will get them.

I don't mean to give the impression that it's a bad book. It's a good book, if you want to learn about some fascinating aspects of modern geometry. But the story was always subservient to the math; it existed solely to illustrate the ideas. Great ideas, cleverly presented, but the story was flat and the characters two dimensional. I'm sorry about that last comment, but really, who could resist?

[Kelvin · Rating 4 out of 5]

I had this one week a while back where I was super into math and science related books and that’s how I stumbled upon Flatterland. I’ve read some of Stewart’s other books and I appreciated how he could make complex math topics more accessible. Flatterland is no different. I’m good at picking up math concepts pretty quickly but some of the topics in this book had me confused the first time I read about them. However, when I read about them in Flatterland, they made much more sense. This, above all, is Stewart’s forte: the ability to make higher math interesting and easy to understand.

Flatterland, like the name suggests, is set in the same world as Edwin Abbot’s Flatland, albeit a century later. We are taken on a tour of the mathverse and all of it’s dimensions with the main character, Victoria-line, who happens to be the great great granddaughter of A-square, the main character of flatland, and a creature called the space-hopper. The mind whirling journey starts when Victoria, affectionately called Vikki, discovers A-square’s book about multidimensional theory and decodes a secret message within that allows her to summon a creature from multidimensions, in this case the space-hopper. The space-hopper has the ability to travel across all of mathverse without any difficulty and lends a hand to Vikki in helping her to see other worlds as well.

I liked how the book was organized like a tour of a safari or a museum and each chapter was another exhibit. This made Flatterland easy to read while still being incredibly informative. But by the 8th chapter or so, the format was starting to feel repetitive since we were just kind of hopping from world to world. I liked that in each world, the characters we met had so much personality and often times had real world counterparts, e.g. Space girls/Spice Girls, the doughmouse and company/doormouse and mad hatter from Alice in wonderland. However, I didn’t like how Vikki loses her sense of 2-dimensionality. By that I mean that for the first couple of chapters she has a lot of difficulty comprehending phenomenon unique to higher dimensions and the space-hopper explains it accordingly, but by the end she doesn’t really have any more comprehension issues and I couldn’t even tell that she was from flatland anymore… I’m not exactly sure if this is intentional, i.e. it is showing that she is a quick learner, or if it is just laziness on Stewart’s part not wanting to explain things so mundane to us but that wouldn’t be to Vikki. This doesn’t really change the comprehensibility of the math since we already understand the things about three dimensions.

And even though we get a very large sampling of mathematical topics, there is a nice flow from chapter to chapter where the current dimension can describe something that couldn’t be described by the last one or was a step up, e.g. upgrading from three dimensions to n dimensions. All of the basic info about the topic in each chapter is there and it was nice that there were “sample problems” that space-hopper would ask and then Vikki would answer, e.g. determining the dimension of a new fractal or determining the signs of living on a torus. And even if I had to reread the section to answer the question, it wasn’t because Stewart’s writing was unclear; it was always that I couldn’t wrap my mind around the concept. The explanations start out succinct in the first couple of chapters but by the time we get to relativity and whatnot, the chapters start to feel a bit endless and space-hopper’s appeal starts to wear off. Still, on the whole the math is nicely incorporated into the story and easily understood.

Okay, so about Flatterland’s story (not the math part): it could have used some help. Like why doesn't her family freak out more about her disappearing? Seriously, your daughter just poofed and was gone and you remain adamant in the belief that she somehow ran away by oh I don’t know punching a hole in the wall? And even at the end, her parents aren’t as emotional as I expected they would be. On the other hand though, there was a nice emphasis on gender equality; it felt forced and way too insistent at times but I get that Stewart was making a point that we have changed since the day when Flatland was published (though even in Flatland, the sexism was being ridiculed).

Overall, all of my complaints about this book basically boil down to the fact that it seems too long and in the final chapters, I just want to speed it up and get to the ending already. However, if you are interested in learning more about dimensionality in math and can stay hooked on the book till the end, I’m sure this will be an amazing read.

[David · Rating 2 out of 5]

I have noticed people putting this on their "to read" shelves and wishlists. I hope they are not as disappointed as I was, but greatly fear that disappointment is likely, almost inevitable. For the reasons in my review below - "Flatland" is a hilarious romp, wittily and successfully executed. This book, with its oh-so-clunky title, is most emphatically not.

