Numbers and angles

by Mark Newbrook
Quite frequently I am contacted (usually emailed) by amateur ‘linguists’ seeking approval for their pet theories – which are often fairly wild and extreme. In fact, my interest in such matters has become so notorious that some such people who have read my publications but cannot find my address contact my skeptical colleagues with a view to being put in touch with me! In yet other cases, mainstream scholars who I happen to meet are happy to off-load onto me fringe works sent to them over the years; in 2003, a retiring professor of Semitic languages who was clearing out his library delightedly gave me five books of this kind. And I also receive items chanced upon by current or former students and colleagues who are not themselves active skeptics but know that I will pounce upon anything like this!
One recent case, forwarded to me by a very talented former student, involves a theory about the origins of the shapes of the ‘Arabic’ (apparently ultimately Indian) characters used to represent numbers (integers). These characters are anomalous in alphabetic scripts – such as the Roman alphabet used to write English and many other languages – because they are ‘logographic’: each character holistically represents an entire word, not an individual sound (as in an alphabet) or a sequence of sounds. The symbols do not, therefore, express the phonology (in lay terms, the pronunciation) of the integer-names, and they are thus cross-linguistic. For example, the character 4 represents English four, French quatre, Malay empat and all equivalent words equally well, and is read off by users of each language with the relevant language-specific pronunciation.

In this respect, these symbols resemble Chinese characters, which are often pronounced quite differently in Mandarin and the various fangyan (‘dialects’) of Chinese such as Cantonese, Hokkien, etc.; for instance, the character meaning ‘person’ is read as ren in Mandarin, yan in Cantonese, etc. This arises because Chinese is really not so much a language as a family of closely related languages with similar structures, united by a shared cultural tradition and a common logographic written script (which suits Chinese very well, for this and other reasons).

In the case of integers, the concepts are so basic and so universally shared that the words of different languages can be represented by common symbols in this way even if these languages have very different vocabulary and grammar structures in other respects. All languages have a word for ‘four’ – except for some ‘tribal’ languages which have only rudimentary integer systems.

The degree to which these symbols reflect the spoken and the full written forms of the integer-names
does vary when they are used in positional combinations. For instance, complex symbols such as 18 reflect the structure of languages where the word itself (e.g. French dix-huit) literally means ‘ten (and) eight’ better than that of English with its eighteen. And single-stem words such as Russian sorok (‘forty’; not related in form to the words for ‘four’ and ‘ten’), and the many such words in languages like Hindi, are not transparently expressed by logographic forms such as 40. Nevertheless, the system itself is much clearer – and much easier to use in arithmetic – than other systems such as Roman numerals, and it works very well in a wide range of language communities.

Chinese and some other languages instead use non-‘Arabic’ logographic symbols; in the case of Chinese, these are obviously of the same nature as Chinese characters generally.. Some such number-symbols, notably ‘Arabic’ 1, appear motivated: the symbol 1 is a single stroke. The Chinese symbol is also a single stroke but in this case horizontal, it is doubled and trebled for ‘two’ and ‘three’ respectively. Most of the ‘Arabic’ symbols, however, appear arbitrary: for example, the character 2 does not obviously express the meaning ‘two’. (In this respect these symbols resemble letters of an alphabet, which do not automatically express the sounds which they represent; their pronunciations have to be learned by users of other scripts, even where a character exists in both systems. For instance, in the Cyrillic alphabet used to write Russian, C represents /s/ and P is /r/, as in CCCP = SSSR = ‘USSR’.)

However, the author in question here holds that the ‘Arabic’ numerals 1-9 and also the zero sign (0) are not in fact arbitrary. His name is apparently Jason King but he is not especially well versed in English; his grammar is strange and he uses the term algorithm to mean ‘number symbol’. King’s ideas are expounded in the file Numbers_0_9-.pps; there is some online discussion (quite sharp exchanges, in fact) on The basic claim is that each symbol was invented so as to have angles corresponding in number with the symbol’s meaning. Thus, 0 has no angles, 1 (written as now usually printed) has one, 2 (written here as Z) has two, etc.

Obviously, King has to make various dubious assumptions in arriving at this view. For instance, he assumes that 1 was originally written as now printed; but in older versions it is typically a single vertical stroke with no angles. Then he has to ignore the foot which is also often used in 1 today, since this would create two additional angles (three in all); but in the case of 7 he is obliged to include the foot to make the number of angles correct. He also has to include the horizontal stroke now used in some hand-writing to distinguish 7 more clearly from 1; this is in fact a relatively recent innovation. And in the case of 9 he has to adopt a form close to a hand-written lower-case G, with a tail curling left from the foot, then upwards and then right again. More generally, he is forced by his ‘angle’ thesis to adopt unfamiliar forms featuring only straight lines (such as Z for 2); and he includes exterior angles only when they are not reflex angles, without justifying this move. King does not offer any actual evidence that his forms are original ones; and he claims that they were invented by the Phoenicians rather than in India. But, as one online commentator notes, the usual Phoenician number-symbols were not similar to the ‘Arabic’ symbols.

In sum, it does not appear that King is right here. The best that can be said is that he has drawn attention to a somewhat neglected matter.