JAPANESE SCIENTIFIC THOUGHT

Shigeru Nakayama

Professional Views of Nature.

In seventeenth-century Europe the goals and approaches of modern science were established by the scientific revolution. The professionalization of science in the nineteenth century, sometimes called the second scientific revolution, was no less important. When science became a full-time vocational activity, even the perception of nature was reorganized.

The second scientific revolution has not attracted the interest of many intellectual historians because it has seemed to be a revolution only of the social system of science. How intellectual its motivations were is a moot point; it has important intellectual implications. As the disciplines separated out of the ancient unity of science, each professional learned to view nature from the standpoint of his own field. The physicist’s nature overlapped little with that of the botanist: the same could be said of the mechanical engineer and the professional philosopher (who in the nineteenth century often, especially in Germany, thought of himself as a Wissenschaftler). Although the assumption survived that one nature underlay the work of all scientists, there was no longer a consensus among professionals as to what it was and how it was articulated. The unity of nature was abandoned to the layman, but the technical perspectives of scientists moved so quickly and divergently that there remained no standpoint from which an overview was possible. The fragmented conceptions of and assumptions about nature, centered in academic specialties and heavily colored by their prejudices, will be referred to here as professional views of nature.¹ People within the specialties tend to see them as universal. The metallurgist or biochemist, when he sets out his opinion on broad questions of natural philosophy, often is unable to transcend the ideology of his own scientific community.

The views of nature imported into Japan in the Meiji modernization period (late nineteenth century) were of the kind described above. When the theory of organic evolution was introduced, the fact that Japan was not a Christian country was largely beside the point in determining its reception. By and large the Japanese sedulously assimilated views that had become international in character. The confrontations oF values that one might expect did not occur. Furthermore, since science was professionalized by fiat of the central government rather than by the piecemeal effort of scientists, there was no natural continuity between traditional Japanese outlooks on nature and the new disciplinary views. The new Japanese scientist could not draw directly upon his native heritage in establishing a career; all that mattered was to conform to the conventional view from abroad.

In order to find views of nature that are in some sense genuinely Japanese, it will be necessary to examine the state of affairs before the Meiji reforms cut off the confrontation of Eastern and Western science. This is not to say that there was a single characteristic Japanese view of nature that can be reconstructed by reading the works of individual thinkers and examining anecdotes about them. The view of nature varied from one period to the next and depended greatly upon social background. It is, in fact, worth pursuing the hypothesis that even in traditional Japan, views of nature were rooted in and bound to professions–although the definition of a profession and the character of membership were very different from those of modern times.

During the Tokugawa shogunate (1603-1867) class hierarchy was tightly maintained, with the hereditary warrior class, the samurai (about 5 percent of the population), at the top of a rigid structure of farmers, artisans, and merchants. The major professions, independent of the four classes, were those of the Confucian scholar, the physician, and the Buddhist priest. Vocation was hereditary in feudal Japan, and even professionals were bound by their inherited callings to a partial view of nature. Given the lack of social mobility, collective, static views of reality are more prominent than the individualistic activity that certainly existed at the same time.

In seeking to identify views of nature, we shall pay particular attention to the prefaces and postscripts of scientific writings. The texts generally were concerned with stylized technical subjects, and there was no place for direct and outspoken expression of the author’s assumptions. In the front matter and end matter, on the other hand, basic philosophical matters often were argued. Frequently, these discussions of fundamentals were merely ornamental, adapted from Chinese arguments using the yin-yang principle and the Five Phases doctrine. Nevertheless, a comparison of Chinese and Japanese prefaces reveals differences in views of nature.

Also useful are prefaces contributed by writers other than the authors. Such prefaces, which tend to be complimentary rather than critical, provide excellent sources for the criteria of evaluation in each profession. Even today these vary: good philosophers are profound, scholars are erudite, and mathematicians bring elegance to their proofs. In old Japan, astronomers, mathematicians, medical doctors, natural historians, linguists, and Confucian scholars differed in their excellences. The differences, I argue, reflect different views of nature.

Astronomy.

Pseudoscience and Science. Technical professions began in Japan with the immigration of Korean and Chinese experts in the sixth to eighth centuries. As their Chinese view of nature began to take root in Japan, it was institutionalized on continental models in the College of Confucian Studies and the Board of Yin-yang (divination) Art. The Yin-yang Board had three departments: observational astrology, calendar making (mathematical astronomy), and yin-yang divination. In principle it was a miniature reproduction of the Astronomical Bureau at the Chinese court. A closer look discloses significant remodeling to meet local requirements. In China the Divination Bureau was administratively separate from, and much inferior in status to, the organizations that computed the ephemerides and observed celestial phenomena for astrological purposes. In Japan all of these activities were subsumed under the single Yin-yang Board, the name of which indicates a clear priority for divination.²

The Japanese yin-yang art was a complex of magical divination techniques. These techniques had little in common with the portent astrology practiced in the Chinese and Japanese courts. which was based on a belief that the natural and political orders influenced each other in such a way that changes in the former could be taken as warnings about inadequacies in the latter. Throughout the sphere of Chinese culture, calendar making was the paradigmatic exact science, used for computing solar, lunar, and planetary positions, forecasting eclipses, and composing a complete lunisolar ephemerides.³

Although both the yin-yang art and portent astrology were ways of forecasting changes in human affairs, the latter depended upon unpredictable omens, such as comets and irregular eclipses, as indexes of mundane crises. The yin-yang art, because it is less passive, was more important in the everyday life of the court –it determined the dates of court ceremonies, fixed propitious directions in which to begin journeys, and so on.

Much of this divination (in particular, the kind called hemerology) was based on cyclic notations of the year, month, and day, and therefore was an outgrowth of calendar making. In general the goals of mathematical astronomy are universal; local differences in the motions of the sun and moon are trivial. Given a Chinese manual from which to determine basic parameters and computational procedures, there was little that local talent or preference could add, at least to the routine work of making the yearly ephemerides. On the other hand, when unforeseen and ominous celestial phenomena were observed, they had to be interpreted without delay. No Chinese book could cover every contingency, and there was no time to consult with the astrologers of the Chinese court. In astrology the Japanese were thrown upon their own resources. In Japan, as elsewhere, the practical applications of imported knowledge were valued over basic theory.

Theoretical elements from Chinese natural philosophy played an important part in the interpretations of the yin-yang art and of astrology. There is an old belief, for instance, that the northeast (Kimon, the gate of the demon) was a channel of unlucky influences. The yin-yang art explained it as “the direction from which the god of Yang enters and the ch’i [energy] of Yin goes out.” But this notion did not imply a strictly deterministic causal principle. It was merely a warning, so that counter-measures might be devised; otherwise the art would have no practical use. For instance, people avoided building houses at places where the configuration of the land opened toward the northeast. Nor was astrology thoroughly deterministic. Before a predicted solar eclipse appeared to cast doubt upon the emperor’s virtue, he could defend himself by calling in Buddhist monks to exorcise it.

Although astrology and alchemy often are called pseudosciences, they are neither misconceived sciences nor forerunners of modern science. Their goals are in no sense those of science, which may be defined as a pursuit of regularities that underlie natural processes. Astrology assumes that the future may be predicted and that defensive measures may avert undesirable futures; alchemy of the Chinese kind assumes that eternal life is possible. It is true that they assume certain regularities in nature, but these are means rather than goals.

Although the astronomers who computed the calendar were considered to be mere functionaries, the master of astrology and the practitioner of alchemy were regarded by laymen as possessing more than ordinary wisdom. As in early Europe, astrology was the higher art. Only in the Tokugawa period, when Confucian rationalism became intellectually predominant, could the official astronomers of the shogunate (the military government) attain high status by monopolizing the scientific aspects of calendar reform. Even so, traditional prerogatives kept them formally subordinate to the Abe family, hereditary masters of the yin-yang art.

Western Orientation Toward the Regular and Japanese Orientation Toward the Extraordinary. As we have just seen, it was not the regularities or eternal truths of mathematical astronomy. but the unforeseeable omens of the astrologers, that attracted attention in Japan. Only after exposure to Western influence did academic disciplines (gakumon; Chinese, hsuehwen) come to be considered predominantly as parts of a converging search for eternal laws and for enduring realities.

We may juxtapose these two tendencies as orientation toward the regular and orientation toward the extraordinary. Exaggerating the difference for heuristic reasons, we may say that the former assumes that there are eternal and universal truths, and seeks to formulate underlying laws. The latter denies that such truths are attainable and therefore is not disposed to debate their existence. Those who relentlessly pursue regularity overlook the individual and the accidental. Those who value the extraordinary pay little attention to persons or events that conform without deviation to stereotyped patterns. If the former are unresponsive to change because of their preoccupation with order and system, the latter reject change reflexively because they lack set principles against which to measure it. Philosophers, especially natural philosophers, strive to discover underlying laws; while historians, including students of natural history, are attracted to discontinuities.

These two tendencies were rivals in the formative period of philosophy in both Europe and the Far East. Over time the emphases became divergent in the two cultural spheres. The main current of the Western academic tradition remained centered upon philosophical and logical inquiries in the Platonic and Aristotelian traditions. Eastern scholarship definitely inclined to history, with the Shih-chi (ca. 100 b.c.) of Ssu-ma Ch’ien as the prototype.⁴

Various conjectures have attempted to explain this bifurcation. Joseph Needham argues that the absence of an anthropomorphic lawgiver in their religion left the Chinese with little motivation to conceive laws of nature.⁵ While intellectual centers shifted from state to state in the West, in China there was one polity and one elite culture; historical records were accumulated in a single language. The record of the past was conceived as that of a single people. The early appearance of a true bureaucracy encouraged the development of chronology and the systematic compilation and classification of administrative precedents. The early availability of paper and the currency of printing by a.d. 1000 made historical literature more subject to ideological control and thus more central to political and social concerns.⁶

Historical analogy rather than tightly constructed chains of logical reasoning became predominant in Eastern learning. This was true even in natural science, so that although there were considerable overlaps of subject matter in East and West, there were enormous differences of style. Abstraction and involved theoretical argument were by no means rare in Chinese science but, as already noted, they were vastly less important in Japan.

It is well known that in ancient China historical scholarship grew out of the recording of astrological portents to provide an empirical foundation for future prognostications. From the time of Ssu-ma Ch’ien, whose duties included astrology and history, such omens were an important component of the imperial chronicles. The positivistic view of history predicts that the horror of celestial omens, such as eclipses, should evaporate with the development of rationality. This was not the case in China, because such foreboding is a social rather than a psychological phenomenon. The astrologer-historians also were mathematical astronomers and strove to remove phenomena from the realm of the ominous by making them predictable. Once that happened, such events lost their significance in astrology. What could be predicted no longer had news value and no longer needed to be individually recorded in the annals.

The Platonic conviction that eternal patterns underlie the flux of nature is so central to the Western tradition that it might seem no science is possible without it. Nevertheless, although Chinese science assumed that regularities were there for the finding, they believed that the ultimate texture of reality was too subtle to be fully measured or comprehended by empirical investigation. The Japanese paid less attention to the general but showed a keener curiosity about the particular and the evanescent. In the early West, in keeping with the orientation toward regularity, phenomena that could not be explained by contemporary theory, such as comets and novae, were classified as anomalous and received scant attention. In the history-oriented East, extraordinary phenomena were keenly observed and carefully recorded. The incomparable mass of carefully dated astrological records that thus accumulated has proved invaluable to astronomers today.

In the classical Western tradition there is an urge to fit every phenomenon into a single box; those unassimilable to the pattern thus formed are rejected. In the Eastern tradition, in addition to the box in which all the regular pieces are assembled, there are a great number of others in which irregularities can be classified. Sorting exceptional phenomena into proper boxes was as satisfying for the Japanese as fitting together the puzzle in his single box was for the Platonist (the Chinese preference was intermediate). If science is defined, as Europeans conventionally do, as the pursuit of natural regularities, the Far Eastern tradition is bound to appear weak because it lacked analytical rigor. Judged less ethnocentrically, there is some merit in its relatively catholic and unprejudiced interest in natural phenomena.⁷

When a court astronomer in Peking or Kyoto found that the position of the moon was radically different from what he computed, one would expect him to consider his theory to be compromised. Such crises often occurred in China, but there was an alternative that can be seen with some frequency both there and, quite often, in Japan. The phenomenon could simply be labeled “irregular.” It was not the astronomer’s fault that the moon moved erratically.

This attitude may be seen in the career of Shibu-kawa Harumi, the first official astronomer to the Japanese shogun, in a form more distinct than that which existed among his Chinese contemporaries. In the preface to his early treatise Shunju jutsureki (“Discussions on the Calendar Reflected in the Spring and Autumn Annals.” the oldest Chinese chronicle), he stated:

Astronomers have rigidly maintained that when Confucius dated the events in his Annals of the Spring and Autumn Era he made conventional use of the current calendar with little care for its astronomical meaning, so that the dates are not very reliable. This error is due to their commitment to mathematical astronomy, so that they do not admit that extraordinary events happened in the sky.… Extraordinary phenomena do in fact take place in the heavens. We should therefore not doubt the authenticity of [Confucius’] sacred writing-brush.

In his own work on mathematical astronomy, Shibukawa remained thoroughly positivistic; but he also left a somewhat problematic astrological treatise, Tenmon keito (“Treasury of Astrology,” 1698), Careful examination of these eight volumes of astrological formulas and interpretations of recorded portents discloses that a large portion was inattentively copied from a famous Chinese handbook, Huang Ting’s T’ien-wen ta-ch’eng kuan-k’uei chi-yao (“Essentials of Astrology,” 1653).⁸ In this work he repeatedly expressed the skepticism toward astrological interpretations that might be expected of a practical astronomer, and would often write “We do not know the basis [of this interpretation].… Is this unreliable?”

Shibukawa believed that a professional astronomer must be thoroughly competent in both major branches of celestial studies: portent astrology and calendrical science. His Jokyo calendrical reform (ca. 1684) provided a “box” for regularities. It was no less important to furnish the means by which astrological portents might be classified. He was convinced that the heavens could not be fully comprehended through mathematical regularity. The sky was a unity of such depth that the tools of no single discipline could plumb it. Although he found astrological interpretations to be often equivocal, the vast historical accumulation of omen records suggested that portent astrology had to be taken seriously. There must have been, he thought, justified passion and reason behind that tireless activity of the ancients.

Once admitting, as Shibukawa did, that regular motion was too limited an assumption, one could easily conceive such notions as that astronomical parameters could vary from century to century. In the official Chinese calendar of the thirteenth century and earlier, the discrepancy between ancient records and recent observations was explained by a secular variation in the length of the tropical year.⁹ Shibu kawa revived this variation in the Japanese calendar, and Asada Gōryū extended it¹⁰ to other basic parameters to account for both Western and Eastern observations then available to him.

The variation terms used in Chinese and Japanese astronomy were too large to survive empirical testing and eventually were discarded. Wherever the Aristotelian notion of an unalterable universe was followed rigorously, irregular motions in the sky were inconceivable. Even the mathematically justified variation in the precession of the equinoxes, which had a brief acceptance in Europe, came from Islam. After Newton, variations in parameters were acceptable to the extent that they could be given mechanical explanations. In the West, the first systematic study of variations in basic parameters was delayed until Laplace, in the late eighteenth century. It is significant for the history of ideas that in China and Japan there was no reason to resist such variations.

