Flatlanders and The Planiverse

Darius Clarke darius at inglang.com
Tue Feb 25 09:58:20 PST 2003


I read "The Planiverse" when I attended university (UC Irvine)… had found it in 
our university library. 

"The Planiverse" is well written and thought provoking. It’s a morality play as 
well as a treatise about how physics, biology, & society could work when one of 
our most common assumptions (a third dimension) is removed. His premises and 
explanations are smoothly woven into the narrative. The narrative maintains a 
good dose of humor.

The book’s best use is to teach how one can extrapolate many interrelated 
implications from an unfamiliar set of rules in a closed system. I’d say that 
the target age group for such reasoning would not be any younger than 14 years 

Some major points in the book:

•	Just as miracles in our world could be explained by a multi-dimensional 
intelligence manipulating multi-dimensional objects through a three-dimensional 
world; so to, three-dimensional people like us, if we could interact with a 
two-dimensional world, could appear to perform miracles in that world.

•	The seeming omnipotent power of such control could lead to moral dilemmas.

•	The time needed for a physical change (chemical, perception, information) 
is a function of surface area, which is *drastically* reduced in a two 
dimensional world. Consequently a 2D object requires a vastly larger size to 
increase its surface area to the point where meaningful interactions can take 

•	Even with the increased size, the number of parallel events that can occur 
in 2D is restricted. Most interactions must be performed in a linear time 

"In terms of eToys in Squeakland":

•	eToys & Morphs are layered 2D objects which imply: 1) a (very limited) 
third-dimension, and 2) The 2D objects are observed by someone positioned 
orthogonal to the 2D objects so that their inside contents can be perceived 
(like papers on a desktop, surprise, surprise). [I’m still looking for a tool 
that fulfills the paperweight metaphor for my desktop metaphor. ;-) ]

•	One could simulate the "Planiverse" in eToys but most of the functionality 
of the Morphs would not help. A new set of rules and a new set of 2D "physics" 
would need to be created by hand. This would need to include the dynamic 
distortion of a 2D object’s shape per the influences on it. Many changes in 
shape are required to replace what equates to the change of position in a 3D 

•	"Planiverse" requires gravity while Abbot's "Flatland" resembles a world 
seen in a microscope slide. "Flatland" might be easier to simulate in eToys. In 
"Planiverse" gravity must replace structure for holding most 2D objects 



-----Original Message-----

From: owner-squeakland at squeakland.org [mailto:owner-squeakland at squeakland.org] 
On Behalf Of Sebastian Hergott

Sent: Monday, February 24, 2003 09:38 PM

To: squeakland at squeakland.org

Subject: Flatlanders and The Planiverse

In terms of eToys in SqueakLAND, has anyone read this book? thoughts?

The Planiverse. Computer Contact with a Two-Dimensional World

Author(s):	A. K. Dewdney

Publisher:	Springer

ISBN: 	0387989161

Format:	softback


Price:	£15.00, $22.00

Review Date:	March 23, 2001

Review:	This book, first published 16 years ago, follows in the genre of 
Edward Abbot's nineteenth century classic Flatland. The story is written in the 
style of an academic - in the computer lab of a large university a group of 
students and their

professor are working on mainframe, modelling an imaginary two-dimensional 
world. Suddenly one student notices that the world that they are building with 
their graphics program is inhabited! They are soon entranced by a universe in 
which astonishing tiny

creatures, 2-D Ardeans, exist solely on an x-y plane. This mental puzzle invites 
the reader to imagine how a two-dimensional world might work.. An appendix 
includes readers' contributions made to Scientific American , following an 
article about the 2-D

universe, from the viewpoints of physics, chemistry, planetary science, biology, 
astronomy and technology.

Source: http://www.booknews.co.uk/Books/1806.htm

The more I discuss Squeak with folks, the richer I become. Thanks to C. Matthews 
for this.


Sebastian Hergott

Teacher/Intermediate Program Coordinator - CyberARTS 

Arts and Information Technology Convener

ASA (Academic Services Associate)

Don Mills Middle School, tel. 395-2320

17 The Donway East, Don Mills, Ontario, M3C 1X6, Canada

sebastian.hergott at tel.tdsb.on.ca

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