“1” is the Loneliest Number
Why “e” May Be Far More Rational Than the Concept of One
Nyles Bauer
Nyles314@hotmail.com
There are moments in one’s life that are so beautiful and so lucid that you feel you may
have just caught an ever so fleeting glimpse of God. I don’t mean this poetically; I mean
they are that substantial, yet so delicate, as if trying to stand on a knife’s edge without
falling. It seems that the instant you become aware of these moments, you stumble and
they are gone. But for that time you’ve lost yourself almost entirely to the event, and
these moments are so brief, so perfect, and so very rare that they stand out in one’s life.
I had a teacher in high school, Linda Kessler, who taught calculus. She was explaining to
the class about the function f(x)=ex using the common method of introduction to a
calculus class, the model of compounding interest. The calculation is done first yearly,
then monthly, then weekly, and so on until you approach the concept of compounding the
interest so frequently that it becomes interest compounded continuously. That was my
moment. Additionally, the beauty was not in anything tangible, not an object, not a
person. It wasn’t even the numbers and symbols written on the board, it was just entering
the cusp of understanding something so beautiful that any description of it wouldn’t even
come close, yet something so beyond us as humans that you really can’t grasp the purity
and simplicity. “e” is an actual number (~2.7182818459045…), though irrational, which
means that it goes on forever and never repeats itself. Pi (π) is also an irrational number
(~3.14159265358979…) and much better known by the average person. I suppose this is
because there is, with a few exceptions, little subtlety to it. It pops out whenever a circle
is analyzed directly or indirectly as with trigonometry. I would certainly encourage those
who are so motivated to further research “e” on their own. It occurs throughout nature
and the universe, again somehow demonstrating the concept of conservation, a basic
fundamental truth within our universe, but this time with pure mathematics and nothing
specific to biology.

It seems that when “e” comes up naturally, conceptual beauty accompanies it. It can be
written as an infinite series of fractions that when summed up yield this number.
However, if the series contains just a little bit “more”, it no longer sums up to any
specific number but diverges, or adds up to infinity, a little “less” and it does add up, or
converge, to a precise number that seems to have no universal truth to it. The number “e”
walks this mathematical edge.
So one question arises, if “e” is ubiquitous in nature, how come we have such a difficult
time comprehending this number?
We adore simple numbers such as the whole counting numbers, 1,2,3 and so on. The
problem is, these numbers don’t really exist on the macroscopic level. Let’s imagine
sending someone out for a dozen eggs; 12 eggs. The math behind the number assumes
that we are getting 12 of the same exact thing. One ostrich egg plus one hummingbird
egg equals two eggs. We are indeed adding similar, but unlike, objects.
A ridiculous example you say?
This time let’s go to the store and get only large white chicken eggs. Take any two of
them. In fact take any two chicken eggs that have ever been in existence. They are indeed
similar, but never exactly the same, different in appearance, different in weight, different
in texture. Though similar, the very fundamental mathematical equation, the most basic
equation we learn, 1+1=2, has a condition that must be fulfilled before it can be used, and
that condition is that the first “1” in the equation and the second “1” in the equation must
be exactly the same, indistinguishable from one another in all respects. This is never the
case in the world we live in.
We might as well be adding apples and oranges, which we do. Please get me 5 pieces of
fruit. In English it may work, but mathematically speaking this is not a rational statement.
As irrational mathematically as telling someone to pick up “e” pieces of fruit would be in
any spoken language.

So we see that “1” is functional in English, but for the most part irrational in pure
mathematics, and “e” in functional in mathematics, but irrational in English.
We think in terms of “1”, whole numbers, counting numbers, though it really doesn’t
exist as anything real in our everyday world, but “e” appears to.
What if we had evolved a mind, different from the one we have, so that “e” appeared to
our brains as something real and easily understood, and “1” appeared almost nonsensical
as it really is. What if we weren’t limited cognitively to “simple” counting numbers, but
apparent universal constants made sense? Would this allow for us to better understand the
world we live in?