In the Far East, not only were irregular motions of the celestial bodies admissible, but the algebraic approach to mathematical astronomy made it unnecessary to take a stand on the spatial relations of the sun, moon, and planets. The earliest astronomical schemes in China (first century b.c.) depended heavily upon a cyclical view of nature. These numerical models explained all of the calendrical phenomena by a vast construction of interlocking constant periods. The cycles of the sun and moon, the synodic periods of the planets, and cycles of recurrence for such phenomena as eclipses were tied together by larger cycles determined by their least common multiples. By the end of the Han period, however, improved observational precision and recording accuracy made it clear that the heavenly courses were too complex to fit such simple assumptions. Eventually the metaphysical commitment to cyclical recurrence was abandoned.¹¹ Periods of recurrence became no more than algebraic constants to be used alongside a great variety of other numerical devices. Neither celestial morphology nor cosmic ontology was of further professional interest to astronomers.

The Chinese tradition of astronomy, including its offshoots in Japan, Korea, and Vietnam, thus did not depend for its direction of development upon a dialectical relation between metaphysics and observation. Computational schemes neither challenged nor strengthened philosophers’ conceptions of cosmic design.

Differences in Chinese and Japanese Views of Science. Ogiu Sorai (1666– 1728), the most influential Japanese Confucian philosopher, had some interest in astronomy. He commented on the variation of astronomical parameters (Gakusokufüroku): “Sky and earth, sun and moon are living bodies. According to the Chinese calendrical technique, the length of the tropical year was greater in the past and will decrease in the future. As for me, I cannot comprehend events a million years ahead.” Since the heavens were imbued with vital force, the length of the year could change freely, and constancy was not to be expected in the sky. Indeed, only a dead universe could be governed by law and regularity. The study of such a world would be of no interest to the natural philosopher. Since it was precisely the vital aspects of nature that interested Ogiu, he remained as agnostic in physical cosmology.

Indifference toward the search for regularities in nature prevailed in the School of Ancient Learning (kogaku), which emerged in the late seventeenth century led by Ogiu. Its anarchistic and dynamic cosmology was bathed in historicism. “All scholarship should finally converge in historical studies,” said Ogiu.¹² Because he was a Confucian philosopher, “history” meant humanistic history. Whenever the philosophers of the Ancient Learning School looked at nature, they saw it in the light of social and ethical concerns.

This moralistic, anthropocentric, and often anthropomorphic view of nature was common among Confucian thinkers throughout the Far East. Many of them were unable to imagine that mathematical astronomy could make any greater contribution than to provide an accurate calendar.¹³ Nevertheless, there were some notable differences between the views of Chinese and Japanese Confucians on the search for regularities in nature, especially with reference to calendrical science. Although these views were not imposed upon astronomers as corresponding ideas were in the West, the importance of philosophy in education makes them worth examining.

In China, computational astronomy was an integral part of the imperial bureaucracy. The head of the Astronomical Bureau, unlike his subordinates, was not a technical expert but a civil service generalist on his way up the career ladder. Many Confucian scholars wrote competently on astronomy, and books on the subject often were ornamented with prefaces and colophons by high officials.

In feudal Japan occupations were hereditary, The post of official astronomer to the shogun was created to recognize the personal achievement of Shibukawa Harumi and was passed down to his descendants. It had no significance beyond the technical acumen and thus was of no interest to the generalist. Technical posts of this kind were from their origin separated from the general samurai bureaucracy. When the official astronomer and his subordinates were compiling the ephemerides, Confucian scholars were not consulted. Even the Tsuchimikado family, for many centuries astrologers to the imperial court in Kyoto, was accorded the courtesy of an invitation to contribute a preface to the ephemerides.

A popular Chinese book of negligible depth, the T’ien-ching huo-wen (“Queries on the Astronomical Classics,” 1675) by Yu I, exerted considerable influence on Japanese cosmological notions. Among the many Japanese editions, the only preface by a Confucian scholar was that of Irie Shukei. Irie states in his preface that he was motivated to write a commentary on the simple work because most astronomical writings were so full of mathematics and technical terms that, although they might be “useful for the narrow calculations of small men engaged in the divinatory and computational arts, they are of no use for the greater mathematical concerns of gentlemen and scholars.” It was no doubt commonly believed in China as well that calendrical astronomy, which Irie looked down upon, had lost its ideological implications and had become nothing but a collection of techniques. Nevertheless, the Chinese, particularly from the mid-seventeenth century on. continued to think of astronomy as part of the Confucian system of learning. As Juan Jüan (1764-1849). a high official and patron of learning, put it, mathematics and astronomy were “a proper study for those scholars who search out the facts to get at the truth, and not a tool for technicians scraping up a living.” In China many Confucian scholars contributed prefaces to T’ien-ching huo-wen, not merely for ornament but often to discuss fundamental technical matters.

What accounts for this difference? Almost without exception the computational schemes and theories used in eastern Asia were discovered by the Chinese. To the Chinese they were integral parts of native culture; to the Japanese they were importations. In China the lingering excitement of discovery clung to knowledge of regularities in nature. In Japan these foreign regularities constituted one more routine skill prerequisite to established occupations.

This was true not only of science but also of Confucianism itself. In China, Confucianism was more than a philosophy; it was the basis of political legitimacy. The government’s use of it as a political ideology demanded that great care be given to defining what orthodox Confucianism should be–just as the imperial monopoly of the calendar made it necessary to have one official system of astronomical computation. Official philosophy and official astronomy were exported to maintain China’s cultural suzerainty over her satellites and neighbors. Confucian philosophy in its contemporary interpretations endorsed and justified these concerns. The commitment of the Chinese elite to civil service channeled a great deal of intellectual energy in this direction. What interpretations should be orthodox and what sorts of learning should be propagated were central subjects of philosophic inquiry. Not all thinkers shared the official view at any given time; but because it determined the content of the civil service examinations, about which much of early education was organized, the official view was enormously influential.

In Japan there was no social or political reason for philosophic orthodoxy to be an important issue. Although nominally based on the centralized Chinese model. Japanese government until the mid-nineteeth century was imposed upon a feudal society and thus remained multifocal. Although dynastic legitimacy could not be taken from the imperial court in Kyoto, real political power lay entirely in the hands of the military dictator, the shogun in what is now Tokyo. He was able to retain that power only by leaving local authority in the fiefs (han). Certain prerogatives in astronomy belonged by tradition to the Tsuchimikado family, the imperial court astrologers: and others were divided between the shogunate astronomers and those of the fiefs. Satsuma, one of the larger fiefs, issued its own calendar. There was no occasion to establish a single orthodoxy, either political or intellectual.

Just as political and astronomical orthodoxy were related in China, so their absence was related in Japan. This contrast is apparent even in the art of divination. The great Chinese treatise Wu-hsing ta-i (“Fundamental Principles of the Five Phases,” ca. 600) set out a coherent synthesis of contemporary knowledge and belief. The early Japanese treatise Hoki naiden (“Ritual Implement,” undated), equally influential upon later practice, was an undigested juxtaposition of hemerological practices from Shinto, Buddhism, and perhaps Taoism, In Japan freedom to choose between several paradigms seems to have been as desirable as the search for a unitary principle was in China.

When the Japanese did originate something, there was no expectation that it would be universally accepted or that it would have influence outside Japan. Although the Chinese did occasionally acknowledge Japanese originality in connection with one development or another, the Japanese did not believe, prior to the twentieth century, that they could contribute to universal systems of knowledge.

From the seventeenth century on, when Western knowledge began to exert claims of its own in the background of Chinese learning, Japanese thinkers were critically attentive. Once convinced that European technical knowledge was superior, they promptly switched to the new paradigm. This was not the first time that the Japanese had modified their attitudes smoothly and quickly to conform to desirable goals presented from abroad. For the Chinese the encounter with European ideas was traumatic; to accept them was to reject traditional values, and to reject them would leave no defense against dismemberment by the Western powers.

The Academicism of Shibukawa Kagesuke. When Shibukawa Harumi founded the shogunate astronomical office, he was in the rare position of initiating a tradition. The older astronomical institutions of Japan were devoted to inherited responsibilities from which the incumbent could not freely deviate. Shibukawa defined his responsibilities in a way that involved considerable political activity. He enlisted the support of powerful figures for a calendar reform not based upon a borrowing from China. He had to overcome the opposition of Confucian scholars, who saw no merit in native independence. The problem that Shibukawa set and the solution that he envisioned constituted a paradigm (in Thomas Kuhn’s sense of the word) – a paradigm of purely local applicability.

As an exact science, calendrical science could be given the solid foundations that enabled normal science to proceed. Shibukawa left to his descendants and disciples the responsibility to work toward greater precision and to improve agreement between observation and theory. For some time there was no need to question the validity of his conception of astronomy. Historical questions that also interested Shibukawa, such as the gradual variation in astronomical parameters, did not retain interest for later generations. The historical orientation of such problems made it impossible to adapt them to the concern of “normal science” with the improvement of precision.

The success of Shibukawa’s program depended on the quality of his successors. Since the family stipends of samurai, even those in professional posts, were inherited only by eldest sons, there was a conflict between the rigid ideal of social structure in feudal Japan and the need for technical talent. There was more than one astronomical institution because new ones had been created at various times to make room for gifted scientists. Certain established families took advantage of another means to maintain their intellectual standards; adopting as successor to the head an intelligent second or third son of a samurai family. The Shibukawa family maintained its tradition in this way. Adopted sons probably contributed more to the cumulative achievement of the family than did eldest natural sons.

Shibukawa Kagesuke (1787-1856), an adopted heir, was perhaps the greatest professional, as well as the last important figure, of traditional astronomy. In his youth he suffered bitterly when his talented brother, Takahashi Kagesuke. was executed after being involved in an attempt by a foreigner, F. von Sieboldt, to smuggle forbidden materials out of Japan. Shibukawa never deviated from the behavior expected of a professional astronomer and maintained unblemished authority in his discipline.

Shibukawa’s passion for rectitude made him particularly apprehensive about criticisms of the official calendar. In order lo safeguard the prestige of his office, it was essential that he have first access to newly imported astronomical literature. This was a time when foreign threat, social change, and natural calamity jeopardized the authority of the shogun, who attempted to minimize unrest and maintain a useful monopoly by prohibiting the diffusion of Western knowledge. The translation of Western literature for official use was confined to the Astronomical Bureau. Shibukawa took full advantage of his privileged position. He left voluminous notes on his wide reading in books forbidden to others–Chinese and European, ancient and contemporary.

Shibukawa’s motivations emerge clearly from the story of his conflict with Koide Shuki (1797-1865), a scholar of astronomy who did not hold a position in any of the government astronomical institutions.¹⁴

The Kansei calendar, then in official use, was almost completely based on Li-hsiang k’ao-ch’eng (“Compendium of Observational and Computational Astronomy.” draft completed 1722. printed 1724). in which the outdated European astronomy introduced to China by the Jesuits was adapted to the needs of a traditional calendar reform. In addition, the compilers of the Kansei computational system had incorporated Asada Gōry’s cyclical variation in length of the tropical year. The official calendrical treatise was not published, for laymen had no business using it. On the other hand, nonre-ligious writings of the Jesuits in Chinese had recently been exempted from the ban on importation, so the Li-hsiang k’ao-ch’eng was available for study by private scholars. If the Kansei calendar had been based entirely upon it, anyone could have checked the validity of the official calendar. In the late I820’s, Koide had an opportunity to calculate an ephemerides on the basis of the Li-hsiang k’ao-ch’eng and compare it with the official calendar. He found considerable disagreement. He suspected that Shibukawa Kagesuke’s father, a disciple of Asada, had introduced Asada’s variation in the last calendar reform, in order to conceal the system of computation under a cloak of security and thus avoid criticism from amateurs. He was unable to prove this suspicion, since the value of Asada’s variation was unavailable to him; it belonged to the private teaching of Asada’s successors.

Determined lo obtain the formula, Koide enrolled in the academy of the Tsuchimikado clan, the hereditary imperial astrologers, where one of Asada’s four major disciples had taught. In 1834, after eight years of discipleship, he was permitted access to the details of Asada’s variation. His heart’s desire having been fulfilled, as he wrote, he immediately calculated the current value for the length of the tropical year. Koide next made precise observations from which to determine the winter solstice, and found a discrepancy of a quarter of an hour between his computations and those given by the official calendrical system. When he ignored Asada’s variation and calculated on the basis of the Li-hsiang k’ao-ch’eng alone, his results coincided closely with observation. Thus he determined that Asada’s formula was a “fake supported by blind belief.¹⁵ In 1835 he visited Edo (now Tokyo), became a disciple of Shibukawa Kage-suke, and questioned him about his view of Asada’s variation. Shibukawa would not give him a clear answer.

Shibukawa had already read Lalande’s Astronomie and had a good understanding of the European astronomy of the previous century. He knew perfectly well that Asada had misled his successors. He did not, however, dare to voice his doubts publicly. In 1835, in fact, Shibukawa drafted a manuscript entitled “Saishu shochō kō” (“On the Variation of the Length of the Tropical Year”).¹⁶ in which he analyzed the origin of, and tried to give a rationale for, Asada’s variation.

Why did he write this essay in that particular year? He must have been influenced by Koide’s criticisms. Although Koide had no official standing, his connection with the Tsuchimikado (an older institution and, to some extent, a rival for power) gave him some authority.

Koide was not prepared to do more than point out numerical discrepancies. Shibukawa had access to vastly greater information and technical skills, and was able to form an analytical overview of the variation question. Since his bureau had come to be responsible for the actual calculation of ephemerides, he felt that a frank answer to Koide’s inquiries might compromise his own official responsibilities. But he was now aware that Koide had found the weak point in the official calendar and would be driven by his remarkable determination to press an attack that was bound to be successful. Although Shibukawa Kagesuke was not responsible for the failure of the Kansei calendar, his office would suffer for it.

Shibukawa had two lines of defense. The only permanent defense was to carry out a calendar reform as soon as possible, discarding Asada’s variation in the interest of accuracy. But calendar reforms in Japan were so infrequent that they could not be proposed and carried out overnight. If a crisis arose too soon. Shibukawa wanted to be prepared with an official interpretation of Asada’s variation to interpose against attack. That was apparently the point of his treatise.

Shibukawa’s fears were soon realized. Koide’s prediction of a solar eclipse in 1839 (based entirely on the Li-hsiang k’ao-ch’eng) proved to be more accurate than that given in the official ephemerides. Koide submitted to the prime minister (rōjū) a proposal for a calendar reform based on the Chinese source,

The official astronomers had no choice but to hurry their own reform. The new Tenpo system of computation became official in 1842. Shibukawa. unlike Koide, did not have to depend upon a century-old treatise. He had the authority to mobilize the best translators in Japan so that his system could he based upon contemporary European data.

