Lincos

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Lincos
Project author Hans Freudenthal
Year of publication 1960
Linguistic
classification
Language codes
ISO 639 -1

-

ISO 639 -2

art (other constructed languages)

ISO 639-3

mis (not coded)

Lincos (abbreviation for the Latin expression "lingua cosmica") is a constructed language that was developed in 1960 by the mathematician Hans Freudenthal in his book LINCOS: Design of a Language for Cosmic Intercourse .

Freudenthal's goal was to create a language that could be used by every intelligent being, i.e. H. also extraterrestrial life forms , although no direct communication via images or with a third language known to both sides is possible.

Freudenthal took up ideas from Lancelot Hogben , who with Astraglossa 1953 describes a system in which mathematical statements can be represented in the form of impulses.

The computer scientist Stephen Wolfram , who worked as a consultant for the film Arrival u. a. was involved in the analysis of the symbols of the alien language used in the film, always had a copy of the book with him on set during filming.

structure

The Lincos dictionary, which should be used at the beginning of a communication, initially contains some very simple patterns to introduce “terms” for the natural numbers and simple arithmetic operations (e.g. addition, subtraction, multiplication, division).

According to Freudenthal's plans, it should begin with simple words first. Numbers are represented by a simple signal such as an X. Using other signals, such as O among others, simple mathematical statements can be made step by step.

Lincos meaning
XOX 1 = 1
XX O XX 2 = 2
XXX O XXX 3 = 3
X OO XX 1 <2
X OO XXX 1 <3
XX OO XXX 2 <3
XX OOO X 2> 1
XXX OOO XX 3> 2

If the transmitted message is sufficiently large and simple enough, it can be concluded from the example that here X stands for one, O for equality, OO for the smaller comparison and OOO for the larger comparison.

The numbers are represented in the unary system, comparison operators (=, <,>,! =) Can also be generated step by step. The information density is obviously unfavorable; however, it is easy to imagine achieving a convention to make the messages more compact. As usual in computer science, the binary system is ideal.

Building on these basic statements, it is easy to imagine that truth values ​​and even logical statements will then be transmitted.

Lincos meaning
XOX ∈ Ver: 1 = 1 true
XX O XX ∈ Ver: 2 = 2 true
XX OO XXX ∈ Ver: 2 <3 true
X OO XX ∈ Ver: 1 <2 true
X OOO XXX ∈ Fal: 1> 3 wrong
XX O XXX ∈ Fal: 2 = 3 wrong
XX OOO X ∈ Ver: 2> 1 true
XOXA XX O XX ∈ Ver: (1 = 1) AND (2 = 2) true
X OO XX A XXX OOO X ∈ Ver: (1 <2) AND (3> 1) true
XO XX AXOX ∈ Fal: (1 = 2) AND (1 = 1) wrong
XO XX AA X OO XX ∈ Ver: (1 = 2) OR (1 <2) true

In this coding, Ver (from Latin verum) obviously stands for true, Fal (from Latin falsum) for false, A for logical AND, AA for logical OR.

These mathematical concepts are illustrated by a series of examples. This is followed by concepts about variables, whole numbers and fractions, which are reminiscent of the arithmetic of school mathematics. Finally, set terms are introduced, the sets of natural, whole, real and complex numbers (Num, Int, Rea, Com) as well as prime numbers (Pri) are introduced and some constants (e, i, π) are defined.

Lincos meaning
XPXO XX ∈ Ver: (1 + 1 = 2) true
XX PX OO XXXX ∈ Ver: (2 + 1 <4) true
XP XX O XXXX AA X OOO XX ∈ Fal: (1 + 2 = 4) OR (1> 2) wrong
XX PP XOX ∈ Ver: (2 - 1 = 1) true
XXX PP X OOO X ∈ Ver: (3 - 1> 1) true
X PPP XXX O XXX ∈ Ver: (1 * 3 = 3) true
XXX PPP XX O XXXXXX ∈ Ver: (3 * 2 = 6) true
Int ⊂ Rea ∈ Ver: (The whole numbers are a subset of the real numbers.) True
XP XX O XX PX ∈ Ver: (1 + 2 = 2 + 1) true

In this coding, the new symbol P obviously stands for calculation rules (P stands for addition, PP for subtraction, PPP for multiplication, PPPP for division).

Subsequently vocabulary to describe the time , ie the measurement of time periods, sent, can be so talked about current and future events.

Lincos meaning
DUR ---- O XXXX SEC Duration ---- = 4 seconds
DUR ----- O XXXXX SEC Duration ----- = 5 seconds
XX SEC OO XXX SEC ∈ Ver: (2 seconds <3 seconds) true

In this example, DUR stands for a new symbol "duration" (SEC for "seconds") and indicates the actual duration of the radio signal in seconds. Concepts of time can be transmitted using simple messages. About three different events E1, E2 and E3 are conceivable, which are also sent one after the other during transmission.

