1. Evidentiality
  2. John Wilkins’s philosophical language
  3. Voynich manuscript
  4. Nüshu
  5. Solresol
  6. Lincos
  7. Pioneer plaque
  8. Dance notation
  9. Notation in knot theory
  10. More notations


In about a quarter of the world’s languages, every statement must specify the type of source on which it is based—for example, whether the speaker saw it, or heard it, or inferred it from indirect evidence, or learnt it from someone else. This grammatical category, whose primary meaning is information source, is called ‘evidentiality’. In [anthropologist Franz] Boas’s words, ‘while for us definiteness, number, and time are obligatory aspects, we find in another language location near the speaker or somewhere else, [and] source of information—whether seen, heard, or inferred—as obligatory aspects’.

Marking one’s information source indicates how one learnt something. Languages vary in how many types of information sources they have to express. Many just mark information reported by someone else. Others distinguish firsthand and non-firsthand sources. In rarer instances, visually obtained data are constrasted with data obtained through hearing and smelling, or through various kinds of inference. These larger systems also tend to have a separate marker for reported information. Tariana, an Arawak language spoken in the multilingual area of the Vaupés in northwest Amazonia, has an even more complex system. In this language, one cannot simply say ‘José played football’. Just like in all other indigenous languages from the same area, speakers have to specify whether they saw the event happen, or heard it, or know about it because somebody else told them, etc. This is achieved through a set of evidential markers fused with tense. Omitting an evidential results in an ungrammatical and highly unnatural sentence.

John Wilkins’s philosophical language

Wilkins’ work concluded the efforts of seventeenth century scholars to invent a universal language, a quest caused by the decline of Latin as a pan-European language and by the struggle to render scientific discovery in the vernacular. These projected languages would sweep away the ambiguities and historical accretions of words in existing languages, and would establish a more definite relationship between words and things.

For Wilkins, this was part of a project to create a taxonomy of natural objects. Although his aim of a universal scientific language was never realised, his work had an indirect result in the classification system of the eighteenth century biologist Linnaeus.

Voynich manuscript

A mysterious, undeciphered manuscript dating to the 15th or 16th century.

Written in Central Europe at the end of the 15th or during the 16th century, the origin, language, and date of the Voynich Manuscript—named after the Polish-American antiquarian bookseller, Wilfrid M. Voynich, who acquired it in 1912—are still being debated as vigorously as its puzzling drawings and undeciphered text. Described as a magical or scientific text, nearly every page contains botanical, figurative, and scientific drawings of a provincial but lively character, drawn in ink with vibrant washes in various shades of green, brown, yellow, blue, and red.

Based on the subject matter of the drawings, the contents of the manuscript falls into six sections: 1) botanicals containing drawings of 113 unidentified plant species; 2) astronomical and astrological drawings including astral charts with radiating circles, suns and moons, Zodiac symbols such as fish (Pisces), a bull (Taurus), and an archer (Sagittarius), nude females emerging from pipes or chimneys, and courtly figures; 3) a biological section containing a myriad of drawings of miniature female nudes, most with swelled abdomens, immersed or wading in fluids and oddly interacting with interconnecting tubes and capsules; 4) an elaborate array of nine cosmological medallions, many drawn across several folded folios and depicting possible geographical forms; 5) pharmaceutical drawings of over 100 different species of medicinal herbs and roots portrayed with jars or vessels in red, blue, or green, and 6) continuous pages of text, possibly recipes, with star-like flowers marking each entry in the margins.


Nüshu is a syllabic script created and used exclusively by women in Jiangyong Prefecture, Hunan Province, China. The women were forbidden formal education for many centuries and developed the Nüshu script in order to communicate with one another. They embroidered the script into cloth and wrote it in books and on paper fans.

Nüshu was mainly used in the creation of San Chao Shu (三朝書) or "Third Day Missives", cloth-bound booklets created by mothers to give to their daughters upon their marriage, or by woman to give to their close female friends. The San Chao Shu contained songs written in the Nüshu script expressing hopes and sorrow, and was delivered on the third day after a woman's marriage.


Solresol was invented by François Sudre (1787-1864). He started working on it in 1817 and work on it continued until 1866. Sudre hoped Solresol would be used to facilitate international communication and deliberately made the language very simple, so it would be easy to learn, and unlike any natural language to avoid giving an advantage to any particular group of people.

Solresol was the first artificial language to be taken seriously as an interlanguage. It is also the first and only musically-based interlanguage; or at least the only one to make any headway.

