COMPUTING SCIENCE
Undisciplined Science
Brian Hayes
"All science is either physics or stamp collecting" said
Lord Rutherford, who was not a stamp collector. The remark did
nothing to win friends for physics among practitioners of other
sciences. But Rutherford got his come-uppance: When he was summoned
to Stockholm in 1908, the prize awaiting him there was not in
physics but in chemistry.
A century later, surveying the state
of physics and its relations with other fields, I am tempted to give
Rutherford's quip an even more inflammatory reading, though he never
intended it. "All science is physics" might be taken as a
territorial claim, annexing other disciplines as provinces to be
ruled by the laws of physics and administered by physicists. This
imperial vision of the destiny of physics is not entirely without a
basis in history, or at least etymology. At one time, the term
physics had a very broad meaning, roughly synonymous with
natural science. The 18th-century
Encyclopédia of Diderot and d'Alembert listed under
the rubric physique particuliere everything from astronomy
and cosmology to meteorology, mineralogy, chemistry, zoology and
botany (but not stamp collecting).
Browsing through recent issues of Physical Review E
(a section of the main journal published by the American Physical
Society), one could form an equally expansive view of the scope of
21st-century physics. Within the past year, the Phys Rev E
table of contents has included titles such as "Outbreaks of
Hantavirus induced by seasonality," "Large-scale
structural organization of social networks," "Topology of
the world trade web," "Generating neural circuits that
implement probabilistic reasoning" and "Number fluctuation
and the fundamental theorem of arithmetic." Evidently, the
boundaries of physics are elastic enough to take in aspects of viral
epidemiology, sociology, market economics, cognitive neuroscience
and number theory. Are all of those fields now absorbed into the
empire of physics?
The story I want to tell here is not about sleeper cells of militant
physicists plotting a coup in the biology department. As a matter of
fact, although physics provides the most dramatic examples, several
other disciplines also have boundaries that seem to be shifting or
growing porous. Intellectual migrants are wandering back and forth
across many academic frontiers, generally without stopping for any
formalities at the customs house. In some cases, the same paper
might be classified as physics, biology, mathematics or computer
science, depending more on the author's affiliation and where it was
published than on the subject matter.
Departmental reshuffling and realignment goes on all the time, but
the present moment seems to be one of particular ferment. Among many
possible causes, I would point to the changing role of computation
in the various sciences. A number of earlier upheavals in the
structure of scientific disciplines have been triggered by new
techniques and instruments, sometimes imported from other fields.
Today, computation is the common thread in many of the areas that
are having a disciplinary identity crisis. Some of these areas rely
heavily on computer simulations or experiments, and others analyze
large data sets accessible only with computer technology. Computer
science also exerts a subtler but deeper influence when laws of
nature are expressed in algorithmic form.
Social Phase Transitions
How does it happen that a sensible and sober-minded physicist strays
into such dangerous neighborhoods as economics, sociology or
political science? Well, one thing leads to another. The road to
ruin may be long and twisting, but each step along the way is easy
enough to trace.
Here's an example. Physics has a long-standing interest in the
phases of matter and the transitions between those phases. This
topic includes not only the familiar solid-liquid-vapor phases but
also related phenomena such as the onset of magnetization in iron.
One strategy for studying phase transitions is to sweep aside all
the intricacy of atomic or molecular structure and build the
simplest model that exhibits the behavior of interest. In the case
of magnetism, the iron atom with its halo of 56 spinning electrons
can be replaced by a single abstract "spin"—which is
merely an arrow that points either up or down and has no other
properties. The spins are arranged on a geometrical grid or lattice,
a cartoon version of the crystal structure of the metal. Quantum
interactions between iron atoms are modeled by a simple tendency for
nearby spins to line up parallel to one another, but this orderly
state can be disrupted by thermal agitation. If this rudimentary
model is a success, then at some temperature most of the spins
should suddenly fall into alignment, mimicking the spontaneous
magnetization of a real magnet.
Having created this model to represent a specific physical system,
you might now discover that the model itself is an interesting
object of study. Variations suggest themselves, with different
lattice geometries or rules of interaction; the variants may or may
not have anything to do with magnetic materials. In some cases the
behavior of the model can be worked out mathematically in full
detail, but more often the only way to understand how the array of
spins evolves is by computer simulation.
