Answering this is like giving a brief summery of your historio-political worldview.
Let's take the first quote - history does repeat itself, but not in the sense that the same things happen over and over again. The principles that govern human behavior are always the same, so similar personality types will keep appearing, repeating their predecessors' mistakes, and eventually occupying the same social niches. Society in itself keeps following the same principles, but we evolve. There are the smaller cycles of the rise and fall of societies, and they follow certain patterns, being repeated on larger scales as society and technology evolve. You change the scale, and though applying the same formula each time, new phenomena (which are variations on the old ones) will occur. Then there is the bigger cycle which, I regret to say, we haven't yet completed in all 10,000 years of civilization building, of 4M years of the existence of the species, if you'd rather look at it this way. As for 'testimony to the stupidity of man', heh, I've heard that so many times, uttered by frustrated and misguided idealists. I disagree. Yes, the majority of mankind is intellectually challenged, that's true. But could Mr. Hamilton do anything about the constant repetition, other that bickering and pointing an accusing finger at, well, the rest of the world (kinda childish, if you ask me). No. So I guess the first quoted statement was made by a stupid person.
History doesn't repeat itself. It rhymes.
That's cute. Not sure it means much. Rhymes - that is, it has structure and beauty? Structure - yes, of course, just like physics has structure, cause and effect, et cetera; beauty.... yes, sure, the world is beautiful. Especially if you're not living in a Brazilian favella, under a totalitarian regime or anywhere else where life hurts.
I really really really disagree with Alexander Tyler. But to address all his points.... it's much easier to make an irresponsible remark such as his than to seriously discuss each of his statements. Rome evolved from democratic barbarism to an oligarchy to a centralized oligarchy, then semi-anarchy, then centralized bureaucratic... whatever (I really should read a book about Diocletian, or something), then it died. China has existed for over 2000 years, and I mean just the Chinese empire. etc., etc.....
As for nuclear theory - I don't think it can be applied to humans, unless you are looking at society from a big distance, not really seeing any individual at all, just like researchers of nuclear physics do with atoms. But we actually can
see individuals, and we can
predict their behavior, sometimes even with extreme ease. Many great artists of government could asses people accurately and quickly - a very important trait (possessed by Caesar and by Genghis Khan).