The Invention of Zero
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Joanne, Kristan & Dayle
Primary/Junior Math
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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!!
Egyptians
Babylonians
-Had no need for a
zero
-Had a sexagesimal
system, which meant
that 11, 601, 36 001, etc
all looked the same
-Had a unique symbol
to represent each
number
-Never progressed
beyond measuring and
counting
-Only practical uses of
mathematics
-By 300 BC were using
a marker for an ‘empty
space’ (a place holder)
-’Zero was a digit, not a
number’ (p. 15)
Ancient Greeks
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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).
Aristotle
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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.
Denial of Zero = Form of Social Control
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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)
Social Control?
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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?
Eastern Thought
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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"
POWER!
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Zero changed from placeholder to number
–
Birth of Algebra
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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
WESTERN THOUGHT
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Introduced to Western world by Fibonacci
in 1202 in his book Liber Abaci
CALENDAR
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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