This book takes as its starting point Abbott's "Flatland", the quirky 19th century mathematical classic which imagines life in a 2-dimensional world, and deepens our intuitions about geometry by imagining how a visitor from a 3D world might be experienced by denizens of the plane. Abbott's book is hilarious, witty, unique. Ian Stewart is a mathematician with a flair for writing well, both technically (his book on Galois theory is a masterpiece of elegant writing), and for a more general audience (e.g. his recent "Letters to a Young Mathematician"). This book is a noble, but deeply flawed, effort to extend the Flatland idea to that of a 3D world, imagining how we would experience a 4th dimension. The conceit is an appealing one - you want him to succeed, but - unfortunately - the whole effort falls pretty, um, flat. The clunky title is a good indicator of the strained attempt to be clever that permeates this whole book, like desperation.

An object lesson in the folly of trying to improve on a classic, this book does nothing to burnish Professor Stewart's reputation as a writer. It should not, however, steer people away from trying some of his other work.

[Richard · Rating 4 out of 5]

I heard about this book from a friend who is a freelance proof reader. She'd read it and admitted that most of it had gone straight over her head. However she did recommend it highly.

I picked up a copy at the same time as Flatland and read the two books one after the other.

Whereas the first book was about a flat being being shown life in three dimensions, Flatterland shows the adventures of a person being taken into a world of many non-euclidian dimensions. The space it talks about is often well understood by mathematicians, but because they bear no resemblance to normal space they are completely mysterious to the uninitiated. And they have strange properties! A flat plane where parallel lines converge (despite the definition of a pair of parallel lines is that they don't do that!) and a myriad of other oddities.

In reality the stories told in this book are not as striking as those of Flatland. This is at least in part because as people in a three dimensional universe we understand almost instinctively the nature of that reality. That means we understand the original story more strongly than those strange worlds that this book talks of. But it is still a magnificent book, and the ideal thought provoker for those interested in geometry and maths.

[Anna · Rating 4 out of 5]

Το βιβλίο είναι εξαιρετικό και πολύ καλογραμμένο. Το θέμα είναι σε ποιον απευθύνεται: αναφέρεται στις διαστάσεις, το χώρο, το χρόνο, τις εναλλακτικές γεωμετρίες... Για να το καταλάβει κάποιος νομίζω ότι χρειάζεται σίγουρα να είναι τελειόφοιτος - στην αντίστοιχη κατεύθυνση - μιας σχολής που ασχολείται με τέτοιες σπουδές. Βέβαια θα μου πείτε οποισδήποτε άλλος γιατί να το διαβάσει;

[Becca · Rating 2 out of 5]

I almost didn't get through this. It starts off well, but then it turns into a dialogue. That would be fine, if not for the fact that the author periodically tries and fails to connect it back to the characters and the world of Flatland. Flatland the book is a political satire in addition to a scientific text; this book abandoned all but a shell of the politics while pretending it was still there. I would have rather had a book which didn't try to have a plot or characters, and did a better job at the science.

[Brian Clegg · Rating 3 out of 5]

Ian Stewart's Flatterland has been around since 2001, but I've only just come across it. It is, of course a sequel to the famous novella Flatland by Edwin Abbott Abbott dating back to 1884. The original Flatland is perhaps the archetype of a book that is based on a brilliant idea, but be distinctly dreary to read. So the key question here is whether Stewart escaped this limitation in his sequel.

We start here with the (literally, not metaphorically) two-dimensional characters familiar to anyone who has read Flatland. The original both explored the nature of existing in two dimensions (and how the inhabitants would see a three-dimensional object), and provided Victorian social commentary, with female Flatlanders both physically different to males (lines, rather than polygons) and limited in what they can do by society. Stewart only mentions the social side in passing, but instead focuses on mathematical experiences.

Guided by a space hopper (the 60s bouncy toy), the central character Victoria Line is taken out of Flatland to experience a wide range of different mathematical spaces. They start off with the conventional three-dimensional space Vicky's ancestor came across (the original book was supposedly written by A. Square, who Stewart tells us was Albert Square) but then go on to a whole range of different mathematical spaces, from fractal space to topological space, finishing off by straying into physics by bringing in Schrödinger's cat, Minkowski space and time travel via the special and general theories of relativity.

All the way through, Stewart seems to be trying to outdo Abbott's weak attempts at humour by piling on cultural references (we've seen a couple above) and resorting to often excruciating puns. This can be distinctly wearing for the reader, though there are occasional gems such as 'he was the black shape of the family'.

If you can cope with the barrage of irritating humour, some parts of the book work really well at introducing concepts such as topology - this section is based in part on the Mad Hatter's tea party in Alice's Adventures in Wonderland. In fact, Stewart clearly takes a significant lead from mathematician Lewis Carroll's approach, though unfortunately lacks Carroll's peak writing skills. This is more Sylvie and Bruno than Alice or Snark. Other parts of the book, though, fail to get the message across. We are dealing here with quite abstruse mathematical concepts and while the portrayal through various characters and their worlds make good use of those concepts in you already know them, they don't act as a useful introduction, leaving the reader potentially baffled.

