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148-470: In communications and information processing , code is a system of rules to convert information —such as a letter , word , sound, image, or gesture —into another form, sometimes shortened or secret , for communication through a communication channel or storage in a storage medium . An early example is an invention of language , which enabled a person, through speech , to communicate what they thought, saw, heard, or felt to others. But speech limits
296-415: A {\displaystyle g(x)=a} and h ( x ) = b {\displaystyle h(x)=b} . As f ( g ( x ) ) = f ( h ( x ) ) {\displaystyle f(g(x))=f(h(x))} , one has f ∘ g = f ∘ h , {\displaystyle f\circ g=f\circ h,} by the uniqueness in the definition of
444-403: A 1 , . . . , a k {\displaystyle a_{1},...,a_{k}} in A {\displaystyle A} . The operations that must be preserved by a homomorphism include 0-ary operations , that is the constants. In particular, when an identity element is required by the type of structure, the identity element of the first structure must be mapped to
592-418: A ) = f ( b ) {\displaystyle f(a)=f(b)} . By definition of the free object F {\displaystyle F} , there exist homomorphisms g {\displaystyle g} and h {\displaystyle h} from F {\displaystyle F} to A {\displaystyle A} such that g ( x ) =
740-476: A code , i.e. a sign system that is able to express the idea, for instance, through visual or auditory signs. The message is sent to a destination, who has to decode and interpret it to understand it. In response, they formulate their own idea, encode it into a message, and send it back as a form of feedback. Another innovation of Schramm's model is that previous experience is necessary to be able to encode and decode messages. For communication to be successful,
888-413: A code word from some dictionary, and concatenation of such code words give us an encoded string. Variable-length codes are especially useful when clear text characters have different probabilities; see also entropy encoding . A prefix code is a code with the "prefix property": there is no valid code word in the system that is a prefix (start) of any other valid code word in the set. Huffman coding
1036-437: A coding system to express information in the form of a message. The message is sent through a channel to a receiver who has to decode it to understand it. The main field of inquiry investigating communication is called communication studies . A common way to classify communication is by whether information is exchanged between humans, members of other species, or non-living entities such as computers. For human communication,
1184-562: A fuzzy concept that manifests in degrees. In this view, an exchange varies in how interpersonal it is based on several factors. It depends on how many people are present, and whether it happens face-to-face rather than through telephone or email. A further factor concerns the relation between the communicators: group communication and mass communication are less typical forms of interpersonal communication and some theorists treat them as distinct types. Interpersonal communication can be synchronous or asynchronous. For asynchronous communication,
1332-440: A military salute . Proxemics studies how personal space is used in communication. The distance between the speakers reflects their degree of familiarity and intimacy with each other as well as their social status. Haptics examines how information is conveyed using touching behavior, like handshakes, holding hands, kissing, or slapping. Meanings linked to haptics include care, concern, anger, and violence. For instance, handshaking
1480-504: A sequence of symbols over T. The extension C ′ {\displaystyle C'} of C {\displaystyle C} , is a homomorphism of S ∗ {\displaystyle S^{*}} into T ∗ {\displaystyle T^{*}} , which naturally maps each sequence of source symbols to a sequence of target symbols. In this section, we consider codes that encode each source (clear text) character by
1628-464: A basis. If a free object over x {\displaystyle x} exists, then every left cancelable homomorphism is injective : let f : A → B {\displaystyle f\colon A\to B} be a left cancelable homomorphism, and a {\displaystyle a} and b {\displaystyle b} be two elements of A {\displaystyle A} such f (
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#17327647006161776-498: A central contrast is between verbal and non-verbal communication . Verbal communication involves the exchange of messages in linguistic form, including spoken and written messages as well as sign language . Non-verbal communication happens without the use of a linguistic system , for example, using body language , touch, and facial expressions. Another distinction is between interpersonal communication , which happens between distinct persons, and intrapersonal communication , which
1924-551: A channel have an impact on the code and cues that can be used to express information. For example, typical telephone calls are restricted to the use of verbal language and paralanguage but exclude facial expressions. It is often possible to translate messages from one code into another to make them available to a different channel. An example is writing down a spoken message or expressing it using sign language. The transmission of information can occur through multiple channels at once. For example, face-to-face communication often combines
2072-405: A conversation, where the listener may respond to a speaker by expressing their opinion or by asking for clarification. Interaction models represent the process as a form of two-way communication in which the communicators take turns sending and receiving messages. Transaction models further refine this picture by allowing representations of sending and responding at the same time. This modification
2220-432: A corresponding sequence of amino acids that form a protein molecule; a type of codon called a stop codon signals the end of the sequence. In mathematics , a Gödel code was the basis for the proof of Gödel 's incompleteness theorem . Here, the idea was to map mathematical notation to a natural number (using a Gödel numbering ). There are codes using colors, like traffic lights , the color code employed to mark
2368-473: A different sense, the term communication refers to the message that is being communicated or to the field of inquiry studying communicational phenomena . The precise characterization of communication is disputed. Many scholars have raised doubts that any single definition can capture the term accurately. These difficulties come from the fact that the term is applied to diverse phenomena in different contexts, often with slightly different meanings. The issue of
2516-403: A field F {\displaystyle F} has a quadratic form , called a norm , N : A → F {\displaystyle N:A\to F} , which is a group homomorphism from the multiplicative group of A {\displaystyle A} to the multiplicative group of F {\displaystyle F} . Several kinds of homomorphisms have
2664-423: A form that the recipient understands, such as English or/and Spanish. One reason for coding is to enable communication in places where ordinary plain language , spoken or written, is difficult or impossible. For example, semaphore , where the configuration of flags held by a signaler or the arms of a semaphore tower encodes parts of the message, typically individual letters, and numbers. Another person standing
2812-430: A free object over x {\displaystyle x} , consider the set W {\displaystyle W} of the well-formed formulas built up from x {\displaystyle x} and the operations of the structure. Two such formulas are said equivalent if one may pass from one to the other by applying the axioms ( identities of the structure). This defines an equivalence relation , if
2960-598: A front for the American Black Chamber run by Herbert Yardley between the First and Second World Wars. The purpose of most of these codes was to save on cable costs. The use of data coding for data compression predates the computer era; an early example is the telegraph Morse code where more-frequently used characters have shorter representations. Techniques such as Huffman coding are now used by computer-based algorithms to compress large data files into
