Zero and the Church
Look around you today. Consider how
much religious beliefs affect everything around you. Notice the names of
cities, think about the laws, the politics, and even what is considered as
positive etiquette. When considering the
significance of zero to the world, religion must be mention. It has had a very
powerful, and very interesting role, in zero becoming a number. Right, or
wrong, the Christian Church has tried and contested academic and
scientific advancement. Note that the Christian church was likely not the only
religious group to do this, just one worth mentioning. But, why would the church care about
zero? I really can't wait to tell you, I
find it quite interesting, but first, let's consider the Catholics Churches
history in a little more detail.
The Church Saves The Mathematical discoveries pre-darkage
This section primarily a side note, and provides background for the churches history in mathematics. Feel free to skip it and move on to the next section
When considering the role of the Catholic
Church in Mathematics, you would probably focus on noting the negative effects
the church had on Mathematics and scientific advancement. However, the church
did contribute significantly in bringing mathematics to what it is today.
During the darkest part of the Dark Ages ("...from the Barbarian invasions
of the fifth century until the eleventh century,"
Fortunately the system of education was never
intended for the education of a large portion of society. Without knowing it,
again the church spurred on scientific advancement. The attraction of its
famous cathedral schools spurred many students and teachers to seek after them,
leaving an overflow of people wanting to learning and teach. Outside the walls
of the cathedrals, with permission from the authorities, non-member teachers
gave lectures on subjects not taught in the catholic based curriculum,
including mathematics. This created a system of
private teaching where education was acquired in return for paying fees. In a
way the Church caused a gathering of Intellectuals where
scientific/mathematical advancement could be pursued, as well as created a
monetary system of education. Throughout
all of this however, the church “intentionally” suppressed “new ideas,”
particularly mathematics.
The Church holds back Mathematics
Now
for the more interesting part. The church definitely held back the advancement
of Mathematics. It began with how they limited the content studied in their
“schools” to the study of church doctoring and content. But from there, as
mathematics began to not exactly support the church, the Church went from not
supporting, to resisting. Fear of how
“new ideas” might be responded to by the church has be prevalent throughout
history. Since the church was not
separate from the government, the power it had was immense and could reach
anyone. The epitome of the defiance of the church and new ideas is with the
Copernican Universe, where the sun in the center of the universe rather than
the earth. Even some 300 years before the Copernican Universe (the sun at the
center 1543 A.D.,) as philosophy and science were
becoming preferred to the history and teachings of the church, the church began
to react to the shift of educational interest. In 1210, the scientific work of
Aristotle, the main cause of the shift of priorities in education, was actually
forbidden to be used at the University of Paris, under pain of excommunication.
The
Church at one time even decreed it illegal to publish any book revealing “new
ideas.” In response to Copernicus’s ideas and especially to the German monk
Luther, and his famous list of complaints he nailed to the churches door in
1517 that began the attack on the church. The same year Copernicus died (The
same year Copernicus finally dared to publish his manuscript of his book De Revolutionibus,
( 1543 A.D.,) "Pope Paul III issued the index of forbidden books,”
So
why did the church not like this scientific advancement? One reason is that they
believed that God created the universe specifically for man. Thus, man is the
center of the universe. Man lives on the world so without too much thought, we
can see how this implies that the earth is the center of the universe. The
Copernicus universe does not support this, and neither does Galileo's research
using the telescope (actually not invented by him,) which supported Copernican views."Such ideas were so disturbing that there were
professors at Padua who refused to credit Galileo's discoveries, refused even
to look into his tellescope for fear of seeing in it
things that would discredit the infallibility of Aristotle and Ptolemy, and
even the Church"
In addition to the
belief that God was the only thing infinite, the Church actually had a proof
that god existed which, the concept of zero and infinity contradicted. They
believed that the earth was the center of the universe and that nothing existed
outside of the universe. Since the earth, planets, and stars revolved, they
understood that it took something to make them move: from their understanding
of the laws of motion. They saw that the earth moved because the planets
outside of it pulled on it, causing it to spin. Then, the next planet away
moved because of the pull from the planets around it, and so on and so on until
the outermost sphere, the sphere of stars. But what caused the outermost layer
to move? There must be something making it move. The Church observed this as
being a proof of god’s existence since it must be through his power that the
outer most planet moves. He is the "prime mover" of the outermost
layer. This proof only holds true under the Aristotelian belief that there is
no such thing as the void (Zero,) and no such thing as infinity. You can see
here why religion was tied so close to the number zero: zero implies infinity,
infinity implies zero, but if there is infinity then there is no proof of God.
