sci am special online issue 2005.no21 - science and art

1 SCIENTIFIC AMERICAN EXCLUSIVE ONLINE ISSUE APRIL 2005COPYRIGHT 2005 SCIENTIFIC AMERICAN, INC.COPYRIGHT 2005 SCIENTIFIC AMERICAN, INC.

http://www.sciam.com/index.cfm?ref=digitalpdf

1 SCIENTIFIC AMERICAN EXCLUSIVE ONLINE ISSUE APRIL 2005COPYRIGHT 2005 SCIENTIFIC AMERICAN, INC.

SCIENCE & ARTScientifi c American may be best known for its coverage of such disciplines as astronomy and biotechnology, but as longtime readers can attest, the magazine has a tradition of examining cultural phenomena as well. It is in this spirit that we have put together a collection of articles exploring the intersection of science and art.

In this exclusive online issue, leading scientists share their expertise on what science can reveal about art—and vice versa. Discover the rock art of southern Africa, some of which dates back to more than 20,000 years ago, offer-ing archaeologists unique insights into the minds of prehistoric humans. Tour the spectacularly decorated tomb of Nefertari, favorite wife of the Egyptian pharaoh Ramses II, which experts have taken great pains to conserve for future study—and public enjoyment. And learn how beautifully engraved wooden tablets hung under the roofs of religious buildings in Japan record a fl ourishing of native mathematics during the country’s period of seclusion from the West.

Art, it is often said, imitates life, and can thus provide a window on society. It can also reveal much about the brain. Studies suggest that a number of great artists have been affl icted with madness and that there exists a link between creativity and mood disorders. Likewise, studies of how the blind sketch their surroundings indicate that touch and vision are closely tied. Two articles in this issue explore those relationships.—The Editors

TABLE OF CONTENTS

Scientifi cAmerican.comexclusive online issue no. 21

2 Rock Art in Southern Africa BY ANNE SOLOMON; SCIENTIFIC AMERICAN MAGAZINE NOVEMBER 1996

Paintings and engravings made by ancestors of the San peoples encode the history and culture of a society thousands of years old

9 Preserving Nefertari's Legacy BY NEVILLE AGNEW AND SHIN MAEKAWA; SCIENTIFIC AMERICAN MAGAZINE OCTOBER 1999

The tomb of this ancient Egyptian queen is testament to the great love of Pharaoh Ramses II. Its preservation is testament to advances in conservation

15 Japanese Temple Geometry BY TONY ROTHMAN; SCIENTIFIC AMERICAN MAGAZINE MAY 1998During Japan’s period of national seclusion (1639-1854), native mathematics thrived, as evidenced in “sangaku”--wooden tablets engraved with geometry problems hung under the roofs of shrines and temples

22 Manic-Depressive Illness and Creativity BY KAY REDFIELD JAMISON; SCIENTIFIC AMERICAN MAGAZINE FEBRUARY 1995

Does some fi ne madness plague great artists? Several studies now show that creativity and mood disorders are linked

27 How the Blind Draw BY JOHN M. KENNEDY; SCIENTIFIC AMERICAN MAGAZINE JANUARY 1997

Blind and sighted people use many of the same devices in sketching their surroundings, suggesting that vision and touch are closely linked

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2 S C I E N T I F I C A M E R I C A N E X C L U S I V E O N L I N E I S S U E A P R I L 2 0 0 5

For more than three hours, a colleague and I walked through the grassy foothills of the Drakensberg Mountains in

KwaZulu-Natal, meeting not a soul on the way. Ultimately, we came to a wide cave half-screened by bushes and a splashing waterfall. Behind this watery veil are some of the finest specimens of ancient San, or “Bushman,” rock painting in South Africa. The water has not damaged them, although vandals have. We gazed at walls covered with more than 1,600 images of humans and animals engaged in myriad activities. That night, we slept in the cave, continuing our trip the next day.

That expedition, 10 years ago, was to obtain paint samples that might be radiocarbon-dated. One sample, from a painting of an eland (the biggest of all antelopes), contained microscopic quantities of organic material that al-lowed the image to be dated to about 400 years ago. Such a direct measure-ment is rare. Most pieces of rock art, painted in red, brown or yellow ocher—a hydrous iron oxide—contain no or-ganic carbon. So radiocarbon dating,

which measures the steady decline of the isotope carbon 14 in organic materi-als, cannot be used. Our earliest date comes from a Namibian cave, where ex-cavated floors contained painted slabs between 19,000 and 26,000 years old. The oldest date we have for painting on cave walls indicates that mural art was being made at least 3,600 years ago.

Rock paintings and engravings, tes-timony to a once ubiquitous hunter-gatherer presence, are found from coast to coast in thousands of diverse sites in southern Africa. Some sites are shelter-ing sandstone caves with hundreds of images; others contain only one or two figures. Some paintings look exquisite, their lines and colors still fresh. Others are faint and crumbling, damaged by time, water and the graffiti of unthink-ing visitors.

By far the most common subjects in rock art are humans—usually shown in profile, sometimes unclothed—and a wide variety of animals. The most re-vered of the animals are the larger her-bivores. The eland is widely celebrated, although different areas have their own

favorites: the elephant in South Africa’s Cape Province, for example, and a spe-cies of antelope called kudu in Zimba-bwe. A variety of other creatures are also pictured. Snakes, lions and fish are not uncommon in the art of the Drak-ensberg Mountains. Hippopotamuses, rhinoceroses, rhebok, baboons, os-triches and domesticated animals ap-pear in the art of many areas. Rarer themes include the aardwolf, aardvark and other creatures both real and imag-inary. With the exception of snakes and bees, the San people rarely painted rep-tiles and insects.

Rock art research is among the most demanding of archaeology’s subdisci-plines. Without recourse to convention-al archaeological methods—weighing, measuring, mapping and statistical comparison—rock art research relies on theoretically and culturally informed interpretations, supported by particu-larly rigorous argument. We do know that the artists were among the earliest inhabitants of southern Africa, the an-cestors of the modern-day San peoples. The term “San” is a linguistic label: the

Southern Africa

Rock Art in

Paintings and engravings made by ancestors

of the San peoples encode the history and

culture of a society thousands of years old

By Anne Solomon originally published in November 1996

COPYRIGHT 2005 SCIENTIFIC AMERICAN, INC.


San and Khoekhoe—formerly Hotten-tot—languages make up the Khoisan group of many related languages and dialects, characterized by click sounds. The plant-gathering and hunting econ-omy of the San has been extensively studied as a model for how people lived until relatively recent times, when ani-mals and plants were domesticated.

Although rock art occasionally pro-vides historical information, paintings and petroglyphs are not historical doc-uments. It is only after the 15th century, when Europeans “discovered” southern Africa, that we begin to have a clearer picture of historical conditions. In 1652 the Dutch established the first perma-nent settlement in Cape Town. As the newcomers expanded their domain over the next three centuries, they frequently displaced indigenous peoples, whose traditional ways of life changed or dis-appeared entirely. In some areas, theft of cattle and horses by the San led to retaliatory raids by European farmers. Episodes are recorded in which entire San groups were massacred. Survivors of these communities were eventually

absorbed into indigenous herding and farming societies or became laborers around European settlements.

The ancient art traditions had ceased by the 20th century. Today rela-tively few San speakers live in the old ways, except in parts of Botswana and Namibia. Only the wide distribution of archaeological sites, place-names and rock art alerts us to the vast areas once occupied by these peoples.

In studying the art, the archaeolo-gist is forced to seek all imaginable clues. There are two classes of work: the paintings, which usually occur in caves and shallow shelters, and incised boulders and other surfaces that are found in the dry interior. The petro-glyphs, which tend to be less figurative, have until recently attracted less atten-tion than the paintings.

The style and, to a lesser extent, the subject matter of the paintings vary be-tween regions. Often a single site in-cludes works in several styles, so that it is impossible to tell whether it is the work of different artists or art from dif-ferent historical periods. Early re-

searchers suggested that simpler or less delicate images, in one color only, are the oldest, with color range and stylis-tic intricacy evolving through time. To-day we know there is no such straight-forward correlation. Some of the less accomplished work is probably the most recent—some perhaps made by shepherds and children.

Devotees have been trying to inter-pret rock art for more than a century. Those interpretations change with new knowledge, discoveries and intellectual currents. San testimonies would be ex-tremely helpful in guiding us, but unfor-tunately, only one exists. It came from a Lesotho San man named Qing, who acted as a guide to a British official, Jo-seph Orpen, in the Lesotho Mountains in 1873. Qing was familiar with the making of rock paintings and com-mented on the paintings that they saw. Qing confirmed what some already sus-pected: that rock painting, as one con-temporary European scholar wrote, was not “the mere daubing of figures for idle pastime” but “a truly artistic conception of the ideas which most deeply moved the Bushman mind.”

In addition to Qing’s direct testimo-ny, researchers also draw on indirect ac-counts from San speakers. By far the richest body of material was collected a century ago, from people speaking a San language known as /Xam (the ini-tial character is a click sound). In 1870 a group of /Xam San men from north-ern Cape Province were imprisoned in Cape Town for offenses ranging from stock theft to murder. Wilhelm H. I. Bleek, a German philologist, acquired custody of the men, who built huts at the bottom of his garden and worked as domestic servants. But their main task was sharing accounts of their traditions. While Bleek focused on the language, his sister-in-law, Lucy C. Lloyd, record-ed thousands of pages of /Xam lore. A selection was published in Specimens of Bushman Folklore, written by W.H.I. Bleek and L. C. Lloyd (George Allen,

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Western Cape

Madagascar

Mozambique

Angola

Congo(Kinshasa)

ZambiaMalawi

Namibia

Botswana

SouthAfrica

Zimbabwe

Congo(Brazzaville)Gabon

KwaZulu-Natal

Rwanda

Burundi

Uganda

Tanzania

Kenya

ROCK ART is found all over southern Africa. Its range attests to the vast areas once occupied by the ancient San. (Except as noted, all the paintings that follow are from KwaZulu-Natal.)

Lesotho

Swaziland



London, 1911).This extraordinary colonial en-

counter revealed the /Xam world: per-sonal histories, myths, religious beliefs, and magical and mundane practices.

Although by the late 19th century these people no longer practiced rock art, their commentaries have proved ex-tremely valuable for interpreting it. To-gether with Qing’s account, the /Xam testimonies have helped show that Af-rican rock art is much more than mere decoration or reflections of everyday concerns. Instead rock art can best be understood as a religious art, reflecting the /Xam people’s relations with the spirit world and to ritual practices. And almost certainly the act of painting it-self had magical importance.

A comparison of Qing’s account with the /Xam testimonies shows broad simi-larities between /Xam and Lesotho San myths. Both San peoples esteemed a cre-ator figure named /Kaggen. Both also spoke of underwater beings and of the creation of the eland. Qing supplied the long-sought link between rock art and myth, whereas the /Xam accounts pro-vided crucial cultural detail that Qing’s commentary lacked. Researchers since have relied heavily on both sources.

Window on Culturesever al schol a rs have noted the extraordinary similarities between the mythology of San groups far distant from one another in time and space. All San peoples tell of a primeval time when animals were people; after an ini-

tial creation event, they were differenti-ated. But these fi rst people were often stupid, lacking customs and manners, and only after a second creation did they become real people.

Many stories recount the doings of these animal people. Some explain the origins of fire, heavenly bodies and oth-er physical phenomena. We hear why the baboon has a hairless rump, why people marry and why death is inevi-table. Other narrative themes include encounters with warlike neighbors or dangerous carnivores. Food is a con-stant preoccupation, with a surprising number of stories featuring autopha-gy—the eating of one’s own body. The stories dramatize the dilemmas of exis-tence that faced San hunter-gatherers and emphasize themes involving death and regeneration.

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DANCING, accompanied by clapping and singing in melodic overtones, is an integral part of San life. Women may dance alone, as in the painting (left); a few are depicted with leather “aprons” that are still occasionally worn. The detail ( right) from another painting of a dance probably depicts a female initiation ceremony.

Dancing into the Night

ANNE SOLOMON is a graduate of the University of Cape Town, where she obtained her Ph.D. She is a former postdoctoral research fellow of the Getty Center for the History of Art and the Humanities in Los Angeles and was, until recently, senior curator of archaeology at the Natal Museum in Pietermaritzburg. Her book on San arts, The Imagination of the San, is to be published in early 2005 by the Uni-versity of KwaZulu-Natal Press.

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THERIANTHROPE (a half-animal, half-human figure) derives from San religious tradition. In the beginning, animals were humans; only after a creation event were they differentiated. This creature seems to be carrying a smaller antelope on its back.



The belief that animals were once people allows an interpretation of the-rianthropes—figures both human and animal. Some of these paintings, and others of fantastic creatures, may por-tray beings from the primordial world. Alternatively, some researchers contend that they depict the shaman’s experi-ence of physical transformation during a trance—when shamans enter the realm of the spirits of the dead.

