While the lack of fuel was a serious concern to the Romans (even during the time of Augustus), I don't think either the population pressures or the lack of fuel had much of an effect on the decline of the Empire.
After the 3rd century, Rome was more likely to face under population than overpopulation. It was estimated that the Crisis of the 3rd Century led to the deaths of about 1/3 of the Empire. Afterwards, (particularly in the West) the severe lack of people led to the development of the patronage system. That was one of the reasons why Rome couldn't defeat Alaric in 410, they had no available people.
Also, for the most part, Rome was "full" even during the peak of the Empire. For the most empty provinces, Gaul and Hispania, they were empty not due to the lack of people, but due to the lack of arable land. The technology to start tilling the hard soils of northern Gaul wouldn't be invented until the 10th century. So the late Empire wouldn't have faced any more population pressures than the Empire of Claudius or Nero.
And finally, the lack of fuel was also a problem during the peak of the Empire. I've once heard (though I don't have a source) that much of the German economy was selling fuel to the Romans circa 100CE. But besides that, the Romans had other alternatives to wood, such as how coal was often used by blacksmiths.
Oh, also I wouldn't say that history has "moved" north overtime, just that the history of the predominant "western" empire has. If looking at the most powerful and/or sophisticated state overtime, the focus of history would constantly move between Egypt, Anatolia, Persia, Northern India, and Southern China for most of history. I think the main western empire has moved overtime simply because it can't go south, west, or east (because of the Sahara, Atlantic, and because if it went East, it wouldn't be considered western anymore).
Yeah, I think that they both had their individual strengths and weak points. I would say that Rome was overall better if you lived in an urban area or valued peace, while Medieval Europe was a more "fair" (in relative terms) society for the rural folk.
I would also include Charlemagne, Otto II, and Justinian onto that list.
For West Africa, I need to read more on the topic, but I believe that a couple empires came and left (Mali and Ghana?), but their descendants eventually split into various small kingdoms and polities. Although, I guess you could include the French as being one unifier.
Oh yeah, sorry, I was mostly replying to the OP. I don't really know much about Jewish history so sorry for any inaccuracies. In my point I was mostly talking about the Republican Era (before Caligula and Vespasian) when Crassus (?) first conquered the area. I've heard that at the time, the governors were pretty lenient, up to (and maybe including, depending on your religious sect) Pontius Pilate.
You're 1000% correct however in saying that the Emperors after Tiberius were very bad to the Jews. However, the time before this --- including the time of Jesus, the Romans and the Jews coexisted.
Also, at a few points in his sermons, Jesus mentions that people should accept the rule of the Romans, e.g. Mark 12:17 (King James version):
And Jesus answering said unto them, Render to Caesar the things that are Caesar's, and to God the things that are God's. And they marvelled at him.
Oh yeah for sure. Europe is very unique in this regard, only really sharing it with West Africa. I don't have any definitive reasons why Europe specifically tends towards disunity, but I would say it is mostly culture.
The Frankish Empire got very close to dominating the entirety of the West (I feel like that's close enough), but then Charlemagne died, and it was split into three due to succession laws. Later, the Holy Roman Empire got close again (around the time of Otto II), but castles and the ratio between the ease-of-building and the defensibly prompted further disunity. The very fine balance of power between the Catholic Church, the nobility, the serfs, and burghers also prevented one from gaining too much power (in Rome the nobility and the urban-poor banded together).
Maybe geography played a small part, because there are no large irrigation-based river bodies to control, but there is the Rhine, Danube, and others (I'm not European, so I don't know which rivers require irrigation). Also, there was the Mediterranean, which Rome used.
Sidenote: I just wrote 150 words on ancient history, completely unprovoked.
This is an interesting theory (one I would love to read more about) but this neglects that the vast majority of people in Rome would not have had access to many of these energy sources. About 75-90% of people lived in rural areas, never seeing the famous baths or mud-bricks. Many who would go into the army came from these areas, only every seeing the glory of Rome itself in a preceding triumph. But I think this theory might hold for energy efficiency in agriculture.
Rome went through many different systems throughout its history: first the small-scale farmers, then the Latifundia and slave-estates, then the local patronage system (circa 300AD), and then fully developed manor estates (sort of like medieval feudalism). One could trace the rise and fall of Rome with the changing of these different agricultural systems, so I wonder if later systems scarified efficiency for stability.
On the other hand, I shouldn't mistake correlation for causation, and so it could be that these systems didn't cause the rise and fall of Rome, but were merely a reaction to it.
I agree with you as a whole on the fact that Rome expanding into the Levant helped cause the rise of Christianity, but for the most part, Rome didn't impose polytheism onto the Jews. I'm not familiar with Jewish history, but Rome mostly allowed the Jews to practice their religion; one example is how the Emperors (before Vespasian) sponsored the Second Temple and the practices there.
Secondly, we shouldn't forget survivorship bias. There were many different "cults" all vying for their share of followers (my favourite being Epicureanism and Manicheanism), it just happened to be that Christianity won out in the end. Until the 3rd century, Manicheanism was in the lead, it really was Constantine who allowed Christianity to become dominant.
But in the end, I think this all ties back to Rome. The late Republican era was a deeply agnostic period for Rome, with many outright disbelieving the classical Hellenic religion and the later Imperial Cult (especially after Octavian straight up committed human sacrifice). These cults were responses to the general agnosticism, allowing people to believe in things beyond themselves.
I think another thing that made Alaric successful was that by 410, Rome was not located in Rome. For the most part, the Western Empire was not as rich as the East, and the city of Rome itself was becoming less and less favoured by emperors (especially after the 3rd century crisis). Alaric was able to capture Rome in part because they had lost the culture of warrior-farmers, but also because Rome was like Philadelphia: Once a great city and capital, but now a medium-sized town with no real attractions (except the Pope, but even then, the Patriarchs were more powerful at the time).
Western historians traditionally view the collapse of the Western Roman Empire as a deviation from normalcy. I think about the rise of the Western Roman Empire as the anomaly and its collapse as a return to normalcy.
I don't know if Rome is the anomaly for most civilizations. When looking at Europe, Rome was the only civilization to unify (most of) the continent, while others couldn't --- though many tried. But when looking at human civilizations as a whole, most centres are unified, and then stay so.
For the Middle East, that was the Assyrian and Achaemenid Empires, later being replaced by the Empires of similar sizes. For India, that was Ashoka and the Mauryan Empires, for China it was the Han, for Ethiopia it was Aksum, and so on.
Europe is (mostly) unique in that Rome came, Rome fell, and then no one was ever able to replace it.
I don't necessarily agree with your depiction of the Romans as being "parasitic". Just because they did not produce food, does not mean that they were not valued.
The Romans were interested in math, its just that most of them weren't located in Italia. Just look at the various mathematicians who lived in Alexandria, Athens, or Constantinople, and invented the fields of trigonometry (among others).
Rome had almost completely absorbed Greek culture and academics, to the point where many prominent Romans often read and wrote in Greek. Unless you were Cato the Censor, you almost certainly learned Greek math, its just that if you wanted to practice it full time, you would live in the east (and spoke Greek). Especially after the 4th century, when the focus of the Empire shifted to the East anyways.
Also, the Romans heavily benefited the economy of the Greeks. An interconnected empire meant that Greek goods (such as amphorae, pottery, or other luxury items) could be traded anywhere in the empire, with only the nominal port taxes placed on it by the Empire. Also Rome wasn't militarily occupying the East either, since the entirety of it was governed by the Senate (except Syria, Mesopotamia, and Armenia).