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

VIRGIL LAURENŢIU SPĂTARU 77
In this work, I try to limit myself only to the roughest part, without
developing baffling consequences, involved by this distinction compared to
the current understanding, held by contemporary mathematicians.
Before presenting the multiple similarities of this aporia, using different
concepts from various domains, disciplines etc., I will make one last
comparative parallel between Bombelli´s equivalences of the imaginary
number and the equivalences of this new theory, mathematically possible, in
order to emphasize the difference between them:
i² = –1;
i³ = –i;
i 4 = +1;
i 5 = +i;
i 6 = –1;
i = √–1;
etc.
(√–1) 2 = –1;
(√–1) 3 = √–1;
(√–1) 4 = +1 ;
(√–1) 5 = √–1;
(√–1) 6 = –1;
On this occasion, we clarify the fact that according to the new
mathematical conventions, we cannot speak of –i or +i, but rather of a
number-sign fusion, that acts simultaneously as a sort of vortex of new
“signs” and new “numbers”, acute relativized between one another, like a
sort of foam, cloud or field of inter-convertibility, that produces signsnumbers,
respectively quantities-qualities. This is why (√–1) is at least one
new “number” with a new “sign”, which generates spontaneously another
new “sign-number”.
This mathematical hybris, (√–1), is like the legendary Chimera,
representing the interaction, fluctuation, between at least three ( perpetually
unstable ) ”numbers” , which would be as a sort of “geodesic”, for this vortex.
These numbers would be: (√–n), regressum - ab (√–n) and progressum – ad
(√–n).
This true coincidentia oppositorum, or contraria sunt complementa,
acts spectrally and interferentially within the dynamism towards its maxims
and minimums, so as it seems to be the fundamental mathematic of a