Origin of the numerals

Abstract

Through the pagination of an Arabian Algerian manuscript of the beginning of the 19th century, we rediscover the original shape, the "Ghubari" shape, of the numerals. Contrary to some assumptions, particularly those which claim that they are derived from Indian characters, this "Ghubari" shape, whose use has completely disappeared, shows that the ten modern numerals derive from ten Arabic letters. The symbol of a "Ghubari" numeral corresponds to the Arabic letter whose "Abjadi" numerical value is equal to this numeral. The assumption of the Indian origin of the numerals is denied by the shape of the numerals and by the right left sociological logic of the representation of the numerals and the algorithms of the basic operations. The numerals are born in Maghreb or in Spain. In Europe, the "Ghubari" numerals became the modern numerals: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and in the Middle East, borrowing two Hebrew letters, they gave the "Mashriki" numerals: ۰ ۱ ۲ ۳ ٩ ٨ ٧ ٦ ٥ ٤ .

Full text

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CSHPS/SCHPS ANNUAL MEETING 29-31 May 2006, YORK UNIVERSITY TORONTO
Origin of the numerals
Ahmed Boucenna
Department of Physics, Faculty of Sciences,
Ferhat Abbas University 19000 Sétif, Algeria
aboucenna@wissal.dz aboucenna@yahoo.com
Abstract
Through the pagination of an Arabian Algerian manuscript of the beginning of the 19th
century, we rediscover the original shape, the "Ghubari" shape, of the numerals. Contrary to
some assumptions, particularly those which claim that they are derived from Indian
characters, this "Ghubari" shape, whose use has completely disappeared, shows that the ten
modern numerals derive from ten Arabic letters. The symbol of a "Ghubari" numeral
corresponds to the Arabic letter whose "Abjadi" numerical value is equal to this numeral. The
assumption of the Indian origin of the numerals is denied by the shape of the numerals and by
the right left sociological logic of the representation of the numerals and the algorithms of the
basic operations.
The numerals are born in Maghreb or in Spain. In Europe, the "Ghubari" numerals became the
modern numerals: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and in the Middle East, borrowing two Hebrew
letters, they gave the "Mashriki" numerals: ٩ ٨ ٧ ٦ ٥ ٤ ٣ ٢ ١ ٠ .
MCS : 01A30
Keywords : "Ghubari" numeral, modern numeral, "Mashriki" numeral, Arabic letters, Hebrew
letters, "Abjadi" calculation, "Abjadi" numerical value, "Abjadi" order, right left sociological
Logic.
Résumé
A travers la pagination mixte d'un manuscrit arabe algérien du début du 19ème siècle nous
redécouvrons la forme originale, la forme "Ghubari", des chiffres. Contrairement à ce que
prétendent certaines hypothèses, particulièrement celles qui les présentent comme dérivant de
caractères indiens, cette forme "Ghubari", dont l'utilisation a complètement disparu, montre
que les dix chiffres modernes dérivent de dix lettres arabes. Le symbole d’un chiffre
"Ghubari" correspond à la lettre arabe dont la valeur numérique "Abjadi" est égale à ce
chiffre. L'hypothèse de l'origine indienne des chiffres et démentie par la forme des chiffres et
par la logique sociologique droite gauche de la représentation des nombres et des algorithmes
des opérations élémentaires.
Les chiffres sont nés au Maghreb ou en Espagne. En Europe, les chiffres "Ghubari" ont donné
les chiffres modernes: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 et au Moyen Orient, en empruntant deux lettres
hébraïques, ont donné les chiffres "Mashriki" : ٩ ٨ ٧ ٦ ٥ ٤ ٣ ٢ ١ ٠ .