3108-462: A given context". This means that the speaker is aware of the social and cultural context in order to adapt and express the message in a way that is considered acceptable in the given situation. For example, to bid farewell to their teacher, a student may use the expression "Goodbye, sir" but not the expression "I gotta split, man", which they may use when talking to a peer. To be both effective and appropriate means to achieve one's preferred outcomes in
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#17327647006163256-419: A great distance away can interpret the flags and reproduce the words sent. In information theory and computer science , a code is usually considered as an algorithm that uniquely represents symbols from some source alphabet , by encoded strings, which may be in some other target alphabet. An extension of the code for representing sequences of symbols over the source alphabet is obtained by concatenating
3404-441: A group, is isomorphic to the additive group of the integers; for rings , the free object on x {\displaystyle x} is the polynomial ring Z [ x ] ; {\displaystyle \mathbb {Z} [x];} for vector spaces or modules , the free object on x {\displaystyle x} is the vector space or free module that has x {\displaystyle x} as
3552-422: A homomorphism between these two groups. It is even an isomorphism (see below), as its inverse function , the natural logarithm , satisfies and is also a group homomorphism. The real numbers are a ring , having both addition and multiplication. The set of all 2×2 matrices is also a ring, under matrix addition and matrix multiplication . If we define a function between these rings as follows: where r
3700-555: A language but rather non-verbal communication. It includes many forms, like gestures, postures, walking styles, and dance. Facial expressions, like laughing, smiling, and frowning, all belong to kinesics and are expressive and flexible forms of communication. Oculesics is another subcategory of kinesics in regard to the eyes. It covers questions like how eye contact, gaze, blink rate, and pupil dilation form part of communication. Some kinesic patterns are inborn and involuntary, like blinking, while others are learned and voluntary, like giving
3848-479: A long history and how people exchange information has changed over time. These changes were usually triggered by the development of new communication technologies. Examples are the invention of writing systems , the development of mass printing, the use of radio and television, and the invention of the internet. The technological advances also led to new forms of communication, such as the exchange of data between computers . The word communication has its root in
3996-412: A more compact form for storage or transmission. Character encodings are representations of textual data. A given character encoding may be associated with a specific character set (the collection of characters which it can represent), though some character sets have multiple character encodings and vice versa. Character encodings may be broadly grouped according to the number of bytes required to represent
4144-439: A person may verbally agree with a statement but press their lips together, thereby indicating disagreement non-verbally. There are many forms of non-verbal communication. They include kinesics , proxemics , haptics , paralanguage , chronemics , and physical appearance. Kinesics studies the role of bodily behavior in conveying information. It is commonly referred to as body language , even though it is, strictly speaking, not
4292-522: A person or an object looks like and can also convey other ideas and emotions. In some cases, this type of non-verbal communication is used in combination with verbal communication, for example, when diagrams or maps employ labels to include additional linguistic information. Traditionally, most research focused on verbal communication. However, this paradigm began to shift in the 1950s when research interest in non-verbal communication increased and emphasized its influence. For example, many judgments about
4440-410: A semigroup, is isomorphic to the additive semigroup of the positive integers; for monoids , the free object on x {\displaystyle x} is { 1 , x , x 2 , … , x n , … } , {\displaystyle \{1,x,x^{2},\ldots ,x^{n},\ldots \},} which, as, a monoid, is isomorphic to the additive monoid of
4588-464: A shopping list. Another use is to unravel difficult problems, as when solving a complex mathematical equation line by line. New knowledge can also be internalized this way, like when repeating new vocabulary to oneself. Because of these functions, intrapersonal communication can be understood as "an exceptionally powerful and pervasive tool for thinking." Based on its role in self-regulation , some theorists have suggested that intrapersonal communication
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4736-659: A single character: there are single-byte encodings, multibyte (also called wide) encodings, and variable-width (also called variable-length) encodings. The earliest character encodings were single-byte, the best-known example of which is ASCII . ASCII remains in use today, for example in HTTP headers . However, single-byte encodings cannot model character sets with more than 256 characters. Scripts that require large character sets such as Chinese, Japanese and Korean must be represented with multibyte encodings. Early multibyte encodings were fixed-length, meaning that although each character
4884-411: A skunk!"), or AYYLU ("Not clearly coded, repeat more clearly."). Code words were chosen for various reasons: length , pronounceability , etc. Meanings were chosen to fit perceived needs: commercial negotiations, military terms for military codes, diplomatic terms for diplomatic codes, any and all of the preceding for espionage codes. Codebooks and codebook publishers proliferated, including one run as
5032-515: A specific name, which is also defined for general morphisms . An isomorphism between algebraic structures of the same type is commonly defined as a bijective homomorphism. In the more general context of category theory , an isomorphism is defined as a morphism that has an inverse that is also a morphism. In the specific case of algebraic structures, the two definitions are equivalent, although they may differ for non-algebraic structures, which have an underlying set. More precisely, if
5180-439: A teacher may decide to present some information orally and other information visually, depending on the content and the student's preferred learning style. This underlines the role of a media-adequate approach. Communicative competence is the ability to communicate effectively or to choose the appropriate communicative behavior in a given situation. It concerns what to say, when to say it, and how to say it. It further includes
5328-477: A thumb . It often happens simultaneously with verbal communication and helps optimize the exchange through emphasis and illustration or by adding additional information. Non-verbal cues can clarify the intent behind a verbal message. Using multiple modalities of communication in this way usually makes communication more effective if the messages of each modality are consistent. However, in some cases different modalities can contain conflicting messages. For example,
5476-435: A transmission of information brought about by the interaction of several components, such as a source, a message, an encoder, a channel, a decoder, and a receiver. The transmission view is rejected by transactional and constitutive views, which hold that communication is not just about the transmission of information but also about the creation of meaning. Transactional and constitutive perspectives hold that communication shapes
5624-448: A universal property. As f {\displaystyle f} is left cancelable, one has g = h {\displaystyle g=h} , and thus a = b {\displaystyle a=b} . Therefore, f {\displaystyle f} is injective. Existence of a free object on x {\displaystyle x} for a variety (see also Free object § Existence ): For building
