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Culture is based on symbols. Flags, traffic lights, diplomas, and mathematical notation are all, in their various ways, symbols. So foundational is symbolism to humans that without it communication would be impossible. The most symbolic aspect of culture is language, but symbolism also plays a role in religion, politics, art, and literature as well as in kinship, commerce, and science. Symbolism is basic to the construction and conveyance of gender, ethnic, and national identities. It is the primary way by which humans create meaning, classify knowledge, express emotion, and regulate society. The ineluctably human ability to generate and interpret symbols is, for example, what allows us to differentiate winks from blinks (Sapir 1932, p. 493). Although both are roughly identical movements involving the rapid closing and opening of the eye, the former is a meaningful gesture transmitting the conspiratorial message that the winker is in on a secret, whereas the latter is a meaningless twitch. The difference is significant but wholly symbolic. Because symbolism is fundamental to human thought and interaction, it is of concern to the social and cognitive sciences, particularly anthropology and linguistics, though it is also studied by psychology, philosophy, and sociology, and to a lesser extent political science and even economics.

At its most basic level, a symbol is anything that represents another thing by virtue of customary association due to a conceptual connection or perceived resemblance. The English word symbol derives etymologically from the Greek súmbolon, meaning tally, contract, or ticket, which referred originally to a token that was broken in two so that each half could be used to confirm the identity of the other. The word stems from the Greek roots syn - (together) and ballein (to throw), and thus has the approximate connotation of to throw together.


Because virtually anything can serve as a symbol and because a symbol conveys information only insofar as it has meaning to a specific community, the connection between a symbol and its referent is not intrinsic to the symbol itself but rather is a function of agreed upon use, custom, or convention. It is in this sense that language is symbolic. The word water designates the liquid object only insofar as members of the English speech community agree that it does. The liquid has no inherent property that compels us to call it by that name. It could just as well be designated by other sounds, for instance agua in Spanish, mayim in Hebrew, or vo in Tzotzil Maya. Exceptions to this arbitrariness may exist in ethnobiological classification (see Berlin 1992) and onomatopoeia.

The meaning of political and religious symbols, often charged with emotion, are likewise dependent on cultural contexts, even when the same or similar signs are employed across cultures. For Christians the Eucharist is a holy sacrament symbolizing the Body and Blood of Christ, yet pagans may see the consumption of bread and wine as a representation of ritual cannibalism. Or again, the swastika has come to be taboo in much of Europe and the United States due to its historic association with Nazi Germany and contemporary white supremacists, but elsewhere, as in the cases of Hinduism, Buddhism, and Native American religions, it remains a sacred symbol with positive connotations. In religions of Indic origin it is a symbol of auspiciousness, as reflected by its original Sanskrit name svasti, meaning luck, well-being, and fortune; in Hindu traditions it is a solar symbol, and in Buddhist regions it adorns the entrance to some temples. The swastika design is also seen in Native American traditions. To the Navajo the symbol is known as the whirling winds, and was used in curing ceremonies, and as a motifwoven into textiles; among the neighboring Hopi it was a conventional sign associated with clan migrations. In short, symbols are without specific meanings aside from the connotations assigned to them.

Depth Psychology Still, certain studies suggest that some symbolism is universal, due to its rootedness in unconscious processes, developmental stages, or panhuman experiences of the body, eating, and sexuality. Sigmund Freud (1989) maintained that the symbolism found in dreams, myths, fairytales, and linguistic utterances expresses in disguised form unresolved childhood conflicts or taboo urges surrounding sexuality and violence that are repressed in the subconscious of individuals. Jung (1964) viewed certain symbols as archetypes of the collective unconscious. Thus, one encounters universal archetypesthe Trickster, Rebirth, the Heros quest, the Great Mother, and so onnot only in the myths and rituals of tribal peoples, the art of the high Renaissance, and modern science fiction, but also in the dream-work, projective fantasy, and free-associations of the patient involved in psychotherapeutic individuation.

