The Physics of Foraging: An Introduction to Random Searches andBiological Encounters
Nicholas Watkins
Citation: Phys. Today 65(1), 44 (2012); doi: 10.1063/PT.3.1401
View online: http://dx.doi.org/10.1063/PT.3.1401
View Table of Contents: http://www.physicstoday.org/resource/1/PHTOAD/v65/i1
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booksEssays on the edge
More and Different
Notes from a Thoughtful
Curmudgeon
Philip W. Anderson
World Scientific, Hackensack, NJ,
2011. $38.00 paper (243 pp.).
ISBN 978-981-4350-13-6
Reviewed by
N. David Mermin

When asked to review
Philip Anderson’s newbook, I had expected
the opportunity to firea few curmudgeonly
shots at the greatest curmudgeon tograce our profession over the past twothirds of a century. But I was wrong. In
More and Different: Notes from a Thoughtful Curmudgeon, Anderson has put
together an entertaining and instructive
collection of highly readable reviews,
columns, talks, and unpublished essays
on science and the scientists he has
known. He is rarely inappropriately
provocative, and he is a pleasure to read.
One of Anderson’s recurrent themesis his refutation of naive reductionism
going back at least 40 years to his
famous 1972 essay in Science, “More isdifferent,” which unfortunately is notincluded here. Reductionism overlooks emergence. In a section entitled“Emergence as the God principle”—awell-deserved swipe at Leon Lederman—Anderson eloquently defines
emergence as “obedient to the laws of
the more primitive level, but not conceptually consequent from that level”(page 90). Nobody contemplating theLagrangian of the electromagnetic andmatter fields would have guessed thatbroken gauge symmetry was the key tothe phenomenon of superconductivity.
Even with the clue provided by the laboratory of Heike Kamerlingh Onnes, it
took 32 years after the creation of quantum mechanics to discover the explanation, which is consistent with, but not
implied by, the quantum laws.
N. David Mermin, a retired professor ofphysics at Cornell University in Ithaca, NewYork, last wrote in PHYSICS TODAY about P. W.
Anderson 30 years ago; in “E pluribus boojum:
The physicist as neologist” (April 1981,page 46) Anderson rescues “boojum” fromthe dustbin of rejected scientific terms.

44

January 2012

Physics Today

We also learn about interpersonal
relations at Bell Labs during its heroicyears. We are given Anderson’s definitely non-postmodernist views on thescience wars. We hear his altogether
admirable opinions on the politicization of science. We get a history of thetheory of superconductivity as seenfrom the frontlines. We get his opinions—almost all respectful, but oftenwith an edge—about John Bardeen,Hans Bethe, Leon Cooper, RichardFeynman, Murray Gell-Mann, Stephen
Hawking, Brian Josephson, Lev Landau, Bernd Matthias, Ilya Prigogine,
J. Robert Schrieffer, William Shockley,and Eugene Wigner, among others. I
could easily have listed more if the bookcame with an index.
The only part of the collection I did
not find a delight to read are Anderson’s
attempts to convey to the generalreader the scientific content of some of
his own contributions. He is aware of
the problem: “I have elsewhere disavowed any ability [to explain technicalscientific matters to laymen], and thereader—especially the true layman—
will surely agree.” I would add thateven a physicist from a different subfield will find some of his explanations
a little terse. Just a touch of strictly pedagogical reductionism might havehelped.
I blame most shortcomings of thebook on the publisher. We are not told
where or, more importantly, when mostof the more than 60 essays were published or written, which often requires
the reader to deduce from internal evidence the state of the issues at the timeof Anderson’s critical discussion. Sometimes an essay contains references toother articles in the unidentified collection from which that essay was taken.
And because many of the themes thatinterest Anderson are taken up in several essays over, one assumes, a span ofmany years, I found the absence of anindex a frequent source of frustration.
I conclude with just a few of themany wonderful obiter dicta, whichgive More and Different a special charm:“When we are all done, it willturn out that there is no exotic
form of ‘dark matter’, merely acomedy of errors in a field where
it is practically de rigueur tounderestimate one’s limits oferror” (page 107).

“Of course I am not religious—I
don’t in fact see how any scientist
who thinks at all deeply can beso” (page 133). And, “We atheists
can . . . argue that, with themodern revolution in attitudes
toward homosexuals, we havebecome the only group that may
not reveal itself in normal socialdiscourse” (page 177).
“Consciousness [is] one of the
major deep problems, alreadyapparent in the 20th century,
which may take most of the 21stcentury to solve” (page 113). And“the greatest puzzle of all [is] theemergence of consciousness”(page 138). (When I complained
to a very distinguished colleague
that his Theory of Everything had
nothing to say about consciousness, he replied, “Consciousnessis an illusion.”)“If there weren’t any solids we’dhave no way to measure space—so by breaking the symmetry ofspace we have in a sense createdspace as a new entity” (page 144).
(I was once charged in the pagesof PHYSICS TODAY with postmodernism for making similar
remarks about time.)
And, most engagingly, “All I cansay to the younger theorists is:
don’t trust anyone over 45, except
maybe me, and I’m not so sure
about me” (p. 159).

