Posted on Wednesday 7 April 2004

In 1678 Leibniz composed a lingua generalis... After decomposing all of human knowledge into simple ideas, and assigning a number to each, Leibniz proposed a system of transcription for these numbers in which consonants stood for integers and vowels for units, tens and powers of ten:

1	2	3	4	5	6	7	8	9
b	c	d	f	g	h	l	m	n

1s	10s	100s	1,000s	10,000s
a	e	i	o	u

In this system the figure 81,374, for example, would be transcribed as mubodilefa. In fact, since the relevant power of ten is shown by the following vowel rather than by the decimal place, the order of the letters in the name is irrelevant: 81,374 might just as easily be transcribed as bodifalemu.

--- The Search for the Perfect language, Umberto Eco

For those too lazy to try the transcription for themselves by hand, why not try this handy Leibniz-a-fier? Just type in the number you want to transcribe and hit the button.

Eco doesn't explain what happens for integers larger than 99,999 in Leibniz's scheme so I've chopped up the numbers into groups of no more that 5 digits. Nor does he explain Leibniz's treatment of zero so I've made an assumption and simply used the next consonant after 9 (i.e. the letter p).

Update: Reader KCinDC points out that my solution for zero was half-baked and that it's actually more likely that Leibniz simply left out the 0s and didn't pronounce them. This works fine because the power of ten is represented by a vowel rather than its place but it does mean that the number zero has no pronounciation at all. I've updated the code to reflect this change.

Please note this piece of code is very alpha so please be gentle with it ;-)

By working on a universal language Leibniz was following up on a particularly baroque idea that had also been pursued by a number of other 17th century luminaries (most notably Athanasius Kircher with his polygraphy and the a priori philosophical language of John Wilkins (via Mark Liberman). Leibniz however was uninterested in the main attraction that universal languages had for other researchers, the ability to facilitate missionary activity or international trade. Instead, his main focus was upon making a mathematical language with which to perform calculations that would automatically lead to the formulation of true propositions.

If we accept the traditional definition of man as a 'rational animal, we might consider man as a concept composed of 'rational' and 'animal'. We may assign numbers to these prime terms: animal = 2, and rational = 3. The composite concept of man can be represented as the expression 2 * 3, or 6.

For a proposition to be true, if we express fractionally the subject-predicate (S/P) relationship, the number which corresponds to the subject must be exactly divisible by the number which corresponds to the predicate. Given the proposition 'all men are animals', the number for the subject (men), is 6; the number for the animals is 2; the resulting fraction is 6 / 2 = 3. Three being an integer, consequently, the proposition is true. If the number for monkey were 10, we could demonstrate the falsity of either the proposition 'all men are monkeys' or 'all monkeys are men': 'the idea of the monkey does not contain the idea of man, nor, vice versa, does the idea of the latter contain the former, because neither can 6 be exactly divided by 10, nor 10 by 6'

--- ibid.

Update: Mark Liberman does the hard yards and actually explains Leibniz's system far better than this very brief intro. Better still, Laputan Logic is cited as "smart" (which coming from Mark I take as a very great compliment indeed) though, alas, not in the same league of smartness that's needed to have a really spectacularly stupid idea. For that, one would need to have a mind as spectacularly brilliant as that of the great Inventor of the Calculus himself.

Leibniz was also very interested in the language and culture of China but the Chinese themselves while never having seen the attraction of a universal language (why would they have when their own writing system was perfectly well understood by all of their neighbours, barbarian and semi-barbarian alike?) but they have long appreciated a cosmic connection between numbers and words.

Chinese culture has a fascination with numbers. Take for example: the Ten Suns, the Nine Aspects of the Dragon, the Eight Immortals, the Seven Sages of the Bamboo Grove, the Six Arts, the Five Elements, the Four Modernizations, the Three Doctrines, the Two Principles and the One way. The Chinese language is also veritable playground for compulsive punners. Chinese is very economical with word-sounds and many words are only of one syllable. The syllables themselves are of a fairly simple form and different meanings are applied by pronouncing it with different tones (e.g. rising, high, falling, etc.) but it's actually quite common for a single syllable with an identical tone to serve as several completely different words.

So, with the aforementioned fascination with numbers and the easy ability to make puns, it seems in retrospect inevitable that the Chinese would merge the two and begin to read whole sentences out of strings of numbers. I first became away of this tendency whilst driving in Malaysia. The driver noticed a car swerve in front of her and she instinctively glanced down at the licence plate. "114", she said, "Ha! Only a fool would drive a car like that!". This was followed by a characteristically Malaysian action, to speed up just enough to check the race of the driver (the candidates being Chinese, Malay, Indian or Other). Sure enough the "fool" was non-Chinese. When I asked her what she meant, she explained that the number meant "Most Surely Die!" - a particularly inauspicious number.

Car dealers, real-estate agents and telephone companies in many countries, including the West, are well aware of this Chinese sensitivity to numbers. They know that a tiny detail like that can be an deal maker or deal breaker (or at least have a big impact on the final price). The correlation between number and meaning comes down to, mundanely enough as it happens, a pun between the pronunciation of a number and a word that sounds like it.

This punning is affected by the dialect so I'll restrict my discussion here to Cantonese numbers and words. The meanings of the numbers 3, 4, 8 and 9 are pretty near universal, however.

1	2	3	4	5	6	7	8	9
guaranteed	easy	life	death	never	road to / profit	certainly	prosper	everlasting

Once again for those too lazy to analyse their street addresses or licence plates by hand, I've included this handy calculator for your convenience. The same disclaimers apply although I would appreciate whatever feedback I can get from native speakers to help me refine it.

There's at least one case where the order of the numbers has a bearing on the meaning. This has to do with the number 4. Four sounds like death and is very bad to end a number with but, surprising, it's generally a good thing to have as an early digit because it acts as an intensifier and means something like "dead sure" or "dead certain".

A business that I was involved in many years ago set up above a shop in a busy street and I was a little nervous that its street address was 148. But it was okay, everyone assured that this was a truly great number, it means "Everyday Definitely Prosper", really you couldn't ask for better one. Alas, after a few years the business didn't go very well and there are lots of reasons for that but at least I can console myself that one of them had to do with moving from this address.

See also:
The Significance of Numbers and Colors
Energy of Numbers
Cantonese Discussion - Using numbers as a phrase or for good luck