by Dr. Alexander Ollongren

Leiden Institute of Advanced Computer Science

Leiden University

The Netherlands




Calling E.T. is the title of a filmed documentary about the work of some of the members of the Permanent Study Group SETI of the International Astronautical Academy. The film was produced in 2008, directed by Prosper de Roos of Amsterdam, The Netherlands. One of the interviewed scientists was the present author. Some aspects of his new Lingua Cosmica, a second generation cosmic language, also featured in the film, are discussed in the present article. Its conceptual design is completely different from that of the first generation LINCOS, described in Design of a Language for Cosmic Intercourse, Part I, a monograph written by the well-known prominent Dutch mathematician Dr. Hans Freudenthal († 1991) of Utrecht University in The Netherlands. The setup chosen for that book, published in 1960, is described in many places, for instance in Wikipedia. The present article provides a resumé of the most important design issues of the new LINCOS, developed in recent years. At the outset it needs to be stated that a basic idea behind the new venue, is to use logic as an integral part in the proposed system for communication with aliens (i.e. Calling E.T.). By taking that approach the fascinating conceptual problem of designing a language for communication between mutually alien intelligent species in the Universe was given a new perspective.

            The orientation of the author’s work Logic Design of a Linguistic System for Interstellar Communication (an as yet unpublished monograph dedicated to the memory of Dr. Freudenthal) is multi-disciplinary, concerned as it is with applied logic, universal aspects of linguistics (referred to as astrolinguistics) as well as conceptual issues in the field of possible message exchange (communication) between intelligent species or information processing artifacts in the Galaxy. The modality of the logic used is constructive, supplying the linguistic system proposed with a solid foundation.



Upon getting acquainted with Dr. Hans Freudenthal’s book years ago, many mathematicians, logicians and other scientists became fascinated by the conceptual problems in designing a language for communication between mutually alien intelligent species in the Universe. The book was the first one (and is the only monograph until now) on this topic. Freudenthal’s design of his Lingua Cosmica has concepts from especially mathematics and some logic as well at the core. It was published in Elsevier’s series Studies in Logic and the Foundations of Mathematics. From the way it was written it is evident that the renowned mathematician rather enjoyed this excursion into an unfamiliar area. Attendees in the nineteensixties of Dr. Freudenthal’s public lectures on the unusual subject, have confirmed this impression. The work was, however, incomplete. Part II, planned to be devoted to the description of societal aspects of humanity was never published. It is unclear whether topics in this field have been studied more than only cursorily by the author.

            A nice comprehensive and in-depth review of Freudenthal’s book written by Bruno Bossi was to be found a few years ago in Wikipedia. It has been revised since then. As the original article presents interesting perspectives not only on the book itself, but also on philosophical aspects of the undertaking, some quotations from the original article are incorporated into the present resumé. In the opening paragraph of the review Bossi stresses the point that there is (beginning of quotations)

‘… 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.’


 He remarks also

 ‘… 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’.


There are some further important points in Bossi’s article, quoted here

‘ …” 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. ... 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’.

‘… 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’.

‘… 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?’.

‘…  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’. (end of quotations).



The publication of Freudenthal’s book, now only available antiquarian, coincides with the beginning of a special epoch in space research: the start of international projects in the Search for ExtraTerrestrial Intelligence (SETI). In the almost fifty years elapsed since then several aspects around SETI have been cleared up. Modern astrophysical research has revealed that it is not to be expected that real time interstellar communication will be possible. We know now that there exist indeed solar type stars of about the same age as the Sun in the habitable zone of our Galaxy, many planets orbiting stars have been found but so far none of them are earth-like (astronomers expect to find this type of planets in the near future). In addition there is the fact that our relatively nearby solar-system-like neighbours (whether or not harbouring intelligent species) are at distances of scores of light years away. Laws of physics forbid the transmission of information with tachyonic velocities. So no highly developed technological society can expect to ‘get in touch’ directly with another one in the Galaxy. Nevertheless such societies (and ours too) can be assumed to be interested in transmitting information about themselves to whoever is ‘listening’ - and listening to whoever is transmitting. One reason can be because they might be inquisitive (as the human species is by nature) about ‘the others’. For those purposes a rather sophisticated astrolinguistic system for interstellar communication is needed - Freudenthal’s design, brilliant as it is, is outdated now. The design of a modern system should satisfy at least some basic properties


-     simple notation and syntax

-         clarity  of expression (self- interpretation of messages)

-         rich contents of messages.