The Physics ofForaging
An Introduction to Random
Searches and BiologicalEncounters
Gandhimohan M. Viswanathan,
Marcos G. E. da Luz, Ernesto P.
Raposo, and H. Eugene Stanley
Cambridge U. Press,
New York, 2011. $50.00(164 pp.).
ISBN 978-1-107-00679-9

In 1996 H. Eugene “Gene”
Stanley, his graduate student Gandhimohan Viswanathan, and collaborators at Boston University
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and the British Antarctic Survey published a paper partly inspired by Yossi
Klafter and Michael Shlesinger’s stimulating suggestion that animal foraging
might be modeled by non-Brownian,superdiffusive, random walks. The
paper reported that a set of flight timesof the wandering albatross followed apower-law distribution t-μ, with μ ≈ 2,
and proposed several tentative explanations including that albatrosses forage in fractally structured natural environments, including the turbulent
atmosphere and oceans. In a second
paper in 1999, Viswanathan and colleagues proposed something evenbolder: They related their power law toa Lévy foraging hypothesis, whichstated that foraging behavior based on
the μ = 2 scaling exponent is optimal
in some instances, and that natural
selection would thus have evolved toexploit it.
Viswanathan (now a professor inBrazil at the Federal University of Rio
Grande do Norte), Stanley, and theircollaborators, Marcos da Luz andErnesto Raposo, have now publishedtheir ideas in The Physics of Foraging: An
Introduction to Random Searches and Biological Encounters, which aims to synthesize anomalous diffusion and animal foraging. As with previous texts
written (or co-written) by Stanley, thisbook provides many clear explanationsof nonintuitive concepts as evidenced
by the lucid presentation of random
walks and critical phenomena in thefirst three chapters. Another example ofthe text’s clarity is the discussion inchapter 4 of the difference between
large values drawn from a power law
distribution and classical outliers.
The Physics of Foraging is strong in its
discussion of the development, during
the past 10 years, of the Lévy foraging
hypothesis, in which foraging can beviewed biologically or more genericallyas a random search problem. Chapters
5 through 8 of the book are devoted tothe early experimental evidence, foraging by animals and humans, and thequality of collected data. The final
6 chapters focus on theory, particularly
variants of the superdiffusive random
walk and the notions of optimality
behind the Lévy foraging hypothesis.
Unfortunately the book presents
only seven figures drawn from experimental data; it also makes at least one
error of fact in its presentation in chapter 4 of a 2007 paper revisiting the albatross data set, coauthored by Andrew
Edwards, then at the British Antarctic
Survey, this book’s authors, me, andothers. The book correctly notes that theJanuary 2012

Physics Today45

longest “flights” in that data set werespurious, but mistakenly lays the blameon the idea that the birds “hadremained for some time in captivity
prior to release.” In fact, the spurious“flights” were a result of the sometimes
long intervals between attaching thetracking devices to the birds and theirsubsequent take-offs or between thebirds’ landings and the devices’ subsequent removal.
I would also have preferred to see awider variety of literature referenced inthe book. Partially stimulated by thereexamination of the albatross data set,some recent papers on non-Brownian
models of foraging present strikingly
different viewpoints on simulation,
data analysis, and statistical inference:
A very recent example of which is the2011 Journal of the Royal Society Interface
paper “Assessing Lévy walks as modelsof animal foraging,” by Alex James,
Michael Plank, and Edwards. I also
think the appendix on maximumlikelihood estimation, which discusses
best practices for statistical inference ofpower laws, would have benefited froman explicit reference to, and discussionof, the 2009 SIAM Review paper,

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books“Power-law distributions in empiricaldata,” by Aaron Clauset, Cosma Shalizi,
and Mark Newman.
Another unfortunate weakness isinadequate proofreading. The backcover, for example, suggests that thebook will interest “ecologists with little
familiarity with the concepts and methods of statistical physics,” whereas thefirst page refers instead to ecologists“already familiar” with the same.
Occasionally one finds apt neologisms,
like a reference to “statistically coercive” quantities, though more often the
proofreading misses typos like “VHS”
radio waves or a reference to thealbatrosses of “southern (instead of“South”) Georgia.” Hopefully such
mistakes will be fixed in a future
edition.
Despite those problems, I think The
Physics of Foraging is useful and willfind a place in the literature of thephysics and ecology communities.
Over the past 40 years, Stanley has
given us a number of excellent books.
His Introduction to Phase Transitions andCritical Phenomena (Oxford UniversityPress, 1971) remains a classic. Threeother books co-written or co-edited byStanley are among a select few thathave inspired many scientists, myself
included, to pursue criticality-based
approaches to the study of complex
systems. They are On Growth andForm: Fractal and Non-Fractal Patternsin Physics co-edited with Nicole
Ostrowsky (Springer, 1985); FractalConcepts in Surface Growth with AlbertLászló Barabási (Cambridge UniversityPress, 1995); and Introduction to Econophysics: Correlations and Complexity inFinance with Rosario Mantegna (Cambridge University Press, 2000).
As the exciting, cross-disciplinary
field of complex-systems science develops, it faces the twin challenges of analyzing rich new data sets (see Stanley’sreview of Complex Webs: Anticipating theImprobable in PHYSICS TODAY, November
2011, page 58) and, at the same time,
incorporating the relevant prior knowledge and expertise of existing disciplines.
I expect to use The Physics of Foraging aspart of that process. For advanced
courses, the book could be supplemented
by Klafter and Igor Sokolov’s excellent
new book on anomalous diffusion, First
Steps in Random Walks: From Tools to Applications (Oxford University Press, 2011);
both books would stimulate learning anddebate among graduate students andpostdocs.
Nicholas Watkins
British Antarctic Survey
Cambridge, UK46

