ATON is a hopefully evolving classification theory. It aspires to unify knowledge around numbers and prefers naive methods. Some of the older posts are wrong but I'll keep them for the sake of continuity.

Monday, April 10, 2006

Light and complex numbers

I previously compared C to H2={,{,{}}} and Light to E1/H1={}/{,{}}.
There is a mistake since the symmetry of light is U(1), the circle group, or the complex unit circle, e^(i*x).
Therefore C has to be like H1={,{}} and R like H0={}.
In fact, it works better if {} is interpreted as {-1,0,+1}, reflecting dual nature of {}.
0 is the content and -1, +1 are the boundary.
Boundary determines the content and vice versa;
+1-1=0
Quantum Mechanics has a similar form as Bra and Ket vectors.
Then C is obtained by an iteration on R;
x^2=-1
x={+i,-i}
Like magnetic field is obtained from electric field.
A complex number can be written in two dual formats;
a+i*b=Sqrt(a^2+b^2)*e^(Arctan(b/a))
Reflecting the collapse;
{,{}} -> (,())+((),)

It is interesting to see that C closes so quickly.
The reason for this is that, {,{}} is the last common form to E and H sets.
E0=,
E1={}
E2={,{}}
H0={}
H1={,{}}
E1=H0 and E2=H1.
After that they diverge.

E1/H1={,}/{,{}} reflects electrical-charge/light duality.
Electrical charge comes with (+,-) duality, like integers.
Light comes with two dualities, (+,-) and (electric, magnetic).

E3/H3={,{},{,{}}}/{,{,{,{}}}} reflects strong-charge/strong-field duality.
SE3/SH3=3!2!1!0!/2^3=6*2/8 indicates 2*6 quarks and 8 gluons.

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