Astraglossa

04 Sep 2014

Lancelot Hogben described Astraglossa in a lecture to the British Interplanetary Society in 1952, later reprinted as Chapter 8 of his book Science in Authority (full text available online) as:

ASTRAGLOSSA or FIRST STEPS IN CELESTIAL SYNTAX

The text is interesting. I don't think I got all the jokes, not being a British person in the 1950s. But it is definitely a lively piece of writing, in an old-timey pre-twitter way. George Orwell once singled out Ogden's use of metaphors as an example of how not to write, and I admit to being struck at how hard it can be to quite follow a fellow human (or co-planetarian as Hogben puts it), never mind communicating further afield. But I'm in no position to cast stones.

Hogben mulls over how to get started communicating and comes up with this:

Number will initially be our common idiom of reciprocal recognition; and astronomy will be the topic of our first factual conversations.

This is the earliest I've seen this idea written down. Hogben expects that:

beings able to contemplate the firmament and to organize settled life in conformity to the dictates of seasonal change will share with us the abstract concept of number.

Others have since made very different arguments for similar expectations of numeracy, for example Marvin Minsky's argument from sparseness. It is good to see the same idea popping out of humans that are quite alien to each other (although not diverse by any means). Astronomy as being a good source of facts to talk about is likewise an idea that keeps cropping up in proposed messages (though granted most people involved in this field are really big into astronomy).

Syntax

Hogben sketches a radio message made up of these parts:

The details are left underspecified, but there are some examples given.

The entrance examination

Hogben imagines sending this message that he calls "the entrance examination":

I + II + III = VI

Which he renders as follows:

1 . . Fa . . 1 . 1 . . Fa . . 1 . 1 . 1 . . Fb . . 1 . 1 . 1 . 1 . 1 . 1

The F parts are "flashes," with Fa corresponding to + and Fb corresponding to =. Numbers are represented in unary, using alternating dashes and dots. Lining up the parts just to make this clear:

I + II + III = VI
1 . . Fa . . 1 . 1 . . Fa . . 1 . 1 . 1 . . Fb . . 1 . 1 . 1 . 1 . 1 . 1

Remember this represents a radio broadcast, don't read too much into the exact characters used. The next thing Hogben suggests is introducing new vocabulary, in this case a symbol Fs for the number 6, by adding an extra equality as follows:

1 . . Fa . . 1 . 1 . . Fa . . 1 . 1 . 1 . . Fb . . Fs . . Fb . . 1 . 1 . 1 . 1 . 1 . 1

The next step

Hogben weighs the next step after these preliminaries:

Here we assume that the class is attentive. We then reach a cross-road. Shall we start the school day with a lesson in arithmetic or with a lesson in astronomy?

He arrives at the conclusion that trying for astronomy would result in trying to teach some arithmetic at the same time, so:

... we now decide to divide our curriculum into a fresher course on number-lore and a sophomore course on star-lore.

He breaks down the purpose of the "number-lore" course as follows:

Then he gets really excited about the triangular numbers for some reason (1, 1+2, 1+2+3, 1+2+3+4), and with some hand-waving suggests that we "can rewrite trigonometry for the Martians by recourse to definitions in terms of infinite series." Don't get me wrong, I'm not complaining about the hand-waving, this was one short lecture after all.

Concretely, he introduces "flashes" for marking statements derived from a particular rule. Here is a rule called Fr·1 in action:

Fr·1 . . 1 . . Fa . . 1 . . Fb . . 1 . 1 (1+1=2)
Fr·1 . . 1 . . Fa . . 1 . . 1 . . Fb . . 1 . 1 . 1 (1+2=3)
Fr·1 . . 1 . . Fa . . 1 . . 1 . . 1 . . Fb . . 1 . 1 . 1 . 1 (1+3=4)

And here is rule Fr·2 in action:

Fr·2 . . 1 . . Fa . . 1 . 1 . . Fb . . 1 . 1 . 1 (1+2=3)
Fr·2 . . 1 . . Fa . . 1 . 1 . . Fa . . 1 . 1 . 1 . . Fb . . 1 . 1 . 1 . 1 . 1 . 1 (1+2+3=6)
Fr·2 . . 1 . . Fa . . 1 . 1 . . Fa . . 1 . 1 . 1 . . Fa . . 1 . 1 . 1 . 1 . . Fb . . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1 . 1
(1+2+3+4=10)

Rules are interesting because they let us show counterexamples and start to ask questions, in a passage Hogben calls:

A first lesson in celestial syntax

Hogben notes that when we establish "rules" with fragments like this we are giving affirmative examples of that rule:

Fr·1 . . 1 . . Fa . . 1 . 1 . . Fa . . 1 . 1 . 1 . . Fb . . Fs (1+2+3=6)

Fr·1 here seems different than what it was earlier in the lecture. Let's not worry about that. Also remember that Fs is just 6. If we can give affirmative examples, why not also give negative examples:

Fn·1 . . 1 . . Fa . . 1 . 1 . 1 . . Fa . . 1 . 1 . 1 . . Fb . . Fs (1+3+3=6)

In notation we've replaced Fr·1 with Fn·1, corresponding to some manipulation of the radio signal.

And then we can consider replacing part of a fragment, replacing it with a "flash" that acts as an interrogative, corresponding to asking the question "what should go here?" This would look something like:

1 . . Fa . . Fq . . Fa . . 1 . 1 . 1 . . Fb . . Fs (1+?+3=6)

I'm simplifying the discussion of Fq a little here, it can have some internal structure that doesn't seem to get used in the lecture.

A second lesson in celestial syntax

Hogben now reuses the interrogative Fq, the affirmative Fr, and the negation Fn as the core of a question-answer pattern. He adds one element, the alternative Fo. Here is the example he gives:

Fq . . 1 . . Fa . . 1 . 1 . . Fa . . 1 . 1 . 1 . . Fb . . Fs . . Fo . . Fq . . 1 . . Fa . . 1 . 1 . 1 . . Fa . . 1 . 1 . 1 . . Fb . . Fs (? 1+2+3=6 or ? 1+3+3=6)
Fr . . 1 . . Fa . . 1 . 1 . . Fa . . 1 . 1 . 1 . . Fb . . Fs (confirmation 1+2+3=6)
Fn . . 1 . . Fa . . 1 . 1 . 1 . . Fa . . 1 . 1 . 1 . . Fb . . Fs (denial 1+3+3=6)

(The text says Nr instead of Fn but I'm pretty sure this is a typo).

We-you

Hogben proposes that:

we can establish the bipolar concept we-you by juxtaposition and repetition of already received and transmitted signals, as soon as we have solved the problem of identifying the interplanetary interrogative particle (Fq).

And then tries to imagine how to ask a question "how many of you are there?" It gets pretty hand-wavy at this point, as befits he end of a lecture.

Should we communicate?

Hogben enjoys this "challenge to cerebration" but does not take for granted that trying for interstellar communication is a good thing:

Before we have proven ourselves worthy to occupy our own planet we may well dread the consequences of publicizing our existence to beings conceivably intelligent enough to forestall any depredations we may contemplate in other parts of the solar system. When we reflect upon the trail of still unsolved problems of race relations in the wake of the slave-raiding bible-punching buccaneers of the first Elizabethan era, we may permissibly share Dean Swift's doubts about the fitness of man to undertake indiscriminate exploits in colonization.

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