Longing for Infinity
Jaigyoung Choe
Man is mortal. All humans have to accept the brutal truth that they die in the end. Yet such finite humans
had once dared to reach infinity in a systematic way. Those attempts toward infinity had been made at least
three times in human history.
The first attempt was made on Tower of Babel as recorded in Genesis(11:1-9) of the Bible: In the
beginning God created the heaven and the earth, and Adam and Eve thereafter. God sent them forth from the
garden of Eden and they spread their offspring. After the great flood God blessed Noah and his descendents
to replenish the earth. And the whole earth was of one language, and of one speech. And it came to pass,
as they journeyed from the east, that they found a plain in the land of Shinar; and they dwelt there. And
they said one to another, Go to, let us make brick, and burn them throughly. And they had brick for stone,
and slime had they for morter. And they said, Go to, let us build us a city and a tower, whose top may
reach unto heaven; and let us make us a name, lest we be scattered abroad upon the face of the whole earth.
And the Lord came down to see the city and the tower, which the children of men builded. And the Lord said,
Behold, the people is one, and they have all one language; and this they begin to do: and now nothing will
be restrained from them, which they have imagined to do. Go to, let us go down, and there confound their
language, that they may not understand one another's speech. So the Lord scattered them abroad from thence
upon the face of all the earth: and they left off to build the city. Therefore is the name of it called
Babel; because the Lord did there confound the language of all the earth: and from thence did the Lord
scatter them abroad upon the face of all the earth.
The second attempt was made through the axiom of infinity. Long long ago there was a tribe of people
who worshiped the sun and kept moving to the east, in the direction of the rising sun. Starting one day they
began counting the rising suns. They counted that day¡¯s rising sun 1, the next day¡¯s sun 2, still the next
suns 3,4,5,6,7¡¦ In this way, numbers corresponding to the rising suns came into being. Those newborn
numbers are each followed by the next number. This is because the sun would rise again the next day.
Those people who were collecting the increasing numbers of the sun came to believe that the numbers
were boundless. Thus arose the notion that there exist infinitely many numbers. This was the beginning
of the concept of infinity among us humans.
However, humans needed a promise to define the concept of infinity: namely, the axiom that guarantees
that there are infinitely many natural numbers. According to our premise, infinity is just what is not
finite, and moreover the numbers are infinite. Only through this indirect method were humans able to tell
the infiniteness of numbers. A being that is not finite is the only endless entity that humans can
conceive of. This passive introduction of infinity can only have a limitation in itself. Something
inevitably doomed? Godel shows that in human logic not all truths are provable. In other words, there
are true statements that are beyond the reach of proof.
The third attempt at reaching infinity was made through the parallel axiom. In the old days the houses
were built in a precise way using the right angle obtained from the triangle with side lengths of 3:4:5.
With this triangle, investigators drew a rectangular shape and thought to themselves, ¡°the two sides
of the rectangle facing each other are parallel. If we extend the two sides infinitely, do they
intersect? Or do they run parallel with each other indefinitely?¡±
Humans had presumed that they never intersect, and the mathematicians had tried to prove it for over
2000 years in vain until the early 19th century. Only then did they realize that this is a parallel
axiom that they cannot prove but must accept as a truth. More surprisingly, they found out that there
exists a space called non-Euclidean space in which the parallel axiom is wrong. There is a space
where two initially parallel lines become more and more distant from each other, and similarly there
is a space where two initially parallel lines eventually intersect each other. Sadly, the space where
you and I can walk together to the east side by side for ever, called Euclidean space, can exist
abstractly only in our head. Our universe is a non-Euclidean space where two people are not able to go
forward parallel with each other for ever.
The human desire to reach unto heaven through Tower of Babel was frustrated by God¡¯s intervention,
only to result in the creation of hundreds of languages and in the difficulty of understanding one
another¡¯s speech. The introduction of infinity through the logic of indefinitely adding the successor
to the natural numbers like 1,2,3,4,¡¦ is not so perfect. Inevitably, it creates unprovable truths as
well as provable truths. The human dream of going forward side by side endlessly is possible only
in their dream, but in reality they will either sink in a black hole or end up on the boundary of the
universe.
However, how beautiful human languages are! It is a blessing that we have hundreds of languages. A
provable truth, once proved, may seem too natural. But how mysterious it is that there are unprovable
truths! It does not matter that you and I cannot go straight side by side for ever. Let us just wander
in the universe toward the end in our finite lifetime.
Shall we be still alive after ten years?
Shall we be the same next year?
No matter what the future will be
Today in this garden of Eden
How about scraping a living
One way or another?
(2014 International Contemporary Art Exhibition,
MATRIX: MATHEMATICS_HEART OF GOLD AND THE ABYSS)