The Human Body Many researchers have posited that the human body provides a template for another set of experiences held in common by all people. Throughout the world, pre-eminence is accorded to the right-hand side in systems of lateral symbolism and dual classification (Needham 1973), while hair is freighted with multiple symbolic meanings and therefore is a focus of ritual in almost all societies. The fact that the same three colors predominate in ritual symbolism cross-culturally may reflect a psychobiological substrate: the common experience of body fluids, through which black is linked to feces, white to semen or breast milk, and red to blood (Turner 1967). However, a caveat is warranted here, for these colors are also worked through local categories of meaning. While black may be associated with feces and therefore ideas of pollution, night, and death in many cultures, in Hinduism it is white, not black, that is associated with death, funerals, and mourning.

Others have suggested that the human body is a natural symbol for any bounded system, not the least of them the well-known organic model of society, in which the categories of the physical body provide the model for the experience of the social body and vice versa (see Douglas 1970).

Alimentary Classification Food constitutes another universal plane of symbolic classification. Claude Lévi-Strauss, who founded the structuralist approach to the analysis of symbols, theorized that the opposition between raw food and cooked food, elaborated symbolically in myths and rituals around the world, is an expression of the universal dichotomy between Nature and Culture (1970). Because in all societies people must not only eat but also marry, he overlays the rules of kinship and marriage on the classification of food. Building on the idea that the boundaries of the natural body and social body reinforce each other reciprocally, Lévi-Strauss demonstrates that eating and intercourse are symbolically equated (although not always consciously) in many societies, making culinary and sexual codes mirror images of each other (1966). In a related vein, Mary Douglas famously argued that the dietary laws in the Old Testament reflect a typology in which the animals prohibited as food to the ancient Israelites were taxonomic anomalies that cross-cut the socially construed ideal categories of creation just as mixed marriages were prohibited because they similarly would produce hybrid children that transected the ideal social divisions ordained by God (1966).


The study of symbolism deals with two different but related issues. One concerns what symbols mean, the other how they work, or the logic by which they come to mean anything in the first place. Analysis depends on a differentiation between signifier (the perceptible vehicle or external form), signified (the meaning, referent, connotation, etc.) and signification (the relation between the two). Some scholars, such as Clifford Geertz, use the word symbol as a blanket term for any object, act, event, quality, or relation which serves as a vehicle for a conception (1973, p. 91). Yet because the word symbol has been used in an enormous variety of ways, other researchers find it necessary to distinguish between symbol, sign, and signal, sometimes making further distinctions by adding index and icon to the list. Despite a large literature on the topic, there is, however, a lack of uniformity as to how this terminology is employed. Still, if one considers the distinctions between symbol, sign, and signal to represent differences in degree rather than kind, there is some consensus as to the way the definitions are drawn.

Signal, Sign, and Symbol A signal generally expresses a relationship between signifier and signified that is dynamic or causal. Animals as well as humans make use of signals, and in both cases the signifiers trigger or incite certain actionsas, for instance, when a male bird arouses the female by signaling with a mating call or car brake lights signal motorists behind to stop. A sign tends to have a singular meaning, in that signifier and signified are closely connected and typically come from the same context, and the signification itself is mostly metonymic that is, a part or attribute stands for the whole. When, for example, a hunter sees a hoofprint of the deer he is pursuing, the hoofprint is a sign of his quarry. In military, technical, and commercial fields signs are often employed as codes, such as Morse code or the North American Industrial Classification System used to designate business type. When signs are used as codes it is because the relation between signifier and signified is conventional rather than intrinsic and because the signification is precise.

Symbols expand the notions of signs and signals. Symbols are characterized by rich meanings that are multiple, fluid, diverse, layered, complex, and frequently predicated on metaphorical associations that assert an analogy between things from different contexts that normally may not be connected. Given that the referents of symbols tend to be general, abstract, and ambiguous, their personally or socially constructed significations may not be apparent except to those who make them.

