Japanese Numbers Game

T Crump

• Publisher: Taylor & Francis
• Year: 2012
• Print ISBN: 9780415056090
• eBook ISBN: 9781134935581
• Edition: 1
• Topic: Social Sciences
• Subtopic: Anthropology
• Index: Social Sciences

An almost obsessional use of numbers characterizes Japanese popular culture. A wide variety of numerical formulae and strategies provide the means for explaining events and solving problems occurring in everyday life. These include such matters as the choice of the name for a child, ranking in almost any game or sport, the diagnosis and cure of illness or the decision to accept a new job. This text provides a general study of the field of Japanese popular numeracy. It introduces the reader to a world of numbers in which fortune-telling, the abacus and games involving numbers, as well as curious numerical names (of both people and places), illustrate the importance of systems of counting, calculation and forecasting. The study explores the cultural roots of attitudes towards numbers and makes suggestions about the contemporary implications of a culture in which mechanical numeracy (and number obsession) is general but the highest levels of academic mathematics still fall short of world standards.

1 The numerical paradox

THE PROBLEM STATED

Any number of questions arise from the Japanese preoccupation with numbers. Intuitively numbers seem so much a part of all human experience, that it is difficult to see precisely what scope there is for understanding, or using them, in some special way.¹ True, certain specialised numerical institutions, such as certain games, may be found to exist only in one particular region—which for this book will be Japan—but even then the actual numerical base can always be expressed in a form which is quite general and not tied to any particular culture.² The symbols used tend to be completely arbitrary, whether they take the form of spoken words or written signs, which need not necessarily correspond to one particular word. Viewed objectively, this is true of the numerical symbols used by the Japanese, although this is not how the Japanese themselves would see things. It is not so much that certain symbols, such as the Chinese character, or kanji,³ for the number 3,

, indicate their meaning by being a member of the class defined by this number, in the present case by being comprised of three horizontal strokes, but that many other kanji numerals, without this property, still have connotations which range far beyond the numbers they represent. Instances will constantly occur throughout this book.

This is the heart of the paradox inherent in the use and understanding of numbers in any culture. In one direction, numbers can always be reduced to a complete abstraction, whose properties give no indication of how they might be used in any practical or cultural context. This is the direction followed by pure mathematics, whose practitioners tend to eschew all practical applications.⁴ In the other direction, numbers are important not for their inherent properties, such as are the basis of any sort of arithmetic,⁵ but for what they connote, and this, far from being general, is highly particular. To give but one example, already noted in the preface, one of the two words for 4 in Japanese, shi, also means ‘death’, which is taken by many Japanese to explain why the word for ‘four men’, yonin, is based on the alternative yon. Japanese culture is extraordinarily rich and creative in such connotations. More than this, it extends the process to identifying certain numbers on the basis of their inherent arithmetical properties and then seeing them as having a special meaning. A typical instance of this, to be looked at in detail later, is to regard numbers, such as 33, which exceed by 1 a power of 2 (so that 33=2⁵+1), as specially significant.

All this is a part of what is now, fashionably, called ‘cognition’. Its basis is the knowledge of the world drawn on to construct perceptions of it (Keesing 1981:97); this is what Gregory (1969) has described as an ‘internal model of reality’. Cognition is for the individual what culture is for society, but, inescapably, culture provides the individual with the means to build his own models. These means, particularly when it comes to numbers, are symbolic. In the result

when seen as a set of symbolic devices for controlling behaviour…culture provides the link between what men are intrinsically capable of becoming and what they actually, one by one, in fact become. Becoming human is becoming individual, and we become individual under the guidance of cultural patterns, historically created systems of meaning in terms of which we give form, order, point and direction to our lives. And the cultural patterns involved are not general but specific. (Geertz 1973:52)

Turning to Durkheim, although Japan is far removed from the lower societies upon which he based his study of religious forms, one’s intuitive reaction is still likely to be that

the slighter development of individuality, the small extension of the group, the homogeneity of external circumstances, all contribute to reducing [cultural] differences and variations to a minimum. The group has an intellectual and moral conformity of which we find but rare examples in [other] advanced societies. Everything is common to all. Movements are stereotyped; everybody performs the same ones in the same circumstances, and this conformity of conduct only translates the conformity of thought. Every mind being drawn into the same eddy, the individual type nearly confounds itself with that of race. And while all is uniform, all is simple and well. (Durkheim 1915:5–6)

If, in relation to Japan, this passage from Durkheim represents both the impression the land makes upon the casual visitor from overseas and the ideal which many Japanese would like to see realised, it is still largely a parody of the true situation. Little is simple about the way Japanese use and understand numbers. Many of the contexts and forms of such use are outside the experience of millions of Japanese, whether by accident or design. Where all the members of one family may be named according to the principles of seimeigaku examined in chapter 5, in another, these may be completely disregarded. Even within the family differences will occur: a businessman, who has forgotten everything he ever knew about the abacus, may have a wife who uses it expertly for managing the family budget. But then once again citing Durkheim (1915:2–3):

The most…fantastic rites and the strangest myths translate some human need, some aspect of life, either individual or social. The reasons with which the faithful justify them may be, and generally are, erroneous; but the true reasons do not cease to exist, and it is the duty of science to discover them.⁶

Science, if it is to discover the reasons which explain all the different uses of numbers in Japan, must look in two directions. The one is nature, the other is cosmos, and it is in coming to terms with nature and cosmos, over a period of some 2,000 years, that the Japanese have developed all their different numerical institutions. What then are nature and cosmos, and what then is their relation with numbers?

