Ciro Santilli @cirosantilli  40

This simply connected is called the universal covering group.

E.g. in the case of $SO(3)$ and $SU(2)$, $SU(2)$ is simply connected, but $SO(3)$ is not.

The orthogonal group has 2 connected components:

It is instructive to visualize how the $\pm 1$ looks like in $SO(3)$:

As a result it is isomorphic to the direct product of the special orthogonal group by the cyclic group of order 2:

A low dimensional example:because you can only do two things: to flip or not to flip the line around zero.

Note that having the determinant plus or minus 1 is not a definition: there are non-orthogonal groups with determinant plus or minus 1. This is just a property. E.g.:has determinant 1, but:so $M$ is not orthogonal.

Ciro Santilli just keep watching that a gazillion times whenever it showed on TV.

All action scenes are useless crap, but the premise with Ciro's precious simulation hypothesis subject, related physics and the illusion of life.

It is a shame that the key premise of using human bodies to produce energy is completely and impossibly stupid. You would obviously get more energy by directing burning the food you feed into humans.

If the film had been made later, maybe the much more plausible concept of AI alignment would would have been used instead. What a shame.

This film is an abomination and disgrace to the bilogy.