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1. Introduction
Before approaching the question of the origin of the modern numerals, let us first begin by
recalling the following terminology. In this work, we designate by :
- Modern numerals or Arabic modern numerals, the numerals whose symbols are the
following: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, which are used in Sciences and Technologies.
- "Mashriki" numerals, or Arabic "Mashriki" numerals, Whose symbols are :
٩ ٨ ٧ ٦ ٥ ٤ ٣ ٢ ١ ٠
which are currently used, up to now, in Middle East.
- "Ghubari" numerals, which are the ancestors of the modern numerals, were often used,
during the Middle Ages, in Maghreb (North Africa) and Spain, at the time when the Arabic
Muslim civilization was flourishing.
In this work, we approach the issue of the origin of the modern numeral symbols and that of
the "Mashriki" ones. Some assumptions have been put forward as to this origin. One of these
assumptions considers the modern numerals as deriving from Indian characters ([Ifrah, 1996],
[Ifrah, 1999], [Ouaknin, 2004] and [Institut du monde arabe, 2005]). Another one makes a
direct relationship between the number of plausible angles in the geometrical numeral shape
and the numeral numerical value [Duchenoud, 1867]. The numeral would quantify the
number of angles of its geometric shape. These assumptions seem to have as a starting point
the modern shapes of the numeral symbols, whereas the origin must be searched through the
original shapes that the numeral symbols had in Maghreb, before passing in Europe. They
were then called the "Ghubari" numerals.
A first tentative to introduce the "Ghubari" numerals in Europe through Cordoba was
undertaken by the Pope Sylvestre II (999-1003). In fact, it is from Béjaïa (Algeria) that the
"Ghubari" numerals passed in Europe with tradesmen and Leonardo Fibonacci (born in 1170).
In Europe, the evolution of the "Ghubari" numerals gave the modern ones, but in Maghreb
they continued to be used under their original shape, regardless of their evolution in Europe
until the beginning of the 19th century. Since the beginning of the second half of the 19th
century, the use of the "Ghubari" numeral, in its original shape, completely disappeared, even
in Maghreb, to the benefit of the "Mashriki" and modern numerals.
In this work, we first rediscover and identify the symbols of the "Ghubari" numerals through
the mixed pagination of an Arabian Algerian manuscript, "Kitab khalil bni Ishak El Maliki",
of the beginning of the 19th century. The correspondence, without ambiguity, between the
modern numerals and their eldest the "Ghubari" numerals will be established. The elements of
the "Abjadi" calculation ("Hissab El-joummel" or "Guematria"), particularly the notions of
the numeric values ("Abjadi" numerical values) of the Arabic and Hebrew letters, will also be
recalled. Then we will show the relation between the "Ghubari" numeral and the Arabic letter
whose numerical value is equal to this numeral and we give the initial transformations
imposed to the Arabic letters to become "Ghubari" numerals. We finish by unveiling the
origin of the "Ghubari" numerals, the modern and the "Mashriki" ones. The right left
sociological logic reinforced our findings.
2. Identification of the "Ghubari" numerals
2.1. Presentation of the manuscript "Kitab khalil bni Ishak El Maliki"
The manuscript is a copy of a book known as "Kitab khalil bni Ishak El Maliki", about the
ritual Islamic Malikite "fik'h", prepared for "Sidi Khelifa" Zaouïa, in the region of Setif
(Eastern Algeria.) The copyist is Mohamed ben Sidi khelifa ben Ali ben Salem ben Sifa. The
manuscript is of 17.5 x cm 12.5 cm format and includes 179 sheets numbered from 1 to 179.
These numbers were written, as a matter of fact, with the help of the "Ghubari" numerals. The
sheets 4 and 23 are missing. The sheet number 77 has been numbered twice, having also
number 78 on its back. The date of the copy, written with the "Maghribi" police of the Arabic

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letters, appears at the end of the manuscript, by means of the traditional expression" Copy
finished at Midday ("Ezzaouel") of Wednesday, eight of the "Safar" month of the year 1225
of the "hegire" era, corresponding roughly to the year 1810, Figure 1. The year of the
manuscript is indicated with "Ghubari" numerals above the expression مﺎــــــــــــــﻋ, which means year.
A transcription attempt, of this date in "Mashriki" numeral , which came later, can be seen as being
unfruitful, since the numeral 5 has been taken for a 6 "Mashriki".
Figure 1:
Last page of the Manuscript
Kitab Khalil bni Ishak El Maliki
Another transcription was attempted, in modern numerals at the bottom of the page this time, also
failed since the numeral 5 of the manuscript has been interpreted as being the numeral 4. This
shows the total confusion to which people, who had just lost their "Ghubari" numerals for the
benefit of the "Mashriki" and the modern ones, were confronted in the Maghreb during the second
half of the 19th century.
2.2. The mixed pagination
Contrary to the pagination of modern books, it is rare to find, in the Arabian manuscripts, the
order of the pages indicated by a series of numbers. It is the traditional pagination that was
extensively used. The latter one consisted in writing down, in the left foot of even page of the
sheet, the first word or the first two words, if there is ambiguity, of the first line of the odd
following page, (see Figure 2).
Figure 2 :
Mixed pagination
In top of the right page, is indicated
the number of the sheet : 36.
At the bottom, on the left of the same
page, the word ﻦﻴ1ﻋ is written which is
the first word of the first line of the
following page, the left page.
In our manuscript, in addition to the traditional pagination, the sheets have been numbered
with the help of the "Ghubari" numerals. So, there is cohabitation between the traditional

