In this modern take on the "Flatland" theme, some academics
investigate the virtual twodimensional world they have created inside
a computer. The sophisticated simulation includes sentient beings,
one of whom is able to communicate with the human investigators.
Though there is a somewhat mathematical flavor to the book, I would
have prefered an even more mathematical account. For instance,
the chapter in which we view the twodimensional shallow sea would
have been a marvelous opportunity to discuss KdV solitons and
KelvinHelmholz instabilities!
Contributed by
anonymous
"I believe this is one of the best blends of Math and Imagination ever written. Very thoroughly researched. This world could exist, it's so detailed! (There is, I suppose, the population/ecosystem problem) This is also the only Math/Science book that has made me cry..." 
Contributed by
Nils Tycho
This book is probably my favorite work of math/science/computer fiction. It is also the only work on this I have taken the time to review.
If you read Flatland, and were critical of squares moving and talking, puzzled by strange hierachical orders based on symmetry and vertices, and wondered how a triangle was able to eat, breathe, thinkthen this book is for you. StartingOK, well it's in the appendixwith twodimentional atoms, working up to planetary physics and ecology, and even sketching out twodimentional neuroscience, Dewdney thoroughly explains in real terms how the world of Yndred and his friends might function.
With a remarkably small amount of willing suspension of disbelief2D brains would not be complex enough for consciousness, the inversesquare law of gravitation might not be compatible with 2D planetary systems, etcDewdney explains the world that Abbot discovered.
For the record, it is also one of the very few books that made me cry. For many people, this confirmes my nerdstatus.
N.B. Although this book is built on mathematical concepts, it is more
science and technology oriented. For this reason, I was forced to give it
a 3 rating on "Math."

Contributed by
Robert Munafo
I have that book, the original version (published in 1984, ISBN 0671463632). I designed the clock shown in the appendix (page 260 in my edition, probably somewhere around 238 in the 2000 edition, assuming they didn't edit for content)
Although it didn't make me cry I do give it a very high rating for attention to detail and believability, also it has the necessary items of plot complexity, characters you believe and sympathize with, and so on. (Literary quality: 4 for 5)

Contributed by
anonymous
This wasn't fiction was it? Yendred lives!
In subgenre of works featuring two dimensional universes, this is by far the most compelling and informative, describing the implications of dimension on weather, biology, engineering, physics etc, indirectly giving more insight into our own threedimensional universe.