Like the original Flatland, this is an interesting and innovative attempt. It has always seemed that fiction should be a good route to explain science or maths painlessly and entertainingly. But for me, the painful punning and the relentless jokiness was too much, while the exposition was often not clear enough to do the job. A for effort, though.

[MTK · Rating 3 out of 5]

Η "συνέχεια" του "Flatland", μιας βικτοριανής νουβέλας με μαθηματικό περιεχόμενο. Το αρχικό βιβλίο ήταν εξαιρετικό, αλλά βοηθούσε το μικρό του μέγεθος και οι πιο απλές μαθηματικές έννοιες με τις οποίες καταπιανόταν. Η συνέχεια είναι αρκετά κουραστική στην ανάγνωση και προσωπικά κάπου με έχασε (ομολογώ ότι δεν έχω ιδιαίτερη σχέση με τις θετικές επιστήμες).

[Kenneth Sutherland · Rating 3 out of 5]

the math part is really good and the narrative part is really not

[Maurizio Codogno · Rating 3 out of 5]

Non so quanti di voi abbiano letto Flatland, il testo scritto da Edwin Abbott alla fine del XIX secolo che con la scusa di raccontare la storia di una figura bidimensionale che scopre le meraviglie del mondo a tre dimensioni fa una feroce satira dell'epoca vittoriana. Ian Stewart riprende l'idea e la espande, per così dire, tanto che persino il titolo del libro è un comparativo: "Flatterland" significa letteralmente "terra più piatta". Stewart non è interessato tanto alla satira sociale, anche se ne lascia qualcosina, quanto alla divulgazione matematico-fisica, arrivando anche alla spiegazione del Big Bang e alla teoria delle stringhe e della supersimmetria. La parte divulgativa è fatta indubbiamente bene ed è alla portata di tutti; bisogna però che il lettore apprezzi lo stile umoristico di Stewart che alla lunga può risultare stucchevole, visto che è sempre alla caccia del bieco gioco di parole. A questo riguardo, onore al merito di Filippo Demonte-Barbera per la sua perfetta traduzione in italiano: nella prefazione spiega anche alcune delle scelte da lui fatte, permettendo al lettore di vedere anche l'originale inglese. Il libro termina con una postfazione di Michele Emmer, che colloca Flatterlandia (e Flatlandia) nel contesto storico e visivo di quello che è capitato negli ultimi centoventi anni.

[Koen Crolla · Rating 3 out of 5]

Stewart is far too pleased with his own jokes and can't write dialogue for shit, even allowing for the limits the subject matter places on the narrative. That narrative often obscures that subject matter unnecessarily, as well; if I hadn't already been familiar with pretty much everything covered, I doubt I would have had the patience to tease meaning from his prose.
If you have more patience than I do, though, I guess Flatterland is a fine enough introduction to non-Euclidian geometries, the various meanings of ``dimension'', and their applications to modern physics, if not feminism. If you enjoyed Flatland, you'll probably enjoy this sequel, at least, and that's a nice (and rare) feature for a sequel — especially a third-party sequel — to have.

[Roberto Rigolin F Lopes · Rating 5 out of 5]

We are in 2008, Ian just invited a citizen from flatland to visit some other geometries. Her name is Vikki. You probably met her at Flatland by Edwin A. Abbott (1884). If not, here goes a summary. Vikki is just like us. Minus one dimension. She is a line with a flat-intellect full of flat-prejudices. See the similarity with us? You are about to read her intellectual adventure setting her FREE within the mathematical universe. Ian shows off his erudition updating Vikki on the various mathematical discoveries, say non-Euclidean geometries, that happened after 1884. Mathematics also supports all the recent developments in Physics, say Relativity and Quantum Mechanics. So Vikki also got puzzled within the new abstractions that the scientists are using to understand nature. Takeaway message: it is important to understand our universe as it is, and not just as you imagine it to be.

[Paulo · Rating 4 out of 5]

In 1884 Edwin Abbott Abbott wrote an awesome classic of scientific divultation called Flatland: A Romance of Many Dimensions. This Flatterland is a derivative work from that. The original had a second purpose, to satirize the rigid social structure of Victorian England, with its hierarchies of status and privilege. Stewart doesn't deepen this, though he deals a bit with the status accorded to women and their emancipation in a male-oriented society.

The main character is young Vikki, Albert's great-great-granddaughter, being this Albert the protagonist in Flatland. She finds out about his book and later inprisonment, and so "calls" an entity named The Space Hopper. He is able to hop between differents spaces, and provider her with a VUE (Virtual Unreality Engine), an object which allows her to visualize the most abstract mathematical concepts.