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pagination and the one carried out with the help of the "Ghubari" numerals. It is the mixed
pagination in which the order of the pages is reported in two different manners, on every
sheet.
2.3. Identification of the symbols of the "Ghubari" numerals
The interest of the mixed pagination is double. First, it gives the symbols of the "Ghubari"
numerals. Second, it eliminates all risk of mistake in the interpretation and the identification
of the numeral symbols, since the number of numbered manuscript sheets is 179 and
therefore, every "Ghubari" numeral is mentioned in more than 18 ordered numerical series.
Figures 3 to 12 show the symbols of the "Ghubari" numerals used for the numbering of the
sheets of the manuscript.
Figure 3 : from left to right
The "Ghubari" numerals 1, 0 and 0 in the manuscript.
Figure 4 : from left to right
The "Ghubari" numerals 2 and 1 in the manuscript.
Figure 5 : from left to right
The "Ghubari" numerals 2 and 2 in the manuscript.
Figure 6 : from left to right
The "Ghubari" numerals 3 and 3 in the manuscript.
Figure 7 : from left to right
The "Ghubari" numerals 2 and 4 in the manuscript
Figure 8 : from left to right
The "Ghubari" numerals 3 and 4 in the manuscript

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Figure 9 : from left to right
The "Ghubari" numerals 3 and 5 in the manuscript.
Figure 10 : from left to right
The "Ghubari" numerals 3 and 7 in the manuscript.
Figure 11 : from left to right
The "Ghubari" numerals 6 and 8 in the manuscript
Figure 12 : from left to right
The "Ghubari" numerals 6 and 9 in the manuscript
The identification of "Ghubari" numeral symbols, deduced from the mixed pagination of the
manuscript, is reported in Table 1. The correspondence is immediate between the modern
numerals and their eldest the "Ghubari" numerals.
Table 1: The "Ghubari" numerals used in the numbering of the sheets
of the manuscript "Kitab khalil bni Ishak El Maliki"
Modern
numerals 0 1 2 3 4 5 6 7 8 9
"Ghubari"
numerals
The modern numerals symbols 0 and 1 are practically the same as the "Ghubari" symbols. In
the modern numeral symbol 2, the two dots completely disappeared. In the modern numeral
symbol 3, the dot and the tail disappeared. The comparison of the modern numerals 4 and 5
with their corresponding "Ghubari" ones shows that the two symbols have been permuted.
Indeed, the numeral "Ghubari" 5 corresponds to the modern numeral 4, while the numeral
"Ghubari" 4 corresponds to the modern numeral 5. The modern numeral symbol 6 is
practically the same as the "Ghubari" numeral symbol 6. A slight evolution is observed in the
modern numeral symbol 7. In the modern numeral symbol 8 the angles are rounded. The
modern numeral symbol 9 does not differ from the numeral "Ghubari" symbol 9. The
disappearance of the dots of the numerals 2 and 3 and the permutation of the numerals 4 and 5
constitute important divergences which, in our opinion, hide the origin of the numerals and
mislead the researchers.

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3. Elements of the "Abjadi" calculation
3.1. The "Abjadi" numerical values of the Arabic and Hebrew letters
The "Abjadi" calculation or "Hissab El-joummel" or Guématria, represents the set of the
numerical operations that are possible from the numerical equivalence of the Arabic and
Hebrew alphabetic letters. In the "Abjadi" calculation, the "Abjadi" numbers are the following
natural numbers : {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 200, 300,
400, 500, 600, 700, 800, 900, 1000}. Every Arabic and Hebrew letter possesses a numerical
value ("Abjadi" numerical value) equal to an "Abjadi" number.
Table 2
Sounds and "Abjadi" numerical values of the 28 Arabic letters arranged according to the "Abjadi" order
"Abjadi"
Order
Arabic
Letter
Sound "Abjadi"
numerical
value
"Abjadi"
Order
Arabic
Letter
Sound "Abjadi"
numerical
value
1 ا Alif 1 15 س Sin 60
2 ب Baa 2 16 ع A'in 70
3 ج Jim 3 17 ف Faa 80
4 د Del 4 18 ص Sad 90
5 ﻩ Haa 5 19 ق K'af 100
6 و Waw 6 20 ر Raa 200
7 ز Zin 7 21 ش Shin 300
8 ح H'aa 8 22 ت Taa 400
9 ط T'aa 9 23 ث Thaa 500
10 ي Yaa 10 24 خ Kh'aa 600
11 ك Kef 20 25 ذ Dhel 700
12 ل Lem 30 26 ض Dzad 800
13 م Mim 40 27 ظ Dzaa 900
14 ن Noun 50 28 غ Ghin 1000
Table 3
Sounds and "Abjadi" numerical values of the 22 Hebrew letters arranged according to the "Abjadi" order
"Abjadi"
Order
Hebrew
Letter Sound
"Abjadi"
numerical
value
"Abjadi"
Order
Hebrew
Letter Sound
"Abjadi"
numerical
value
1 א Aleph 1 12 ל Lamedh 30
2 ב Beth 2 13 ם מ Mem 40
3 ג Gimel 3 14 ן נ Nun 50
4 ד Daleth 4 15 ס Samek 60
5 ה He 5 16 ע Ayin 70
6 ו Vav 6 17 ף פ Fe 80
7 ז Zayin 7 18 ץ צ Tsahde 90
8 ח Cheth 8 19 ק Q'oph 100
9 ט Teth 9 20 ר Regh 200
10 י Yodh 10 21 ש
ש
Sin
Shin
300
11 ך כ Kaph 20 22 ת Tav 400
The alphabet of a language is expressed according to a conventional order. In the "Abjadi"
order, the Arabic and Hebrew letters are arranged in increasing order of their "Abjadi"

