a4108
| 8 |
|---|
The general matrix:
(105b)
corresponds to a rotation around the origin, possibly combined with a symmetry with respect to a plane passing through the origin O.
Inhabitants of a 3D world are 3D structures. Remember that time does not exist in 3D Euclidean space.
Orientation exists in 2D worlds. Earlier, we presented a transformation R encountering a Russian letter "ia". In 3D, this becomes:
(106)
(107)
(108)
(109)
Do a right hand and a left hand belong to different species? It depends on the group you choose. In 3D, you can use two groups. The first is what we called the special Euclidean group. (110)
You cannot find any element of this group whose action would transform a right hand into a left hand, or vice versa.
But this becomes possible with the full Euclidean group:
(111)
You might ask: which group governs my life today?
... In today’s world, we see various objects. In particular, our reflection in a mirror each morning while shaving. We then have two choices:
1 - You decide that your mirror image is not real (even though you use it daily), so your geometric world corresponds to the first group.
2 - You decide that the objects you see on the other side of your mirrors are real.
-
Then your world corresponds to the second group.
-
This drastically increases the volume of your flat world.
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Go to the nearest psychiatric hospital as soon as possible.
