-- Hans Freudenthal (1960), Lincos: Design of a Language for Cosmic Intercourse. (Labelled "volume I", but it seems a second was never written.)
This text contains the systematic design of language conceived to be transmitted as radio pulses toward other worlds, and to be understandable to a distant species with no background knowledge except receiving the message itself. The assumption is that clusters of beeps, with pauses of different set lengths, can form arbitrary "words" (represented for convenience in the book by symbols or by three-letter words), whose meaning can be conveyed by context and example.
Chapter 1 (Mathematics). At first, a list of "words" is provided without context, in the hope they will be recognized later within longer strings.
The first actual signal is obvious: a number of beeps, representing natural numbers by simple counting; they are used to establish equality and inequality, addition, substraction, and other elementary arithmetic operations. (e.g., after a few variations on * * § * * * @ * * * * *, it becomes clear that § represents addition and @ represents equality).
After a while the numbers change from being a count of beeps to their binary representation: declare * = 1, ** = 10, *** = 11, and so on. It becomes possible to talk about very large, negative, fractional, or irrational numbers.
More elementary arithmetics follows, to make the meaning of these numbers clear. Soon, free variables such as "x" are introduced, as well as sets such as "integers", and concepts of set theory like belonging, union, and intersection. The rules of arithmetic can be summarized: a = b -> b = a.
This also makes clear the meaning of ->, representing logical implication. Logical operators like "and", "if", "or", "not" enter the transmitted vocabulary. Infinite iteration allows a definition of e and א, as well as an approximation of π. Simple theorems, such as the infinity of prime numbers, can be conveyed. The concept of true, false, proposition, and question are introduced.
Chapter 2 (Time). The first definition of time is very simple: the duration of various beeps. The concept of duration and the unit second are introduced immediately. Frequency and wavelength are introduced similarly, taking advantage of the nature of radio waves. Moments, stretches of time, sequences, and events can be determined.
Chapter 3 (Behaviour). Hereon most information is conveyed through dialogues: characters (Ha, Hb, etc.) are created, with statements of the form "Ha tells Hb statement". One of the characters can comment on the other's statements, such as by saying "good" or "bad", which is separate from "true" or "false" ("log(e^5)" is a true answer to "what is 2+3?", but not a good one).
Eventually the characters start reporting on the dialogues themselves. There is indirect speech, criticism of statements, and requests for justification, then politeness and deception; the characters express wishes and state the limits of their own knowledge. Complex statements, such as a brief biography of Julius Caesar or the history of Fermat's last theorem, are provided.
There is some discussion of ethics, based on the wishes and actions of people. Simple games like "matching pennies" are introduced, and with them the concept of probability, and developed into game theory.
Chapter 4 (Space, Motion, Mass). Time has already been established. Now location and distance are explained, using time and the speed of light (i.e. speed of the radio signals) as reference. The centimeter is set as unit for distance. Descriptions of motion follow.
The properties of Euclidean space, lines, planes, and spheres are described, coordinate systems and vector transformations. The size of humans and common animals are provided.
After motion comes causality. Hydrogen is defined through its emission spectrum, and so on other elements, also allowing a definition of mass, and the establishment of the gram as unit. From this, basic mechanics can be described, as well as the characteristics of Earth and other celestial bodies, and their orbital motion.
The last thing described in the first and only Lincos is relativity. Reportedly, the unwritten second volume should have described further the composition of Earth and the traits of living organisms.
Transcription of the history of Fermat's last theorem as told in Lincos (p. 138). Every word and symbol is actually shorthand for a series of radio signals.
germansingergirl
janainaart
romaincrisis
ellievsbear
stormborns
2087
snowghoul