Now comes the next step down the path leading out of the Garden of
Physics. After spending some time exploring the universe of abstract
models, you may begin to notice that the lattice of spins could be
given a variety of interpretations; the spins could represent many
things other than magnetic moments of atoms. In particular,
up and down spins might be mapped onto
pro and contra opinions held by people in some
social context. In this new view of the model, the interactions that
were once seen as magnetic couplings now represent the tendency of
people to influence (and be influenced by) their neighbors'
opinions. The phase transition in which the spins all line up
pointing the same way corresponds to the sudden emergence of a
consensus within the population. And thus a physicist becomes a
social scientist.
For another example, consider the process of percolation, where a
fluid trickles through the mazelike passages of a porous medium. Can
the fluid penetrate the entire region, or will it be blocked by
dead-end passages? Again the essentials can be captured in a lattice
model. Each link between adjacent nodes of the lattice is open to
fluid flow with some fixed probability p or is blocked with
probability 1-p. At low values of p, most links
are blocked, and the lattice consists of many small, isolated
clusters of connected nodes. As p increases, there is a
threshold value where a giant connected cluster suddenly appears,
allowing a fluid to infiltrate the entire lattice.
Like the lattice spin system, the percolation model has many
variationsÑand many interpretations distant from the physical
process that inspired it. The idea of something spreading
probabilistically through a network can also model the transmission
of rumors, or the progress of a forest fire or the spread of an
infectious disease. Indeed, maybe the percolation model could model
itself, documenting its own spread from one discipline to the next.
These are a few of the paths radiating from physics to other areas.
But the landscape of science is criss-crossed with trails
going in other directions as well. A mathematician studying random
graphs—structures formed when you start with a set of isolated
nodes and then add links between them at random—would also
discover an abrupt transition where a giant connected component
spontaneously emerges. This sudden change in the structure of the
graphs has all the characteristics of a phase transition, and so the
mathematician wanders onto turf usually claimed by physicists.
A computer scientist could have a similar experience. The
computational problem known as satisfiability concerns Boolean
formulasÑlogical statements such as ((p OR
q) and ((not q) OR r)), where each of the
variables p, q and r has a value of either true or
false. The question is: Can you find an assignment of values that
makes the overall proposition true? For the example given here it's
easy to answer this question by trial and error, but large formulas
are challenging. In the 1980s computer scientists detected an
interesting pattern: As a certain parameter measuring the complexity
of the formula increases, there is a sudden transition. Below the
threshold, almost all satisfiability problems are solvable, but
above it almost none are. The resemblance to phase transitions is
obvious, and so computer scientists found themselves doing physics,
and physicists took up work on the satisfiability problem.
One more example from farther afield: In 1971 Thomas C. Schelling
published a lattice model of racial segregation. Black and white
residents, initially scattered at random over the nodes of the
lattice, were assumed to prefer living among neighbors of the same
race; those who were unhappy with their current surroundings could
move. Schelling's most provocative finding was that it doesn't take
vicious bigotry to produce a sharply segregated housing pattern;
even the mildest preference for neighbors of the same race leads to
a phase separation. Schelling's diagrams look very much like
simulations of a lattice model of magnetic materials, but the paper
makes no reference to the physics literature. (Indeed, it predates
much of it.) Schelling is an economist and political scientist.
Fishing Expeditions
The lattice models constitute a set of problems and tools that span
an impressive diversity of disciplines. But which of those
disciplines is their true home? Who owns those models?
From one point of view, such a question doesn't even deserve an
answer. The "intellectual property" of the pure sciences
is still considered a public trust, freely available to anyone with
the wit to use it. You don't have to be a licensed mathematician to
write a differential equation. And unsolved problems are like fish
in the sea—there for the taking by anyone who has the right
bait and tackle. Nevertheless, academic communities get nervous when
foreign fleets begin trawling in local waters. And no wonder. When
you've been chasing the big fish all your life, it takes an
uncommonly generous turn of mind to rejoice in watching someone else
land it.