5772-419: A way that follows social standards and expectations. Some definitions of communicative competence put their main emphasis on either effectiveness or appropriateness while others combine both features. Many additional components of communicative competence have been suggested, such as empathy , control, flexibility, sensitivity, and knowledge. It is often discussed in terms of the individual skills employed in
5920-461: A way that may be generalized to any class of morphisms. A homomorphism is a map between two algebraic structures of the same type (e.g. two groups, two fields, two vector spaces), that preserves the operations of the structures. This means a map f : A → B {\displaystyle f:A\to B} between two sets A {\displaystyle A} , B {\displaystyle B} equipped with
6068-498: A wider sense, encompassing any form of linguistic communication, whether through speech, writing, or gestures. Some of the challenges in distinguishing verbal from non-verbal communication come from the difficulties in defining what exactly language means. Language is usually understood as a conventional system of symbols and rules used for communication. Such systems are based on a set of simple units of meaning that can be combined to express more complex ideas. The rules for combining
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6216-394: Is a (homo)morphism, it has an inverse if there exists a homomorphism such that If A {\displaystyle A} and B {\displaystyle B} have underlying sets, and f : A → B {\displaystyle f:A\to B} has an inverse g {\displaystyle g} , then f {\displaystyle f}
6364-432: Is a homomorphism. If ∗ {\displaystyle *} is a binary operation of the structure, for every pair x {\displaystyle x} , y {\displaystyle y} of elements of B {\displaystyle B} , one has and g {\displaystyle g} is thus compatible with ∗ . {\displaystyle *.} As
6512-439: Is a key factor regarding whether a person is able to reach their goals in social life, like having a successful career and finding a suitable spouse. Because of this, it can have a large impact on the individual's well-being . The lack of communicative competence can cause problems both on the individual and the societal level, including professional, academic, and health problems. Barriers to effective communication can distort
6660-611: Is a monomorphism if, for any pair g {\displaystyle g} , h {\displaystyle h} of morphisms from any other object C {\displaystyle C} to A {\displaystyle A} , then f ∘ g = f ∘ h {\displaystyle f\circ g=f\circ h} implies g = h {\displaystyle g=h} . These two definitions of monomorphism are equivalent for all common algebraic structures. More precisely, they are equivalent for fields , for which every homomorphism
6808-563: Is a monomorphism in the category of topological spaces . For proving that, conversely, a left cancelable homomorphism is injective, it is useful to consider a free object on x {\displaystyle x} . Given a variety of algebraic structures a free object on x {\displaystyle x} is a pair consisting of an algebraic structure L {\displaystyle L} of this variety and an element x {\displaystyle x} of L {\displaystyle L} satisfying
6956-399: Is a monomorphism, and for varieties of universal algebra , that is algebraic structures for which operations and axioms (identities) are defined without any restriction (the fields do not form a variety, as the multiplicative inverse is defined either as a unary operation or as a property of the multiplication, which are, in both cases, defined only for nonzero elements). In particular,
7104-456: Is a real number, then f is a homomorphism of rings, since f preserves both addition: and multiplication: For another example, the nonzero complex numbers form a group under the operation of multiplication, as do the nonzero real numbers. (Zero must be excluded from both groups since it does not have a multiplicative inverse , which is required for elements of a group.) Define a function f {\displaystyle f} from
7252-415: Is a split monomorphism if there exists a homomorphism g : B → A {\displaystyle g\colon B\to A} such that g ∘ f = Id A . {\displaystyle g\circ f=\operatorname {Id} _{A}.} A split monomorphism is always a monomorphism, for both meanings of monomorphism . For sets and vector spaces, every monomorphism
7400-505: Is a split monomorphism, but this property does not hold for most common algebraic structures. An injective homomorphism is left cancelable : If f ∘ g = f ∘ h , {\displaystyle f\circ g=f\circ h,} one has f ( g ( x ) ) = f ( h ( x ) ) {\displaystyle f(g(x))=f(h(x))} for every x {\displaystyle x} in C {\displaystyle C} ,
7548-415: Is another influential linear transmission model. It is based on the idea that a source creates a message, which is then translated into a signal by a transmitter. Noise may interfere with and distort the signal. Once the signal reaches the receiver, it is translated back into a message and made available to the destination. For a landline telephone call, the person calling is the source and their telephone
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#17327647006167696-401: Is another negative factor. It concerns influences that interfere with the message on its way to the receiver and distort it. Crackling sounds during a telephone call are one form of noise. Ambiguous expressions can also inhibit effective communication and make it necessary to disambiguate between possible interpretations to discern the sender's intention. These interpretations depend also on
7844-520: Is at its core non-verbal and that words can only acquire meaning because of non-verbal communication. The earliest forms of human communication, such as crying and babbling, are non-verbal. Some basic forms of communication happen even before birth between mother and embryo and include information about nutrition and emotions. Non-verbal communication is studied in various fields besides communication studies, like linguistics, semiotics , anthropology , and social psychology . Interpersonal communication
7992-617: Is based on five fundamental questions: "Who?", "Says what?", "In which channel?", "To whom?", and "With what effect?". The goal of these questions is to identify the basic components involved in the communicative process: the sender, the message, the channel , the receiver , and the effect. Lasswell's model was initially only conceived as a model of mass communication, but it has been applied to other fields as well. Some communication theorists, like Richard Braddock, have expanded it by including additional questions, like "Under what circumstances?" and "For what purpose?". The Shannon–Weaver model
8140-624: Is between natural and artificial or constructed languages . Natural languages, like English , Spanish , and Japanese , developed naturally and for the most part unplanned in the course of history. Artificial languages, like Esperanto , Quenya , C++ , and the language of first-order logic , are purposefully designed from the ground up. Most everyday verbal communication happens using natural languages. Central forms of verbal communication are speech and writing together with their counterparts of listening and reading. Spoken languages use sounds to produce signs and transmit meaning while for writing,
8288-664: Is bijective. In fact, f {\displaystyle f} is injective , as f ( x ) = f ( y ) {\displaystyle f(x)=f(y)} implies x = g ( f ( x ) ) = g ( f ( y ) ) = y {\displaystyle x=g(f(x))=g(f(y))=y} , and f {\displaystyle f} is surjective , as, for any x {\displaystyle x} in B {\displaystyle B} , one has x = f ( g ( x ) ) {\displaystyle x=f(g(x))} , and x {\displaystyle x}
8436-423: Is closely related to efficiency , the difference being that effectiveness is about achieving goals while efficiency is about using few resources (such as time, effort, and money) in the process. Appropriateness means that the communicative behavior meets social standards and expectations. Communication theorist Brian H. Spitzberg defines it as "the perceived legitimacy or acceptability of behavior or enactments in