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numerical values. Table 2 gives the sounds and the "Abjadi" numerical values of the 28
Arabic letters arranged in the "Abjadi" order and Table 3 gives the sounds and the "Abjadi"
numerical values of the 22 Hebrew letters arranged in the "Abjadi" order.
3.2. Representation of Numbers
Because of their "Abjadi" numerical values, the Arabic and Hebrew letters served as numerals
to represent the numbers. All numbers between 1 and 1999 can be represented by a set of
Arabic letters (a word), using the "Abjadi" numerical values of the letters. In the same way all
numbers between 1 and 499 can be represented by a set of Hebrew letters (a word). To
represent the number 1245, for example, the Arabic used the word "غﺮﻤه" composed of the
Arabic letters: ـه of "Abjadi" numerical value 5, م of "Abjadi" numerical value 40, ر
of "Abjadi" numerical value 200 and غ of "Abjadi" numerical value 1000. Notice the
attached feature of the Arabic letters. Beyond, the class of the units is represented by a word
having at most three Arabic letters, the class of the thousands is represented by another word,
followed by the word "alf" (one thousand) to specify that it is thousands, the millions are
represented by another word followed by the word "alf alf" to specify that it is millions (one
thousand thousands). The number 23 456 789, for example, is written as:
ﺬﻔﻃ و ﺚﻧو) ﻒﻟأ ( وﻚﺟ ) ﻒﻟأ ﻒﻟأ(
By taking into account the "Abjadi" numerical values of each letters, it reads as, [9 and 80
and 700] and [6 and 50 and 400] "alf" (thousand) and [3 and 20] "alf alf" (thousand
thousands : million)
3.3. Evaluation of expressions or "Hisseb el-joummel"
A whole sentence can be evaluated while calculating the sum of the "Abjadi" numerical
values of the letters composing the words of this sentence. For example, the value of the
expression "ﺐﻨﻳز ﺪﻤﺣا" is:
1 + 8 + 40 + 4 + 7 + 10 + 50 + 2 = 122.
This kind of digitalisation of expressions using the "Abjadi" numerical values of the letters is
used in astrology. The values of the expressions are treated with well defined algorithm
calculations and the final result is compared to astrological tables.
4. "Ghubari" numerals and Arabic letters
4.1. The "Ghubari" numerals 1, 2, 3, 4, 5, 6, 7, 8 and 9
The dot and the shape of the "Ghubari" numeral 3, do recall us the Arabic letter ج (Jim), and
one is attempted to ask the following question:
Are the "Ghubari" numerals simply Arabic letters?
Already, the fact that the "Ghubari" numeral 4 is our modern numeral 5 proves that the
hypothesis that makes a direct relation between the number of possible angles in the
geometrical numeral shape and the numeral value is false, since the "Ghubari" numerals 4 and
5 do not correspond to the number of angles of their geometrical shapes.
In Table 4, we show the first ten Arabic letters of the "Abjadi" order written with the
"Maghribi" police and the "Ghubari" numerals as identified from our manuscript. Let us now
examine in more details, one by one, all the symbols of the "Ghubari" numerals and let us
compare them, to the symbols of the first ten Arabic letters of the "Abjadi" order.
The Arabic letter ج (Jim) has indeed the "Abjadi" numerical value 3, correctly corresponding
to the numeral "Ghubari" 3, as we suspected it. The coincidence is remarkable. For all
"Ghubari numerals, we can note that, (see Table 4):
The "Ghubari" numeral 1 precisely corresponds to the Arabic letter ا (Alif), of "Abjadi"
numerical value 1.

