PictureThe abacus, or soroban 算盤
It is often said that mathematics is the only true universal language, and many different cultures have discovered many of mathematics theorems independently. Japan also has a rich history of developing its own mathematics. It was, as expected, developed from Chinese mathematics, but during the closed years of the Tokugawa period it developed more or less independently of external sources.A good place to start the story of traditional Japanese mathematics is the introduction of the soroban 算盤, or abacus, to Japan. It is believed that the first abacus was brought to Japan during Hideyoshi's unsuccessful invasion of Korea at the end of the sixteenth century. This is because the oldest surviving abacus that has been found in Japan was in the possession of one of Hideyoshi's soldiers at the port of Hakata around 1592. Usage of the soroban was popularized in great part by the mathematician Mōri Shigeyoshi who among other things published a primer on how to run divisions using the soroban.

PictureTwo pages from Jinkō-ki
Although Mōri Shigeyoshi and the introduction of the soroban had great implications for the development of Japanese mathematics, it is the publication of the book Jinkō-ki 塵劫記 in 1627 that is usually seen as the beginning of wasan 和算. Wasan is the term that is used to refer to traditional Japanese mathematics and will be used in this post hereon after. The term was not used until the Meiji period, and was then used in order to differentiate Japanese mathematics from western mathematics. The Jinkō-ki was published by the mathematician Yoshida Mitsuyoshi (1598-1672) and became a bestseller. It was revised and re-published in more than three hundred versions over the next three hundred years. This brought on a new culture of mathematics and more and more mathematical books and schools appeared all over the country. Although wasan might not have contributed much or anything to the development of international mathematics, Japanese mathematicians discovered many of the same things as western mathematicians, some things also before they were discovered in the west. For instance, the most famous Japanese mathematician, Seki Takakazu developed a theory of determinants before Leibniz. Also, Soddy's hexlet that was previously believed to have been discovered in the west in 1937, has been discovered on a tablet in Japan dating from 1822. For more detail on these matters see Chapter 8: East and West in the book Sacred Mathematics: Japanese Temple Geometry by Fukugawa Hidetoshi and Tony Rothman.

PictureSangaku tablet
Perhaps the most interesting part of wasan, at least for a non-mathematician like me, is the tradition of sangaku 算額. Sangaku refers to tablets containing mathematical puzzles, most often of the geometrical type. These tablets were offered to Buddhist temples and Shinto shrines and hung there on display for other mathematicians to see. Usually the tablets also included the answer, but not the complete solution or proof. In this manner, they were also challenges to other mathematicians, basically saying "Prove this!", or "How can this be solved?". Mathematicians often published their solutions to problems made by others, and also published new problems for others to solve. Unfortunately, many tablets have not survived, but we know about the existence of many of them through collections of sangaku problems that were published in books in the Edo period. For instance, the mathematician Yamaguchi Kanzan travelled extensively throughout Japan and wrote a diary about his travels where he also wrote down sangaku problems that he encountered. Another book, dedicated only to sangaku problems, is the Shinpeki Sanpo 神壁算法 published in 1790 by Fujita Kagen. For an excellent collection of surviving sangaku tablets, visit http://www.wasan.jp/ .

PictureFrom Shinpeki Sanpo
The sangaku and many of the problems recorded in books are generally visually pleasing and should be treated as cultural treasures regardless of their mathematical relevance. Nevertheless, the tradition of wasan faced an abrupt end. With the modernizing of Japan in the Meiji period and the introduction of western mathematics, wasan was deemed inferior and was no longer to be taught in school. There seems to be quite an interest in the subject though, and people are playing around with the old puzzles. Although this post has focused on the culture of wasan, there might be people reading this who want to twist their brains and wrestle with these puzzles. If you're one of those, I recommend checking out the book mentioned earlier, Sacred Mathematics: Japanese Temple Geometry. It is stated in the book that it contains problems ranging from incredibly easy to impossible. You can also check out this link: http://www.wasan.earth.linkclub.com/english-nagano/english.html . If your browser has problems reading the characters, change the encoding to Japanese (Shift_JIS).

Sources and recommended reading

Fukagawa, Hidetoshi, and Tony Rothman. Sacred Mathematics: Japanese                Temple Geometry. Princeton, N.J.: Princeton University Press, 2008.
Wikipedia (Jap)

_A while ago I wrote an introduction to the setsuyōshū 節用集 genre and promised to write more detailed posts about the various content of such books. This is the first post in what I hope to become a running series of sorts. As will be the case for most of these posts, the majority of the examples used will come from the Eitai Setsuyō Mujinzō, the same as was used in the introduction.
In this installment we will look at the content of a double page at the beginning of the Eitai Setsuyō Mujinzō which gives information about some cosmological beliefs in the Edo period. I am not saying that this represents the dominant cosmological world view of the period, but the fact that it appears within such a popular work as the Eitai Setsuyō Mujinzō makes it worth it to have a closer look. Below the image I will provide the complete translation along with some comments. I can't say that I'm satisfied with my translation, it doesn't read very well and I struggled to find good translations for some of the terms. If you have any suggestions that would improve the translations, please tell me in the comments.

