I must say that I am confused by this. I do not know what all your sources say, but am only looking at SP's lecture.
He is making a big claim, and should have substantial evidence to back it up. After 1945 he may have it, I cannot judge that. But before that, it is more than flimsy!
Leo9 explained about HG's fault in source, which makes his point of start and his first graf invalid.
His next stop is from coming of agriculture right up to medieval times, and here his entire support for his ideas during this vast span of time is quoting the bible's Hebrew laws. Apparently he thinks that All civilisations around the globe are the same, and wars are not mentioned at all.
Medieval times: 'Europe' has draconian laws, but 7 countries have decline in crimes. We must assume that this is representative for the whole globe regardless of culture, as this is all we have.
As for wars, which went on and on all during that period, they are not mentioned at all.
Medieval to 1945: No evidence of anything. What about slave trade, for instance, in which millions of people were killed?
As for the two world wars, they do not matter, he says. One wonders what exactly he thinks violence is, and how he arrives at this conclusions: what is counted in, and what not?
He has nothing, and that's a fact. His claim is much, much too sweeping!
What he has after 1945 is another thing, but here he changes his viewpoint to the Western world, which is apparently to be taken as representative for all the world. I find that more than hard to believe.
Believe me, I do not want a violent world, and if violence is in fact going down after 1945, I would be extremely glad to hear it. But judging from how he goes on in the first part of his lecture, I am really not believing him.
I would tend to assume that violence is not on a steady curve, (more of less) any more than any other thing to do with humanity. I think things work up and down and in and out according to what happens with wars, science, religion, politics, economy and so on.
I believe that what we do with technology will tell the tale about the future, whether it will be used aggressively or in the real service of peace and survival. But I do not believe in any curve going automatically downwards.