8584-409: Is commonly defined as the transmission of information . Its precise definition is disputed and there are disagreements about whether unintentional or failed transmissions are included and whether communication not only transmits meaning but also creates it. Models of communication are simplified overviews of its main components and their interactions. Many models include the idea that a source uses
8732-410: Is communication between distinct people. Its typical form is dyadic communication , i.e. between two people, but it can also refer to communication within groups . It can be planned or unplanned and occurs in many forms, like when greeting someone, during salary negotiations, or when making a phone call. Some communication theorists, like Virginia M. McDermott, understand interpersonal communication as
8880-664: Is communication that takes place within an organism below the personal level, such as exchange of information between organs or cells. Intrapersonal communication can be triggered by internal and external stimuli. It may happen in the form of articulating a phrase before expressing it externally. Other forms are to make plans for the future and to attempt to process emotions to calm oneself down in stressful situations. It can help regulate one's own mental activity and outward behavior as well as internalize cultural norms and ways of thinking. External forms of intrapersonal communication can aid one's memory. This happens, for example, when making
9028-400: Is communication with oneself. Communicative competence is the ability to communicate well and applies to the skills of formulating messages and understanding them. Non-human forms of communication include animal and plant communication . Researchers in this field often refine their definition of communicative behavior by including the criteria that observable responses are present and that
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#17327647006169176-835: Is especially relevant for parent-young relations, courtship, social greetings, and defense. Olfactory and gustatory communication happen chemically through smells and tastes, respectively. There are large differences between species concerning what functions communication plays, how much it is realized, and the behavior used to communicate. Common functions include the fields of courtship and mating, parent-offspring relations, social relations, navigation, self-defense, and territoriality . One part of courtship and mating consists in identifying and attracting potential mates. This can happen through various means. Grasshoppers and crickets communicate acoustically by using songs, moths rely on chemical means by releasing pheromones , and fireflies send visual messages by flashing light. For some species,
9324-428: Is less intuitive and often does not result in the same level of linguistic competence . The academic discipline studying language is called linguistics . Its subfields include semantics (the study of meaning), morphology (the study of word formation), syntax (the study of sentence structure), pragmatics (the study of language use), and phonetics (the study of basic sounds). A central contrast among languages
9472-459: Is more basic than interpersonal communication. Young children sometimes use egocentric speech while playing in an attempt to direct their own behavior. In this view, interpersonal communication only develops later when the child moves from their early egocentric perspective to a more social perspective. A different explanation holds that interpersonal communication is more basic since it is first used by parents to regulate what their child does. Once
9620-575: Is more difficult to judge whether tactile or chemical changes should be understood as communicative signals rather than as other biological processes. For this reason, researchers often use slightly altered definitions of communication to facilitate their work. A common assumption in this regard comes from evolutionary biology and holds that communication should somehow benefit the communicators in terms of natural selection . The biologists Rumsaïs Blatrix and Veronika Mayer define communication as "the exchange of information between individuals, wherein both
9768-455: Is needed to describe how the listener can give feedback in a face-to-face conversation while the other person is talking. Examples are non-verbal feedback through body posture and facial expression . Transaction models also hold that meaning is produced during communication and does not exist independently of it. All the early models, developed in the middle of the 20th century, are linear transmission models. Lasswell's model , for example,
9916-412: Is often seen as a symbol of equality and fairness, while refusing to shake hands can indicate aggressiveness. Kissing is another form often used to show affection and erotic closeness. Paralanguage, also known as vocalics, encompasses non-verbal elements in speech that convey information. Paralanguage is often used to express the feelings and emotions that the speaker has but does not explicitly stated in
10064-499: Is that human communication is frequently linked to the conscious intention to send information, which is often not discernable for animal communication. Despite these differences, some theorists use the term " animal language " to refer to certain communicative patterns in animal behavior that have similarities with human language. Animal communication can take a variety of forms, including visual, auditory, tactile, olfactory , and gustatory communication. Visual communication happens in
10212-408: Is that humans and many animals express sympathy by synchronizing their movements and postures. Nonetheless, there are also significant differences, like the fact that humans also engage in verbal communication, which uses language, while animal communication is restricted to non-verbal (i.e. non-linguistic) communication. Some theorists have tried to distinguish human from animal communication based on
10360-474: Is that it is often difficult to assess the impact of such behavior on natural selection. Another common pragmatic constraint is to hold that it is necessary to observe a response by the receiver following the signal when judging whether communication has occurred. Animal communication is the process of giving and taking information among animals. The field studying animal communication is called zoosemiotics . There are many parallels to human communication. One
10508-503: Is the degree to which the speaker achieves their desired outcomes or the degree to which preferred alternatives are realized. This means that whether a communicative behavior is effective does not just depend on the actual outcome but also on the speaker's intention, i.e. whether this outcome was what they intended to achieve. Because of this, some theorists additionally require that the speaker be able to give an explanation of why they engaged in one behavior rather than another. Effectiveness
10656-394: Is the image of an element of A {\displaystyle A} . Conversely, if f : A → B {\displaystyle f:A\to B} is a bijective homomorphism between algebraic structures, let g : B → A {\displaystyle g:B\to A} be the map such that g ( y ) {\displaystyle g(y)}
10804-544: Is the most known algorithm for deriving prefix codes. Prefix codes are widely referred to as "Huffman codes" even when the code was not produced by a Huffman algorithm. Other examples of prefix codes are country calling codes , the country and publisher parts of ISBNs , and the Secondary Synchronization Codes used in the UMTS WCDMA 3G Wireless Standard. Kraft's inequality characterizes
10952-514: Is the process of ascribing meaning to them and encoding consists in producing new behavioral cues as a response. There are many forms of human communication . A central distinction is whether language is used, as in the contrast between verbal and non-verbal communication. A further distinction concerns whether one communicates with others or with oneself, as in the contrast between interpersonal and intrapersonal communication . Forms of human communication are also categorized by their channel or
