Zero. The biography of a dangerous idea (Q2724077)

This book deals with the same subject as \textit{R. Kaplan} [The nothing that is. A natural history of zero, London, Penguin Books (2000; Zbl 0984.01001), see above]. More attention is paid to the philosophy and religion in different civilizations, especially how they treated the void and infinity. Influenced by Zeno's paradoxes, the Aristotelian system rejected both of them. Archimedes was the only thinker of his day to glimpse the infinity. Also medieval monks did not know of zero. In the sixth century Dionysius Exiguus, fulfilling the order of pope John I to calculate the Easter tables, decided that the year after the birth of Christ should be the year 1 Anno Domini. About 200 years later Beda, who did not know 0, wrote that the year that came before 1AD was 1BD. This causes `the `silly, childish discussion' -- whether the new century (or millennium) begins on the year ..00 or the year ..01'. In the medieval philosophy the fear of the void and of the infinity was so great that Christian scholars tried to fix the Bible to match Aristotle rather vice versa. NEWLINENEWLINENEWLINEBut in India and later in the Arabic lands zero flourished. India was insulated from Aristotle's philosophy and never had a fear of the infinite or of the void. For Hinduism the cosmos was infinite and never truly abandoned its original emptiness. Indian numbers had become distinct from geometry, they were used to do more than merely measure objects. Also negative numbers first appeared. When Arabs adopted the Hindu numeral system, they also adapted zero (Indian \textit{sunya} turned into \textit{sifr}, then Latin-sounding \textit{zephirus}, the root of \textit{zero}). In the Renaissance painting zero appeared as the vanishing point representing infinity of space, by drawing in perspective. The medieval Aristotelian doctrine that Earth was unique, the universe's very center, fell under suspicion after Nicolas of Cusa and Nicolaus Copernicus. The Catholic Church could no longer be tolerated and turned orthodox once again. Zero was heretic, the nutshell universe had to be accepted, the void and infinite must be rejected. The Spanish Inquisition started to burn Protestants in 1543. Giordano Bruno, who published in 1580 \textit{On the Infinite Universe and Worlds}, was burned in 1600 at the stake, but the famous Galileo Galilei was ordered in 1616 by the church to cease his scientific investigations. René Descartes was trained as a Jesuit and denied the existence of the void. He did not extend his coordinate system to the negative numbers. For him everything in the universe moved in a circular path, because moving in a straight line would leave a vacuum behind it. Torricelli was the first who created in 1643 a sustained vacuum. After Pascal's experiment scientists stopped fearing the void and began to study it.NEWLINENEWLINENEWLINEIn the Scientific Revolution a powerful new tool -- calculus -- was invented dividing by zero and adding an infinite number of zeros together. The idea of the infinitely distant point (a zero at infinity) was developed to projective geometry. The Riemannian sphere and stereographic projection showed that zero and infinity sit on opposite poles of the complex number sphere. In the battle between Kronecker and Cantor the final result was that Kronecker's precious integers, and even the rational numbers, were nothing at all -- they were an infinite zero.NEWLINENEWLINENEWLINEIn quantum mechanics the Casimir effect about the force of the vacuum, produced by nothing at all, seems like science fiction predicted in 1948, but Steven Lamoreaux measured in 1995 this effect directly. This is zero in quantum mechanics. The relativistic zero is the black hole. In the 1970s the string theory was created to get rid of these zeros. But for the foreseeable future banishing zero from the universe with string theory is a philosophical idea rather than a scientific one. Zero seems to be what created the cosmos through the Big Bang, and also is its end. Astronomers have begun to measure the change in the universe's expansion. In late 1997 they announced that this expansion is not slowing down, it might even be speeding up. The universe will die a cold death and ends with zero.