Intuitional Science (4) – Mystery and Magic of ‘i’

This i is neither the self (ego) nor is it the Self (Soul). This i is more mundane than the self but it is mysterious and magical. This i is the square-root of -1.

The i=\sqrt{-1} is a paradoxical number. There is no real number that gives you -1 when multiplied by itself. The square of a positive number is positive and the square of a negative number is positive as well. So, what do we mean by square-root of -1?

Instead of rejecting it as nonsensical mathematicians and physicists treated it as an abstract symbol and followed the consequences. They discovered a magical world.

The reason i is used in mathematics is because you can build a very powerful calculus. Unsolvable equations become solvable in this calculus. There are many textbooks but the best books that explain the magical properties of i are Roger Penrose’s book “The Road to Reality” [1] and Paul J. Nahin’s book “An Imaginary Tale” [2].

We use i in physics because Nature uses it. We cannot explain the electromagnetic waves without i. We cannot explain quantum physics without i either. The i has far deeper implications. This magical number represents something more fundamental. We need i to explain electromagnetic waves and quantum wavefunctions but at a deeper level we discover that i is truly built into Nature. The i is not an artifact of the human mind. It is part of the Nature.

Abstractly speaking, the square-root operation creates two entities from one. For example the square-root of 25 is 5. This means: 5 times 5 is equal to 25. The square-root operation is similar to analysis. When we analyze something we are creating multiplicity, we are discovering the constituents of the whole. So, in the abstract sense, taking the square-root of an entity means splitting that entity into 2 equal parts the multiplication of which reproduces the original entity. The square-root operation in general and the square-root of 2 in particular symbolizes the “fundamental interaction”. A visual representation of the “fundamental interaction” is the Fermat’s spiral

The mathematical expression of the Fermat’s spiral involves the square-root.

The red spiral is described by the formula

radius= a \sqrt{angle}

The blue spiral is described by this formula

radius= -a \sqrt{angle}

where ‘a’ is a constant. As the angle increases the radius increases to create the spiral.

In an earlier article titled “Prometheus and Chronos”, I mentioned that the Fermat’s spiral is a model of the Higgs field which supposedly pervades the entire space. Physicists are trying to prove this theoretical concept experimentally at the Large Hadron Collider (LHC). The center regions of these red and blue spirals represent the “fundamental interaction” which I described as a “twist” of a thread of the primordial fabric. The “fundamental interaction” creates 2 from 1 just like the square-root operation.

The magic of i=\sqrt{-1} comes from the fact that it causes a dynamic binding between the two parts of the whole. The i represents an oscillation or a fluctuation between the two aspects of the whole. We can also describe i as the mathematical representation of the principle that mediates 2 opposing tendencies.

According to Tantra Yoga philosophy Nature has 3 fundamental tendencies known as “3 gunas”.

  • Sattvaguna (sentient guna): tendency towards sentiency, the tendency for straightness, the tendency towards limitlessness, the force responsible for symmetry, the force resisting curvatures.
  • Tamoguna (static guna): localizing, internalizing, limiting, symmetry breaking tendency.
  • Rajoguna (mutative guna): the principle that mediates the opposing forces of the sentient and static gunas, the principle of evolution, the principle of energy.

The i is the mathematical key to the mysteries of the Rajoguna.

I will conclude this article by mentioning what Rajoguna means to me.

  • Basis of quantum mechanical nature
  • Basis of vacuum fluctuations
  • Transmutation
  • Transformation


[1] “The Road to Reality: A Complete Guide to the Laws of the Universe”, Roger Penrose, Vintage (2007), ISBN: 978-0679776314

[2] “An Imaginary Tale”, Paul J. Nahin, PrincetonUniversityPress, ISBN 978-0-691-12798-9


About Suresh Emre

I have worked as a physicist at the Fermi National Accelerator Laboratory and the Superconducting Super Collider Laboratory. I am a volunteer for the Renaissance Universal movement. My main goal is to inspire the reader to engage in Self-discovery and expansion of consciousness.
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