Solresol has seven syllables based on the Western musical scale: do re mi fa so la si, though you don't have to be familiar with music in order to learn it. The total number of Solresol words is 2,660: 7 words with one syllable; 49 with two syllables; 336 with three syllables and 2.268 with four syllables.


In the introduction to Lincos, [mathematician Hans] Freudenthal announced that his primary purpose “is to design a language that can be understood by a person not acquainted with any of our natural languages, or even their syntactic structures … The messages communicated by means of this language [containing] not only mathematics, but in principle the whole bulk of our knowledge.”

To this end, Freudenthal developed Lincos as a spoken language, rather than a written one—it’s made up of phonemes, not letters, and governed by phonetics, not spelling. The speech is itself made up of unmodulated radio waves of varying length and duration, encoded with a hodgepodge of symbols borrowed from mathematics, science, symbolic logic, and Latin. In their various combinations, these waves can be used to communicate anything from basic mathematical equations to explanations for abstract concepts like death and love.

The very first message sent in Lincos, Freudenthal wrote, should contain numerals that introduce the receiver to mathematics. This would consist of short, regular pulses or “peeps,” the number of pulses corresponding to a particular numeral—one peep for 1, two peeps for 2, and so on. The next step, he wrote, would be to transmit basic formulas, using symbols such as =, +, or > to demonstrate properties of human notation and mathematical knowledge (for example: . . . . . > . . . . to show that 5 is greater than 4). Each successive message would increase in complexity, moving from numerals and basic formulas to complex subjects like human behavior.

Pioneer plaque

The Pioneer Plaque is a physical, symbolic message affixed to the exterior of the Pioneer 10 spacecraft. At the core of this message is a fundamental concept that establishes a standard of distance and time, which, thereafter, is employed by the other components of the plaque. The design team postulated that hydrogen, being the most abundant element in the cosmos, would be one of the first elements to be studied by a civilization. With this in mind, they inscribed two hydrogen atoms at the top left of the plaque, each in a different energy state. When atoms of hydrogen change from one energy state to another—a process called the hyperfine transition—electromagnetic radiation is released. It is this wave that harbors the standard of measure used throughout the illustrations on the plaque. The wavelength (approximately 21 centimeters) serves as a spatial measurement, and the period (approximately .7 nanoseconds) serves as a measurement of time. The final detail of this schematic is a small tick between the atoms of hydrogen, assigning these values of distance and time to the binary number 1.

Dance notation

How do you tell a person in another place or time what a dance looks like, and how it should be performed? You could use words, describing, second by second, the movements made by every dancer on stage—but inaccuracies would creep in. Take an instruction as simple as “lower your arm”: How would the precise angle, attitude, and displacement of the arm be explained? As an algebraic vector? And what about the hand, the fingers, the knuckles, the rest of the dancer’s body—what are they doing? Such a method would come to resemble programming code, in which reams of language and symbols come to stand for something that’s supposed to look simple and elegant. The problem is that a dance is read by a human, not a machine.

What about images, then? You could reduce the dance to two dimensions, represented frame by frame, using diagrams and drawings. Yet even for a short sequence, you’d need so many! It would come to resemble a flip-book or an animated GIF, preempting the most efficient and simple method we’ve ever had to record dance: moving images, or film.

Before we had image-capturing technology, the need to preserve dance, as a record, gave way to attempts to write dance down. Dance notation, the symbolic representation of human movement, has developed into systems for making graphics recognizable as living movement. Traditional dance notation marks a path through space and a relationship to music. As Edward Tufte writes in Envisioning Information (1990), “Systems of dance notation translate human movements into signs transcribed onto flatland, permanently preserving the visual instant.” It’s a question of “how to reduce the magnificent four-dimensional reality of time and three-space into little marks on paper flatlands.” Dance never looks the same twice, unless it’s on film.

Notation in knot theory

In 1967 mathematician J. H. Conway wrote: “In this paper, we describe a notation in terms of which it has been found possible to list (by hand) all knots of 11 crossings or less, and all links of 10 crossings or less, and we consider some properties of their algebraic invariants whose discovery was a consequence of this notation. The enumeration process is eminently suitable for machine computation, and should then handle knots and links of 12 or 13 crossings quite readily. Recent attempts at computer enumeration have proved unsatisfactory mainly because of the lack of a suitable notation… Little tells us that the enumeration of the 54 knots of [6] took him 6 years—from 1893 to 1899—the notation we shall soon describe made this just one afternoon’s work!”

More notations

Katherine Ye has collected “quotes on interesting notations—both powerful ones and bad ones—and how they influence thought.”