Yeah...it's political, so below the fold it goes...

1 Couple of thoughts:

First, the thing about the hard left is that while they will form a circle and defend themselves from outside attacks no matter the truth of them, they will form a circular firing squad if they see dissent within the ranks.  If you can prod them in the right direction, the fireworks can be spectacular.

That's why they haven't ever managed to completely take over; they are all too ready to eat their own.

Second, those dates for the rise and fall of empires are, basically, garbage.  The Roman Entity lasted from 509 BC (the founding of the Republic) to 1453 AD (the last days of the Byzantine Empire).  That's nearly two thousand years.  Things were rather a mess after the Fourth Crusade in 1204, but even if we discount the Byzantine successor states and the re-establishment (and entirely ignoring the Holy Roman Empire and modern Italy) that's still 1700 years, not ~200.

For Greece he's only chosen the Hellenistic period, ignoring both the Classical and Roman periods (which three periods were culturally a single continuous civilization) and the whole Byzantine period, as well as the earlier Mycenaean and Minoan cultures (fair enough in that case; they essentially disappeared in the Bronze Age Collapse), and also the Archaic period, which presaged Classical Greece, and was a not inconsiderable, if rather loosely-organised, state.  The Archaic period ended with the Persian invasion - but the Greeks won that war, so that's hardly a reason to ignore it.

For Britain, he chooses the dates of 1700 to 1950.  But while the Acts of Union were passed in 1707, the kingdoms were united under a common monarch since 1603, and a unified England goes back to 1042 - albeit with one or two (or three) hiccups over the centuries.  Picking the dates for the rise and fall of Britain and ignoring both Elizabeths seems problematic.

I'm no expert on the Ottoman Empire, but given that it was one of the Central Powers in WWI, while it was certainly in decline by then (and had been for quite some time) I think an expiration date of 1570 is stretching the truth a little.

I think the predictive power of his model is limited at best.

2 I've been arguing with a Bernie Sanders supporter for four days.  It really brings home how a person with no grounding in civics, physics, or logic would vote.  Not that I'm saying all Bernie supporters are like that.  I'm sure some of him actually like his record, or maybe just look at the rest of the field and say "what the hell."  But this is a kool-aid drinker.  This guy is one of the ones who thought Obama was Jesus, and now thinks it may actually be Bernie.

It's an incredibly superficial discussion compared to the content of this blog post, which was fascinating and thoughtful.

Oh, and I was going to post something similar to what Pixy did, although I think the discussion of when one would say Britain became truly representative in nature is debatable.  Interesting and worth the discussion, of course.

3 Pixy, you are in Australia. You're looking at the chart upside down.
Actually....
The chart and some made from it has been cropping up lately (usually unattributed) and has been referenced occasionally with the chants of "DOOM!" and "Lets cast aside the rules and go down fighting".
I think the possibility of a general collapse is greater than many suppose and more worrisome since the sort of enlightenment we grew out of is rare.  However I specifically wanted to use the pre-and post Rubicon Rome (and the omission of Venice) to debunk the notion that the 200-250 year lifespan is inevitable. 
On the other hand, all your points are valid Pixy. These are all specific political arraignments more akin to nation states than civilization itself. I swear I had one or two sentences  in there quibbling with Spain (which was bankrupt and virtually a spent force after the Armada but did not loose meaningful territory until the 1800s) and the UK, for which we probably should start the clock after the Fall of Cromwell though I've heard other places refer to "About 1700" for the start of the Empire...and I'd really draw the curtain just a bit later (at the Suez Crisis) for the point where keeping it up truly became impossible. 
The point you make regarding Eastern Rome is well taken and a lot of people agree with it. Although Byzantium was a distinct entity it was arguably only a bit more so than the Republic/Empire divide for Rome. On the other hand, as I point out, Rome reinvented itself and was certainly Rome before and after the Rubicon. 
With the exception of the Western Roman Empire none of those ended with the sort of calamitous dark age we associate with civilizational collapse (and even the chaos of the post Roman period is overblown) so civilizational collapse does not mean to him what it does to most people. 
The Mamelukes he mentions (as opposed to three other Mamelukes) were a sort of predecessor to the Ottomans trying to rebuild the Caliphate and based in Cairo...they were succeeded by what we call the Ottomans, though that is a western term and it refers to several dynasties. They were kind of like Spain in that they pretty much were a zombie empire after a debt crisis and military reversal, though I'd put the date at or around the siege of Vienna for their decline.
Persia should not be on the list at all. 
Sir Glub makes some good points, but that chart, while probably intended to be a conversation starter is counterproductive.  Using the criteria he does you could (with a few exceptions like the Yuan) be talking about Chinese dynasties but that wouldn't fit neatly into the time span Glub has chosen. On the other hand, using numbers that are not very close to the current age of the U.S.A. ie: 100-300 years would involve a TL;DR of a list.
No nation lasts forever but predestination is not a meaningful influence upon history unless a citizenry chooses to believe in it and give up.

4 The Tokugawa Shogunate began in 1603 and ended in 1868, 265 years.

5 China is a good counter-example - dynasties changed, but there's been a recognisable Chinese political entity for 4000 years.  Egypt is another counter example - 2800 years of self-rule across 31 dynasties (with a couple of Persian incursions and a mild case of Sea Peoples), and nearly 1000 years of Greco-Roman rule.

France in the late 18th and 19th centuries is an example in the other direction - the government was overthrown from without or within 9 to 12 times (depending on what you count) but at the end of it all, it was still France.

The Polish-Lithuanian Commonwealth, though....  226 years.

6 Anyway, I'd argue that Western civilisation is a single entity; and it's been continuously flourishing at least since 1543 despite the best efforts of various categories of barbarian along the way.

7 Although Russia cannot hold a handle to China in this regard, it existed as a nation since 988 A.D. or so, and continues to exist today. Although the Romanov dynasty only lasted for 234 years, the preceding dynasty, Ryuriks, lasted for 736 years (through the Mongol occupation, natch), and the Communist rule lasted for 74 years. So there is quite a range of numbers to pick.

8

That's only really true if you're taking the Duchy of Moscow to be "Russia". Russia in that era was like Germany, a lot of independent city-states who spoke the same language.

A lot of those city-states were annihilated by the Mongols and that left a power vacuum which the Duchy of Moscow capitalized (heh) on, but modern Russia as we know it doesn't go back that far AFAIK. I'd put the start at Peter the Great, myself.

9 Yep, which goes back to how arbitrary it becomes.  Except in cases like the fall of Rome or the Bronze Age Collapse, you have a lot of leeway about where you draw your lines, and your conclusions are only as good as your justifications for those lines.

10 Jaques Barzun explicitly argued in From Dawn to Decadence that European or "Western" culture terminated with the long world war, and that we're in the early stages of a post-Western cultural moment.  That's a very Eurocentric point of view - he clearly didn't consider Americans to be part of "Western civilization" - but that list of "civilizations" or even "nations" is pretty dubious.  There was a Persia of some sort intermittently for two thousand years, a Rome of some sort for about as long, and Russia existed before the Romanovs and continued under communist bastards after the Romanovs were exterminated.  Culture is upstream from politics and all that.
And Japan's been in cultural existence forever and aye - the Tokugawa were a regime, not the nation.