The action occurs in 2099 (Flatand calendar), a century later of the events related in Flatland. The book is written in form a diary, with Vikki constantly addresing to her Diary to explain everything he is learning. Nevertheless, the story is a pretext to offer a serious mathematical divulgation, the true objective of the book. Stewart aims at the ideas and concepts of dimension, space and geometry.

Among others, in the book the author explains us the basics about fractals, topology, projective geometry. plane Euclidean, 3D Euclidean, nD Euclidean, transformations or hyperbolic geometry. Besides, the last chapters are devoted to physics, bury us in the nature of space, time an matter through topics like relativity, black holes or the Doppler effect.

Within all that scientific divulgation, I specially liked the IMAGER, the way to experience the so called Mathiverse: Imagination, Mathematics, Analogy, Generalization, Extrapolation and Recursion. Besides, there isn't a single formula in this book, only word explanations of all the concepts and ideas.

Stewart uses frequently in his writing a lot of puns, for example naming squarrel to a squared squirrel or quoting "2c or not 2c, that is the question"... being 'c' the speed of light.

[Deleted Account · Rating 4 out of 5]

"ويبقى الرعاع البؤساء من المثلثات متساوية الساقين لا تنتظمهم خطة ولا يتقدمهم زعيم، فإما يكون مصيرهم السقوط دون مقاومة، أمام فرقة من إخوانهم يحتفظ بها الكاهن الأكبر لمواجهة الأزمات المشابهة، أو ينتهي بهم الأمر إلى الانهيار الداخلي بفعل الأحقاد و الشكوك التي تتفنن جماعة الكهنة في إثارتها بين صفوفهم، فيقتتلون فيما بينهم ويهلكون أنفسهم بأيديهم. يسجل تاريخنا ما لا يقل عن مائة وعشرين محاولة للتمرد إلى جانب الإنتفاضات الصغرة التي يصل عددها إلى مائتين وخمسة وثلاثين، وقد آلت كلها إلى نفس المصير."

قمع فتنة الألوان.
"الآن لم يعد للون وجود في بقية أنحاء الأرض المسطحة، و لم يعد من بين الأحياء من يتقن فن صنعه إلا شخصاً واحداً هو الكاهن الأكبر، في كل عصر من العصور وليس له أن يبوح بسره إلا ساعة إحتضاره، ولايبوح به إلا لخليفته في منصبه ولا يعمل في إنتاج الألوان إلا مصنع واحد، وكل عام يعدمون العمال و يستبدلون بهم عمالاً جدداً، خشية أن يقوم أحدهم بإفشاء السر، و حتى هذه الأيام لم يزل الأرستقراطيون عندنا يرتعدون فرقاً وهم يستعيدون ذكرى تلك الأيام السحيقة لثورة المشروع العالمي لقانون الألوان."

رائعة هذه الرواية وذكيّة جداً! انصح من يحبون الفلسفة العميقة بقراءتها!!

لا احب إعادة قراءة كتب قرأتها مسبقاً، ولكن هذه الرواية بالذات ستكون الكتاب الأول الذي اضعه في رف الكتب التي تحتاج الى إعادة قراءتها.. لازالت قد تعطيني المزيد.

[David · Rating 4 out of 5]

The shapes got crazier

[Lilli Feldeborn · Rating 2 out of 5]

dnf at 47%, decided i do not want to drag myself through the whole second half, could use my time wiser than that

[Nathan Albright · Rating 3 out of 5]

This is why we can't have any nice things.  This book is a sign of why it is that our times are not nearly as good as the late Victorian period.  For all its flaws, the Late Victorian era did have virtues that we do not possess, and this book demonstrates how one can take a book that was a classic and turn it into one of those virtue signalling tedious bores that flops and leaves people to blame the public for not approving of the travesty that is inflicted upon originals.  Flatland was a subtle work written to lightly criticize the norms of the time, especially as they involved the treatment of women, by placing them in the mouth of someone who was both sympathetic as well as somewhat uninformed, thus placing the reader in a privileged position that could subtly overcome some of the prejudice that the reader might possess.  This book does not have any of that subtlety, and it suffers dramatically for that lack, leading to a book that is but a pale imitation of what it copies, and a work that the author is likely to think of far more fondly than the reader, unless the reader is of the same mind as the writer.

This book is set a century after Flatland when Victoria Line finds the diary of her ancestor and is intrigued by the thought of a third dimension beyond the two of her world.  She is, of course, one of those bratty young people who assumes that they know more than their parents and one of this book's chief failings is that it reinforces that prejudice with a plot that involves her calling a being to visit her and visiting all kinds of dimensions with strange people with strange habits who teach Victoria new ways of looking at the world and also attempt in a clumsy way to teach these aspects of mathematics to the reader as well.  This includes nonwhole dimensions, time travel, topology, and even the geometry of snowflakes.  Some of the characters are agreeable enough but the main fault of the book is that the reader is saddled with Victoria as the stand-in for the audience and this makes for a lot of whining and complaining and plotting and general frustration given the fact that she is nowhere as gracious a figure as her much-maligned ancestor.  That said, there is at least some worthwhile math discussed here so it is not a complete loss.

