Lingua cosmica

[Спадар Антось]

ЛИНКОС (неологизм от полного названия «Lingua cosmica») - один из искусственных языков науки, основы которого разработаны нидерландским профессором Г. Фройденталем с учетом возможной перспективы использования его как космического (межпланетного) языка для общения с внеземными цивилизациями. Звуками этого языка служат радиосигналы различной длительности, передаваемые на разных длинах волн. Из звуков составляются слова, из слов фразы, из фраз - программные тексты. Вместо собственно слов используются кодовые слова, большинство которых представляет собой сокращения латинских слов. В качестве базы Л. используется логистический синтаксис, в котором отсутствуют союзы, имена существительные, глаголы, склонения, спряжения и времена. Роль пунктуации играют паузы различной длительности. Дальнейшая разработка и модификация Л. (и др. аналогичных языков) представляет определенный интерес для решения космических и земных задач человечества.
Новейший философский словарь. 2009.

Очень заинтересовался этим чудом, только информации не нашёл практически никакой. Статейка в Википедии + артикул Бруно Басси "Were it Perfect, Would it Work Better?", отрывок из которого привожу ниже; и всё... Если у кого-то есть в электронном варианте книга Freudenthal, Hans "Lincos - Design of a Language for Cosmic Intercourse". Amsterdam, North Holland. 1960 или какие-нибудь другие материалы - поделитесь, будьте любезны.

'Lincos' is an abbreviation for the Latin phrase 'Lingua cosmica'. Its intended purpose is to enable us humans to communicate with other intelligent beings that may live somewhere in space, on a faraway planet. This idea is somewhat out of fashion today, but it was quite alive a few decades ago; therefore I'd suggest to the reader to try to take it as a serious problem seeking a good solution.

Spoken and written Lincos

Lincos proper ('spoken Lincos') will be broadcasted in space, its 'phonemes' being radio signals of different duration and wavelength. For us humans though it is obviously convenient to work on a written version of it. This written Lincos will use symbols already familiar to us, corresponding to Lincos words in an arbitrary fashion. Lincos 'phonetics' is not discussed in Dr. Freudenthal's book, though it is claimed that it should be as systematic as possible, in the sense that syntactic and semantic categories should be marked phonetically.

Mathematics

After a presentation of some Lincos vocabulary, in the form of loose words transmitted out of context, the Lincos program starts with simple comparisons and operations on natural numbers. A good reason for this choice is that we need to start talking about something that is presumably known to the receiver, and that we have some means to show.

  · · · · · > · · ·
[and so on] (p. 45)

In this instance the sequences of dots are transmitted as sequences of peeps and should work as 'ideophonetic words', naming numbers by ostension. The 'greater than' sign is a Lincos word initially incomprehensible for the receiver, who is assumed to infer its meaning after a large number of utterances in which it is applied to different numbers.

  · · · < · · · · ·
[and so on]

  · · · · = · · · ·
[and so on]

  · · · · + · · = · · · · · ·
[and so on]

  · · · · · · - · · = · · · ·
[and so on]

Once 'equals' is known, algorithmic numerals are substituted for ostensive ones:

· = 1

· · = 10

· · · = 11

· · · · = 100

· · · · · = 101

· · · · · · = 110

· · · · · · · · · · · · · = 1101

[and so on] (p. 46)

Dr. Freudenthal goes on using binary notation throughout the whole book but, since written Lincos words bear an arbitrary relationship to spoken ones, within the scope of this paper we will arbitrarily replace such notation with the decimal one, just as if the above had been:

· = 1

· · = 2

· · · = 3

· · · · = 4

· · · · · = 5

· · · · · · = 6

· · · · · · · · · · · · · = 13

[and so on]

This is just the beginning of the broadcasting program, but it gives the flavor of the kind of educational policy Dr. Freudenthal is adopting. New Lincos words and rules (number spelling in this instance) are introduced exclusively through examples, in which the new term is introduced within a context that can be considered as already interpretable on the basis of previous texts. Note that a formal definition of what a natural number is, such as Peano's postulates, is deliberately missing.

Another example of this policy is the next Lincos learning step, that concerns the introduction of variables: after a sequence of formulae that are identical with the exception of one varying number, a new symbol standing for a variable is substituted for this number.

4 + 3 > 2 + 3

4 + 13 > 2 + 13

4 + 1 > 2 + 1

[...]

4 + a > 2 + a

[and so on] (p. 46)

Following the same criteria, a set (such as 'natural number', 'prime number') is not given a name until a certain number of objects both belonging and not belonging to it are known. The word for 'set' is introduced only after a few sets have been named.

