Posted in Science & Nature

Mathematical Beauty

What is the most “beautiful” mathematical equation? For millenia, many mathematical formulas and concepts have been described as beautiful (and some defining beauty, as the golden ratio does). In the mathematical world, the adjective “beautiful” is used in the sense that certain mathematical concepts, despite the fact they are rational and objective, are so pure, simple and elegant that they can only be described as art.

One such formula is Euler’s identity:


Renowned physicist Richard Feynman described it as “the most remarkable formula in mathematics”. What makes this array of symbols and numbers so beautiful? Firstly, it contains the three basic arithmetic operations exactly once each: addition, multiplication and exponentiation. It also connects five fundamental mathematical constants with nothing other than themselves and the arithmetic operations.

0 is the additive identity, as adding it to another number results in the original number. 1 is the multiplicative identity for the same reason as 0. Pi(π) is one of the most important mathematical constants in the history of mathematics that is ubiquitous in Euclidean geometry and trigonometry. Euler’s number(e) is the base of natural logarithms and is used widely in mathematical and scientific analysis. i(√-1) is the imaginary unit of complex numbers, a field of imaginary numbers that are not “real”, allowing for the calculation of all roots of polynomials. Euler’s identity neatly sums up the relation between these five numbers that are so crucial in the field of mathematics. It is also interesting to note that these five numbers were discovered at different points in history spanning over 3000 years.

Some people describe mathematics as a distinct language in itself. Not only that, but mathematics is considered the universal language as it is both universal and ubiquitous. If that is the case, than Euler’s identity can be considered an extremely pithy literary masterpiece.

Posted in Philosophy

The Number System

The number system represents the advancement of life and consciousness.

In a number, the curves represent love, the crossroads represent hardship and the horizontal lines represent binding.
Let’s take a look at each number.

“1” is a mineral. It has one vertical line and has no binds.
There are no curves and ergo no love.
Rocks are not bound to anything nor love anything.
There are no crossroads and ergo no hardship.
Minerals merely exist as the first step of matter.

“2” is a plant. Life begins here.
The bottom line shows that plants are bound to the ground.
Plants are rooted to the ground and cannot move.
The curve on the top represents the plant’s love for the sky and sunlight.
Plants love the sky and is restrained by the earth.

“3” is an animal. It is formed from two curves.
Animals love both the earth and the sky.
But it is not bound to either.
Animals only have pure feelings.
Animals live in fear and greed.
The two curves are two mouths.
If one is a mouth that bites, the other is one that kisses.

“4” is a human. Humans are beings on the crossroad between “3” and “4”.
They can advance to a higher step.

“5” is an enlightened person. This number is a mirror image of “2”.
The top line shows the limit by the sky, the bottom line shows the love for the earth.
He distances himself from other humans but love both people and the Earth.

“6” is an angel. It is a spiral, curve of love rising towards the sky.
An angel is a pure soul and mind.

“7” is a god cadet. “7” is another number with a crossroad.
It is the image of a “4” flipped around.
A god cadet is on the crossroad between an angel and what is next.

“8” is an infinite god. An endless, twisting curve of love.
But this curve spins on the spot and does not rise nor fall.

“9” is a curve. It is a “6”, an angel, turned around.
In other words, it is love coming down instead of going up.
From the sky down to the ground.
It is a curve that spins and spins and congeals mayonnaise.

(from God by Bernard Werber)