One can consider me an engineer by the virtue of my
education and I understand phenomenon as undulating lines on a Cartesian plane.
The properties of such lines were understood in terms of the laws of Calculus.
As I advanced in my studies there was a topic called the Laplace
transforms where function’s expression was viewed from a different perspective
albeit simpler and lot more algebra like. In the great traditions of rote
learning I rammed the methods of such transformation in my head always quashing
any niggling conviction – "It is not clear". You see an engineer needs only a
little understanding. All he needs are rules that make sure that his designs do
not explode into a big problem. After many years an ordinary mind working into
the mysteries asking a question-“What is underneath all this?” finally fathoms
it and laughs.
Coming to the calculus question, Laplace
transform leverages a particular function- number e raised to the variable say
x. e is a special number, muse of a poet. ex is a self similar function-
the differential of ex with respect to the variable x yields ex.
d ex = ex
dx
This innocuous looking statement refers to an indestructible
entity in the sense that it cannot be deconstructed in terms of anything else
but itself. God like isn't it? But what is this magical number ‘e’ mathematically? The only way the
above function is true is if
ex
= 1 + x + x2 + x3 + …to infinity
2! 3!
And therefore e is
e
= 1 + 1 + 1 + 1 + …to
infinity
2! 3!
That roughly adds up 2.718…not quite 3 though but
essentially an irrational number. Why is it irrational? You cannot describe it
in terms of something being some part of something else. This number holds its
own ground; do whatever you might damn well please. That’s quite irrational, e
will not budge no matter how much you try and try to make it budge. It doesn’t
belong to anybody. It doesn’t even belong to the physical realm because the
numbers of decimal places will simply extend to infinity. This number just
chooses to make its presence felt because some fool wanted to understand what phenomenon
on a Cartesian plane is.
The significance of this number would be clear when one realizes that every control system on earth owes its existence to e. Every building owes it existence to e. Every man made creation owes knowingly or unknowingly to e. This is a very important number in our civilization because
this is the basis of the entire Trigonometry, already mentioned Calculus, and
therefore the whole of engineering. No wonder only because of the unshakeable
strength within it were Mathematicians able to unfurl their wings. All this
thanks to the infinite irrationality in e. Not only e, we owe our understanding about our world to many other irrational numbers. In short if I dare say we owe our rational understanding about anything to irrationality of existence.
Thanks to Gods infinite irrationality
that we can enjoy some of our rational lives.
For a more sound reference
http://en.wikipedia.org/wiki/E_%28mathematical_constant%29
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