Notation

"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."

"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."

"The process of writing has something infinite about it. Even though it is interrupted each night, it is one single notation."

"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."

"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”."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"Such is the advantage of a well-constructed language that its simplified notation often becomes the source of profound theories."

"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."

"It is worth noting that the notation facilitates discovery. This, in a most wonderful way, reduces the mind's labour."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"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."

"A good notation [is]... like a live teacher."

"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."

"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."

"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."