Steven Pinker is a careful, non-doctrinaire thinker---a position that does not come easily to a scholar not steeped in the aesthetics of mathematics, the aesthetics that illustrates the intense pleasure of discovering truths instead of imposing one's tastes on others. (It suffices that there exist a group of others who share the relevant tastes.)
Pinker's point that the realised violence in the Westernised world has historically declined is persuasive. For making predictions, however, it is the past potential (i.e., expected), not realised, violence that matters. Potential violence may have gone up in the last century, if only due to the risk of a nuclear catastrophe. Pinker's goal is not to make predictions, however, but to alert the reader to the fact that one lives in the best of the worlds that have ever existed, which presents one with the extraordinary opportunity to make the world even better and make it last a little longer.
Pinker's unified theory of technological and cultural progress is compelling. These are the restless young who create (and also destroy and degrade). Just as the Internet is believed to help the citizens who hold dissenting beliefs recognise each other and coordinate on an uprising, so did television, radio, and the interstate highways in the 1960s help the young recognise the condition of youth in the millions of others all over the world, declare this condition normal, and resist the excessive civilisation by the old.
Before the authority of the older generation was fruitfully challenged, the authority of the dead and the fictional had been---with the invention of the printing press and the rise of the Republic of Letters. Once the conditions of being alive and sometimes young had been framed as acceptable, the young and the alive found themselves contributing to mainstream culture and technology, instead of armed conflicts, thereby accelerating the progress of the civilisation.
One economist's model of the world derailed and has been cast as one of the evil ideologies of the twentieth century. The perception of the malice in the theory can be traced back to the elevation by the practitioners of the idea of the class struggle to a necessary condition for progress. In the long term, however, those social visions are most fruitful which seek mutually beneficial transactions, not those that artificially pit one social group against the other and dissipate resources in the course of the struggle. Mutually beneficial transactions require ingenuity and empathy (to experience the warm glow from making a gift or recognising others' rights, or to imagine others' needs and innovate); these are not too hard to come by.
Technological and moral progress are intertwined. The free circulation---and an occasional case of theft---of ideas promote both.