«”Zéro” véhicule certaines propriétés: il n’est ni positif, ni négatif, il est plus petit que tous les réels positifs et plus grand que tous les réels négatifs, etc.
Le zéro, dans le texte d’ Al-Khwarizmi, est un pur non-être, un “vide”, “rond” (traduction littérale par le latin “circulus”). Dès le début de son ouvrage, Al-Khwarizmi rappelle «qu’il n’y a en aucune position plus de 9 ni moins que 1, à moins qu’il y ait un rond, qui n’est rien».
Le système décimal ne peut en effet comprendre que neuf chiffres. L’écriture du nombre 10 – et ensuite des dizaines – ne peut être désigné par une seule lettre (chiffre). Al-Khwarizmı nous dit: «… une représentation des dizaines a été pour eux [les Indiens] nécessaire puisqu’elle était semblable à la représentation de un, afin que l’on sache par elle qu’il s’agissait de 10. Ils ont donc posé devant celle-ci une position et posé en elle un petit rond en ressemblance avec la lettre O pour savoir par là que la position des unités était vide, qu’il n’y avait en elle rien d’un nombre sinon ce petit rond don’t nous avons dit qu’il l’occupait, et pour montrer que le nombre qui occupait la position suivante était une dizaine…».
Le même problème se pose évidemment quand il s’agit d’écrire un nombre dont l’une des positions «ne contient rien». Alors «tu poseras un rond pour que la position ne soit pas vide, mais qu’il y ait en elle un rond qui l’occupe, de peur que lorsqu’elle est vide on ne réduise les positions et que l’on croie que la seconde est la première, et qu’ainsi tu te trouves trompé dans ton nombre».
La multiplication d’un nombre quelconque par zéro était égale à zero, écrit al-Khwarizmı: «…tout rond qui est multiplié par un nombre quelconque n’est rien, c’est-à-dire, qu’ aucun nombre ne résulte de lui, que tout ce qui est multiplié par un rond n’est de même rien…
On rappelle «qu’au XIIIe siècle, en France, le langage populaire qualifiait un homme dépourvu de valeur de “Cyfre d’angorisme” ou encore de “Cifre en algorisme”».
Le mot “sifr” c’est la traduction arabe du sanscrit “sunya” qui signifie “vide”, “exempt de”, dont dérive étymologiquement le mot latin “ciffre” – qui origine “chiffre” – ainsi que le mot latin “zephirum” – qui origine “zéro”».
Adapted from source
«The Sanskrit term “sunya” (in Punjabi, “sunn”, in Pali, “sunna”) is derived from the root “svi” connected with the root “su”; both these roots mean ‘to swell’, ‘to expand’ or ‘to increase’.
The term “sunya” is often used in the sense of ‘zero’ or ‘cipher’ (in Arabic, “sifr”), a symbol of naught. However, notice that ‘zero’, when used by a mathematician along with a figure, increases the value of that figure ten times.
The word “sunya” belongs to the religious and philosophical terminology of India. Its meaning has to be explored in relation to two other cognate words, viz. “sunyata” and “sunyavada”, concepts widespread throug Buddhist literature.
“Sunya” means void, empty, a lonely place or solitude. “Sunyata”, means voidness, emptiness, vacuity or nothingness, ‘the ism of void’, ‘the doctrine of empty’.
At numerous places in the Pali scriptures it is stated that «the world [“loka”] is empty [“sunya”]»; it is empty of self (“atman”) and empty of anything belonging to self. There is nothing in the world with which one could identify one’s self, or of which one could say ‘this is myself.’
A class of Buddhist Sanskrit literature consisting of the Prajnaparamitasutras is devoted to the exposition of emptiness. The Prajnaparamitasutras teach that “sunyata” is the nature of all phenomenal things or entities called “dharmas”. Things are empty (“sunya”) because they are conditioned; they are conditioned because they depend on a multiplicity of causes. Nothing is uncaused; therefore nothing is free from “sunya”, emptiness. The dependence of entities on causes and conditions constitutes their emptiness. All things or phenomena are subject to dependent origination (“pratiya-samutapada”); therefore all phenomena are characterized by emptiness (“sunyata”). This fact is called “dharma-sunyata”, the emptiness of “dharmas” or the phenomena.
Nagarjuna, who flourished in the first century AD, is the main originator of the doctrine of “sunya” which in fact offers the critique of all the philosophies. Going beyond the dialectical viewpoints of “asti” (is) and “nasti” (is not) about the Supreme Truth, the “sunyavadins” adopt a method which seeks to abolish all viewpoints but, side by side, they do not claim to have “sunyavad”, a viewpoint in itself. The aim of this teaching is soteriological and not philosophical.
