From Chapter 10 Origin of the Arabic Numerals

The question as to which came first, the numerals or the letters, was an-swered convincingly a century ago with the conclusion that the “use of visible signs to represent numbers and aid reckoning is not only older than writing, but older than the development of numerical language on the denary (deci-mal) system.” Two additional conclusions may be considered: 1) that a qui-nary system is older than a decimal system if proven to be a subsystem of the decimal system; and 2) that numeral alphabets preceded language alphabets, and indeed some numeral symbols may have been used to construct language scripts with or without prior knowledge of their original function. The con-sensus of researchers and historians of numbers is that among primitive tribes hands and fingers have been employed for the most common purposes of calculation since ancient times, as well as among the more cultivated na-tions to the present day.
In considering the history and evolvement of the Arabic numeral picto-grams, we feel more comfortable in describing these pictograms as ‘Arabian’ or ‘ancient Arabian’ rather than Arabic. We have no hesitation in claiming that the historical origin of the numeral pictograms is embodied in the hawa’i calculus more than any other branch of the science of numbers. The hawa’i calculus is known as the “calculus of the hand” and the numeral pictograms are known as the “hawa’i numerals”. Every concept related to this branch of calculation is given a distinctly Arabic name, and Jahiliah poetry and tradi-tion attest to its pre-Islamic roots. Yet, we cannot exclude the possibility that unspecified elements of this calculus were known to the old South Arabians and others. One of the reasons is that both the South Arabian and Palmyrene numeral systems, like the Arabic system, appear to have been quinary at one point in their development, a characteristic shared by the three systems to the exclusion of all other numeric systems for which we have records of usage in the Middle East. In describing the numeral system as ‘Arabic, we are not claiming it on behalf of Northern Arabs whose language is Arabic, but simply describing a universal system known by this name and, in the process, aim-ing to avoid confusion.
Before we present the complete set of Arabic numeral pictograms, it may be helpful to remind ourselves of the following number of points explained or referred to earlier:

10.1. Only a camera can produce an exact image of the ‘thing’ (i.e., house, camel, finger, hand, etc.,) for which a need develops to communicate to other members of the community. In most cases, any attempt to represent the “thing” by drawing is an approximation and miniaturisation of the original ‘thing’. The result is a drawing that varies in representational quality from one person to another. A correct assumption is that early attempts at repro-ducing the ‘thing’ were crude but sufficiently capable of resembling the ‘thing’ they were supposed to represent. These are the pictograms or picto-graphs discussed earlier, and many are attested in inscriptions five thousand years old or more. In a number of cases, such as that related to Chinese char-acters, the original pictograms are believed to have resembled the ‘things’ they stood for. Over the years, the original pictograms were gradually modi-fied and stylised for speed, elegance and other reasons. The pictographic identification was substituted by symbolic identification through learning. For this reason, pictograms are sometimes described as one of the earliest numeral and character representations known to man, and they belong to an ancient and primitive stage of development. At a later stage, some pictograms resembling the ‘things’ were used as hints to express concepts related to the ‘things’. These are sometimes called ideograms or ideographs. The concept of safr (zero) is such. The pictogram of numeral 10 was ‘emptied’ of its number quantity to a degree that it became a nil-number, and its size was corre-spondingly reduced to reflect, visually and graphically, the new quantity val-ue. Two pictograms were invented to resemble the conceptualised ‘shell’ of the former numeral 10: the small circle and the numeric dot. The Arabic nu-merals, therefore, are a combined pictogramic and ideogramic system. It is a “natural” system dependent for the representation of its nine units on finger and hand formations. It owes its excellence to the astonishing concept of the principle of local value and the use of safr. For this reason, it may be de-scribed as a “cypher numeric system”. There are several reasons why Arabic numerals retained their original shape throughout the ages. The graphical representation of a house may differ from one culture to another because choices for such variations are available. This is not the case as far as human hands and fingers are concerned because both are obviously constant. The preservation of the various shapes of “eastern-style” Arabic numerals is due to the availability of permanent references to the original shapes in the form of the known finger and hand poses. At a later stage, the integrity of those shapes was largely maintained by the inclusion of the Arabic numerals in the Qur’an. A number of graphical variations of certain numerals exist for cul-tural and religious reasons, but the variations, both eastern and western, largely maintained the quantity value of the original numeral. The awareness of an inherent quantity value in the Arabic numerals appears to be shared by humans and certain animals alike. A combination of human ingenuity and natural elements has turned one of the most primitive and localised numeric communicative systems into one of the most advanced universal systems in history.

10.2. In discussing Arabic numerals, Arab and Muslim writers made no specific distinction between numerals and letters. Thus, al-Yaqubi referred to Arabic numerals as ahruf (letters) , and both ibn al-Nadim and ibn al-Wahshiya did the same when they produced the numeric alphabet and de-scribed it as qalam (language script). Arab and Muslim mathematicians and arithmeticians referred to numerals as qalam (قلم) and khatt (خط), both to mean a language script.

10.3. Following in the footsteps of Arab and Muslim writers before us, we may suggest that the pictograms of various Arabic numerals or numeral-shaped characters have remained largely distinctive, whether used in Ca-naanite, Aramaic, Arabic, or written partly in Nabataean script or any other script mentioned by ibn al-Nadim and ibn al-Wahshiah without specifying which nations used them as alphabets.

