Two more books on my to buy list
Probably even [mumblety-mumble] years ago, ideas were changing among professors of medieval history… 
But they have been changing more rapidly since the 1990s, due to more and more information from primary sources being analysed, and more and more archaeological work being done.
For those who are interested in the complexity and diversity of the middle ages, I’ve made some extracts from the last chapter of Prof. Wickham’s book on Medieval Europe, with his final conclusions:
(Spoilered for length)
[Spoiler]CHAPTER THIRTEEN
Conclusion
What really changed in Europe in the medieval millennium? I listed what I see as the most important single moments of change at the start of Chapter 1, and we have followed them across the whole of this book. Now, however, we need to step back a little, and get a sense of Europe as a whole, with some wider generalisations, ending up with the late medieval world we have been looking at in the last three chapters. One thing which remained constant throughout the middle ages was the importance of the old Roman imperial frontier.
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That was a marker of structural continuities, then, across the agrarian world of the middle ages. But there were plenty of structural changes too. As we saw in Chapters 7 and 11, the population of Europe went through some sharp shifts; after a decrease in the early middle ages, it picked up again around 900, and tripled in size between then and 1300, after which the Black Death halved it again. This had an effect on agricultural production, which, by and large, followed these developments quite closely, the central middle ages being a period of intensification and land clearance, and the late middle ages being a period in which agrarian specialisation became more widespread, as there was a less intense demand for grain as the basic staple for human life. The long boom also produced a commercial complexity, focused on Flanders and northern Italy, which was sufficiently well based that it could survive the Black Death, and indeed increase its geographical range in the later middle ages. Economic activity was much more broadly based at the end of the middle ages than it had been at the beginning, then, and it was beginning to lessen even the long-standing economic differences between north and south.
As to cultural change: the Christianisation of most of Europe, spreading outwards from the ex-Roman provinces to the north and east of the continent in the second quarter of the middle ages in particular, was one major shift, even if, as I argued in Chapter 5, its effects were very regionally diverse. It brought the structures of the church with it, which meant that from the twelfth century onwards there was a single ecclesiastical hierarchy which covered the whole of Latin Europe, although not the more decentralised Orthodox east. Church leaders tried to use that structure to impose consistent patterns of belief, or at least observance, across over half the continent. They failed – Europe never became culturally homogeneous, a point I will come back to – but it is at least significant that they tried. Perhaps more important than this, however, was the slow extension of literate practices across more and more of Europe, and also, from the thirteenth century onwards, to a greater range of social strata: from lay élites to townspeople, then even, occasionally, to a few sectors of the peasant majority.
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If we focus on these sociopolitical changes, in fact, we can see a particularly clear division between the first half of the medieval millennium and the second. The political developments in Latin Europe after the Black Death which we have looked at in the last two chapters had earlier roots, but these went back, above all, to the eleventh century. The eleventh century indeed marked more of a break in the history of medieval western Europe than any century after the fifth, in several crucial respects. Before then, despite the dramatic regionalisation of the post-Roman world, which led to the loss of wealth and power of most rulers and élites (except in part in Francia), the larger early medieval kingdoms, Spain, Francia and Italy, had inherited from the Roman empire a political practice and a sense of a public power which lasted for centuries. This public world led to some very ambitious politics indeed under the Carolingians, when kings, lay aristocrats and clerics worked more tightly together to further political ‘reform’ than in any other period of the middle ages.
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In the west, the political practice of the eleventh century onwards was however very different. We have seen in the last half of this book how it initially depended on three underlying changes. First, the breakdown of Carolingian political structures in much of western Europe, into a network of counties, lordships and local urban and rural communities, in the so-called ‘feudal revolution’, at different moments between 950 and 1100 or so. Second, the reconstruction of political power in the twelfth and thirteenth centuries, which was henceforth, however, set against the cellular network of these partly autonomous communities. Third, the long economic boom of the tenth to thirteenth centuries, just mentioned, which left a Europe with considerable economic prosperity and flexibility, continuing into the later middle ages. The second and third of these, put together, allowed the development of more complex forms of taxation by some rulers, which in their turn allowed for the expansion of new strata of paid officials, who were more often trained, in universities and other schools, institutions by now themselves made possible because a more complex economy could sustain them. Most of these developments can soon be found, in slightly different forms, in the Ottoman empire as well; but there the processes of development were more continuous, after the decentralisation of the period 1200–1400 in south-eastern Europe, for the Ottomans inherited so much from Byzantium – notwithstanding sharp changes, of course, in their religion and political language.