In many ways this book is an attempt to continue the original work in a new generation, but it suffers dramatically compared to the original.  One of the areas where Flatterland suffers is with regards to the lack of sympathy that the reader is going to have with a privileged, bratty, leftist activist of a character.  Where A. Square came off as humble and confused and worthy of our sympathies, especially once he was arrested, his reputed descendant here is an insufferable know-it-all who does not receive her just deserts for the treason that she plots against her own world.  And where the original author was restrained his attempt to force down math onto his reader, this book is unrestrained in its idolotry of theoretical mathematicians, to the point where the book can be somewhat tiresome in that regard as well.   In nearly every area it falls short of its model, in that the mathematical explanations are more intrusive, the general approach is more heavy-handed and less subtle, and the characters are far less likable.  If the book is still an acceptable read it is because the model chosen for it was a good one.

[Bruce · Rating 2 out of 5]

I should perhaps be clear at the outset. This is not a review of Edwin Abbott's Flatland. That book's terrific, a fine, fun satire of Victorian gender and class politics atop an exposition of multidimensionality so brilliantly done that Carl Sagan himself borrowed it verbatim for use in Cosmos. Five stars for an eternally entertaining classic.

No, here I am reviewing Ian Stewart's annotations to Abbott's work, as well as his attempted follow-up Flatterland, both of which were... disappointing. To identify fodder for annotation, Stewart follows the guidance laid out by mathemagician Martin Gardner. Gardner's suggestion is to write about whatever strikes the annotator's fancy and then keep whatever he thinks will entertain. That's fine, but unlike those of his mentor, Stewart's annotations are mostly failures of editing, editorializing, and entertainment. By beginning with an explanatory preface he commits the cardinal sin of serial repetition, sometimes using the same copy. So frequently does he inflict redundant passages in the early going, he shakes faith in the value of his future digressions. In this tiresome way, Stewart is thorough to a fault in documenting every one of Abbott's Fourth Dimension-contemplating contemporaries, so it's startling that he cannot yet deliver a clear chronology of who met whom and wrote what when. Even Stewart's extrapolations from Abbott can come across as unclear and insufficiently illustrated, thereby losing whatever mathematical point Stewart intended to make (see, e.g., illustrations at pages 118 [Euclid's pons asinorum diagram], 130 [dimensional scaling of a unit line to that of a unit cube to make it "three times as large"], and 179 [polytopes], to name a few).

Stewart is a mathematician by trade, so his admiration of Abbott is understandable. His sequel Flatterland, then, was well-intentioned homage. The idea was to revisit and update the world of Flatland as a means of exploring -- well, explaining -- other geometries to a lay audience. The tone is not an issue: Stewart is a devotee of wordplay whose prose comes across as an amusing mashup of Lewis Carroll and Douglas Hofstadter with a smidge of Norton Juster thrown in for good measure. In fact, there are passages here -- the Topologist's Tea Party, the projective plain with its sociably-meeting parallel lions, and the grape theory accounting that transpires in the wine bar of Running Turtle, a bar which serves wines like Chordonnay, Modulot, Quadrati, Rhombolo, Bouzo and hogsburgers made of ground oxagon, among a myriad of other puns -- that nod to each of these authors. Stewart's execution is rather the problem.

In borrowing Abbott's parable universe, Stewart's creates Albert Square's granddaughter Victoria Line to serve as an audience surrogate. So far, so good. Vikki is a rebellious, teenaged diarist launched from the 1960s on a tour of the Mathiverse thanks to her friend and guide the Space Hopper (a pun on an eponymous British children's toy, sort of a free-range, orange, elastic hobby horse). (Why the 1960s? Who knows?)

Unlike Abbott, who had a serious satirical purpose to pursue, Stewart's story (such as it is) is unengaging, unenlightening, and wholly unnecessary to his primary purpose. He could still have paid tribute to Flatland and written a better book had he simply chosen to abandon the fictional frame. Vikki's a great character, and she's even given a semi-serious purpose (Flatland women's emancipation), but it's an afterthought at best, a bookend at worst, and one that Stewart seems to have little interest in telling. Even Stewart initially has trouble sticking with the conceit, conflating his voice with Vikki's on occasion, with at least one of Vikki's diary entries referring inconsistently to her mother by name rather than as 'Mom,' and later breaking the fourth wall via direct address of the reader (see, e.g., at page 29, during his definition of what constitutes the Mathiverse). Given this, it comes as more of a nuisance than a matter of interest when Stewart chooses to break up the flow of his Mathiverse explorations by telling us that Vikki is experiencing pangs of homesickness or that the Squares back home are telling their other children awkward lies about Vikki's hasty departure to Numerica. None of these brief diversions serve any point or lead anywhere storywise.