Some experts, notably David Lewis-Williams and his colleagues at the Uni-versity of the Witwatersrand, Johan-nesburg, have correctly observed that the art does not illustrate the mythol-ogy. They propose instead that rock art is connected to ritual—and to one ritu-al in particular: a healing dance that is still practiced by communities in Bo-tswana and Namibia (these peoples do not make rock art). During a ritual

dance that may last all night, shamans enter an altered state of consciousness induced by rhythmic movement, sing-ing and clapping. In this hallucinatory state, they believe that they travel to the spirit realm to battle supernatural forc-es that cause illness.

Lewis-Williams and his associates have proposed that shamanic halluci-nations may have prompted the first making of art, in Africa and elsewhere. A

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HUMANS are represented in varying styles. The men carrying quivers of arrows on their backs shown here (top) are exceedingly tall and thin, whereas the women are voluptuous (below left). The clothed figures (below right), wearing leather cloaks known as karosses, have strange concave faces.



They hypothesize that because humans all share the same neurological circuit-ry, visual hallucinatory forms should be similar throughout time—and that geometric designs drawn in the Euro-pean Paleolithic and Bronze ages, as well as North American Indian art, may also be understood in terms of the healing trance dance and shamanic hallucinatory experiences.

It is certainly true that many crea-tures in San mythology are not por-trayed in the rock art. Yet mythology does provide a crucial context for un-derstanding ritual. Myths tell of the origin of death and disease, the trials of life that ritual practices address. Art-making can probably best be seen as being linked to ritual practices—such as rainmaking and initiation—recorded from recent San peoples.

Rainmakersr ece n t st udies have shown that hunting scenes in rock art are not as common as early researchers believed. Some paintings originally thought to depict hunts almost certainly portray rainmaking. Testimonies from the /Xam show that they viewed the rain cloud as an animal walking the coun-tryside on “legs” of streaming rain. Rainmakers had to lead a large herbi-

vore from its home in a water hole, take it to a high place and slaughter it; where its blood ran, rain would fall. The rain animals depicted in rock art resemble large herbivores, such as cattle, hippos or antelopes, but often with strange features and proportions. The rain bull in myths and stories embodied the le-thal thunderstorm, whereas the female rain animals brought gentle rain.

Qing, in Lesotho, also described rainmaking. He described one rock painting as depicting underwater be-ings who tamed “eland and snakes.” This painting shows six humanlike fig-ures and two bristly animals of no known species, one led by a thong at-tached to its nose, the other being ap-proached by two men with spears. De-spite their geographic separation, both Qing and the /Xam described mark-edly similar beliefs regarding rain.

Some have argued that rainmakers depicted in such paintings were living shamans, but there is ample evidence that they were in fact considered to be benevolent spirits—dead family mem-bers who helped their living kin. Qing, for example, described antelope-headed men in rock paintings as “men who had died and now lived in rivers.” These men, as well as the underwater beings leading the rain animals, can best be in-

terpreted as spirits of the dead. /Xam commentators specifically stated that “sorcerers of rain” were dead people, as were “game sorcerers” to whom the liv-ing would appeal for help in the quest for food.

Understanding San beliefs about rain is crucial to understanding their art. Like Kalahari peoples today, the San told of two important beings, a creator figure and a master of death and disease. In the /Xam narratives, this death deity is the Rain Bull. He is the dangerous thunder-storm and the water in the waterhole. People became stars after they died, which then fell into the water where the Rain Bull lived. Qing’s accounts of dead people living underwater derive from this same complex of beliefs.

Clearly, rock art images of people catching a rain animal allude to more than just controlling the weather. As master of the spirit world, the Rain Bull controls not just rain but also life and death, sickness and health. The “rain paintings” common in rock art can therefore be linked to people’s efforts to prevent disease and misfortune and not just storms or drought.

Importance of Initiationhun t er-gat her er societies such as the San are egalitarian, with both A

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ENGR AVINGS are found in arid areas, and the choice of subjects is puzzling. The boulder from northern Cape Province in South Afri ca, depicts antelopes. (Near its top left are sticklike figures of a European couple, probably added later.)

Mysterious Engravings



sexes having equal access to resources. Nevertheless, social distinctions do ex-ist, and the two most important in these societies—gender and age—meet in the institution of initiation. Ceremonies for girls at puberty, copiously documented, seem to eclipse male initiation, which seems at most to have been a lesser cel-ebration of a boy’s fi rst kill. Contempo-rary Kalahari hunter-gatherers also have conspicuous female initiations. Numerous /Xam stories tell of female initiates who disobeyed the puberty se-clusion rules, sneaked off, and were then abducted and drowned by the Rain Bull. (After entering the cultural repertoire, the Rain Bull and other vi-

sual images may have been used in var-ied contexts for different purposes. Ini-tiation paintings, for example, do not seem to involve interactions with the spirit world.)

/Xam initiation stories tell of the dangers attractive female initiates posed to men. The purpose of the rites, how-ever, was probably equally to protect young women from inappropriate male attention. In the close proximity of band societies, members are highly dependent on social cooperation and harmony. Tensions between kin arising from sex-ual jealousies and misdemeanors may be socially and economically destructive. A purpose of initiation was surely to regu-

late interpersonal behavior and avoid such conflicts.

Though not abundant, some rock art sites and compositions may have been part of gender-specifi c initiation rites. Hugely voluptuous female fi gures with genital details, brandishing cres-cent-shaped objects, may well relate to female initiation. Paintings of women’s dances may be linked to initiation or birth. A remote shelter high in the south-western Cape Province mountains—un-usual for its abundance of female fi gures and total absence of male imagery—may also pertain to female initiation or birth. Another composition apparently depict-ing a female initiation ceremony is found in a KwaZulu-Natal Drakensberg site. It shows a prone fi gure and three clapping women in a circular enclosure. Other fi gures dance outside. On the periphery of the composition (not shown in the il-lustration) is a male fi gure with consid-erably overemphasized genitalia.

Many sites contain a profusion of diverse imagery, different in theme and style. Some may have been used over centuries for a variety of purposes, oth-ers only once or twice, for a particular end. Recent interpretations have em-phasized healing of the sick, an action only rarely rendered explicitly in rock art. However, some images previously thought to depict rain animals may be of the Rain Bull himself. Because he is the death fi gure, these images may have been painted in an effort to cure physi-cal illnesses.

Of course, paintings and engrav-ings depicting European colonists, wagons, soldiers and domestic animals may well be records of real events rath-er than ritual occasions. In addition, some rock art appears to reflect inter-actions between the San and other groups. John E. Parkington and his collegues at the University of Cape Town have suggested that handprints found along the southwestern coast, usually overlying earlier art, may have been the work of Khoi herders. Depic-tions of cattle introduced by the mi-grating herders and farmers, as well as iron artifacts, maize cobs and glass beads found in excavations, all testify A

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PROBABLE R AIN CEREMONY, showing an animal being captured by rainmakers (top), is painted in red ocher. The eland (bottom) is the southern San creator’s favorite animal—and, along with other large herbivores, is associated with rain.



to San involvement in other African economies.

New Interpretationsthe f inal im ages themselves may not be alone in creating signifi cance to the prehistoric artists. The act of paint-ing itself may also have been important. Recent research in anthropology and art history has drawn attention to the process of art making and of the materi-als used, as opposed to creating an end product for viewing (as is usual in West-ern arts). This may be especially rele-vant to understanding San arts.

Probably each step of the painting process in San art carried cultural sig-nificance. One indigenous account from 1910 mentions ritual preparations that involved pigments being ground by women at full moon. In my research, I have emphasized the symbolic and spir-itual significance of technically nones-sential substances, such as fat and eland blood, that were said to be added to the paint mixture, presumably as magical aids. The act of making art, it appears, exerted magical effects that could influ-ence the spirits and help control fate.

Powerful analytical techniques are now available for identifying these paint ingredients and culture-specific “reci-pes” of ancient paintings. This informa-tion would not only help us understand

the significance of rock art but is also of interest for reasons ranging from re-source exploitation to ancient trade to contemporary conservation.

I have researched the use of pigments and paints, with a view to identifying “magical” additives. This work, with the assistance of soil scientists at the University of KwaZulu-Natal, has in-volved a suite of techniques, including x-ray fluorescence (to provide quantita-tive data on minor and trace element composition), x-ray diffraction (to re-veal crystal structure and parent rock types of paint ingredients), and environ-mental scanning electron microscopy (to yield qualitative data on elements present). Another promising technique that we have used experimentally is syn-chrotron radiation analysis. This tech-nique, suitable for tiny samples, allows

for x-ray fluorescence and x-ray diffrac-tion of the same spot. So far these so-phisticated research tools have gener-ated more questions and problems than answers. The variability in both pig-ments and paints may be too vast to pro-duce results relevant to answering ar-chaeological questions.

The function and many meanings of rock art in history and prehistory still generate debate, although a broadly spiritual role is now well established. As an extraordinary and evocative record of the past, San rock art is becoming part of the culture of postapartheid South Africa. Yet paintings face many threats. Through the combined efforts of a spectrum of specialists, we hope to ensure that the rock art will endure as a testament to an ancient African culture, tragically displaced.

Rocky Bestiary

DIVERSE ANIMAL S occur in San art. Some rain animals resemble a hippo potamus (top); this one is from Zimbabwe. The delicate rhebok (bottom) is a game animal. The painting actually contains two rhe boks, superposed. (The second rhebok has its head downward.) Humans and large herbivores are believed to possess n/ow, a quality linked to birth, death and weather: good n/ow brings rain, whereas bad n/ow is associated with harsh conditions. The San’s preference for portraying humans and large herbivores may have to do with their possessing n/ow. A

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M O R E T O E X P L O R E

People of the Eland. Patricia Vinnicombe. University of Natal Press, 1976.

Images of Power: Understanding Bushman Rock Art. J. David Lewis-Williams and Thomas A. Dowson. Southern Book Publishers, 1989.

Hunters and Herders of Southern Africa. Alan Barnard. Cambridge University Press, 1992.

The Rain and Its Creatures: As the Bushmen Painted Them. Bert Woodhouse. William Waterman Publications, Johannesberg, 1992.

Miscast: Negotiating the Presence of the Bushmen. Edited by Pippa Skotnes. University of Cape Town Press, 1996.

Rock Paintings of South Africa: Revealing a Legacy. Stephen Townley Bassett. David Philip, Cape Town, 2001.

The Broken String: The Last Words of an Extinct People. Neil Bennun. Viking (Penguin U.K.), 2004.


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Little is known about Ne-fertari, favorite wife of

Ramses II, the pharaohwho ruled Egypt from about1290 to 1224 B.C. But it isclear she was beloved by herhusband. He ensured that thestatue dedicated jointly toNefertari and the goddessHathor at Abu Simbel wason the same scale as his, anhonor no other Egyptianqueen achieved. His namesfor Nefertari bespoke greatlove as well: “lady of charm,”“sweet of love,” “beautiful offace,” “for whom the sunshines.” And after her death,Ramses II bestowed on Nefer-tari a final, spectacular trib-ute: even though she was notof royal lineage, he buriedher in a decorated tomb inthe Valley of the Queens.

The wall paintings in Ne-fertari’s tomb are among themost beautiful of all phara-onic funerary art. As in other tombs, the images of Nefertariare solely about her journey to the afterlife and her encoun-ters with Osiris and Isis, among other deities; no paintings de-pict her everyday life with Ramses II or her six or seven chil-dren. But even as they describe a ritualized journey—followinga strict formula laid out in the 174 or so chapters of the Egyp-tian Book of the Dead—the paintings in Nefertari’s tomb areunique in their vivid color and detail and richness.

Ramses II’s devotion to his queen may have protected her asshe moved into the afterlife, but it could not protect her as shemoved through the ages. When Italian archaeologist ErnestoSchiaparelli discovered the tomb in 1904, it had already beenbroken into and looted. The treasures that were to accompanyNefertari in her death were gone, her sarcophagus smashed and

her mummy spirited away.The tomb’s wall paintings

were severely disturbed aswell, but this was the result ofnatural processes, not of graverobbers. Salt had leached fromthe limestone bedrock intowhich the tomb was carvedand had crystallized below thepainted plaster, destroying alarge proportion of the paint-ings. Over the next decades,visitors to the spectaculartomb inadvertently accelerat-ed this deterioration: the mainculprit was most probablytheir incessant touching of thefragile surfaces, but moisturefrom their breath and sweatmay have contributed as well.Archaeologists and art histori-ans became increasingly con-cerned, and in the 1920s theMetropolitan Museum of Artin New York City sponsoredextensive photographic docu-mentation of the murals. (This

record supplemented 132 glass plate negatives that Schiapa-relli’s photographer had assiduously made in 1904 and 1905,as well as other photographic records that had been made inthe intervening years.) But the paintings remained in danger;finally, they were so obviously imperiled that the Egyptiangovernment closed the tomb to the public in the late 1930s.