And this brings us back to the late middle ages. By 1350 in the west, legal expertise was sufficiently widely spread that written law could become more visible in localities, a process that would extend literate practices further and further into the different communities of Europe. And after 1350 the steady extension of tax-raising powers itself contributed in much of Europe to the development of communities of taxpayers, whether cities or newly appearing collective kingdom-wide bodies, that is to say parliaments. But a greater access to writing, and a reaction to a growing intrusiveness of central power, themselves contributed to the coherence of local communities, and to their capacity to react against outsiders, whether rival communities, out-groups, or the state. Rulers were thus stronger, but so were the communities of the ruled. In this environment, the need to consent to taxation, and often legislation, created a public sphere which after 1350/1400 was stronger than it had ever been before in the middle ages, except in the high days of Carolingian assembly politics.
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To repeat, however: this apparently Europe-wide politics was not homogeneous. European cultures, it is true, had moved closer together in some ways, as communications, and indeed commerce, linked nearly everywhere, at least at a couple of removes – and that again included the Ottoman world too, and even Muscovy, where Italian architects were building churches and secular buildings in the Moscow Kremlin from the 1470s.1 The fact that Scandinavian kings in their dealings with their parliaments sometimes look as if they are trying to imitate the immensely richer and more powerful kings of France is a sign that some practices did indeed cover almost the whole of Europe. Perhaps only Lithuania and Muscovy at one edge of Europe, and the Irish princes at the other, had by now presuppositions about political action which would have been really unfamiliar to other Europeans. Some form of parliamentary politics was close to universal, at least in Latin Europe, and intellectuals moved about in it everywhere, including to (and from) Poland, Sweden and Scotland. But, once again, this was a far from complete process. The growth of vernaculars, which reintroduced problems of translation, actively impeded it; so did the revival of nationally focused churches in the fifteenth century, and the increasing antagonism between the Ottomans and the Latin polities. We have seen that similarities in political practices covered up major differences in political resources. And other aspects of local society and culture travelled much less well than the patterns of politics.
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But these divergences do not detract from the basic argument of the second half of this book. Which is that the strength of local, cellular, politics, plus the extension of literate practices to ever-wider social groups, plus a continuing high-equilibrium economic system, plus a newly intrusive state, made possible by taxation, communications and, once again, literacy, helped to create political systems across Europe which allowed engagement, nearly everywhere. This marks the last century of the middle ages, not the supposedly late medieval features which mark so many textbooks: crisis, or anxiety, or the Renaissance, or a sense that the continent was, somehow, waiting for the Reformation and European global conquest. And it is one of the main elements that the medieval period handed on to future generations.[/Spoiler]
Huh! You are quite right. The second part of that article is missing. 
I tracked it down:
Ok, I haven’t read on yet, but that explains why the first part ended with such a crucial cliffhanger :D.
Well, in the meantime I have read the rest of the article, and while it expanded on the theory a bit, it still didn’t provide much of alternative explanations. I understand that the classes weren’t as rigidly separated as we’ve learned at school, and that social mobility was looser than we might have thought, but there still had to be some kind of common thread in social relationships across Europe in that time (even if you would just restrict it to, say, the Holy Roman Empire in the 13th century, for example). And the article doesn’t really come up with convincing alternatives.
Yeah, it’s an interesting contrast with evolution. Darwin established that evolution occurred, postulated a mechanism that upon further discussion appeared to have serious flaws, so others (Haeckel in particular) postulated other mechanisms - but no one of note doubted that the phenomenon was real (and of course, once Mendel’s work was rediscovered, Darwin’s mechanism was recognized as being real as well).
Wegener proposed a mechanism (continental drift) to explain the matchup between coastlines of the various continents. This mechanism had obvious flaws and the matchups tended to be dismissed as coincidence. Mid-20th century however, additional evidence (maps of the continental shelves that matched even better than the coastlines, and magnetic reversals), and a better mechanism (plate tectonics) led to relatively quick acceptance of the new theory.
Lessons learned -
Proving that a phenomenon is real and requires explanation is different than establishing that a possible explanation is right. Phenomena that have no known reasonable explanation generally fall into scientists’ “Let’s think about this later” file. A good explanation explains a lot of different phenomena not previously recognized as being related.
Just a note: Theories are not “promoted” to laws. A law is an equation.* A theory is a testable model supported by the preponderance of data. (Except legal “theories”, but I won’t go there.) A hypothesis lacks such support but invites exploration. Theories evolve as more data creeps in. As suggested, acceptance of new models may require “paradigm shifts” i.e. the old-school folks croak and the youngsters [del]muddle[/del] drive on. See Kuhn. Also see a philosophical view of scientific change
- All equations are correct if elements are properly defined. Thus Ohm’s Law: E=IR with known units of electrical potential, current, and resistance. And 1+1=3 for large enough values of 1.
