What technologies were lost when rome fell?

No, Not really and somewhat.

The trade uses changed involving bigger loads (at the point where Gaul merchant used camels) with less dense flux. I council everyone to read Henri Pirenne works about high-medieval trade.

The commerce, including international one, was still going and not at all loss. Even the Muslim closure of Mediterranea never severed totally the western-easter trade (more the western-byzantine trade, and only for a moment).

And for Northern Europe, actually these regions were opened for the first time to a more dense international travel : Saxe, Frisia, Bavaria, etc became connected to Mediterranean trade like never they were before.
So not only trade significantly lowered during the high middle ages after Roman Empire fall, but region benefited of it for their trade dynamics.

For the urban civilisation...Yes and no. Yes, the cities knew a real decline during the first centuries in some lands that were often the less romanized anyway. (But in mediterranean Gaul, in Italy and Hispania, city kept a major role).
The saracenic, norman and hungrese raid helped paradoxally to separe the viable cities from the ones they're not (mainly created by roman for their own purposes). But the remaining knew a flourishing era since the XI.

And actually, the city role never really disappered. In southern France, it was not really about the demographical importance, but its political : you have towns of 2000 inhabitants that were considered as cities with their own leaders.

A city like Tolosa was considered as a republic by the contemporaries.

I was referring to soon after the collapse, not the High Middle Ages.
 
I was referring to soon after the collapse , not the High Middle Ages.

Well, which collapse? The problem is that the Roman Empire never really collapsed as Napoleonian Empire or Qing China, but withdraw little by little at the point to be limited to Italy only in facts and by giving the locals leaders (roman or barbarian) a control of institutions that they have interest in keeping.

The "barbarian" sucessors believed then to be the sucessors of Rome and maintained what they can of roman empire, even it was not adapted.

If by collapse you mean the entiere process, i stay on my opinion : we have no trace of a disappearing international trade but at the contrary proofs that he was kept on a different form admitedly.

And for the urban civilization, except the less romanized (or not romanized at all) places as you pointed, it was kept. As during the roman empire, the first patria wasn't the empire but the city.
If you mean that the cities were more isolated one from each other, it's something that existed during the High Empire.

I mean, 476 meant nothing for demographic and commercial purpose, the sack of Rome means a little, and the VII crisis meant a lot for this features.

In fact the only very important demographical and institutional change of the Late Antiquity not due to the withdraw of mediterranean culture and plague i can think of (there's probably some others, but this one is important as hell) is the Gothic wars between Ostrogoths and Byzantines.

As during the visigothic civil war, agricultural features ceseasd to be correctly maintained, italo-roman elite was killed by both sides, somes cities were taken by both many times, and 20 years of continual warfare. It most probably achieved to make Rome a secondary city, to weaken Italy and Byzance in the same move.
But it's not really the Western Roman Empire collapse.
 
The medieval Northwestern European tradition of the bathhouse (heated water in tubs, commercial operations, medical and/or personal services on offer) is a very different thing from the roman baths, and separated from them in most of the areas it existed by at the very least 500 years. That is about as far back as the Aztec Empire. I find it very diffilut to argue continuity, especially since that's obviously not necessary (we have continiuty in the Mediterranean, even with some bath complexes remaining in use).
 
The medieval Northwestern European tradition of the bathhouse (heated water in tubs, commercial operations, medical and/or personal services on offer) is a very different thing from the roman baths, and separated from them in most of the areas it existed by at the very least 500 years. That is about as far back as the Aztec Empire. I find it very diffilut to argue continuity, especially since that's obviously not necessary (we have continiuty in the Mediterranean, even with some bath complexes remaining in use).

Well, the use of many roman baths as etuves, the fact that roman baths have too medical and personal services on offer (plus the fact that the medieval name for heat baths was caldarium) all of that contribue to make the medieval etuves the heir of roman baths.

Of course, it was the bastard child of these and north-western bathouse. But it's not deniying anything regard of the legacy of Rome. It can be traced, and when Charlemagne takes a bath at Aachen, he takes one "roman way".

Furthermore, the commercial aspect of etuves compared to thermae is explained by the fact thermae were a public or semi-public building : it was an instrument of power and fame for the one who financed it. In middle-ages, with the dissaperence of imperial elite and the ambigous reputation of such places such public financment disapperead opening such the way to private initiatives.

For the argumentation, i don't know where you find a difficulty : yes different cultures have baths, such as Aztecs. But the existence of etuves is directly from roman baths with an influence from germano-celtics uses and probably arab and christian maintenance and creation of iberic baths.

A bath like the one of Girona is clearly showing roman legacy.

Now if you want the discussion to end here as we acknowledging that we're disagreeing, it's fine.
 
For western Europe, both Andalucian baths and Christian etuves (i don't know the word in english)

Englishmen of the time called them the "stews," which, if I don't misremember, was a corruption of "etuves." They were closely associated with prostitution, which is another reason the church didn't care for them.
 
Mass Production: making that much bronze and leather to equip hundreds of thousands of troops (who wear stuff out, break it, lose it) for armor, shields, pilums, javelins, gladiuses, arrowheads, ballistae, scorpions, etc. is the only way you get it done. The creation of a Roman war fleet by duplicating a single Carthaginian galley is a very significant application of the principles. Setting up jigs and gauges for standardized, fast production as well as investment casting, the heat-treating processes (some of this has surely been lost along with some alloy formulas for what they were able to do with copper as well as bronze and iron)...it's very easy stuff to lose just with transitions (we call it trade secrets/process know-how in manufacturing and it matters a lot.) I think industrial engineering practices of the Romans were both boring and out of sight for the writers still studied from the period, much like few writers discuss it now.

Jack Whyte's novels refer to a level of medical and surgical knowledge at least among Roman Army medical officers that was at least at early 20th Century U.S./European knowledge (circulation of the blood, functions of most organs, opiate anesthetics, sanitation, etc.), narrowly known by specialists so easy to lose in the breakdown of the training pipeline.

Roman civil engineering in water and wastewater systems, flushing toilets, port facilities like Caesaerea's, the capacities of the Colosseum to host ship battles (ask your local public arena manager about booking that event today), and the Roman roads and bridges...all of this stuff is really useful for nearly any sized community but most of it gradually fades from first new construction and then from maintenance despite it's utility and critical nature. Seems like lost knowledge to me and lost engineering knowledge and project management skills are common (we couldn't build Hoover Dam in 5 years now, much less Oak Ridge's 400 buildings in a year, or the Saturn 5 Rocket Boosters of the 1960's and those are all in a society where supposedly all knowledge survives and can be found on the Internet!)

Chris Wickham's new book on the much slower decay of Rome is fascinating. The earlier book by two English archeologists, "Ancient Inventions" is fascinating too and makes a compelling case for all sorts of what you're looking for.
 
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