Making matters worse is the book's apparent structural incoherence, although perhaps the author's topical selection would make better sense to someone with a deeper mathematical foundation than I have. Stewart starts off logically enough, traveling initially from Euclidian spaces of different dimensions to non-Euclidian ones (including fractals, topology, and the projective plane). From there, he digresses to whatever grape theory is before questioning the meaning of geometry itself; retreats back into nonEuclidian, hyperbolic, curved space; and bridges the two halves of his book with a discursive examination of symmetry. From there he pivots squarely to theories on the nature of spacetime itself as anticipated by relativity, quantum mechanics, and the behavior of subatomic particles, much of which I failed fully to follow and the whole of which felt like a sharp left turn from the pure mathematical abstractions that preceded them.

Given his tone, gloss, and choice of protagonist, Stewart's intended audience seems to be high schoolers. Certainly his frequent, futile forays into fiction as much as his all-too-brief explanations of complex ideas served to thoroughly flummox this adult. So Stewart's Flatland-inspired works leave me flat. Perhaps a reader with better mathematical intuition might get more mileage out of them. I'd love to hear from those readers. For everyone else interested in mathematical curiosities, my suggestion would be to stick with Martin Gardner.

[Laurie · Rating 5 out of 5]

Absolutely lovely book.
I learned so much at the time.
Don't know what was retained, though.

Amazon.com Review
In 1884, an amiably eccentric clergyman and literary scholar named Edwin Abbott Abbott published an odd philosophical novel called Flatland, in which he explored such things as four-dimensional mathematics and gently satirized some of the orthodoxies of his time. The book went on to be a bestseller in Victorian England, and it has remained in print ever since.
With Flatterland, Ian Stewart, an amiable professor of mathematics at the University of Warwick, updates the science of Flatland, adding literally countless dimensions to Abbott's scheme of things ("Your world has not just four dimensions," one of his characters proclaims, "but five, fifty, a million, or even an infinity of them! And none of them need be time. Space of a hundred and one dimensions is just as real as a space of three dimensions"). Along his fictional path, Stewart touches on Feynman diagrams, superstring theory, time travel, quantum mechanics, and black holes, among many other topics. And, in Abbott's spirit, Stewart pokes fun at our own assumptions, including our quest for a Theory of Everything.

You can't help but be charmed by a book with characters named Superpaws, the Hawk King, the Projective Lion, and the Space Hopper and dotted with doggerel such as "You ain't nothin' but a hadron / nucleifyin' all the time" and "I can't get no / more momentum." And, best of all, you can learn a thing or two about modern mathematics while being roundly entertained. That's no small accomplishment, and one for which Stewart deserves applause.

[Zana · Rating 3 out of 5]

I used Flatland and the first few chapters of this book when I taught Calculus. :)

The first half of this book was 4 stars, no question. About the time it got into the theory of general relativity, it started zipping along way too fast and lost the storyline. The fun mathematical playfulness turned into an infodump with reeeeeallly bad math jokes. Really, really bad math jokes. Indescribably bad math jokes.

That said, I loved the first half. The book suffered for having been written almost 12 years ago, and some of the science and a little of the math has changed since then. I'd love to see this updated...

Let's be honest, some of the second half didn't work for me because I was 1) reading it while waiting in the park for a date to show up and being progressively annoyed when he didn't and 2) reading it on the Metro as it inched along because there'd been an earthquake and I *needed* to be home by 10:30 and surely an hour and a half was enough to go 7 measely stops?? So I was a bit distracted

[Morgan · Rating 4 out of 5]

Based off of the Book "Flatland" written by Edward A. Abbott, one of my all-time favorites, i stumbled upon this book scavenging the library. Curious, i checked it out and began to read. The main character, Victoria Line, is the great great granddaughter of the main character of the original book, Albert Square. A main difference between the two books is the obvious time-periods in which the books were written. "Flatland" was written in 1884 and the language was often difficult, but this book, having been publish in 2001, is much easier to read. It also uses many modern theories of multidimensional space only recently thought about and makes references to things such as the "Interline" (internet). Flatland was more of a reference to the era - the way people were treated and the basics of society/monarchy. Flatterland reserves much of this, but allows some progression to be shown, although not to the point where the different people are treated as equally as today.