The program goes on with the introduction of more mathematical and logical devices such as various mathematical relations, connectives, quantifiers, predicates (sets), functions, and the definite article. Predicate calculus is not exposed in the book though it should be in the actual program. Our ET finishes the chapter with the overall competence of a first year student of logic, and knows such words as 'prime number', 'proposition', 'set', 'there exists', 'the', 'true', and 'false'. In the meantime he has learned some other useful words, such as 'etcetera' (thanks to the endless progression of digits in periodic numbers), and some interesting grammatical features such as the one that allows questions to be posed:

  ?x x+2=7
asked for an the x such that x+2=7

  x+2=7 --> x=5
if x+2=7, then x=5
       
  ?x a<b and x+a=b
asked for an x such that a<b and x+a=b

  a<b and x+a=b --> x=b-a
if a<b and x+a=b, then x=b-a

  (p. 52)
   
Punctuation

Complex mathematical formulae need punctuation devices such as brackets; natural language texts also need some means of expressing the relations between their parts. These punctuation problems are handled in written Lincos through pauses: a longer pause means ('ideophonetically') a greater separation (written Lincos has a special apparatus for writing pauses, which is ignored in the present examples for the sake of clarity).

Time

The chapter about time provides means for measuring durations and for mentioning past, present and future events. The time unit 'Sec' (second) is introduced with reference to the duration of a peep (here written as a horizontal line):

Dur_____ = Sec 3 [for instance] (p. 79)

Then a clock is installed, that will continue to tick during the whole subsequent program. It is possible to refer to moments in time by mentioning the position of the clock. Amidst other things, a word meaning 'happen' is introduced. This allows utterances like the following:

t1 [noise] t2
t1 Usq t2 Fit [noise]
(p. 84)

to be read as: "a noise [occurring between moments t1 and t2, as marked by the clock]; from t1 till t2 there happened [noise]."

Behavior (or rather: Chatting)

The chapter about behavior is certainly the more interesting one from the point of view of the completeness and efficacy of Lincos as a language to be used for communication. The task of expressing mathematical concepts could be seen as relatively straightforward on the basis of logical formalisms; here an attempt is made to describe human behavior, including for instance conversation, judgment, wishing, and playing.

As it cannot be formalized through general rules, behavior is shown. The receiver is then free to infer, if he pleases, some conversational rules.

As the communicative environment is immaterial, and there aren't yet means for representing bodies, what is shown are communicative events between actors. The receiver is supposed to realize that fictional events are happening, and to behave interpretatively as if they were actually happening, in a disposition similar to the one of a spectator at a theater. At the start the actors speak about mathematics, which is for now the only topic available.

After some introductory statements in which it is said that Ha, Hb, Hc etc. are not numbers (which is all that has been talked about so far), but some kind of different entities, texts like the following are sent:

  Ha Inq Hb
?x 2x=5
Ha says to Hb: What is the x such that 2x=5?

  Hb Inq Ha
5/2
Hb says to Ha: 5/2.

  Ha Inq Hb
Ben
Ha says to Hb: Good.

  [and so on] (p. 92)
             
  Ha Inq Hb
?x 4x=10
Ha says to Hb: What is the x such that 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
1/4
Hb says to Ha: 1/4.

  Ha Inq Hb
Mal
Ha says to Hb: Bad.

  Hb Inq Ha
5/2
Hb says to Ha: 5/2.

  Ha Inq Hb
Ben
Ha says to Hb: Good.

  (p. 93)
     
The receiver already knows the interrogative form. After a considerable number of different texts of the sort he should be able to infer that Ha and Hb are actors communicating to each other, that Inq means something like 'to say', and that 'Ben' and 'Mal' mean respectively 'good' and 'bad', as expressions of approval and disapproval.

This may appear to be quite a hard step; in Dr. Freudenthal's book it is supported by a fairly large amount of different examples, aimed for instance at making clear that 'Ha Inq Hb' is not to be taken as a single unanalyzed expression, or that in it Ha is the sender and not the addressee of the utterance.

Note that 'Ben' and 'Mal' are kept carefully distinct from the concepts of 'true' and 'false' (introduced previously): in the last example, Ha disapproves a true statement because Hb did not reduce the fraction to its lowest terms.

The interrogative form easily allows to express W-questions of any form. For instance:

  t1Ha Inq Hb
?x 4x=10t2
Ha says to Hb: What is the x such that 4x=10?

  Hb Inq Hc
?y t1 t2 y Inq Hb ?x 4x=10
Hb says to Hc: Who asked me for the x such that 4x=10?

  Hc Inq Hb
Ha
Hc says to Hb: Ha.

  (p. 98)
     
The broadcasting program goes on with many more 'behavioral' texts. Between the terms introduced there are words for 'why', 'because', 'how', 'whether', 'to know', 'to wish', and 'to play (a game)'.

Actors frequently refer to other actor's speech; this kind of quoting is approximate, as it is in ordinary conversation. Discourses get more complex, the use of ellipses and abbreviations becomes more and more frequent. While the part about mathematics consisted in a fairly context-free formalism, Lincos now becomes a highly context-sensitive language in which expressions can be interpreted only with reference to the context in which they are uttered.

[nonexyst]

Да, загадочная штука. Вот это действительно априорный язык. (Хотя плохой~mal как бы намекает). Интересно, как, например, создать википедию на таком языке. И где бы, наконец, найти его учебник в эл.виде?