Language is the critical element in the establishment of extended groups of humans, providing as it does a mechanism through which individuals within the group can communicate in complex concepts and can communicate across time and space. Language is a means of communication, between people, machines, and between people and machines. Languages are traditionally split in two categories: natural languages, which are typically learned by all children early in life, and formal languages, which are learned later, typically at school and university, for many purposes such as mathematics and computer programming. Natural language is by no means the only natural way of communication between people. Babies communicate via gestures and mimicking long before their first word, and they absorb interpersonal communication in various forms of play and representations, such as dancing, long after their first word.

All forms of communication involve sensori-motor activities. For language, sound is the first medium of transmission, later followed by writing in many societies. Even there, language is not unique; music is a communication mechanism based on sound, and painting is a communication mechanism based on graphical representation.

As presented for example by Michael Tomasello in Constructing a Language, hearing children learn language by associating social situations with sequences of sound that progressively allow them to designate objects, and actions on these objects, in ways that affect the situations in directions of their choice (“Mamma, bring bear!”). As presented by David McNeill in Hand and Mind, deaf children do the same with sequences of signs. As children grow up, situations become more involved, and so does their use of language, building up from sensori-motor actuations to abstract considerations (from “I see the bear” to “I see your point”).

Technically, the description of spoken languages starts with sounds (phonetics). From sounds are built individual units, called phonemes, that coalesce, for example, all "r" sounds, however they are pronounced, into a single category. One level up in the construction of language, phonemes allow assembly of sounds into morphemes (say "eat" and "-ing"), which in turn are constituents of words ("eating"). Words are built up into sentences according to rules of syntax ("I love eating." is good syntax; "I love eated." is not). Then sentences are assembled into discourse, completing an overall construction of representational logic where all elements contribute their part, together with context interpretation. Meaning eventually refers to the sensori-motor experience. As presented by George Lakoff and Mark Johnson in their seminal Metaphors We Live By, "I see the bear!" provides a direct reflection of observable facts, while "I see your point of view." maps back to the sensori-motor experience by building an abstract landscape modeled after a concrete one. The point you see may not exist in the sensori-motor reality, but it follows nevertheless the same construction ("Your points of view are all very close.") via the set process called metaphor. Abstract constructs can themselves be assembled into higher meaning by mixing disparate elements into coherent wholes (“Pythagoras retorts to your point via his theorem.”). Experiences from different domains can be therefore be elaborated into new information by set mechanisms defining how the mixing operates. This operation, called blending, is described in details by Gilles Fauconnier and Mark Turner in The Way We Think. From such narratives are established complete stories that can in turn be brought back to the sensori-motor level by inversing the blending and metaphor processes, which is essentially the derivation of mythology.

A formal language is much simpler than a natural language. Whereas the latter has to contend with sounds, phonemes, morphemes, words, sentences and discourses, we can say, rather generally speaking, that formal languages make do with words, sentences and discourses. Whereas an educated person may have a vocabulary of 50,000 words in natural language, a formal language will contain perhaps tens of them. An example of formal language is that of arithmetic. In this

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