I mean, there definitely seems to have been a large decline in population, economic output, political cohesion, urbanization, record keeping, trade, etc., in much of the former Roman world following the fifth/sixth century. I suppose it's a value judgement on whether one considers that a "bad time."
The dark ages also saw a huge disparity in education between the East and the West.
Until the 15th century less than 5 people in Europe could do long division. For comparison, Aryabhatta discovered calculus in 5th century India and Madhava made large contributions in the 13th century (Newton/Leibniz were wrongly credited for similar work many years later).
The way I heard it, Aryabhatta and those who followed discovered some of the ideas behind calculus and a few useful results, but not calculus itself, neither the basic ideas like derivatives and integrals nor the vast conclusions that followed from those.
> Until the 15th century less than 5 people in Europe could do long division.
That’s wildly inaccurate. Arithmetic was very much a subject at several schools with the addition, subtraction, multiplication, and division all being taught. https://en.m.wikipedia.org/wiki/Quadrivium
Long division being difficult in Roman numerals is one of the reasons for the switch.
>That’s wildly inaccurate. Arithmetic was very much a subject at several schools...
I'm talking specifically about "long division" in Europe... and have heard this factoid from multiple mathematicians including Nasim Taleb. So I expect there is a basis for the claim...
Well, especially Taleb's claims are worth it to source check. Especially if they are these really juicy stories (like only 5 people in Europe knowing long division).
He has bit of a habit exaggerating and elaborating on stories for the sake of making tasty reading. There was a story in Black Swan about two hospitals and a simple statistical riddle that he claimed professional statisticians would get wrong. It wasn't even a trick question, most people would get it right. I found this hard to believe but I was still sort of surprised when the source spoke of a much harder statistics question that was surveyed at a psychologists convention, not statisticians. That was the first (and the last) source I checked on him. I'd have checked a few more but I don't have the book any more.
But now I guess I can add this one to the list of examples.
Let’s be clear, if you mean the modern notation, that was was ‘invented’ after the dark ages. So under that definition it’s ~0 people world wide in the dark ages. Excluding independent discovery.
However, if we are talking about the number of people being able to accurately do 1234 / 56 = 22 r 2. That was regularly taught in the Middle Ages with plenty of examples of such calculations being available.
There's an excellent book on the subject called The Fall of Rome and the End of Civilization, by Bryan Ward-Perkins. It includes a detailed overview of the archeological evidence, which shows a very clear and dramatic decline in the economy and living standards -- and some areas of technology -- between circa 350 and 600 in the Western Empire. (And the recovery afterwards took centuries.) The Eastern Empire, interestingly, doesn't show any signs of a similar decline until the 7th Century.
For example, peasant households in Italy at the height of the empire had a wide variety of well-made pottery, some of it originating from production centers hundreds of miles away, along with tiled roofs; after the collapse, the variety and quality of pottery was greatly reduced, and tiled roofs disappear. (Tiled roofs provide better protection against rain, are less flammable, and require less maintenance and rebuilding than wooden shingles or thatch; but they also require large kilns, lots of clay and fuel, and a good transportation network.)
And ice cores from Greenland show extensive metalworking going on in Western Europe (in the form of copper and lead pollution carried through the air) during the Roman Empire; after the collapse of the Western Empire, the pollution levels don't return to Roman-era values until the 16th Century.
Another source, in addition to the one cited by Keysh, is Social Development by Ian Morris which goes into some more depth on the data he used in Why the West Rules--for Now.
Well, someone has a bone to pick with the early Middle Ages. What an angry rant to prove that the dark ages really existed. He sometimes has a point but in total it really is a non-historian making some weird arguments to prove that 800AD was terrible (look at the difference in these maps! Just completely ignore any cultural and artistic context that matter why they look the way they do!). I’m surprised he didn’t compare Greek statues with medieval paintings to prove his point.