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The "Ghubari" numeral 2 with its two dots, does not have any tie with the Arabic letter ب
(Baa) of "Abjadi" numerical value 2. The two dots lead us to think about the Arabic letter ي
(Yaa) of "Abjadi" numerical value 10. It is precisely one of the final shape of the Arabic letter
ي(Yaa) written in the "Maghribi" police. In the manuscript, the two dots are sometimes
omitted as with the two dots of the final Arabic letter ى (Yaa).
The "Ghubari" numeral 3 is the slightly modified final bounded shape of the Arabic letter ج
(Jim) of "Abjadi" numerical value 3. The presence of the dot of the ج (Jim) in the "Ghubari"
numeral 3 can be noticed. The letter ج (Jim) has been doubled by its initial shape, without the
dot however.
Table 4
The "Ghubari" numerals, the first ten Arabic letters of the "Abjadi" order
and the transformations imposed to the Arabic letters to become "Ghubari" numerals
The "Ghubari" numeral 4 is precisely the "Maghribi" shape of the Arabic letter د (Del), of
"Abjadi" numerical value 4.
The "Ghubari" numeral 5 is the modified final bounded shape of the Arabic letter ﻪـ (Haa), of
"Abjadi" numerical value 5.
The "Ghubari" numeral 6 is the up-side down shape of the Arabic letter و (Waw), of "Abjadi"
numerical value 6.
The "Ghubari" numeral 7 is the slightly modified shape of the Arabic letter ز (Zin), of
"Abjadi" numerical value 7. The dot has been substituted by a small feature linked to the body
of the letter.
Arabic
letter Sound
"Abjadi"
numerical
value
"Maghribi" shaped arabic
leter Transformation
"Ghubari"
numeral
ا Alif 1 NONE
ب Baa 2
ي Yaa 10
NONE
ج Jim 3
د Del 4 NONE
ﻩ Haa 5
و Waw 6
UP-SIDE-DOWN
ز Zin 7
ح H'aa 8
ط T'aa 9
UP-SIDE-DOWN
ص Sad 90 NONE

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The "Ghubari" numeral 8 is the final shape of the Arabic letter ح (H'aa), of "Abjadi"
numerical value 8. The tail of the letter ح (H'aa) is bound to its beginning.
The "Ghubari" numeral 9 is the up-side down shape of the Arabic letter ط (Taa), of "Abjadi"
numerical value 9.
The correspondence between the shape of the Arabic letter whose "Abjadi" numerical value is
equal to the "Ghubari" numeral and the symbol of this numeral is perfect for the "Ghubari"
numerals 1, 3, 4, 5, 6, 7, 8 and 9. The coincidences are remarkable. The "Ghubari" numeral 2
does not correspond to the second Arabic letter of the "Abjadi" order but corresponds to the
Arabic letter having the "Abjadi" numerical value 10.
The "Ghubari" numerals, ancestors of our modern numerals, are therefore derived from the
first ten Arabic letters of the "Abjadi" order. The initial strategy for obtaining the "Ghubari"
numeral symbols consisted therefore to choose, as a symbol of a "Ghubari" numeral, the
Arabic letter whose "Abjadi" numerical value is equal to this numeral.
4.2. The "Ghubari" numeral 0
The discovery of 0, in its present conception which has simplified the representation of the
numbers and the algorithms of the basic operations, was certainly a very crucial event. If the
choice of the symbols representing the "Ghubari" numerals 1, 2,…, 9 can be justified by the
"Abjadi" numerical values of the Arabic letters chosen to represent them, the symbol
representing the "Ghubari" numeral 0 cannot be explained in the same way since the value
zero is not an "Abjadi" numerical value. Like all new inventions, it is necessary to choose for
it a name and a symbol.
The chosen name is the word "Sifr". Is it an Arabic word? Figure 13 shows a part of an
Arabic dictionary page which gives the meaning of the word "Sifr" and its derivatives. One
can see that the word "Sifr" is not a foreign word to Arabic. It has not been borrowed from
another language to describe a new state, unknown in Arabic, as for example the case of the
word "Falsafa" that refers to "philosophy", which is borrowed from Greek to describe a new
state. The word "Sifr" does not derive, as some authors,([Ifrah, 1996], [Ifrah, 1999],
[Ouaknin, 2004] and [Institut du monde arabe, 2005]) pretend, from of the Indian word
"Shûnya", since the word "Sifr" and its derivatives existed in Arabic long before the
appearance of zero itself.
Figure 13 :
Meaning of the Arabic word "Sifr"
and of its derivatives