Nefertari’s lovely legacy then sat in dusty silence, visited onlyby a few scholars. Beginning in the late 1970s, several groups—including the United Nations Educational, Scientific and Cul-tural Organization (UNESCO), the International Center for theStudy of Preservation and the Restoration of Cultural Property,and Cairo University—conducted a series of studies about thecondition of various important tombs. The research broughtto light, again, the deplorable state of the Nefertari wall paint-ings and ultimately led conservators at the Getty Conserva-tion Institute and the Egyptian Antiquities Organization topropose saving the remaining paintings—and potentially re-opening the tomb to the public.

Between 1986 and 1992 the two organizations conservedthe paintings, employing advanced tools and techniques. The

10 SCIENTIFIC AMERICAN EXCLUSIVE ONLINE ISSUE APRIL 2005

The tomb of this ancient Egyptian queen is testament to the great love of Pharaoh Ramses II.

Its preservation is testament to advances in conservation

Preserving Nefertari’s Legacyby Neville Agnew and Shin Maekawa

PAST AND PRESENT come face to face as conservator LorenzaD’Alessandro examines a painting of Queen Nefertari (previouspage), assessing how best to save it. As its colorful entrance reveals,the tomb of Nefertari in the Valley of the Queens contains some ofthe most spectacular paintings of its era (above).

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originally published in October 1999


project combined the skills of art historians, conservationists,Egyptologists, environmental scientists, topographers, chem-ists, technicians and other specialists. It was not only a matterof protecting the wall paintings—a challenging enough task—but the microclimate and hydrological conditions of the en-tire tomb had to be understood and addressed so that the de-struction would not start anew once the work was finished.

Now, seven years after completion, it is apparent that thepaintings are stable and that the project is an enduring suc-cess. Visitors are once again able to see the marvelous imagesand to admire the serene beauty of Queen Nefertari. Andthey know they are looking at originals, not at the work of20th-century hands. The team that labored on the undertak-ing agreed from the outset that no restoration would bedone. In other words, no paint would be applied where ithad been lost—despite the fact that the photographic recordscould have permitted such restoration.

The restoration of works of art is sometimes done, even ifreluctantly, to re-create the original visual harmony and con-sistency of a piece. This process, however, inevitably compro-mises the integrity of the object. In the case of Nefertari’stomb—a site of great antiquity—everyone involved decidedthat the wall paintings should show evidence of the passageof time and that the ancient should not be hybridized withthe modern.

Assessing the Damage

The team began the conservation process by evaluatingthe overall condition of the paintings. They studied every

inch of plaster to see where it had fallen off, whether it washolding together or holding to the wall, and whether it hadcracked; they also looked for places where rock fragmentswere jutting through the plaster. They examined the paint to


SALT CRYSTALS, which formed as water infiltrated the lime-stone into which the tomb was carved, forced the plaster awayfrom the bedrock and destroyed a large proportion of the paint-ings before the conservators began their work (above, top). Ear-lier efforts at restoration had tried, unsuccessfully, to stem thedamage by holding the plaster in place with gauze (above, bot-tom). This time the approach was thorough: conservators re-moved the salt crystals, reattached the plaster to the walls andcleaned the paintings (right).


see whether it was flaking, being abraded or losing its cohe-siveness and whether it was covered with dirt, dust or insectnests. At the same time, the team recorded the extent of thesalt crystallization on the surface of the paintings and be-tween the rock face and the plaster. Finally, they located theearlier interventions: the places where paintings had been re-touched, holes patched, and facing—such as gauze or adhe-sive tape—applied.

Once the condition survey was finished, Paolo Mora, formerchief conservator of the Central Institute of Restoration inRome, and his wife, Laura Mora, began the laborious workof conserving the paintings. The Moras and their colleaguesstarted by taking minute pigment samples from the paintingsas well as samples of the plaster underneath. Because of so-phisticated machines and techniques—including x-raydiffraction, x-ray fluorescence, polarizing light microscopy,and gas and liquid chromatography—the scientists needed

only the tiniest of samples to determine the chemical compo-sition of the materials. Once the ingredients were known, theresearchers could figure out how best to save or stabilize theancient paintings. In the interim, they prevented further degra-dation by applying strips of Japanese mulberry bark paper tothe plaster, which kept it from falling off the walls and whichcould be easily removed once they were ready to begin work.

They discovered that the pigments were, not surprisingly,typical of Nefertari’s time: Egyptian green; Egyptian blue (orcuprorivaite); red from iron oxide, with a trace of manganeseand arsenic; ocher for yellow; calcite, anhydrite and huntitefor white; and charcoal for black. The binding medium—which holds the pigments together—was largely gum arabic,a natural resin from a local acacia tree. The workers alsofound that some of the paintings had been varnished withtree resin and egg white—although two modern syntheticresins showed up as well in lab analyses, suggesting that there


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had been some earlier, undocumented restoration effort. Theplaster was composed of gypsum, anhydrite and Nile silt,with some crushed limestone mixed in; wheat straw had beenused to reinforce it and to prevent it from cracking as it dried.

Once they knew what they were dealing with, the teammembers could set about the work. For 469 days—spreadover five years—they cleaned paintings, removed salt crystalsfrom rock faces and in places underneath the plaster, andthen reattached the plaster to the bedrock using an acrylicadhesive mixed with local sand and gypsum powder. Theyreattached flakes of paint and in places where the bindingmedium had degraded added a compound called acryliccopolymer to prevent it from breaking down further. Theyfilled in holes with lime mortar and removed old, badlydone repairs.

It was critically important that these efforts not affect theoriginal colors. So before they even started any of this con-servation work, Michael Schilling of the Getty ConservationInstitute made 1,500 color measurements at 160 locationsthroughout the tomb. He used a chromometer (in this case, aMinolta CR-121) to assess exact hue. These records not onlyhelped to guide the process by demonstrating that no shift inthe color had occurred but also will aid ongoing monitoringof the paintings.

Keeping the Salt Out

Concern about the future of these paintings centers on themost obvious threat: salt. When work began on the tomb,

thick, 15-millimeter (0.6-inch) layers of salt were discoveredunder the plaster, forcing it from the wall. The salt camefrom Theban limestone, the marine sediment into which thetomb was cut. Salt is not a worry in most tombs, because theextremely dry Egyptian climate serves as a powerful preserva-tive, keeping mummies and their artifacts sere and intact. Butthe site of Nefertari’s tomb had some source of water that dis-solved the salt and made it mobile.

Not everyone who has worked on the project agrees—even

today, after years of study—about where exactly the watercame from. Some was clearly introduced in the wet plasterapplied by Ramses’s wall painters themselves. That moisture,however, would not have caused thick layers of crystals toform. A more probable explanation is the very occasional,but very heavy, rain that falls about every 50 years on aver-age. Many of the tombs in the region, including those in theValley of the Kings, have flooded repeatedly since antiquity.Moisture infiltration is evident in Nefertari’s tomb, especiallyat the entrance. It is likely that water seeped slowly throughfissures, leaching salt from the bedrock as it traveled andleaving salt behind and on the painted surfaces as it evapo-rated from the walls.

To monitor humidity and temperature, one of us (Maekawa)recorded both the external climate and the microclimate of thetomb over several years and seasons. He found that the exter-nal temperature varied from a high of 40 degrees Celsius (104degrees Fahrenheit) in the summer to 10 degrees C (50 degreesF) in the winter mornings; external humidity fluctuated wildlyas well, from 80 percent in the winter to as low as 10 percentduring the rest of the year. These outside conditions could af-fect the tomb because of leaks at the entrance, but for the mostpart, the internal temperature remained about 29 degrees Cand humidity was stable at 50 percent. Maekawa also notedthat there was natural ventilation during the winter: cooler airentered the tomb at floor level, forcing warmer air out throughthe entrance stairway. This movement caused the paintingsand plaster to stay dry. When visitors entered the tomb, how-ever, humidity rose sharply.

Maekawa had to take into account the fact that peaktourist season falls primarily during the summer—just whenair is not circulating back outside and humidity could easilybecome trapped in the tomb. The more sweat and moisturein the tomb, the more likely it is that microflora, such asmold and bacteria, will grow on the surface of the paintingsand destroy them and that salt crystals could begin to devel-op again.

In addition to monitoring temperature and humidity, Maeka-


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ENVIRONMENTAL MONITORING is crucial to the future ofthe paintings. Shin Maekawa used a solar-powered system to studythe microclimate of the tomb (left); he determined that the numberof visitors had to be carefully regulated so that the temperature andhumidity in the tomb did not catalyze the growth of salt crystalsagain. No more than 150 tourists are allowed in per day (below).

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wa had to carefully track levels of carbon dioxide. Because thetomb’s natural ventilation is poor, this gas does not move outof the tomb easily and can pose a health hazard for tourists.Carbon dioxide can also react with moisture in the air, pro-ducing carbonic acid, which can discolor the wall paintings.Maekawa found that ambient levels of 340 parts per million(ppm) surged to 2,500 ppm when tourists visited the tomb. Forhealth reasons, levels should not get higher than 1,000 ppm.

Keeping these findings in mind, the Egyptian AntiquitiesOrganization—now the Supreme Council of Antiquities—de-signed a system that would ostensibly protect the tomb andyet would allow visitors to see it. They installed lights thatgave off very little heat. And they set up a ventilation systemthat extracts air from the tomb, allowing unfiltered, dry airfrom the outside to flow in and replace the humid air generat-ed by the visitors. Since late 1995 a maximum of 150 people aday, in groups of 10 to 15, have been allowed in for no morethan 15 minutes. (They pay $30 for the visit, a fee that hasgenerated about $1.5 million each year for the Egyptian gov-ernment.) To date, the only noticeable impact of the stream ofvisitors has been an influx of dust, which has settled on thepaintings, obscuring them somewhat.

Despite this careful monitoring, the potential damage of thesevisitors needs to be considered carefully and periodically evalu-ated. Although people should be free to see the beautiful paint-ings, to experience the mystery and awe of this gate to ourpast, we must establish a balance—a difficult task that extendsfar beyond Nefertari’s tomb to all other threatened archaeolog-ical sites. Because damage is irreversible and cumulative—andbecause we seem to be able to destroy in just a few decadeswhat has survived for millennia—it may not be right for ev-eryone to have the access they expect. After all, that is whatRamses II intended for his wife: a peaceful, sealed existence.


Further Reading

The Great Belzoni: Archaeologist Extraordinary. StanleyMayes. Walker, 1961.

Art and Eternity: The Nefertari Wall Paintings Conserva-tion Project 1986–1992. Edited by M. A. Corzo and M. Afshar.Getty Conservation Institute, Los Angeles, 1993.

Daily Life in Ancient Egypt. Andrea G. McDowell in ScientificAmerican, Vol. 275, No. 6, pages 100–105; December 1996.

House of Eternity, the Tomb of Nefertari. John K. McDon-ald. J. Paul Getty Museum, Los Angeles, 1996.

The Authors

NEVILLE AGNEW and SHIN MAEKAWA work together at theGetty Conservation Institute in Los Angeles and have collaboratedon archaeological projects all over the world. Agnew, who receivedhis doctorate in chemistry, is group director for information andcommunications at the GCI. Maekawa, who specializes in environ-mental monitoring and the control of microenvironments, is a se-nior scientist at the institute. Maekawa developed the oxygen-freedisplay cases for pharaonic mummies that are used in the EgyptianMuseum in Cairo.

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WALL PAINTINGS are now fully conserved, and the images ofQueen Nefertari’s voyage to the afterlife remain vibrant. Theircontinued survival depends on striking a careful balance be-tween public access and protection of the paintings.

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Of the world’s countless cus-toms and traditions, perhapsnone is as elegant, nor as

beautiful, as the tradition of sangaku,Japanese temple geometry. From 1639to 1854, Japan lived in strict, self-im-posed isolation from the West. Accessto all forms of occidental culture wassuppressed, and the influx of Westernscientific ideas was effectively curtailed.During this period of seclusion, a kindof native mathematics flourished.

Devotees of math, evidently samurai,merchants and farmers, would solve awide variety of geometry problems, in-scribe their efforts in delicately coloredwooden tablets and hang the works un-der the roofs of religious buildings. Thesesangaku, a word that literally meansmathematical tablet, may have been actsof homage—a thanks to a guiding spirit—or they may have been brazen challeng-es to other worshipers: Solve this one ifyou can!

For the most part, sangaku deal withordinary Euclidean geometry. But theproblems are strikingly different fromthose found in a typical high school ge-ometry course. Circles and ellipses playa far more prominent role than in West-ern problems: circles within ellipses, el-lipses within circles. Some of the exercis-es are quite simple and could be solvedby first-year students. Others are nearlyimpossible, and modern geometers in-variably tackle them with advancedmethods, including calculus and affinetransformations. Although most of theproblems would be classified today as

recreational or educational mathemat-ics, a few predate known Western re-sults, such as the Malfatti theorem, theCasey theorem and the Soddy hexlettheorem. One problem reproduces theDescartes circle theorem. Many of thetablets are exceptionally beautiful andcan be regarded as works of art.

