A LESSON ABOUT NOTHING
How the number zero influenced religion and philosophy throughout the centuries
Egyptian numbers were base 10
Greek numbers based on Egyptian numbers - base 10
Around 500 BC the Greeks switched to using letters for numbers
Hebrews also used letters for numbers
The Roman numeral system took a step back to the old Greek number system.
So far we have not seen the number zero.
The zero comes in (kind of) thanks to Babylonian numbers around 1750 BC
The Babylonians use a numerical system with 60 as its base.
Is there anything that uses the number system with the base 60?
Their base of 60 survives even today in the 60 seconds and 60 minutes of time, in the 180
degrees of a triangle and in the 360 degrees of a circle
Babylonian Numbers. The symbol for 1 is the same as the symbol for 60. The only way
to tell which number is represented was by the column where it was placed on an abacus.
This didn’t help in writing so around 300BC, they started using a placeholder symbol in
writing.
However, the symbol, like our zero, was only a place holder. It made sure digits fell in
the right places. It had no numerical value.
222 = 2*100 + 2*10 + 2*1
Without placeholder one couldn’t tell if
22 was 22 or 202 or 2002
Another civilization, that of the Maya, independently arrives at a place-value system - in
their case with a base of 20
The number zero clashed with the central tenets of Western philosophy. The whole
Greek universe rested upon the idea that there is no void and no infinite.
Note: Infinity is found by dividing by zero.
The Greek universe was created by Pythagoras, Aristotle, and Ptolemey and survived
long after the collapse of Greek civilization. In that universe there was no such thing as
nothing, no void, no infinity, and no zero.
The West could not accept zero for nearly 2000 years. To accept zero, philosophers in
the West would have to destroy their universe.
Pythagoras was born around 570BC. Pythagoras modeled the universe with the earth in
the center and the sun, moon, planets and stars revolved around the earth, each pinned
inside a sphere.
It was not ignorance that led the Greeks to reject zero, it was philosophy. Zero conflicted
with the fundamental philosophical beliefs of the West because of two dangerous ideas
contained within zero.
VOID AND INFINITY
The infinite threatened to make all motion impossible and the void threatened to smash
their universe into pieces
Aristotle came along around 384BC. He was a student of Plato. Aristotle declared that
mathematicians do not need or use the infinite. He essentially wished infinity away by
stating it was simply a construct of the human mind.
Now based on the Pythagorean universe, the cosmos of Aristotle (later refined by
Ptolemy) had the earth at the center of the universe with all other bodies moving around
the earth in spheres (picture bubbles within bubbles).
Now comes the interesting part. Since there was no infinity, there could not be an
endless number of spheres. The outermost sphere was midnight blue with tiny points of
light, the stars. There was no such thing as “beyond the outermost sphere”. Aristotle’s
cosmos was finite and filled with matter There was no infinite, no void, and no zero.
This line of reasoning led to another consequence.
ARISTOTLE’S SYSTEM PROVED THE EXISTENCE OF GOD!
In Aristotle’s cosmos, the earth was stationary with the spheres spinning in their places.
Something had to be causing that motion. The earth was not the source.
It was thought that each sphere was being moved by the next outermost sphere. Since
there was no infinity, then the outermost sphere, the stars, was being moved by God.
As Christianity swept through the West, it became closely tied to the Aristotelian view of
the universe and the proof of God’s existence.
To question the Aristotelian doctrine, a doctrine with no zero and no infinity,
became the same as questioning the existence of God.
Aristotle’s most famous student was Alexander the Great and as his empire spread, so did
the teachings of Aristotle. Through this invasion, Indian mathematicians first learned
about the Babylonian system of numbers, including the zero placeholder.
After Alexander’s death, his generals divided his empire into pieces. Rome swallowed
up Greece, but it did not extend to India. Thus India was insulated from the rise of
Christianity and the fall of Rome.
India was also insulated from Aristotle’s philosophy. The philosophy was introduced to
India but never took hold. India had no fear of the infinite or the void and embraced the
ideas mainly because the void had an important place in the Hindu religion.
Indian mathematicians did more than accept zero, they transformed it from a mere
placeholder to an actual number. They also used base 10 and our numeric symbols
evolved from the Indian symbols.
Another civilization came into power in the 7th century, Islam. Islam would take zero
from India, and the West would eventually take it from Islam.
The Muslim world was still contaminated by the teachings of Aristotle thanks to
Alexander the Great. The Indian mathematicians had made it quite clear that zero was
the embodiment of the void, thus if Muslims were to accept zero, they would have to
reject Aristotle and they did.
