## Chapter Ⅱ Hands of Salvation Extended to an Atheist❶

## Section A Math/Physical Intuition ～Complex Analysis and Set Theory～

Yet unable to give up, I was asking to myself the following questions everyday.

－`Isn’t SHE anywhere? Isn’t there any young woman who can save a junk like me? A woman with extraordinary wisdom?

But what kind of wisdom could it be? I can’t even imagine it. SHE doesn’t exist in the real world anyway. I might as well cut off the carotid artery…’

Tortured by incessant desire to kill myself, one day, I was suddenly given an amazing inspiration.

Looking back from today, that must have been the very moment the hands of Jesus were extended to me.

I’d like to explain.

The conclusion of structuralism/post-structuralism is very simple.

－Everything continues to transform by means of `power’ (puissance) which creates `difference’ (diffrence). But nothing is known yet about this `power’.

In short, it wants to say `Everything is meaningless’, just as Buddhism insists.

Yet I couldn’t give up by any means. I couldn’t renounce the idea of the Only Truth.

Was it because I had educational background in mathematics and science?

Aren’t scientists seeking the Only Truth through mathematical formulas?

I arrogantly thought as follows.

－`Liberal arts could never go further than this sort of nonsense conclusion. Aren’t there any sciences to decipher the riddle left by post-structuralists?’

With this vague feeling in mind, one day, I was reading a math textbook while standing at a bookstore.

It was an introduction textbook on Complex Analysis, but I don’t remember whatsoever how I came to take that book in my hands.

Complex Analysis or Complex Function Theory indicates a mathematical field which deals with Complex Numbers or Imaginary Numbers.

Although the imaginary unit

was introduced into mathematics to describe the solution of the equation

when it came to the practical question about what it serves for in the real world, nobody could give any

sensible answers.

Complex Numbers have nothing to do with human activities such as counting numbers, measuring length, size, weight, calculating money, describing order, rank and so on.

In consequence, Complex Numbers were even neglected at least until the 19^{th} century, when Newton
Mechanics－a science described with
real numbers alone－was considered
to be almighty.

The naming of Imaginary Number might explain the situation well, since Imaginary means something which doesn’t really exist.

Thus, we had to wait for the advent of Quantum Mechanics, which was founded in the early 20^{th} century, until
it was shown that Complex Numbers were indispensable to describe the World.

Through the physics called Quantum Mechanics, it was understood that we can describe by means of Complex Numbers the behavior of the elementary particles, the minimal components of the World, which cannot be identified exactly.

－I’d like to emphasize again their mysterious nature of being unidentifiable.

Before going on with my testimony, I should give some preliminary knowledge

As shown in the Fig. (3), any Complex Number z can be plotted on the Complex Plane, which is composed of the Real Axis (R) and the Imaginary Axis (I), so z=a +bi.

Here, both a and b are Real Numbers, with i referring to the imaginary unit

－ a is called the real part (Re) of z; b is called the imaginary part (Im) of z.

When a=0, z is called a pure imaginary number. We can also consider a Complex Number as a vector, which means z=(a,b).

As shown in the Fig. (4), Complex Numbers are the broaden concept of Real Numbers.

As shown in the Fig. (5), by using 2 dimensional polar coordinates, a Complex Number can be also described as below.

❏Proof of the Eq.1:

First, by replacing x(real variable) with z(complex variable) in the formula

From Euler’s formula, we can immediately understand the fact that Complex Numbers represent waves themselves.