Let me first take up the Euler’s theorem or Euler’s Identity. It is an equation as neat as Einstein’s e=mc2 and in the words of Prof. David Percy of the Institute of Mathematics and its Applications, it was “a real classic and you can do no better than that … It is simple to look at and yet incredibly profound, it comprises the five most important mathematical constants.”
Euler’s Identity is written simply as: eiπ + 1 = 0
The five constants are:
- The number 0.
- The number 1.
- The number π, an irrational number (with unending digits) that is the ratio of the circumference of a circle to its diameter. It is approximately 3.14159…
- The number e, also an irrational number as π . It is approximately 2.71828….
But the weirdest thing about Euler’s formula—given that it relies on imaginary numbers—is that it’s so immensely useful in the real world. By translating one type of motion into another this equation has application in real world. π and e are deeply related, but in a very weird way, as adventures of Alice after falling through the rabbit hole.
Such irrational events that Alice experienced are in a dimension perpendicular to the world of real things—a place measured in units of i. The square root of –1, which of course doesn’t exist. Mathematicians call it an imaginary number.
Because Alice shows effects from obeying instructions ‘Drink me or Eat me’ down there is in literal sense while in real world what one faces is no less embarrassing as losing face or feeling small. In short our existence is the axis around which both irrational and real world make their claims on us, even if it is only limited to a nightmare. This equation is all pervasive in human affairs where an element of irrationality is in-built.
We cannot multiply a number by itself to produce a negative number anymore than we can repeat a dream by our will, The letter i is therefore used as a sort of stand-in to mark places where this was done.
The Queen of Hearts in the Lewis Carroll’s story might order about but Alice holds the ultimate authority and when she asserts it shows what is wrong with the authority of the Queen. She is only a number in the deck of playing cards.
eiπ + 1 = 0
In the Euler’s Identity Alice is the constant 1. As seen earlier her place in the equation makes the pother and the strange procedure of the trial of the Knave of Hearts as zero another constant!
The beauty of the Euler’s theorem is that it has a transcendental quality of human existence where a person or an event (represented by the number 1) can undo all the carefully orchestrated Power Games of nations to mean nothing. Even while Austro-Hungarian monarchy or Dual Monarchy was lording over the ethnic minorities of the Balkans little did it realize a single event like assassination of the Archduke of Austria (1914) would bring down the empire like a pack of cards!
Similarly all that the Great Britain had amassed as a maritime nation, with colonies stretched into far corners of the globe (The Sun will never set on their empire’) shall with two Great Wars evaporate.(the constant 1 can represent both Great Wars as one set)