Conference noted::sf

  An old favorite is "And He Built A Crooked House..." by R. A. Heinlein.
  In this one, an architect in Southern California builds a house in the
  form of tesseract unfolded in three dimensions.  Architect and
  owners-to-be are inside when a temblor causes the house to fold itself
  back through the fourth dimension. 

  Rudy Rucker wrote a book called "White Light" that may or may not have
  been about other dimensions -- math deficiency prevented me from figuring
  it out...  But I enjoyed the book anyway.

  JP

    THE UNIVERSE BETWEEN by Alan E. Nourse
    
    --- jerry

    There was one really INTENSE book, absolutely MAGNIFICENT,
    stirring, funny, dripping with pathos and the human condition,
    in which a teenager (a really COOL kid, spunky and bright) goes
    searching for his lost uncle in the 4th dimension.  The description
    of the place was so clear you could almost SMELL it.  4D was essential
    infinite space filled with extruded lava cones that sprawled
    everywhere, populated with various modern and archaic earth life-forms
    of varying sizes.  Whoever designed that place really knew his science.
    
    The book is called "The 4D Funhouse", by some guys Emery and Wajenberg.
    It's still in print, $2.95 from TSR publishing.
    
    But you probably haven't read it.

    A long time back, I read a collection of stories that featured
    problems/themes in topology and multiple dimensions.  "Crooked House"
    was included in the collection.  Also a story about the New York
    subway folding into extra dimensions when the tunnel system got
    too complex, the uses of a Moebius strip in getting rid of an overly
    officious efficiency/safety officer, and a lot more.  I can't remember
    the title of the collection.  Anybody else out there remember?
    
    /D

    I, too, dimly recall at least one such collection.  I think it was
    called "Mathematical Fantasy."  The story about the subway was set
    in Boston and entitled "A Subway Called Moebius."
    
    This collection divided itself into parts with names like "Odd
    Numbers," "Irrationals,"  "Improper Fractions" (rude verses), and
    "Imaginary Numbers."
    
    Earl Wajenberg

Another dim memory is of a story by Eric Frank Russell (maybe), where 
a party of explorers go to a particularly dangerous area of the 
galaxy and discover a planet populated by giant 4D amoeba.  The creatures
could appear anywhere, first as a point, then as a growing sphere as 
more of their bodies intersected the 3D plane.  They eat several of 
the crew, and the others barely escape.  Title?  Collection?

/jlr

Try 'Mathenauts' a collection of short stories by Rudy Rucker.

Dave 8*)

Article: 215
From: [email protected] (Steve Brock)
Newsgroups: alt.books.reviews
Subject: Fourfield:  Computers, Art, and the 4th Dimension by Tony Robbin 
         (Computers/Art/Mathematics)
Date: 26 Aug 92 01:22:55 GMT
Sender: [email protected] (news)
Organization: Colorado SuperNet, Inc.
 
FOURFIELD:  COMPUTERS, ART, AND THE 4TH DIMENSION BY Tony Robbin. 
Bullfinch Press, 1271 Avenue of the Americas, N.Y., NY  10020. 
Illustrated, index, bibliography, notes, glossary, two appendices,
one pair of 3D glasses.  199 pp., $35.00
 
                             REVIEW
 
     Tony Robbin is frustrated with the restrictions of three
dimensions.  For the many years he has been painting in two
dimensions and sculpting in three dimensions, he has been musing on
how to break the fourth dimensional barrier.

     Using philosophy, mathematics, and most importantly, the
computer, Robbins has finally broken the barrier.  Others have
preceded him, but he has finally done it himself.  His four
dimensional designs and details of his quest are presented in
"Fourfield."

     Exposed to the pioneering work of the creation of polytopes (a
mathematically computed "solid shadow" of a four dimensional
object) by Thomas Banchoff at Brown University, Robbin initially
had nightmares out of H.P. Lovecraft stories - punching a hole into
a higher dimension and letting all its demons into the lower one.

     Robbin's work is with a pattern called a hypercube.  The
emphasis on this formation is that some parts of it remain
motionless while other parts change position.  

     This can readily be seen by looking at the enclosed 3D card
through the enclosed glasses.  Nine hypercubes are tesselated
(repeated in differing aspects), and as you move the card or your
head, the lines of the cubes toward the periphery (toward and away
from you and to the sides) move while the interior lines are
immobile.  The effect is amazing.  

     To demonstrate the effect, Banchoff and Charles Strauss have
made a film which shows the tesselated hypercube turning in upon
itself.  The farthest cell of the farthest hypercube expands and
shrinks, and a cross shape appears and disappears.

     "Fourfield" begins with an exploration of the use of space in
mathematics and art, concluding that neither the mathematician nor
the artist "is free to make progress in his or her respective
formalisms without the other.  Hidden in every newly discovered
equation is a new emotion...  Mathematicians must wait for artists
to make them ready for their discoveries, and artists must wait for
mathematicians to give them the means to make our experiences in
life sensible and acceptable to us."  

     The mathematician creates the equation, while the artist draws
its representation.  The difference between the two, with the help
of the computer, shrinks every day.

     Science-fiction has stayed ahead of mathematics and computer
science, Robbin says, in the cyberpunk and virtual reality worlds
of William Gibson, Bruce Sterling, and others.

     Robbin goes into much detail in describing the geometry of the
hypercube and its tessellation, then goes on to quasicrystals (a
combination of a fat and a skinny rhombus) which are nonrepeating
patterns, an apparent paradox.  

     Robbin the artist takes the computer-generated formations and
sculpts them.  "Fourfield" is packed with drawings and photographs
of hypercubes and quasicrystals.  One is a sundial.

     At the end of the book, Robbins includes a section of 24 color
and 17 black-and-white photographs that further illustrate the
conceptions.  The book also comes with an order form for disks
which contain the programs, including source code, discussed by
Robbin.  Incredibly, he asks for only $1.00.  This is less than the
cost of a blank disk!

     The idea of the fourth dimension is hard to grasp. 
"Fourfield," however, sheds new light on the intricate figures, and
then moves it around, as the shadows are part of the formation. 
This is an astounding and impressive work.  I'm still not sure,
however, that H.P. Lovecraft's monsters aren't lurking somewhere in
the center of the constructs, waiting to jump out.

    Banchoff has also written a book titled "Beyond the Third Dimension",
    published as part of the Scientific American Library, which explores
    (with many illustrations) this subject matter.
    
    len.