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The Planiverse: Computer Contact with a Two-Dimensional World

A.K. Dewdney
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The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition.

[Reviewed by
Geoffrey D. Dietz
, on
The Planiverse by A.K. Dewdney, is not new as it was originally published in 1984, and this review is being written in 2019. The primary concept, a tale about life in a two-dimensional world, is also not new as E.A. Abbott wrote Flatland a century earlier. However,  The Planiverse accomplishes something impressive and unique that the other literary descendants of Flatland do not. Whereas Flatland was written as a satire of English class culture of the time with residents that are simple polygons, The Planiverse sets out to build a scientifically, technologically, and culturally realistic world that might have evolved naturally when restricted to a plane.  
The Planiverse is essentially a science fiction story about a group of computer science students and their faculty mentor who make contact with a two-dimensional universe via a mysterious computer connection forged while building a simulated two-dimensional world in the lab. The connection allows the lab team to meet and communicate with a sentient creature named Yendred who lives on a circular planet in a flat universe. Unlike Flatland, which has length and width but no height, Yendred lives in a world with width and height but no depth. The lab team is able to view Yendred and his world on a computer screen allowing them  a view from the outside resembling a cross-sectional cut of our world. As such the team can see the internals of all creatures, structures, and devices in Yendred's world, a fact that is a bit disconcerting to Yendred. As the book contains many highly-detailed illustrations, the reader is able to see many of these things as well as hear about them.
The primary story in the book follows Yendred as he journeys across his country on a search for meaning and enlightenment. Given this lengthy journey we learn a lot about Yendred's physical world and culture. When your entire country is laid out on the edge of a circle, you eventually must pass everything in order to make such a journey. This linearity gives Dewdney plausible excuses for Yendred to visit a scientific institute, an art studio, the center of government, a sporting event, and an orchestral concert. In the course of Yendred's trip, he runs into various problems and complications culminating in a rather mysterious conclusion that may leave the reader wishing for more knowledge about the ultimate fate of Yendred. 
Dewdney also weaves in some drama taking place in our world. The lab team struggles with whether they should keep the discovery of this new universe a secret or not and whether the whole thing is ``real" or just a computer hoax being played on them. There are also some ethical dilemmas that arise about how much they should interfere in the life of Yendred and whether the team's three-dimensional knowledge is helping or hurting Yendred throughout his journey. The plot alone sets up The Planiverse as a creative adventure story with a science fiction setting.
Beyond the plot, however, the real star is the planiverse itself. The level of thought Dewdney put into the design of his flat universe left an impression on me that has lasted almost thirty years since I first read the book as a kid. For example, Yendred has four arms, two on each side allowing him to handle objects on the left and right as he cannot turn around. He also has a symmetric head that can pivot to direct his attention to the left or right as needed. Dewdney also illustrates and describes a system of internal organs that can zip and unzip to allow the passage of fluids. When Yendred hears that his three-dimensional friends are filled with systems of tubes, he asks, ``Why do you not then fall into two pieces?" Yendred eventually discusses how his various biological systems function in his world, including nervous, digestive, and reproductive systems. 
We also learn about how Yendred's people build mostly underground (to prevent walls being insurmountable obstacles to travel), rely on batteries for power (as long loops of cabling would trap or suffocate people), rely on glue for assembly (as nails and screws are useless or impossible), build boats with only a mast but no sails, play sports, play music, write, print, and make art. Dewdney even thought out a system of etiquette for what two people do when they run into each other while traveling in opposite directions. Stepping ``aside" is not an option.
Plenty of scientific inserts exist throughout the book attempting to answer basic questions. In a two-dimensional world, which molecules are possible? What would a periodic table look like? How do air currents work? Why are many of the physical laws in our universe governed by inverse square laws while they would be governed by inverse linear laws in two dimensions? Is it possible to build a vehicle that uses wheels? If you are still curious beyond what the characters learn in the course of the story, Dewdney also wrote twenty pages of appendices going into even more detail about science and technology in the planiverse.
Some modern readers may find some defects in the book that have arisen with time passed. Younger readers may not be able to relate to monochrome monitors attached to terminals which are dependent upon large mainframes to function. Others may object to the fact that the lab team includes only one female member, who also happens to be the most outwardly emotional one on the team.  The flaws in the characters, I hope, can be overlooked as they are not central to the story. If you will pardon the intentional pun, the human characters are all rather flat while Yendred has the most depth. 
All told, The Planiverse stands out as a memorable book that falls somewhere between literature and a scholarly treatise about a hypothetical universe. I believe the book succeeds on both levels and will be entertaining and informative to readers of all ages with an inquisitive mind. (My twelve-year-old eagerly read the book in one day.) The Planiverse is a book that deserves to be more well known and read more often than has been the case in the thirty-five years since its publication.

Geoffrey Dietz is a Professor of Mathematics at Gannon University in Erie, PA. He is married and has six children.


Intro: 2DWorld.- Arde.- A House by the Sea.- On Fiddib Har.- Walking to Is Felblt.- City Below Ground.- The Trek.- The Punizlan Institute.- Traveling on the Wind.- High on Dahl Radam.- Drabk the Sharak of Okbra.- Higher Dimensions.- Appendix.- Acknowledgements.