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July 24, 2006
The Expert Mind
Studies of the mental processes of chess
grandmasters have revealed clues to how people
become experts in other fields as well
By Philip E. Ross
A man walks along the inside of a circle of chess
tables, glancing at each for two or three seconds
before making his move. On the outer rim, dozens
of amateurs sit pondering their replies until he
completes the circuit. The year is 1909, the man
is José Raúl Capablanca of Cuba, and the result
is a whitewash: 28 wins in as many games. The
exhibition was part of a tour in which Capablanca won 168 games in a row.
How did he play so well, so quickly? And how far
ahead could he calculate under such constraints?
"I see only one move ahead," Capablanca is said
to have answered, "but it is always the correct one."
He thus put in a nutshell what a century of
psychological research has subsequently
established: much of the chess master's advantage
over the novice derives from the first few
seconds of thought. This rapid, knowledge-guided
perception, sometimes called apperception, can be
seen in experts in other fields as well. Just as
a master can recall all the moves in a game he
has played, so can an accomplished musician often
reconstruct the score to a sonata heard just
once. And just as the chess master often finds
the best move in a flash, an expert physician can
sometimes make an accurate diagnosis within
moments of laying eyes on a patient.
But how do the experts in these various subjects
acquire their extraordinary skills? How much can
be credited to innate talent and how much to
intensive training? Psychologists have sought
answers in studies of chess masters. The
collected results of a century of such research
have led to new theories explaining how the mind
organizes and retrieves information. What is
more, this research may have important
implications for educators. Perhaps the same
techniques used by chess players to hone their
skills could be applied in the classroom to teach
reading, writing and arithmetic.
The Drosophila of Cognitive Science
The history of human expertise begins with
hunting, a skill that was crucial to the survival
of our early ancestors. The mature hunter knows
not only where the lion has been; he can also
infer where it will go. Tracking skill increases,
as repeated studies show, from childhood onward,
rising in "a linear relationship, all the way out
to the mid-30s, when it tops out," says John
Bock, an anthropologist at California State
University, Fullerton. It takes less time to train a brain surgeon.
The preponderance of psychological evidence
indicates that experts are made, not born.
Without a demonstrably immense superiority in
skill over the novice, there can be no true
experts, only laypeople with imposing
credentials. Such, alas, are all too common.
Rigorous studies in the past two decades have
shown that professional stock pickers invest no
more successfully than amateurs, that noted
connoisseurs distinguish wines hardly better than
yokels, and that highly credentialed psychiatric
therapists help patients no more than colleagues
with less advanced degrees. And even when
expertise undoubtedly exists--as in, say,
teaching or business management--it is often hard
to measure, let alone explain.
Skill at chess, however, can be measured, broken
into components, subjected to laboratory
experiments and readily observed in its natural
environment, the tournament hall. It is for those
reasons that chess has served as the greatest
single test bed for theories of thinking--the
"Drosophila of cognitive science," as it has been called.
The measurement of chess skill has been taken
further than similar attempts with any other
game, sport or competitive activity. Statistical
formulas weigh a player's recent results over
older ones and discount successes according to
the strength of one's opponents. The results are
ratings that predict the outcomes of games with
remarkable reliability. If player A outrates
player B by 200 points, then A will on average
beat B 75 percent of the time. This prediction
holds true whether the players are top-ranked or
merely ordinary. Garry Kasparov, the Russian
grandmaster who has a rating of 2812, will win 75
percent of his games against the 100th-ranked
grandmaster, Jan Timman of the Netherlands, who
has a rating of 2616. Similarly, a U.S.
tournament player rated 1200 (about the median)
will win 75 percent of the time against someone
rated 1000 (about the 40th percentile). Ratings
allow psychologists to assess expertise by
performance rather than reputation and to track
changes in a given player's skill over the course of his or her career.
Another reason why cognitive scientists chose
chess as their model--and not billiards, say, or
bridge--is the game's reputation as, in German
poet Johann Wolfgang von Goethe's words, "the
touchstone of the intellect." The feats of chess
masters have long been ascribed to nearly magical
mental powers. This magic shines brightest in the
so-called blindfold games in which the players
are not allowed to see the board. In 1894 French
psychologist Alfred Binet, the co-inventor of the
first intelligence test, asked chess masters to
describe how they played such games. He began
with the hypothesis that they achieved an almost
photographic image of the board, but he soon
concluded that the visualization was much more
abstract. Rather than seeing the knight's mane or
the grain of the wood from which it is made, the
master calls up only a general knowledge of where
the piece stands in relation to other elements of
the position. It is the same kind of implicit
knowledge that the commuter has of the stops on a subway line.
The blindfolded master supplements such knowledge
with details of the game at hand as well as with
recollections of salient aspects of past games.