Whether a signifier is a symbol, signal, or sign is determined not by the object itself but rather by how it is used. In fact, the same signifier can function as all three depending on the situation; for example, the color red functions as a signal in stoplights, as a sign of blood in a painting of the crucified Christ, and as a symbol in a national flag. Moreover, the meanings of symbols, insofar as they are conventional, are context-dependent and variable, both across and within cultures. In ancient Rome red was associated with the god of war, Mars, whereas in China red is an auspicious color associated with luck, money, success, happiness, and traditional wedding attire. In the United States, a red rose is a statement of love, but being in the red means one has suffered economic losses, and seeing red means one is angry.

Icons and the Problem of Likeness Symbols are usually iconic that is, a sensory likeness-relation is intended or interpreted (Firth 1973, p. 75). Of course, from an anthropological perspective, what is seen as the associated or analogous sensory likeness-relation between signifier and signified is culturally determined; as Victor Turner appositely remarks, one cultures analogy is another cultures puzzle (1975, p. 151). Therefore, because iconicity is culturally constructed, many scholars prefer to use the term icon only when there is a geometrical similarity between signifier and signified, as with formal pictures, portraits, or models. Typical icons of this sort, which often involve a change in scale between signified and signifier, include maps, the Roman numeral II, and religious images of the Buddha, Christ, and saints.

While such icons clearly manifest likenesses, or analogous qualities, much symbolism rests on the predication of resemblance between things that are neither ostensibly similar nor physically in contact. Even science relies on symbolism when, associating things that are profoundly unlike, it uses analogies to explain causation, whereas magic uses analogies to connect unlike things through associations of co-occurrence.

Metaphor and Metonym A distinction between metaphor and metonym is basic to symbolism. Metaphor is principally a way of conceiving one thing in terms of another, and its primary function is understanding. Metonymy, on the other hand, has primarily a referential function, that is, it allows us to use one thing to stand for another (Lakoff and Johnson 1980). Metonymy is a form of signification in which an attribute or name of something is used to denote the wider semantic field to which the thing belongs, signifier and signified being drawn from the same general context. Thus, the word brass is a metonym for military officers, just as crown is used metonymically for kingship. Metaphors, on the other hand, are comparisons, similes, or analogies, and rely on a sensory resemblance or asserted conceptual similarity between things belonging to different cultural contexts, and imply the transference of qualities from one context to another. For instance, when a brand of beer uses a crown on its label to assert that it is the king of beers, it is making a metaphoric association, as royalty and alcoholic beverages belong to different domains (Leach 1976, p. 14). Metonyms and metaphors, like signs and symbols, frequently co-occur in the same communication event, with one level of meaning characteristically being played off the other.


Symbols are especially useful in showing what one cannot say ; that is, they express ineffable concepts, abstract ideas, and particularly complex emotional significations that are difficult or impossible to fully articulate. Because they powerfully sum up many things at once, symbols are frequently deployed in political and, especially, religious domains. While the existence of different political parties shows that not everyone agrees about what their country stands for, everyone does agree that their countrys flag stands for their country. One way in which symbols can be used to condense a constellation of meanings is through the invocation of physical attributes that are associated with moral character: The straight or upright man can be contrasted with a man who is crooked or low.

Multivocality Symbols predominate in political and religious contexts because their wide spectrum of connotations, which permits multiple understandings among subdivisions within a population, allows them to appeal to a broad audience. The more public a symbol is, the wider is its range of referentsand the broader its range of signification, the richer and more complex its meaning becomes, allowing for diverse and sometimes even contradictory interpretations. Key symbols (Ortner 1973), those that characterize whole peoples, nations, religions, and political movements, tend to be among the most abstract and polysemous, yet still provide basic orientations for thought and actionsuch as with the Virgin of Guadalupe, who is used to symbolize Mexico.

