# Notation

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In linguistics and semiotics, a **notation** is a system of graphics or symbols, characters and abbreviated expressions, used in artistic and scientific disciplines to represent technical facts and quantities by convention.

## Quotes[edit]

*Quotes are arranged alphabetically by author*

### A - F[edit]

- There was yet another disadvantage attaching to the whole of Newton’s physical inquiries, … the want of an appropriate notation for expressing the conditions of a dynamical problem, and the general principles by which its solution must be obtained. By the labours of LaGrange, the motions of a disturbed planet are reduced with all their complication and variety to a purely mathematical question. It then ceases to be a physical problem; the disturbed and disturbing planet are alike vanished: the ideas of time and force are at an end; the very elements of the orbit have disappeared, or only exist as arbitrary characters in a mathematical formula.
- George Boole in:
*Artificial Intelligence and Symbolic Computation:International Conference AISC 2000 Madrid, Spain, July 17-19, 2000*, Springer Science & Business Media, 25 April 2001, p. 3

- George Boole in:

- Aryabhata's work, called Aryabhatiya, is composed of three parts, in only the first of which use is made of a special notation of numbers. It is an alphabetical system in which the twenty-five consonants represent 1-25, respectively; other letters stand for 30, 40, …., 100 etc. The other mathematical parts of Aryabhata consists of rules without examples. Another alphabetic system prevailed in Southern India, the numbers 1-19 being designated by consonants, etc.
- Florian Cajori in:
*A History of Mathematical Notations*, Courier Dover Publications, 26 September 2013, p. 47

- Florian Cajori in:

**The process of writing has something infinite about it. Even though it is interrupted each night, it is one single notation.**- Elias Canetti in" M.P. Singh
*Quote Unquote (A Handbook of Quotations)*, Lotus Press, 1 January 2005, p. 302

- Elias Canetti in" M.P. Singh

- A term used in Linguistics and Phonetics to refer to any system of Graphic representation of speech (as in Phonemic notation, where the term transcription is widely used). Specifically it refers to the set of symbols which represent a mode of linguistic analysis, as in the ‘Phrase-structure notation’ in general grammar. An analytic convention, in this sense, which is introduced into an analysis to facilitate the formulation of a statement such as a Rule, is often termed a notational device, e.g. the use of ( ) to indicate optionality in generative syntax.
- David Crystal in:
*Dictionary of Linguistics and Phonetics*, John Wiley & Sons, 23-Sep-2011, p. 337

- David Crystal in:

- An English sentence like 'every whale is a mammal' transcribes directly into algebraic notation as '-W+M'. Similarly, its equivalent, 'no non-mammals are whales', transcribes directly as '-(+(-M)+W)'. Sentences that come ready made for direct transcription are called “Canonical”.
- George Englebretsen, in:
*Something to Reckon with: The Logic of Terms*, University of Ottawa Press, 1 January 1996, p. xiv

- George Englebretsen, in:

- The fact is that, while Leibniz did insist on a subject-predicate analysis of statements, this attitude was well thought out, and the failures of his logic are due only to his inability to devise an appropriate system of notation for his logical algorithm.
- George Englebretsen in: "Something to Reckon with: The Logic of Terms”, p. 34

- Instead, he [De Morgan] introduced his "spicular" notation. In this notational scheme, parentheses are used to indicate the quantity (distribution) of a term, and negation is indicated by a dot or the use of a lowercase term letter. Distribution is indicated by a parenthesis facing the term, otherwise parenthesis faces away from the term.
- George Englebretsen in: "Something to Reckon with: The Logic of Terms”, p. 45

- More specifically, we must not say this in a language of "adequate notation" (6.122; also 3.325, 5.533, 5.534). In other words, in a logically adequate, or correct, notation—-a Begriflrchrift (4. l273)...a notation in which sentences consist only of simple names naming simple objects.
- George Englebretsen, in: "Something to Reckon with: The Logic of Terms”, p. 112

- Peano's scheme [system of symbolization for logic] became the dominant system of notation for the majority of mathematical logicians; Russell's popularity and the influence of Principia Mathematica, which made use of Peano's notation, were mainly responsible for this.
- George Englebretsen, in: "Something to Reckon with: The Logic of Terms”, P. 233