Through the years of mounting conflict between Shibukawa and Koide, the goal of both was complete agreement between computation and observation. Nevertheless, they differed in their conceptions of the astronomer’s work and thus of astronomy. From Shibukawa’s viewpoint, Koide’s painstaking efforts had no significance whatever for the advancement of astronomy. Koide was simply duplicating outmoded results. The only positive service he could perform was to prevent the corruption of the astronomical functionaries who monopolized research facilities and tools under government protection. Koide began with a simple puzzle: why the official calendar failed to agree with observation. Since he had only limited access to scientific and political information, all he could do was deal with each step as it unfolded from the last. What began as a technical exercise in the testing of computational theory was reduced to the unraveling of bureaucratic prerogatives.

Here the conflict between Koide and Shibukawa finally lay. Although both accepted the commitment of the astronomer to accurate prediction, Shibukawa’s dedication to his profession gave the administrative order precedence over the celestial order. This Koide could not accept; but he was bound to be drawn into intrigue, for Shibukawa’s professional standing reserved to him alone the initiative to define the rules of the game.

Western Cosmology and the Traditional Calendrical Science. Elaboration and precision were the criteria by which calendrical treatises were evaluated in prefaces written by astronomers. The holders of astronomical sinecures needed to fear no crisis so long as these criteria were satisfied. In view of the moderate level of precision needed for the traditional ephemerides, why should Shibukawa have wanted to involve the Astronomical Bureau in the active dissemination of European natural philosophy? Such a major departure from his inherited duties would seem to carry as much risk as gain. Nevertheless, Shibukawa wrote an account of Copernican theory and Newtonian mechanics for government use (not for publication) in his “Shinpo rekisho zokuhen” (“Sequel to the Astronomical Treatises According to the New Methods” [to the series of works compiled by the Jesuits in China before 1635]).¹⁷ Again his motive seems to have been bureaucratic caution. It was essential to formulate an official view of European cosmology as awareness of it gradually became more general in Japan: otherwise a query by a high official might result in grievous embarrassment.

Heliocentric theory had been previously introduced by Motoki Ryoei (1735-1794), an official interpreter; Shizuki Tadao (1760-1806). an independent intellectual: and Shiba Kokan (1739-1819), a free-lance popularizer. Partly because cosmology was not traditionally an important topic in Japan, and partly because they understood Copernicanism only superficially, these writers and those who read their works were not shaken by heliocentricism as Europe had been. Motoki considered it merely an exotic European curiosity. Shiba adhered to it for the sake of sensation. Shizuki treated it incidentally to his main interest, the philosophical implications of Newtonianism, which he tried to assimilate to Chinese natural philosophy.

Shibukawa disdained these amateur writings. For his account of Copernicanism he depended heavily upon an explanation written in Chinese by the French Jesuit missionary Michel Benoist (1760). It was little known in Japan and did not so much as mention Newton. This work allowed Shibukawa to deal with the subject while completely ignoring the Japanese literature (based upon much later secular sources). Although not enthusiastic about the sun-centered system, Shibukawa did accept it with critical reservations. He agreed with Benoist that the difference between heliocentricism and geocentricism was merely a matter of transforming coordinate systems. He contributed the notion that theories of a moving earth were not original in the modern West but had existed long before in China and India –a theory first advanced by Shizuki Tadao.¹⁸ “Shibukawa’s discussion of the technical aspects of Newtonianism was superior to that of Shizuki, but the latter’s philosophic depth was totally missing. For Shibukawa. Newton’s work was not the foundation of a world view but a peripheral issue on the margins of calendrical science. Shibukawa was successfully guided by his motto, “Let us melt down the mathematical principles of the West and recast them in the mold of our tradition,” a cliché in earlier Chinese writing. Newtonianism was so well assimilated in Shibukawa’s presentation that it did not perceptibly challenge the traditional definition of mathematical astronomy. Like his ancestors who had headed the Astronomical Bureau before him, Shibukawa devoted his erudition and energy to the perfection of routine, not to the development of new fields of investigation.

In the scientific revolution of seventeenth-century Europe, astronomy played a great role because of its implications for cosmology and world view. Japanese astronomy had no such implications, and its social matrix gave it no scope for free inquiry into nature. During the seventeenth and eighteenth centuries it remained the vanguard of disciplines oriented upon mathematical regularity. Its paradigm was so well insulated from challenge by professionalism that even the impact of Western exact science did not throw it into doubt. The most important function of European astronomy was to fürnish numerical data and computational techniques, by use of which traditional calendrical goals could be better met.

The Tenpo calendar reform brought the accuracy of prediction to as high a level as the traditional calendrical art envisioned (solar eclipses to the nearest quarter-hour, for instance). It was no coincidence that the esteem of intellectuals for astronomy was practically lost in the process. At a time when the revolutionary implications of foreign science were gradually coming to be understood, the astronomical profession was seen as too routinized and unimaginative to make any important contribution to change. It was finally the physicians. who lacked both the advantages and the disadvantages of a tightly organized profession, and whose proficiency in the exact sciences was inferior to that of the astronomers, who were able to introduce the true core of Western scientific thought. The structure of the scientific revolution they brought about in Japan was bound to be different from the one led by astronomy in seventeenth-century Europe.

Medici.

The Chest as the Seal of the Mind. Even as late as the middle of the nineteenth century, the Japanese did not believe that thought takes place in the head. As Shibukawa Kagesuke put it, “Mathematical principles all originate in the breast of the mathematical astronomer.… [Thoughts] are stored in the chest.”¹⁹ He was typical in situating both memory and arithmetical thinking in the chest.

To the Japanese such expressions as “a dull head” or “a clear head” have a modern and exotically occidental flavor: they were never used until the Tokugawa period. The cognitive and imaginative functions of the brain were unknown, and their anatomical substrate undemonstrated in Japan, until the beginning of Westernization.

Traditional Chinese medicine, upon which the learned tradition of Japan depended, was concerned primarily with function and only secondarily with tissues and organs. The sites of function to which most attention was paid were two groups in the thorax, a set of six fu that fermented food, separated energy from waste, and excreted the latter. and five tsang that stored the refined energy. These spheres of function were identified with the familiar viscera; but the physiological nature of the latter was of such minor importance that little was known about it, and it played only a small abiding role in medical discourse. Occasional drawings of the body ignore both the interior of the head and the nerve tissues, neither of which was assigned specific functions, at least in the Chinese medical writing that was influential in Japan.

To my knowledge, the brain’s function was first discussed in China in Wu-li hsiao-chih (“Notes on the Principles of the Phenomena.” 1664), by the idiosyncratic Fang l-chih, who was acquainted with the writings of the Jesuit missionaries. His knowledge originated in Western medicine.

In Japan thought was first located in the brain in an Amakusa edition (1593) of Aesop’s Fables, in which it was said, “if we have intelligence in our heads.…” Again it is clear that this idea was imported into Japan along with Catholicism. The notion did not spread until the study of the Dutch language (and consequently of secular sources) became widespread in Japanese society: and in the early period there was not the slightest influence upon developing knowledge of anatomy, physiology, or pathology.

It is well to remember that the interrelation between the brain and mental processes could not be proved before the development of cerebral physiology. The idea has a long history in Europe, but it is the history of a belief rather than of a fact.²⁰ Plato and Aristotle held quite different views on the location of mental processes. Plato believed that the immortal and holy rational soul is located in the brain. Aristotle placed the center of sensation and perception in the heart, and did not believe that it was related to the brain or spinal cord in any way.

These were not isolated opinions but were integral with coherent views of the body and its functions. Plato and others who placed mental functions in the head have tended to think of them as quite separate from the physical body; schemata that consider the heart and mind as identical have tended to think of mind and body as integral. Traditional Chinese and Japanese views must be classed with the organismic and naturalistic group to which Aristotle belongs rather than with Plato’s idealists. The experimental work of Galen settled the matter in the West, providing an authoritative basis for the doctrine that the brain is the center of perception and of all other mental processes. The introduction of this idea into the Far East had implications at least as revolutionary as those of Copernican astronomy. It challenged the doctrine of bodily functions and the rather negligible notions about internal organs related to them, and posed a range of questions about the physical basis of sensation that had not been previously considered.

Ogawa Teizo has located²¹ the first appearance in Japanese of terms that correspond to “nerve” and to “consciousness” as associated with the brain in the Kaitai shinsho (“New Book of Anatomy, 1774), by Sugita Genpaku and others. Otsuki Gentaku, in his Chotei kaitai shinsho (“New Book of Anatomy. Revised” [compiled 1798, published 1826], enthusiastically described the significance of the new study of the cerebral and nervous system in this way:

We have not come across anyone in the long Chinese and Japanese traditions who discussed the active functions of these organs of sentience. They were taken up superficially and in an elementary way only at the close of the Ming dynasty [early seventeenth century]. Most regrettably, in the two hundred years since that time no one has taken up the problem in closer detail. It is a great pleasure that now we are able to explore it more deeply. This is not particularly due to my personal endeavor, since we are all influenced by the trends of the times.

The learned treatises of the Chinese and Japanese medical traditions lacked terminology not only for brain functions but also for mental processes. Conventional Chinese discourse was not much concerned with what we would consider epistemology. Some late Confucian schools were somewhat concerned with how knowledge becomes certain but tended to connect this problem with that of attaining enlightenment. The vocabulary for mental operations remained rudimentary and to a considerable extent was borrowed from Indian Buddhism.

Although the spheres of function within the body were thought to process nutriment and to store the energy refined from it –and Japanese terms that predate Chinese influence, such as kuso-watafukuro and yuharifukuro, are literally types of containers –knowledge was never thought of as localized and stored. There was no reason to investigate the physiological basis of cognition.

In short, the need to explore the relations between mind and brain did not exist in China because the Chinese assumed neither the mind-matter dualism nor the dualism between the self and the outer world. They saw all of nature as united in a single pattern of function in which the patterns of function of individual things (li) participate. The dualistic terminology used today in Japan, except for a few terms borrowed from fundamentally religious Buddhist dualism, was for the most part devised by Nishi Amane and others at the beginning of the Meiji period (1870– 1890).

Anatomy and Energetics. In the East, the apparently rudimentary association of physical functions with internal organs does not indicate a low state of medical theory. Although the Chinese lacked the sophistication of Galen’s anatomy, attempts to study rigorously the Chinese language of function in its own terms, a very recent development, suggest an artfulness that was obscured by the imposition of modern viewpoints. From the historical point of view, the fundamental question is not whether, before modern times, the Chinese or the European tradition incorporated the greater number of correct facts, but how their theoretical paradigms, and the views of nature on which they depended, differed.

In Western medicine the rivalry before modern times between solidists and humoralists is well known. The aim of the former was to locate the seat of a disorder in a solid part of the body, such as the stomach or brain. The motivation to pursue anatomical research is obvious. The humoralists, on the other hand, thought of health primarily as a balance of the various humors that circulate in the body. Anatomy had a great deal less to contribute to their holistic diagnoses.

Traditional Chinese theories of bodily function and of pathology are closer to the humoralist tradition than to that of the solidists. Health was related to the balance of ch’i, which is the basis of material organization and function not only in the human body but throughout the physical universe.

Ch’i was not a ponderable fluid, as the humors were. It originated very early as the word for air–not as an inorganic gas but as an enveloping substance that maintains vital functions. Its closest analogue in the West was the Stoic pneuma. In medical theory its vital or energetic aspect–in a purely qualitative sense–became preponderant in discussions of etiology. Ch’i was not only inspired air but also the energy refined from food that circulated throughout the body and was responsible for all vital functions. The concept of ch’i as a material pneuma was to some extent reconciled with this energetic approach and was never abandoned: for instance, certain tumors and internal swellings were thought to be stagnated or congealed ch’i. Indeed, the seventeenth-century Japanese physician Goto Gonzan attempted to explain the cause of all medical disorders by stagnation of this kind. Since ch’i was involved in processes in physical nature and in the body, it assumed different qualities or characteristics in different phases of such processes. If the whole process was analyzed into two phases, the two different types of ch’i were characterized as yin and yang; if a fivefold analysis was used, the five types of ch’i were described by the language of the Five Phases theory. A dynamic balance between the two or five types of ch’i defined health: ethical disorders were always identified with an imbalance.

The language of yin-yang and the Five Phases theory were used to establish sets of correspondences that governed bodily function. For instance, the Five Phases corresponded to the five spheres of function (loosely identified with the heart, lungs, spleen, liver, and kidneys). But discourse about health and pathology was never anatomical. The system identified with the spleen amounted to the ensemble of functions that would be ascribed today to the urogenital system and was thought of in functional terms.

Internal disorders were never local in Chinese medicine. Although they might be concentrated in a particular sphere of function, the connection of the spheres by the energetic circulation system meant that the whole body was affected and that as the pathological process developed, its seat would move. There was no value in local treatment, for the site of treatment often was far removed from the center where the disorder was concentrated for the moment. Abstract correspondences often were used in discussions of pathology and therapy –for instance. Five Phases correspondences between the heart and the ears and between the liver and the eyes. These were not so much statements about physical connections (although such connections were claimed to make the model plausible pneumatically) as about similarities and analogies of function.

Early Far Eastern anatomical charts were extremely simple and crude. As Lu Gwei-djen and Joseph Needham have said,²² they incorporate a much more rudimentary level of knowledge than the texts that they accompany. Why were Chinese physicians satisfied with them? Their purpose obviously was different from that of Western anatomical diagrams. They were simply meant to depict the broad outlines of the general system of physical function. One might think of them as half anatomical diagram and half flow chart.

According to this view of the theoretical entities of Chinese medicine, reconstructed largely through the painstaking work of Manfred Porkert,²³ it is possible to conclude that it was closer to the European humoralist point of view, although it was pneumatic in a sense that does not fit the European theory. It had no use for exact anatomy. For the latter to be accepted in the Far East, its utility would have to be proved; and it could be proved only by an appeal to a different conception of nature and of the human body.

Anatomy in Japan. When anatomical inquiry began in mid-eighteenth-century Japan, did its demand for an analytical approach to the human body have revolutionary consequences?

Even before the serious study of anatomy began in Japan, Yamawaki Toyo questioned traditional Chinese anatomical charts on the basis of his own anatomical findings (1759), and his criticism entitles him to be considered the forerunner of anatomical students. Yamawaki’s interest in anatomy must have been stimulated by access to a Western anatomical chart. Although he could not read the legends, his experience must have convinced him that the Western schema was a great deal more accurate than the Chinese. What led him to evaluate both Schemas as anatomical rather than as functional?

First of all, when Western knowledge began filtering into Japan during the Tokugawa period, it was natural that it should have been compared with the official Chinese academic knowledge, since the latter had become firmly entrenched not very long before. It was also natural to ask which set of ideas was better–the situation was different from the case in China, where traditional ideas were so strongly rooted that such a question could only be radical. In mathematical astronomy, criteria of predictive accuracy were so obvious that Western superiority was quickly recognized. This was equally true in China, since the criteria for that recognition could be traditional ones. In medicine, however, there is good reason to doubt that there was any difference in therapeutic efficacy between the two systems before the late nineteenth century. It is above all in the comparison of anatomical charts that the strength of Western medicine would be apparent. But if the foregoing argument is correct, the difference between Chinese and European ideas about the interior of the body would be anatomically significant only after acceptance of the idea of anatomy and of the more general medical and philosophical ideas on which it was based.