Christianity initially rejected zero, but trade would soon demand it. Leonardo of Pisa
reintroduced zero to the West.
Zero and infinity were at the center of the Renaissance, and would eventually destroy the
Aristotelian foundation of the church and open the door to the scientific revolution.
The attack on the Catholic church began in earnest in 1517 when Martin Luther nailed a
list of complaints on the door of a church. In the Reformation, intellectuals everywhere
began to reject the authority of the pope. Copernicus created a view of the universe with
the sun in the middle.
The Catholic church in Rome, which considered itself to be the seat of the one true
church had major problems with this. The questioning of Aristotle could no longer be
tolerated. The Catholic church began to strike back.
No one could question the old doctrines. Zero was a heresy. The void and the infinite
had to be rejected. The church had tools to fight the heresies such as the Spanish
Inquisition.
In 1543, they started burning Protestants at the stake, and the pope issued an index of
forbidden books.
In 1600, Bruno was burned at the stake for suggesting that the earth was not the center of
the universe.
In 1616, Galileo was ordered by the church to stop his scientific studies. An attack on
Aristotle was considered to be an attack on the church. In 1632, he was tried by the
Inquisition, found "vehemently suspect of heresy," forced to recant, and spent the rest of
his life under house arrest.
Zero and infinity were at the very center of the philosophical war taking place during the
16th and 17th centuries. The void weakened Aristotle’s philosophy and the idea of an
infinitely large cosmos shattered his idea of the universe. Mathematician / philosophers
like Descartes and Pascal began to look for ways to prove the existence of God in the
world of zeros and infinity.
The old idea of the Aristotelian universe was pretty much gone by the middle of the 17th
century.
Pascal used probability theory to investigate the value of accepting Christ as Savior, and
concluded that one should assume that God exists.
First, a test case to help us understand the concept.
Assume that there are two envelopes, marked A and B. Flip a coin to determine which
envelop has money in it. If the coin is heads, A has $100 in it and B is empty, if the coin
is tails then envelop B has $1,000,000 in it and A is empty.
Which envelope would you choose?
There is a tool in probability theory called expectation which measures how much we
expect each envelope to be worth.
For envelope A
1/2 chance of winning $0
1/2 x $0 = $0
1/2 chance of winning $100 1/2 x $100 = $50
Expectation
$50
For envelope B
1/2 chance of winning $0
1/2 x $0 = $0
1/2 chance of winning $1,000,000 1/2 x $1,000,000 = $500,000
Expectation
$500,000
Imagine that there is a 50-50 chance that God exists. If God exists, as a Christian, then
you go to heaven for eternity, if God does not exist, then you go into nothingness.
For being a Christian
1/2 chance of going to nothing
1/2 chance of going to heaven
1/2 x 0 = 0
1/2 x infinity
= infinity
Expectation
infinity
For being an atheist
1/2 chance of going to nothing
1/2 chance of going to hell
Expectation
1/2 x 0 = 0
1/2 x - infinity
= - infinity
0
We originally supposed that there was a 50-50 chance that God exists. But suppose there
was only 1/1000 chance that God exists.
For being a Christian
999/1000 chance of going to nothing 999/1000 x 0 = 0
1/1000 chance of going to eternity 1/1000 x infinity
Expectation
infinity
= infinity
So from a purely logical standpoint, the obvious choice is to choose to be a
Christian.
CLASH OF THE CALENDARS
Rome was the seat of the church and Christians used the Roman solar calendar which
was 365+ days. Jesus was a Jew and used the Jewish lunar calendar which was 354+
days. The two calendars made it difficult to keep track of major holidays.
In the 6th century, the pope asked Dionysius to extend the Easter tables (dates for Easter).
While doing this, Dionysius found that he could determine the year Christ was born. He
called it 1 anno domini. He said the birth happened on December 25, the previous year,
but started it on January 1.
Dionysius created two problems. One, the Bible says that Joseph and Mary fled from
King Herod, and Herod died in 3BC. Most scholars today believe Christ was born on
4BC.
The second problem was that there was no year zero. When counting our birthdays, we
begin with the zero year and our first birthday makes the end of our first year.
In 731AD, an English monk named Bede was asked to once again extend the Easter
tables. He didn’t want to abandon the new dating system, so when he went back in time,
the year before 1AD was 1BC. There was no year zero because to Bede as well as
Dionysius, zero did not exist.
Most people celebrated the end of the millennium on December, 31 1999, one year too
soon.