11100-406: Is the subject of linear algebra . The concept of homomorphism has been generalized, under the name of morphism , to many other structures that either do not have an underlying set, or are not algebraic. This generalization is the starting point of category theory . A homomorphism may also be an isomorphism , an endomorphism , an automorphism , etc. (see below). Each of those can be defined in
11248-409: Is the transmitter. The transmitter translates the message into an electrical signal that travels through the wire, which acts as the channel. The person taking the call is the destination and their telephone is the receiver. The Shannon–Weaver model includes an in-depth discussion of how noise can distort the signal and how successful communication can be achieved despite noise. This can happen by making
11396-502: Is the unique element x {\displaystyle x} of A {\displaystyle A} such that f ( x ) = y {\displaystyle f(x)=y} . One has f ∘ g = Id B and g ∘ f = Id A , {\displaystyle f\circ g=\operatorname {Id} _{B}{\text{ and }}g\circ f=\operatorname {Id} _{A},} and it remains only to show that g
11544-407: Is thus a bijective continuous map, whose inverse is also continuous. An endomorphism is a homomorphism whose domain equals the codomain , or, more generally, a morphism whose source is equal to its target. The endomorphisms of an algebraic structure, or of an object of a category , form a monoid under composition. The endomorphisms of a vector space or of a module form a ring . In
11692-403: Is to distinguish between linear transmission, interaction, and transaction models. Linear transmission models focus on how a sender transmits information to a receiver. They are linear because this flow of information only goes in a single direction. This view is rejected by interaction models, which include a feedback loop. Feedback is needed to describe many forms of communication, such as
11840-601: The Ancient Greek language : ὁμός ( homos ) meaning "same" and μορφή ( morphe ) meaning "form" or "shape". However, the word was apparently introduced to mathematics due to a (mis)translation of German ähnlich meaning "similar" to ὁμός meaning "same". The term "homomorphism" appeared as early as 1892, when it was attributed to the German mathematician Felix Klein (1849–1925). Homomorphisms of vector spaces are also called linear maps , and their study
11988-596: The Latin verb communicare , which means ' to share ' or ' to make common ' . Communication is usually understood as the transmission of information: a message is conveyed from a sender to a receiver using some medium, such as sound, written signs, bodily movements, or electricity. Sender and receiver are often distinct individuals but it is also possible for an individual to communicate with themselves. In some cases, sender and receiver are not individuals but groups like organizations, social classes, or nations. In
12136-621: The Unicode character set; UTF-8 is the most common encoding of text media on the Internet. Biological organisms contain genetic material that is used to control their function and development. This is DNA , which contains units named genes from which messenger RNA is derived. This in turn produces proteins through a genetic code in which a series of triplets ( codons ) of four possible nucleotides can be translated into one of twenty possible amino acids . A sequence of codons results in
12284-543: The automorphism group of the structure. Many groups that have received a name are automorphism groups of some algebraic structure. For example, the general linear group GL n ( k ) {\displaystyle \operatorname {GL} _{n}(k)} is the automorphism group of a vector space of dimension n {\displaystyle n} over a field k {\displaystyle k} . The automorphism groups of fields were introduced by Évariste Galois for studying
12432-561: The cultural background of the participants . Significant cultural differences constitute an additional obstacle and make it more likely that messages are misinterpreted. Besides human communication, there are many other forms of communication found in the animal kingdom and among plants. They are studied in fields like biocommunication and biosemiotics . There are additional obstacles in this area for judging whether communication has taken place between two individuals. Acoustic signals are often easy to notice and analyze for scientists, but it
12580-397: The roots of polynomials , and are the basis of Galois theory . For algebraic structures, monomorphisms are commonly defined as injective homomorphisms. In the more general context of category theory , a monomorphism is defined as a morphism that is left cancelable . This means that a (homo)morphism f : A → B {\displaystyle f:A\to B}
12728-462: The senses used to perceive the message, i.e. hearing, seeing, smelling, touching, and tasting. But in the widest sense, channels encompass any form of transmission, including technological means like books, cables, radio waves, telephones, or television. Naturally transmitted messages usually fade rapidly whereas some messages using artificial channels have a much longer lifespan, as in the case of books or sculptures. The physical characteristics of
12876-503: The ability to receive and understand messages. Competence is often contrasted with performance since competence can be present even if it is not exercised, while performance consists in the realization of this competence. However, some theorists reject a stark contrast and hold that performance is the observable part and is used to infer competence in relation to future performances. Two central components of communicative competence are effectiveness and appropriateness. Effectiveness
13024-471: The actual message from what was originally intended. A closely related problem is whether acts of deliberate deception constitute communication. According to a broad definition by literary critic I. A. Richards , communication happens when one mind acts upon its environment to transmit its own experience to another mind. Another interpretation is given by communication theorists Claude Shannon and Warren Weaver , who characterize communication as
13172-507: The audience aware of something, usually of an external event. But language can also be used to express the speaker's feelings and attitudes. A closely related role is to establish and maintain social relations with other people. Verbal communication is also utilized to coordinate one's behavior with others and influence them. In some cases, language is not employed for an external purpose but only for entertainment or personal enjoyment. Verbal communication further helps individuals conceptualize
13320-421: The auditory channel to convey verbal information with the visual channel to transmit non-verbal information using gestures and facial expressions. Employing multiple channels can enhance the effectiveness of communication by helping the receiver better understand the subject matter. The choice of channels often matters since the receiver's ability to understand may vary depending on the chosen channel. For instance,
13468-407: The behavior of others. On a practical level, interpersonal communication is used to coordinate one's actions with the actions of others to get things done. Research on interpersonal communication includes topics like how people build, maintain, and dissolve relationships through communication. Other questions are why people choose one message rather than another and what effects these messages have on
13616-408: The case of a vector space or a free module of finite dimension , the choice of a basis induces a ring isomorphism between the ring of endomorphisms and the ring of square matrices of the same dimension. An automorphism is an endomorphism that is also an isomorphism. The automorphisms of an algebraic structure or of an object of a category form a group under composition, which is called