**We could, of course, use any notation we want; do not laugh at notations; invent them, they are powerful. In fact,mathematics is, to a large extent, invention of better notations.**- Richard P. Feynman in: R.F. Feynman, R.B. Leighton, M. Sands
*The Feynman Lectures on Physics*, Рипол Классик,

- Richard P. Feynman in: R.F. Feynman, R.B. Leighton, M. Sands

### G - L[edit]

**Any phase of the growth of mathematical notation is an interesting study, but the chief educational lesson to be derived is that notation always grows too slowly.**Older and inferior forms possess remarkable longevity, and the newer and superior forms appear feeble and backward. We have noted the state of transition in the sixteenth century from the Roman to the Hindu system of characters, the introduction of symbols of operation +, -, and the slow growth towards decimal notation.- Lambert Lincoln Jackson in: Florian Cajori :A History of Mathematical Notations", p. 228

**There are now two systems of notations, giving the same formal results, one of which gives them with self-evident force and meaning, the other by dark and symbolic processes. The burden of proof is shifted, and it must be for the author or the supporter of the dark system to show that it is in some way superior to the evident system.**- Jevons in: “Something to Reckon with: The Logic of Terms”, p. 99

- All my paintings are usually done in drawing form, very small. I make notations in drawings first, and then I make a collage for color. But drawing is always my notation. And I think artists all work that way really. I'm not special. But I like plants, and I don't think anyone else draws like this, today. I'm special in that way.
- Ellsworth Kelly in: Kimberly Chou
*An Abstract Master Puts on a Plant Show*, The Wall Street Journal, May 25, 2012

- Ellsworth Kelly in: Kimberly Chou

**Such is the advantage of a well-constructed language that its simplified notation often becomes the source of profound theories.**- Pierre Simon Marquis de Laplace in : George Englebretsen
*Something to Reckon with: The Logic of Terms*, University of Ottawa Press, 1 January 1996, p. 99

- Pierre Simon Marquis de Laplace in : George Englebretsen

**It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an bsolute value;**a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease with which it has lent to all computations put our arithmetic in the first rank of useful inventions and we shall appreciate the grandeur of this achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.- Piere Simon Laplace, in Joseph Mazur
*Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers*, Princeton University Press, 23 March 2014, p. 38

- Piere Simon Laplace, in Joseph Mazur

**It is worth noting that the notation facilitates discovery. This, in a most wonderful way, reduces the mind's labour.**- Gottfried Wilhelm Leibniz in: Eberhard Zeidler
*Quantum Field Theory III: Gauge Theory: A Bridge between Mathematicians and Physicists*, Springer Science & Business Media, 17 August 2011, p. 439

- Gottfried Wilhelm Leibniz in: Eberhard Zeidler

- As the mother teaches her children how to express themselves in their language, so one Gypsy musician teaches the other. They have never shown any need for notation.
- Franz Liszt in: Arthur Friedheim
*Life and Liszt: The Recollections of a Concert Pianist*, Courier Dover Publications, 13 June 2013, p. 270

- Franz Liszt in: Arthur Friedheim

- There is also general agreement that notations operating on a level higher than the word fall outside writing proper, although there are exceptions. In his typology Hill (1967, 93) includes a category 'discourse systems' which he considers as one of the main three divisions of writing systems.
- Hartmut Guenther, Otto Ludwig in:
*Schrift und Schriftlichkeit (Writing and Its Use): Ein Interdisziplinaeres Handbuch Internationaler Forschung - An Interdisciplinary Handbook of International Research, Volume 2*, Walter de Gruyter, 1 January 1996, p. 1381

- Hartmut Guenther, Otto Ludwig in:

- A writing system is wider than a spelling system. English uses many w:Logogramslogograms which have as unambiguous correspondence with a single morpheme but give no indications of pronunciations:1,2,3 etc, L, @, &, %, +. Many more are in use in mathematics and formal logic. Other specialized uses include proofreading symbols (e.g. for delete, insert). Many of these symbols are not specific to English, and more detailed discussion would shade off into special purpose writing systems such as shorthands and scientific notations. However, “normal” uses of English also include a wide range of such forms.
- Hartmut Guenther, Otto Ludwig in: "Schrift und Schriftlichkeit (Writing and Its Use): Ein Interdisziplinaeres Handbuch Internationaler Forschung - An Interdisciplinary Handbook of International Research, Volume 2", p. 1443

### M - R[edit]

- We are driven by the usual insatiable curiosity of the scientist, and our work is a delightful game. I am frequently astonished that it so often results in correct predictions of experimental results. How can it be that writing down a few simple and elegant formulae, like short poems governed by strict rules such as those of the sonnet or the waka, can predict universal regularities of Nature? Perhaps we see equations as simple because they are easily expressed in terms of mathematical notation already invented at an earlier stage of development of the science, and thus what appears to us as w:Eleganceelegance of description really reflects the interconnectedness of Nature's laws at different levels.
- Murray Gell-Mann, in
*Banquet Speech at the Nobel Banquet in Stockholm*, nobelprize.org , December 10, 1969

- Murray Gell-Mann, in

- Roman-based alphabetic notations make use of Roman letters, sometimes with diacritical marks, graphic transformations, and other letters added. The alphabet adopted by the International Phonetic Association (IPA) in 1888 is Roman based. This system has become widely recognized as the international phonetic alphabet. Following Daniel Jones (1914) phoneticians have distinguished between the more detailed narrow and the less specific broad transcription. Among the latter systems are phonemic notations, which transcribe only phonemes and no phonetic variants.
- Winfried Nöth in: Handbook of Semiotics, Indiana University Press, 1 January 1995, P.258

**Alphabetic notations represent the articulatory features of speech sounds by a composite formula of symbols indicating the active speech organs.**One of the Phoenicians who has developed such symbols is Pike.- Winfried Nöth in: "Handbook of Semiotics", p. 258

**An important step in solving a problem is to choose the notation. It should be done carefully. The time we spend now on choosing the notation carefully may be repaid by the time we save later by avoiding hesitation and confusion.**- G.Polya in : “Something to Reckon with: The Logic of Terms”, p. 99

- Imagine someone so infatuated by a band that they have every different pressing of every album the band made. Most of the time, the only difference in the album is the matrix number or a different 'made in' notation on the back cover or label. This is enough to make some people extremely excited. Actually, much more than excited.
- Henry Rollins in:
*Henry Rollins: The Column! Are You Collector Scum?*, LA Weekly, Jan 19, 2012

- Henry Rollins in:

- Language is music. Written words are musical notation. The music of a piece of fiction establishes the way in which it is to be read, and, in the largest sense, what it means. It is essential to remember that characters have a music as well, a pitch and tempo, just as real people do. To make them believable, you must always be aware of what they would or would not say, where stresses would or would not fall.
- Marilynne Robinson in:
*When I Was A Child I Read Books*, Hachette UK, 22-Mar-2012, p. 79

- Marilynne Robinson in:

**A good notation [is]... like a live teacher.**- Bertrand Russel in : : “Something to Reckon with: The Logic of Terms”, p. 99

### S - Z[edit]

- After all, quantity, like quality, is oppositional, which suggests a +/- notation. To determine which quantity is + and which - Sommers relies on the equivalences established by valid conversion.
- F. Sommers in: "Something to Reckon with: The Logic of Terms”, p. 112

- Traditional logic's failure to do so [incorporating relations into term logic] was due not to its syntax, but to (i) the absence of an adequate system of formal notation, and (ii) the failure to make explicit the logical forms of pronouns.
- F.Sommers in: "Something to Reckon with: The Logic of Terms”, p. 128

- My being a teacher had a decisive influence on making language and systems as simple as possible so that in my teaching, I could concentrate on the essential issues of programming rather than on details of language and notation.
- Niklaus Wirth in: Richard Morris
*Geek of the Week: Niklaus Wirth*, Red Gate Software, 26 July 2012

- Niklaus Wirth in: Richard Morris