[ivan · Rating 3 out of 5]

I have mixed feelings about this book. Although I love the idea — a sequel to the classic Flatland: A Romance of Many Dimensions that explores additional dimensions, higher math, and fundamental physics (of classical, quantum, and string theory varieties) — the narrative is kind of wobbly. The blurb on the back compares it to the wonderful The Phantom Tollbooth, but that book had a clear, compelling story with a relatable protagonist. Yes, along the way Milo experienced strange (mathy) things, but only in the context of an engaging story.

Flatterland's story is frankly clumsy, accommodating new or unusual theories in math and physics with utterly incomprehensible plots. And perhaps most troublingly, these narratives often make the concepts harder to understand, rather than easier. For instance, the theory of Schrödinger's Cat is not that hard to explain; it's honestly considerably easier than meeting a multiphasic cat in a subatomic wonderland in which a talking electron explains wave-functions and (poorly) illustrates Young's double-slit experiment with light.

I actually think, as overwhelming as the technical ideas are, a book like Brian Greene's The Elegant Universe makes ideas like light cones, wormholes, and membranes in string theory more comprehensible. At least then, if you're confused, it's with the concepts themselves — not by a Cockney heptagon or a strangely surly Stephen Hawking anthropomorphism.

The other complication is that for narrative reasons, the protagonist is a descendant of the original character in Flatland. In the original book, the creature from two-dimensional space worked because it illustrated (fallacious) believes about our own visible universe by entering from the "outside." In Flatterland, the 2D character is now given the task of being our stand-in to learn things, generally entirely invisible and counterintuitive, about higher dimensions, galactic distances and time scales, and Planck-length physics. Thus one has to take "Victoria Line's" encounter, filter it first through her 2D home-understanding, and then into our own more common viewpoint. This creates constant additional mental labor in trying to untangle the pieces Victoria is trying to understand because of her background alone, and the pieces that are understandably hard for us to visualize as well. A bizarre, clumsily-animated children's toy was for some reason chosen as Victoria's (and thus our) Virgil through multiple dimensions, who puts forth a kind of clockwork enthusiasm — but a Richard Feynman lecture this is not.

The final narrative "twist" — really the only feint toward an actual storyline's normal conventions — is a nice bit of satisfaction that hints back to Edwin A Abbott's secondary goal of criticizing Victorian society's rigid classes and misogyny. But it's really not enough.

Just go read popular science. Feynman, Hawking, Michio Kaku, Neil deGrasse Tyson, or Greene. (Yes, even if you're twelve.) Or read The Phantom Tollbooth!

[Phoenix · Rating 5 out of 5]

Warm and Fuzzy Mathematical Sequel

It certainly helps to have read and enjoyed the original Flatland by Edwin Abbot. This book written over a century later continues by following the adventures of Victoria Line, the grand-daughter of Flatland's A. Square, who proves to have greater depth than first imagined. Finding her grandfather's diaries she attempts to invoke and invitation to the Sphere he once met, but instead reaches higher and finds herself face to surface with the multi-dimensional "Space Hopper".

What follows is a series of pun filled excursions to different mathematical worlds which in turn are compared to our own existence on "Planeturth". Together with our intrepid duo we get to visit a Fractal Forest, grab a taxi on a Cartesian grid (Quadratic City) and experience life on a Platterverse where objects shrink as you get closer to the edge, so that a whereas to an outsider the universe if finite, it appears to be be infinite to someone inside. And while the discussions of curved space may be a bit counter-intuitive at first, they are quite understandable if you can let go of preconceived notions.

Sequels are not usually as good as the original but Ian Stewart has a gift both for narrative and for explaining ideas. There have been other attempts - Burger's Sphereland: A Fantasy about Curved Spaces and an Expanding Universe, Ruddy Rucker's Spaceland, and A. K. Dewdney's The Planiverse: Computer Contact with a Two-Dimensional World none of which I found were as clear or as entertaining. This one succeeds, and has the additional subtext that girls not only CAN do math, but that it is an enjoyable experience. I've read this book to each of my children when they were just preteen before going to bed, though it is probably a requirement that you have the background and affinity for the subject in order to discuss the ideas. A bright 11 or 12 year old with an aptitude for math or physics would enjoy it too.

I've grown quite fond of the book and it is definitely a keeper.

[Heather · Rating 3 out of 5]

I read this book because it was a follow-up to my beloved Flatland. Unfortunately, I ended up wishing Ian Stewart had just written his own book and not tried to attach it to that delightful and mind-expanding little volume.

Stewart is endlessly inventive in his puns and clever characters, and he obviously has a deep understanding of the the complex geometries and quantum theories he is laying out. Yet somehow, it all just doesn't work as one would wish.