The radical polysemy of symbolic signification led anthropologist Victor Turner to conclude that an outstanding feature of all symbols was what he termed their multivocality ; that is, they stand for many objects, activities and relationships; there is not a one-to-one relationship between symbol and referent but a one-to-many relationship (1967, p. 284). According to Turner, one must consider three fields of meaning: the exegetical meaning, or what members of the culture say the symbol means; the operational meaning, revealed by how the symbol is used; and the positional meaning, which derives from the relation between a symbol and other objects and symbols in the same or related cultural complexes (pp. 20, 284285). Symbols are further characterized by a polarization of meaning (p. 28), one pole having to do with the symbols sensory aspects or the emotional impulses it arouses, the other indexing related normative values or principles of ideology or social organization.

The Logic of Binary Oppositions For Lévi-Strauss in his studies of symbols in myth, totemism, and other systems of symbolic classification (1966), symbols cannot be interpreted as having meaning in themselves but only in terms of structural opposition, a binary logic that exists in culture because it is in fact a reflection of the binary structure of the human mind. Drawing intellectual capital from the structural linguistics of Saussure (1966) and Jakobson (1956), as well as mathematics and the natural sciences, Lévi-Strauss reasoned that meaning was created symbolically in culture in a way that was analogous to the way it was created in information theory and in language. In the digital world of computers, everything from words to pictures to music is based on a binary logic that involves only two numerical symbols, 1 and 0. In linguistic phonemic analysis, meaning comes about through discerning phonetic differences within minimal pairs. For instance b and p in English are both labial stops, the only difference being that the former is voiced and the latter is not, yet it is that minimal difference that allows us to differentiate between a bat and a pat. So too, in culture, symbols have meaning because they also are based on binary oppositionsraw/cooked, hot/cold, high/low, rough/smooth, light/dark, right/left, and so onthat reflect sensory contrasts and ultimately relate back to the primary symbolic opposition between nature and culture. Moreover, not just oppositions but also the logical relations between sets of oppositions are important to the analysis of symbolic systems. These logical relations may be expressed in terms of reciprocity, analogy, homology, reflection, inversion, isomorphism, and so on.

Models of and Models For Another anthropologist, Clifford Geertz, took his cues not from the sciences but instead from literature, philosophy, and the humanities generally. He takes an interpretive approach to culture, which in his view is essentially a system of symbols, the analysis of which is akin to formulating a critical reading of a manuscript or interpreting a poem, as culture itself is likened to an assemblage of texts. Geertz proposes that cultural patterns, that is, systems or complexes of symbols are artifacts in the public domain; they are not private cognitions or meanings accessible only through the specialized techniques of psychologists and philosophers (1973, pp. 9192). Geertz also holds that cultural patterns are models composed of sets of symbols whose relations to one another model relations among other psychological, social, and physical entities, activities, processes, and so forth by paralleling or simulating them. Geertzs most novel insight, however, comes from his observation that the term model has two senses, an of sense and a for sense, and it is this dual aspect that gives symbols their special quality, for when they are configured together into cultural patterns they are both a model of reality and a model for reality; that is, they both reflect the world and shape it. If one sees religion as a cultural system, as Geertz does, and as a complex of symbols, then the models on which these constructs are based have this dual aspect in that they both describe the world as it is and prescribe the way it ought to be.

Multiplex and Transflective Displays Symbols display two other noteworthy characteristics: They are multiplex as well as transflective. Both ideas derive from the electrical sciences. As used in electronics, telecommunications, and computer networking, the term multiplex refers to the simultaneous transmission of two or more signals along one communications channel or the sharing of information in a single medium. Symbols can be thought of as wires or channels. When, for example, a man sends a red rose to the object of his affection, two messages symbolizing love are being communicated simultaneously through the same communications channel, yet they are being modulated via different sensory receptors (namely, vision and smell): The red color connotes the heart and passion and the scent connotes the sweetness of romance. This multiplex modulation or sensory fusion causes many symbols, especially metaphors, to evoke experiences comparable to synesthesia the coupling of different bodily sensations or the crossing of sensory wirescompelling persons to hear colors, taste sounds, or in the case of the rose, simultaneously see as well as smell something felt.