January 2012

Physics Today

The Shaping of Life
The Generation ofBiological PatternLionel G. Harrison
Cambridge U. Press, New York, 2011.
$99.00 (247 pp.).
ISBN 978-0-521-55350-6

In 1917 D’Arcy Wentworth
Thompson penned the classic
On Growth and Form (revisededition, Dover, 1992), in which
he argued, contrary to the Darwinian orthodoxy of the time,that structure originates before
function and that growth and form canbe explained through mathematics andphysics. By the early 1950s, Alan Turing
would demonstrate how spatial patterns could arise through chemical
instabilities inherent in a simple set of
coupled reaction–diffusion equations.
Turing patterns, as they came to beknown, are evident in nature; for example, some resemble the spots on a leopard, others the stripes on a zebra or
the complex fractal-like patterns onseashells. But it was not until the 1980s
that chemists could actually set up
reactions that would produce Turingpatterns.
Though embraced by mathematicians and physicists, Turing’s mathematical approach to biological patternformation is hardly accepted by mostexperimental biologists. The late physical chemist and theoretical biologist
Lionel Harrison laments such resistance in The Shaping of Life: The Generation of Biological Pattern, which hedrafted before his untimely death in2008 and which was completed byfriends and colleagues. Harrison pioneered a quantitative approach todevelopmental biology in the 1970s, an
era when few thought it was useful tomathematically model the complexitiesof biological growth and development.
The Shaping of Life makes the case forsimple coarse-grained mathematicalmodels in biology—simple, that is, incomparison to models that explain thephenomena at a genetic or systems
level. Many of the topics in the book’s
first half are drawn from Harrison’s
own research on plant development.
His work had led him to investigate avariety of novel creatures such as
Acetabularia, a seaweed that grows to
several centimeters and generates multiple whorls of hair-like filaments along
its exterior. Those organisms are ideal
laboratories for studying the dynamicsof growth, since they are mostly transparent and grow in two-dimensional

sheets. Another favorite of Harrison’s
are the somatic embryos of conifers,
such as the hybrid larch Larix x leptoeuropaea. As an embryo, Larix is a multicellular organism accessible to observation in much the same way as
Acetabularia. Despite its multicellular nature, the development of outgrowths called
cotyledons from Larix embryos
greatly resembles the whorl
formation in the single-cell
Acetabularia and, indeed, can bemodeled on a similar mathematical formalism.
In the second half of thebook, Harrison turns the reader’s gazefrom plant development to animaldevelopment. Here one learns about
segmentation in the Drosophila egg,
amphibian heart development, therearrangement of stripe patterns inangelfish, vertebrate limb development, the growth of slime molds, andmuch more. The examples are highlyvaried, some touched on in moredetail than others, but taken together
they clearly display that there is no
shortage of complex developmental
behavior that can be understood
through mathematics.
One notable omission, which Harrison admits early on in the manuscript,
is any discussion about the genetics ofdevelopment. That is fair; as Harrison’s
numerous examples show, much canbe said about understanding complex
developmental behavior throughcourse-grained mathematical modelsof pattern formation at the level ofabstraction presented in The Shaping ofLife. In fact, a mathematical approach todevelopmental modeling is the subjectof numerous complementary books,
including Biological Physics of the Developing Embryo (Cambridge UniversityPress, 2005) by Gabor Forgacs andStuart Newman and The Self-Made
Tapestry: Pattern Formation in Nature(Oxford University Press, 1999) byPhilip Ball. For a technical discussion ofthe genetic origin of bodily form, interested readers can consult Imaginal Discs:
The Genetic and Cellular Logic of PatternFormation (Cambridge University Press,2002) by Lewis Held Jr; for a more readily accessible popular account on thesame topic, readers can check out theimmensely pleasurable Endless Forms
Most Beautiful: The New Science of Evo
Devo and the Making of the Animal Kingdom (W. W. Norton, 2005) by Sean B.
Carroll.
Besides being a text about biologicalpattern formation, The Shaping of Life isan exposition on how human beings
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