Let us say he has somehow forgotten the precise
position of a pawn. He can find it, as it were,
by considering the stereotyped strategy of the
opening--a well-studied phase of the game with a
relatively limited number of options. Or he can
remember the logic behind one of his earlier
moves--say, by reasoning: "I could not capture
his bishop two moves ago; therefore, that pawn
must have been standing in the way...." He does
not have to remember every detail at all times,
because he can reconstruct any particular detail
whenever he wishes by tapping a well-organized system of connections.
Of course, if the possession of such intricately
structured knowledge explains not only success at
blindfold play but also other abilities of chess
masters, such as calculation and planning, then
expertise in the game would depend not so much on
innate abilities as on specialized training.
Dutch psychologist Adriaan de Groot, himself a
chess master, confirmed this notion in 1938, when
he took advantage of the staging of a great
international tournament in Holland to compare
average and strong players with the world's
leading grandmasters. One way he did so was to
ask the players to describe their thoughts as
they examined a position taken from a tournament
game. He found that although experts--the class
just below master--did analyze considerably more
possibilities than the very weak players, there
was little further increase in analysis as
playing strength rose to the master and
grandmaster levels. The better players did not
examine more possibilities, only better ones--just as Capablanca had claimed.
Recent research has shown that de Groot's
findings reflected in part the nature of his
chosen test positions. A position in which
extensive, accurate calculation is critical will
allow the grandmasters to show their stuff, as it
were, and they will then search more deeply along
the branching tree of possible moves than the
amateur can hope to do. So, too, experienced
physicists may on occasion examine more
possibilities than physics students do. Yet in
both cases, the expert relies not so much on an
intrinsically stronger power of analysis as on a
store of structured knowledge. When confronted
with a difficult position, a weaker player may
calculate for half an hour, often looking many
moves ahead, yet miss the right continuation,
whereas a grandmaster sees the move immediately,
without consciously analyzing anything at all.
De Groot also had his subjects examine a position
for a limited period and then try to reconstruct
it from memory. Performance at this task tracked
game-playing strength all the way from novice to
grandmaster. Beginners could not recall more than
a very few details of the position, even after
having examined it for 30 seconds, whereas
grandmasters could usually get it perfectly, even
if they had perused it for only a few seconds.
This difference tracks a particular form of
memory, specific to the kind of chess positions
that commonly occur in play. The specific memory
must be the result of training, because
grandmasters do no better than others in general tests of memory.
Similar results have been demonstrated in bridge
players (who can remember cards played in many
games), computer programmers (who can reconstruct
masses of computer code) and musicians (who can
recall long snatches of music). Indeed, such a
memory for the subject matter of a particular
field is a standard test for the existence of expertise.
The conclusion that experts rely more on
structured knowledge than on analysis is
supported by a rare case study of an initially
weak chess player, identified only by the
initials D.H., who over the course of nine years
rose to become one of Canada's leading masters by
1987. Neil Charness, professor of psychology at
Florida State University, showed that despite the
increase in the player's strength, he analyzed
chess positions no more extensively than he had
earlier, relying instead on a vastly improved
knowledge of chess positions and associated strategies.
Chunking Theory
In the 1960s Herbert A. Simon and William Chase,
both at Carnegie Mellon University, tried to get
a better understand-ing of expert memory by
studying its limitations. Picking up where de
Groot left off, they asked players of various
strengths to reconstruct chess positions that had
been artificially devised--that is, with the
pieces placed randomly on the board--rather than
reached as the result of master play. The
correlation between game-playing strength and the
accuracy of the players' recall was much weak-er
with the random positions than with the authentic ones.
Chess memory was thus shown to be even more
specific than it had seemed, being tuned not
merely to the game itself but to typical chess
positions. These experiments corroborated earlier
studies that had demonstrated convincingly that
ability in one area tends not to transfer to
another. American psychologist Edward Thorndike
first noted this lack of transference over a
century ago, when he showed that the study of
Latin, for instance, did not improve command of
English and that geometric proofs do not teach the use of logic in daily life.
Simon explained the masters' relative weakness in
reconstructing artificial chess positions with a
model based on meaningful patterns called chunks.
He invoked the concept to explain how chess
masters can manipulate vast amounts of stored
information, a task that would seem to strain the
working memory. Psychologist George Miller of
Princeton University famously estimated the
limits of working memory--the scratch pad of the
mind--in a 1956 paper entitled "The Magical
Number Seven, Plus or Minus Two." Miller showed
that people can contemplate only five to nine
items at a time. By packing hierarchies of
information into chunks, Simon argued, chess
masters could get around this limitation, because
by using this method, they could access five to
nine chunks rather than the same number of smaller details.