The term transflective is used in electrical engineering to refer to a type of liquid crystal display (LCD) screen in which the pixels are illuminated from both the front of the monitors screen by ambient light and from behind the screen by an internal light. Analogously, symbols, especially in ritual, are regarded as both transmitting and reflecting the spiritual effluence that animates them and makes them foci of intense cultural meaning. A symbol is illuminated from behind in that it transmits general meanings, moods, energy, and radiance from a source that is internal to itthat is, from a power that is within or behind the symbol. It is also reflective, or illuminated from the front, in that it absorbs the particular conditions, meanings, emotions, and intentions projected onto it in a particular moment and reflects these back out again. In the study of ritual, one can think in terms of the dual illumination coming from and reflected on the Christian cross, or coming from and reflected on quartz crystals used in Navajo rituals. In varying degrees all symbols, but especially sacred symbols, both transmit public meanings and reflect private ones, and it is this dual aspect that makes them boundless sources of meaning, energy, and significance.

SEE ALSO Anthropology; Anthropology, Linguistic; Communication; Critical Theory; Culture; Disease; Food; Freud, Sigmund; Geertz, Clifford; Hinduism; Identity; Lévi-Strauss, Claude; Myth and Mythology; Nazism; Philosophy; Psychology; Rhetoric; Rites of Passage; Rituals; Romance; Science Fiction; Semiotics; Signals; Sociology; Totemism; Turner, Victor; Universalism


Berlin, Brent. 1992. Ethnobiological Classification: Principles of Categorization of Plants and Animals in Traditional Societies. Princeton, NJ: Princeton University Press.

Douglas, Mary. 1966. Purity and Danger: An Analysis of Concepts of Pollution and Taboo. New York: Praeger.

Douglas, Mary. 1970. Natural Symbols: Explorations in Cosmology. London: Barrie & Jenkins; New York: Basic Books.

Firth, Raymond. 1973. Symbols: Public and Private. Ithaca, NY: Cornell University Press.

Freud, Sigmund. [1917] 1989. Introductory Lectures on PsychoAnalysis. Trans. and ed. James Strachey. New York: Norton.

Geertz, Clifford. 1973. The Interpretation of Cultures: Selected Essays. New York: Basic Books.

Jakobson, Roman, and Morris Halle. 1956. Fundamentals of Language. Janua Linguarum: Series Minor 1. The Hague: Mouton.

Jung, C. G., ed. 1964. Man and His Symbols. Garden City, NY: Anchor Books/Doubleday.

Lakoff, George, and Mark Johnson. 1980. Metaphors We Live By. Chicago: University of Chicago Press.

Leach, Edmund. 1976. Culture and Communication: The Logic by Which Symbols Are Connected: An Introduction to the Use of Structuralist Analysis in Social Anthropology. Cambridge, U.K.: Cambridge University Press.

Lévi-Strauss, Claude. 1966. The Savage Mind. Chicago: University of Chicago Press.

Lévi-Strauss, Claude. 1970. The Raw and the Cooked: Introduction to a Science of Mythology. Vol. 1. Trans. John and Doreen Weightman. New York: Harper and Row.

Sapir, Edward. 1932. Symbolism. In Encyclopedia of the Social Sciences, ed. Edwin R. A. Seligman and Alvin Johnson, Vol. 14, 492495. New York: Macmillan.

Saussure, Ferdinand de. 1966. Course in General Linguistics. Ed. Charles Bally and Albert Sechehaye, with Albert Reidlinger; trans. Wade Baskin. New York: McGraw-Hill Paperbacks.

Turner, Victor. 1967. The Forest of Symbols: Aspects of Ndembu Ritual. Ithaca, NY: Cornell University Press.

Turner, Victor. 1975. Symbolic Studies. Annual Review of Anthropology 4: 145161.

