Bruno Bassi (
Were it Perfect, Would it Work Better?
Survey of a Language for Cosmic Intercourse

In this paper we will be concerned with Lincos, a language designed for cosmic intercourse. An exposition of this language is contained in a book by Dr. Hans Freudenthal [1], published in 1960. [2]

'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.

We shall examine Dr. Freudenthal's solution in some detail, and we will conclude stressing a sort of paradox that is implicit in the whole enterprise, an oscillation between a formalist and a communicative trend that makes Lincos a hybrid experiment from the point of view of the design of a perfect language.

1. The problem

Suppose, then, that there actually are other intelligent beings somewhere, a hypothesis that we have no reason to exclude. Getting in touch with them should be very interesting, but how can we manage it?

Dr. Freudenthal's proposal is grounded on the conviction that in order to communicate effectively we should use a language, rather than rely on other less powerful forms of communications. This language should be supported by radio signals of different duration and wavelength.

But how can we use language for communicating with ETs? Obviously, we cannot assume to share any language with them at the start; it is therefore necessary to construe a language that they may be able to interpret and learn through the very fact of receiving some messages expressed in it.

We will have to transmit signals that will be nonsense at the start for the receiver and assume that he will try to interpret them, which is what we ourselves would do in case we started to receive complex signals from outer space. We will have to enable him to interpret the signals; this can be achieved by starting our communication talking about things the receiver (presumably) knows already, and introducing gradually new aspects of the language and new topics, with the simultaneous purposes of communicating meanings and teaching the language itself.

Seen in this way, Lincos is a very peculiar educational (gedanken-) experiment. Usually, linguistic education takes place either through the use of a language already known to the learner (as in case of learning by adults), and/or in real-world contexts in which people smile, frown, gesticulate, point at objects, and in which the learner can observe other speakers' behavior and get feedback from them (as happens to children and anthropologists). On the contrary, in the ET case we can rely neither on a known language nor on an extra-linguistic context. All we can do is to speak pure Lincos. The language is to be taught through the language itself, used one-way in an absolutely pure fashion.

Obviously, the ETs we are hoping to reach must fulfill a few requirements. We will come to this point later on.

2. Excerpts from the Lincos broadcasting program

Before discussing the general features of Lincos as a language -- and as a language partially designed from within the tradition of the quest for a perfect universal language -- we'd better have a quick look at a few examples of its use and scan briefly the learning program incorporated into it. Some readers may find it a fascinating construction; others may get annoyed by some technicalities, and should feel free to skip this whole section.

Dr. Freudenthal's book is divided into four chapters, covering respectively 'Mathematics', 'Time', 'Behavior', and 'Space, motion, mass'. A second volume is announced, but it was, presumably, never written (it should deal with 'Matter', 'Earth', 'Life' and 'Behavior 2'). 'Mathematics' starts from natural numbers and goes on introducing concepts from advanced mathematics, propositional calculus, set theory and predicate calculus. 'Time' introduces means for measuring durations, referring to moments in time, and talking about past and future events. 'Behavior' introduces actors speaking to each other, asking questions, disapproving, quoting other people, knowing and wanting things, promising, and playing. 'Space, motion, mass' reaches as far as describing physical features of human beings and of the Solar System.

2.1. 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.

2.2. 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)


2.3. 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).

2.4. 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]."

2.5. 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


Hb says to Ha: 5/2.


Ha Inq Hb


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


Hb says to Ha: 10/4.


Ha Inq Hb


Ha says to Hb: Bad.


Hb Inq Ha


Hb says to Ha: 1/4.


Ha Inq Hb


Ha says to Hb: Bad.


Hb Inq Ha


Hb says to Ha: 5/2.


Ha Inq Hb


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


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.

3. Requested ET features

"Decoding Lincos would be an easy job" (Freudenthal 1974:1828). Provided that the ETs who are receiving it fulfill certain requirements. A basic requirement concerns their technology: they must be able to receive radio signals and to measure their duration and frequency.

In order to understand Lincos texts they should be humanlike with regards to mental states and communicative experiences. In particular, if they are to understand the initial part of the program, they should have intuitive arithmetical conceptions somehow similar to ours. This may seem a strong assumption. However, given that we have to start off with some universally understood topic, the choice of natural numbers arithmetic seems to be, after all, quite a reasonable one.

Then, our ETs must of course have some sort of language of their own. It may be completely different from our languages, but its handling of context, of presupposition and of implication should be essentially the same as what we are accustomed to. Pauses have to be intuitively understood as separators, and longer pauses as stronger separators.

Anyway, it is not requested that ETs already know all the things we are telling them about. A lot of mathematics as well as 'behavioral rules' are learnable through Lincos itself once an agreement about the fundamentals has been reached.

4. Syntax and vocabulary

Dr. Freudenthal sees two main points of departure between formal and natural languages: punctuation and the treatment of variables. About the two, the features of formal languages turn out to be advantages in view of the Lincos project, and are included within it.

1) In formal languages syntactic structure is expressed by means of a systematic use of punctuation (brackets), which avoids many of the syntactic ambiguities present in natural languages. The use of pauses as punctuation marks adopted in Lincos is equivalent to a system of brackets and appears much more intuitive.

2) The second point of departure concerns the treatment of variables. In natural language, the unit corresponding to a variable would be a generic name such as 'stone'. This variable can range only over the domain of stones, and it is the only available variable that can range over that domain. On the contrary, in formal languages a more systematic handling sees all variables ranging freely over any domain.

