Subject: REVIEW: ALTERNATE GEOMETRIES edited by Nick Bourbaki

From: [email-masked] (Mark R. Leeper)
Date: Fri, 1 Apr 1994 04:22:46 GMT

ALTERNATE GEOMETRIES edited by Nick Bourbaki
	     Springer-Verlag, ISBN 2-718-28182-8, 1994,	$4.99.
		      A	book review by Mark R. Leeper
		       Copyright 1994 Mark R. Leeper

     Well, Nick Bourbaki is back with another mind-bending alternate world
extravaganza.  While I enjoyed the first two (ALTERNATE GREEN VEGETABLES and
ALTERNATE SHIRT-PACKING MATERIALS), I found this one slightly lacking in
imagination.  I think that Euclid's Parallel Postulate is pretty much self-
evident to even the casual reader.  I think that it is one thing to say that
someplace else there is kale with roots like a carrot and to follow that
idea through, but you can see right on a piece of paper in front of you that
the Parallel Postulate is true and it is pretty tough to envision it any
other way.  Maybe it's the focus.  There seems to be a subgenre of science
fiction these days that concentrates on knocking the old masters like
Euclid, mostly by people not fit to carry Euclid's pencil-box, if he had a
pencil box.  Some of the ideas here are well thought out, but the authors
keep knocking their heads against the difficulty in suspending disbelief.
(The claim has been made that this category is aimed at adolescent boys of
all ages, without a strong foundation in mathematics, so I'm sure some will
say that's why I find it usually dull and often offensive in its
glorification of purely abstract mathematics, but there you have it.)  Only
the alternate world aspect of this anthology made it intriguing to me, and I
found that part was often a let-down.  Why?  Well, let's see.

     First, though, let me talk about the *best* ideas.  "The Land Where All
Lines Meet" by Georg Friedrich Bernhard Riemann (and isn't that a mouthful?)
is set in a world where every line intercepts every other line.  This seems
to have the nastiest implications for the transportation industry.  Railroad
locomotives have to be designed with wheels that are flexible enough to move
in and out and travels on any set of tracks are limited by the fact that
some place the two rails have to come together and the locomotive tends to
fall over because the base is too small.  On the other hand human relations
turn out to be totally affected.  There is less petty crime and far more
violent crime since if a criminal is robbing somebody he is virtually
assured that the victim will run into him again.  Since all paths eventually
meet, the victim has only to wait long enough and he is sure to run into the
criminal again.  The criminal, knowing this, is more likely to kill his
victim or not to bother robbing him in the first place.  If killing is the
choice the police have only to wait long enough since the killer is totally
certain to return to the scene of the crime.  There were many good ideas
that could have been explored but for reasons not entirely clear, Riemann
kept returning to the same concepts.

     The other intriguing story was Nick Lobachevksy's "A Life in the
Saddle."  He tells his story in a world where there are many different
parallels to given line through a given point.  In this world society has
never really had much chance to develop since human relationships are very
short.  All work that is accomplished is done by people who are constantly
in each other's presence since once two people separate, they can never be
certain of finding each other again.  What little architecture that can be
built is extremely shoddy and prone to falling apart since one is never
really sure in building a four wall structure if the fourth wall will or
will not meet the first.  To improve the chances most buildings are built
with three walled sides and a fourth that is left open to the elements.

     The next best story in the anthology is "Kikuyu and the Gnu Yu Rode In
On" by newcomer Mike Resnick.  He presents a universe in which all lines in
space and time converge in pre-revolutionary Kenya.  Resnick tells a good
story but one wonders why the universe would choose such an arbitrary point
on which to center.

     From there the stories fall off rapidly.  Patrick Robertson contributes
(if that is the word) a story "If I Ran the Circus" in which the whole
question of Euclid's fifth postulate because there is only one line in all
of space time and it goes straight back to some idealized point in the past.

     Will Clinton's story "Random Acts of Kindness, Other People's Money"
starts with a similar premise to the Robertson story.  Time travelers go
back in time to find the idealized point only to discover that it cannot be
found  They conclude that the line took too sharp a turn to the right and
the travelers could not follow it.

     Albrecht Durer adds a touch of artistry with "Affine Mess You've Gotten
Me Into" which has a painter enter his own painting and finds himself in a
world where one can actually walk to the horizon.  In this world any two
lines do meet, but only once.  If they do not meet any place else they
always meet on the horizon as a rendezvous of last resort.  The horizon
then, in this world, functions as sort of a singles bar for pickup lines
which seem to arrive at the horizon in polyester suits and listen to ear-
splitting music.  Unfortunately, they are doomed to frustration since the
horizon affords them little privacy and meeting at the horizon they find
they cannot get together anyplace else.

     Adam Baum's "The Long Way Round," is set in the world of spherical
geometry.  A man stopped for suspected drunk driving is told to walk a
straight line and suddenly finds himself on a great circle.

     The anthology concludes with Rene Descartes' "At Seventh Avenue and
52nd Street."  It is set in an alien, dehumanized future.  A man complains
to his bartender that everyone and everything in the world is being reduced
to numbers.  When the bartender asks the man if the numbers do not make
things easier the man responds "I think not" and instantly disappears.

%B	Alternate Geometries
%E	Nick Bourbaki
%D	1994
%I	Springer-Verlag
%O	paperback, US$4.99
%G	ISBN 2-718-28182-8
%P	314pp

					Mark R. Leeper
					att!mtgzfs3!leeper
					[email-masked]