Pleasing the Kami

It is natural to wonder who createdthe sangaku and when, but it is easier

to ask such questions than to answerthem. The custom of hanging tablets atshrines was established in Japan cen-turies before sangaku came into exis-tence. Shintoism, Japan’s native religion,is populated by “eight hundred myriadsof gods,” the kami. Because the kami, itwas said, love horses, those worshiperswho could not present a living horse asan offering to the shrine might insteadgive a likeness drawn on wood. As a re-sult, many tablets dating from the 15thcentury and earlier depict horses.

Of the sangaku themselves, the oldestsurviving tablet has been found in To-chigi Prefecture and dates from 1683.Another tablet, from Kyoto, is dated1686, and a third is from 1691. The19th-century travel diary of the mathe-matician Kazu Yamaguchi refers to aneven earlier tablet—now lost—dated1668. So historians guess that the cus-tom first arose in the second half of the17th century. In 1789 the first collec-tion containing typical sangaku prob-lems was published. Other collections

followed throughout the 18th and 19thcenturies. These books were either hand-written or printed with wooden blocksand are remarkably beautiful. Todaymore than 880 tablets survive, with ref-erences to hundreds of others in thevarious collections. From a survey ofthe extant sangaku, the tablets seem tohave been distributed fairly uniformlythroughout Japan, in both rural and ur-ban districts, with about twice as manyfound in Shinto shrines as in Buddhisttemples.

Most of the surviving sangaku con-tain more than one theorem and are fre-quently brightly colored. The proof ofthe theorem is usually not given, onlythe result. Other information typicallyincludes the name of the presenter andthe date. Not all the problems deal sole-ly with geometry. Some ask for the vol-umes of various solids and thus requirecalculus. (This point raises the interest-ing question of what techniques thepractitioners brought into play; somespeculations will be offered in the fol-lowing discussion.) Other tablets con-tain Diophantine problems—that is, al-gebraic equations requiring solutions inintegers.

In modern times the sangaku havebeen largely forgotten but for a fewdevotees of traditional Japanese mathe-matics. Among them is Hidetoshi Fu-kagawa, a high school teacher in AichiPrefecture, roughly halfway betweenTokyo and Osaka. About 30 years agoFukagawa decided to study the historyof Japanese mathematics in hopes offinding better ways to teach his courses.A mention of the math tablets in an oldlibrary book greatly astonished him, forhe had never heard of such a thing. Sincethen, Fukagawa, who holds a Ph.D. inmathematics, has traveled widely in Ja-pan to study the tablets and has amasseda collection of books dealing not only


Japanese Temple GeometryDuring Japan’s period of national seclusion (1639–1854), native

mathematics thrived, as evidenced in sangaku—wooden tablets engravedwith geometry problems hung under the roofs of shrines and temples

by Tony Rothman, with the cooperation of Hidetoshi Fukagawa

SANGAKU PROBLEMS typically involve multitudes of circles within circles or ofspheres within other figures. This problem is from a sangaku, or mathematical wood-en tablet, dated 1788 in Tokyo Prefecture. It asks for the radius of the nth largest bluecircle in terms of r, the radius of the green circle. Note that the red circles are identical,each with radius r/2. (Hint: The radius of the fifth blue circle is r/95.) The original so-lution to this problem deploys the Japanese equivalent of the Descartes circle theorem.(The answer can be found on page 21.)

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This striking problem was written in 1912 on a tablet extant inMiyagi Prefecture; the date of the problem itself is unknown.At a point P on an ellipse, draw the normal PQ such that it in-tersects the other side. Find the least value of PQ. At firstglance, the problem appears to be trivial: the minimum PQis the minor axis of the ellipse. Indeed, this is the solution if b < a ≤ √2b, where a and b are the major and minor axes, respectively; however, the tablet does not give this solution but another, if 2b2 < a2.

Here is a simple problem that has survived on an 1824tablet in Gumma Prefecture. The orange and blue circlestouch each other at one point and are tangent to thesame line. The small red circle touches both of the largercircles and is also tangent to the same line. How are theradii of the three circles related?

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This beautiful problem, which requires no more thanhigh school geometry to solve, is written on a

tablet dated 1913 in Miyagi Prefecture. Threeorange squares are drawn as shown in

the large, green right triangle. Howare the radii of the three blue

circles related?

Typical Sangaku Problems*

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with sangaku but with the general fieldof traditional Japanese mathematics.

To carry out his research, Fukagawahad to teach himself Kambun, an archa-ic form of Japanese that is closely relat-ed to Chinese. Kambun is the Japaneseequivalent of Latin; during the Edo pe-riod (1603–1867), scientific works werewritten in this language, and only a fewpeople in modern Japan are able to readit fluently. As new tablets have been dis-covered, Fukagawa has been called into decipher them. In 1989 Fukagawa,along with Daniel Pedoe, published thefirst collection of sangaku in English.Most of the geometry problems accom-panying this article were drawn fromthat collection.

Wasan versus Yosan

Although the origin of the sangakucannot be pinpointed, it can be lo-

calized. There is a word in Japanese,wasan, that is used to refer to nativeJapanese mathematics. Wasan is meantto stand in opposition to yosan, orWestern mathematics. To understandhow wasan came into existence—andwith it the unusual sangaku problems—one must first appreciate the peculiarhistory of Japanese mathematics.

Of the earliest times, very little is defi-nitely known about mathematics in Ja-pan, except that a system of exponen-tial notation, similar to that employedby Archimedes in the Sand Reckoner,had been developed. More concrete in-formation dates only from the mid-sixthcentury A.D., when Buddhism—and,with it, Chinese mathematics—made itsway to Japan. Judging from the worksthat were taught at official schools atthe start of the eighth century, histori-ans infer that Japan had imported thegreat Chinese classics on arithmetic, al-gebra and geometry.

According to tradition, the earliest ofthese is the Chou-pei Suan-ching, whichcontains an example of the Pythagore-an theorem and the diagram commonlyused to prove it. This part of the tomeis at least as old as the sixth century B.C.

A more advanced state of knowledgeis represented in the Chiu-chang Suan-shu, considered the most influential ofChinese books on mathematics. TheChiu-chang describes methods for find-ing the areas of triangles, quadrilater-als, circles and other figures. It also con-tains simple word problems of the typethat torment many high school studentstoday: “If five oxen and two sheep cost

eight taels of gold, and two oxen andeight sheep cost eight taels, what is theprice of each animal?” The dates of theChiu-chang are also uncertain, but mostof it was probably composed by thethird century B.C. If this information iscorrect, the Chiu-chang contains per-haps the first known mention of nega-tive numbers and an early statement ofthe quadratic equation. (According tosome historians, the ancient Egyptianshad begun studying quadratic equationscenturies before, prior to 2000 B.C.)

Despite the influx of Chinese learn-ing, mathematics did not then take rootin Japan. Instead the country entered adark age, roughly contemporaneouswith that of Western Europe. In theWest, church and monastery becamethe centers of learning; in Japan, Bud-dhist temples served the same function,although mathematics does not seem tohave played much of a role. By someaccounts, during the Ashikaga shogun-ate (1338–1573) there could hardly befound in all Japan a person versed inthe art of division.

It is not until the opening of the 17thcentury that definite historical recordsexist of any Japanese mathematicians.The first of these is Kambei Mori, whoprospered around the year 1600. Al-though only one of Mori’s works—abooklet—survives, he is known to havebeen instrumental in developing arith-metical calculations on the soroban, orJapanese abacus, and in popularizing itthroughout the country.

The oldest substantial Japanese workon mathematics actually extant belongsto Mori’s pupil Koyu Yoshida (1598– 1672). The book, entitled Jinko-ki (lit-erally, “small and large numbers”), waspublished in 1627 and also concerns op-erations on the soroban. Jinko-ki wasso influential that the name of the workoften was synonymous with arithmetic.Because of the book’s influence, compu-tation—as opposed to logic—became themost important concept in traditionalJapanese mathematics. To the extentthat it makes sense to credit anyonewith the founding of wasan, that honorprobably goes to Mori and Yoshida.

A Brilliant Flowering

Wasan, though, was created not somuch by a few individuals but

by something much larger. In 1639 theruling Tokugawa shogunate (during theEdo period), to strengthen its powerand diminish challenges to its reign, de-

In this problem, from an 1803 san-gaku found in Gumma Prefecture, thebase of an isosceles triangle sits on adiameter of the large green circle.This diameter also bisects the red cir-cle, which is inscribed so that it justtouches the inside of the green circleand one vertex of the triangle, asshown. The blue circle is inscribed sothat it touches the outsides of boththe red circle and the triangle, as wellas the inside of the green circle. A linesegment connects the center of theblue circle and the intersection pointbetween the red circle and the trian-gle. Show that this line segment isperpendicular to the drawn diameterof the green circle.

This problem comes from an 1874tablet in Gumma Prefecture. A largeblue circle lies within a square. Foursmaller orange circles, each with adifferent radius, touch the blue circleas well as the adjacent sides of thesquare. What is the relation betweenthe radii of the four small circles andthe length of the side of the square?(Hint: The problem can be solved byapplying the Casey theorem, whichdescribes the relation between fourcircles that are tangent to a fifth circleor to a straight line.)

* Answers are onpage 21.



Hidetoshi Fukagawa was so fascinated with this problem,which dates from 1798, that he built a wooden model of it.Let a large sphere be surrounded by 30 small, identicalspheres, each of which touches its four small-sphereneighbors as well as the large sphere. How is the radius ofthe large sphere related to that of the small spheres?(The inset shows a three-dimensional view of the problem.)

This problem is from an 1822 tablet in Kanagawa Prefecture. It pre-dates by more than a century a theorem of Frederick Soddy, the fa-

mous British chemist who, along with Ernest Rutherford, discoveredtransmutation of the elements. Two red spheres touch each other and

also touch the inside of the large green sphere. A loop of smaller, dif-ferent-size blue spheres circle the “neck” between the red spheres.

Each blue sphere in the “necklace” touches its nearest neighbors, andthey all touch both the red spheres and the green sphere. How many

blue spheres must there be? Also, how are the radii of the blue spheresrelated? (The inset shows a three-dimensional view of the problem.)

From a sangaku dated 1825, this problem was probablysolved by using the enri, or the Japanese circle principle. Acylinder intersects a sphere so that the outside of the cylin-der is tangent to the inside of the sphere. What is the surfacearea of the part of the cylinder contained inside the sphere?(The inset shows a three-dimensional view of the problem.)

* Answers are on page 21.

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creed the official closing of Japan. Dur-ing this time of sakoku, or national se-clusion, the government banned foreignbooks and travel, persecuted Christiansand forbade Portuguese and Spanishships from coming ashore. Many ofthese strictures would remain for morethan two centuries, until CommodoreMatthew C. Perry, backed by a fleet ofU.S. warships, forced the end of sakokuin 1854.

Yet the isolationist policy was not en-tirely negative. Indeed, during the late17th century, Japanese art and cultureflowered so brilliantly that those yearsgo by the name of Genroku, for “re-naissance.” In that era, haiku developedinto a fine art form; No and Kabukitheater reached the pinnacle of their de-velopment; ukiyo-e, or “floating world”pictures, originated; and tea ceremoniesand flower arranging reached newheights. Neither was mathematics leftbehind, for Genroku was also the ageof Kowa Seki.

By popular accounts, Seki (1642– 1708) was Japan’s Isaac Newton orGottfried Wilhelm Leibniz, althoughthis reputation is difficult to substanti-ate. If the numbers of manuscripts at-tributed to him are correct, then mostof his work has been lost. Still, there isno question that Seki left many disci-ples who were influential in the furtherdevelopment of Japanese mathematics.

The first—and incontestable—achieve-ment of Seki was his theory of determi-nants, which is more powerful than thatof Leibniz and which antedates the Ger-man mathematician’s work by at least adecade. Another accomplishment, morerelevant to temple geometry but of de-batable origin, is the development ofmethods for solving high-degree equa-tions. (Much traditional Japanese math-ematics from that era involves equa-tions to hundreds of degrees; one suchequation is of the 1,458th degree.) Yeta third accomplishment sometimes at-tributed to Seki, and one that might alsobear on sangaku, is the development ofthe enri, or circle principle.

The enri was quite similar to the meth-od of exhaustion developed by Eudox-us and Archimedes in ancient Greecefor computing the area of circles. Themain difference was that Eudoxus andArchimedes used n-sided polygons toapproximate the circle, whereas the enridivided the circle into n rectangles. Thus,the limiting procedure was somewhatdifferent. Nevertheless, the enri repre-sented a crude form of integral calculus

that was later extended to other figures,including spheres and ellipses. A type ofdifferential calculus was also developedaround the same period. It is conceiv-able that the enri and similar techniqueswere brought to bear on sangaku. To-day’s mathematicians would use mod-ern calculus to solve these problems.