13764-426: The child has learned this, they can apply the same technique to themselves to get more control over their own behavior. For communication to be successful, the message has to travel from the sender to the receiver. The channel is the way this is accomplished. It is not concerned with the meaning of the message but only with the technical means of how the meaning is conveyed. Channels are often understood in terms of
13912-650: The claim that animal communication lacks a referential function and is thus not able to refer to external phenomena. However, various observations seem to contradict this view, such as the warning signals in response to different types of predators used by vervet monkeys , Gunnison's prairie dogs , and red squirrels . A further approach is to draw the distinction based on the complexity of human language , especially its almost limitless ability to combine basic units of meaning into more complex meaning structures. One view states that recursion sets human language apart from all non-human communicative systems. Another difference
14060-532: The common source of g {\displaystyle g} and h {\displaystyle h} . If f {\displaystyle f} is injective, then g ( x ) = h ( x ) {\displaystyle g(x)=h(x)} , and thus g = h {\displaystyle g=h} . This proof works not only for algebraic structures, but also for any category whose objects are sets and arrows are maps between these sets. For example, an injective continuous map
14208-503: The communicator, such as height, weight, hair, skin color, gender, clothing, tattooing, and piercing, also carries information. Appearance is an important factor for first impressions but is more limited as a mode of communication since it is less changeable. Some forms of non-verbal communication happen using such artifacts as drums, smoke, batons, traffic lights, and flags. Non-verbal communication can also happen through visual media like paintings and drawings . They can express what
14356-543: The communicators and their relation. A further topic is how to predict whether two people would like each other. Intrapersonal communication is communication with oneself. In some cases this manifests externally, like when engaged in a monologue , taking notes, highlighting a passage, and writing a diary or a shopping list. But many forms of intrapersonal communication happen internally in the form of an inner exchange with oneself, like when thinking about something or daydreaming . Closely related to intrapersonal communication
14504-434: The complex numbers to the real numbers), since it does not preserve addition: As another example, the diagram shows a monoid homomorphism f {\displaystyle f} from the monoid ( N , + , 0 ) {\displaystyle (\mathbb {N} ,+,0)} to the monoid ( N , × , 1 ) {\displaystyle (\mathbb {N} ,\times ,1)} . Due to
14652-404: The confidentiality of communications, although ciphers are now used instead. Secret codes intended to obscure the real messages, ranging from serious (mainly espionage in military, diplomacy, business, etc.) to trivial (romance, games) can be any kind of imaginative encoding: flowers , game cards, clothes, fans, hats, melodies, birds, etc., in which the sole requirement is the pre-agreement on
14800-435: The corresponding identity element of the second structure. For example: An algebraic structure may have more than one operation, and a homomorphism is required to preserve each operation. Thus a map that preserves only some of the operations is not a homomorphism of the structure, but only a homomorphism of the substructure obtained by considering only the preserved operations. For example, a map between monoids that preserves
14948-463: The different names of corresponding operations, the structure preservation properties satisfied by f {\displaystyle f} amount to f ( x + y ) = f ( x ) × f ( y ) {\displaystyle f(x+y)=f(x)\times f(y)} and f ( 0 ) = 1 {\displaystyle f(0)=1} . A composition algebra A {\displaystyle A} over
15096-491: The encoded strings. Before giving a mathematically precise definition, this is a brief example. The mapping is a code, whose source alphabet is the set { a , b , c } {\displaystyle \{a,b,c\}} and whose target alphabet is the set { 0 , 1 } {\displaystyle \{0,1\}} . Using the extension of the code, the encoded string 0011001 can be grouped into codewords as 0 011 0 01, and these in turn can be decoded to
15244-465: The existence of a socially shared coding system that is used to interpret the meaning of non-verbal behavior. Non-verbal communication has many functions. It frequently contains information about emotions, attitudes, personality, interpersonal relations, and private thoughts. Non-verbal communication often happens unintentionally and unconsciously, like sweating or blushing , but there are also conscious intentional forms, like shaking hands or raising
15392-409: The fields of experience of source and destination have to overlap. The first transactional model was proposed by communication theorist Dean Barnlund in 1970. He understands communication as "the production of meaning, rather than the production of messages". Its goal is to decrease uncertainty and arrive at a shared understanding . This happens in response to external and internal cues. Decoding
15540-453: The following universal property : for every structure S {\displaystyle S} of the variety, and every element s {\displaystyle s} of S {\displaystyle S} , there is a unique homomorphism f : L → S {\displaystyle f:L\to S} such that f ( x ) = s {\displaystyle f(x)=s} . For example, for sets,
15688-434: The form of diagrams showing the basic components and their interaction. Models of communication are often categorized based on their intended applications and how they conceptualize communication. Some models are general in the sense that they are intended for all forms of communication. Specialized models aim to describe specific forms, such as models of mass communication . One influential way to classify communication
15836-806: The form of movements, gestures, facial expressions, and colors. Examples are movements seen during mating rituals , the colors of birds, and the rhythmic light of fireflies . Auditory communication takes place through vocalizations by species like birds, primates , and dogs. Auditory signals are frequently used to alert and warn. Lower-order living systems often have simple response patterns to auditory messages, reacting either by approach or avoidance. More complex response patterns are observed for higher animals, which may use different signals for different types of predators and responses. For example, some primates use one set of signals for airborne predators and another for land predators. Tactile communication occurs through touch, vibration , stroking, rubbing, and pressure. It
15984-408: The free object on x {\displaystyle x} is simply { x } {\displaystyle \{x\}} ; for semigroups , the free object on x {\displaystyle x} is { x , x 2 , … , x n , … } , {\displaystyle \{x,x^{2},\ldots ,x^{n},\ldots \},} which, as,
16132-448: The identities are not subject to conditions, that is if one works with a variety. Then the operations of the variety are well defined on the set of equivalence classes of W {\displaystyle W} for this relation. It is straightforward to show that the resulting object is a free object on x {\displaystyle x} . In algebra , epimorphisms are often defined as surjective homomorphisms. On
16280-425: The infantry on the battlefield, etc. Communication systems for sensory impairments, such as sign language for deaf people and braille for blind people, are based on movement or tactile codes. Musical scores are the most common way to encode music . Specific games have their own code systems to record the matches, e.g. chess notation . In the history of cryptography , codes were once common for ensuring
16428-415: The location of nectar to bees through their colors and shapes. Other definitions restrict communication to conscious interactions among human beings. Some approaches focus on the use of symbols and signs while others stress the role of understanding, interaction, power, or transmission of ideas. Various characterizations see the communicator's intent to send a message as a central component. In this view,
