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III B.C. China 300 B.C. Babylon 500 A.C. Maya (South America) First Nations and populations with positional notation Zero originated as a blank space, not as a number Tolomeo and Giamblico used the letter of the greek alphabet “o” (omicron) as symbol for 0 I B.C. Greece 458 A.C. 800 A.C. Arabs 1000-1200 A.C. Europe Oldest example of using a symbol for zero Arabs learnt from Indians positional notation and zero Zero appeared in Europe thanks to Arabs and - around 1200 – thanks to Fibonacci
When Tolomeo and Giamblico gave a symbol to zero, the name they gave it was “nothing”. The Greeks invented the concept of 0, but they never accept 0 as a number, because in greek philosophy the idea of nothing can not be thought, named or indicated The Indians learnt the concept of 0 from the Greeks after Alexander’s conquests. They first used a symbol for 0: at the beginning it was a dot, then it became the current symbol and it was then spread in China
“Only two things are infinite, Universe and human stupidity, and I’m not sure about the former” (A. Einstein) “There is a concept which corrupts or upsets all others. I refer not to Evil, whose limited realm of ethics; I refer to the Infinitive” (Jorge Luis Borges, Argentine novelist and poet) “Look at the Zero, and you’ll see nothing; look throught the Zero, and you’ll see the world” (Robert Kaplan) Black holes are created when God divides by zero (anonymous)
Greeks didn’t accept the use of zero as a number and yet they talk about the infinite. The concept of the infinite didn’t mean really no end, but always meant finished quantities with the possibility to always “be able to add something” PLATO: current infinite (hyperuranios) unknowable ARISTOTLE: potential infinite is something in which we can go beyond. It is like a prologation of knowable’s segment After Plato, Aristotle and Zeno, Math dealt in finished form for about 2000 years. Zeno’s paradoxes are based on the endless divisibility of the space and the difference between logical and mathematical infinite
Xuan-ye’s theory appeared in China in 220 B.C. sky has no shape and no limits Astronomical Infinite Philosophical turning Nicola Cusano (1440) united infinite and finished. Giordano Bruno we have the infinite as a Universe With Spinoza and Blanqui the concept of zero came up to the absolute’s concept PARMENIDE To be = n Not to be = 0 (nothing)
God (infinite) Nothing (zero) Humanity Mystery of creation God created the Universe from the Nothing, before this creation nothing existed, not even God How was God born? Was he born from the Nothing? The Infinite (=God) was born from the Zero (=Nothing)? The concepts of infinite and of Nothing (=zero) are considered in different ways depending on the different religions and cultures
The Buddhist conception of the world: in the infinite space exist infinite worlds, where a lot of creatures live It is impossible to make a clear distinction between finished and infinite finished things only exist as parts of the Universe Men consider the Nirvana the Nothing (blank space), but it is a relative nothing the one who obtained it considers it the Everything “Infinite” is one of the God’s names God is infinite God is unmentionable you can’t try to contain it in a definition God created an infinite world, but because of the original sin, God set a limit to this infinite world the world became finished
The Koch snowflake (also known as the Koch star and Koch island) is a mathematical curve and one of the earliest fractal curves to have been described. It has an infinite perimeter, but a finished area Möbius band is a surface with only one side and only one boundary component.
The Infinite (temporary infinite) is quoted in Pink Floyd song “Empty spaces”. “What shall we use to fill the empty spaces […]“ In his song the composer John Milton Cage represents the Nothing. The track (9’33’’) is only a long musical break Contemporary painting represented the Nothing. Lucio Fontana created works of art cutting a piece of cloth. His works represented the Nothing and the Infinite This solitary hill has always been dear to me And this hedge, which prevents me from seeing most of The endless horizon. But when I sit and gaze, I imagine, in my thoughts Endless spaces beyond the hedge, An all encompassing silence and a deeply profound quiet, To the point that my heart is almost overwhelmed. And when I hear the wind rustling through the trees I compare its voice to the infinite silence. And eternity occurs to me, and all the ages past, And the present time, and its sound. Amidst this immensity my thought drowns: And to flounder in this sea is sweet to me. Giacomo Leopardi _ L’infinito «Sempre caro mi fu quest'ermo colle, e questa siepe, che da tanta parte dell'ultimo orizzonte il guardo esclude. Ma sedendo e mirando, interminati spazi di là da quella, e sovrumani silenzi, e profondissima quïete io nel pensier mi fingo, ove per poco il cor non si spaura. E come il vento odo stormir tra queste piante, io quello infinito silenzio a questa voce vo comparando: e mi sovvien l'eterno, e le morte stagioni, e la presente e viva, e il suon di lei. Così tra questa immensità s'annega il pensier mio: e il naufragar m'è dolce in questo mare» Homerus _ Odyssey Concept of nothing Ulysses was kept by Cyclops, menaged to escape with a trick, saying his name was “No one” We can find the concepts of Nothing and Infinite also in the novel’s cycle of Michael Ende “The neverending story”. Two guys try to sove the kingdom of “Fantasy” from the nothing,which feeds on with the lack of fantasy and men’s hope. Ende’s Nothing rappresented men’s depression. We can find the concepts of Nothing and Infinite also in the novel’s cycle of Michael Ende “The neverending story”. Two guys try to save the kingdom of “Fantasy” from the nothing,which feeds on with the lack of fantasy and men’s hope. Ende’s Nothing represented men’s depression.
Seife Charles - Zero: The Biography of a Dangerous Idea http://en.wikipedia.org/wiki/Main_Page 0 (number) - Wikipedia, the free encyclopedia http://digilander.libero.it/maffini/lab%20filo%201/specializzandi/inf- grec/Lezione%20Infinito%20nel%20pensiero%20greco-Mucaria.pdf http://digilander.libero.it/maffini/lab%20filo%201/specializzandi/inf- grec/Lezione%20Infinito%20nel%20pensiero%20greco-Mucaria.pdf http://xmau.com/mate/art/infinito.html http://insegnomatematica.splinder.com/post/18473514/la-storia-dello-zero http://sarcastycon3.wordpress.com/2008/06/22/lo- % E2%80%9Czero%E2%80%9D-non-solo-matematica/ http://sarcastycon3.wordpress.com/2008/06/22/lo- %E2%80%9Czero%E2%80%9D-non-solo-matematica/ Written sources :Video sources : http://www.youtube.com/watch?v=X7cphFGbuBc&NR=1 http://www.youtube.com/watch?v=owiplctOx84&feature=related http://www.youtube.com/watch?v=_Ds6XtElf3E http://www.youtube.com/watch?v=t-n1zHX0wXg&feature=related Audio sources : http://www.youtube.com/watch?v=DUzsNkKTXMU http://www.youtube.com/watch?v=ib49PoOOm4c&NR=1 http://www.youtube.com/watch?v=7uBwINqWfU8
The concept of Zero and the concept of Infinite are still discussed by mathematicians, scientists and philosophers. Human being is naturally inclined to make questions about things that surround it. The concept of Nothing (=the concept of Zero) is quite recent in the history of math, because men have always had difficulty to explain themselves what they can’t touch or see. The concept of Infinite is delicate too, because it is connected to Universe, God, Religions, Time and Afterlife. From the III century BC to today, no universal answers has been given, and even math and science haven’t gotten all the answers they are looking for. (1C, Liceo Classico Cristoforo Colombo, Genova, Italia) Annalisa Biggi Bianca BellucciSofia Di PatriziSerena Salvi Elena Brogi