Spheres within Ellipsoids

During Seki’s lifetime, the first booksemploying the enri were published,

and the first sangaku evidently madetheir appearance. The dates are almostcertainly not coincidental; the followersof Yoshida and Seki must have influ-enced the development of wasan, and, inturn, wasan may have influenced them.Fukagawa believes that Seki encoun-tered sangaku on his way to the shogun-ate castle, where he was officially em-ployed as court mathematician, andthat the tablets pushed him to furtherresearches. A legend? Perhaps. But bythe next century, books were being pub-lished that contained typical native Jap-anese problems: circles within triangles,spheres within pyramids, ellipsoids sur-rounding spheres. The problems foundin these books do not differ in any im-portant way from those found on thetablets, and it is difficult to avoid theconclusion that the peculiar flavor of allwasan problems—including the sanga-ku—is a direct result of the policy of na-tional seclusion.

But the question immediately arises:Was Japan’s isolation complete? It iscertain that apart from the Dutch whowere allowed to remain in NagasakiHarbor on Kyushu, the southernmostisland, all Western traders were banned.Equally clear is that the Japanese them-selves were severely restricted. The mereact of traveling abroad was consideredhigh treason, punishable by death. Itappears safe to assume that if the isola-tion was not complete, then it was mostnearly so, and any foreign influence onJapanese mathematics would have beenminimal.

The situation began to change in the19th century, when the wasan gradual-ly became supplanted by yosan, a pro-cess that produced hybrid manuscriptswritten in Kambun with Western math-ematical notations. And, after the open-ing of Japan by Commodore Perry andthe subsequent collapse of the Toku-gawa shogunate in 1867, the new gov-ernment abandoned the study of nativemathematics in favor of yosan. Some

practitioners, however, continued tohang tablets well into the 20th century.A few sangaku even date from the cur-rent decade. But almost all the prob-lems from this century are plagiarisms.

The final and most intriguing ques-tion is, Who produced the sangaku?Were the theorems so beautifully drawnon wooden tablets the works of profes-sional mathematicians or amateurs?The evidence is meager.

Only a handful of sangaku are men-tioned in the standard A History of Jap-anese Mathematics, by David E. Smithand Yoshio Mikami. They cite the 1789collection Shimpeki Sampo, or Mathe-matical Problems Suspended before theTemple, which was published by KagenFujita, a professional mathematician.Smith and Mikami mention a tablet onwhich the following was appended af-ter the solution: “Feudal district of Ka-kegawa in Enshu Province, third monthof 1795, Sonobei Keichi Miyajima, pu-pil of Sadasuke Fujita of the School ofSeki.” Mikami, in his Development ofMathematics in China and Japan, men-tions the “Gion Temple Problem,”which was suspended at the Gion Tem-ple in Kyoto by Enkyu Tsuda, pupil ofEnri Nishimura. Furthermore, the tab-lets were written in the specialized lan-guage of Kambun, signifying the markof an educated class of practitioners.

From such scraps of information, it istempting to conclude that the tabletswere the work primarily of professionalmathematicians and their students. Yetthere are reasons to believe otherwise.

Many of the problems are elementaryand can be solved in a few lines; theyare not the kind of work a professionalmathematician would publish. Fuka-gawa has found a tablet from Mie Pre-fecture inscribed with the name of amerchant. Others have names of wom-en and children—12 to 14 years of age.Most, according to Fukagawa, werecreated by the members of the highlyeducated samurai class. A few wereprobably done by farmers; Fukagawarecalls how about 10 years ago he visit-ed the former cottage of mathematicianSen Sakuma (1819–1896), who taughtwasan to the farmers in nearby villagesin Fukushima Prefecture. Sakuma hadabout 2,000 students.

Such instruction recalls the Edo peri-od itself, when there were no collegesor universities in Japan. During thattime, teaching was carried out at pri-vate schools or temples, where ordinarypeople would go to study reading, writ-


ing and the abacus. Because laypeopleare more often drawn to problems ofgeometry than of algebra, it would notbe surprising if the tablets were paintedwith such artistic care specifically to at-tract nonmathematicians.

The best answer, then, to the questionof who created temple geometry seemsto be: everybody. On learning of the san-gaku, Fukagawa came to understandthat, in those days, many of the Japan-ese loved and enjoyed math, as well aspoetry and other art forms.

It is pleasant to realize that some san-

gaku were the works of ordinary math-ematics devotees, carried away by thebeauty of geometry. Perhaps a villageteacher, after spending the day with stu-dents, or a samurai warrior, after sharp-ening his sword, would retire to hisstudy, light an oil lamp and lose theworld to an intricate problem involvingspheres and ellipsoids. Perhaps he wouldspend days working on it in peacefulcontemplation. After finally arriving ata solution, he might allow himself ashort rest to savor the result of his hardlabor. Convinced the proof was a wor-

thy offering to his guiding spirits, hewould have the theorem inscribed inwood, hang it in his local temple andbegin to consider the next challenge.Visitors would notice the colorful tabletand admire its beauty. Many peoplewould leave wondering how the authorarrived at such a miraculous solution.Some might decide to give the problema try or to study geometry so that theattempt could be made. A few mightleave asking, “What if the problemwere changed just so.. . .”

Something for us all to consider.


The Author

TONY ROTHMAN received his Ph.D. in 1981 from the Centerfor Relativity at the University of Texas at Austin. He did postdoc-toral work at Oxford, Moscow and Cape Town, and he has taughtat Harvard University. Rothman has published six books, most re-cently Instant Physics. His next book is Doubt and Certainty, withE.C.G. Sudarshan, to be published this fall by Helix Books/Addi-son-Wesley. He has also recently written a novel about nuclear fu-sion. Scientific American wishes to acknowledge the help ofHidetoshi Fukagawa in preparing this manuscript. Fukagawa re-ceived a Ph.D. in mathematics from the Bulgarian Academy of Sci-ence. He is a high school teacher in Aichi Prefecture, Japan.

Further Reading

A History of Japanese Mathematics. David E. Smith and YoshioMikami. Open Court Publishing Company, Chicago, 1914. (Alsoavailable on microfilm.)

The Development of Mathematics in China and Japan. Sec-ond edition (reprint). Yoshio Mikami. Chelsea Publishing Compa-ny, New York, 1974.

Japanese Temple Geometry Problems. H. Fukagawa and D. Pedoe.Charles Babbage Research Foundation, Winnipeg, Canada, 1989.

Traditional Japanese Mathematics Problems from the 18thand 19th Centuries. H. Fukagawa and D. Sokolowsky. ScienceCulture Technology Publishing, Singapore (in press).

Answer: r/[(2n – 1)2 + 14]. The originalsolution to this problem applies theJapanese version of the Descartes circle

theorem several times. The answer givenhere was obtained by using the inversion

method, which was unknown to the Japanesemathematicians of that era.

Answer: 1/√r3 = 1/√r1 + 1/√r2,where r1, r2 and r3 are the radiiof the orange, blue and redcircles, respectively. The prob-

lem can be solved by applying the Pythagoreantheorem.

Answer: PQ =

The problem can be solved by using analytic ge-ometry to derive an equation for PQ and thentaking the first derivative of the equation andsetting it to zero to obtain the minimum valuefor PQ. It is not known whether the original au-thors resorted to calculus to solve this problem.

Answer: r22 = r1r3, where r1, r2

and r3 are the radii of the large,medium and small blue circles,respectively. (In other words, r2

is the geometric mean of r1 and r3.) The problemcan be solved by first realizing that all the interiorgreen triangles formed by the orange squaresare similar. The original solution then looks athow the three squares are related.

Answer: In the original solution tothis problem, the author draws aline segment that goes through the

center of the blue circle and is per-pendicular to the drawn diameter of

the green circle. The author assumes that thisline segment is different from the line segmentdescribed in the statement of the problem onpage 87. Thus, the two line segments should in-tersect the drawn diameter at different locations.The author then shows that the distance be-tween those locations must necessarily be equalto zero—that is, that the two line segments areidentical, thereby proving the perpendicularity.

Answer: If a is the length of thesquare’s side, and r1, r2, r3 and r4 arethe radii of the upper right, upperleft, lower left and lower right or-ange circles, respectively, then

Answer: 16t√t (r – t), where r and tare the radii of the sphere andcylinder, respectively.

Answer: Six spheres. The Soddy hex-let theorem states that there must besix and only six blue spheres (thus the

word “hexlet”). Interestingly, the theo-rem is true regardless of the position of the firstblue sphere around the neck. Another intriguingresult is that the radii of the different blue spheresin the “necklace” (t1 through t6) are related by1/t1 + 1/t4 = 1/t2 + 1/t5 = 1/t3 + 1/t6.

Answer: R = √5r, where R and r arethe radii of the large and smallspheres, respectively. The prob-lem can be solved by realizing

that the center of each smallsphere lies on the midpoint of the

edge of a regular dodecahedron, a 12-sided solidwith pentagonal faces.

√27 a2b2

(a2+ b2)3/2

a =2(r1r3 – r2r4) + √2(r1 – r2)(r1 – r4)(r3 – r2)(r3 – r4)

r1 – r2 + r3 – r4

Answers to Sangaku Problems

BRYA

N C

HRI

STIE

SA


APRIL 2005

Men have called me mad,” wrote Edgar Allan Poe, “but the question isnot yet settled, whether madness is or is not the loftiest intelligence—whether much that is glorious—whether all that is profound—doesnot spring from disease of thought—from moods of mind exalted at

the expense of the general intellect.”Many people have long shared Poe’s suspicion that genius and insanity are entwined. In-

deed, history holds countless examples of “that fine madness.” Scores of influential 18th-and 19th-century poets, notably William Blake, Lord Byron and Alfred, Lord Tennyson,wrote about the extreme mood swings they endured. Modern American poets John Berry-man, Randall Jarrell, Robert Lowell, Sylvia Plath, Theodore Roethke, Delmore Schwartzand Anne Sexton were all hospitalized for either mania or depression during their lives.And many painters and composers, among them Vincent van Gogh, Georgia O’Keeffe,Charles Mingus and Robert Schumann, have been similarly afflicted.

Judging by current diagnostic criteria, it seems that most of these artists—and many oth-ers besides—suffered from one of the major mood disorders, namely, manic-depressive ill-ness or major depression. Both are fairly common, very treatable and yet frequently lethaldiseases. Major depression induces intense melancholic spells, whereas manic-depression,a strongly genetic disease, pitches patients repeatedly from depressed to hyperactive andeuphoric, or intensely irritable, states. In its milder form, termed cyclothymia, manic-de-pression causes pronounced but not totally debilitating changes in mood, behavior, sleep,thought patterns and energy levels. Advanced cases are marked by dramatic, cyclic shifts.

Could such disruptive diseases convey certain creative advantages? Many people findthat proposition counterintuitive. Most manic-depressives do not possess extraordinaryimagination, and most accomplished artists do not suffer from recurring mood swings. Toassume, then, that such diseases usually promote artistic talent wrongly reinforces simplisticnotions of the “mad genius.” Worse yet, such a generalization trivializes a very seriousmedical condition and, to some degree, discredits individuality in the arts as well. It wouldbe wrong to label anyone who is unusually accomplished, energetic, intense, moody or ec-centric as manic-depressive. All the same, recent studies indicate that a high number of es-tablished artists—far more than could be expected by chance—meet the diagnostic criteriafor manic-depression or major depression given in the fourth edition of the Diagnostic andStatistical Manual of Mental Disorders (DSM-IV). In fact, it seems that these diseases cansometimes enhance or otherwise contribute to creativity in some people.

By virtue of their prevalence alone, it is clear that mood disorders do not necessarilybreed genius. Indeed, 1 percent of the general population suffer from manic-depression,also called bipolar disorder, and 5 percent from a major depression, or unipolar disorder,during their lifetime. Depression affects twice as many women as men and most often, butnot always, strikes later in life. Bipolar disorder afflicts equal numbers of women and men,and more than a third of all cases surface before age 20. Some 60 to 80 percent of all ado-lescents and adults who commit suicide have a history of bipolar or unipolar illness. Beforethe late 1970s, when the drug lithium first became widely available, one person in five withmanic-depression committed suicide.

Manic-Depressive Illness and CreativityDoes some fine madness plague great artists? Several studies now show that creativity and mood disorders are linked

by Kay Redfield Jamison

22 SCIENTIFIC AMERICAN EXCLUSIVE ONLINE ISSUE

The Author

KAY REDFIELD JAMISONis professor of psychiatry atthe Johns Hopkins UniversitySchool of Medicine. Shewrote Touched with Fire:Manic-Depressive Illness andthe Artistic Temperament andco-authored the medical textManic-Depressive Illness.Jamison is a member of theNational Advisory Councilfor Human Genome Re-search and clinical director ofthe Dana Consortium on theGenetic Basis of Manic-De-pressive Illness. She has alsowritten and produced a seriesof public television specialsabout manic-depressive ill-ness and the arts.

originally published in February 1995


Major depression in both unipolarand bipolar disorders manifests itselfthrough apathy, lethargy, hopelessness,sleep disturbances, slowed physicalmovements and thinking, impairedmemory and concentration, and a lossof pleasure in typically enjoyable events.The diagnostic criteria also include sui-cidal thinking, self-blame and inappro-priate guilt. To distinguish clinical de-pression from normal periods of unhap-piness, the common guidelines furtherrequire that these symptoms persist fora minimum of two to four weeks andalso that they significantly interfere witha person’s everyday functioning.

