From D. R. LADD
Michael Ecker’s ‘words to numbers’ game (‘Caution: black holes at work’,
19/26 December) – in which you always end up at the black hole ‘4’ by writing
the name of a number in English, counting the letters, writing the names
of that number, and so on – is, as he notes, ‘clearly language-dependent’.
But the game has interesting general properties regardless of what language
you play it in.
First, it’s obvious that to be a black hole, a number has to have the
same number of letters in its name as its numerical value. So Italian tre,
Spanish cinco, and German vier all qualify. In addition, for any such number
name to function as a black hole, there has to be another number name with
the same number of letters (such as Italian sei, Spanish siete, most of
the other cardinals 1-10 in German). Lithuanian penki (5) is a potential
black hole, but it is never reached because no other Lithuanian number
name has five letters.
In languages with no working black holes, the game seems to fall just
as inexorably into a closed loop. This is illustrated by the French sequence
trois, cinq, quatre, six. Wherever you start the game, you will eventually
hit one of those four numbers and then go round the loop forever. Some languages
have both a loop and a black hole, such as Turkish iki (2) and muc (3) –
which form a loop – and dort (4) – which is a black hole. Again, which you
fall into depends on where you start.
It’s my conjecture that any natural language, written in any writing
system that allows you to count letters or components of characters, will
have at least one closed loop if it doesn’t have a black hole. But I’m a
linguist; are there any mathematicians out there who could tell me whether
this is true, and if so why?
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D. R. Ladd University of Edinburgh
