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Flatterland
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.
If you are interested in this sort of stuff, look for books by Lillian Lieber. She wrote:
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
...richie - It is a good day to code.
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"
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.
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.
Expanding a vast wasteland since 1996.
perl -e 'fork||print for split//,"hahahaha"'
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.
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.
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.
Information wants to be anthropomorphized.
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".)
Information wants to be anthropomorphized.
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.
http://www.geom.umn.edu/~banchoff/Flatland/
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 .
CrazyLegs
"Pork!!" said the Fish, and we all laughed.
My .02,
My
Limekiller
I have a copy of Alice in Quantumland, and I can say without hyperbole that it should replace most high school freshman physics texts.
I'm the stranger...posting to
"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!
I'm the stranger...posting to