Mood Elevation

During episodes of mania or hypo-mania (mild mania), bipolar pa-

tients experience symptoms that are in

many ways the opposite of those asso-ciated with depression. Their mood andself-esteem are elevated. They sleep lessand have abundant energy; their pro-ductivity increases. Manics frequentlybecome paranoid and irritable. More-over, their speech is often rapid, excit-able and intrusive, and their thoughtsmove quickly and fluidly from one topicto another. They usually hold tremen-dous conviction about the correctnessand importance of their own ideas aswell. This grandiosity can contribute topoor judgment and impulsive behavior.

Hypomanics and manics generallyhave chaotic personal and professionalrelationships. They may spend largesums of money, drive recklessly or pur-sue questionable business ventures orsexual liaisons. In some cases, manicssuffer from violent agitation and delu-sional thoughts as well as visual andauditory hallucinations.

Rates of Mood Disorders

For years, scientists have documentedsome kind of connection between

mania, depression and creative output.In the late 19th and early 20th centuries,researchers turned to accounts of mooddisorders written by prominent artists,their physicians and friends. Althoughlargely anecdotal, this work stronglysuggested that renowned writers, artistsand composers—and their first-degreerelatives—were far more likely to expe-rience mood disorders and to commitsuicide than was the general population.During the past 20 years, more system-atic studies of artistic populations haveconfirmed these findings. Diagnosticand psychological analyses of livingwriters and artists can give quite mean-ingful estimates of the rates and typesof psychopathology they experience.

In the 1970s Nancy C. Andreasen ofthe University of Iowa completed the firstof these rigorous studies, which madeuse of structured interviews, matched

control groups and strict diagnostic cri-teria. She examined 30 creative writersand found an extraordinarily high oc-currence of mood disorders and alco-holism among them. Eighty percent hadexperienced at least one episode of ma-jor depression, hypomania or mania; 43percent reported a history of hypoma-nia or mania. Also, the relatives of thesewriters, compared with the relatives ofthe control subjects, generally performedmore creative work and more often hada mood disorder.

A few years later, while on sabbaticalin England from the University of Cali-fornia at Los Angeles, I began a studyof 47 distinguished British writers andvisual artists. To select the group as bestI could for creativity, I purposefullychose painters and sculptors who wereRoyal Academicians or Associates ofthe Royal Academy. All the playwrightshad won the New York Drama CriticsAward or the Evening Standard Drama(London Critics) Award, or both. Halfof the poets were already represented inthe Oxford Book of Twentieth CenturyEnglish Verse. I found that 38 percent

of these artists and writers had in factbeen previously treated for a mood dis-order; three fourths of those treated hadrequired medication or hospitalization,or both. And half of the poets—thelargest fraction from any one group—had needed such extensive care.

Hagop S. Akiskal of the University ofCalifornia at San Diego, also affiliatedwith the University of Tennessee atMemphis, and his wife, Kareen Akis-kal, subsequently interviewed 20 award-winning European writers, poets, paint-ers and sculptors. Some two thirds oftheir subjects exhibited recurrent cyclo-thymic or hypomanic tendencies, andhalf had at one time suffered from a ma-jor depression. In collaboration with Da-vid H. Evans of the University of Mem-phis, the Akiskals noted the same trendsamong living blues musicians. More re-cently Stuart A. Montgomery and his

wife, Deirdre B. Montgomery, of St.Mary’s Hospital in London examined50 modern British poets. One fourth metcurrent diagnostic criteria for depres-sion or manic-depression; suicide wassix times more frequent in this commu-nity than in the general population.

Ruth L. Richards and her colleaguesat Harvard University set up a systemfor assessing the degree of original think-ing required to perform certain creativetasks. Then, rather than screening formood disorders among those alreadydeemed highly inventive, they attempt-ed to rate creativity in a sample of man-ic-depressive patients. Based on theirscale, they found that compared withindividuals having no personal or fami-ly history of psychiatric disorders, man-ic-depressive and cyclothymic patients(as well as their unaffected relatives)showed greater creativity.

Biographical studies of earlier genera-tions of artists and writers also showconsistently high rates of suicide, depres-sion and manic-depression—up to 18times the rate of suicide seen in the gen-eral population, eight to 10 times that


Highly creative indiviuals experience major mood disorders more often than

do other groups in the general population.


of depression and 10 to 20 times that ofmanic-depressive illness and its mildervariants. Joseph J. Schildkraut and hisco-workers at Harvard concluded thatapproximately half of the 15 20th-cen-tury abstract-expressionist artists theystudied suffered from depressive or man-ic-depressive illness; the suicide rate inthis group was at least 13 times the cur-rent U.S. national rate.

In 1992 Arnold M. Ludwig of theUniversity of Kentucky published an ex-tensive biographical survey of 1,005 fa-mous 20th-century artists, writers andother professionals, some of whom hadbeen in treatment for a mood disorder.He discovered that the artists and writ-ers experienced two to three times the

rate of psychosis, suicide attempts, mooddisorders and substance abuse that com-parably successful people in business,science and public life did. The poets inthis sample had most often been manicor psychotic and hospitalized; they alsoproved to be some 18 times more likelyto commit suicide than is the generalpublic. In a comprehensive biographi-cal study of 36 major British poets bornbetween 1705 and 1805, I found simi-larly elevated rates of psychosis and se-vere psychopathology. These poets were30 times more likely to have had man-ic-depressive illness than were their con-temporaries, at least 20 times more like-ly to have been committed to an asylumand some five times more likely to have

taken their own life.These corroborative studies have con-

firmed that highly creative individualsexperience major mood disorders moreoften than do other groups in the gener-al population. But what does this meanfor their work? How does a psychiatricillness contribute to creative achieve-ment? First, the common features ofhypomania seem highly conducive tooriginal thinking; the diagnostic criteriafor this phase of the disorder include“sharpened and unusually creative think-ing and increased productivity.” Andaccumulating evidence suggests that thecognitive styles associated with hypo-mania (expansive thought and grandi-ose moods) can lead to increased fluen-


Alfred, Lord Tennyson, who experienced recurrent, debilitating depressions and probable hypo-

manic spells, often expressed fear that he might inherit themadness, or “taint of blood,” in his family. His father, grandfa-ther, two of his great-grandfathers as well as five of his sevenbrothers suffered from insanity, melancholia, uncontrollablerage or what is today known as manic-depressive illness. Hisbrother Edward was confined to an asylum for nearly 60 yearsbefore he died from manic exhaustion. Lionel Tennyson, oneof Alfred’s two sons, displayed a mercurial temperament, asdid one of his three grandsons.

Modern medicine has confirmed that manic-depressionand creativity tend to run in certain families. Studies of twinsprovide strong evidence for the heritability of manic-depres-sive illness. If an identical twin has manic-depressive illness,the other twin typically has a 70 to 100 percent chance of alsohaving the disease; if the other twin is fraternal, the chancesare considerably lower (approximately 20 percent). A reviewof pairs of identical twins reared apart from birth—in which atleast one had been diagnosed as manic-depressive—foundthat in two thirds or more of the sets, the illness was presentin both twins. —K. R. J.

ELIZABETHb. 1776

Recurrent bouts of depression

GEORGEDied in infancy,

1806

FREDERICK1807–1898

Irritability; eccentric; violent temper and volatile; obsessed with spiritualism

Recurrent depressive illness

ELIZABETH FYTCHE�1781–1865

“Easy-going” and“sweet tempered”

MARY1810 –1884

“...of a wild sortof countenance”;

obsessed with spiritualism

CECILIA1817–1909

“Mental disturbanceand depression”;

eccentric

EMILY1811–1889

SOURCE: Adapted from Touched with Fire: Manic-Depressive Illness and the Artistic Temperament; based on biographies, autobiographical writings and letters.

GEORGE CLAYTON TENNYSON1778–1831

Vacillating moods “between frenzy and lethargy”; spendthrift; alcoholic; “fits”; insanity

MARY�b. 1777

“Ferocious pessimism”; constant quarreling

and gloominess

CHARLES (D'EYNCOURT)�1784–1861

“Inherited his father’s instabilityand fretfulness”; spendthrift

tendencies; expansive, grandiose activities and interests

Manic-depressive illness

ALFRED1809–1892

Recurrent depression that re-quired treatment; trances, possibly

epileptic but not thought so by physician; possibly transient

hypomanic episodes; “dwelling in an element of gloom”

ARTHUR1814–1899

“Suffered much from depression”;

one year in Crichton

Institutionfor the Insane

CHARLES1808 –1879

Addicted to laudanum;“complete nervous break-

down”; had to be segregated from outside world; extreme

mood swings and “recurrent fits of

psychopathic depression”

EDWARD1813–1890

Confined in insane asylum for almost 60

years; severemelancholia; death

from manic exhaustion

SEPTIMUS1815 –1866

“Suffered from ner-vous depression”; fre-quent treatments for

melancholia; “the most morbid

of all the Tennysons”

HORATIO1819–1899

“Strange personality was legendary”; “rather unused

to this planet”; per-ceived himself as vulner-

able to the “weakness of the Tennysonian temperament”

Rage, unstable moods and/or insanity

MATILDA1816–1913

“Some mental derangement,”occasionally attributed to

childhood accident; religiousobsessions; “did not entirelyescape the black-blooded-

ness of the Tennysons”

LISA

BU

RNET

T

The Tainted Blood of the Tennysons


cy and frequency of thoughts.

Mania and Creativity

Studying the speech of hypomanicpatients has revealed that they tend

to rhyme and use other sound associa-tions, such as alliteration, far more of-ten than do unaffected individuals. Theyalso use idiosyncratic words nearly threetimes as often as do control subjects.Moreover, in specific drills, they can listsynonyms or form other word associa-tions much more rapidly than is consid-ered normal. It seems, then, that both thequantity and quality of thoughts buildduring hypomania. This speed increasemay range from a very mild quickeningto complete psychotic incoherence. It isnot yet clear what causes this qualita-tive change in mental processing. Nev-ertheless, this altered cognitive statemay well facilitate the formation ofunique ideas and associations.

People with manic-depressive illnessand those who are creatively accom-plished share certain noncognitive fea-tures: the ability to function well on afew hours of sleep, the focus needed towork intensively, bold and restless atti-tudes, and an ability to experience aprofound depth and variety of emo-tions. The less dramatic daily aspects ofmanic-depression might also providecreative advantage to some individuals.The manic-depressive temperament is,in a biological sense, an alert, sensitivesystem that reacts strongly and swiftly.

It responds to the world with a widerange of emotional, perceptual, intellec-tual, behavioral and energy changes. Ina sense, depression is a view of theworld through a dark glass, and maniais that seen through a kaleidoscope—of-ten brilliant but fractured.

Where depression questions, rumi-nates and hesitates, mania answers withvigor and certainty. The constant tran-sitions in and out of constricted and thenexpansive thoughts, subdued and thenviolent responses, grim and then ebul-lient moods, withdrawn and then out-going stances, cold and then fiery states—and the rapidity and fluidity of movesthrough such contrasting experiences—can be painful and confusing. Ideally,though, such chaos in those able totranscend it or shape it to their will canprovide a familiarity with transitionsthat is probably useful in artistic endeav-ors. This vantage readily accepts ambi-guities and the counteracting forces in

nature.Extreme changes in mood exaggerate

the normal tendency to have conflictingselves; the undulating, rhythmic andtransitional moods and cognitive chang-es so characteristic of manic-depressiveillness can blend or harness seeminglycontradictory moods, observations andperceptions. Ultimately, these fluxes andyokings may reflect truth in humanityand nature more accurately than coulda more fixed viewpoint. The “consis-tent attitude toward life” may not, asByron scholar Jerome J. McGann of theUniversity of Virginia points out, be asinsightful as an ability to live with, andportray, constant change.

The ethical and societal implicationsof the association between mood disor-ders and creativity are important butpoorly understood. Some treatment stra-tegies pay insufficient heed to the bene-fits manic-depressive illness can bestowon some individuals. Certainly most


EXPECTED RATEIN GENERAL POPULATION

ANDREASEN’S STUDYOF WRITERS (1987)

JAMISON’S STUDY OFARTISTS AND WRITERS (1989)

SCHILDKRAUT AND HIRSHFELD’SSTUDY OF ARTISTS (1990)

AKISKAL AND AKISKAL’S STUDY OFARTISTS AND WRITERS (UNPUBLISHED)

JAMISON’S STUDY OF BRITISH POETS BORN BETWEEN 1705 AND 1805 (1989)

MONTGOMERY AND MONTGOMERY’SSTUDY OF POETS (1993)

LUDWIG’S STUDY OF POETS (1992)

MAJOR DEPRESSIVE ILLNESS

0 10 20 30 40

PERCENT

50 60 70 80

MANIC-DEPRESSIVE ILLNESS

CYCLOTHYMIA

SUICIDE

LISA

BU

RNET

T

INCREASED RATES OF SUICIDE, depression and manic-de-pression among artists have been established by many separatestudies. These investigations show that artists experience up to

18 times the rate of suicide seen in the general population, eightto 10 times the rate of depression and 10 to 20 times the rate ofmanic-depression and its milder form, cyclothymia.