Jerome M. Levi


views updated May 29 2018


Symbols are part of the language of mathematics. The use of symbols gives mathematics the power of generality: The ability to focus not only on a specific object, but also on a collection of objects. For instance, variables symbols with the ability to vary in value used in place of numbersmake it possible to write general equations. Consider the equation 3 + 4 = 7. This equation is specific. Suppose we are interested in all pairs of numbers whose sum is equal to 7. Using variables, x and y, to denote the two numbers, we would write the general equation x + y = 7. The variables, x and y, stand for many different pairs of numbers; x can be 5 and y can be 2 or x can be 9 and y can be 2. The only condition is that the sum of x and y is 7.

Symbols also include special notation for mathematical operations, like + for addition and for taking the square root. Some common symbols and their uses are explained in the accompanying table.

Basic Mathematical Symbols

The Set. The foundation of mathematics rests on the concept of a set, which is a collection of objects that share a well-defined characteristic. The elements of a set are written in braces {}. An element x that belongs to a set A is written as x A. An element y that does not belong to A is written as y A. {0} is a set that contains zero as its only element. This set has one element. {} is the empty set and does not contain any element. The empty set is also called a null set and sometimes written with the symbol Ø.

Operations. Numbers are the building blocks of mathematics. They can be combined by four operations: addition and its inverse operation,

subtraction, and multiplication and its inverse operation, division. The additive inverse of a number b is b and the sum of a number and its additive inverse is always 0, that is, b + (b) = 0. The additive inverse of 4 is 4. Similarly, the multiplicative inverse of a nonzero number b is b1, or , and the product of a number and its multiplicative inverse is always 1, that is, . The multiplicative inverse of 7 is.

Size. Numbers can be compared according to their magnitude, or size. Given any two numbers, say x and y, there are three possibilities: x is equal to y (x = y ), or x is less than y (x < y ), or x is greater than y (x > y ). Two numbers, x and y, can also be compared by taking their ratio, x :y, or x /y. A number percent, say 5 percent denotes the ratio of 5 to 100 or 5/100. In some problems, it is not important to know if a given number, say x, is positive or negative. The only important thing is its magnitude and it is represented by its absolute value, |x |. For instance, |5| = 5 and |5| = 5.

Exponents. If a number is multiplied by itself two or more times, it can be written more compactly using an exponent that appears as a superscript to the right of the number. For example, if 4 is multiplied by itself three times, then it can be written as 4 × 4 × 4, or 43, where 3 is the exponent. An exponent is also called a power. In general, x n is read as "x raised to the power n." Raising a number to powers that are fractional, like ½ or , is called a radical, or root of the number. denotes the n th root of the number b ; where n is called the index and b is called the radicand. For n = 2, the index is omitted and is the square root of b. For n = 3, is called the cube root of b.

Functions. A fundamental idea in mathematics is that of a function that describes a relationship between two quantities. In symbols, it is written as y = f (x ) and read as "y is the function of x," which means that the value of y depends on x. A function is sometimes called a map, or mapping. Logarithm, y loga x, is a particular type of function. By definition, a logarithm is an exponent. If 10x = y, then log10 y = x.

Algebra. In algebra, numbers are represented as both variables and constants. A variable is a number whose value can change. Variables are mostly denoted by lowercase, terminating letters of the alphabet like x, y, or z. A constant is a fixed number, denoted mostly by first few lower case letters a, b, and c, or k. Algebraic expressions called polynomials contain one or more variable and/or constant terms. For example, 3x, and x2 + 3x + 2 are all polynomials: 3x is a monomial (one term), is a binomial (two terms), and x 2 + 3x + 2 is a trinomial (three terms). A constant number that multiplies a variable in an equation, or polynomial, is called a coefficient. For example, 2 is a coefficient of 2x in the equation 2x + 3 = 0. In ax 2, a is the coefficient of x 2.

Equations. Solving different types of equations appears in many situations in mathematics. The simplest equation is linear, in which the highest power of the variable, x, is 1, for example, 3x + 2 = 1. If the highest power of the variable is 2, then the equation is a quadratic equation. For example, x 2 = 4 and 2x 2 + 3x + 1 = 0 are quadratic equations.

