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Nought (copied verbatim from N Series Talk)

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Zziggy
1166426.  Sat Jan 02, 2016 7:06 pm Reply with quote

Zero - or nought if you prefer.

People were scared of zero for a very long time. Zero represented nothingness, the void, chaos: it was the very definition of evil for mediaeval scholars, who reasoned: God is omnipotent; there is nothing he can't do. But God is the ultimate good, and cannot do evil. Therefore, evil is nothing. This fear came partly from Western society's basis on Greek philosophy zero was anathema to the Greeks.

Zero violates the Axiom of Archimedes, which states that if you add any number to itself enough times it will eventually exceed any other number. Zero makes no geometric sense you can't take a physical ratio of zero to some number and all mathematics was geometry to the Greeks. Most importantly, zero violated one of the most fundamental tenets of Greek wisdom: there is no void. The only time you will ever see zero in ancient Greek texts is within the realm of astronomy, where Babylonian notation was used but they used it as seldom as possible, and neglected it when the results were translated back into Greek.

The Greek rejection of zero lasted two millennia. It was challenged by Zeno's paradox an attempt to prove that the universe was changeless and immobile but, although the atomists came up with a solution which embraced the void, it was eventually Aristotle who won out with his philosophy of the finite universe and prime mover. Zero had become heresy.

In contrast, by the ninth century, India had a symbol for zero, and gave it a place on the number line. They nevertheless still saw the connection to the supernatural: Bhaskara wrote, [the] fraction of which the denominator is a cipher [zero], is termed an infinite quantity [adding a number gives] no alteration as no change takes place in the infinite and immutable God. Nearly a thousand years later, in September 1997, the billion-dollar missile cruiser USS Yorktown was crippled by this piece of philosophy, when its computer system tried to divide by zero and it was left dead in the water.

Zero was finally introduced to the West in Liber Abaci by Fibonacci, who had learned Arabic numerals from Muslim scholars. Zero and infinity started to take hold in Western thought; Aristotle's philosophy was losing its authority, and eventually the church would face the rise of Protestantism.

The Catholic counter-reformation reaffirmed that zero was heresy, but even devout scholars had a hard time accepting this. Descartes, a Jesuit, started his coordinate system at (0,0) but insisted to his death that the void does not exist.

The acceptance of zero and infinity means that today we can talk about black holes in physics and limits in algebra, we can draw paintings with perspective and play with quantum mechanics. The idea of extraterrestrial life is open to us, we can draw fractals ... and a sprinter can overtake a tortoise.


Reference: Zero: The Biography of a Dangerous Idea, Charles Seife

 
gruff5
1183705.  Thu Mar 24, 2016 6:18 pm Reply with quote

N Series Talk wrote:
...

The acceptance of zero and infinity means that today we can talk about black holes in physics ...

Au contraire - zero and infinity (currently) mean we can not talk about what is really going on at the 'singularity' of a black hole. Quantum loop gravity avoids the infinite densities and zero width of the singularity, so such approaches might provide a solution, one day.

 

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