16576-472: The meaning by both the sender and the receiver. Other examples of encoding include: Other examples of decoding include: Acronyms and abbreviations can be considered codes, and in a sense, all languages and writing systems are codes for human thought. International Air Transport Association airport codes are three-letter codes used to designate airports and used for bag tags . Station codes are similarly used on railways but are usually national, so
16724-406: The medium used to transmit messages. The field studying human communication is known as anthroposemiotics. Verbal communication is the exchange of messages in linguistic form, i.e., by means of language . In colloquial usage, verbal communication is sometimes restricted to oral communication and may exclude writing and sign language. However, in academic discourse, the term is usually used in
16872-418: The message partially redundant so that decoding is possible nonetheless. Other influential linear transmission models include Gerbner's model and Berlo's model . The earliest interaction model was developed by communication theorist Wilbur Schramm . He states that communication starts when a source has an idea and expresses it in the form of a message. This process is called encoding and happens using
17020-414: The message. They may result in failed communication and cause undesirable effects. This can happen if the message is poorly expressed because it uses terms with which the receiver is not familiar, or because it is not relevant to the receiver's needs, or because it contains too little or too much information. Distraction, selective perception , and lack of attention to feedback may also be responsible. Noise
17168-402: The monoid operation and not the identity element, is not a monoid homomorphism, but only a semigroup homomorphism. The notation for the operations does not need to be the same in the source and the target of a homomorphism. For example, the real numbers form a group for addition, and the positive real numbers form a group for multiplication. The exponential function satisfies and is thus
17316-411: The nature and behavior of other people are based on non-verbal cues. It is further present in almost every communicative act to some extent and certain parts of it are universally understood. These considerations have prompted some communication theorists, like Ray Birdwhistell , to claim that the majority of ideas and information is conveyed this way. It has also been suggested that human communication
17464-415: The nominal value of the electrical resistors or that of the trashcans devoted to specific types of garbage (paper, glass, organic, etc.). In marketing , coupon codes can be used for a financial discount or rebate when purchasing a product from a (usual internet) retailer. In military environments, specific sounds with the cornet are used for different uses: to mark some moments of the day, to command
17612-472: The nonnegative integers; for groups , the free object on x {\displaystyle x} is the infinite cyclic group { … , x − n , … , x − 1 , 1 , x , x 2 , … , x n , … } , {\displaystyle \{\ldots ,x^{-n},\ldots ,x^{-1},1,x,x^{2},\ldots ,x^{n},\ldots \},} which, as,
17760-407: The nonzero complex numbers to the nonzero real numbers by That is, f {\displaystyle f} is the absolute value (or modulus) of the complex number z {\displaystyle z} . Then f {\displaystyle f} is a homomorphism of groups, since it preserves multiplication: Note that f cannot be extended to a homomorphism of rings (from
17908-473: The offspring depends on the parent for its survival. One central function of parent-offspring communication is to recognize each other. In some cases, the parents are also able to guide the offspring's behavior. Homomorphism#Formal language theory In algebra , a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups , two rings , or two vector spaces ). The word homomorphism comes from
18056-422: The operation or is compatible with the operation. Formally, a map f : A → B {\displaystyle f:A\to B} preserves an operation μ {\displaystyle \mu } of arity k {\displaystyle k} , defined on both A {\displaystyle A} and B {\displaystyle B} if for all elements
18204-473: The other hand, in category theory , epimorphisms are defined as right cancelable morphisms . This means that a (homo)morphism f : A → B {\displaystyle f:A\to B} is an epimorphism if, for any pair g {\displaystyle g} , h {\displaystyle h} of morphisms from B {\displaystyle B} to any other object C {\displaystyle C} ,
18352-431: The participant's experience by conceptualizing the world and making sense of their environment and themselves. Researchers studying animal and plant communication focus less on meaning-making. Instead, they often define communicative behavior as having other features, such as playing a beneficial role in survival and reproduction, or having an observable response. Models of communication are conceptual representations of
18500-445: The participants benefit from the exchange. Animal communication is used in areas like courtship and mating, parent–offspring relations, navigation, and self-defense. Communication through chemicals is particularly important for the relatively immobile plants. For example, maple trees release so-called volatile organic compounds into the air to warn other plants of a herbivore attack. Most communication takes place between members of
18648-493: The parties take turns in sending and receiving messages. This occurs when exchanging letters or emails. For synchronous communication, both parties send messages at the same time. This happens when one person is talking while the other person sends non-verbal messages in response signaling whether they agree with what is being said. Some communication theorists, like Sarah Trenholm and Arthur Jensen, distinguish between content messages and relational messages. Content messages express
18796-451: The process of communication. Their goal is to provide a simplified overview of its main components. This makes it easier for researchers to formulate hypotheses, apply communication-related concepts to real-world cases, and test predictions . Due to their simplified presentation, they may lack the conceptual complexity needed for a comprehensive understanding of all the essential aspects of communication. They are usually presented visually in
18944-624: The process, i.e. the specific behavioral components that make up communicative competence. Message production skills include reading and writing. They are correlated with the reception skills of listening and reading. There are both verbal and non-verbal communication skills. For example, verbal communication skills involve the proper understanding of a language, including its phonology , orthography , syntax, lexicon , and semantics. Many aspects of human life depend on successful communication, from ensuring basic necessities of survival to building and maintaining relationships. Communicative competence
19092-409: The proof is similar for any arity , this shows that g {\displaystyle g} is a homomorphism. This proof does not work for non-algebraic structures. For example, for topological spaces , a morphism is a continuous map , and the inverse of a bijective continuous map is not necessarily continuous. An isomorphism of topological spaces, called homeomorphism or bicontinuous map ,
19240-452: The range of communication to the distance a voice can carry and limits the audience to those present when the speech is uttered. The invention of writing , which converted spoken language into visual symbols , extended the range of communication across space and time . The process of encoding converts information from a source into symbols for communication or storage. Decoding is the reverse process, converting code symbols back into