Nature and cosmos have in common that they are that part of the environment which are given in the experience of any community. They are manifest in immutable laws, which define the scope of all human initiative. Man cannot escape from the laws of nature, nor from the cosmic order. At the same time such law and order are a projection of purely cultural forms, although the culture from which they derive makes certain that their origin is suppressed. The point is simple enough: culture continually improves upon nature, and justifies the rules necessary for achieving and sustaining any improvement by an appeal to the abstract order of the cosmos. The process can be illustrated by the case of wet rice cultivation in Japan, which at the same time may be used to point out the essential difference between nature and cosmos.

The cultivation of rice, like any other form of agriculture, cannot escape from the inherent properties of the plant upon which it is based. At the same time, the technology developed within any culture can ensure that these properties are exploited so that yields far exceed what nature, left to itself, could ever produce.⁷ Nowhere has this process gone further than it has with the cultivation of rice on irrigated terraces, as practised in Japan for well over a thousand years.⁸ The rice terraces reflect not only the vast investment in human capital required for their construction and maintenance, but also provide for the sustenance and livelihood of the population which this represents. Wild rice, if it ever existed in Japan, could never have provided the basic means of subsistence.⁹

The success of wet rice cultivation was tied to the use of numbers in two quite different ways. In the first place, the terrace system of cultivation, allowing for no economies of scale (Bray 1986:15), always depended upon the co-ordination of the work of a large number of small family farms. The economic problem of regulating land and labour was essentially numerical, the more so when the heavy tax burden resting on the village fell to be shared by the different households comprising it.¹⁰ In the second place, the cultivation of rice was still dependent upon the annual cycle of the seasons, as recorded in the calendar, which was itself determined by the cosmic order. This in turn gave rise to considerable numerical problems (which I discuss further in chapter 7, ‘Time’), particularly in relating the length of the month (as determined by the moon) to that of the year (as determined by the sun).

One faces here a critical distinction between nature and cosmos. Although the course of nature up to a certain point can be directed and contained (which fact underlies all successful cultivation), beyond this point it is unpredictable and uncontrollable. The Japanese sansai, or three natural calamities of fire, storm and flood, occur capriciously, leaving behind devastation which no advance planning can counteract. Events of this kind can be accounted for post hoc, sometimes by being related to such cosmic events as eclipses, which occur outside the normal calendar.¹¹

The cosmic order is, in principle, predictable (for otherwise it would be disorder) and not so much uncontrollable as simply beyond control. Knowledge of the cosmic order is a matter of observation and deduction, requiring the keeping of records and arithmetical calculation for the purpose of interpreting them. Both of these operations are essentially numerical: the first requires the linguistic base described in chapter 2; the second, an efficient instrumental means such as is provided by the abacus described in chapter 9.

The object is not to master the cosmic order, which is impossible, but to understand and explain it. The question is: what sort of explanations are acceptable in the local culture? In answering this question one comes to a parting of the ways between east and west. Modern western man accepts a disjunctive view of the universe, which sees no necessity for the observations of astronomy to regulate day-to-day life, save in so far as the phenomena observed control natural events, such as tides and seasons. As Needham (1969:26) puts it, ‘from the beginning of their thought history, Europeans have passed continually from one extreme world outlook to another, rarely finding any synthesis…. Theological spiritualism and mechanical materialism maintained perpetual war.’¹² The result is that cosmology is essentially demythologised; its basis is logical, and it is a part of mathematics. This is the world of modern, western astronomy, in which mathematical notation ignores, so far as possible, the traditional configuration of the heavens.¹³

The traditional world of Japanese numbers has another interpretation of cosmology. The order, reflected in the universe, is a conscious order, a manifestation of some ideal plan, so that the phenomena observed can be interpreted as signals requiring an appropriate response from the observers. Solstices and equinoxes are imperatives in a moral order, expressed in the calendar, in a way explained in detail in chapter 7.

THE TYPOLOGY OF NUMBERS

The discovery of the true nature of numbers is a logical problem inherent in any culture in which numbers occur.¹⁴ Few, if any, cultures have ever achieved an adequate solution, for the problem itself is extremely difficult to formulate.¹⁵ To begin with the most elementary level of cognition—which may be taken to be that of the child as it first becomes familiar with numbers—numbers are intuitively associated with counting. But counting, since it assumes the existence of numbers, cannot be any part of their logical basis. Judged culturally, the essential intuition is that numbers are there, whether or not counting, or any other process, is necessary to make them part of everyday cognition. Numbers in this elementary sense are generally known as natural numbers, so that instances of numbers are no more than events necessary to bring such numbers within human experience.

To speak simply of ‘numbers’ or ‘natural numbers’ is an over-simplification. Any analysis of contexts in which numbers occur will disclose two logical types, ordinal and cardinal, each with their own distinctive lexical forms (considered further in chapter 2).¹⁶ Both types presuppose the existence of sets containing more than one member, and capable of being submitted to some sort of intellectual process, which will determine in the case of every set some number characteristic of it. The process is inevitably linguistic,¹⁷ and so in practice will involve counting, at least implicitly.

Order is a property of the members of any set in which there is a recognised relation of precedence and succession. Such a relationship imposes a unique order upon all the members of the set. Theoretically there may be a problem in establishing the relationship, but in practice circumstance tends to define the principle to be applied. Time is the classic case, since in any set based upon points in time (which may, for instance, be the dates of birth of the members of a family) the concept of time automatically de...

Table of contents

• Cover
• Halftitle
• Title
• Copyright
• Contents
• List of figures
• List of tables
• General editor’s preface
• Preface
• 1 The numerical paradox
• 2 Numbers in the written and spoken language
• 3 Alternative number systems
• 4 The culture of numbers
• 5 What’s in a Japanese name?
• 6 Fortune-telling
• 7 Time
• 8 The spatial world of numbers
• 9 The Japanese abacus
• 10 Games-ancient and modern
• 11 The ecology of numbers-past and present
• Notes
• References
• Index