Notation system

Notation systems are an interpreted system of tokens having a syntax and a semantics.

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The medium used by a notational system defines and delimits the possible characteristics of its tokens. The tokens of a notational system designate (refer to) abstractions that are reified by the notational system.

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Commonly, "notation" refers to the typographical conventions or rules of symbol usage that are followed, e.g., within a book or article.

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Under its broader definition, notational systems would include speech (a way of inscribing semantically meaningful vibrations upon the medium of air); money (a combined token-and-medium that attempts to represent value); logical notation; cartography; and of course writing. While the alphabet is the most famous revolutionary notational system, there have been many notational revolutions in the development of homo sapiens sapiens.

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While notational systems have had a great impact on civilization, they are not themselves studied comparatively and longitudinally as a coherent subject, but rather are considered bit layers within the disciplines they support and enable.

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The following is a small set of examples of notational systems used in various disciplines:

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• In mathematics, mathematical notation is used to represent mathematical ideas, such as:
• Conway's chained arrow, Knuth's up-arrow notation and Steinhaus polygon notation are systems to iterate exponentiation, for representing very^veryvery large numbers.
• Cartesian Coordinate System, for representing position and other spatial concepts in analytic geometry
• Leibnitz notation is the standard representation for Calculus
• Big O notation, used for example in analysis to represent less significant elements of an expression, to indicate that they will be neglected
• Z notation - a formal notation for specifying objects using Zermelo-Fraenkel set theory and first-order predicate logic
• Notation in probability
• In physics physics notation:
• In quantum mechanics, Dirac's Bra-ket notation is another representation of probability amplititudes
• In general relativity, for example, Tensor notation is a general way to represent a gravitational field
• In chemistry, the Lewis notation denotes chemical bonds
• Musical notation - to represent music in a musical composition
• Dance notation - to document various forms of is used to dance movement such as Labanotation, Benesh Notation, and Eshkol-Wachman notation.