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THE ALTERNATURA EQUATION

THE ALTERNATURA OPERATOR

THE NUMBERS INVOLVED

	The base of Napier or natural logarithms
	The imaginary unit. Basic for the introduction of the imaginary numbers field. Equals (-1)^1/2
	^Pi

THE OPERATOR APPLICATION: THE EQUATION

The most simple application is over another important number: 1

And the result of "transforming" 1 by the ALTERNATURA operator is another bold number: -1

This wonderful equation is perhaps one of the most significant ones, since with an unbelievable simplicity relates 5 of the boldest numbers of Mathematics and Science: e, i, pi, 1 and -1

(1) = -1

ADVANCING FROM THE BASIC APPLICATION: THE COMPLETE TRANSFORMATION

But the transformation applies not only to 1, or to the natural or integer or real numbers. It is a transformation of the imaginary (or irrational numbers) into the same numeric field of the imaginary numbers.

Geometrically the imaginary numbers represents all the points in over a plane. The plane is called the imaginary plane.

Each imaginary number is represented by a pair of values that corresponds to the Cartesian coordinates of the corresponding point in the imaginary plane. Since this the point (x, y) in the plane corresponds to the imaginary number x+iy with i the imaginary unit.

More generally the ALTERNATURA operand transforms any point in the plane in the symmetric one with respect to the origin of coordinates. It turns the things 180 degrees.

In other words, referencing our metaphor, if "the Ordinary World" is the semi-plane at the right of the Ordinates axis (the Y axis), or saying in other way, the set of points with 0<x=Real(x+iy); "the Hidden World" must be the complementary semi-plane, at the left of the ordinates axis, with x<0.

TRANSFORMING THE ORDINARY WORLD INTO THE HIDDEN WORLD

The ALTERNATURA operand transform the whole right semi-plane in the left one, with a twist of course.

So then, if you apply it to the ordinary known "Ordinary world", it give you a tool to try to device the "Hidden World", and by joining both have an idea of "the Universe".

(The Ordinary World) = The Hidden World

DISCOVERING THE UNIVERSE

The Universe =
The Ordinary World + The Hidden World =

(The Ordinary World) + The Ordinary World

So, here is a tool, for even those that only can conceive "the Ordinary World", to take a look into "the Universe".

"The Universe", where, here, at ALTERNATURA, we try to work, or better, to live.