Yamawaki Toyo was one of the leaders of a new group called the Koihō (“Back to Ancient Medicine School”), who rejected the theoretical entities of Chinese medicine and undertook an empirical approach to clinical treatment. Their utilitarian goals made the very elaborate conceptual superstructure of the Chinese tradition seem an impediment. Because they wished to confront as directly as possible the ills of the body, its role as a microcosm of physical nature could be rejected. As Yoshimasu Todo (1701-1773). the foremost figure of this school, declared, “Yin and yang are the ch’i of the universe, and thus have nothing to do with medicine^”24 This group was prepared, then. to take a position much closer to that of the solidists than had previously been possible in Japan. Functional analysts lost its importance, and the physical organs could be studied for their own sake. From this point of view the traditional anatomical charts were recognized as crude and inaccurate representations of material organs. This was nothing less than a change of gestalt.

Nevertheless, this conceptual radicalism was circumscribed. Yamawaki’s accomplishment was not to do away with the old scheme of six processing spheres and five storage spheres but, rather, to alter them so that they made sense in anatomical terms. He had no reason to be curious about the contents of the skull. It was only later figures with considerable knowledge of Western anatomy, such as Sugita Genpaku, who could abandon the Chinese tradition entirely and display as much anatomical interest in the brain as in the viscera. At that point the confrontation between champions of the two systems becomes interesting.

Lately there has been a tendency to emphasize the value of organismic and synthetic thought, of the sort that Joseph Needham has found predominant in Chinese science, to the detriment of the early modern habits of physical reductionism and remorseless analysis. Although the pneumatic ch’i doctrine, and the yin-yang and Five Phases theories that qualified it, are not precisely reductionist, they are not modern either. All of these concepts, although originally taken from everyday phenomena, were too abstract to have fixed empirical significances. They remained satisfactory only because, as N. Sivin has shown,²⁵ the goal of Chinese science was not complete understanding of the natural world but limited knowledge for practical purposes. The body was clearly not the cosmos, but the correspondence between the two set limits upon what could be asserted about the body.

Because of the special character of Chinese medical thought as it was received in Japan, we have examined in some detail the reasons that traditional doctors would find anatomy, and thus dissection, irrelevant to the improvement of medical therapy. There were other objections as well. The idea was deeply ingrained in Confucian ethics that keeping intact the body one has received from one’s parents is a major obligation of filial piety. This prohibition against mutilating the body effectively ruled out dissection in China. In Japan, however, it had practically no effect on medical specialists.

A second objection to dissection originated in traditional physiology. In his Hi zoshi²⁶ (“A Refutation of the Anatomical Charts.” 1760) Sano Antei said,” What the tsang [the word for the spheres of function and their associated viscera] truly signify is not a matter of morphology; they are containers in which vital energy with various functions is stored. Lacking that energy, the tsang become no more than emptied containers.” In other words, the internal organs were characterized not by their morphology but by the differences in their functions, which were defined by the energy they stored. Nothing could be learned by dissecting a cadaver, since it lacked this vital energy. The anatomical charts that captured the imagination of Yamawaki, since they were based on dissection, could cast no light on the dynamic functions of the body. The same point emerges in another criticism that Sano made. He noted that Yamawaki’s anatomical charts did not distinguish the large and small intestines. He did not believe, in fact, that those organs were morphologically or physiologically dissimilar. What made them utterly different was that the large intestine was responsible for absorbing and excreting solid wastes, while the small intestine performed those functions for fluid wastes. He emphasized that this crucial difference would be undetectable in a dead body. Figure and appearance could be significant only to the extent that they were related to function. Sano,unlike the Koihō radicals, had no use for pure empiricism. “The observation of two obvious facts is of much less value than groping speculation… even a child is as good an observer as an adult.” A scholar who refrained from speculatively tracing the connections between form and function was no better than a child.

Beginnings of a Solidist Approach. After accurate European anatomical charts were introduced into China, even the traditional schools of medicine that admitted anatomy as the basis of surgery (an undeveloped art in the Chinese tradition) still adhered to an energetic and functional view as the basis for internal medicine. But a shift to a solidist approach had at least begun.

It would be a mistake to see this shift purely in terms of the increasing accuracy of anatomical description. The Koihō school, like Western empiricism, could not dispense with metaphysical entities, but depended upon them without acknowledging them. Its physiological and pathological ideas were not only less explicit than those of earlier speculative Chinese medicine but also a great deal less sophisticated. The move toward solidism was not a rejection of models, but the construction of a new model.

Yoshimasu Todo, for instance, rejected the elaborate Chinese theories but was unable to translate his solidist thinking into diagnosis without the aid of a theory that Chinese doctors would have considered primitive: he saw all disease as the action of one fundamental poison on the various organs and tissues of the body. This was not really a pharmacological theory about the effect of poison, but merely a rationale for locating the part of the body on which treatment should be concentrated. He also rejected the traditional pulse diagnosis, which had served as a way of reading functional characteristics of the chi’ circulation. Thus faced with the problem of how to determine the condition of the internal organs without dissection, he did not so much eliminate pulse reading as substitute abdominal palpation for it. This technique had been used to a very limited extent in traditional medicine, chiefly to determine whether existing abdominal pain increased or decreased when the belly was pressed. Yoshimasu enormously increased its importance as the most direct way of learning about the conditions of the internal organs and thus founded a Japanese diagnostic tradition that still flourishes among traditional doctors.

The solidist tradition begun by the Koihō school eased the way for Western anatomy. In the second half of the eighteenth century. Sugita Genpaku took up the study of anatomy because it seemed the most tangible, and therefore the most comprehensible, part of Dutch medicine. Following the solidist breakthrough, the successors of Sugita in medicine studied physics and chemistry, thus opening up the world of modern science. The Copernican influence was minor by comparison, because the Japanese cosmos had not been defined by religious authority. The impact of anatomy challenged the energetic and functional commitments not only of medicine but also of natural philosophy. Its effect was bound to be revolutionary.

Medicine and Science After “Kaitai Shinsho,” Publication of Kaitai shinsho (1774), the first Japanese anatomical treatise based directly on Western materials, not only led to recognition that Western knowledge of the interior of the body was superior to that of China but also provided a new paradigm for Japanese science. Once the Japanese were prepared to compare accounts of the interior of the body from a purely morphological point of view, the superiority of the West became obvious. Chinese-style conservatives could dismiss European anatomical charts as superficial, but they could not convince others.

The first Japanese to realize the power of Western anatomical knowlege naturally assumed that the European system also was therapeutically more effective, although there is no reason to believe that this proved to be the case. Indeed, on therapeutic grounds there is very little to choose between the systems of internal medicine evolved in the various high civilizations before the end of the nineteenth century. Moreover, it is unlikely that the relatively frequent resort to surgery in the European tradition led to consistently higher recovery rates before the introduction of anesthesia and asepsis. Some scholars actually give the edge too Chinese internal medicine because it tended to use milder and less drastic drugs than were prevalent in Europe. It is ironic that one of Yoshimasu Todo’s innovations was the frequent use of poisonous drugs to” fight poison with poison.²⁷

Among the great diversity of schools in Japan were eclectic groups that prescribed both Chinese and Western drugs for a single symptom, but that was about as far as eclecticism could go. The views that underlay Chinese and Western medicine, or even Koihō medicine and practice of a more traditional kind, were irreconcilable.

It was quite possible to introduce European data into traditional calendrical astronomy without challenging the paradigm on which the latter was based. An analogous accommodation was impossible in internal medicine, for there was little overlap of the conceptions of relevance. Acceptance of the European view of the body came only with the publication of Kaitai shinsho. The Koihō school can be considered a vanguard in this scientific revolution. Such a transition did not take place in China because the Chinese maintained their traditional medical world view much more rigidly than did the Japanese.

An important characteristic of early modern science was mechanical reductionism, in which every phenomenon was believed to be ultimately explainable in terms of matter and motion. This reductionism gave birth to the positivists “hierarchical arrangement of the sciences. Comte ranked the abstract sciences in the order in which he believed they would be entirely quantified, beginning with mathematics, then astronomy, then physics, with sociology at the end of the list. At about the same time Japanese physicians were constructing an analogous but very different schema.

After the publication of Kaitai shinsho, some medical practitioners, exploring the newly available writings on European physical science, recognized and responded to its reductionism. In the prefaces to Aochi Rinso’s Kikai kanran (“Contemplating the Waves in the Ocean of Chi’; 1825) and Kawamoto Komin’s sequel, Kikai kanran kogi (1851). the authors claimed that physics must be the basis of medicine and the other practical sciences. Kawamoto described a hierarchical order from physics to physiology to pathology, eventually encompassing practical therapy. It is not clear how seriously his fellow practitioners took him. It is likely that they saw no clear role for physics in medicine, except perhaps for embellishing prefaces, as disquisitions on yin-yang had done in traditional books of therapy.²⁸ Physics and chemistry were introduced into Japan by European medical men only for their limited direct value to clinical medicine, just as anatomy, physiology, and pathology were subordinated to the same use. Hoashi Banri, a natural philosopher whose background was in medicine, was disappointed and disillusioned with Western science when he examined books on microscopy and chemistry and found them of no help in the understanding of drug therapy. The disciplines such books represented underlay techniques of measurement in materia medica and of extracting the active essences from herbs. Those applications were the basis for their initial study by physicians. Their value for a new philosophy unfolded only gradually.

Social Status of Medical Practitioners. In Japan mathematical astronomers were minor bureaucrats, responsible for preparing the national ephemerides. Although they were the earliest to recognize superior aspects of Western science, they overlooked its basic paradigms and remained within the traditional mold. Their academic style, as we have seen, tended to be greatly shaped by their proximity to sources of power.

Medical practitioners, who first took up the challenge of the Western sciences, constituted the largest scientific profession during the Tokugawa period. Medicine, unlike astronomy, was a private concern and thus free of one kind of constraint upon the response to new ideas. Because there was no public health program at the time, medical practice was essentially a relationship with individual patients. There usually was a private physician in each community. The samurai class had its government doctors and fief doctors, and townsmen and peasants had their local practitioners; but the profession was not tied together or controlled by the central government. Although Edo, as the seat of the shogunate, was a center of professional activity, the important schools of medicine were scattered as far as Nagasaki. This decentralization made medicine one of the few geographically mobile professions in Japan.

Toward the close of the Tokugawa period, in the first half of the nineteenth century, it became conventional for medical students to visit the various centers of instruction and to be initiated into the different schools of clinical medicine. Moreover, practitioners who distinguished themselves often were called to serve the fief governments or the shogunate. Although their stipends were small, the prestige they gained raised their fees in subsequent private practice. The competitive market for medical practices in Japan was most untypical of the society as a whole. Western-style physicians took advantage of it as they moved into spheres of health care that previously had been monopolized by traditional practitioners. There is a loose analogy between this situation and that of the nineteenth-century German academic market described by Joseph Ben-David.²⁹ In Japan, fürthermore. there was no guild organization of physicians to limit or control competition.

Unlike the medical profession in Europe, which was well integrated into society and could reproduce itself in the universities, Japanese doctors were socially marginal. Their mobility was anomalous in a society where status was supposed to be hereditary and where the only elite was supposed to be the hereditary warrior class, the samurai.

The Taki family, hereditary physicians to the shogunate, once tried to centralize medical standards by founding an official medical school that all sons of doctors were to attend and at which they were to be examined for a license to practice medicine. This attempt failed, in contrast with the ease with which central authority was established in other fields. The main impediment to uncontrolled competition in medicine was not guild or government organization but the hereditary system on which the Tokugawa social order was based.

The samurai, the military elite, inherited ranks and stipends that depended upon the contributions of their ancestors to the foundation of the Tokugawa shogunate in the early seventeenth century. Merchants, artisans, and others did not depend upon fixed stipends as the samurai did, but their social class was fixed through inheritance. This system could not easily find a place for intellectual professions, which could flourish only in situations where advancement was based on talent rather than birth. In the Tokugawa period there were three such professions: Confucian philosopher, medical doctor, and mathematical astronomer. In all of them people of outstanding ability often remained subordinate to incompetent samurai and, if they worked for the government, received lower stipends.

Attempts were continually made to subordinate these professions on the hereditary principle. It was expected, for instance, that the son of a doctor would eventually be registered as a doctor, regardless of how little intelligence or motivation he might have. At the same time, the shogunate and the fief governments needed talented professionals. The conflict often was resolved by the governmental authorities, who would advise a professional family to adopt a gifted youngster.

Government employment was only one possible source of income for a physician. Osaka, for instance, was famous for a medical center patronized mainly by merchants. The clinical experience of the therapist mattered a great deal more than his formal education. The son of a village doctor would begin by working with his father, then spend many years as an apprentice to more distinguished doctors, and finally return to his native village to take over his father’s practice. From generation to generation the number of patients would gradually increase until such a medical family was expected to provide doctors for the whole village. Because such hereditary traditions were quite independent of the government hierarchy, doctors were among those most responsive to liberal thought in the period shortly before the modernization of Japan. Mathematical astronomers were not independent in the same way.

Although Confucian scholars formed a professional group, they lacked the social mobility and economic security of physicians. Their official social status was a good deal higher, but the revenue that they might earn by private teaching could not compare with the fees of the doctors. In essays of the Tokugawa period the social commitments of the two often were compared, to the detriment of physicians, Confucian scholars were concerned with society as a whole, and physicians only with individuals; Confucian scholars dealt with the mind, and physicians only with the body; Confucian scholars were generally poor, while physicians gouged fees and lived in luxury. It is clear from such remarks that establishment values favored the scholars, and found the practical skills of the doctor a little too close to those of the artisan.

This difference should not be overstressed, since Chinese-style medicine emphasized that practice must be based upon Confucian ethics. Young men who chafed under this devaluation of medicine as a pursuit in its own right were especially attracted to Western medicine, which seemed free of philosophic and moral constraints.

Those attracted to intellectual pursuits found them most attainable if they left clinical medicine and became teachers or public figures. Western-style medical doctors gradually distinguished themselves into two groups, one that concentrated upon medical practice and one that mainly taught foreign languages and Western science. In the difficult international situation following the Opium War (1839-1842), it was from medical schools of the latter group, such as that of Ogata Koan, that there appeared political activists such as Hashimoto Sanai who renounced their inherited professions to pursue political careers.

Of the three intellectual professions in the Tokugawa period, only physicians were able to achieve an independent stance from which to view the world in a new light. It was naturally they who brought modern universal science to Japan. But their independence was bought at the cost of alienation from the true sources of power in Japan.

The Science of the Physician und the Science of the Samurai. The pattern of response to Western science changed fundamentally when Japan was opened to the free flow of foreign ideas in the 1860’s. The initiative passed from the physicians to the samurai. Among graduates in the class of 1890 at Tokyo University, the percentage of those who came from samurai families were as follows:³⁰

Why was the proportion of students from the elite class so high in science and engineering, and so much lower in medicine and agriculture? As we have seen, it was customary for the sons of doctors to become doctors. They did not belong to the samurai class, unless they were employed by the government. Similarly, many agriculture students were the sons of wealthy farmers. The downfall of the samurai regime (which made the foundation of the European-style university possible) had little effect on the livelihoods of either doctors or farmers.