Calculus. Calculus is a branch of mathematics that partly deals with rate of changes. For a variable x, Δx denotes a small change in x. Further, measures the change in variable y with respect to change in x. When Δx becomes increasingly smaller and approaches 0, the rate of change equals the instantaneous rate of change and is denoted by and is called the derivative of y with respect to x. Also, calculus deals with finding the area of a region under the curve, or graph, of a function f (x ). If the region is bounded by lines x = a and x = b, then the area is denoted by the integral of the function f. In symbols, it is written as

see also Algebra; Calculus; Functions and Equations; Number System, Real.

Rafiq Ladhani


Amdahl, Kenn, and Jim Loats. Algebra Unplugged. Broomfield, CO: Clearwater Publishing Co., 1995.

Dugopolski, Mark. Elementary Algebra, 2nd ed. Boston: Addison-Wesley Publishing Company, 1996.

Dunham, William. The Mathematical Universe. New York: John Wiley & Sons Inc., 1994.

Miller, Charles D., Vern E. Heeren, and E. John Hornsby, Jr. Mathematical Ideas, 6th ed. New York: Harper Collins Publishers, 1990.


views updated May 29 2018

Symbols, symbolism (Gk., sumbolon, ‘sign, token, pledge’; sumballein, ‘cast together’). The representation in visible form of ideas, beliefs, actions, persons, events, etc., frequently (in the religious case) of transcendent realities, which bring the observer into connection and participation. So pervasive is the human use of symbols that E. Cassirer (An Essay on Man, 1944) called the human species animal symbolicum. Although it might seem obvious to define a symbol as that which stands for something which it represents (as a flag might be said to ‘stand for’ the country which it represents), in fact a symbol involves far more complex conditions of meaning—to be seen not least in the fact that symbols frequently stand for themselves, especially in the religious case (see R. Wagner, Symbols that Stand for Themselves, 1986): the symbolic actions of the Hebrew prophets, for example, do not stand for (i.e. summarize in advance) a future event, but rather bring the reality of that event into being in the present. Beyond that, symbols may be non-referential and of effect in creating community and meaning (see A. P. Cohen, The Symbolic Construction of Community, 1985).

Since religions in that way are often evocative in their use of language, it is not surprising that the religious use of symbols can be paralleled in the turn to symbolism in arts and literature at the end of the 19th cent. The Symbolists were a loose association of artists and writers who turned strongly against the realist (and referential) ambitions of, for example, the Pre-Raphaelites or the neo-Impressionists, or of such writers as Flaubert and Zola. The importance of decoration in the symbolist sense is profoundly important in religious symbolism, though largely overlooked: there is an aesthetic satisfaction no matter what other purposes are being served. Most accounts of religious symbolism look at their function, especially as codes. An early meaning of sumbolon in Christianity is that of creed, where the function of symbols in compressing (Gk., sumballein, ‘to throw together’) meaning and making it publicly available is emphasized. As C. S. Peirce realized, humans use different kinds of signs and symbols, each bearing some of the characteristics of the others. As a consequence of his work, the study of symbolism is firmly embedded in semiotics (Gk., sēma, ‘a sign’). Peirce drew a distinction between three types of sign: icon, index, and symbol. An icon is a sign containing some of the qualities associated with the thing signified (e.g. maps and diagrams); an index is a sign which is in a dynamic relation with the thing signified and calls attention to what is signified (e.g. the column of mercury in a thermometer measuring temperature and indicating health or illness); a symbol is a conventional sign with an agreed connotation. Symbols are economies of statement and feeling which conserve successful accounts of context (success being measured crudely by persistence) and which evoke coherence by their power to unite immense diversities of human being and experience. But equally they set forward new opportunities of exegesis and action. See also FEMININE SYMBOLS AND RELIGION; ICONOGRAPHY.

