Zero

• Book Title: Zero - The Biography of a Dangerous Idea
• Author: Charles Seife
• Year written/published: 2000
• Summary: History of the birth of Zero and its concept.
• Some extracts:

Some mathematics quotations…

• There was neither non-existence nor existence then; there was neither the realm of space nor the sky which is beyond. What stirred? Where? ~Rig Veda 
• Where there is the infinite there is joy. There is no joy in the finite. ~ Chandogya Upanishad
• I am in a sense something intermediate between the God and the naught. ~Rene Descartes, Discourse on Method
• What is man in nature? The Nothing in relation to the infinite, everything in relation to nothing, a mean between nothing and everything ~ Blaise Pascal, Pensees
• God made integers; all else is the work of man ~Leopaold Kronecker
• [The Star] like the Cheshire Cat, fades from the view. One leaves behind only its grin, the other, only its gravitational attraction [black hole] ~John Wheeler
• However, if we do discover a complete theory, it should in time be understandable in broad principle by everyone, not just a few scientists. Then we shall all, philosophers, scientists and just ordinary people, be able to take part in the discussion of the question of why it is that we and the universe exist. If we find the answer to that, it would be the ultimate triumph of the human reason - for we would know the mind of God. ~Stephen Hawking, A Brief History of Time
• Concealed in the heart of all beings is the Atman, the Spirit, the Self. Smaller than the smaller atom, greater than the vast spaces. ~ Hindu Scriptures

zero…

• zero is powerful because it is infinity’s twin. They are equal and opposite, yin and yang. They are equally paradoxical and troubling. The biggest questions in science and religions are about nothingness and eternity, the void and the infinite, zero and infinity. The clashes over zero were the battles that shook the foundations of philosophy, of science, of mathematics and of religion. Underneath every revolution lay a zero - and as infinity.

Egyptian maths…

• The Egyptians’ innovation of the solar calendar was a breakthrough but they made an even more important mark on history: the invention of the art of geometry. Even without a zero, the Egyptians had quickly become masters of mathematics. Zero’s place in the Babylonian maths… - Though zero was useful, it was only a placeholder. It was merely a symbol for blank place in the abacus, a column where all the stones were at th bottom.

Zero’s weirdness…

• Add a number to itself and it changes. one and one is two… …  but zero and zero is zero. The violates the basic principle of numbers called the axiom of Archimedes, which says that if you add something to itself enough times, it will exceed any other number in magnitude.
• … Multiplying by zero collapses the number line. But dividing by zero destroys the entire framework of mathematics. There is a lot of power in this simple number. It has to be the most important tool in mathematics.

Numbers and geometry…

Unlike the Greeks, the Indians did not see squares in square numbers or the areas of rectangles when they multiplied 2 values.Instead they saw the interplay of numerals - numbers stripped of their geometric significance. This was the birth of what we now know as algebra. .. … ….  Once numbers shed their geometric significance, mathematicians no longer had to worry about mathematical operations no longer had to worry about mathematical operations making geometric sense.

The infinite and the void had powers that frightened the Greeks. The infinite threatened to make all motion impossible, while the void threatened to smash the nutshell universe into a thousand flinders. By rejecting zero, the Greek philosophers gave their view of the universe the durability to survive for 2 millennium.

Mistake in Calendar because of no zero…

Bede didn’t want to abandon the new dating system, so he extended Dionysius’ calendar backward. To Bede, also ignorant of the number zero, the year that came before 1 AD was 1BC. There was no year zero… … … Bede’s style of counting went… -3, -2, -1, 1, 2, 3… zero whose proper place is between -1 and 1 is nowhere to be seen.

vanishing point…

it is no coincidence that zero and the infinity are linked in the vanishing point. Just as multiplying by zero causes the number line to collapse into a point, the vanishing point has singularity, a concept that became very important later in the history of science.

vacuums

It is a subtle point: vacuum don’t suck; the atmosphere pushes. But Pascal’s simple experiment demolished Aristotle’s assertion that nature abhors a vacuum…. … … Aristotle was defeated and the scientists stopped fearing the void and began to study it.

Projective Geometry…

The person who combined these 2 ideas was a Student of Gauss’s: Georg Friedrich Bernhard Reimann merged projective geometry with the complex numbers, and all of a sudden lines became circles and circles became lines and zero and infinity became the poles on a globe full of numbers

the start and the end..

All that scientists know is the cosmos was spawned from nothing and will return to the nothing from whence it came. The universe begins and ends with zero.