-         possibility of structuring and sizing messages.


In addition the system should be able to describe dynamic processes (one could argue that it is not necessary to introduce time and time intervals for that purpose).

            It can safely be assumed that an intelligent species receiving an interstellar message unmistakably bearing a linguistic signature, will put automatic information processing machines at work to do the decoding/interpretation. We would do the same thing! Therefore messages should be large-size and contain a large amount of redundancy.



Computer scientists eldery now, but  belonging to a generation younger than Prof. Freudenthal’s, have been exposed intensively since the early but also late fifties to basic concepts in computer science: low-level assembly systems, also procedural (ALGOL-like) and functional (LISP-like) programming languages, besides formal languages and automata – and the mathematical/logical lambda calculus. All of the computer programs in low-level languages had to be written in the early days of computer science in linear notation, preferably in operator prefix form, the Polish version. Years later, those experiences supplied the present author of the new Lingua Cosmica with the idea that Freudenthal’s abundant use of super- and subscripts and the numerous ad hoc agreements resulting in a rather unwieldy notation, might be simplified with some effort by using ingredients from ‘modern’ computer programming. At the same time it was realised that the overall purpose of Freudenthal’s work might be achieved in a better way if one abstained from using just a single level - that of the Lingua Cosmica itself.

            Thus an idea was born: messages meant for interstellar communication with extra-terrestrial intelligent societies should be essentially multi-level, they could consist in part of a (large) text in some natural language supplemented with annotations in a formal system at another level; in fact more than two levels can be introduced in the setup of a second generation cosmic language discussed here. Using a logic formal system as an integral part of a Lingua Cosmica for that purpose enables one to describe not only the logic contents of texts in such messages but also the definitional framework. The latter, i.e. the universe of discourse in the sense of logic, is comparable with an environment created by the vehicle of declarations in computer programming. In the wake of this view Freudenthal’s idea of using mathematical notions as a central core in the language was abandoned. Instead it was realized that sophisticated type declarations and basic notions from proposition and predicate logic should be given central positions in a setup with an orientation towards astrolinguistics.

            The present author of the new LINCOS got well-acquainted with the French Coq1 implementation of the calculus of constructions with induction (CCI) based on the typed lambda calculus. It appeared then that the basics of that proof system could provide the vehicle needed for the design of an astrolinguistic system for interstellar communication. The specific formal system in logic on which the new system is based, has by its nature rich declarative and expressive powers.

            One might argue that the first thing to do next would be to translate Freudenthal’s expressions into terms in constructive logic. A better idea, however, is to use the calculus  and the underlying type theory in a totally different way and circumvent at the same time some of the problems present in the first generation LINCOS. One of these is that that system is very suitable for expressing mathematical relations, but much less for describing structural aspects of human societies. As mentioned before Freudenthal’s unpublished Part II was meant to deal with aspects as these. However, in the late nineteeneighties Prof. Freudenthal, once in conversation with the present author, gave the impression of having lost interest in the project.


A predominant requirement for the novel undertaking was, right from the beginning, that messages meant for an extra-terrestrial civilisation should be large-sized and that they should in some way carry information for interpretation of the formal language employed - or methods for achieving this goal. So instruments for auto-interpretation have been incorporated and worked out in the system. The new Lingua Cosmica to be described in the forthcoming monograph rests on concepts of CCI formulated in terms of type theory using linear notation. Several computer implementations of this particular logic are available1. Some of these systems have been used for verifications of new LINCOS terms, lemmas and facts in the book. Therefore occurring facts (in the form of term expressions) in the book are guaranteed to be correct – a remarkable, important aspect. The elimination machinery employed is slightly different from that in the Coq system. The notation, based on the conventions of that system, has been adapted in order to improve readability. The set of primitives is kept very small. As a result the dynamics of verifications become transparent. The requirement of obtaining an ‘easy to handle’ linear notation is met as well. All of these aspects are explained in detail in the book.


The study of interstellar communication in the context of astrolinguistics requires ipso facto an interdisciplinary approach. One is concerned with cosmology, astrophysics, chemistry, biology, but also with information processing, natural language linguistics and coding theory besides concepts in mathematics and logic. The new Lingua Cosmica is designed to be used for describing in a concise and interpretable manner aspects of physical reality as we humans experience it. For that purpose abstractions of reality and more in particular logic relations occurring in reality need to be modeled. They are represented mostly as strictly logical forms, but elements from symbolic computation can be admitted as well.