On the other hand, that transformation was catastrophic for the hereditary military elite, whose traditional occupations in the bureaucracy of the old regime, as well as their hereditary stipends, were lost. The fields of medicine and agriculture were largely occupied. The law was not considered a dignified occupation; and until the Civil Service Examination Act of 1890, the law schools did not provide a route to upper-level civil service careers.

The only promising professions left for the samurai were science and engineering. In nineteenth-century Europe, the upper class tended to occupy the legal and medical professions, and science and engineering were largely shaped by the rising middle class. In Meiji Japan, on the contrary, scientists and engineers were drawn largely from the top 5 percent of the population.

In the wealthier European countries the scientific and engineering professions drew on the ideology of the middle class rather than on that of the old aristocracies, whereas in Meiji Japan they were entirely subservient to the social and international aims of the imperial government. Scientists were indispensable to the policy of modernizing and Westernizing, and engineers played key roles in building the physical structure of a modern state. Much of the increased demand for engineers was for survey work and telegraph network construction. From the time these professions began to form on the Western model, those who entered them were government officials. The descendants of samurai, who valued public over private occupations, were thus attracted to engineering. The result was a group of public-spirited engineering professionals oriented toward civil service, in contrast with English engineers in Britain, for example, who came mostly from the class of skilled mechanical people and served private interests.

Before the Meiji period. Western-style physicians took up the physical sciences as intellectual pursuits; those who continued to study them did so largely out of an interest in natural philosophy. Although they legitimized their study, in the Meiji period the formation of scientific and engineering professions became the concern of the samurai and the doctors largely returned to their family practices. Samurai entered science and technology because of their contributions to the state. Their response was not so much intellectual as institutional.

Mathematics.

The Royal Society and Tokugawa Mathematicians. Many would consider the appearance in 1660 of such a disinterested group as the Royal Society of London to be quite unthinkable outside the sphere of Western civilization, but Japanese mathematicians of the Tokugawa period (urasanka ka) were similar in many ways. Members of the Royal Society secured a charter from the king for reasons of prestige and frequently studied subjects of no economic importance. Leisured gentlemen constituted the entire membership and dues financed most of the activities. Similarly, groups of mathematicians in Japan were purely private in nature, consisting of samurai, rich merchants, and affluent peasants; they gathered solely for leisure activities.³¹

In its early period the Royal Society tried to realize certain Baconian ideals, but the activities of the amateurs declined in prominence after the first generation³² Learned societies in the British provinces also tended to become philosophical societies after the model of the Royal Society. That is, salaried officials–journal editors, directors of libraries and museums–became central in both while the socially more prominent members were relegated to support functions and retreated from front-line research.³³ In Japan, however, interest in wasan activities grew over time, spread outside urban centers, and expanded until the nineteenth century. Participants were increasingly recruited from lower strata of society. Because mathematical activities lacked a significant occupational base, distinctions between professionals and amateurs did not arise. Mathematics was enjoyed by leisured groups in the same way as waka, haiku, or the lea ceremony. In fact, modern historians of Japanese mathematics have commonly observed that wasan was more of an art form than a field of scholarly inquiry³⁴ Here, however, I should like to raise the question of how art and scholarship differ from each other and to consider wasan in that context.

Scholarship and Art. While wasan may be considered an art from, it is by no means easy to distinguish art forms (gei) from scholarship (gaku). Activities that individuals consider scholarly in nature are not necessarily so regarded by society; such evaluations depend on the views of certain social groups in specific locations during a particular period. They may also depend on the value standards of intellectuals and be subject to influence by the presence or absence of official authorization as well as by popular impressions.

I shall not attempt conceptually rigorous definitions of scholarship and art here, but merely note that scholarship is usually thought to have some public function, while art forms are often regarded as private indulgences that may or may not have significant social value. This distinction was consciously employed by many writers during the Tokugawa period. For example. Seki Takakazu (Seki Kowa), often called the sansei or “sacred mathematician” for creating the dominant wasan paradigm, wrote on a student’s diploma in 1704, as a way of conferring legitimacy on his field: “Mathematics, after all, is more than an art from.^”35 He thus refused to define mathematics as an art and tried, instead, to establish it as a dignified, prestigious form of scholarship. He even referred to mathematicians as “scholars.^”36 Among themselves mathematicians acted as if they were pursuing an art form, but in the presence of non mathematicians they tried to present their work in such a way as to give it prestige. Some kind of legitimation was necessary for mathematicians to succeed in this effort. While a leisure activity does not require public legitimation, scholarship does; and there had to be some basis on which to differentiate the one from the other. The evidence of this concern for social legitimation is best seen in Seki’s introductions,

Introductions to mathematical treatises usually did not reflect the authors’ personal views, since they were written by Confucian scholars according to a fixed, decorative formula in order to partake of the prestige of Confucianism. Confucian scholars were asked to insert hackneyed phrases into mathematical texts even when they confessed ignorance of the subject. One of these phrases declared that mathematics had been mentioned in the Chou Li as one of the six classical arts. Another alluded to its association with divination and numerology (esoteric doctrines about the nature of the universe). Mathematicians who wrote the introductions themselves said the same things in other words. These introductions, however, had no connection whatever with the highly technical matters discussed in the main text and were essentially empty, formalistic passages.

The basis for the contention that contemporary people should respect mathematics was its high status in antiquity, stemming from Confucius’ esteem for it, and from its designation by the sages as one of the six classical arts. This Confucian form of legitimation derived from the conceptions of classical scholars. Tokugawa mathematicians, however, generally were socially marginal curiosity-seekers and thus did not care whether mathematics had been one of the six classical arts. During the more than 2,000 years since the time of Confucius, Confucianism had become securely established; but astrology, mathematical astronomy, medicine, and arithmetic had come to be considered lesser crafts and were consigned to a peripheral, low status in the hierarchy of disciplines. Arithmetic, which was associated with such mundane matters as surveying and tax collecting, was assigned a status well below that of astrology and even further below that of mathematical astronomy, which described the principles governing the heavens and earth. Even so, unlike chemistry or other sciences, arithmetic had a guaranteed position in the Chinese bureaucratic system: and in Japan’s prefeudal period there were doctors of mathematics and official arithmeticians.

During the Tokugawa period, however, mathematics was not formally recognized in the governmental structure. Astronomy had its hereditary doctors in the Tsuchimikado family of Kyoto; the more competent astronomers in the shogun’s government were officially, if nominally, subordinate to them. The Tokugawa mathematical tradition, however, existed entirely in the private sector and had no link to the prefeudal tradition of the mathematical doctors. In fact, Tokugawa mathematicians had no interest in the tradition of court mathematics.³⁷ From the introductions to their writings one perceives instead a recognition of Seki Kowa as forebear or perhaps of Mori Shigeyoshi or Yoshida Koyu. Historical awareness of founding fathers, in other words, did not antedate the Tokugawa period. Consequently, Japanese mathematicians, unlike the school of such Ch’ing mathematicians as Mei Wen-ting, did not try to use the ancient designation that made arithmetic one of the six classical arts as a basis for defining their own identity.

Belief of the Pythagorean type that numbers permeate all objects in space, or constitute the basic principle of the cosmos, was certainly part of the Chinese mathematical tradition; it was specifically the creed of Chinese diviners and specialists in yin-yang cosmology. Even Kawakita Chorin, a mathematician at the end of the Tokugawa period, wrote: “Numbers constitute the elements of the heavens, the earth and all of nature. Everything that happens is a result of their presence.³⁸ This kind of belief was often used to justify the activities of mathematicians; but such an argument was more commonly espoused by cosmologists, astronomers, and specialists in calendrical science than by mathematicians themselves. An attempt like the Pythagorean to explain the cosmos by numerical cycles and the cyclical world view as such existed in the Chinesse tradition into the second century a.d.: but as astronomical observation became more precise, cycles came to be described algebraically in more complicated ways, and this cosmological view collapsed.³⁹ Experts in calendrical science in the T’and ear (seventh through ninth centuries) who became specialists in exact, empirical science did not consider expatiating on the cosmos to be a legitimate part of their work and they rejected cosmologizing, altogether.⁴⁰ In the eleventh and twelfth centuries, cosmology once again became a subject of discussion among Confucian scholars; but the calendar makers were inclined to think that Chu Hsi “talked nonsense because he did not understand mathematics” and generally refused to consider the problem.

During the earlier period Japanese mathematicians, especially their founding father, Seki Kowa, frequently studied problems in calendrical science. Seki’s investigations, however, were confined to the technical aspects of the Shou-shih calendar. As scientific mathematical activity of a kind that might be called “normal science” continued, the classical Pythagorean view of nature as based on mathematical principles disappeared from the problematique of Seki’s followers. This was at a time when the essayist Nishimura Tosato was claiming that suzgaku (the scholarly study of numbers) was an important subject while san (arithmtic) was a minor practical art.⁴¹ Propounding a mathematical view of nature, he designated sugaku as a learned discipline that “investigates basic principles, constitutes a major element of divination,and was expounded by the Sages.” Nishmura also criticized the activities of the wasan mathematicians as “arithmetic done by people of little consequence.” This mathematical view of nature had to conform to the Confucian values of a Confucian society. Consequently, mathematical studies were not considered scholarly unless they made a contribution to “self-cultivation, husbandry and the pacification of society.” They were devalued if the practitioner admitted a “desire to investigate mathematical principles merely for amusement.^”42

It is said that mathematicians such as Wada Yasushi made a living by practicing divination during the Tokugawa period, but this report may be based on a popular misconception deriving from the fact that diviners and mathematicians both used sangi (computing rods). In fact, mathematical calculations and divination based on calculating rods were entirely different.

Mathematics during the prefeudal period was completely practical and thus was at least socially legitimate. Even in the Tokugawa period appeals to practicality appear in introductions to mathematical works designed for such purposes as surveying, and these appeals apparently were accepted al face value. Practical mathematics, however. did not interest most mathematicians. wasan lost even its practical character and became explicitly nonutilitarian, a situation that readily allowed Nishimura Tosato to dismiss it as simply an art form.

Let us compare this experience with that of the West. According to Alexander Koyré Platonism had an important influence on early modern science because of its program for the mathematicizing of nature.⁴³ Although Platonism dominated intellectual discourse during the Renaissance, its indispensability for the Galilean school may well be doubted. A close reading of Plato’s Timaeus shows that it had almost nothing in common with Koyre’s notion of Platonism.⁴⁴ Galileo did, however, use popular Platonist ideas to legitimize his mathematical methods, an effort that had precisely the social effect intended. Thus Galileo presented Plato as the defender of geometry against the Aristotelians, who emphasized logic: and thus Platonism had an important role justifying the inclusion of mathematics in school curricula, and eventually in the emergence of modern science.

Unfortunately, Japanese mathematicians had no charismatic figure to invoke in opposing the Confucian tradition. If Mo-tzu had not been forgotten for two millenia, this might been possible: but Mo-tzu and the yin-yang natural philosophers had almost totally disappeared from intellectual discourse in Tokugawa Japan. The mathematicians would have needed something in their own tradition approximating Galileo’s Platonism to have become full members of intellectual society. No reiteration of references to divination or the six classical arts in the introductions to their books could have raised their status significantly.

Social Position of Tokugawa Mathematicians. Whenever scholars demand legitimacy from society, they display a sense of mission that reinforces their commitment. This sense of mission is associated with the rise of professions that in Western society are intellectually based associations not explicitly connected with worldly gain. Theology, law, and medicine were recognized as professions in medieval universities. In the early modern period. scientific researchers and technicians were also recognized as professional men. The largest profession in Tokugawa Japan was probably the class of Confucian scholars. One might also consider physicians, astronomers, and specialists in calendar making as professionals. But whether the mathematicians could be called professional is a difficult question.

A sense of mission includes a desire to achieve a lofty objective beyond immediate personal interest. Scholarship or science for their own sakes seemingly represent an early modern form of “consciousness that developed after the emergence of scholarly elitism, especially that of the universities. Before this modern attitude became established, a scholarly discipline could form only when learning proved to be useful to the sacred or secular establishment that monopolized universes of meaning.

But as society became more complicated, intellectual groups managed to secure autonomy as third parties between various powerful agencies and were expected to ignore matters of direct economic interest. Since the Middle Ages, universities have proclaimed their independence as professional bodies, mean while maneuvering between religious and secular authorities. Even in Tokugawa Japan, with its very strict regulations, officially sponsored Confucian schools, and even heterodox Confucian schools were generally recognized as authentic disciplines by the establishment. Nor was there any problem with medicine, even for doctors in the private sector, because practical utility assured recognition. Fields of knowledge related to commercial production or manufacturing were invariably supported on their own terms. It was difficult, however, to discover in either Confucianism or in Baconian pragmatism any grounds on which to legitimate the activities of the wasan mathematicians.

The popular image of mathematics was that of the abacus. The social position of mathematicians was probably based on demand for their services in teaching people how to use this device. But daily use of the abacus did not require anything like the elaborate technique of the mathematicians. In merchant families, abacus manipulation was considered a form of spare-time study. Apprentices were introduced to it by the head of the business. There was a saying to the effect that “While use of the abacus in one of the most important things a merchant must learn, he should not take it too seriously. Excessive study will hurt business.^”45 Studying more advanced mathematics than was required in business generally was forbidden, being considered a form of dissipation. Some mathematicians managed to make a living by opening schools. The majority of such schools were run by masterless samurai. I lie mathematical braining they gave usually stopped with simple arithmetic and the calculation of interest rates. Thus, according to Professor Oya Shin’ichi. the enri calculus, which included the most sophisticated problems studied by the mathematicians, was not generally taught in these schools.

From the government’s point of view, mathematics was closely associated with simple calculation and land surveying. But in the Ryochi shinan (“Introduction to Surveying”) one finds such statements as” People who study mensuration say that not all mathematics is intended to be used by surveyors. According to them, there is nothing about mathematicians’ theories that is contradictory to mensuration;), but if you look at their work, it seems too much involved in mathematical theory and divorced from practice. And in general mathematicians’ talk about surveying is all of this sort.⁴⁶ Or “Mathematicians’ techniques are a distraction, with no utility whatever”.⁴⁷ The traditions of the academic mathematician and of the practical surveyor were quite distinct. Because of an attack on the Sampo jikata taisei (“Manual of Practical Mathematics,” 1837),written by Akita Giichi and edited by Hasegawa Kan’ei (both mathematicians of the Seki school), surveyors subject to feudal authority were reluctant lo publish significant mathematical works for fear of their lords’ reactions. Even Seki Kowa, founder of the wasan mathematical tradition, was warned about this. He disregarded the admonition, however, and later wrote a text describing approximate or simple methods for solving problems in the style of Yoshida Koyu’s Jinkoki. Seki’s disciples, however, considered that text a disgrace to their school.

