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The Invention of Zero Joanne, Kristan & Dayle Primary/Junior Math Tuesday January 19th, 2010

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Why were numbers needed? - To count sheep - To keep track of property - To keep track of time These tasks had no use for a zero!!

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Egyptians -Had no need for a zero -Had a unique symbol to represent each number -Never progressed beyond measuring and counting -Only practical uses of mathematics Babylonians -Had a sexagesimal system, which meant that 11, 601, 36 001, etc all looked the same -By 300 BC were using a marker for an ‘empty space’ (a place holder) -’Zero was a digit, not a number’ (p. 15)

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Ancient Greeks Zero – linked with the void and chaos = FEAR Pythagoras – connection between shapes and numbers – zero doesn’t fit. "Zero was a number that didn't seem to make any geometric sense, so to include it, the Greeks would have had to revamp their entire way of doing mathematics. They chose not to" (p.34-35).

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Fractions Greek philosophy, which was inseparable from numbers, stated that contained within zero are two ideas that were poisonous to Western doctrine…the void and the infinite”(p.39).

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Aristotle Aristotelian Doctrine was based on Pythagorean concepts of a universe without Zero. Because of the number-shape duality in Greek Numbers, it was easy to deny the existence of Zero as it doesn't have a shape. BUT even this wasn't the real reason fro the Ancient Greeks' denial of Zero. It was Philosophy, in particular, concepts of the void and the infinite. The concept of the universe as a Finite space was adopted by Aristotle from Pythagorus and later adapted by Ptolemy. The idea being that the universe was comprised of planets that moved within a number of celestial spheres the outermost sphere being a midnight blue colour with fixed stars and Earth at the centre. To him, infinity didn't exist, so Zero didn't exist. No infinity, no void. This philosophy endured for centuries because to them, it proved the existence of God. If the universe was comprised of spheres layered upon spheres, each one causing the next one to move, then God must be the Prime Mover who causes the outermost sphere to move. If there are an infinite number of spheres, then there's no Prime Mover (no God) but Atheists were frowned upon so, yeah, there's a God. As such, the universe must be finite and anyone who suggests that the universe is infinite is a heretic.

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Denial of Zero = Form of Social Control The concept of Zero is tied up in the void and the infinite. Zero = The Void which implies the existence of the Infinite. a) There could be an infinite amount of void, so the infinite exists b) There could be a finite amount of void, but since void is a lack of matter, there must be an infinite amount of matter to make sure that there's only a finite amount of void, thus infinity exists. Since Zero is essentially the Void, it had to be suppressed. This was easier said than done. (See page 47, last paragraph)

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Social Control? IS THIS A TYPE OF SOCIAL CONTROL? IF THE UNIVERSE IS A FINITE PLACE, THEN GOD EXISTS (AS PER ARISTOTLE'S DOCTRINE). IF GOD EXISTS, WE NEED TO OBEY HIS RULES & REGULATIONS. HIS RULES & REGULATIONS ARE ARTICULATED TO THE ILLITERATE MASSES BY THE PEOPLE WHO CONCLUDED THAT THE UNIVERSE IS A FINITE PLACE. IF WE THROW ZERO INTO THE MIX, THIS ALL FALLS APART, DOESN'T IT? NOW, LEST WE SHAKE OUR HEADS AT THE 'ILLITERATE MASSES', CONSIDER THIS... WHAT IS IT? HOW MUCH IS IT WORTH? WHY IS IT WORTH THAT?

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Eastern Thought Embraced void/zero – Hinduism steeped in symbolism of duality Shiva also represented nothingness "ultimate void, the supreme nothing - lifelessness incarnate. But out of the void, the universe was born, as was the infinite...Nothingness was what the world came from, and to achieve nothingness again became the ultimate goal of (hu)mankind"

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POWER! Zero changed from placeholder to number –

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Birth of Algebra Zero had a specific value, a fixed place on the number line. "Since zero was equal to 2-2, then it had to be placed between one (2-1) and negative one (2-3). Nothing else made sense"(p.70). Arab world/Muslims accepted zero and rejected Aristotle 9th century

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WESTERN THOUGHT Introduced to Western world by Fibonacci in 1202 in his book Liber Abaci

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CALENDAR What year did the millennium take place? Controversy because no ZERO in our calendar Egyptian calendar was the ancestor of our own calendar Dionysius Exiguus – two problems with his calendar 1) Christ'’s birth 2) Century/millennium beginnings

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In mathematics, zero, symbolized by the numeric character O, is both: In mathematics, zero, symbolized by the numeric character O, is both: 1. In a positional.

In mathematics, zero, symbolized by the numeric character O, is both: In mathematics, zero, symbolized by the numeric character O, is both: 1. In a positional.

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