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In Arabic the meaning of the word "sifr" describes an empty state which one did not expect.
The emptiness described by the word "sifr" is in all cases an abnormal situation. The name
"Sifr" given to 0 expresses exactly the role that the 0 must play in the representation of the
numbers with the help of the numerals. The numeral 0 must replace a numeral that made
defect in a given rank. It does not represent the emptiness, it fills the emptiness.
The chosen symbol to represent the "Sifr" is the symbol 0. Does this symbol derive from an
Arabic letter as the other "Ghubari" numerals? If yes, which one? As the value 0 is not an
"Abjadi" numerical value, one cannot find an Arabic letter having the good "Abjadi"
numerical value, to represent the "Ghubari" numeral 0. The strategy of choice of the symbols
must be modified so that one will not take into account the "Abjadi" numerical values of the
letters. One could think then about choosing the tenth Arabic letter ي (Yaa) of "Abjadi"
numerical value 10 to represent the "Ghubari" numeral 0. This was not the case. In my
opinion, it is the initial shape of the Arabic letter ص (Sad), first letter of the Arabic word ﺮﻔﺻ
"Sifr", which served to manufacture the symbol of the "Ghubari" numeral 0. The choice of the
symbol 0, has not been motivated therefore as some authors pretend ([Ifrah, 1996], [Ifrah,
1999], [Ouaknin, 2004] and [Institut du monde arabe, 2005]), by high philosophical
considerations. The fact that the difference of two equal numbers is exactly equal to the
numeral 0, is a consequence of the representation of the numbers with the help of the
"Ghubari" numerals.
4.3. The initial transformations
The initial strategy for obtaining the "Ghubari" numeral symbols consisted to choose, as a
symbol of a "Ghubari" numeral, the Arabic letter whose "Abjadi" numerical value is equal to
this numeral. As the numerical value 0 is not an "Abjadi" numerical value, the numeral
"Ghubari" 0 was the first numeral formed regardless of the "Abjadi" numerical values of the
Arabic letters. The idea to manufacture the other "Ghubari" numerals 1, 2,…, 9 independently
of the Arabic letters comes right after to confirm definitively the separation between the
numerals and the letters with their "Abjadi" numerical values. Indeed, the "Abjadi" numerical
values would have led to the representation of the "Ghubari" numeral 5 by the isolated shape
of the letter ﻩ (Haa), having the "Abjadi" numerical value 5. However this kind of circle has
probably already been used to designate the numeral "Ghubari" 0. It was necessary to find
another symbol to designate the numeral "Ghubari" 5. One deduces from this priority that the
"Ghubari" numeral 0 was the first "Ghubari" numeral put in shape. The table 5 gives the
likely initial transformations having succeeded to the "Ghubari" numerals. In the likely initial
version of the "Ghubari" numerals, the numerals are simply Arabic letters, the "Abjadi" order
of the Arabic letters was scrupulously respecting. In the Final version of the "Ghubari"
numerals, the initial transformations imposed by the Master of the numeral were taking into
account. The invention of the "Ghubari" numerals has been achieved in a very short time.
Once the idea of the numeral discovered, it took 1 to 2 days to form all "Ghubari" numerals
including the 0. This explains the freedom taken by the Master of the numerals, during the
elaboration of all the "Ghubari" numerals. He did not take the Arabic letter ب (Baa),
according to the "Abjadi" order of the letters to designate the numeral "Ghubari" 2, but he
chose the final shape of the "Maghribi" shaped Arabic letter ي (Yaa) with its two dots. Arabic
words are written with attached letters, to put in shape the "Ghubari" numerals, the Master
made some transformations in the Arabic letters in order to hide their attached feature. So he
did not take directly the letter و (Waw) of "Abjadi" numerical value 6 to represent the
"Ghubari" numeral 6, but he decided to take the up-side down shape of the letter و (Waw). He
did not take directly the letter ط (Taa) of "Abjadi" numerical value 9 to represent the numeral
9, but he took the up-side down shape of the letter ط (Taa). Our Master had the same attitude
during the formation of all "Ghubari" numerals.

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Table 5
Likely initial transformations having succeeded to the "Ghubari" numerals and the modern numerals
Arabic letter Sound
abjadi
numerical
value
Initial version of
the
"Ghubari"
Numeral
final version of
the "Ghubari"
Numeral
European
version of
"Ghubari"
Numeral
Chiffres
Modernes
Alif 1 1
Baa 2 2
Jim 3 3
Del 4 4
Haa 5 5
Waw 6 6
Zin 7 7
H'aa 8 8
T'aa 9 9
Yaa 10
Sad 0
This freedom shows the exhibited intention to completely depart from the old representation
of the numbers that was intimately bounded to the "Abjadi" numerical values of the Arabic
letters. It is a new era that begins and our Master was well conscious of the importance of his
realization. He acted freely, with a new spirit, but without completely forgetting the "Abjadi"
numerical values of the Arabic letters. Therefore, the shapes of the "Ghubari" numerals really
originated from the Arabic letters but their spirit was completely different from the spirit of
the "Abjadi" numerical values.
4.4. The right left sociological Logic
The numerals have an interest by their impacts on the representation of the numbers and on
the algorithm calculations. When closely examining this representation of the numbers and
these algorithm calculations, we discover a logic, called here, the right left sociological logic.
If a person has the right left sociological logic, Figure 14, he writes and reads a word or a
number from the right to the left. To write, for example, the number : 12457892, he starts by
writing the units, the ten, the hundreds of the units, then the units, the ten, the hundreds of the
thousands etc. starting by the right. The same person will proceed similarly for reading:
starting by right: 2 and 90 and 800; 7 and 50 and 400 thousands ; 2 and 10 million. In the left
right sociological logic, one writes and reads a word or a number from left to right. Reading
the same number 12457892 which is written with the right left sociological logic, one starts
by putting himself in the right-left sociological logic by isolating the numerals composing this

