- Barrow, John D.
The Infinite Book.
New York: Vintage Books, 2005.
ISBN 1-4000-3224-5.
-
Don't panic—despite the title, this book is
only 330 pages! Having written an entire book about
nothing (The Book of Nothing,
May 2001), I suppose it's only natural the author
would take on the other end of the scale. Unlike Rudy
Rucker's
Infinity and the Mind,
long the standard popular work on the topic, Barrow spends only
about half of the book on the mathematics of infinity.
Philosophical, metaphysical, and theological views of
the infinite in a variety of cultures are discussed, as well
as the history of the infinite in mathematics, including
a biographical portrait of the ultimately tragic life of
Georg Cantor.
The physics of an infinite universe (and
whether we can ever determine if our own universe is
infinite), the paradoxes of an infinite number of identical
copies of ourselves necessarily existing in an infinite
universe, the possibility of machines which perform an infinite number
of tasks in finite time, whether we're living in a simulation (and how
we might discover we are), and the practical and moral
consequences of immortality and time travel are also explored.
Mathematicians and scientists have traditionally been very
wary of the infinite (indeed, the appearance of infinities
is considered an indication of the limitations of theories
in modern physics), and Barrow presents any number of
paradoxes which illustrate that, as he titles chapter
four, “infinity is not a big number”: it is
fundamentally different and requires a distinct kind of
intuition if nonsensical results are to be avoided. One of
the most delightful examples is Zhihong Xia's
five-body
configuration of point masses which, under Newtonian
gravitation, expands to infinite size in finite time.
(Don't worry: the
finite speed of light,
formation of an horizon
if two bodies approach too closely, and the emission of
gravitational radiation keep this from working in the
relativistic universe we inhabit. As the author says
[p. 236], “Black holes might seem bad but,
like growing old, they are really not so bad when you consider
the alternatives.”)
This is an enjoyable and enlightening read, but I found it
didn't come up to the standard set by
The Book of Nothing and
The Constants of Nature
(June 2003). Like the latter book, this one
is set in a hideously inappropriate font for a work on mathematics:
the digit “1” is almost indistinguishable from the letter
“I”. If you look very closely at the top serif
on the “1” you'll note that it rises toward the right
while the “I” has a horizontal top serif. But why
go to the trouble of distinguishing the two characters and
then making the two glyphs so nearly identical you can't tell
them apart without a magnifying glass? In addition, the horizontal
bar of the plus sign doesn't line up with the minus sign, which
makes equations look awful.
This isn't the author's only work on infinity; he's
also written a stage play,
Infinities,
which was performed in Milan in 2002 and 2003.
September 2007 