The Case of Vincent van Gogh

Many clinicians have reviewed the medical and psychiatric problems of thepainter Vincent van Gogh posthumously, diagnosing him with a range of disor-

ders, including epilepsy, schizophrenia, digitalis and absinthe poisoning, manic-depres-sive psychosis, acute intermittent porphyria and Ménière’s disease.

Richard Jed Wyatt of the National Institute of Mental Health and I have argued in de-tail that van Gogh’s symptoms, the natural course of his illness and his family psychiatrichistory strongly indicate manic-depressive illness. The extent of the artist’s purporteduse of absinthe and convulsive behavior remains unclear; in any event, his psychiatricsymptoms long predate any possible history of seizures. It is possible that he sufferedfrom both an epileptic disorder and manic-depressive illness. —K. R. J.


manic-depressives seek relief from thedisease, and lithium and anticonvulsantdrugs are very effective therapies formanias and depressions. Nevertheless,these drugs can dampen a person’s gen-eral intellect and limit his or her emo-tional and perceptual range. For thisreason, many manic-depressive patientsstop taking these medications.

Left untreated, however, manic-de-pressive illness often worsens over time—and no one is creative when severely de-pressed, psychotic or dead. The attacksof both mania and depression tend togrow more frequent and more severe.Without regular treatment the diseaseeventually becomes less responsive tomedication. In addition, bipolar and uni-polar patients frequently abuse mood-altering substances, such as alcohol andillicit drugs, which can cause secondarymedical and emotional burdens formanic-depressive and depressed patients.

The Goal of Treatment

The real task of imaginative, com-passionate and effective treatment,

therefore, is to give patients more mean-

ingful choices than they are now afford-ed. Useful intervention must control theextremes of depression and psychosiswithout sacrificing crucial human emo-tions and experiences. Given time andincreasingly sophisticated research, psy-chiatrists will likely gain a better under-standing of the complex biological ba-sis for mood disorders. Eventually, thedevelopment of new drugs should makeit possible to treat manic-depressive in-dividuals so that those aspects of tem-perament and cognition that are essen-tial to the creative process remain intact.

The development of more specific andless problematic therapies should beswift once scientists find the gene, orgenes, responsible for the disease. Pre-natal tests and other diagnostic measuresmay then become available; these possi-bilities raise a host of complicated ethi-cal issues. It would be irresponsible toromanticize such a painful, destructiveand all too often deadly disease. Hence,3 to 5 percent of the Human GenomeProject’s total budget (which is conser-vatively estimated at $3 billion) hasbeen set aside for studies of the social,ethical and legal implications of genetic

research. It is hoped that these investi-gations will examine the troubling is-sues surrounding manic-depression andmajor depression at length. To help thosewho have manic-depressive illness, orwho are at risk for it, must be a majorpublic health priority.


ROBERT SCHUMANN’S MUSICAL WORKS, charted byyear and opus number (above), show a striking relation betweenhis mood states and his productivity. He composed the mostwhen hypomanic and the least when depressed. Both of Schu-mann’s parents were clinically depressed, and two other first-de-

gree relatives committed suicide. Schumann himself attemptedsuicide twice and died in an insane asylum. One of his sonsspent more than 30 years in a mental institution.

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144130129125097096090089088087083

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Further Reading

Tennyson: The Unquiet Heart. R. B.Martin. Oxford University Press, 1980.

Creativity and Mental Illness: Preva-lence Rates in Writers and TheirFirst-Degree Relatives. Nancy C. An-dreasen in American Journal of Psychia-try, Vol. 144, No. 10, pages 1288-1292;October 1987.

Manic Depressive Illness. Frederick K.Goodwin and Kay R. Jamison. OxfordUniversity Press, 1990.

Creative Achievement and Psycho-pathology: Comparison among Pro-fessions. Arnold M. Ludwig in AmericanJournal of Psychiatry, Vol. 46, No. 3,pages 330–356; July 1992.

Touched with Fire: Manic-DepressiveIllness and the Artistic Temperament.Kay R. Jamison. Free Press/Macmillan,1993.

SA


APRIL 2005

Ifirst met Betty, a blind teenager inToronto, as I was interviewing par-ticipants for an upcoming study of

mine on touch perception in 1973. Bet-ty had lost her sight at age two, whenshe was too young to have learned howto draw. So I was astonished when shetold me that she liked to draw profilesof her family members. Before I beganworking with the blind, I had alwaysthought of pictures as copies of the visi-ble world. After all, we do not drawsounds, tastes or smells; we draw whatwe see. Thus, I had assumed that blindpeople would have little interest or tal-ent in creating images. But as Betty’scomments revealed that day, I was verywrong. Relying on her imagination andsense of touch, Betty enjoyed tracingout the distinctive shape of an individu-al’s face on paper.

I was so intrigued by Betty’s abilitythat I wanted to find out if other blindpeople could readily make useful illus-trations—and if these drawings wouldbe anything like the pictures sighted in-dividuals use. In addition, I hoped todiscover whether the blind could inter-

pret the symbols commonly used bysighted people. To bring the blind intothe flat, graphical world of the sighted,I turned to a number of tools, includingmodels, wire displays and, most often,raised-line drawing kits, made availableby the Swedish Organization for theBlind. These kits are basically stiff boardscovered with a layer of rubber and a thinplastic sheet. The pressure from any ball-point pen produces a raised line on theplastic sheet.

Thanks to this equipment, my col-leagues and I have made some remark-able findings over the past 20 years, andthis information has revised our under-standing of sensory perception. Mostsignificantly, we have learned that blindand sighted people share a form of pic-torial shorthand. That is, they adoptmany of the same devices in sketchingtheir surroundings: for example, bothgroups use lines to represent the edgesof surfaces. Both employ foreshortenedshapes and converging lines to conveydepth. Both typically portray scenesfrom a single vantage point. Both ren-der extended or irregular lines to con-

note motion. And both use shapes thatare symbolic, though not always visual-ly correct, such as a heart or a star, to re-lay abstract messages. In sum, our workshows that even very basic pictures re-flect far more than meets the eye.

Outlines

After meeting Betty, I wondered whether all blind people could ap-

preciate facial profiles shown in outline.Over the years, I asked blind volunteersin North America and Europe to drawprofiles of several kinds of objects. Mostrecently, I undertook a series of studieswith Yvonne Eriksson of Linköping Uni-versity and the Swedish Library of Talk-ing Books and Braille. In 1993 we test-ed nine adults from Stockholm—threemen and six women. Four were con-genitally blind, three had lost their sightafter the age of three, and two had min-imal vision. Each subject examined fourraised profiles, which Hans-Joergen An-dersen, an undergraduate psychologystudent at Aarhus University in Den-mark, made by gluing thin, plastic-coat-


How the Blind DrawBlind and sighted people use many of the same

devices in sketching their surroundings, suggesting that vision and touch are closely linked

by John M. Kennedy

originally published in January 1997


ed wires to a flat metal board [see up-per illustration on next page].

Eriksson and I asked the volunteersto describe the most prominent featureon each display using one of four labels:smile, curly hair, beard or large nose.Five of them—including one man whohad been totally blind since birth—cor-rectly identified all four pictures. Onlyone participant recognized none. On av-erage, the group labeled 2.8 of the fouroutlines accurately. In comparison, when18 sighted undergraduates in Torontowere blindfolded and given the sameraised-line profiles, they scored onlyslightly better, matching up a mean of3.1 out of four displays.

Many investigators in the U.S., Japan,Norway, Sweden, Spain and the U.K.have reported similar results, leaving lit-tle doubt that blind people can recognizethe outline shape of familiar objects. Atfirst, it may seem odd that even thosewho have never had any vision whatso-ever possess some intuitive sense of howfaces and other objects appear. But withfurther thought, the finding makes per-fect sense. The lines in most simpledrawings show one of two things: wheretwo surfaces overlap, called an occlud-ing edge, or where two surfaces meet ina corner. Neither feature need be seen tobe perceived. Both can be discerned bytouching.

Not all blind people read raised-linedrawings equally well, and these indi-vidual discrepancies can reflect the ageat which someone lost his or her sight.For example, people who have beenblind from birth or infancy—termed theearly blind—sometimes find raised-linedrawings challenging. But in 1993 Ya-tuka Shimizu of Tsukuba College ofTechnology in Japan, with colleaguesShinya Saida and Hiroshi Shimura,found that 60 percent of the early-blindsubjects they studied could recognize theoutline of common objects, such as afish or a bottle. Recognition rates weresomewhat higher for sighted, blindfold-ed subjects, who are more familiar withpictures in general.

Interestingly, subjects who lose visionlater in life—called the later blind—fre-quently interpret raised outlines morereadily than either sighted or early-blind individuals do, according to Mor-ton Heller of Winston-Salem University.One likely explanation is that the laterblind have a double advantage in thesetasks: they are typically more familiarwith pictures than are the early blind,and they have much better tactile skills

than do the sighted.

Perspective

Just as Betty prompted me to studywhether the blind appreciate pro-files in outline, another amateur art-

ist, Kathy from Ottawa, led me to inves-tigate a different question. Kathy firstparticipated in my studies when she was30 years old. Because of retinal cancerdetected during her first year of life,Kathy had been totally blind since agethree and had never had detailed vision.Even so, she was quite good at makingraised-line drawings. On one occasionKathy sketched several different arrange-ments of a cube and an L-shaped blockthat I used to test how relative distancesappear in line art. When the blocks satside by side, she made them the samesize—as they were in actuality. But whenthe cube was farther from her than theother block, she made it smaller in herdrawing.

This second drawing revealed a fun-damental principle of perspective—name-ly, that as an object becomes more dis-tant, it subtends a smaller angle. (Thinkabout viewing a picket fence at an angle


OUTLINE DRAWINGS, made by Kathy,totally blind since age three, demonstratethat blind artists use many of the samedevices as sighted illustrators do. Theyuse lines to represent surfaces, as Kathy’spicture of the eagle on her charm braceletshows (top). Blind people portray objects,such as a house, from a single vantagepoint (at right). Blind artists use shapes toconvey abstract messages: Kathy drew aheart surrounding a crib to describe thelove surrounding a child (at right). Andthey use foreshortening to suggest per-spective: Kathy drew the L-shaped blockand the cube to be the same size whenthey were side by side but made the cubesmaller when it was placed farther awayfrom her (bottom).

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and how its posts appear shorter closerto the horizon.) Kathy’s use of this basicrule suggested that some aspects of per-spective might be readily understood bythe blind. Again the proposition seemedreasonable, given some consideration.Just as we see objects from a particularvantage point, so, too, do we reach outfor them from a certain spot. For proofof the theory, I designed a study withPaul Gabias of Okanagan UniversityCollege in British Columbia, who wasthen at New York University.

We prepared five raised-line drawings:one of a table and four of a cube [see up-per illustration on following page]. We

showed the drawings to 24 congenitallyblind volunteers and asked them a se-ries of questions. The table drawing hada central square and four legs, one pro-truding from each corner. The subjectswere told that a blind person had drawnthe table and had explained, “I’ve drawnit this way to show that it is symmetri-cal on all four sides.” They were thentold that another blind person haddrawn an identical table but had offereda different explanation: “I’ve shown itfrom underneath in order to show theshape of the top and all four legs. If youshow the table from above or from theside, you can’t really show the top andall four legs, too.”

Next we asked our volunteers to pickout the cube drawing that had mostlikely been made by the person whodrew the table from below. To answerconsistently, they needed to understandwhat strategy had been used in drawingthe table and each cube. One cube re-sembled a foldout of a box, showing thefront face of the cube in the middle,surrounded by its top, bottom, left andright faces. Another drawing showedtwo squares, representing the front andtop of the cube. A third picture depict-ed the front of the cube as a square andthe top as a rectangle—foreshortened be-

cause it was receding away from the ob-server. A fourth illustrated two trapezi-ums joined along the longest line; theextra length of this line revealed that itwas the edge nearest to the observer.

Which cube do you think was drawnby the person who intended to show thetable from below? Most of the blind vol-unteers chose the drawing that showedtwo trapeziums. That is, they selectedthe illustration that made the most so-phisticated use of perspective. Accord-ingly, they picked as the least likely matchthe flat “foldout” drawing—the one thatused no perspective whatsoever. Thefoldout drawing was also the one theyjudged most likely to have been made bythe person who, in drawing the table,had hoped to highlight its symmetry.