Most of us who study Japanese history wish that we could somehow go back and experience daily life in our respective periods of interests. Until my time machine is built and ready this is of course impossible. In the meantime, there are some other wonderful ways to get a visual glimpse of history. One obvious way is to look at contemporary sources. I was reading a book the other day where I stumbled upon such a source, namely a scroll named Kidai Shōran (熈代勝覧). I had never seen or heard about this scroll before, so I quickly made a Google search to see if I could find some pictures. I was glad to see that someone had actually made a panorama video of the entire scroll and made it available on YouTube. If you don't have the patience to sit through the entire video can look at a picture of it. Story continued below the video.

The scroll itself is actually a bit taller than what you see in the video, but the person who made it has zoomed in to better reveal the details in the street. The scroll is more than 12 meters long and depicts a ca 760m long stretch of road between Nihonbashi and Kanda Imagawabashi in Edo (that is present day Tokyo, as if you didn't already know) in the year 1805. The scroll shows 88 houses and stores, 1671 people (1439 men, 200 women and 32 kids), 20 dogs, 13 horses, 4 cows, 1 monkey and 2 falcons. The fact that it shows the street in 1805 is quite interesting, because the buildings shown were destroyed the year after in a great fire.
The scroll was actually discovered not so long ago; in 1999 it was found stowed away in the Museum of East Asian Art in Berlin. A label on the scroll says 「熈代勝覧 天」. 天 (heaven) means that the scroll is number one in a set of three scrolls (天、地、人), but unfortunately only this one was found. It is a rather comforting thought, however, that new sources keep getting dug up from deep inside archives around the world.



In this post I will give a brief introduction to the setsuyōshū (節用集) genre. In the future I plan to write some posts on some of the content of these books, so this introduction felt necessary to get out of the way first.
The setsuyōshū are a kind of dictionary with encyclopedic elements. When the genre first surfaced in the Muromachi period (1336-1573), however, they only contained a dictionary part. These dictionary-only setsuyōshū were copied by hand and were used by the elite (priests, nobility) for artistic and bureaucratic purposes. Such setsuyōshū are usually referred to as "old-book setsuyōshū" 古本節用集.
In the Edo period (1600-1868), however, the genre underwent major changes. Because factors such as the commercialization of the printing press, ever increasing literacy skills among the people, more time for leisure in times of peace, and improved economic conditions, books were printed and published in ridiculous amounts. Along with this revolution of the printing culture, publishers started to add more and more information to the setsuyōshū genre, making them into everyday encyclopedias. These books were immensely popular, and we can assume that most people who were economically fit had access to one. They were the go-to source whenever people needed information quickly, much like a Wikipedia of the day. These kinds of setsuyōshū are commonly called "encyclopedia-type setsuyōshū" (百科型節用集).

Although new parts were added, the dictionary part remained the biggest part of most editions, so let's have a quick look at how the dictionary works. On the left hand you see the first page of the dictionary part from the Eitai Setsuyō Mujinzō (永代節用無尽蔵) (1849). This was one of the most popular editions, if not the most. In this particular edition the dictionary part takes up a little bit less than two thirds of the total pages, although as you can see from the image on the left there is also a top row of encyclopedic information on these pages. This particular page shows the beginning of Japanese history which continues all the way to the year the book was published.
The entries in the dictionary are organized on two levels. First it is organized in the iroha-order (the ABC of pre-modern Japan), as opposed to the gojūon-order (the ABC of modern Japan). On the picture above you can see the first syllable i (い). Underneath each syllable, the entries are organized according to various categories. The number of categories used varied between different editions, but the 13 categories used in the Eitai Setsuyō Mujinzō seems to have been the most standard. The categories are as follows:

