VOL. IV (XXI) 2009 - Departamentul de Filosofie si Stiinte ale ...

74 ON WITTGENSTEIN AND THE IMAGINARY NUMBER
hermeneutics, I will endeavor to show the mystique of this alternative
imaginary number, just like "inequalities" Śiva and “his Dance (Play)”.
So what are we talking about here? ... First of all we know that
Bombelli was quite inspired using the neutral role of number 1. That is why
multiplying this number helps to remove the negativity from the root of a
negative number, which is known as universal mathematical formalism,
represented as:
√–a = √–1a = (√a)(√–1); iar √–1 = i => i² = –1;
thus we have the following equivalences:
i = √–1; i² = –1; i³ = –i; i 4 = 1; i 5 = i etc.
So without getting into other details on the complex numbers, what I
propose does not follow this algoritm. Firstly, the starting point will be the rule
of multiplication of signs. As it is well known:
+ + = +;
– – = +;
– + = – ;
+ – = – ;
From here one can easily deduce that:
+² = + ;
–² = + ;
–³ = – ;
It follows that: √+ = (+ V –) and ³√– = – . Thus it appears that, in the
present case, we can distinguish two kinds of +: i. e. that which we might call
conventional maximum (absolute), from which we could draw only one other
+ and the minimum (atomic), from which we can draw only one – . Due to
this new agreement on the negative sign we notice that it is the most basic
up to now. This sign is the "imparity" (especially on its exponents) and
asymmetric par excellence, to the "structure" plus.
In such a state of things let us notice what surprises could be brought
by √–, bearing in mind that – it is the imparity par excellence. Therefore in
this case we have P √–1, i. e. root (which is "parity" of order, i.e. even order)
of something that is exponentially (for self-consistency) only to the
“imparity”(or odd numbers). The next step in this approach would be:
P √– I = √– 3 = √– – 2 = –√– = –√– – 2 = +√– = +√– – 2 = – +√– = –√– … and so on;
Then we could continue their equivalents: