ASTROLINGUISTICS: A GUIDE FOR CALLING E.T.
by Dr. Alexander Ollongren
Leiden Institute of Advanced Computer Science
The
INTRODUCTION
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
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Interstellar Communication (an as yet unpublished monograph dedicated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.
BACKGROUND
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).
OUTLINE
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.
HISTORY
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.
AN EXAMPLE
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,
Alexander
Ollongren, November 2008