“Sunya” means that all the objects of the world are lacking in their ‘own-nature’ (“svabhava dharma”) or ‘self-existence’ (“atmabhava”); that is to say, the “dharmas” are without an essence of inward nature of their own and are without self. The absence of own-nature (“nihsvabhavata”) and the absence of self (“nairatmya”) are thus synonyms of emptiness.
Not only the persons are characterized by emptiness (“pudgala-nairatmya”) but also the things are characterized by emptiness (“dharma-nairatmya”). He who realizes this twofold emptiness (“sunyata”) attains transcendental wisdom (“prajnaparamita”). The Prajnaparamitasutras have employed the master symbol “sunyata” not only for the phenomenal things but also for the Absolute. The phenomenal things are called “sunya” because they are dependent on causes and conditions. The Absolute is called “sunya” because it is devoid of distinctions and discriminations. “Sunyata” demonstrates the ultimate unreality of entities and the unseekability of the Absolute which transcends thought and speech.
The concept of “sunya” (or “sunn”) was transmitted by the Siddhas and the Nathas to the “sant”-poets of medieval Vaisnavism. In the works of the Sikh Gurus we find the last phase of the development of the concept of “sunya” outside Buddhism. The Sikh Gurus have used the words “sunn”, “sunn kala”, “anahat-sunn” and “sunn-samadhi” numerous times in their religious compositions, but a careful analysis of the use of these key-terms in the Sikh canon shows that their meaning is, in most cases, different from that found in Buddhism.
In one case, however, there seems to be a continuity of the word and meaning from the time of the Buddhist Sutras to that of the hymns sung by the Gurus. This continuity is found in those cases in which “sunn” or “sunya” is employed as a symbol of the Absolute. Thus, for example, it is said that when one is awakened to the teaching of the Guru, one merges into the Void (“sunn samaia”) even while alive – «jivat sunni samania gur sakhi jagi» (GG, 857).
Of course the concept of the Absolute in Sikhism differs from that in the Madhyamika, but there can be no doubt that the Absolute is called “sunn” because it is devoid of duality and discrimination. This negative structure in speech with regard to the Reality is the basic function of the symbol “sunn”. All positive descriptions imply limitation and determination. The word “sunn” declares that the Truth is beyond limitations and determinations. Emptiness of Buddhism means ‘no doctrine about Truth’; “sunn” in Sikhism means ‘no conception about the Inconceivable.’
An important feature of the conception of the Void in Sikhism is that it can be realized through transcendental devotion (“naam”) which consists in the constant mindfulness of the Divine (“simran”). This feature brings in many positive elements as a matter of course and consequently the ecstatic experience of the Divine is characterized by positive attributes. Nevertheless, these positive attributes do not exhaust the innate state of “sahaj” or the Void (“sunn”). Kabir uses “sunn” in the sense of space, finite as well as infinite, i.e. “ghatakash” and “mahakash”.
The three “lokas” enveloping “sunya” is nothing but Brahman with Maya but the fourth “sunya” about which Guru Nanak stresses more is pure Brahman who is “nirakar” and “nirguna”. In Rag Maru, Guru Nanak defines “sunn” as the creative power of the Almighty – “paunu pani sunnai te saje” (GG, 1037). The sense of “nada” has also been exacted from the term “sunn” in the Sidha Gosti where Guru Nanak says: «nau sar subhar dasavai pure tah anahat sunn vajavahi ture [after filling up the nine pitchers with love, through the tenth gate the entry is made; the “anahat sunya” in the form of melodies is realized]» (GG, 943). The term “sunn” in the Guru Granth Sahib is thus used in a variety of senses, of which predominantly are Brahman with and without Maya, the creation, the power of Brahman and “nada”.
Here the unstruck sound, inaccessible to ears, goes on as ‘the music of spheres’ as it were, and the wonderful (“acharaj”) bewilderment (“bismad”) characteristic of it cannot be described (“kahanu na jai”). Peace (“santi”), bliss (“sukh”, “ananda”) and satiety (“santokhu”) are attained in this state. But here in the ultimate state there is neither he who attains these things nor he who listens to their description; void has gone to Void, emptiness had merged into Emptiness. He says: «sunnahi sunnu milia samdarsi [the individual spirit has joined the supreme spirit]» (GG, 1103).
Bhai Gurdas, explicator of Gurbani, uses “sunya” in the sense of cosmic silence — «diti bangi nivaji kari sunni samani hoa jahana» (1.35). As in the Hathayogapradipika, Guru Nanak also accepts that “sunya” is within, “sunya” is without and the three “lokas” are also imbued with “sunya”. Whosoever becomes the knower of the truth, “sunya”, goes beyond sins and virtues. He transcends both error and excellence.
It may be observed that like the word Nirvana, the word “sunya” also underwent a gradual process of transformation in its meaning and use in the literature of medieval India. The Madhyamika conception of “sunyata” was almost completely changed in Nathapantha, Kabirpantha and Sikhism.»
Adapted from source
Various Mayan forms of zero