PW_mar13_sample_issue

Princeton University Press
Reviews
Between the lines
Hidden message
The cover of The
Universe in Zero
Words cleverly hides
equations in the
Milky Way.
64
On beyond zero
The Universe in Zero Words sounds
like the title of a coffee-table book
of astronomy photos. The image
on its cover – a photograph of the
Milky Way – does little to suggest
otherwise. But the book Dana
Mackenzie has actually written is
a very different beast indeed. A
closer look at that star-spangled
cover reveals a host of equations
scattered through the night sky, and
inside it is an elegantly illustrated
history of mathematical thought,
rather than a series of nebula
photos. Mackenzie’s chronicle is
impressive in its scope, running all
the way from 1+1=2 (an expression
with some surprisingly interesting
properties) through to 20th-century
revelations such as Lorenz’s
equations of chaos theory and the
realization that some infinities are
bigger than others. Understandably,
Mackenzie, a mathematicianturned-writer,
uses rather more
than zero words to describe these
discoveries: the book is divided
into 24 semi-independent essays,
each nominally based on a single
equation or group of equations.
Most of these expressions will be
familiar to physicists, but there
are also a few oddities, such as the
Chern–Gauss–Bonnet equation,
and even “old favourites” such
as Maxwell’s equations are often
presented with a fresh twist. This
tendency is apparent from the first
few essays, which frequently give
credit to ancient mathematicians
who lived outside the Greco-
Roman world of Euclid and
Archimedes. In particular, an
account of Liu Hui, a Chinese
mathematician and commentator
from the third century AD, enlivens
the essay on the “Pythagorean”
theorem – which, as Mackenzie
makes clear, was not Pythagoras’
invention, having been known to
the Babylonians for more than a
millennium before Pythagoras
started teaching in the 6th century
BC. This cross-cultural focus is
particularly appropriate given the
book’s title, which refers to the
Platonist idea that numbers and
equations express truths about the
universe that are independent of
words, language or culture. What
was that old proverb about books
and covers, again?
● 2012 Princeton University Press
£19.95/$27.95hb 224pp
Proof positive
Prove that a parallelogram with
equal diagonals must be a rectangle.
Show that the surface area of a
sphere is exactly two-thirds that
of its (closed) cylinder. Derive the
equation for a hyperbola. If these
instructions induce puzzlement,
a vague sense of “I used to know
how to do that” or even a barely
suppressed twinge of panic, then
Measurement deserves a place
on your shelf. Written by Paul
Lockhart, a New York-based
mathematics teacher and education
advocate, the book aims not only
to teach mathematics, but also
to instil in readers a genuine
appreciation for the subject and
an understanding of why it is
beautiful and worth learning. In
his introduction, Lockhart admits
that this will not be an easy process;
mathematics, he writes, is like a
jungle, and “the jungle does not
give up its secrets easily…I don’t
know of any human activity as
demanding of one’s imagination,
intuition and ingenuity”. On the
other hand, mathematics is also
“full of enchanting mysteries”,
many of which are accessible even to
novices – provided they are willing
to play around with ideas and also
develop a high tolerance for getting
stuck. To help readers build their
mathematical muscles, Lockhart has
peppered his book with questions
and puzzles like the ones that
opened this review. The solutions to
some of them are worked out (or at
least worked around) in the text, but
most are left as an exercise for the
reader, without further comment
or explanation from Lockhart. In a
formal textbook, such an approach
would be frustrating – especially
for students with problem sets due
every week, who seldom have the
luxury of letting it “take hours or
even days for a new idea to sink
in”, as Lockhart advises. In the
more relaxed and playful context
of Measurement, however, it seems
to work, and readers who try some
of the easier puzzles will soon
find themselves ready for more
challenging fare. And if you do get
stuck, Lockhart advises you to start
working on another problem, as “it’s
much better to have five or six walls
to bang your head against” than
only one.
● 2012 Harvard University Press
£20.00/$29.95hb 416pp
physicsworld.com
Einstein the inventor
Albert Einstein’s early career as
a clerk in the Swiss Patent Office
is sometimes perceived as an
aberration. Having failed to get a
job as a teacher, or to have his true
talents properly appreciated by the
physics establishment, the story
goes that he took this rather boring
job only because he needed to eat,
or because it allowed him time to
construct a gedankenexperiment or
two in periods of idleness. There is
some truth to this: although Einstein
later looked back on the patent
office with fondness (calling it “that
worldly cloister where I concocted
my finest ideas”) he left his job there
as soon as he reasonably could,
after obtaining an academic post
at the University of Zurich. Yet
Einstein’s experiences of the patent
office never really left him. Even
after his theoretical work made him
the world’s most famous scientist,
he maintained an avid interest in
technology and practical inventions.
These inventions – along with his
musings and expert opinions on
other people’s gadgets – are the
subject of The Practical Einstein:
Experiments, Patents, Inventions by
József Illy, a visiting historian at the
California Institute of Technology.
In this slender book readers will find
some fascinating anecdotes about
Einstein’s lesser-known scientific
results, including a refrigerator he
invented with Leó Szilárd and a
paper he wrote on the meanderings
of rivers. Not all of these efforts
were successful. For example,
an experiment he conducted on
molecular currents in 1915 produced
a result that, in Illy’s understated
words, “did not stand the test of
time”. Similarly, Einstein’s career
as an impartial witness for patent
disputes – which began after he
had moved into academia – was
marked by a number of lost cases
and bungled court appearances.
Even the successful and innovative
Einstein–Szilárd refrigerators were
preceded by Einstein’s abortive
efforts to develop an “ice machine”
with his chemist colleague Walther
Nernst. The Practical Einstein reads
more like a series of stories than
a narrative, but Illy does deserve
credit for gathering the often
incomplete records of Einstein’s
practical side into one book.
● 2012 Johns Hopkins University
Press £31.50/$60.00hb 216pp
Physics World March 2013