How invented the figure designating “nothing“? History zero
“... - And one more university wizard somehow told me that there is such piece, “nothing“, well, you for certain know, and so, it - that klatchets also thought up. And I also ask it: “How so? That anything?“ - “Aga, - says. - It is also their big contribution to an arkhimetika. Namely - zero“.
- And really, seemingly, not very clever people that, - noticed Shnobbi. - I here too, for example, invented nothing. So everyone can.
- To what I also conduct, - supported Colon. - I speak to this wizard: there are supposedly people who thought up, let us assume, four … or … or … of
- … Seven …
- Precisely, seven. These people are the real geniuses. And it is not necessary to invent ANYTHING. It already is“.
(T. Pratchett “Patriot“)
Today it can seem surprising, but the European mathematical tradition long time did not know any zero. And even after learned, tried to do without it longer. And it is valid - why the number which estimates nothing is necessary? Some Brad... And the first European systems of calculation of zero did not demand as they were not position.
We use one not position system still. To whom is the Roman numbering which we designate centuries, kings - namesakes and sections in books not familiar? Zero in this system is absent. Number 20 registers in two tens (XX =10+10), and 102 - one hundred and two units (CII=100+1+1)., It seems, everything is simple, but here trouble - for each new category it is necessary to invent a new sign (I-1, V-5,X-10, L-50, C-100, D-500, M-1000), otherwise the large number from one units will become long and illegible. However and with addition of new signs of number often looked it is bulky. On a pedestal of the well-known Petersburg Bronze Horseman date of opening of a monument - MDCCLXXXII is written. Whether at once you will guess that it is 1782? And to make calculations, operating with such numbers, it was even more difficult.
However, in practice nobody sticks, birdies and crosses considered. For this purpose used calculating boards - abacuses. Abacuses in different appearances it was very hardy invention. Only calculators managed to force out scores which still my grandmother - the accountant perfectly knew. Abacuses also scores were divided into several position rows. So that to designate number two hundred seven on schyota, on the first wire (the category of units) rejected towards seven bones, on the third (a number of hundreds) - two, and on the second (the category of tens) rejected nothing as tens in number were not. This gap, this blank space also became the first prototype of zero. Speaking in images, zero as number and figure appeared practically from nothing.
There was it, of course, not at once. One business - a blank space, another matter - a sign, and absolutely the third - number. The first steps from a gap to a sign were taken by Babylonians. Their system of the account was position, as well as ours, but if at us each new category is ten times more previous, then at Babylonians - in sixty. The essence of position system was that each new category registered the same signs, only had them more to the left of the previous category. At Babylonians of signs was two: a vertical klinyshk designated unit, and horizontal - to ten. Thus wrote down numbers to 59, and again designated number 60 a vertical klinyshk. As it looked, you can see in drawing below.
If some category was absent, Babylonians put a gap, and in the 5th century BC began to designate the passed category two klinyshka. However, at the end of number lack of the category was not designated, as a result numbers 1 and 60 looked equally and differed, probably, proceeding from a context of what was considered.
As the homeland of the real zero by right consider India which mathematics, apparently, combined the position principle of Babylonians with decimal system of Chinese. Record of any numbers by means of ten figures which we use until now and which not absolutely fairly we call Arab became an ingenious result of the Indian mathematics (Arabs, by the way, always called them Indian). After all awarded with a sign ill-fated zero.
The concept of zero (Indians called its “sunye / shunye“ - empty) apparently arose in the middle of the 5th century. The first image of zero was revealed in number 270 traced on a wall of Gwalior (876 g) . It is very important that zero here for the first time costs at the end of number and resembles a hole familiar to us from a bagel superficially (unless a little less than other figures). A form of zero it was displayed also in our speech, when we want to leave only large categories in number, having replaced the others with zero, we speak “to round“.
There is a hypothesis that Indians adopted a sign of zero at Greeks. Yes, the Greek not position system suited for small numbers, but for exact and bulky astronomical calculations Claudius Ptolemaeus had to use the Babylon system - with its help he wrote down fractions. Instead of the passed category the astronomer put a letter “O“. As well as Babylonians, at the end of number Ptolemaeus did not designate the passed category and as number did not consider.
Notice, zero makes sense only where we tell SOMETHING about absence. In Christian divinity there was even a reception of the proof of God`s life through denial. It was called apofatichesky and was that God was defined through what it is not. And zero serves for the calculation which is ABSENT in categories which are existing. The category in number - category real and concrete, but if it is empty, then we use zero for its quantitative characteristic.
Is even simpler to explain it on the example of several cans for milk. Lack in one of them of milk does not cancel at all the can therefore the number “zero liters“ has quite concrete relation both to a can, and to the milk which is absent in it. In mathematics one of determination of zero and says: “Zero is a measure of an empty set, number of elements in a set in which there is no element“.
Emergence of zero in decimal position system made revolution in mathematics, having facilitated both record of numbers, and arithmetic actions with them. The Arabs who intruded on the territory of India in the 7th century could not pass by this great opening. They accepted the Indian system and developed it (a set of mathematical terms - the algebra, algorithm - have the Arab origin). The famous mathematician Al - Horezmi (9th century) wrote in the book “Indian Art of the Account“: “If there is no nothing left, then write a small circle that the place did not remain empty. This circle has to take the place because otherwise we will have less categories, and the second, for example, we can consider for the first“.
By the way, long time the word “figure“ meant “zero“ and nothing else (Indus. “sunye“, Arab. “al - sifr“, lat. ciffra). From ciffra there was a set of names, including the words “code“ and “zero“, well-known to fans of game in a roulette. Later the term “figure“ extended to all signs of the Arab numbering. The word “zero/zero“ became current in the 16th century and came from the Greek nullus - “any“.
Through Arabs the Indian system of the account came to Europe.
One of the first propagandists of the Arab system in Europe was the Italian mathematician Leonardo Fibonacci. In 1202 he wrote in “To the book an abacus“: “Nine Hindu signs essence following: 9, 8, 7, 6, 5, 4, 3, 2, 1. By means of these signs and a sign 0 which is called on - Arab zephirum it is possible to write any number“.
Fibonacci`s Advertising not especially worked on the European professorate, she preferred not to contact suspicious zero and Arabs and continued to consider in the old manner - by means of antique system or an abacus. So, the Italian mathematician Geronimo Cardan (1501-1576) managed to solve cubic and quadratic equations, without using zero that made calculations extremely difficult.
But the Arab system merchants and bankers, far from lofty matters, estimated at once, it was irreplaceable for calculations, and by the 15th century shopkeepers used it with might and main. Finally ten Arab signs were approved in the European science only by the beginning of the 18th century.
of the Reason of so resistant hostility to zero deserve separate conversation because they root in features of antique attitude.