A scientific discipline—whether physics or mathematics or
anthropology—is more than just a body of knowledge. It's also
a community of people, together with the organizations and cultural
traditions that bind them together—the journals they read, the
meetings they attend, the jokes they tell. Such institutions resist
change, and most of them are quite stable over the span of a human
lifetime. But upheavals are not unknown. In retrospect these events
may look exciting and rejuvenating, but some of the participants
must have found them traumatic. Two historical examples worth
pondering are the rise of astrophysics in the 19th century and the
invention of molecular biology in the 20th.
Astronomy had its first close encounter with physics in the era of
Kepler and Newton, but the consequences of that conjunction extended
only to the limits of the solar system. Astronomy as applied to the
stars remained the kind of science that Rutherford derided as stamp
collecting. There wasn't much you could do with the stars but
catalog them—give them names and note their positions, their
brightness, and perhaps some hint of their color. Nothing was known
of their mass and size, their composition, their age or the source
of their radiant energy. The French philosopher August Comte cited
the chemistry of the stars as an example of something that would
remain forever unknowable.
What overturned this pessimistic assessment was an infusion of new
instruments and methods, most notably spectroscopy. The discovery
that narrow lines observed in stellar spectra could be matched up
with corresponding lines in the spectrum of a candle flame brought
the stars right into the laboratory. Almost immediately,
spectroscopists were identifying chemical elements in the stars
(including, in the case of helium, an element that had not yet been
found on Earth). Later, subtler features of the spectra allowed
inferences about temperature and pressure in stellar atmospheres,
and even the measurement of stellar magnetic fields. This new style
of stellar science was thoroughly multidisciplinary. There were
astronomers (John Herschel) but also chemists (Robert Bunsen),
physicists (Gustav Kirchhoff) and even a polymath pioneer of
photography (William Henry Fox Talbot). The instigator of the whole
spectroscopic revolution was an optician (Joseph von Fraunhofer).
The term astrophysics, coined by the German physicist J. K.
F. Zölner, must have sounded odd at the outset—as
sociophysics and econophysics do today—but
it has entered the mainstream now. In most universities, the
Department of Astronomy is now named Astronomy and Astrophysics.
In biology, the quest to understand the molecular basis of life also
involved ideas and personnel recruited from other disciplines, and
yet the story is a little different. The prominent role of
physicists in this undertaking is often remarked. Of the four people
most closely associated with the double-helix model of
DNA—Francis Crick, Rosalind Franklin, James Watson and Maurice
Wilkins—three began their careers in physics or physical
chemistry. Another seminal figure was Max Delbrück, who studied
quantum physics with Niels Bohr before turning to biology. At least
one major technology was imported from physics: X-ray
crystallography became a tool for mapping the structure of
biomolecules. Although Delbrück and Crick brought no new
instruments with them, perhaps they passed along a physicist's style
of problem-solving. Delbrück set out to find the simplest
possible biological system for investigating the mechanism of
heredity—he chose the bacterial viruses called
phages—much as a physicist would reduce a magnet to a lattice
of spins. Still, however much molecular biology may have been
influenced by the physicists who helped create it, the field remains
a province of biology, not a colonial outpost of physics.
In describing events like these, the choice of a metaphor makes all
the difference. When physicists turned their attention to genes and
proteins, did they come as a plundering horde, descending on the
defenseless villages of innocent biologists? Or were they refugees
from the war-blasted landscape of physics, grateful for a new home
in a more peaceable realm, and eager to earn their keep by helping
with the chores? Or was it an alliance, a marriage of equals but
opposites, demonstrating the benefits of hybrid vigor? It would
doubtless make everyone feel better if we could adopt the last of
these fables, but such symmetrical unions are rare. For one thing,
some disciplines just have more to export, whereas others tend to
run a trade deficit. Physics and mathematics are defined as much by
their methods as by their subject matter, but in fields such as
geology or entomology the tricks of the trade tend to be more specialized.
Physics Outside Physics
Will the current round of interdepartmental incursions or
cross-fertilizations create new disciplines comparable to
astrophysics or molecular biology? There may well be enough
intellectual content for such new departments, but as yet there are
few signs of the concomitant institutional changes. I have not heard
of any university creating a Department of Sociology and Sociophysics.
A year ago, an international symposium held in Poland confronted the
theme of "Statistical Physics Outside Physics." In an
introductory talk (published, along with the rest of the
proceedings, in the journal Physica A), Dietrich Stauffer
of Cologne University asks what sort of welcome physicists ought to
expect when they venture into economics, sociology or biology.
