Letters that double as numbers
Before the Hindu-Arabic digits became standard in the Arabic-speaking world, and alongside them for a long time afterwards, the letters of the Arabic alphabet could serve as numerals. The scheme is called abjad, after the first four letters of the traditional order: alif, ba, jim, dal. The same idea is found in Hebrew gematria and in the Greek Milesian numerals, and the Arabic order is generally traced to the older Semitic alphabet sequence that Hebrew and Phoenician share.
This article is about the Arabic version and, in particular, the literary game it made possible. The use of the letters as numbers is a matter of record. Beliefs about hidden meaning in the sums are a separate and more disputed subject, mentioned only briefly below.
The values
In the eastern ordering, the first nine letters stand for the units, the next nine for the tens, and the next nine for the hundreds, with one last letter for a thousand. In the pronounceable mnemonic words that medieval teachers used to remember the order, the pattern looks like this:
| Letters (transliterated) | Values |
|---|---|
| alif, ba, jim, dal, ha, waw, zayn, ha, ta | 1 to 9 |
| ya, kaf, lam, mim, nun, sin, ayn, fa, sad | 10 to 90, in tens |
| qaf, ra, shin, ta, tha, kha, dhal, dad, za | 100 to 900, in hundreds |
| ghayn | 1000 |
Because the Arabic alphabet in everyday use is arranged by letter shape and not by this older order, the abjad sequence was learned separately, usually as a set of memorable nonsense words.
North Africa and al-Andalus, often called the Maghrib, followed a somewhat different order for some of the later letters, so the same letter can carry a different value depending on region. A reader had to know which convention a writer used. This is one of the reasons chronograms are sometimes disputed.
Two quick examples
The word for God, Allah, is spelled alif, lam, lam, ha. The values are 1, 30, 30 and 5, which add up to 66. The name Muhammad is spelled mim, ha, mim, dal, with values 40, 8, 40 and 4, a total of 92. These sums are simple arithmetic; they are noted here because they are often cited as the standard demonstrations of how the system works.
Short vowel marks did not count, and variant spellings could change a total, so a chronogram writer had to be careful about how each word was written.
Chronograms
The best-known use of abjad was the chronogram, called tarikh in several languages of the Islamic world. A poet composed a phrase or a line whose letters, once added up, gave a year, usually counted in the Hijri calendar. The year might mark the completion of a building, a death, a birth, an accession or the copying of a manuscript.
The pleasure of a chronogram was double. The phrase had to make sense, often as a blessing or a lament, and its letter total had to match the date.
Chronograms were written in Arabic, and they were also popular in Persian, Ottoman Turkish and Urdu poetry, where poets wrote them for notable events. They appear on gravestones, mosque gates, fountains and bridges, often in carved or painted calligraphy. A passer-by who could add up the letters could read the year in the building’s own text.
Europeans developed a similar game in Latin, picking out the letters of Roman numerals such as M, D, C, L, X, V and I hidden in a phrase. The trick is old, but the Arabic version is distinctive because every letter counts, not just a few.
Other uses
Besides poetry, abjad numbers turned up in practical settings. Some medieval astronomers and calculators used letters to write numbers in tables, because they were compact and could be set in the same script as the text. Manuscript pages were sometimes numbered the same way.
In addition, a body of writing on the science of letters, sometimes called the science of the letters or ilm al-huruf, treated the sums of names and words as meaningful in themselves. Practitioners held views about this that were developed within particular Sufi and esoteric traditions, and other scholars rejected or ignored them. They are beliefs held by those communities, and not a method with any demonstrated effect.
How it differs from everyday numerals
It is easy to confuse the two systems. The digits written in Arabic-speaking lands, in both their eastern and western forms, descend from Indian numerals and are positional, so that the place of a digit determines its value. Abjad values are additive: the total is just the sum of the letters, with no regard for order. The additive method works well for names and short phrases, but it is awkward for large calculations, which is why it was never the main tool for arithmetic.
The persistence of the abjad into the age of printed books shows how tightly it was woven into literary taste. Some dedication lines and colophons in manuscripts still end with a hidden year, waiting for a reader to add up the letters.