Heller and I joined forces to prepareanother task for demonstrating that theblind understood the use of perspective.(You might like to try it, too; it appearsat the bottom of the opposite page.) Wearranged three solids—a sphere, a coneand a cube—on a rectangular tabletop.Our blind subjects sat on one side. Weasked them to draw the objects fromwhere they were sitting and then toimagine four different views: from theother three sides of the table and fromdirectly above as well. (Swiss child psy-

PROFILES, made from plastic-coated wires mounted on a thin metal board, were giv-en to nine blind subjects in Stockholm. The subjects were asked to describe each dis-play using one of four labels: smile, curly hair, beard or large nose. On average, thegroup described 2.8 of the four displays accurately, showing that blind people oftenrecognize the outline of simple objects. Blindfolded, sighted control subjects given thesame task did only slightly better.

SOLIDS—a sphere, a cone and a cube—arranged on a table are commonly usedto test spatial ability. The arrangement isshown from overhead at the far right.Which drawing at the near right showsthe solids from the edge of the table fac-ing the bottom of the page? Which draw-ing shows them from the opposite edge?From the edge facing left? Facing right?Blind and sighted individuals do equallywell on this task, proving that the blindcan determine how objects appear fromparticular vantage points.

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chologist Jean Piaget called this exercisethe perspective-taking, or “three moun-tains,” task.) Many adults and childrenfind this problem quite difficult. On av-erage, however, our blind subjects per-formed as well as sighted control sub-jects, drawing 3.4 of the five imagescorrectly.

Next, we asked our subjects to namethe vantage point used in five separatedrawings of the three objects. We pre-sented the drawings to them twice, inrandom order, so that the highest possi-ble score was 10 correct. Of that total,the blind subjects named an average of6.7 correctly. Sighted subjects scoredonly a little higher, giving 7.5 correct an-swers on average. The nine later-blindsubjects in the study fared slightly bet-ter than the congenitally blind and thesighted, scoring 4.2 on the drawing taskand 8.3 on the recognition task. Again,the later blind probably scored so wellbecause they have a familiarity with pic-tures and enhanced tactile skills.

Metaphor

From the studies described above, itis clear that blind people can appre-

ciate the use of outlines and perspectiveto describe the arrangement of objectsand other surfaces in space. But picturesare more than literal representations.This fact was drawn to my attentiondramatically when a blind woman inone of my investigations decided on herown initiative to draw a wheel as it wasspinning. To show this motion, shetraced a curve inside the circle. I wastaken aback. Lines of motion, such asthe one she used, are a very recent in-vention in the history of illustration. In-deed, as art scholar David Kunzlenotes, Wilhelm Busch, a trendsetting

19th-century cartoonist, used virtuallyno motion lines in his popular figuresuntil about 1877.

When I asked several other blindstudy subjects to draw a spinningwheel, one particularly clever renditionappeared repeatedly: several subjectsshowed the wheel’s spokes as curvedlines. When asked about these curves,they all described them as metaphoricalways of suggesting motion. Majorityrule would argue that this device some-how indicated motion very well. Butwas it a better indicator than, say, bro-ken or wavy lines—or any other kind ofline, for that matter? The answer wasnot clear. So I decided to test whethervarious lines of motion were apt ways ofshowing movement or if they weremerely idiosyncratic marks. Moreover, Iwanted to discover whether there weredifferences in how the blind and thesighted interpreted lines of motion.

To search out these answers, Gabiasand I created raised-line drawings offive different wheels, depicting spokeswith lines that curved, bent, waved,dashed and extended beyond the peri-meter of the wheel. We then asked 18

blind volunteers to assign one of the fol-lowing motions to each wheel: wob-bling, spinning fast, spinning steadily,jerking or braking. Which wheel do youthink fits with each motion? Our con-trol group consisted of 18 sighted un-dergraduates from the University ofToronto.

All but one of the blind subjects as-signed distinctive motions to each wheel.In addition, the favored description forthe sighted was the favored descriptionfor the blind in every instance. What ismore, the consensus among the sightedwas barely higher than that among theblind. Because motion devices are unfa-miliar to the blind, the task we gavethem involved some problem solving.Evidently, however, the blind not only

MOTION can be suggested by irregularlines. When blind and sighted volunteerswere shown five diagrams of movingwheels (right), they generally interpretedthem in the same way. Most guessed thatthe curved spokes indicated that the wheelwas spinning steadily; the wavy spokes,they thought, suggested that the wheel waswobbling; and the bent spokes were takenas a sign that the wheel was jerking. Sub-jects assumed that spokes extending be-yond the wheel’s perimeter signified thatthe wheel had its brakes on and thatdashed spokes indicated that the wheelwas spinning quickly.

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PERSPECTIVE is readily understood by the blind. To prove this point, the author and Paul Gabias of Okanagan University Collegeasked 24 congenitally blind volunteers to examine a drawing of a table (far left) and four drawings of a cube. They were told thatone blind person drew the table in a star shape to show how it appeared from underneath and that another blind person drew anidentical table, intending to show its symmetry instead. The subjects were then asked which cube was most likely drawn by the per-son who drew the table from underneath. Most chose the cube composed of two trapeziums (far right), the one that made the mostsophisticated use of perspective.


figured out meanings for each line ofmotion, but as a group they generallycame up with the same meaning—at leastas frequently as did sighted subjects.

We have found that the blind under-stand other kinds of visual metaphorsas well. Kathy once drew a child’s cribinside a heart—choosing that symbol,she said, to show that love surroundedthe child. With Chang Hong Liu, a doc-toral student from China, I have begunexploring how well blind people under-stand the symbolism behind shapes suchas hearts, which do not directly repre-sent their meaning. We gave a list of 20pairs of words to sighted subjects andasked them to pick from each pair theterm that best related to a circle and the

term that best related to a square. (Ifyou wish to try this yourself, the list ofwords can be found at the left.) For ex-ample, we asked: What goes with soft?A circle or a square? Which shape goeswith hard?

All our subjects deemed the circle softand the square hard. A full 94 percentascribed happy to the circle, instead ofsad. But other pairs revealed less agree-ment: 79 percent matched fast and slowto circle and square, respectively. Andonly 51 percent linked deep to circleand shallow to square. When we testedfour totally blind volunteers using thesame list, we found that their choicesclosely resembled those made by thesighted subjects. One man, who hadbeen blind since birth, scored extremelywell. He made only one match differingfrom the consensus, assigning “far” tosquare and “near” to circle. In fact, onlya small majority of sighted subjects—53percent—had paired far and near to theopposite partners. Thus, we concludedthat the blind interpret abstract shapesas sighted people do.

Perception

We typically think of sight as theperceptual system by which

shapes and surfaces speak to the mind.

But as the empirical evidence discussedabove demonstrates, touch can relaymuch of the same information. In someways, this finding is not so surprising.When we see something, we know moreor less how it will feel to the touch, andvice versa. Even so, touch and sight aretwo very different senses: one receivesinput in the form of pressure, and oneresponds to changes in light. How is itthat they can then interpret somethingas simple as a line in exactly the sameway? To answer this question, we mustconsider what kind of information it isthat outlines impart to our senses.

The most obvious theory is that eachborder in a basic drawing represents onephysical boundary around some surfaceor shape. But it is not that simple, be-cause all lines, no matter how thin, havetwo sides or contours—an inside and anoutside border, if you will. As a result,thick lines are perceived quite different-ly from thin ones. Consider a thick linetracing a profile. If it is thick enough, itappears to show two profiles, one peredge, gazing in the same direction [seeillustration below]. When the line is thinand its two borders are close together,though, an observer perceives only oneface. As it turns out, touch produces asimilar effect. I prepared a series of pro-file drawings in which both edges of thedefining line were raised. When the edg-es were only 0.1 centimeter apart, myblind volunteer, Sanne, a student at Aar-hus University, said they showed oneface. When they were 0.8 centimeterapart, she reported that they showedtwo faces.

Another theory of outline drawingssuggests that lines substitute for any per-ceptible boundary, including those thatare not tangible, such as shadows. Butthis theory, too, fails in a very tellingfashion. Look at the illustration at the


WORD PAIRS were used to test the sym-bolism in abstract shapes—and whetherblind and sighted people perceived suchmeanings in the same way. Subjects weretold that in each pair of words, one fit bestwith circle and the other with square. Forexample, which shape better describessoft? According to the number given afterthe soft-hard word pair, everyone thoughta circle did. These percentages show thelevel of consensus among sighted subjects.Blind volunteers made similar choices.

THICKNESS of these outlines determines whether their two contours are viewed as one profile or two. The same ambiguity occurswith touch. Blind subjects interpret raised edges placed near each other as a single surface boundary and those placed farther apartas two.

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WORDS ASSOCIATEDWITH CIRCLE-

SQUARE

AGREEMENTAMONG

SUBJECTS(PERCENT)

SOFT-HARD

MOTHER-FATHER

HAPPY-SAD

GOOD-EVIL

LOVE-HATE

ALIVE-DEAD

BRIGHT-DARK

LIGHT-HEAVY

WARM-COLD

SUMMER-WINTER

WEAK-STRONG

FAST-SLOW

CAT-DOG

SPRING-FALL

QUIET-LOUD

WALKING-STANDING

ODD-EVEN

FAR-NEAR

PLANT-ANIMAL

DEEP-SHALLOW

100

94

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89

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87

85

81

81

79

79

74

74

62

62

57

53

53

51


right, which shows two pictures of theauthor. In one image, shadow patterns,defined by a single contour separatinglight and dark areas, cross my face. Inthe second image, a dark line having twocontours traces the same shadow pat-terns. Despite the fact that the shapes inthe second picture are identical to thosein the first, the perceptual results arevividly different. The first is easily rec-ognized as a face; the second is not.

Again, this example shows that ourvisual system, like our tactile system,does not read two contours of a line inthe same way as it interprets a singlecontour. The implication is that thebrain region responsible for interpret-ing contours in sensory input from busyenvironments is a general surface-per-ception system. As such, it does not dis-criminate on the basis of purely visual

matters, such as brightness and color.Rather it takes the two contours of adark line and treats them as indicatorsfor the location of a single edge of somesurface. Whereas sighted individualstreat brightness borders as indicators ofsurface edges, the blind treat pressureborders in the same way.

Because the principles at work hereare not just visual, the brain region thatperforms them could be called multi-modal or, as it is more commonlytermed, amodal. In one account, whichI have discussed in my book on draw-ings by the blind, such an amodal sys-tem receives input from both vision andtouch. The system considers the inputas information about such features asocclusion, foreground and background,flat and curved surfaces, and vantagepoints. In the case of the sighted, visual

and tactile signals are coordinated bythis amodal system.

As we have found, the ability to inter-pret surface edges functions even whenit does not receive any visual signals. Itis for this very reason that the blind soreadily appreciate line drawings and oth-er graphic symbols. Knowing this factshould encourage scholars and educa-tors to prepare materials for the blindthat make vital use of pictures. Severalgroups around the world are doing justthat. For instance, Art Education for theBlind, an organization associated withthe Whitney Museum of American Artand the Museum of Modern Art inNew York City, has prepared raised-lineversions of Henri Matisse paintings andof cave art. It may not be long beforeraised pictures for the blind are as wellknown as Braille texts.


The Author

JOHN M. KENNEDY was born in Belfast in 1942and was raised in one of the few Unitarian families inNorthern Ireland. He attended the Royal Belfast Aca-demical Institution and Queen’s University of Belfast,where his interests included fencing and theater. Hecompleted his Ph.D. in perception at Cornell Universi-ty and began his research with the blind shortly there-after as an assistant professor at Harvard University.He currently lectures at the University of Toronto,Scarborough College, where he won his college’s teach-ing prize in 1994. Notes from his courses on percep-tion are available through the university’s World WideWeb site at http://citd.scar.utoronto.ca/Psychology/PSYC54/PSYC54.html

Further Reading

Picture and Pattern Perception in the Sighted and the Blind: The Ad-vantage of the Late Blind. M. A. Heller in Perception, Vol. 18, No. 3, pages379–389; 1989.

Drawing and the Blind: Pictures to Touch. J. M. Kennedy. Yale UniversityPress, 1993.

Profiles and Orientation of Tactile Pictures. J. M. Kennedy and Y. Eriks-son. Paper presented at the meeting of the European Psychology Society, Tam-pere, July 2–5, 1993.

Symbolic Forms and Cognition. C. H. Liu and J. M. Kennedy in Psyke & Lo-gos, Vol. 14, No. 2, pages 441–456; 1993.

Tactile Pattern Recognition by Graphic Display: Importance of 3-D In-formation for Haptic Perception of Familiar Objects. Y. Shimizu, S. Sai-da and H. Shimura in Perception and Psychophysics, Vol. 53, No. 1, pages43–48; January 1993.

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SHADOWS, and other intangible bound-aries, are not recognizable in outline—ex-plaining in part why the blind can under-stand most line drawings made by sightedpeople. In the picture of the author on theleft, a single contour separates light anddark areas of his face. In the picture onthe right, a line, having two contours,makes the same division. Note that al-though the shapes are identical in bothimages, the perceptual results are quitedifferent. Only the image on the left clear-ly resembles a face.
