On ‘Western numerals’

For the past nine years, really ever since I defended my dissertation proposal, I have been using the term ‘Western numerals’ to describe the set of signs 0-9 used in a decimal fashion with the place-value principle.  This is not standard practice (although it is not unique to me), and after someone asked me about this, I thought I’d explain myself, since I’ll undoubtedly be using the term repeatedly in my numerical posts.

In the English-speaking world, we all learn these signs under the name ‘Arabic numerals’, which reflects the fact that they were borrowed by Western Europeans from Arabs living in Spain, Sicily, and North Africa in the tenth century CE.  In the scholarly literature on numerals, these are most often called ‘Hindu-Arabic numerals’, which reflects a little more of the history of the system, because the Arabic script got its numerals from an antecedent system used in northern India as early as the fifth or sixth century CE.   The historian of mathematics, Carl Boyer, whose early work on numeral systems played an important role in my development as a ‘numbers guy’, argued somewhat facetiously that we might more properly call it the ‘Babylonian-Egyptian-Greek-Hindu-Arabic’ system (1944: 168) – although in this case I think he was wrong, and that ‘Egyptian-Mauryan-Hindu-Arabic’ would get the history straight.

The most basic problem with these formulations ‘Arabic’ and ‘Hindu-Arabic’ is that they do not adequately distinguish the set of signs 0123456789 from the set of signs ٠١٢٣٤٥٦٧٨٩ used in Arabic script from the set of signs ०१२३४५६७८९ used in the modern Devanagari script, and any number of other decimal, place-value systems, all descended ultimately from that 5th-6th century CE Indian ancestor.  To make matters more confusing, in Arabic the numerals used alongside Arabic script are called arqam hindiyyah (Hindi numerals).

The problem of ambiguity is thus a serious one.  Because several such systems are in active use (particularly the Western European 0-9 and the ‘Arabic’ set) it becomes a nightmare to try to distinguish these systems meaningfully.  We need different terms for each set of numerals.  Not only is there potential ambiguity, but using the term ‘Arabic’ or ‘Hindu-Arabic’ for 0123456789 tends to obscure the continued existence and active use of actual ‘Arabic’ and ‘Hindi’ numerals in the Middle East and south Asia.

So I talk about Western, Arabic, and Indian numerals to refer to the place-value systems used in three different script traditions.  Structurally the systems are identical, but paleographically – in terms of the history of the signs themselves – they are quite distinct. Now, one could argue that just as we talk about the ‘Latin alphabet’ we could call 0123456789 the ‘Latin numerals’ instead of ‘Western’, but this would only create confusion with the ‘Roman numerals’.  ‘Western numerals’ reflects the fact that the particular graphemes (sign-forms) developed in a Western European context and were first and most prominently used in Western Europe.

Now, there is a counterargument, that by calling them ‘Western numerals’ I am denying them their history, obscuring the fact that they derived from Indian and Arabic notations, which I certainly do not wish to do!  But I think that Boyer has a point – why stop at ‘Hindu’, since the Hindu place-value numerals derive from a non-positional system used in Brahmi inscriptions in India as early as the 4th century BCE, which in turn probably derive from Egyptian hieratic writing going back as early as the 26th century BCE!  And if we decide that the history is wrong, do we change the name?

Basically I am dissatisfied in general with the notion that we should name extant phenomena after their place of origin; it causes so many problems, including ambiguous nomenclature, that I decided to give up the practice entirely.  Hence ‘Western numerals’.

Works Cited

Boyer, Carl. 1944. Fundamental steps in the development of numeration. Isis 35(2): 353-368.

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