Astronomy offered mathematicians far more sophisticated problems than did surveying. Examples from traditional Chinese astronomy include indeterminate procedures for calculating multiple conjunctions, the problem in spherical trigonometry of transforming equatorial coordinates into ecliptic coordinates into eliptic, and interpolation procedures for handling the equation of the center. The trigonometry and algebra that came to Japan with the Jesuits’ later transmission of European astronomy may have opened up new mathematical vistas. There also were problems in navigational astronomy that the mathematicians Honda Toshkaki and Sakabe Hironao investigated. These topics were, however, considered astronomical problems and, as such, were separated from the mainstream of mathematical activity.

In the han schools, which were for the training of the sons of samurai, mathematics apparently became part of the curriculum about the 1780’s.⁴⁸ Textbooks published by various domains seem to have included problems an applied mathematics taken from surveying, calendrical science, and navigational astronomy. Some mathematicians served as Bakufu astronomers, and others worked as accountants or surveyors in the domains. They saw their public duties as separate from their research in mathematics, however, considering the latter a private activity. They apparently honored this distinction to the point of not publicizing their research. Astronomers and astrologers employed by the domains all used the algorithms of wasan mathematicians when they calculated but, aside from the writings of Nishimura Tosato, one finds no significant public comment on the wasan tradition in works by astronomical specialists. This may have been due to their bureaucratic consciousness. They gave no thought to the work of mathematicians. who belonged to the private sector. The result was that mathematics had no real place either in the government or in private life.

Nor did mathematical research have any base in the occupational system. Mathematicians’ researches were separate from their occupations – which ran the gamut from warrior to farmer, artisan, or merchant.⁵⁰ The orthodox Seki school was typical in this respect.

In general, the mathematicians1 greatest achievements appeared in their early years, although Mikami Yoshio’s research showed that the wasan mathematicians were most active in their later lives.⁵¹ According to him, this was due to the shallowness of the roots of wasan mathematics in the educational system, the inadequacy of the available textbooks, and the extraordinary amount of time required to become proficient. All of these factors surely had an important impact, but an even more influential factor may have been that the time and money required to indulge in such a leisurely activity came only in later life. Anyone who gave up his regular occupation for mathematics encountered financial problems, including difficulties in paying publication costs. In particular, samurai employed in the government had scruples about participating in such activities and, for the most part, published mathematical works only after retirement.

Unlike astronomers or physicians, mathematicians did not have to deal with occupational inheritance. Because of the special ability required to produce original achievements in mathematics, the occupation could not be passed on –indeed, in the economic sense it was not worth passing on. Mathematics thus did not establish itself as a specialty of certain families. The status of wasan teacher had no economic implications (such as guild protection), despite the licensing system established by Seki Kowa. Nor, in consequence, was there any basis for giving academic autonomy to mathematics, such as the modern university has provided in the West.

The prestige of any field of scholarship is bound up with the social status of those engaged in it. From that point of view, there is little reason to think that mathematicians were particularly respected by society in general. In China, Chu Shihchieh and Ch’eng Ta-wei, authors, respectively, of the Suan-hsüeh ch’i-meng and the Suan-fa t’ungtsung, from which wasan mathematics derived, were itinerant teachers. In Japan there also were mathematicians who traveled from place to place and were supported by wealthy patrons.⁵² In point of livelihood, these intellectual salesmen were no different from traveling artists.

The gentlemen members of the Royal Society were not professionals in the sense of earning their livings by research but, rather, in the sense that royal patronage gave them a degree of institutional independence. In a formative period in either scholarship or the arts, when institutional protection is lacking, a leader will assemble a supporting constituency and create an occupational base for his activity. When scholarship becomes systematized, institutionalization and professionalization occur simultaneously. The Royal Society, which was officially recognized yet lacked an occupational base, was exceptional; but its recognition made its dignity and status as a scholarly organization secure. wasan mathematicians had no such recognition. There was no system for training or recruitment. The occupational base consisted solely of the inadequate patronage of a few wealthy individuals. As a result, there was no agency to press the claims of mathematics upon society. Because their organizations lacked status, wasan mathematicians could not defend the scholarly aspects of their work effectively. They received little or no social recognition. Nevertheless, in certain respects, they were more active than the Royal Society.

The artistic character of wasan mathematics helps to explain this fact. In publishers’ catalogs of the Tokugawa period, books on wasan were classified with materials on the tea ceremony and on flower arranging, which suggests that wasan was mainly viewed as a popular art. Art, however, involves the pursuit of aesthetic pleasure, while purely intellectual matters are regarded as scholarly. During the Tokugawa period there were several pursuits that were not scholarly occupations and had no academic prestige–for example, Japanese chess (go and shogi). It was probably the aesthetic and playful aspect of mathematics which provided scope for the development of wasan and its diffusion down to the commoners.

In his book Les jeux el les hommes (published in English as Man, Play, and Games), Roger Cailloit defines recreation as activity that is free, isolated, indeterminate, unproductive, rule-bound, and unrealistic, The activities of wasan patrons fit these six conditions perfectly.

Internal Logic of wasan Development. What distinguished wasan from poetry, haiku, and the arts in general? In what sense was it a scholarly rather than an artistic form? While it would not be quite accurate to say that the methodology of was-an was that of a modern scientific discipline, it definitely did come closer than any other field of inquiry existing during the Tokugawa period. It had, for example, a way of asking questions that was very similar to that of modern science. Thomas Kuhn states that all scientific traditions begin with a paradigm or model for raising and answering questions in terms of which scientific progress will necessarily occur.⁵³wasan conformed to this pattern rather well. It did not command a very extensive body of knowlege, but it stated its problems and questions in a precise way. Among the disciplines of the Tokugawa period, wasan and mathematical astronomy were methodologically closer to modern exact sciences than were the schools of moral philosophy or of clinical medicine. Since the questions raised in wasan were not limited by traditional structures (save those it evolved itself), it was free to move off in new directions,

In its formative period wasan mathematics developed the unique custom of idai (bequeathed problems), A mathematician would pose scores of problems of several kinds at the end of a book. Another mathematician would publish answers to these problems and present his own in the same manner. According to convention a third mathematician might propose answers to the second set of problems and issue his own. in relay fashion. This interest in mathematical puzzles greatly stimulated the formation of wasan groups. They were influenced by Chinese experience, but there does not appear to have been anything like the custom of posing idai in China. The tradition began with twelve problems from the Shimpen jinkoki (1641). A succession of mathematical lineages soon developed and reached a peak during the lifetime of Seki Kowa. Certain themes continued to appear in these problems, which passed through a number of phases. Practically all of the important problems in the history of wasan date from the period of these idea⁵⁴

Mathematics has a strong puzzle-solving character. Problems need not be constrained by physical or social reality. Mathematicians can freely create new intellectual worlds which may violate the logical forms of daily language.

During the early period there were two types of idai problems used in daily computation and those relating to geometry. In the Chinese mathematical tradition that influenced wasan, practical problems were more common, but later more whimsical problems were added. The Jinkoki, which defined the popular image of wasan, also emphasized practical problems. As idai passed through many generations, a trend toward purely intellectual or recreational problems developed among the heirs to the tradition, enthusiastic puzzle-solvers uninhibited by utilitarian constraints. The puzzlelike character of wasan mathematics made this development entirely predictable. Given the sense of problematique, practitioners were not inclined to select problems with practical applications. Moreover, other factors reinforced the trend. Once a problem had been abstracted in the form of a diagram, people did not concern themselves with its utility and could enlarge or develop it freely. The purer the mathematical character of a problem and the greater its detachment from practicality, the greater was the enthusiasm with which it was received. We shall consider below a typical example, the yojutsu, which involved fitting various large and small circles into a triangle.

It also seems significant that the impracticality of wasan precluded links to mechanics or optics like those of mathematics in Western science. The seventeenth-century idai were probably responsible for the leisure-oriented character of wasan.⁵⁵

Commerce, surveying, and calendar making represented practical applications of mathematics. The first two. however, did not offer very sophisticated problems. The degree of precision required in their calculations was much less than that demanded in the theory of errors or in higher-degree equations. Calendar making, of course, was an exact science; but the major problems presented by the Shou-shih calendar had already been solved by such eminent mathematicians as Seki Kowa and Takebe Katahiro, In theory, the planetary motions should have generated problems fully as interesting as the theory of epicycles in Western astronomy. The Japanese art did not emphasize planetary movements, so they were not investigated very thoroughly. Ultimately the absence of kinematic and dynamic problems in Japan’s scientific tradition handicapped and retarded wasan’s approach to analysis and proved decisive in its race with the Western tradition,

When idai were popular, from about 1650 to the early eighteenth century, the natural sciences did not develop to any extent. Science from the West had not yet been imported. It was during this period and from these idai that wasan mathematics created and established its significant problems, although in certain respects prematurely. The topics investigated were taken from such concrete problems as the volume of a rice bag or measuring cup. They were often focused on diagrams of circles or cones that had to be solved for a numerical value. As this trend progressed, the enthusiasts of pure mathematics gave little thought to the relationship between observation and its practical meaning: they simply invented fictitious problems whenever they wished. Once they discovered a strategic or paradigmatic problem, practical problems of astronomy. trigonometry, or Western logarithms were no longer considered legitimate. The eccentric genius Kurushima Yoshihiro wrote: “In mathematics it is more difficult to raise a problem than to give the answer. Only mathematicians who cannot invent problems borrow them from calendrical science.^”56 In short, the idea that looking for subject matter in society or nature was undesirable had already developed by the eighteenth century. when the notion of mathematics for its own sake emerged.

In the practical problems of applied mathematics, it is important to obtain an answer stated as a numerical value. Given the determination of topics in this field by social or natural conditions, it is entirely appropriate that obtaining numerical solutions should be considered more important than inventing problems. On the other hand, the asking of questions is essentially unlimited in pure mathematics. as Kurushima implied, and is necessarily considered supremely important. As with crossword puzzles, inventing the question is more difficult than supplying the answer. That one person paves the way by inventing a problem, while many others follow in trying to solve it, is part of the normal science tradition and further underscores the process by which normal science is conducted.

This was not. however, the way in which idai were developed and passed on in the early period (before Seki Kowa’s time). The form of the problems at that time was not fixed: and when people invented problems, they did not simply adhere to those devised by predecessors. During that time there was a shift from practical to pure mathematical problems. Numerical solutions converged toward diagrammatic problems using the tengen algebra (based on the use of computing rods). wasan did not yet have a characteristic type of problem.

As time passed, the problems became more intricate and multifaceted. Inventors did not simply present problems that they themselves had already solved, since other mathematicians considered that too simple –even foolish. There was an emphasis on solving problems by some unusual means or in presenting problems for which it was not known whether a satisfactory solution existed. People would lake up a mathematical challenge and expend considerable energy trying to solve it. The way in which idai were presented gave an enormous stimulus to the competitive spirit of later mathematicians. Difficult problems constituted an enduring challenge. There have been, of course. similar examples in the history of Western mathematics–for instance, the unsolved problem of trisecting an angle, which has continued to engage the interest of mathematicians.

As problems became more complex, however, impossible problems appeared, and mathematicians began expending excessive energy to little effect. In the Sampo kokon tsuran the following comment appears: “The shallowness of present technique and reasoning, together with the enormously complicated effort expended, lead one to think that the really interesting problems have all been exhausted.” Such problems could not constitute paradigms, could not lay the groundwork for normal science, and could do nothing but create confusion. Indeed, the confusion suggests that Japanese mathematics was at a preparadigm stage. Consequently, what brought Seki Kowa his enormous reputation was his creation of the basic paradigm for posing and answering questions in an intellectual setting where almost total confusion had prevailed earlier.

After the importation of the tengen technique, changes occurred in the way questions were posed through the idai. In the earlier period, idai were highly diverse and multifaceted; now they emphasized higher-degree equations solved through the use of the computing rods. The confusion of the period was compounded by the popularity of idai deliberately designed to solve increasingly complicated problems by transforming systems of simultaneous equations into a single equation of increasingly higher degree. These problems were known as handai (troublesome problems). The tendency may have been an aberration, but it prompted Seki Kowa to introduce an important innovation –the tenzem algebra, a system for expressing unknowns in symbols similar to A, B, C. in order to use simultaneous equations freely⁵⁷

Seki also developed a theory of equations based on the existence of negative and imaginary roots, which he treated in his Daijutsu bengi (“Discussion of Problem Specification”) and Byodai meichi (“Clarification of Impossible Problems”).⁵⁸From China’s pragmatic mathematical tradition wasan had inherited the idea that an equation can have only one root.⁵⁹ Seki. however, introduced discussion of negative and imaginary roots, and tried to interpret their meaning. Taking an approach characteristic of wasan, he transformed and “corrected” such problems to provide real positive solutions, rejecting the implications of the original problem setting. Thus his theory of equations ruled out further development toward imaginary and complex number theory in wasan.⁶⁰

Seki’s writings on the theory of equations perpetuated wasan s orthodox way of asking questions. These writings were included in a seven-volume work transmitted esoterically by the Seki school. They were studied and passed on by pupils who were eminent enough to devise new problems themselves. Since Seki had previously laid down guidelines for solutions in the tenzan algebra, one may say that he fully paved the way for wasan’s later development.

Seki Kowa was not the only outstanding mathematician of the period. He certainly had the intuition of a genius: but if he had been an isolated figure too far ahead of his lime, the paradigm he laid down would not have paved the way for normal science and there would have been no Seki school. During Seki’s lifetime his school was extended by such eminent disciples as Takebe Katahiro and Matsunaga Ryohitsu. Seki was placed on a pedestal within the tradition. One may suppose that the special treatment accorded him was instrumental in establishing the diploma system. In the introductions to wasan books, the origin of the discipline is always attributed to Seki, not only in his own school but also in the Saijo school of Aida Yasuaki. Certainly the tendency of the wasan mathematicians to revere Seki limited their field of vision, yet it would seem from comparing such works as the Suan hsüeh ch’ing and the T’ien-wen ta-ch’ang kaan-k’uei chi-yao with his own that Seki himself was more influenced and informed by Chinese writings than his later disciples ever imagined. Everything in the wasan tradition was. however. referred back to Seki, and the original Chinese mathematical works were ignored⁶¹ This was very different from the attitudes of Chinese mathematicians at the ch’ing period, who turned their attention toward ancient Chinese mathematics as they mastered the Jesuits’ astronomy.