Take the sentence "Mary had a little lamb." The
number of information chunks in this sentence
depends on one's knowledge of the poem and the
English language. For most native speakers of
English, the sentence is part of a much larger
chunk, the familiar poem. For someone who knows
English but not the poem, the sentence is a
single, self-contained chunk. For someone who has
memorized the words but not their meaning, the
sentence is five chunks, and it is 18 chunks for
someone who knows the letters but not the words.
In the context of chess, the same differences can
be seen between novices and grandmasters. To a
beginner, a position with 20 chessmen on the
board may contain far more than 20 chunks of
information, because the pieces can be placed in
so many configurations. A grandmaster, however,
may see one part of the position as "fianchettoed
bishop in the castled kingside," together with a
"blockaded king's-Indian-style pawn chain," and
thereby cram the entire position into perhaps
five or six chunks. By measuring the time it
takes to commit a new chunk to memory and the
number of hours a player must study chess before
reaching grandmaster strength, Simon estimated
that a typical grandmaster has access to roughly
50,000 to 100,000 chunks of chess information. A
grandmaster can retrieve any of these chunks from
memory simply by looking at a chess position, in
the same way that most native English speakers
can recite the poem "Mary had a little lamb"
after hearing just the first few words.
Even so, there were difficulties with chunking
theory. It could not fully explain some aspects
of memory, such as the ability of experts to
perform their feats while being distracted (a
favorite tactic in the study of memory). K.
Anders Ericsson of Florida State University and
Charness argued that there must be some other
mechanism that enables experts to employ
long-term memory as if it, too, were a scratch
pad. Says Ericsson: "The mere demonstration that
highly skilled players can play at almost their
normal strength under blindfold conditions is
almost impossible for chunking theory to explain
because you have to know the position, then you
have to explore it in your memory." Such
manipulation involves changing the stored chunks,
at least in some ways, a task that may be likened
to reciting "Mary had a little lamb" backward. It
can be done, but not easily, and certainly not
without many false starts and errors. Yet
grandmaster games played quickly and under
blindfold conditions tend to be of surprisingly high quality.
Ericsson also cites studies of physicians who
clearly put information into long-term memory and
take it out again in ways that enable them to
make diagnoses. Perhaps Ericsson's most homely
example, though, comes from reading. In a 1995
study he and Walter Kintsch of the University of
Colorado found that interrupting highly
proficient readers hardly slowed their reentry to
a text; in the end, they lost only a few seconds.
The researchers explained these findings by
recourse to a structure they called long-term
working memory, an almost oxymoronic coinage
because it assigns to long-term memory the one
thing that had always been defined as
incompatible with it: thinking. But brain-imaging
studies done in 2001 at the University of
Konstanz in Germany provide support for the
theory by showing that expert chess players
activate long-term memory much more than novices do.
Fernand Gobet of Brunel University in London
champions a rival theory, devised with Simon in
the late 1990s. It extends the idea of chunks by
invoking highly characteristic and very large
patterns consisting of perhaps a dozen chess
pieces. Such a template, as they call it, would
have a number of slots into which the master
could plug such variables as a pawn or a bishop.
A template might exist, say, for the concept of
"the isolated queen's-pawn position from the
Nimzo-Indian Defense," and a master might change
a slot by reclassifying it as the same position
"minus the dark-squared bishops." To resort again
to the poetic analogy, it would be a bit like
memorizing a riff on "Mary had a little lamb" by
substituting rhyming equivalents at certain
slots, such as "Larry" for "Mary," "pool" for
"school" and so on. Anyone who knows the original
template should be able to fix the altered one in memory in a trice.
A Proliferation of Prodigies
The one thing that all expertise theorists agree
on is that it takes enormous effort to build
these structures in the mind. Simon coined a
psychological law of his own, the 10-year rule,
which states that it takes approximately a decade
of heavy labor to master any field. Even child
prodigies, such as Gauss in mathematics, Mozart
in music and Bobby Fischer in chess, must have
made an equivalent effort, perhaps by starting
earlier and working harder than others.
According to this view, the proliferation of
chess prodigies in recent years merely reflects
the advent of computer-based training methods
that let children study far more master games and
to play far more frequently against
master-strength programs than their forerunners
could typically manage. Fischer made a sensation
when he achieved the grandmaster title at age 15,
in 1958; today's record-holder, Sergey Karjakin
of Ukraine, earned it at 12 years, seven months.
Ericsson argues that what matters is not
experience per se but "effortful study," which
entails continually tackling challenges that lie
just beyond one's competence. That is why it is
possible for enthusiasts to spend tens of
thousands of hours playing chess or golf or a
musical instrument without ever advancing beyond
the amateur level and why a properly trained
student can overtake them in a relatively short
time. It is interesting to note that time spent
playing chess, even in tournaments, appears to
contribute less than such study to a player's
progress; the main training value of such games
is to point up weaknesses for future study.
