“Almost at the bounds of science fiction, though still with an undoubted scientific interest, is the project of the Dutch mathematician Hans A. Freudenthal (Lincos, 1960) for a language in which eventual encounters with the inhabitants of other galaxies may be conducted (see Bassi 1992).
Lincos is not designed as a language to be spoken; it is rather a model for inventing a language and at the same time teaching it to alien beings that have presumably traditions and biological structure different from ours.
Freudenthal starts off by supposing that we can beam into space signals, which we might picture as radio waves of varying length and duration. The significance of these waves derives not from their expression-substance, but rather from their expression-form and content-form.
By endeavoring to understand the logic that determines the expression-form being transmitted to them, the space aliens are supposed to extrapolate a content-form that will not be alien to them.
During the first phase, the messages consist of regular sequences of pulses. These are intended to be interpreted quantitatively–four pulses standing for the number 4, etc. As soon as it is assumed that the aliens have correctly interpreted these first signals, the transmission passes to the second phase, in which it introduces simple arithmetic operators:
* * * < * * * *
* * * * = * * * *
* * * * + * * = * * * * * *
In the next phase, the aliens are taught to substitute for the pulses a system of binary numbers (in which * * * * = 100, * * * * * = 101, * * * * * * = 110); this makes it possible, using only ostension and repetition, to communicate some of the principle operations in mathematics.
The transmission of temporal concepts presents a more complex problem. Freudenthal, however, presumes that by constantly receiving a signal of the same duration, constantly associated to the same number of pulses, the aliens will begin to compute a certain duration in seconds. Lincos also teaches conversational rules, training the aliens to understand sequences such as “Ha says to Hb: what is that x such that 2x = 5?”
In one sense, we are treating the space aliens like circus animals; we subject them to a repeated stimulus, giving them positive reinforcement whenever they exhibit the desired response. In the case of animals, however, the reinforcement is immediate–we give them food; in the case of aliens, the reinforcement cannot but be a broadcast signal that they should interpret as “OK.”
By this means, the aliens are meant to learn to recognize not only mathematical operations but also concepts such as “because,” “as,” “if,” “to know,” “to want,” and even “to play.”
The project presupposes that the alines have the technological capability to receive and decode wave-length signals, and that they follow logical and mathematical criteria akin to our own.
They should share with us not only the elementary principles of identity and non-contradiction, but also the habit of inferring a constant rule through induction from many similar cases.
Lincos can only be taught to those who, having guessed that for the mysterious sender 2 x 2 = 4, will assume that this rule will remain constant in the future. This is, in fact, a big assumption; there is no way of ruling out that there exist alien cultures who “think” according to rules which vary according to time and circumstances.
What Freudenthal is aiming for is, explicitly, a true characteristica universalis; in Lincos, however, only a handful of original syntactic rules are formulated in the beginning. As to the rest (as to, for example, the rules governing questions and answers), the model implicitly assumes that the interlocutors will use the rules, and even the pragmatics, of a natural language.
We can, for example, imagine a community of angels, each of whom either reads the thoughts of the others or learns truths directly through beholding them in the mind of God: for such beings, the set of interactional rules governing questions and answers would make no sense at all.
The problem with Lincos is that, although provided with a formal structure, it is conceived as an instrument for “natural” communication, and thus it is inherently uncertain and imprecise. In other words, it cannot possess the tautological structure of a formalized language.
Lincos is probably more interesting from a pedagogical point of view: can one teach a language without ostension?
If the answer is positive, Lincos would allow a situation different from that imagined by philosophers of language, when they skeptically imagine a scene in which a European explorer interacts with a native, each party tries to communicate with the other by pointing at bits of space-time and uttering a given sound, and there is no way for the explorer to be certain whether the native is denoting a given object located in that space-time portion, or the fact that something is happening there, or is expressing his or her refusal to answer (see Quine 1960).”
Umberto Eco, The Search for the Perfect Language, translated by James Fentress, Blackwell. Oxford, 1995, pp. 308-10.