  1. 乾坤: Stands for heaven and earth or the universe. Includes words on the sun and the moon, celestial bodies and stars, rain and snow, winds and clouds, and other natural phenomena, as well as famous places, palaces and so forth.
  2. 時候: Stands for seasons or time. Includes various names for the seasons, months, days and so forth.
  3. 神仏: Stands for gods and buddhas. Names of gods and buddhas are included here, as well as names for temples and shrines.
  4. 官位: Means office and rank. Names of official positions, court titles and so forth are included in this category.
  5. 名字: Means name and includes exactly that, names.
  6. 人倫: Means human relations. Words on family, friendship, etc.
  7. 支体: Stands for limbs of the body. Includes words about the human body.
  8. 食服: Means food and clothes and includes words in those categories.
  9. 器財: Means tools and utensils. Hammers, spades, pots and pans. You name it, it's in this category.
  10. 気形: Means living things and includes words on animals.
  11. 草木: Stands for grass and trees and includes words on plants etc.
  12. 数量: Means quantity or volume. Includes number words and measurements.
  13. 言語: Simply means language or words. Includes mostly what does not fit in elsewhere like verbs, particles etc., but also common phrases and flowery words.

The dictionary was mostly used to look up the writing of the Chinese character of an indigenous Japanese word. So if you were, for instance, looking for the word hana はな (the Japanese word for flower), you would first find the syllable ha (the third one in iroha-order). Then you would find the appropriate category, in this case the grass and trees category (草木) and find the word written in kana (the Japanese "alphabet") on the right side of the character. The image on the right shows what you would find if you used the Eitai Setsuyō Mujinzō. It shows three different characters that mean flower in Chinese, and one of the characters is written twice in two different handwritten forms. On the left side the square style of the characters are written, as well as the "Chinese" reading of the character (on-yomi). If you are familiar with modern Japanese, you probably noticed that the kana on the upper right does not look at all like はな. This is because it is written in an older set of kana, now dubbed hentaigana (変体仮名). This ha developed from the kanji 者 as opposed to the modern one that developed from 波. The na is actually the same as な only written a little bit differently. It developed from 奈. I will write about kana and hentaigana in greater detail in a future post.

Although the dictionary part of setsuyōshū is very interesting, to me the encyclopedic parts are much more intriguing. The dictionary parts have also been well studied by historical linguists, while the encyclopedic parts have barely been touched by anyone. This is a bit perplexing, because it is well known that it was a very popular genre. I will just give a very brief overview of some of the typical entries that appear in setsuyōshū. Somewhere at the beginning of the setsuyōshū there is typically a map of Japan, and in some also a map of the world. Maps of the three metropolises, Edo, Kyoto and Osaka also often appear. Scattered through the books are also illustrations and textual information about various famous places throughout Japan, such as the illustration of Mt. Fuji at the top of this post.There are instructions on good etiquette, astrology, palm-reading. Illustrations and information about famous warriors and poets, warrior equipment and catalogs of elite samurais, their retainers and how many koku rice they are worth. Rules and tactics of the games of shōgi (将棋) and go (碁), information about festivals, shrines and temples, tea ceremony, and a plethora of various subjects are also available. In other words, you can find just about anything in these books.

One of the fascinating aspects of the setsuyōshū genre is that most, if not all, of the encyclopedic information it contains is taken from somewhere else; it is just copy-pasted if you will. The competition among various editions of setsuyōshū was fierce, so it is reasonable to assume that the compilers of these books wanted to include exactly the kind of information the consumer wanted. Thus, the setsuyōshū can be seen as a looking glass into the information that the people deemed relevant and interesting at the time. The study of setsuyōshū can therefore be seen as a very useful shortcut of studying popular knowledge of early modern Japan.
One of the important things we can deduce from the study of these books is how a new knowledge culture emerged in the early modern period. Whereas a lot of the typical information in the setsuyōshū - such as the tea ceremony or etiquette - were reserved for the elite in pre-Edo times, this kind of information now had become mass culture. Thanks to the improved informational networks such as the gokaidō road-network the books also spread to the far reaches of the country where it would be hard to come by in earlier times. The setsuyōshū genre can thus be said to be a testimony of a spread of knowledge and information both "downwards" socially and outwards geographically.

That's it for this brief introduction of the setsuyōshū genre. I will post more detailed descriptions of some of the information in the books in the near future. I've included a small gallery of some setsuyōshū pages below. All images used in this post are from the Eitai Setsuyō Mujinzō from the Library at the University of Oslo and are taken by myself._

Sources and recommended reading:

Berry, Mary Elizabeth. Japan in Print: Information and Nation in the Early Modern     Period. Berkeley, Calif.: University of California Press, 2006
Eitai Setsuyō Mujinzō. Kyōto: Katsumura Jiuemon ...[et al.], 1849.
Kornicki, Peter F. The Book in Japan: A Cultural History from the Beginnings to         the Nineteenth Century, Handbuch Der Orientalistik, 5. Abteilung, Japan.             Leiden: Brill, 1998.
Yokoyama, Toshio. "Even a Sardine's Head Becomes Holy: The Role of                     Household Encyclopedias in Sustaining Civilisation in Pre-Industrial Japan." In     SANSAI: An Environmental Journal for the Global Community, 41-57, 2006.
———. "In Quest of Civility: Conspicuous Uses of Household Encyclopedias in         Nineteenth-Century Japan." Zinbun 34, no. 1 (1999): 197-222.