Stauffer himself has done distinguished work in all three fields,
and so the answers come from direct personal experience. And yet the
question itself seems to me premature. If the work that physicists
do "outside physics" is still labeled as physics—and
in particular if it is still published in physics
journals—then physicists may get no welcome at all. Not all
sociologists, economists and biologists are readers of Physical
Review E or Physica A.
The conference proceedings also include a paper by a sociologist,
Barbara Pabjan of Wroclaw University, that is not exactly a warm
embrace of the visiting physicists. It's understandable that social
scientists are testy on this point. Their field, like a company with
weak quarterly earnings, has been a constant takeover target. Even
the biologists once made a bid, in the "socio-biology"
movement of the 1970s.
Another newly emerging subdiscipline, bio-informatics, provides an
interesting contrast. The subject matter here is the quantitative
analysis of biological data, most notably billions of base
pairs of DNA sequences. The field has brought together biologists
with mathematicians and computer scientists, apparently to the
satisfaction of both parties. The introductory talks at
bioinformatics conferences tend to focus less on friction or tension
between disciplines and more on cooperation and collaboration. As
far as I can tell, biologists do not worry that nerdy interlopers
will poach all the best results, and mathematicians do not feel they
are being exploited like some sort of outsourced tech-support
hotline. Problems such as identifying genes and calculating the
evolutionary distance between species are perceived as being both
biologically significant and mathematically engaging.
The Higher Stamp Collecting
Setting aside all questions of institutional context, much of the
recent cross-disciplinary work—the sociophysics as well as the
bioinformatics—is fascinating and fun. Personally, when I scan
Phys Rev E, it is the "unconventional"
articles, the ones that transgress disciplinary boundaries, that I
am likely to read first. If institutional constraints discourage
such coloring outside the lines, perhaps the institutions need to be reformed.
Do we need disciplines at all? The idea of organizing universities
along topical or departmental lines is not one of those
long-hallowed principles without which civilization would crumble.
American universities in particular resisted faculty specialization
until the middle of the 19th century. Specialist journals and
societies came along even later. For example, Physical
Review and the American Physical Society are not much more than
a century old. (Publications for stamp collectors go back further.)
Realistically, though, it is probably too late to bring back
professors without portfolio.
What may still be possible is to shake up the Tree of Knowledge. As
an armature for classifying ideas, a tree is a rigid structure. Its
definitive feature is that branches diverge but never rejoin, so
that every node can have but one parent. The proliferation of
portmanteau disciplines—astrophysics, biochemistry and so
on—suggests that this single-parent principle is under strain.
Perhaps we should replace the tree with a matrix: Given n
"prime" sciences labeling the columns and rows, we'd have
cubby-holes for n 2 combinations. On a campus
built to reflect this architecture, you could always find your
department by locating the intersection of the appropriate streets.
("Meet me at the corner of Bio and Soc.")
It's no surprise that computation is a conspicuous element in many
of the recent disciplinary upsets. The computer has altered the
scientist's way of life even in routine affairs (controlling
experiments, communicating with colleagues, writing papers). In
fields like statistical mechanics the influence is deeper. Where the
aim is to understand the collective behavior of vast numbers of
interacting entities, computation offers a more direct mode of
investigation than has ever been possible in the past. Occasionally
the role of computing gets explicit acknowledgment, as in the
subdiscipline called computational chemistry. But if all science
becomes computational, there's no point in mentioning it. Like
mathematics, computation becomes everyone's silent partner.
Computation has even rehabilitated some of Rutherford's
stamp-collecting disciplines. Those who compile lists and catalogs,
who survey and classify, find their work newly glamorized in the age
of data mining. The human-genome project has much to do with this
change in attitude. Craig Venter, one of the principals of that
project, has now begun another giant list, sailing the Sargasso Sea
to create a catalog of all the organisms living there. Astronomy has
its own megacatalog: the Sloan Digital Sky Survey will list 100
million objects. What has made such undertakings newly fashionable
is the possibility of doing more with the data once the gigabytes
have been gathered up. In a sense, the database itself becomes an
object of study, in much the same way that physicists study lattices
rather than what the lattices model. Rutherford might still insist
that all science is either physics or stamp collecting, but maybe he
would confess some interest in the physics of stamp collecting.