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See also:
http://www.medparse.com/gwmcv.htm .............
http://www.medparse.com/rvgodell.htm .............
http://www.medparse.com/rvneuroc.htm .............
http://www.medparse.com/rvcognis.htm
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Published in: Neurocomputing. 2001 Jan;42(1):337.
Stewart I.
Flatterland. Like Flatland. Only More So.
Cambridge, MA: Perseus Publishing. 2001.
ISBN 0-7382-0442-0.
FLATTERLAND, by Ian Stewart, is a modern sequel
to FLATLAND, by Edwin A. Abbott, published over a century earlier,
and discussed recently in Stephen Hawking's
popular book, A BRIEF HISTORY OF TIME.
Abbott's original work is a mathematical popularization
that imagines a world in which everyone lives
in two dimensions on a flat, Euclidean plane.
Abbott was headmaster at a Victorian England school,
and he used his book at his own institution.
The inhabitants consisted of classical geometrical figures,
such as lines, triangles, squares, pentagons, etc.
Social status was indicated by the number of sides you had:
in England's class-conscious society, poor men were triangles (3 sides);
middle-class men were squares (4 sides);
priests were circles (infinite-sided polygon);
and (disenfranchised) women were lines (one side).
The purpose of Abbott's book was to suggest
the possibility of life in four dimensions to educated Englishmen,
by exploring a world in which everyone lived in two dimensions,
and suddenly had to respond to a third.
Abbott's imaginary world preceded Einstein's rigorous concepts
of four-dimensional space-time by over two decades.
FLATTERLAND carries us into the world
of modern physical concepts, making them
understandable to the generally educated reader.
FLATTERLAND projects forward the quaint
Victorian language, the wordplay, and the social satire
of the original book. Our guide is Vikki Line
(Victoria Line, like the London rail line),
great-great-granddaughter of Albert Square,
the original protagonist of FLATLAND.
Albert Square eventually ended up in prison for his
blasphemous suggestion of a third dimension.
Vikki must deal with her old-fashioned parents,
who aren't even connected to cyberspace,
and who don't seem to be very imaginative
about the world outside themselves.
The action begins with Vikki surfing the InterLine.
Remember, the Internet would be a three-dimensional structure,
unimaginable in Vikki's world. Vikki is visited by Space-Hopper,
a complex topological structure that first appears
to Vikki as a collection of synchronous circles in two-space.
Space-Hopper employs a Virtual Unreality Engine,
or VUE, to explore the Mathiverse, a transcendant
universe of all possible structures imaginable by mathematicians.
Planiturth is 'reality',
wherein live the persons who create concepts in the Mathiverse.
One of the deep philosophical conundrums is whether
the Planiturthians are a consequence of the laws of the (true) Mathiverse,
or whether the Mathiverse is a mere construct
projected by the minds of the Planiturthians.
Did God invent man or did man invent God?
The Space-Hopper uses his VUE-screen to explore
infinite dimensions; fractional dimensions (fractals);
topologies (donuts turning into teacups); projective geometries;
group theory as a model for fundamental particles in physics;
non-Euclidean geometries; and, especially,
hyperbolic geometries (cleverly called PLATTERLAND,
and diagrammed on a curved dinner platter).
Quantum mechanics, including the issues of relativistic observers and
uncertainty principles, is discussed in 'Cat Country',
the land of Schrödinger's Cat,
who changes form depending upon whether it is being observed.
Finally, FLATTERLAND covers Black Holes, White Holes, Wormholes,
quantum time travel, and the reasons why physicists care about
the so-called Theory of Everything. Is it a metaphysical quest
for a monotheistic explanation of everything,
akin to the quest for the Holy Grail;
or a practical desire not to have to
change theories as the universe enlarges
from the moment of the Big Bang into its present expanse?
The book is a great way for an amateur
to travel through the major realms of physics in an afternoon's reading.
Regrettably, the book has no bibliography, not even a few major works.
Now that it has become so easy to order up
books and some journals from the Internet, this is an inexcusable lapse.
The index has the interesting conceit that personal names have the given name
and surname run together, as for example, Alberteinstein or Isaacnewton.
Since Euclid has no given name, he becomes Euclidthegreek.
A real purist might insist that Newton be indexed as Sirisaacnewton.
This indexing method is adequate for persons like Einstein or Newton,
whose given names are household words. However, a casual reader
who may have heard about Schrödinger Equations in quantum theory
may not know that the professor's given name is Erwin.
In FLATTERLAND's index, the man is listed in the E's under
Erwinschrödinger; whereas his famous cat (who assumes different forms
depending upon whether he is being observed or not)
is listed in the S's under Schrödinger's Cat.
The wordplay becomes very heavy at times, and I despair that
a reader whose first language is not English can understand
all the nuances. I suppose that this wordplay is consistent with the
Victorian attitude that God must be an Englishman, let the lesser
nations keep up if they can. Even as an American English reader,
I'm certain that some of the subtler humor passed me by.
Despite these minor flaws, the book is fun to read,
and simplifies many otherwise complex ideas of modern physics.
I recommend it wholeheartedly.
Last updated: 1/6/2006, by G. William Moore, MD, PhD.