Perhaps he tries to take on too much or to add too many levels to the narrative. I certainly could never figure out why he periodically dropped in diary entries written by the main character, when the information contained therein could have been handled in dialogue.

And whereas Abbott in the original volume could awaken our minds and imaginations precisely because the idea of higher dimensions is simple, even while outlandish, Stewart presents so many baffling possibilities that it is hard for the reader to imagine any of them actually being reality. The attempt to echo Abbott's social critique was also painful and unnecessary. Flatterland essentially ends on a note of Feminist triumph.

I give the book three stars because it is not terribly written and because it does make a valiant effort to explain complex concepts. However, I would not recommend it to others.

[Ashley Lambert-Maberly · Rating 2 out of 5]

Not fun to read (and I absolutely adored Flatland). In fact, when I came to assign a genre category, I was flummoxed ... ostensibly SF (or fantasy), in that Flatland doesn't exist, but since the frame story is so obviously a pretext for a lecture on math, I ended up labelling it non-fiction science, essentially. And if I want non-fiction science, I'll read non-fiction science, thank you very much.

Here's an analogy (Stewart likes those, he wrote a whole book about them, in a way): this book reminds me of the time I was four years old, and my father, frustrated with my stubborn refusal to eat green beans, took away my plate and stuffed the beans in a chocolate cake and served me the cake. I eagerly bit into it, encountered beans, and threw up. Beans are beans and cake is cake and the two don't mix well.

So I have stopped reading this, and moved on to Wait Till Helen Comes which is completely different but entirely cake.

Note: I have written a novel (not yet published), so now I will suffer pangs of guilt every time I offer less than five stars. In my subjective opinion, the stars suggest:

(5* = one of my all-time favourites, 4* = really enjoyed it, 3* = readable but not thrilling, 2* = actually disappointing, and 1* = hated it. As a statistician I know most books are 3s, but I am biased in my selection and end up mostly with 4s, thank goodness.)

[Valerie Madsen · Rating 3 out of 5]

I absolutely loved the beginning of this book, and it had my mind in a slightly obsessive state for a bit (in a good way). The author is clever and has great humor. I liked the characters, and the pacing starts off great.

However, around mid-way through the book I began to struggle because the examples were drawing out far too long. Concepts, which I felt, could have been maybe 2-3 pages were drawing out for 5, 7, sometimes 10 pages and much of that being filler conversations between the main character and side characters. Unnecessary chit-chat which didn't expand the story or the concepts of Flatland.

For example, there are many conversations that go something like this:
"I don't understand," said Vikki, and so the fox explained the concept to Vikki [interesting to read explanation].
"Oh, I see, that makes a lot of sense," said Vikki.
"I knew it would if you put your mind to it," said the fox.
"So it did!" said Vikki.
"Surely it would, with the right explanation," said the fox.
"Right!" said Vikki.

It's still a fun book, though I couldn't finish it and made it only a bit over halfway because of the complaint I've expressed.

[Brian · Rating 2 out of 5]

Flatterland is a follow on to Flatland by Edwin Abbott. Flatland involves a two-dimensional world in which a three-dimensional creature discusses dimensionality with a two-dimensional creature. Flatterland involves the same situation, but in this case, the three-dimensional creature also teaches his two-dimensional student about higher dimensions and other higher mathematical concepts as well as physics. I enjoyed much of it, but the conceit of the archaic language and mannerisms detracted from the exposition. In addition, the section on physics didn't work as well as the mathematical section. I'm sure the fact that I have a physics degree might influence my disappointment. The simpler concepts were explained in simplified terms that did not do them justice, and explanations of more advanced concepts were even worse. Frankly, I was disappointed.

[Christopher Folts · Rating 3 out of 5]

I consider myself to have an above-average understanding of mathematics and physics, and I found this tedious and, at times, challenging.

This mostly is the result of the twee, hokey adaptation of a Victorian-era story that many modern readers (myself included) would find particular dull. It's also result of the choice of medium: higher-dimensional geometry is not surprisingly difficult to discuss and explain with words and 2D greyscale illustrations.

Having said that, Brian Greene has skillfully accomplished a more comprehensive and satisfying discussion of higher dimensions, quantum theory, multiverses, superposition, string theory, and more in his books (The Elegant Universe, etc). So maybe I'll just say read those instead.

[J. Jobe · Rating 5 out of 5]

Fun, Informative, Playful, Educational

This feels like the kind of book I could read aloud to a child. It has the same level of word play as Phantom Tollbooth and the same level of absurdity as (and many references to) Alice in Wonderland. And despite or perhaps because of all the silliness, I still feel I’ve learned so much about mathematical concepts. It was not the same experience as reading Flatland, but I got over that and experienced it for what it was, and enjoyed it very much.