Even the novice engages in effortful study at
first, which is why beginners so often improve
rapidly in playing golf, say, or in driving a
car. But having reached an acceptable
performance--for instance, keeping up with one's
golf buddies or passing a driver's exam--most
people relax. Their performance then becomes
automatic and therefore impervious to further
improvement. In contrast, experts-in-training
keep the lid of their mind's box open all the
time, so that they can inspect, criticize and
augment its contents and thereby approach the
standard set by leaders in their fields.
Meanwhile the standards denoting expertise grow
ever more challenging. High school runners manage
the four-minute mile; conservatory students play
pieces once attempted only by virtuosi. Yet it is
chess, again, that offers the most convincing
comparison over time. John Nunn, a British
mathematician who is also a grandmaster, recently
used a computer to help him compare the errors
committed in all the games in two international
tournaments, one held in 1911, the other in 1993.
The modern players played far more accurately.
Nunn then examined all the games of one player in
1911 who scored in the middle of the pack and
concluded that his rating today would be no
better than 2100, hundreds of points below the
grandmaster level--"and that was on a good day
and with a following wind." The very best
old-time masters were considerably stronger but
still well below the level of today's leaders.
Then again, Capablanca and his contemporaries had
neither computers nor game databases. They had to
work things out for themselves, as did Bach,
Mozart and Beethoven, and if they fall below
today's masters in technique, they tower above
them in creative power. The same comparison can
be made between Newton and the typical newly minted Ph.D. in physics.
At this point, many skeptics will finally lose
patience. Surely, they will say, it takes more to
get to Carnegie Hall than practice, practice,
practice. Yet this belief in the importance of
innate talent, strongest perhaps among the
experts themselves and their trainers, is
strangely lacking in hard evidence to
substantiate it. In 2002 Gobet conducted a study
of British chess players ranging from amateurs to
grandmasters and found no connection at all
between their playing strengths and their
visual-spatial abilities, as measured by
shape-memory tests. Other researchers have found
that the abilities of professional handicappers
to predict the results of horse races did not
correlate at all with their mathematical abilities.
Although nobody has yet been able to predict who
will become a great expert in any field, a
notable experiment has shown the possibility of
deliberately creating one. László Polgár, an
educator in Hungary, homeschooled his three
daughters in chess, assigning as much as six
hours of work a day, producing one international
master and two grandmasters--the strongest
chess-playing siblings in history. The youngest
Polgár, 30-year-old Judit, is now ranked 14th in the world.
The Polgár experiment proved two things: that
grandmasters can be reared and that women can be
grandmasters. It is no coincidence that the
incidence of chess prodigies multiplied after
László Polgár published a book on chess
education. The number of musical prodigies
underwent a similar increase after Mozart's
father did the equivalent two centuries earlier.
Thus, motivation appears to be a more important
factor than innate ability in the development of
expertise. It is no accident that in music, chess
and sports--all domains in which expertise is
defined by competitive performance rather than
academic credentialing--professionalism has been
emerging at ever younger ages, under the
ministrations of increasingly dedicated parents and even extended families.
Furthermore, success builds on success, because
each accomplishment can strengthen a child's
motivation. A 1999 study of professional soccer
players from several countries showed that they
were much more likely than the general population
to have been born at a time of year that would
have dictated their enrollment in youth soccer
leagues at ages older than the average. In their
early years, these children would have enjoyed a
substantial advantage in size and strength when
playing soccer with their teammates. Because the
larger, more agile children would get more
opportunities to handle the ball, they would
score more often, and their success at the game
would motivate them to become even better.
Teachers in sports, music and other fields tend
to believe that talent matters and that they know
it when they see it. In fact, they appear to be
confusing ability with precocity. There is
usually no way to tell, from a recital alone,
whether a young violinist's extraordinary
performance stems from innate ability or from
years of Suzuki-style training. Capablanca,
regarded to this day as the greatest "natural"
chess player, boasted that he never studied the
game. In fact, he flunked out of Columbia
University in part because he spent so much time
playing chess. His famously quick apprehension
was a product of all his training, not a substitute for it.
The preponderance of psychological evidence
indicates that experts are made, not born. What
is more, the demonstrated ability to turn a child
quickly into an expert--in chess, music and a
host of other subjects--sets a clear challenge
before the schools. Can educators find ways to
encourage students to engage in the kind of
effortful study that will improve their reading
and math skills? Roland G. Fryer, Jr., an
economist at Harvard University, has experimented
with offering monetary rewards to motivate
students in underperforming schools in New York
City and Dallas. In one ongoing program in New
York, for example, teachers test the students
every three weeks and award small amounts--on the
order of $10 or $20--to those who score well. The
early results have been promising. Instead of
perpetually pondering the question, "Why can't
Johnny read?" perhaps educators should ask, "Why
should there be anything in the world he can't learn to do?"
--
((Udhay Shankar N)) ((udhay @ pobox.com)) ((www.digeratus.com))