Signs (Paranormal)

views updated May 23 2018

Signs (Paranormal)

At various moments in history and in times of great stress, suffering, and persecution, reports of paranormal signs (believed to portend great events) frequently emerged. Under these conditions it was not unusual for ecstatic states to become epidemic, prophecies to be uttered, and unusual physical phenomena to appear. Many of these reports appear to be a mixture of misobservation of mundane if unusual occurrences and hallucinations.

The ancient historians Josephus and Tacitus wrote of fearful sights and great signs from heaven before the judgment on Jerusalem. When, three centuries later, Julian the Apostate attempted to rebuild Jerusalem, fiery balls burst forth upon the workmen and took strange shapes. This was recorded not only by Julian's own historian but by Jewish and non-Roman writers as well. Many accounts testify of the signs and wonders during the persecution of the Huguenots in France.

From the dawn of printing onward, unnatural events and prodigies of nature became the subject of broadside balladsheets and chapbook pamphlets, the street literature of poor people. Monstrous births and other signs and wonders were made the occasion for moralizing about the sins of the day and predicted divine judgment. Even in modern times, visions of the Virgin Mary are often considered signs of divine wrath at a sinful world.

(See also Fatima ; Garabandal )


Eniatos. Mirabilis Annus; or, The Year of Prodigies and Wonders; Being a Collection of Several Signs That Have Been Seen in the Heavens, in the Earth, and in the Waters, Together with Many Remarkable Accidents and Judgments Within the Space of One Year Last Past. London, 1661.

Grey, E. Howard. Visions, Previsions and Miracles in Modern Times. London: L. N. Fowler, 1915.

Rollins, Hyder E., ed. The Pack of Autolycus or Strange and Terrible News of Ghosts, Apparitions, Monstrous Births, Showers of Wheat, Judgments of God, and other Prodigious and Fearful Happenings as told in Broadside Ballads of the Years 1624-1693. Cambridge, Mass.: Harvard University Press, 1927.

Thompson, C. J. S. The Mystery and Lore of Monsters. London: Williams & Norgate, 1930. Reprint, New Hyde Park, N.Y.: University Books, 1968.


views updated May 29 2018


operation, etc.


AND operation, conjunction

∧ .

OR operation, disjunction

∨ +

NOT operation, negation

′ ¬ ∼

NAND operation

| Δ

NOR operation

↓ ∇

For set S and/or set T:

x is a member of S


x is not a member of S


S is a subset of T


S is a proper subset of T


complement of S


union of S and T


intersection of S and T


Cartesian product of S and T

S × T



function of x

f(x), etc.

function f from set X to set Y

f: XY

inverse function


inverse relation


sum, with limits

i = 1n

integral, with limits

ba dx

elements of matrix A


transpose of matrix A


inverse of matrix A



— ≡


— ≡


→ ⇒

general binary operation


universal quantifier

existential quantifier

greater than


greater than or equal to

less than


less than or equal to

approx. equal to

not equal to



views updated Jun 27 2018

Signs ★★★ 2002 (PG-13)

Shyamalan takes on crop circles in this eerily potent psycho-thriller. Widowed father Gibson, a lapsed minister, lives on a farm with children Culkin and Breslin, along with younger brother Phoenix when things start to get strange. Everything seems normal, but even simple everyday actions are steeped in the brand of moodiness and unspoken dread that Shyamalan does best. By the time mysterious circles appear in the cornfields, it's clear that the question of whether or not aliens are to blame for the crop circles is secondary to how the characters will react. Quiet and intense, what doesn't happen is as important as what does in this top-notch suspenser. Film was shot in the director's native Pennsylvania. 120m/C VHS, DVD . US Mel Gibson, Joaquin Rafael (Leaf) Phoenix, Rory Culkin, Abigail Breslin, Cherry Jones, Patricia Kalember, M. Night Shyamalan; D: M. Night Shyamalan; W: M. Night Shyamalan; C: Tak Fujimoto; M: James Newton Howard.


views updated May 14 2018

Signs: see SYMBOLS.