19388-471: The right definition affects the research process on many levels. This includes issues like which empirical phenomena are observed, how they are categorized, which hypotheses and laws are formulated as well as how systematic theories based on these steps are articulated. Some definitions are broad and encompass unconscious and non-human behavior . Under a broad definition, many animals communicate within their own species and flowers communicate by signaling
19536-463: The same code can be used for different stations if they are in different countries. Occasionally, a code word achieves an independent existence (and meaning) while the original equivalent phrase is forgotten or at least no longer has the precise meaning attributed to the code word. For example, '30' was widely used in journalism to mean "end of story", and has been used in other contexts to signify "the end". Communication Communication
19684-530: The same information to be sent with fewer characters , more quickly, and less expensively. Codes can be used for brevity. When telegraph messages were the state of the art in rapid long-distance communication, elaborate systems of commercial codes that encoded complete phrases into single mouths (commonly five-minute groups) were developed, so that telegraphers became conversant with such "words" as BYOXO ("Are you trying to weasel out of our deal?"), LIOUY ("Why do you not answer my question?"), BMULD ("You're
19832-461: The same species. The reason is that its purpose is usually some form of cooperation, which is not as common between different species. Interspecies communication happens mainly in cases of symbiotic relationships. For instance, many flowers use symmetrical shapes and distinctive colors to signal to insects where nectar is located. Humans engage in interspecies communication when interacting with pets and working animals . Human communication has
19980-443: The same structure such that, if ⋅ {\displaystyle \cdot } is an operation of the structure (supposed here, for simplification, to be a binary operation ), then for every pair x {\displaystyle x} , y {\displaystyle y} of elements of A {\displaystyle A} . One says often that f {\displaystyle f} preserves
20128-409: The sequence of source symbols acab . Using terms from formal language theory , the precise mathematical definition of this concept is as follows: let S and T be two finite sets, called the source and target alphabets , respectively. A code C : S → T ∗ {\displaystyle C:\,S\to T^{*}} is a total function mapping each symbol from S to
20276-798: The sets of codeword lengths that are possible in a prefix code. Virtually any uniquely decodable one-to-many code, not necessarily a prefix one, must satisfy Kraft's inequality. Codes may also be used to represent data in a way more resistant to errors in transmission or storage. This so-called error-correcting code works by including carefully crafted redundancy with the stored (or transmitted) data. Examples include Hamming codes , Reed–Solomon , Reed–Muller , Walsh–Hadamard , Bose–Chaudhuri–Hochquenghem , Turbo , Golay , algebraic geometry codes , low-density parity-check codes , and space–time codes . Error detecting codes can be optimised to detect burst errors , or random errors . A cable code replaces words (e.g. ship or invoice ) with shorter words, allowing
20424-412: The signaller and receiver may expect to benefit from the exchange". According to this view, the sender benefits by influencing the receiver's behavior and the receiver benefits by responding to the signal. These benefits should exist on average but not necessarily in every single case. This way, deceptive signaling can also be understood as a form of communication. One problem with the evolutionary approach
20572-416: The signs are physically inscribed on a surface. Sign languages , like American Sign Language and Nicaraguan Sign Language , are another form of verbal communication. They rely on visual means, mostly by using gestures with hands and arms, to form sentences and convey meaning. Verbal communication serves various functions. One key function is to exchange information, i.e. an attempt by the speaker to make
20720-422: The speaker's feelings toward the topic of discussion. Relational messages, on the other hand, demonstrate the speaker's feelings toward their relation with the other participants. Various theories of the function of interpersonal communication have been proposed. Some focus on how it helps people make sense of their world and create society. Others hold that its primary purpose is to understand why other people act
20868-451: The transmission of information is not sufficient for communication if it happens unintentionally. A version of this view is given by philosopher Paul Grice , who identifies communication with actions that aim to make the recipient aware of the communicator's intention. One question in this regard is whether only successful transmissions of information should be regarded as communication. For example, distortion may interfere with and change
21016-407: The two definitions of a monomorphism are equivalent for sets , magmas , semigroups , monoids , groups , rings , fields , vector spaces and modules . A split monomorphism is a homomorphism that has a left inverse and thus it is itself a right inverse of that other homomorphism. That is, a homomorphism f : A → B {\displaystyle f\colon A\to B}
21164-565: The units into compound expressions are called grammar . Words are combined to form sentences . One hallmark of human language, in contrast to animal communication, lies in its complexity and expressive power. Human language can be used to refer not just to concrete objects in the here-and-now but also to spatially and temporally distant objects and to abstract ideas . Humans have a natural tendency to acquire their native language in childhood . They are also able to learn other languages later in life as second languages . However, this process
21312-399: The use of colors and fonts as well as spatial arrangement in paragraphs and tables. Non-linguistic sounds may also convey information; crying indicates that an infant is distressed, and babbling conveys information about infant health and well-being. Chronemics concerns the use of time, such as what messages are sent by being on time versus late for a meeting. The physical appearance of
21460-456: The verbal part of the message. It is not concerned with the words used but with how they are expressed. This includes elements like articulation, lip control, rhythm, intensity, pitch, fluency, and loudness. For example, saying something loudly and in a high pitch conveys a different meaning on the non-verbal level than whispering the same words. Paralanguage is mainly concerned with spoken language but also includes aspects of written language, like
21608-410: The way they do and to adjust one's behavior accordingly. A closely related approach is to focus on information and see interpersonal communication as an attempt to reduce uncertainty about others and external events. Other explanations understand it in terms of the needs it satisfies. This includes the needs of belonging somewhere, being included, being liked, maintaining relationships, and influencing
21756-475: The world around them and themselves. This affects how perceptions of external events are interpreted, how things are categorized, and how ideas are organized and related to each other. Non-verbal communication is the exchange of information through non-linguistic modes, like facial expressions, gestures , and postures . However, not every form of non-verbal behavior constitutes non-verbal communication. Some theorists, like Judee Burgoon , hold that it depends on
21904-500: Was represented by more than one byte, all characters used the same number of bytes ("word length"), making them suitable for decoding with a lookup table. The final group, variable-width encodings, is a subset of multibyte encodings. These use more complex encoding and decoding logic to efficiently represent large character sets while keeping the representations of more commonly used characters shorter or maintaining backward compatibility properties. This group includes UTF-8 , an encoding of
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