To help understand
why this makes sense, let Seife (pp.47) explain it in
his own words, quote
...after all, there were only two logical possibilities for the nature
of the void, and both implied that the infinite exists. First, there could be
an infinite amount of void-thus infinity exists. Second, there could be a
finite amount of void, but since void is simply the lack of matter, there must
be an infinite amount of matter to make sure that there is only a finite amount
of void-thus infinity exists.
The churches
defiance of mathematics can largely be summed into a category pertaining to
zero. With zero, you found infinity
and nothing all at once, both questioning the existence and principles of God. Seife sums this up by saying, "As Europe slowly
awakened from the Dark Ages, the void and the infinite-nothing and
everything-would destroy the Aristotelian foundation of the church and open the
way to the scientific revolution."
Science responds to zero
The Academics of
science also had stakes in the matter of Zero and Infinity. One example is with
the atomists. They believed that the universe is made up of Atoms. Movement of objects or people, was the
movement of atoms. They theorized that for the atoms to move, there must be
space for them to move, called the vacuum (the infinite Void). Without the
vacuum, the atoms would just be all stuck together. Since this line of though
pushed for an infinite amount vacuum, and suggested an infinite amount of
matter, this opposed the Church: God created the Universe, and there is nothing
outside of the universe.
Parmenides, a
member of the Eleatic school of thought, held the belief that, "the
underlying nature of the universe was changeless and immobile"
Achilles
runs at 1 foot per second. A tortoise runs at half that speed and gets a head
start of 1 foot. Let the race start. Achilles, in order to pass the tortoise,
must at some point pass the one foot mark where the tortoise started, but by
the time he has gotten there(1 second,) the tortoise has moved forward(half a
foot.) Now he must get to where the tortoise is (the 1.5 ft. mark.) Again, it
takes him time to get there, giving the tortoise time to move forward. This
will continue on time after time, appearing to never end. Since he will have to do this infinitely many
times, and each time takes an amount of time, how would Achilles ever catch up
to the tortoise? This paradox lay unsolved for almost 2,000 years.
Click on this Applet to learn more about Zeno's Paradox
You can see how this supports the philosophy
that nothing in the universe actually moves.
The Atomists actually countered this by explaining that the atom was the
smallest element and they were indivisible.
Thus, there is a point when all things cannot be divided, including the
space left for Achilles to catch up to the turtle. At this final step, Achilles
simply hurtles an atom where the tortoise doesn't have enough time to hurtle
the next one, putting the two racers even with each other. However the most provocative part of Zeno's
paradox is that if you choose to accept 0/infinity, nothing in the world can
move. A pretty persuasive argument as to why zero isn't actually a number and
really doesn't exist at all.
Zero causes issues in the Calendar
I
cannot finish off this section without talking about the significance zero has
had with our calendar system. Have you ever noticed that looking back to 1
A.D., it follows directly after 1 B.C.. Where exactly is year zero? If you look at
many publicized timelines, they even choose to ignore this fact and actually
put in a year zero even though it doesn't exist. Now think about this, if someone
was born on the first second of 1 A.D., they wouldn't be a 1 year old until 2 A.D.. They wouldn't
be five years old until 6 A.D. and so on until when they are 100 years old. The
year would then be 101 A.D. You know how keeping track of what century it is
kind of confusing, is it starting to make more sense? One century is 100 years,
and 100 years haven't been completed until 101 A.D., so in 101 A.D. the second
century begins. In 1901, 19 centuries
have been completed and the 20th century begins. A funny realization you might be making is that the 20th century ends on December
31, 2000, and the new millennium/the-21st-century begins on January 1, 2001.
What day did you celebrate the new millennium?