I just finished reading the book Breaking Barriers: Travel and the State in early Modern Japan by Constantine Nomikos Vaporis and I can say right off the bat that it is an excellent book.
Vaporis states himself that the purpose of the book is to "[...] examine Tokugawa society [...] through the prism of travel and transport." And in doing that, I think he does a mighty fine job. A great deal of the book looks at road barriers around the country and how these barriers restrained (or did not restrain) peoples physical mobility in the Edo period.
The book is thematically structured into six chapters plus an introduction and a conclusion. The chapters are laid out in a very logical order and the information in each chapter builds on the preceding ones. Throughout the chapters, however, he aptly uses repetition in such a way that each chapter can be read and fully understood on its own.
The first chapter is named The arms and Legs of the Realm and gives a thorough overview of the infrastructure of the gokaidō-network (a network of five roads, where the most famous ones are the Tōkaidō and the Nakasendō).
The next chapter, The Social Organization of the Gokaidō Network, deals for the most part with sukegō taxation, a kind of labor tax put on villages close to post stations on the roads. Neighboring villages were obligated to provide porters and pack horses if traffic became too much for the post station. The villagers were compensated for their efforts, but usually this did not make up for their lost time in the fields. Needless to say this led to complications between the villagers and the authorities.
Chapter three is named A Curious Institution and here Vaporis looks at the two kinds of barriers that were put up throughout the country, sekisho and bansho. He goes into rather impressive detail, and lists for instance how many guns, bows, spears and staves various sekisho had in stock. One of the main concerns for the sekisho was to monitor and prevent the movement of guns eastward towards Edo, and the movement of women westward away from Edo. The bakufu did not want guns in Edo in fear of an uprising, and women traveling away from Edo might have been hostages in the alternate attendance system (sankin kōtai).
The fourth chapter, Permits and Passages, investigates different kinds of passports and permits that were required to pass the various barriers and how they could be acquired.
Chapter five, The Benevolence of the Realm, gives a detailed description of various ways and methods to circumvent the sekisho system. There were for instance many side roads one could use to get around the barriers; women sometimes dressed up as boys to avoid attention; or one could simply bribe one's way through. This shows an inability or unwillingness from the authorities to fully enforce the system.
The last chapter, Travel as Recreation, deals with the emergence of a travel industry. Most travel at the time took the guise of pilgrimage, and pilgrimage was also one of the only legitimate reasons you could have for applying for travel permits. As time went by, however, pilgrimage became more and more secularized, and the visiting of shrines and temples became only one of the many stops on the journey.
Breaking Barriers is a well written book and is maybe most impressive in the plethora of sources it draws upon, both primary and secondary. Historians have often been criticized for analyzing society from a top-down perspective, looking mostly on the authorities and the elite often neglecting the majority of the population. Vaporis is definitely not of that kind. In this book he looks at society both from top-down, and bottom up. He looks at official documents and such things as travel diaries and travel guides. If we take the official documents at face value, early modern Japan indeed looks like a country where physical mobility was greatly hampered. When including the bottom-up perspective, we get a different story and the discrepancies between official policies and social reality is revealed. This is why this book tells us a great deal about society in the early modern period, not just travel in general. Go read!


Vaporis, Constantine Nomikos. Breaking Barriers: Travel and the State in Early         Modern Japan, Harvard East Asian Monographs. Cambridge. Mass.: Harvard     University Press, 1994.

_I was reading through A History of Japan: From stone age to superpower by Kenneth G. Henshall and I came across an interesting term I had never heard of before. This term was he-gassen (屁合戦), or 'farting competition'. This, of course, spurred my interest and I quickly made a google search for the term. The search revealed a digitized scroll hosted at the database for Japanese and Chinese classics at Waseda University Library. (Which is, by the way, an excellent source for finding primary sources) The picture below is from said scroll, and you can also peruse the scroll in its entirety here.
Apparently, similar drawings were used to ridicule westerners towards the end of the Edo period, with images depicting the westerners blown away by Japanese farts. (Henshall 2004:70)


Hegassen emaki. Date and publisher unknown
Henshall, Kenneth G. A history of Japan: From Stone Age to Superpower. New York: Palgrave Macmillan, 2004.