Some of the easier to understand ideas behind the proposed new LINCOS are illustrated below by a simple example. We use for that in the present notes one of the basic well-known syllogisms of the Greek philosopher Aristoteles (384 – 322 B.C.). The important concept of Aristotelian basic syllogisms has survived more than two thousand years of development in logic and has been enormously influential. At one level (say the top level) we use the following example of such a syllogism:


all Humans are Mortal and all Greeks are Human

so all Greeks are Mortal.


This expression, called Barbara by medieval scholars because of the three occurring all (logic quantifiers), is evidently representative of a whole class of logic expressions.

In Aristotelian logic there are four mutually distinct basic classes of expressions. In order to describe in new LINCOS at another level (one might call it the deep level) the logic contents of the particular expression shown above, a suitable environment is needed. It consists of a base D for the universe of discourse, and moreover representations of humans, mortality and Greeks. These are introduced as follows using the proposed new LINCOS notation


            CONSTANT D : Set. (* base of universe of discourse *)

            CONSTANTS Human, Mortal, Greek : D Prop.

            (* maps representing subjects and predicates *)


These are declarative items, specifying the global environment needed.


. Set is a predefined type and D of type Set is introduced.

. Prop is also a predefined type, distinct from Set.

If a and b are abstract representations of logic propositions (assertions) then

a, b : Prop, i.e. they have type Prop.

. The type of Human is D Prop, i.e. a (mathematical one to one) mapping or function. So if x has type D, then the functional application of Human to x, written (Human x) has type Prop. Human, Mortal and Greek have the same type.



The syllogism itself is written in the spirit of Aristotelian logic as a lemma, stating the non-elementary type of Barbara

            FACT Barbara :

            (ALL x : D)

            ((Human x) (Mortal x)) /\ ((Greek x) (Human x))

            (Greek x) (Mortal x).


Here denotes logic implication and /\ is used for logic conjunction. Above fact is easily understood by humans - it hardly needs verification. But in order to explain it in a logical sense it needs a proof. For that purpose there are mechanisms to verify facts in a formal sense within the system itself. In above case Barbara can be shown to be equal (in Leibniz’s sense) to a constructed lambda form, not given here.


Suppose that in one of our messages for interstellar communication the Aristotelian syllogism as shown (in the form of a text file so to say) is embedded. I.e. in it are embedded above declarations and the fact Barbara of the non-trivial type shown - perhaps augmented with a proof of the fact. A recipient of this message wishing to decode and understand the contents of this fragment faces several non-trivial problems. In order to simplify things we suppose that it is recognised that one of the natural languages spoken on Earth (unknown to the receiver) is used at one level, and that the logic structure of the sentence is explained at a deeper level. The recipient knowing logic, upon analysing the incoming signals (text), recognises that a constructive form is used, and will discover soon the meaning of ALL (universal quantification), (implication) and /\ (conjunction). He/she/it might immediately add to these E (existence), \/ (disjunction) and ~ (negation), absent in this example. Furthermore the items Human, Mortal and Greek appear in the text as well as in the deep structure (and in the proof of the fact). All of this is helpful for the decoding and interpretation problem.

            However, we may well assume that small size messages are unintelligible an sich for recipients or their information processing artifacts (i.e.  E.T.). In order to effectively provide help in the interpretation problem messages should therefore contain much or very much redundancy. Thus, as a part of a more extensive message in new LINCOS, one could include and formulate at least one example of all four basic Aristotelian syllogisms – not necessarily in the form meant to be informative for humans. The necessary formalisations in terms of the system have been developed. Each of the four basic syllogisms has been formulated as a fact, verifiable within the framework of the language itself. This powerful aspect of the system may prove to be one of the most important keys for decoding purposes.

            There are other instruments as well for explaining in our messages for E.T. the structure and conceptual set up of new LINCOS. These are feasible and effective because the system is based on extremely simple grammatical rules. One could e.g. use music at a third level with annotations to the score in new LINCOS. Also useful for this purpose is pictorial information (at again another level) as for instance available on board the famous anodized gold plaques on board the Pioneer 10 (launched in 1972) and Pioneer 11 (launched in 1973) unmanned space crafts. The contents of the pictures can, at least partially, be described in the system.


1 Gérard Huet et al. 1999-2003, The Coq Proof Assistant, A Tutorial, Version 7.x, INRIA, France

Alexander Ollongren, November 2008