In Dr. Freudenthal's view, these two features borrowed from symbolic logic should emancipate Lincos from natural languages, let us say Indo-European ones, and give it a structure of its own.

In spite of the systematic treatment of punctuation and variables, other Lincos features do not seem to derive from an overall coherent and systematic set of principles. There lacks a classification of terms on the grounds of syntactic and semantic categories. New terms are introduced when needed on the basis of the educational criterion exposed above. The syntactic behavior of a new word is shown through examples: it can either reproduce some other word's behavior or be an ad hoc construction for that word only. Anyway, criteria for determining the rules of Lincos syntax are not given.

Here and there, one can find some curious irregularities. For instance, as we have seen, interrogative sentences usually start with a question mark. However, this symbol is used exclusively as a variable-binding device and not as a marker of illocutionary force. As a consequence, questions introduced by the words for 'why' and 'whether' (which for some reason do not bind a variable to the requested answer) are syntactically indistinguishable from affirmative statements.

From a semantic point of view, the vocabulary of Lincos has no particular predefined structure. Words that are considered to be useful are added whenever this is possible. A direct inspiration appears to be drawn from the lexicon of natural languages. Linguistic considerations lead Dr. Freudenthal to disambiguate some polysemic natural language terms (for instance, there are two different words for 'but'); in other cases, the author relies on natural languages and deliberately preserves those polisemies that can have "deep roots in human behavior" (p. 112), as is the case with 'why'.

5. Lincos as a characteristica universalis?

Dr. Freudenthal explicitly introduces his language as a step towards the design of a 'characteristica universalis'. Due to the progress achieved in this century by formal logic, we should be much closer to such a result than Leibniz, for instance, was. The only trouble is the difficulty of choosing a starting point. We need to start with a "concrete, sharply defined and narrow problem" (p. 12). The problem of communicating with ETs should serve as such a starting point.

Yet, as we have stressed in the previous section, there are some unsystematic aspects about the Lincos language that don't really look like steps in the direction of a perfect universal language as the one Leibniz was thinking about. There seem to be some sort of inconsequentiality in the history of the Lincos project. To recap:

A man decides to build a perfect language. The philosophical tradition in which he places himself is one that pursued formalization, both as a requirement to be fulfilled by the artificial languages it produced and as a deep principle to be posited underneath the surface structure of natural languages. He claims that the formal instruments at his disposal are adequate to the task. Then, in the actual design of the language, he applies his formal devices only to a few specific syntactic features, and for the rest he relies on the structure of natural languages. People usually build perfect languages in order to override traditional 'unsatisfactory' features of natural languages, such as the fact that they are subject to nonsense, ambiguity, lexical and grammatical irregularity, context-dependency. Yet, many of these features are still somehow present in Lincos. Why did Dr. Freudenthal, who has not at all a naive approach to this sort of issues, let things go this way?

5.1. Communication vs Formalization

The idea of applying achievements from symbolic logic to the design of a complete language is deeply linked to a strong criticism towards the dominant 20th century trend of considering formal languages as a subject matter in themselves and of using them almost exclusively for inquiries about the foundations of mathematics. "In spite of Peano's original idea, logistical language has never been used as a means of communication ... The bounds with reality were cut. It was held that language should be treated and handled as if its expressions were meaningless. Thanks to a reinterpretation, 'meaning' became an intrinsic linguistic relation, not an extrinsic one that could link language to reality" (p. 12).

In order to rescue the original intent of formal languages, Lincos is bound to be a language whose purpose is to work as a medium of communication between people, rather than serve as a formal instrument for computing. It should allow anything to be said, nonsense included. In Lincos, "we cannot decide in a mechanical way or on purely syntactic grounds whether certain expressions are meaningful or not. But this is no disadvantage. Lincos has been designed for the purpose of being used by people who know what they say, and who endeavor to utter meaningful speech" (p. 71).

As a consequence, Lincos as a language is intentionally far from being fully formalized, and it has to be that way in order to work as a communication tool. It looks as though the two issues of communication and formalization radically tend to exclude each other. What Lincos seems to tell us is that formalization in the structure of a language can hardly generate straightforward understanding.

Our Dr. Freudenthal saw very well this point. "there are different levels of formalization and ... in every single case you have to adopt the one that is most adaptable to the particular communication problem; if there is no communication problem, if nothing has to be communicated in the language, you can choose full formalization" (Freudenthal 1974:1039).

But then, how can the solution of a specific communication problem ever bring us closer to the universal resolution of them all? Even in case the Lincos language should effectively work with ETs, how could it be considered as a step towards the design of a characteristica universalis? Maybe Dr. Freudenthal felt that his project needed some philosophical justification. But why bother Leibniz?

Lincos is there. In spite of its somewhat ephimeral 'cosmic intercourse' purpose it remains a fascinating linguistic and educational construction, deserving existence as another Toy of Man's Designing.


[1] Hans Freudenthal, born 1905, was at the time professor of mathematics at the University of Utrecht.

[2] Freudenthal (1960). Throughout the present paper, page numbers in parentheses refer to this book.


Freudenthal, Hans
1960 Lincos - Design of a Language for Cosmic Intercourse, Amsterdam, North Holland
1974 "Cosmic Language", in T. A. Sebeok (ed), Current Trends in Linguirstics, vol 12, The Hague: Mouton, pp. 1019-1042.

Questo scritto è stato pubblicato in: Le lingue perfette, a cura di Roberto Pellerey, Versus 61/63, 1992.