12
number from right to left as follow : 12 457 892 and returns to his left right sociological
logic, and reads : 12 million 457 thousands 892.
Figure 14:
Sociological Logic
Reading the number: 12457892 ?
A person who has the Right Left Sociological Logic :
Reading in one step :
2 and 90 and 800 and 7 and 50 and 400 thousand and 2 and 10 millions
A person who has the Left Right Sociological Logic:
Reading in two steps :
First step : using the Right Left Sociological Logic:
12 457 892
Second Step : returning to the Left Right Sociological Logic and reading:
12 millions 457 one thousand 892
All basic operations, for which "Ghubari" numerals simplified the algorithms, were
accomplished in the right left sociological logic. This logic is imposed to us, by the "Ghubari"
numerals, every time we deal with numbers. When stocking a number, in the computer
memory, for example, the weakest bit is in the right position.
5. Evolution of the numeral
The "Ghubari" numerals are born in Maghreb or in Spain, emigrated toward the Mashrik to
become, after evolution, the "Mashriki" numerals and toward Europe to become after
evolution, the modern numerals.
5.1. The modern numerals
Except the permutation of the numerals 4 and 5 and the disappearance of the dots of the
numerals 2 and 3, the comparison of the "Ghubari" numerals and modern numerals shows that
the transformations especially touched the esthetic form. Table 5 shows the evolution of the
"Ghubari" numerals to European version of "Ghubari" numerals and toward the modern
numerals.
5.2. The "Mashriki" numerals
In the Middle East, the "Mashriki" numerals are used up to now. From where do these
"Mashriki" numerals come ? The meticulous observation of the "Mashriki" numerals,
particularly the numerals 1, 4, and 9 permits to affirm that they have the "Ghubari" numerals,
and therefore the Arabic letters, as origin, see Table 6. The changes made to pass for
"Ghubari" numerals to the "Mashriki" numerals likely were meant to re-establish the
ascendancy of the "Abjadi" numerical values of the Arabic letters on the numerals. The
strategy of the transformations consisted to:
- pratically redraw the shape of the numerals by scrupulously respecting the "Abjadi" order of
the letters, starting with the numeral 1. The numeral 0 is not the first numeral put in shape,
- replace the dots of the Arabic letters by a sort of leg attached to the body of the letter,
- avoid taking identical symbols to the "Ghubari" numerals to represent different numerals to
prevent all confusion,
- borrow Hebrew letters instead of Arabic ones every time that might be confusion with the
"Ghubari" numerals.

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The table 6 shows the transformations undergone on the Arabic and Hebrew letters and the
"Ghubari" numerals to get "Mashriki" numerals. The likely initial version of the "Mashriki"
numerals respects scrupulously the Arabic letters "Abjadi" order and the final version of the
"Mashriki" numerals, takes into account the mentioned transformations.
One notes that:
The "Mashriki" numeral 1: is precisely the Arabic letter ا (Alif), of the "Abjadi" numerical
value 1.
The "Mashriki" numeral 2: is represented by a modified shape of the Arabic letterب (Baa), of
"Abjadi" numerical value 2. The dot is replaced by a sort of a leg attached to the body of the
letter. The numeral 2 is not represented by the Arabic letter ي (Yaa) corresponding to the
"Abjadi" numerical value 10, as was the case for the "Ghubari" numeral 2.
The "Mashriki" numeral 3: is a shape; modified by a rotation of π/2 to the right, of the
numeral "Ghubari" 3, wich is the slightly modified final bound shape of the Arabic letter ج
(Jim) of "Abjadi" numerical value 3. As for the numeral 2, the dot is replaced by a leg
attached to the body of the letter.
The "Mashriki" numeral 4: is a slightly distorted shape of the "Ghubari" numeral 4, which is
precisely the "Maghribi" shape of the Arabic letter د (Del), of "Abjadi" numerical value 4.
Table 6
Evolution of the Arabic and Hebrew letters and "Ghubari" numerals toward the "Mashriki" numerals
Abjadi
Numerical
value
Arabic
Letter
Sound
Hebrew
letter
Sound Transformation
Likely
Initial
version of
the
Mashriki
numeral
Final
version
of the
Mashriki
numeral
Ghubari
numeral
1 Alif א Aleph NONE ١
2 Baa ב Beth ٢
3 Jim ג Gimel ٣
4 Del ד Daleth NONE ٤
5 Haa ה He NONE ٥
6 Waw ו Vav NONE ٦
7 Zin ז Zayin ٧
8 H'aa ח Cheth
ROTATION
2
π ٨
9 T'aa ט Teth UP-SIDE-DOWN ٩
10 Yaa י Yodh NONE ٠

