1.4.12 Summary

In this chap­ter, we have taken the an­cient geo­met­ric sub­ject of conic sec­tions, to find it serves as the back­bone for our ap­proach to group theory in com­plex spaces. A typ­i­cal treat­ment of the group theory sub­ject matter in Stan­dard Model physics presents $U(1),U(1) \times SU(2),\ \text{and}\ U(1) \times SU(2) \times SU(3)$ as the group rep­re­sen­ta­tions to define the gauge spaces, with little in­tu­ition gained per­tain­ing to a global co­he­sive form. But there does exists a beau­ti­ful and co­he­sive geo­met­ric arrange­ment of group theory in the con­text of conics in com­plex space. A true ex­pla­na­tion of what space­time and light are, is lack­ing in physics. At­tempts at these ex­pla­na­tions will be des­tined to fail be­cause the litmus of physics is lim­it­ed to a sub­group of the higher-or­dered sym­me­try group, under the guise of the spe­cial uni­tary groups $SU(2)$ and $SU(3)$. In com­plex conic sec­tions, we find the first hints at ra­tio­nal ex­pla­na­tions on the sub­ject matter and the geo­met­ric ec­cen­tric­i­ty of a group is at the heart of it. A matrix group's ec­cen­tric­i­ty trans­lates to higher-de­grees of ro­ta­tion when the value is closer to zero and higher-de­grees of radial ex­pan­sion as the ro­ta­tion/boost ar­gu­ment moves fur­ther away from zero.

In the up­com­ing volume, Phe­nom­e­nol­o­gy and the Geom­e­try of Light, we take an in-depth ap­proach to the sub­ject, con­sid­er­ing the geom­e­try of light as cone number gen­er­a­tors, the Eu­clid­ean-like metric spaces of the $SU(2)$-type and iso­mor­phic quater­nions, the con­nec­tion that hy­per­bol­ic geom­e­try has with spe­cial rel­a­tiv­i­ty and black hole dy­nam­ics, and quan­tum chro­mo­dy­nam­ics as a man­i­fes­ta­tion of $U(3)$. In the ul­ti­mate volume, Co­he­sive Meta­physics, there will be much more to ex­plore in the higher-or­dered sym­me­try group per­tain­ing to the foun­da­tion of the mind and causal­i­ty.