Seki Kowa left answers to a large number of idai during the period of their greatest popularity. In fact, the theory of equations seems to have been born from the many different kinds of idai that he considered. There is no indication, however, that Seki himself left behind any idai and after his time the practice of issuing them declined considerably. Their frequent appearance corresponded to a pre-paradigm stage in the delineation of mathematical problems. idai were scrutinized and restated according to the principles of equation theory, and the significant ones were passed on. The paradigm emerged when the techniques for solving these problems by means of tenzan algebra were given; and at that point a way of asking and answering mathematical questions emerged that was quite different from what had existed in the preparadigm period. Creation of the paradigm was not the achievement of Seki Kowa alone: but circumstances led to his being given credit for it and he was, in fact, at the center of the wasan tradition. Since the procedures for raising and answering questions were fixed, it was meaningless to set forth a large number of idai With the issues about structure clarified, subsequent mathematicians readily resolved particular problems, Enri (circle theory) calculus was one of the areas that attracted attention. This technique developed from mensuration of the circle and led to the development of linear progressions and analysis. It probably began with either Seki or his leading disciple, Takebe Katahiro.⁶² In any event, its inclination to the analytical approach of Ajima Naonobu is apparent. Enri calculus was applied not only to problems involving the circle, but also to curves and curved surfaces in general. Wada Yasushi helped to develop mathematical analysis by compiling tables of definite integrals and applying them to the mathematically infinite and infinitesimal. The Takuma school of Osaka developed a calculus that in some respects was superior to that of the Seki school.

Mathematical problems are not limited to those posed in nature or by society. But a pattern of development in mathematics will change according to the kinds of problems taken up; different choices of problems may create different mathematical worlds. The enri calculus, which developed from problems concerning the arc, an important topic in astronomy, coincided in its results with the Western-style calculus. The course it followed, however, was completely different from that of Western mathematics, which began with problems in dynamics. We should say, on the other hand, that dynamical problems offered mathematics greater scope for development than those concerned with arcs and circles, simply because the element of time was involved. There were greater limits to the problem development possible in enri.

Another stimulus to the development of wasan was the ema sangaku (pictured mathematical tablet) form that came after the idai tradition. On these wooden plaques were written both problems and answers; they were offered at shrines and displayed there. The best mathematicians made their accomplishments known through books, but it was largely the custom of sangaku that supported the activities of the wasan enthusiasts. That wasan was a hobby costing money to pursue is best shown by the elegant diagrams that embellished such work. In fact, the offering of sangaku had a strong attraction for local gentlemen over other art forms –drama, music, poetry –as a way of making their work known; and their frequent indulgence in it shows a desire to keep themselves more or less before the public at all limes.

The most important kind of problem taken up in sangaku was called vojutsu (packing problems), which involved the attempt to inscribe the largest possible number of small circles in a larger circle. sangaku also treated problems involving solar eclipse predictions in the Shou-shih calendar; but table of eclipses, with their arrangements of letters and numbers, could not attract attention even if displayed as framed pictures. Popular interest was limited to vojutsu decorated with designs of circles and squares. The pictures were intended, as far as possible, to produce the impression that the designer had obtained the solution to a difficult problem through a complex diagram. Thus, while yojutsu seemed to concern itself with very difficult problems, its emergence was not very significant mathematically.

In the early development of yojutsu. there was a tendency for different techniques to compete on the same problem. Later, however, the method of solving them became fixed. There was a tendency to devise new problems to which the standard technique could be applied. Problems became increasingly complicated while the technique scarcely developed.

Enri calculus and yojutsu both developed as normal sciences but in somewhat different ways. The enri calculus developed step by step: when one problem was solved, its result was used to solve a problem requiring deeper investigation; and in the process there appeared what migth be called subparadigms. In principle yojutsu was also a problem-solving technique, but its pattern of development amounted to merely a series of transformations and variations. Moreover, its technique was not based on a demonstrational logic in the Euclidean style, and did not aspire to general principles of problem solving. During its 200–year history, yojutsu yielded several useful by-products, but its reliance on casual inspiration ranks it well below enri calculus in scholarly value.⁶³ One could have referred to yojutsu as a Japanese form of geometry only if it had gone beyond mere puzzle solving and had achieved a general methodology. In fact, it did not move very far toward analytical geometry. Because it was purely a puzzle-solving technique, it did become an acceptable recreation for amateurs, who were inclined to consider logical rigor in bad taste.

wasan mathematicians apparently did not fully realize the importance of logical foundations: rather they valued insignificant, complicated, and overly elaborate problems.⁶⁴ When Euclid’s Elements first appeared in Japan, people said the simplistic, poorly developed, and inferior character of European mathematics compared with wasan could be determined just from looking at its pictures–a reaction suggesting that wasan was not the kind of discipline to raise basic questions. One might even call it an art form that had as its major goal the refining of trivialities. On rare occasions someone like Takebe Katahiro, who respected precision, would come along; but because the wasan mathematicians did not generally raise basic questions, they made no revolutionary breakthroughs and confined themselves to refinements and improvements on the paradigm set forth in Seki Takakazu’s time.

Mathematics, especially a pure form like wasan, differs from the natural and social sciences in the absence of checks imposed on it by the objects it investigates. It does not follow the same development as physics, in which the interpretation of a phenomenon can change completely during a scientific revolution. Non-Euclidean geometries can coexist with Euclidean geometry, and the replacement of the latter by the former is far from inevitable. Non-Euclidean geometries are not so much replacements as variations on Euclidean geometry. But unless one counts such trivialities as different assortments of diagrams in yojutsu problems, one would have to say that wasan had very few basic variations and, what is more, that almost none of its basic notions were conceptually deep.

Perhaps the conceptual poverty of wasan can be explained by the derivative character of the culture in which it developed. Most of Japan’s basic cultural patterns were of foreign origin. Highly refined art forms evolved from these patterns, but the fact that they were borrowed precluded critical examination of them. By contrast, the Chinese were forced to reconsider their mathematical heritage during the intellectual crisis precipitated when the Jesuits introduced European exact sciences. The Chinese approach was characteristic of a society with strong autochthonous values: scholars used the new learning to resuscitate forgotten mathematical conceptions from China’s past, and thus preserve the identity of traditional science. In Japan, wasan mathematicians raised neither the question of historical origin nor any other involving the theoretical foundations of mathematics.

Given that Japanese astronomers and physicians constantly compared China and Europe and look from either what they judged to be good, why did the mathematicians remain in their own world? In the first place, there was a difference in disciplinary structure between medicine or the natural sciences and mathematics. Practitioners of the former could readily determine what was better and what was worse by having both Eastern and Western examples before them. In natural science the search for a single truth could more or less readily lead to replacement of inferior Chinese conceptions by Western ones. In mathematics the belief that wasan and Western mathematics differed only in style allowed the two to exist side by side. This difference was rather like that between Japanese shogi and European chess. In this sense wasan and other forms of pure mathematics are closer to art forms than scholarship. The wasan mathematicians did not feel threatened by the importation of Western mathematics and remained in their own artistic world. Comparing the applied mathematics of China, which emphasized astronomical orientation, with the pure mathematical tradition of wasan. one perceives a clear difference in the extent to which practitioners of each considered the Western impact threatening.

According to the Tokyo-fu kaigaku meisai sho (“Survey of Schools in Tokyo”), a report on private academies in Tokyo prepared for the inauguration of the early Meiji school system, Western-style mathematicians trained at the Survey Office or Nagasaki’s Naval Training Center, and the more numerous wasan mathematicians of the Seki tradition belonged to sharply differentiated groups. Contact or movement between the two groups seems to have been quite difficult. Modern Japanese mathematics really began when wasan mathematicians were superseded by those who had adopted Western styles. It would seem that differences in the ability of astronomers, physicians, and mathematicians to restructure their disciplines and respond to foreign knowledge is explained primarily by the fact that the first two groups were professions and the last had no recognized occupational base. Occupational concerns of the first two groups made some awareness of Dutch studies inevitable.

It seems significant that wasan mathematics persisted longest in the northeast, where contacts with Europe and general cultural development lagged fürthest.⁶⁵ During the Meiji period. Western mathematics came to dominate in the cities, following the establishment of the modern school system. and wasan was essentially banished to the countryside. It became, so to speak, an exotic flower blooming by the roadside of civilization.

Japanese Mathematics and the Pure Mathematics of the West. Could early modern mathematics in the West also be described as an art form? After all, people no longer accept the Pythagorean notion that cosmic mysteries can be discovered in the nature of numbers, nor do they believe that divine attributes can be deduced from the transcendental axioms of Euclidean plane geometry. J. W. N. Sullivan. author of A History of Mathematics in Europe (1925), asks why mathematicians enjoy greater social esteem than chess players, given that they no longer claim to be pursuing a single absolute truth.⁶⁶ The artistic spirit of wasan, moreover, seems to embody the essential ethos of mathematics; and one suspects that Platonism gave mathematics an excessively authoritarian aura that may not he essential to its nature.

The European public apparently viewed mathematics as the handmaiden of science. This handmaiden proved to be more competent in the West than did its Chinese or Japanese counterpart. It helped bring about the seventeenth-century scientific revolution and constituted one of the keystones of the mechanical view of nature. The common image of the mathematical practitioner in that period was apparently that of a man who makes a living by producing and selling calendars or maps, or by conducting land surveys. The names of such people seldom appear in the histories of mathematics – in contrast with those who enjoyed royal patronage. Thomas Wright, a notable figure in the history or cosmological theory, was such a man. He came from a tradition separate from academic mathematics, and is thus excluded from histories of scientific astronomy.

Academic mathematics, however, retained its links with science well into the eighteenth century. Wasan’s weaning from science, by contrast, occurred quite early. In the eighteenth century, applied mathematicians sought numerical solutions. The more academic applied mathematics became, however, the greater was its tendency to seek elegant solutions of differential equations in preference to crude numerical calculations. This trend seems to have been somewhat similar to the dominant mentality in yojutsu.

Since applied mathematics dealt with issues posed in nature or society, numerical solutions were essential. In contrast, because wasan problems were recreational in character, practical issues and numerical values were beside the point. Nevertheless it remained characteristic of yojutsu that solutions were expressed concretely.

During the nineteenth century, pure mathematics in Europe tried to detach itself from various practical applications. Thus, even if numerical solutions were obtained, they remained nonessential and had little meaning. To this extent mathematics inevitably became more abstract. By contrast. wasan could be described as a form of pure but not abstract mathematics. The kind of numerical answers sought by wasan had no practical significance. Numerical solutions were sought only to determine the winner of what amounted to a sporting competition.

After the seventeenth century, the abandonment of Archimedean mathematical rigor in the West opened the way for the development of a normal scientific tradition in the application of calculus to mechanics⁶⁷ In the nineteenth century, through a search for precision and logical rigor, mathematics became independent of science for the first time. Mathematicians of that era were very proud of this development and sought the origins of their discipline not in the Renaissance or the seventeenth century but in classical Greece. They even styled themselves the Greeks’ successors.⁶⁸ Thus Greece was revived as the fount of “modern” mathematics.

In this context the differences between the Euclidean tradition and that which developed from the Jinkoki would seem to be clear. Western mathematics was moving toward greater reliance on generalization and rigor, while wasan emphasized the solution of puzzles by finely honed intuition. Although wasan won its independence before Western mathematics arrived, it did so in a rather problematical manner. Wasan’s independence was merely separation from science and practical application. Separate though it was, computational mathematics did not extricate itself from the form of mathematics that seeks numerical solutions to problems. So long as the major emphasis was placed on quantitative calculation, questions about the quality of the underlying theory were difficult to raise.

Nor was Western mathematics prompted to raise basic questions through a concern with such quantitative problems as how to obtain an approximate decimal fraction. Potentially revolutionary developments were hidden in problems of quality. A new paradigm finally did separate itself from. and became independent of, science by returning to qualitative fundamental questions. From the fact of its independence or separation it developed the possibility of a new intellectual universe.

In trying to explain how this separation occurred, one must necessarily look to the institutional background. In the Western academic tradition, Platonism supported the recognition of mathematics as a legitimate and established subject. Thus, in the early modern period, calculus and analytic geometry, unlike other new disciplines, could be recognized immediately because there were posts for mathematicians in the university system.

In the history of science, the nineteenth century was a period during which the German university system occupied center stage. Kant’s Der Streit der Fakultät tells how the universities reconstituted, under the impact of modern science, an organizational structure that had existed since the Middle Ages. The newly constituted faculty of philosophy in particular acquired equal status with the traditional faculties of theology, law, and medicine. As such, it was able to offer more than preparatory training for the three higher faculties. Elementary algebra and Euclidean plane geometry were introduced into the Gymnasium, while differential and integral calculus and analytic geometry were taught in the university. It is conceivable that mathematics might have had to serve as the exclusive handmaiden of such physical sciences as mechanics, physics, and astronomy. In the nineteenth century there were disciplinary wars among the various specialized subjects, particularly over the constitution of chairs in the faculty of philosophy. Were mathematics to hold a subordinate position to physics, it might well be absorbed into the dominant disciplines. In the eyes of the public the value of a new field was recognized to the extent that it contributed to society; but in the universities, disciplines that raised fundamental questions had higher status than pragmatic ones, and were more appealing to students capable of responding to their professors’ enthusiasms. Each specialty and every chair justified itself in this academic system.

For mathematics to become independent in the universities it first had to sever its ties to physics. Rigorously questioning the logical basis of mathematical assertions used by physicists elevated mathematics to be the queen of the sciences. A typical example is found in the career of Karl Weierstrass (1815 – 1877). preeminent figure in the German academic community and founder of the mathematics seminar at the University of Berlin. We do not know how far Weierstrass played academic politics as he developed his discipline. We may assume, however, that students who decided to prepare at the university for careers in mathematics were glad that he had enhanced the prestige of the mathematical profession.

Fundamental paradigms (such as that of Galois) by their nature emerge outside the established line of development, and often outside the universities. They are eventually accepted there, developed there into disciplines, and follow the course of a normal science. All disciplines represented by chairs in the German universities were considered Wissenschaften. Even if a discipline had no stronger link to a more comprehensive system of values than that of the advancement of learning, its status, once it became part of the university system, was secure.

Since no tradition of university scholarship existed in Tokugawa Japan, it is unlikely that any of wasan’s supporters would have rejoiced at (or even comprehended) the advent of a Weierstrass. There was no university environment to tolerate or even encourage questioning of fundamentals. As for the local devotees of yojutsu who patronized the Japanese mathematicians, they viewed the study as an embellishment, and were uninterested in close scrutiny of fundamentals.

As we have seen. Western mathematics, by precise and rigorous questioning of fundamentals, overcame its position as the handmaiden of science, and came to be widely considered the most basic and independent of disciplines. But Tokugawa mathematics merely separated itself from practical problem-solving and indulged in aesthetic pursuits. It would appear that the difference between European and Japanese mathematics is related to a difference in patronage. Through its recognition in a university system, the former shared state patronage redistributed according to academic criteria. The latter had only the direct patronage of individuals enthusiastic about an art form, with their own ideas about how their money was to be spent.

Conclusion: The Japanese View of the Laws of Nature.

Primarily through discussing Tokugawa practitioners. I have tried to describe the dominant view of science and of the laws of nature that existed during that period. What I have tried to argue in part is that aside from notions of law, the Japanese at that time had a conception of nature different from what we have today.

Our present conception of law in nature, stated in value-free terms, was produced in the nineteenth-century university. Earlier intellectual activity pursued much wider goals than the rigor of modern science allows. In that early intellectual world, modern concepts of the laws of nature were applied only in limited situations. Similarly, in Japan one readily discovers, from the tone of the introductions to books on calendrical science, medicine, and mathematics, that the academic notion of science for its own sake did not exist in Tokugawa society.

