The USA didn't invent the concept of police or government.

The first police were appointed to investigate and punish minor crimes commited agains civilians.

Then why are most “uncivilized” societies have more egalitarian and non-violent than “civilized” ones?

Uncivilized societies engage in violence much more frequently than civilized societies.

That's the case for individual/personal violence, and also for institutional/mass violence.

Civilized societies are better than uncivilized society in anything they do collectively, be it science, production, or murder.

Since civilized societies are so much better at murdering, the few cases where mass murder does happen are much more significant.

However, such cases remain an exception, as opposed to what is the case for uncivilized societies.

Uncivilized societies may be harmless, but they are certainly not peaceful.

Civilized societies are more powerful, but they yield their power much more carefully.

When I went to college the dot was used for the dot product (scalar product) of two vectors while the cross was used for the cross product (vector product) of two vectors.

Since in this case numbers (read: one-dimensional vectors) are multiplied, the dot product is used, which should be denoted by a dot.

(But really, if I were to write a formula in Latex I would just use the * symbol, too.)

Do not climb.

Play on and around pipe.

A class of 200 students performing much worse than the last class is very unlikely. 200 Students is enough to make even small differences statistically significant.

A single test being much harder than the last test is much more likely, since it isn't an averahe of 200, it's a single datapoint.

That's why if this semester's class performed much worse than last semester's, you can assume it's because of the test, not the students.