Re: The splendor of true

Le 09/03/2025 à 01:28, Python a écrit :

Le 09/03/2025 à 00:54, Richard Hachel a écrit :
...

Into what strange world would we fall, if, instead of using Z=aa'-bb'+i(ab'+a'b), we used the much more logical and natural equation Z=aa'+bb'+i(ab'+a'b).

 What makes you claim that ( aa' + bb', ab' + a'b ) is "more logical and natural" than ( aa' - bb', ab' + a'b) ?

Several reasons.
First, the simplicity of writing, all in positive terms.
The concordance with statistical science.
The ease of natural understanding (Plougastel high school).
The perpetual monitoring of derivations using i=-1 as a simple numerical concordance check.
The simplicity of the explanation and the generalization of i^x=-1
The visualization of the associated curves symmetrical in $(0,y).
Roots often much simpler to calculate and write...
So basically, it's simpler and more beautiful.
Now what does that change for fractals, for Gauss's representation, for experimentally validated equations, I don't know.
R.H.