----------------------Messaggio originale------------------------
> Da: Elena Marchisotto <vcmth01c@csun.edu>
> A: historia-matematica@chasque.apc.org
> Data: sabato 24 aprile 1999 1.30
> Oggetto: [HM] The Zero Story: a question
>
> Hello Everyone,
>
> A colleague has asked me about the accuracy of what follows.
> Appreciate your help.
>
> Elena
>
>
> THE ZERO STORY:
> -----------------------------
> Source: Unknown, from the Siemens Network Magazine.
>
> A plural is possible only if there is a singular.
> A singular is possible, if there is nothing to begin
> with. And what is the number of nothingness?
This is a corollary of a well established "topos" in the
pre-Aristotelean Greek culture: the so-called "negative judgement paradox":
<If a statement represents something which is, then a rejection represents
something which is not, but a sentence about something which is not, is
about nothing and then impossible>, whose origin can be ascribed to
Parmenides and was very common among the Sophists.
The paradox was very 'virulent' in Greek culture for the linguistic
structure of "being" and "knowing" in ancient Greek (if you like I can give
more references).
It was very common in Plato's dialogues and was partially solved in his
Sophista. It was definitely "removed" (more than solved) by Aristotle.
The "arithmetic" corollary asserts the impossibility of a "nothing"
multitude and appears explicitly in Plato's Sophista (237 c-e)
> It was a subtle Indian mind, Aryabhata's, who bestowed a name
> and number upon a gap, the profound Shunya, Zero. He
> used the symbol of a circle with a dot within, perhaps
> to show the immense space captured within a mere circle.
> He knew the potential.
>
> Indians became adept mathematicians around 3000BC, when
> the Mohenjadaro and Harappa civilizations flourished. Its
> usage became well known around the 6th century when
> Brahmagupta of Multan formulated the rules of operation of
> Aero in his treatise, Brahmasphutasiddantha, in which he
> treated Zero as just another number: A+0=A, A-0=A; Ax0=0
> A/0=0. He went wrong on the last count. Any quantity divided
> by zero is infinity. The mistake was corrected some centuries
> later when Bhaskara (AD 1114) of Bijapur wrote Leelavati.
> He claimed that the division of any quantity by zero is an
> infinity, or immutable god, a god who does not change when
> worlds are created or destroyed. Only the tangible changes;
> zero the intangible, immutable. For 400 years from the 6th
> century, India was foremost in maths and zero began its journey
> around the world. With the rise of trade among Arabs, Greeks
> and Indians, caravans carried more than goods to China, Arabia
> and Greece.
Claudius Ptolomeus employed the zero, as a small circle, in his
astronomical work, as a crucial ingredient of the sexagesimal system,
following an already known (even if not universally applied) caldean
practice.
> Though Arabs used Indian numbers and Zero, it was
> the Arab mathematician Al-Khowarizmi, who popularised its use
> Shunya became al-sifr or sift, sifr became Zero. al-jabr into
> algebra.
>
> When the Arabs invaded Palestine, the putative Arabic origin of
> Indian numbers earned them the label of infidel Numbers.
> When Turks captured Constantinople in 1453, the city's scholars
> fled to distant parts of Europe, taking the 'zero' with them.
> By the end of 16th century, the zero was all over the world.
>
The western diffusion (by traders) was earlier. In Leonardo da Pisa
(XIII century) zero was employed but accepted with some cautions. In fact
the wrote in his Liber Abaci about the "nine indian ciphers" ("novem figure
(sic) Indorum") and the "zero sign" ("hoc signum 0").
Yours sincerely
Luigi Borzacchini