Logarithm
was another term that seemed to be important. I learned that the
logarithm of a given number is the power by which you need to raise a fixed
number, called the base, in order to produce the given number. So, for
example, if the fixed number, or base, is 10, the logarithm of 100 is 2: 100 =
10
2
or log
10
100.
The decimal system uses measurements whose units are powers of ten. Ten
is actually known as the "common logarithm." But logarithms in base e also
play an extremely important role, I discovered. These are known as "natural
logarithms." At what power of e do you get a given number?—that was what
you called an "index." In other words, e is the "base of the natural
logarithm." According to Euler's calculations:
e
=
2.71828182845904523536028.... and so on forever. The calculation itself,
compared to the difficulty of the explanation, was quite simple:
But the simplicity of the calculation only reinforces the enigma of
e
.
To begin with, what was "natural" about this "natural logarithm"? Wasn't it
utterly unnatural to take such a number as your base—a number that could
only be expressed by a sign: this tiny e seemed to extend to infinity, falling
off even the largest sheet of paper. I could not begin to understand this never-
ending number. It seemed as chaotic and random as a line of marching ants
or a baby's alphabet blocks, and yet it obeyed its own inner sort of logic.
Perhaps there was no fathoming God's notebooks after all. In the entire
universe there were only a handful of especially gifted human beings able to
understand a tiny part of this order, and then there were the rest of us, who
could barely appreciate their discoveries.
The book was so heavy I needed to rest my arms for a moment before
flipping back through the pages. I wondered about Leonhard Euler, who was
probably the greatest mathematician of the eighteenth century. All I knew
about him was this formula, but reading it made me feel as though I were
standing in his presence. Using a profoundly unnatural concept, he had
discovered the natural connection between numbers that seemed completely
unrelated.
If you added 1 to e elevated to the power of π times i, you got 0: e
πi
+ 1 =
0.
I looked at the Professor's note again. A number that cycled on forever and
another vague figure that never revealed its true nature now traced a short
and elegant trajectory to a single point. Though there was no circle in
evidence, π had descended from somewhere to join hands with e. There they
rested, slumped against each other, and it only remained for a human being
to add 1, and the world suddenly changed. Everything resolved into nothing,
zero.
Euler's formula shone like a shooting star in the night sky, or like a line of
poetry carved on the wall of a dark cave. I slipped the Professor's note into
my wallet, strangely moved by the beauty of those few symbols. As I headed
down the library stairs, I turned back to look. The mathematics stacks were
as silent and empty as ever—apparently no one suspected the riches hidden
there.
The next day, I returned to the library to look into something else that had
been bothering me for a long time. When I found the bound volume of the
local newspaper for the year 1975, I read through it a page at a time. The
article I was looking for was in the September 24 edition.
On September 23, at approximately 4:10 P.M., on National Highway ... a
truck belonging to a local transport company crossed the center line,
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