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The "Mashriki" numeral 5: is represented by the isolated shape of the Arabic letter ﻩ (Haa), of
"Abjadi" numerical value 5. This shape is very close to that of the one kept by the Master of
the numeral to represent the "Ghubari" numeral 0.
The "Mashriki" numeral 6: has been represented by the shape of the Hebrew letter ו (Vav),
of "Abjadi" numerical value 6. The choice of the Arabic letter و (Waw) of "Abjadi"
numerical value 6 is prevented by the possible confusion with the "Ghubari" numeral 9.
The "Mashriki" numeral 7: is a modified shape of the Arabic letter ز (Zin), of "Abjadi"
numerical value 7. Like the case of the numeral 2, the dot is replaced by a leg attached to the
body of the letter.
The "Mashriki" numeral 8 : is a modified shape, by a rotation of π/2 to the left, of the Arabic
letter ح (H'aa), of "Abjadi" numerical value 8.
The "Mashriki" numeral 9 : is the up-side down shape of the Arabic letter ط (Taa), of
"Abjadi" numerical value 9. It is also the symbol of the "Ghubari" numeral 9.
The "Mashriki" numeral 8 : is a modified shape, by a rotation of π/2 to the left, of the Arabic
letter ح (H'aa), of "Abjadi" numerical value 8. The shape of The "Mashriki" numeral 8 lead
us to think about the hebrew letter ח (cheteh) of "Abjadi" value 8
The "Mashriki" numeral 9 : is the up-side down shape of the Arabic letter ط (Taa), of
"Abjadi" numerical value 9. It is also the symbol of the "Ghubari" numeral 9.
The "Mashriki" numeral 0 : has been represented by the shape of the Hebrew letter the letter
י (Yodh), of "Abjadi" numerical value 10. The symbol 0 kept by the Master of the numeral to
represent the "Ghubari" numeral 0 has a shape very close to the one ٥ (haa) chosen to
represent the numeral "Mashriki" 5. Therefore it was necessary to choose another symbol for
the Mashriki" numeral 0. A possible strategy of choice of the symbols would consist in taking
the Arabic letter ي (Yaa) of "Abjadi" numerical value 10 as symbol of the "Mashriki"
numeral 0. This choice may lead to confusion with the numeral "Ghubari" 2. To prevent this
confusion, it might be possible to borrow the Hebrew letter י (Yodh), of "Abjadi" numerical
value 10. This choice shows that the first "Mashriki" numeral put in shape was not the
numeral 0. The choice of the symbol "Mashriki" numeral 0, has not been motivated by high
philosophical considerations.
6. CONCLUSION
Since his early beginning, the man tried to quantify the nature by using numbers. To represent
these numbers he used numerals. Every civilization had its numerals. The "Ghubari"
numerals, with their zero, were, for different reasons, a revolution. They simplified the
representation of the numbers and the algorithm calculations. They provided us with a small
calculator to perform complicated operations. This mini calculator is not an instrument but a
simple method that only requires a sheet and a pencil.
Through the mixed pagination of an Arabian Algerian manuscript of the beginning of the 19th
century we rediscover the "Ghubari" numerals whose use has completely disappeared. The
"Ghubari" numerals gave in Europe the modern numerals. Contrary to some assumptions, the
"Ghubari" shape shows that the ten numerals we presently use are ten slightly modified
Arabic letters given in the "Abjadi" order. The symbol of a "Ghubari" numeral corresponds to
the Arabic letter whose "Abjadi" numerical value is equal to this numeral.
The right left sociological logic is imposed to us, in the representation (reading and writing)
of the numbers and in the algorithms of the basic operations, by the "Ghubari" numerals,
every time we deal with numbers.
The "Ghubari" numerals have for origin the "Maghribi" shaped Arabic letters. The "Ghubari"
numerals that simplified the writing of the numbers and the algorithms of the basic operations

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have been often used in the Ghubari (calculation) in the Maghreb until the beginning of the
19th century.
From what we have just seen we can conclude that, the ten "Ghubari" numerals are originated
either in the Maghreb or in Spain during the flourishing time of the Arabic Muslim
civilization.
From the city port Béjaïa (Algeria) the "Ghubari" numerals travelled and introduced to
Europe and became there, after evolution the modern numerals: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. They
also travelled to the Middle East to became, after transformations and by adding two Hebrew
letters, the "Mashrikis" numerals: ٩ ٨ ٧ ٦ ٥ ٤ ٣ ٢ ١ ٠ .
For historical reasons, decline and colonization, the "Ghubari" numerals became, during the
second half of the 19th century and the first half of the 20th century, foreign and unknown in
their own country, the Maghreb. Today the "Ghubari" numerals, becoming the modern
numerals, have returned from Europe to be the official numerals in the Maghreb countries
(Algeria, Morocco and Tunisia).
References
1) Ifrah, G, 1996, Histoire universelle des chiffres, Librairie Eyrolles.
Ifrah, G, 1999, The Universal History of Numerals, John Wiley and Sons.
2) Ouaknin, M. A., 2004, Mystère des chiffres, Edition Assouline, Paris.
3) Institut du monde arabe, 2005, L’age d’or de Sciences arabes, Exposition du 25/10/2005 au
19/03/2006, Sciences et Vie, Editeur Excelsior Publication SAS.
4) Duchenoud, C., 1867, Recueil d'adages et de pensées détaches empruntées la plupart aux
langues orientales …, 1867.