10.4. When we compare the shapes of what we call the Arabic numeric al-phabet to the same or similar shapes used in earlier alphabets to represent a chosen sound, we find that the entire Arabic numeric alphabet (including the zero and the Qur’anic 2 (2) were used in Canaanite, Aramaic and Demotic. Possibly three or four numeral-shaped characters are also found in the Musnad script. This should be no surprise, since many nations have given numeric values to certain letters of their alphabet and we may expect the op-posite to have taken place, especially when numeric signs are known to be older than letters and thus readily available for any group of people contem-plating the construction of a language alphabet.

10.5. Of all scripts, Arabic may look like the only eastern alphabet absent from which are the distinctive shapes of the Arabic numerals. This should not be surprising since Arabic is a fully cursive script and accommodating the cursive-resistant numeral shapes is difficult in writing styles such as Kufic, Naskhi, Persian and others. However, if we study the alphabet shapes closely, we may find that و (waw) was originally the numeral-shape 9 seen in the epi-taph of Imru-ul Qais and assigned the same sound, ع (‘ayn) is probably de-rived from numeral 4, alef from numeral 1, س (s) from the upper part of nu-meral 3, while both ه (h) and م (m) are probably derived from numeral 5 (5), etc.

10.6. In attempting to determine the origins of the scripts developed in the Middle East, it may be prudent to avoid applying to them the known rules and historical backgrounds governing Latin and modern European scripts. The first group of scripts is much older, and their origin is not sufficiently known. An alternative is to think of an ancient ‘reservoir’ of linguistic and alphabetical knowledge maintained indefinitely and preserved in tribal tradi-tions. From such a reservoir, segments of the tribal structure would be able from time to time to draw upon the needed knowledge to build their own scripts. Because it is a common tribal reservoir, elements of new scripts may be added to older elements, and the enriched reservoir in turn becomes available to newer tribal segments desirous of building their own scripts ei-ther by modifying older shapes or by designing new ones. This may explain why many Semitic languages share identical or similar words for the numer-als from “one” to “one thousand”, and why many scripts appear to reproduce at least some of the numeral-shaped signs correctly, despite considerable ge-ographical and temporal differences.

10.7. We are unable to suggest a timeframe for the development of the Ar-abic numeral pictograms. As we have seen earlier, most of the numerals share common roots with Proto-Semitic. The fact that some numerals were origi-nally related to a finger, a hand, a fistful, etc., might lead the reader to con-clude that the numeral pictograms are probably 5,500 to 7,000 years old and maybe older. Considered as a set, the Arabic numerals may be the oldest known fully pictographic alphabet in history, and their distinctive picto-graphic representation has been preserved in the eastern-style Arabic nu-merals to the present day.

10.8. At least three scholars have used the words “drawings” or “drawn” when referring to the Arabic numerals and written scripts: Al-Beiruni, ibn al-Nadim and Hajji Khalifa. However, no recorded mention was made that the Arabic numerals are finger and hand poses. This led us to the conclusion that all writers who discussed the Arabic numerals failed to identify their origins. Nevertheless, the fact that references are made to these numerals as “draw-ings” may give rise to the possibility that at one time the origin of the numer-als was known to most people who dealt with them, and no reference was made to the origins because it was thought that such a fact is common knowledge and there was no need to remind people of it. This would be a typ-ical Arab attitude. Lookup the word “white” in the dictionary and you will find the meaning: “opposite of black”. Lookup “black” and the meaning is given as “known”.

10.9. There appears to be a definite connection between major trading ac-tivity and the development of literary and numerical scripts. More accurate historical accounts could shed much-needed light on the origin of scripts, but we can now ask, if the Canaanites were not the first trade masters of the world, then who were their masters? If new research points to a thriving Iram three thousand years before our current era, would the Iramaeans not have their own language and numeral scripts? Such questions are justified by the fact that, in addition to the Canaanites, Nabataeans, South Arabians, and Palmyrenes, the North Arabians had their own trading empire and their own distinctive literary and numeric scripts whether numeric, alphanumeric, or both. We know that the Prophet Mohammad and his companions used a so-phisticated finger-counting system, but we have no evidence that the system was not supported by a numeric script to preserve the results of finger and hand computation.

10.10. It is helpful to remember that the basic Arabic numeral system was essentially visual, produced by known finger and hand poses. Such a consid-eration is essential to understanding the origin of the positional system.

10.11. The pictograms 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 of the eastern-style Arabic numerals are not symbolic representations of the numerals but the numerals themselves.

10.12. The Arabic numeric system as it stands is a base-10 system and can be termed “decimal”, but historically it is not. It is a hybrid system that passed through three distinct stages of development:

1) A quinary stage during which the system consisted of five different finger formations with a single-shape group number “five”;

2) a biquinary stage during which five more pictograms were added to the sub-quinary system, drawn from four hand formations and a sin-gle-shape group number “ten”;

3) A positional stage attained by altering the function and numerical value of the group number “ten”, replacing it with two pictograms of numeral “one” and “safr” (zero).

10.13. Two pictograms of safr (zero) were made available to users to choose from: the small circle and the numeric dot. There is absolutely no difference in the function of safr and the positional system using either pictogram.

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