In earlier times, science in the West was pursued on the assumption that its investigations would demonstrate the glory of God; in Japan the ideology of Tokugawa science derived from Confucian emphasis on individual moral cultivation and social harmony. Morality was the basis of law; laws of nature conformed to and were necessarily subordinate to it. Thus, astronomy and medicine in Japan ultimately had to subordinate themselves to an essentially Confucian set of priorities in order to guarantee respect for their status as disciplines. Pursuits like wasuu, which diverged from moral values or had nothing to do with them, not only became isolated from the Confucian framework but remained a recreational art.

In its unconcern for moral values wasan was the discipline closest to modern science in the Tokugawa period. Takebe Katahiro consciously used the term “law” in his methodological writings, saying: “The establishment of” laws provides the basis for technique; thus mathematics needs to have laws.⁶⁹ Modern science’s objectives consist in trying to establish or prove certain laws, not in defining the metaphysical realities that preoccupied scientists for centuries. Neither does modern science have such grandiose and Far-reaching objectives as alchemy, which tried to prolong life indefinitely, or astrology, which sought to predict the course of nature and human affairs. It tries, rather, to achieve immediately foreseeable objectives. As Japan accepted modern science, astronomers, unlike Shibukawa Harumi, maintained a mechanistic framework, and avoided using historical changes in the celestial movements to explain changes in the heavens. In coping with disease, early modern physicians emphasized solidistic explanations rather than supposing that the human body is governed by temporal vicissitudes as doctors in the Chinese tradition had done. Attempts to prolong life indefinitely and to interpret celestial phenomena as portents were believed to impede technical progress, and thus were abandoned.

As science has restricted itself to universal and objective features of physical phenomena, the idea that values inhere in the physical world has been excluded; as the center of activity shifted from one European state to another national tendencies have dropped out. These tendencies toward objectivity and universality would have been uncongenial to Tokugawa thinkers, to whom the ideals of modern Japanese scientists would make little sense.

Unlike Joseph Needham, 1 do not believe that the Chinese and Japanese scientific traditions were converging toward the same ends as early Western science. Perhaps because of Needham’s great esteem for Chinese science, he stresses China’s priorities in discovery and invention.⁷⁰ Some of these claims of priority are unquestionable, but when Needham compares and evaluates the contributions of China and the West, he uses proximity to today’s standard of knowledge and technique as his criterion of value.

Today’s standard, however indispensable to the working scientist, is too parochial to be useful in evaluating the past. It gives unwarranted normative value to knowledge much of which will shortly become outdated, and it accepts the research emphases of fields shaped and dominated by the educational, career, and fiscal patterns of North American, Western European, and Soviet instititutions.

Treating today’s understanding as more than transitory may seem to Needham unavoidable if he is to make China’s great contributions intelligible to Westerners. Nevertheless there is ample room for doubt that, as Needham believes, Chinese and Western science had the same objectives.⁷¹ Would Chinese science or that of Tokugawa Japan have developed in the same direction as that of Europe in the absence of influence from the latter? Needham can offer no convincing support, beyond a profession of faith, for his affirmative opinion. It seems to me more likely that East Asian and European science were diverging. The goals that were explicitly stated in China and Japan differed fundamentally from those articulated in the West, and the intellectual frameworks too were so different that the implicit goals we deduce from them also do not greatly resemble their Occidental counterparts. Many discoveries which seem to have been made on both sides of the world lose much of their similarity (especially similarity of significance) once they are examined carefully in context.

Japanese science developed within a framework of Confucian values. When Chinese culture was first accepted by Japan, science was included as part of the court culture and bureaucratic system. Japan was earlier practically a tabula rasa so far as the intellectual aspect of science was concerned. But by the time Western science entered Japan during the Tokugawa period, the ideological aspects of traditional Japanese science had been fortified by the recently developed Japanese Confucian system. To put it as simply as possible, the naturalistic and metaphysical aspects of Japanese science had been deemphasized, while its moral dimensions were stressed. The collision of Western science with traditional values was headed off by transforming the new science according to the dictum of Sakuma Shozan about “Eastern morality, Western art forms.” The outcome in the early Meiji period was a highly pragmatic science, utilitarian and materialistic, quite lacking in moralistic connotations. Whether strictly speaking it was an art form was debatable, but its impact on the intellectual and spiritual transformation of Japan was delayed and minimized.

NOTES

1. Al the end Of the nineteenth century, Theodore Merz, in A History of European Thought in the Nineteenth Century, 4 vols. (London, 1903-1914. classified views of nature as astronomical, atomistic, mechanical, physical, morphological, genetic, vitalistic, psychophysical, and statistical.

2. Shigeru Nakayama, A History of Japanese Astronomy, Chinese Background and Western Impact (Cambridge, Mass., 1969), 19.

3.Ibid, ch. 6..

4. Kawakatsu Yoshio, “Shigaku ronshu” (“Treatise on Historiography”), in Asahi shinbun (Chugoku bunmei sen 12, 19731,24-25.

5. Joseph Need ham. Science tin J Civilisation in China, II (Cambridge. 1956), see. IK

6. Shigeru Nakayama. “Educational Institutions and the Developmet of Scientific Thought in China and the West,” b Japanese Studies in the History of Science, no. 5 (1966), 172-179.

7. Shigeru Nakayama, Rekishi toshite no gakumon (“Academic Traditions”: Tokyo, 19741,74-78.

8. I showed a table of contrasts between these two treatises in Nihon shisoshi taikei, Kinsei kagaku shiso ge (“Japanese Thought (series), Modern Scientific Thought, II”: Tokyo, 1971).

9. Shigeru Nakayama, “Accuracy of Pre-modern Determinations of Tropical Year Length,” in Japanese Studies in the History of Science, no. 2 (1963). 101-118.

10. Shigeru Nakayama, “Cyclic Variation of Astronomical Parameters and the Revival of Trepidation in Japan,” ibid., no. 3(19641, 68-80.

11. Nathan Sivin, “Cosmos and Computation in Early Chinese Mathematical Astronomy,” in T’oung Pao. 55 (1969), 1-73.

12.Sorai sensei tomonsho (“Queries and Answers of Master Sorai”: 1727).

13. Shigeru Nakayama. “Edo .jidai niokeru jusha no kagakukan” (“Confucian Views of Science During the Tokugawa Period”), in Kagakusi kenkvu. no. 72 (1964), 157-168.

14. The main source of information on this conflict is koide Shuki, “Rarande yakureki zenbun” (“Preface to the Translation Of Lalande”), preserved in the Japan Academy.

15.ibid

16. Preserved in Kunaisho. Zushoryo.

17. Preserved in Naikaku Bunko.

18. Shigeru Nakayama. “Diffusion of Copernicanism in Japan,” in Studio Copernicana, 5 (1972), 153-188.

19. “Tengaku zatsuroku” (“Miscellaneous Records on Astronomy”: n.d.t. preserved in Naikaku Bunko.

20. Gregory Zilboorg, A History of Medical Psychology (New York. 1941).

21. Ogawa Teizo. “Meiji zen Nihon kaibo gakushi” I “History of Anatomy in pre-Meiji Japan”), in Meiji zen nihon igakushi (“History of Medicine in pre-Meiji Japan”), (Tokyo, 1955), 159– 166. Also see his “kindai igaku no senku” (“Forerunners of Modem Medicine”), in Nihon shiso tai-kei. yogaku, ge (“Japanese Thought [series], Western Learning, II”: Iwanami, 1972). 506-509.

22. Joseph Needham, “Science and China’s Influence on the World.” in Raymond Dawson, ed. The Legacy of China (Oxford. 19641, p. 239.

23. Manfred Porkert, The Theoretical Foundations of Chinese Medicine (Cambridge, Mass.. 1974),

24. Tsuruoki Genitsu, Idan (“Medical Critique”; 1795).

25. “Shen kua,” inDictionary of Scientific Biography, XII. 369-393.

26. Ogawa Teizo, op. cit 92 ff.: and Uchiyama koichi. “Nihon seiri gakushi” (“History of Physiology in Japan”), in Meiji zen nihon igakushi. II, 122 ff,

27. Yakucho (“Pharmacological Effects”), vol. II; repr. in Nihon shiso taikei. Kinsei kagaku shiso, ge, 256. Also sec Otsuka keisetsu. “Kinsei zenki no igaku” (“Medicine in the Early Tokugawa Period”), ibid.

28. Shigeru Nakayama, “Kindai kagaku to yogaku” (“Modern Science and Western Learning”), ibid 460-461.

29. “Scientific Productivity and Academic Organization in Nineteenth-Century Medicine.” in Bernard Barber and Walter Hirsch, eds. The Sociology of Science (New York. 1962), 305-343.

30. Amano Ikuo. “Kindai Nihon ni okeru koto kyoiku to shakai ido” (“Higher Education and Social Mobility in Modern Japan”), in Kvoiku sbakaigaku kenkyu. no. 24(1969), 84.

31. Maruyama Kiyoyasu. “Chiho ni okeru wasanka no shiso to seikatsu” (“Thought and Lives of Local Traditional Mathematicians”), in Shiso. no. 356 (Feb. 1954); repr. in Kyodo shiso no bunkenshu, no. 2 (1966). 13-31.

32. Robert G. Frank. “Institutional Structure and Scientific Activity in the Early Royal Society,” in XlVth International Congrèss of the History of Science. Proceedings (1974), IV. 82-99.

33. Arnold Thackray, “Natural knowledge in Cultural Context: The Manchester Model,” in American Historical Review. 79, no. 3 (June 1974), 672-707.

34. For instance, Mikami Yoshio, Bunkashijo toil mitaru Nihon no suguku (“Japanese Mathematics From the Viewpoint of Cultural History”: Tokyo, 1947); and Ogura Kinnosuke, Nihon no sugaku (“Japanese Mathematics”: Iwanami, 1940).

35. Hirayama Akira. Seki Takakaz.(koseisha, Tokyo, 1959), 178-179.

36. For instance, Daijutsu bengi (“Discussions on Problems and Solutions”), reprinted in Sekiryu santō shichibusho (“The Seven Books of the Seki School”: Tokyo. 1907).

37. There is not much citation of traditional doctors of mathematics. but Aida Yasuaki wrote a few words on the Miyoshiand kotsuki families in his preface to Seiyo stmpō.

38. Kawakita Chorin, Ken’o sanpo (Tokyo, 1863), preface.

39. Sivin, op. cit.

40.Hsin T’ang shu (“New History of the T’ang”), Li chih (“Treatise on Mathematical Astronomy”). Also see Yabu-uchi kiyoshi, Zutiō rekihoshi no kenkyū (“Researches in the History of Calendrical Science During the Sui and T’ang Periods”: Tokyo, 1944).4L “Sugaku, sangaku no hanashi” (“Topics on Mathematics and Arithmetic”), in Sudo shodan, I (1773).

41.ibid.

42. Koyre’s assertion that “the allusions to Plato so numerous in the works of Galileo… are not superficial ornament born from his desire to conform to the literary mode or the Renaissance… nor to cloak himself against Aristotle in the authority of Plato. Quite the contrary, they are perfectly serious and must be taken at their face value” is groundless. Alexandre koyré. “Galileo and Plato,” in Philip Wiener and Aaron Noland, eds.. Roots, of Scientific Thought (New York. 1957), 174.

43. Shigeru Nakayama, “Galileo and Newton’s Problem of World-Formation,” in Japanese Studies in the History of Science, no. I (1962), 76-82.

44. Okumura Tsuneo, “Kinsei shōnin no sanyo ishiki” (“Mathemetical Concern of Modern Merchants”), in Shit-zankai, 19(Sept. 1969), 5.

45. Murai Masahiro, Ryochi shinan. kohen (“Introduction to Surveying”: II, 1754),preface.

46.ibid..4.

47. kasai Sukeharu. Kinsei hanko niokeru gakuto gukuha no kenkvtt (“Researches on Academic Tradition and Schools in Modern Fief Schools”), I (Tokyo, 1969), 9,75.

48. Akabane Chizuru, “Shomin no wasanka to hanshi no wasimka” (“Commoner Mathematicians vs. Samurai Mathematicians”), in Kagakusi kenkyu, no. 34 (1955), 25.

50. Hirayama Akira, “wasanka no shokugyo (“Occupations of Japanese Traditional Mathematicians”). in Kvodo sugaku no bunkensha.no. I (1965), 192-198.

51. Mikami Yoshio, “Sugakushijo yori mitaru nihonjin no dokuso noryoku” (” Japanese Creativity in (he History of Mathematics“, in wasan kenkyu. no, II (Oct, 1961),7-8, Originally written in 1927.

52. Mikami Yoshio, “Yureki sanka no jiseki (“Facts About Wandering Mathematicians”), in Kyodo sugaku no bunkenshu, no. I (1965), 166– 184.

53. Thomas Kuhn, Structure of Scientific Revolutions (Chicago. 1962).

54. Hosoi So, wasan shisō no tokushitsu (“Characteristics of Mathematical Thought in the wasan Tradition” Tokyo, 1941), 44.

55. For instance. Ogura Kinnosuke. Nilson no sugaku (“Japanese Mathematics”: Tokyo, 1940).

56. Ajima Naonobu, Seivo sanpō; (1779). postscript.

57. Hosoi, op. ci, 48-49.

58. Both repr. in Sekiryu sanpō shichibusho (see note 36),

59. Fujiwara Matsusaburo. Nihon sugakuski yo (“Epitome of lupurcse Mathematics” Tokyo, 1952). 127.

60. Hosoi. op. cit., 69-78.

61. Yabuuchi Kiyoshi, Chugoku no sugaku (“Chinese Mathematics” Tokyo, 1974). criticizes the narrowness of Japanese mathematicians.

62. Mikami Yoshio, “Enri no halsumci ni kansuru ronsho (“Arguments on the Discovery of Enri”), in Sugakushi kenkyu. no. 47 (1970), 1-43. and no. 48 (1971), 1-42, Originally written in 1930.

63. Hosoi. wasan shiso, 298– 300.

64.Yamaji Kunju sensei chawa (“Table Talks of Master Yamaji Kunju”), repr. in Rekizan shiryo. 1 (1933)

65.Mikami, Btmkashi…,77-80.

66. J. W. N. Sullivan, A History of Mathematics in Europe (London, 1925), inlro.

67. Dirk Struik. A Concise History of Mathematics (New York, 1948),

68. Mori Tsuyoshi, Sugaku no rekishi (“A History of Mathematics” Tokyo, 1970). 126.

69. Takebe Katahiro, “Tetsujutsu” (1722), in Saegusa Riroto, ed., Nihon tetsugaku zensho, V111 (Tokyo, 1936), 375.

70. Joseph Needham and Shigeru Nakayama, “Chugoku no kagakushi o megutie” (“On the History of Chinese Science”), in Gekkan Economist (Oct. 1974). 86-87.

71. Joseph Needham, “The Historian of Science as Ecumenical Man.” in S. Nakayama and N. Sivin, eds., Chinese Science (Cambridge, Mass., 1973). 1-8. Sivin has outlined an approach to Chinese science less bound to such assumptions in his preface to Science and Technology in East Asia (New York, 1977)