To the transmission (unspecified here) with certain events E1, E2, E3

Lincos meaning
E1 PAUSE E2 PAUSE E3 Event E1 followed by Event E2 followed by Event E3

can e.g. B. follow the following code

Lincos meaning
E1 Ant E2 ∈ Ver: (E1 BEFORE E2) true
E1 Ant E3 A E2 Ant E3 ∈ Ver: (E1 BEFORE E3) AND (E2 BEFORE E3) true
E3 Pst E2 ∈ Ver: (E3 AFTER E2) true
E1 E3 Fit E2 ∈ Ver: (E2 BETWEEN E1 and E3) true
E2 E3 Fit E1 A E2 Pst E1 ∈ Fal: (E1 BETWEEN E2 and E3) AND (E2 AFTER E1) incorrect
E1 Ant E2 <-> E2 Pst E1 E1 PRIOR TO E2 if and only if E2 AFTER E1

The symbols Ant (from Latin ante), Pst (from Latin post) and Fit (from Latin fit) stand for the temporal relationships “before”, “after” and “between”. Temporal terms such as past and future can be made clearer, such as B. the finiteness of life.

Perhaps the greatest difficulty is the complex expressions relating to behavior and conversation between individuals. Two actors are introduced who talk to each other, quote each other, ask about things and make promises to each other. In games between two players, game theory (e.g. in the game with the matching pennies) explains human behavior such as opposition, and in a game between three players the concept of cooperation is explained. Finally, linguistic expressions for mass , space and movement are defined. Among other things, human nature and the solar system are to be described.

A second book with further considerations (including about the earth, life and further behavior) was planned, but was not completed.

Use and discussion

In the movie Contact , SETI astronomers receive and decipher extraterrestrial messages that are reminiscent of Lincos in their structure.

In 1974, as part of the Arecibo embassy, a message was transmitted based on the concepts of Lincos. The first actual transmission in Lincos took place in 1999 as part of the “Call Messenger I” mission.

Regardless of the success of such attempts at communication, considering the phenomenon of language by purely mathematical means remains extremely interesting and raises a number of questions. In this context, reference should be made to the Sapir-Whorf hypothesis , which makes the actual possibilities of communication with beings with other worlds of experience seem improbable. Above all, it seems uncertain whether the other person understands the (cultural) idea behind the mathematical statement and how many examples are necessary to understand the statements.

More complex example

An example of Lincos from the third chapter of Freudenthal's book shows how two individuals ask each other questions.

Lincos meaning
Ha Inq Hb  ? x 2 x = 5 Ha says to Hb: What is the x for 2x = 5?
Hb Inq Ha 5/2 Hb says to Ha: 5/2.
Ha Inq Hb Ben Ha says to Hb: Good.
Ha Inq Hb  ? x 4 x = 10 Ha says to Hb: What is the x for 4x = 10?
Hb Inq Ha 10/4 Hb says to Ha: 10/4.
Ha Inq Hb Mal Ha says to Hb: Bad.
Hb Inq Ha 4 * 10/4 = 10 ∈ Ver: Hb says to Ha: 4 * 10/4 = 10 is true.
Ha Inq Hb Ver Tan Mal: ​​x = 5/2 Ha says to Hb: True, but bad: x = 5/2.

In this case Mal (from Latin male) stands for “bad”, Ben (from Latin bene) for “good”, Tan (from Latin tamen) for “but”, Inq (from Latin inquit) for “say , ask". Ha, Hb, Hc are representatives of the set Hom (from Latin homo), i.e. people.

In addition, even indirect questions about speakers are possible.

Lincos meaning
Ha Inq Hb  ? x 4 x = 10 Ha says to Hb: What is the x for 4x = 10?
Hb Inq Hc  ? y y Inq Hb  ? x 4 x = 10 Hb says to Hc: What is the y for "y says to Hb: What is the x for 4x = 10?"?
Hc Inq Hb Ha Hc says to Hb: Ha.

The specific coding was modified to make it easier to read.

literature

  • Hans Freudenthal : Lincos: Design of a Language for Cosmic Intercourse . North Holland, Amsterdam. 1960
  • Alexander Ollongren: Astrolinguistics - Design of a Linguistic System for Interstellar Communication Based on Logic. Springer, New York 2013, ISBN 978-1-4614-5467-0
  • Paolo Musso: From Maths to Culture. Towards an effective message . Pontifical University of the Holy Cross, Rome. 2003
  • John S. Davidson: ET come home. Communicating with the extraterrestial . In: Language and Society 13. 1984, pp. 32-36
  • Alexander Ollongren: Large-size Message Construction for ETI. Non-deterministic typing and symbolic computation in Lincos . Leiden Institute of Advanced Computer Science, Leiden. 2004
  • Alexander Ollongren: On the signature of LINCOS. Acta Astronautica, Vol.67, Issues 11-12, 2010, pp. 1440-1442, doi : 10.1016 / j.actaastro.2010.04.006

Web links

Individual evidence

  1. ↑ Astraglossa & LINCOS daviddarling.info