Flatterland

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.

Comments

Flatland is social sattire

[divec]

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, thanks to Project Gutenberg.

For more Flatland antics...

[nicky_d]

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.

Nits too big to ignore

[VSarkiss]

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.

See also:

[mblase]

• Sphereland: A Continuing Speculation On An Expanding Universe
• Alice in Quantumland: An Allegory of Quantum Physics

Flatland online

[SCHecklerX]

http://www.geom.umn.edu/~banchoff/Flatland/