Zero & Infinite

1. Trailer Zero & Infinite * Click on the link to start watching the video http://www.youtube.com/watch?v=ZPzcABkklCo

2. 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 0 300 B.C. Babylon 500 A.C. Maya (South America) III B.C. China I B.C. Greece First Nations and populations with positional notation 1000-1200 A.C. Europe 800 A.C. Arabs 458 A.C. Zero appeared in Europe thanks to Arabs and - around 1200 – thanks to Fibonacci Oldest example of using a symbol for zero Arabs learnt from Indians positional notation and zero

3. 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

4. “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) “Only two things are infinite, Universe and human stupidity, and I’m not sure about the former” (A. Einstein) Black holes are created when God divides by zero (anonymous) They said about Zero & Infinite

5. PLATO: current infinite (hyperuranios)  unknowable Greeks didn’t accept the use of zero as a number and yet they talk about the infinite . ARISTOTLE: potential infinite is something in which we can go beyond. It is like a prologation of knowable’s segment ? Zero & Infinite in philosophy Zeno’s paradoxes are based on the endless divisibility of the space and the difference between logical and mathematical 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” After Plato, Aristotle and Zeno, Math dealt in finished form for about 2000 years.

6. To be = n PARMENIDE Not to be = 0 (nothing) 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 Blanquithe concept of zero came up to the absolute’s concept

7. - Christianity - Zero & Infinite in Religions God (infinite) Mystery of creation God created the Universe from the Nothing, before this creation nothing existed, not even God The concepts of infinite and of Nothing (=zero) are considered in different ways depending on the different religions and cultures • How was God born? Humanity • Was he born from the Nothing? • The Infinite (=God) was born from the Zero (=Nothing)? Nothing (zero)

8. - Judaism - - Buddhism - “Infinite” is one of the God’s names God is infinite  God is unmentionable  you can’t try to contain it in a definition 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 God created an infinite world, but because of the original sin, God set a limit to this infinite world  the world became finished Men consider the Nirvana the Nothing (blank space), but it is a relative nothing the one who obtained it considers it the Everything

9. Zero n 0 : = Zero & Infinite in Math 0 0 n = X n n = - - Zero & Infinite in Math n n + + =

10. Infinite 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.

11. Zero & Infinite in literature Zero & Infinite in painting Zero & Infinite in music Homerus _ Odyssey Concept of nothing  Ulysses was kept by Cyclops, menaged to escape with a trick, saying his name was “No one” Giacomo Leopardi _ L’infinito «Sempre caro mi fu quest'ermo colle,e questa siepe, che da tanta partedell'ultimo orizzonte il guardo esclude.Ma sedendo e mirando, interminatispazi di là da quella, e sovrumanisilenzi, e profondissima quïeteio nel pensier mi fingo, ove per pocoil cor non si spaura. E come il ventoodo stormir tra queste piante, io quelloinfinito silenzio a questa vocevo comparando: e mi sovvien l'eterno,e le morte stagioni, e la presentee viva, e il suon di lei. Così tra questaimmensità s'annega il pensier mio:e il naufragar m'è dolce in questo mare» This solitary hill has always been dear to meAnd this hedge, which prevents me from seeing most ofThe endless horizon.But when I sit and gaze, I imagine, in my thoughtsEndless 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 treesI 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. • The Infinite (temporary infinite) is quoted in Pink Floyd song “Empty spaces”. “What shall we use to fill the empty spaces […]“ Contemporary painting represented the Nothing. Lucio Fontana created works of art cutting a piece of cloth. His works represented the Nothing and the Infinite 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. • In his song the composer John Milton Cage represents the Nothing. The track (9’33’’) is only a long musical break 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.

12. Sources : Written sources : Video sources : Audio sources : • 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://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://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 • http://www.youtube.com/watch?v=DUzsNkKTXMU • http://www.youtube.com/watch?v=ib49PoOOm4c&NR=1 • http://www.youtube.com/watch?v=7uBwINqWfU8

13. Serena Salvi Sofia Di Patrizi Bianca Bellucci 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. _ZERO & INFINITE_ (1C, Liceo Classico Cristoforo Colombo, Genova, Italia) Annalisa Biggi Elena Brogi