No “probably” about it: it’s incontrovertible that the general concept of a “Pythagorean” triple, including many different specific numerical triples was known to Old-Babylonian scholars nearly 4000 years ago.
It’s highly unlikely that Pythagoras himself (if that somewhat legendary philosopher ever actually existed) made any kind of breakthrough in “coming up with a proof for the general rule”. Some sort of geometric rationale for the general rule was probably widely known for centuries or millennia before him, even if it didn’t have the more rigorous form that it acquired in, e.g., the later Elements of Euclid.
Logical mathematical demonstration isn’t something that a few named early Greek philosophers just suddenly invented out of nothing, even though later Greek historians sometimes described it that way.
OK, what happened when Constantinople fell? More to the point: If the Roman Empire never fell… where is it? I get that this is meant as a joke, more-or-less, but it does lead into my actual point:
There’s a fundamental disconnect here:
Historians are reacting against people who think the Dark Ages meant European Civilization completely fell down and was replaced with Vikings torching picturesque Irish monasteries and everyone living in shit. That’s wrong. That’s very wrong. So historians want to break that idea quickly, and deny the existence of any so-called “Dark Ages” in the strongest terms… even though, yeah, the period preceding 1000 CE wasn’t as nice to the peoples of Western Europe as previous eras might have been, and the Roman Empire lost Rome around that time, and other little things which seem a bit dark to those of us who see cities as a hallmark of civilization.
Now, add a bunch of people who apparently cannot see shades of gray, and watch the historical method burn. Burn like Lindisfarne.
The Pythagorean theorem was known in ancient Mesopotamia, ancient China, ancient India and ancient Egypt. Some of these ancient cultures could also solve quadratic equations, and so on. BUT the idea of theorems rigorously proved from axioms seems to have been an invention unique to classical Greece, beginning with Thales, the Pythagoreans, Hippocrates of Chios, Theaetetus, Euclid, etc. No?
The concept of proving things logically of course emerged gradually over the course of time. But for any individual mathematical theorem, there was still some single individual who first proved it. The guy who first proved what we now call the Pythagorean Theorem might or might not have been the leader of that weird cult, and he might or might not have been named Pythagoras, and it’s quite possible that his true identity has been lost to history. But he was somebody. My guess would be that it was some lower-ranking member of Pythagoras’ cult, but that’s just a guess. And Euclid, the best-known of the classical Greek mathematicians, mostly just compiled the work of others whose names we mostly don’t remember (though he probably had some novel ways of proving things that had already been proven in other ways, and he probably advanced knowledge in some other ways).
In any event, though, special cases of that equation were certainly known before that formal proof, and the general formula may well have been known, so the proof wasn’t completely revolutionary.
I have often wondered about the 3,4,5 triangle. Was it really “known” or just considered an excellent approximation? Was the difference between the two understood?
Evolution was widely believed long before Darwin. His grandfather Erasmus Darwin was a strong advocate. What Charles proposed was natural selection as the mechanism. But he was also aware that under his quite natural assumption of graded inheritance (mate short peas with tall peas and get medium peas) even favorable mutations would take a long time to spread. Mendel showed otherwise and thereby inferred the existence of genes or something like them. After that it was widely accepted (except in Tennessee).
I would expect that Newtonian gravity was accepted almost immediately since it literally explained everything from the elliptical orbits to the falling apple. Anomalies like 43 seconds of arc per century in the perihelion of Mercury came later. In fact I have no idea how to go about measuring the perihelion of Mercury, let along how to measure .43 seconds per year, an incredibly small angle, about .0006 of a degree.
On the other hand, results in math are generally accepted almost immediately. Even the incredibly complicated argument in Wiles’s theorem was fully accepted in under a year, once the original gap had been filled.
That’s my impression. But some exceptions might include non-euclidean geometry and Cantor’s work with infinite cardinalities. And, historically, it took a while before negative numbers (and, later, imaginary numbers) were generally accepted.
Newton developed the equations which described how gravity affects the interaction of objects, and Einstein described in terms of the curvature of space. Even after centuries, we still don’t really know the mechanism by which gravity works.
Actually, the observations of Mercury’s orbit are even more impressive than that. 43 arcseconds per century is not the amount of Mercury’s perihelion precession: The actual number is over twice that. But most of the precession was calculated as being due to the influence of the other planets-- 43 arcseconds per century was just what was left over once that was accounted for. And in fact, people did try to explain it (before Einstein) by assuming the existence of another planet, usually referred to as Vulcan, unobserved because it was too close to the Sun.
I’m not fond of statements like this. Anyone who’s ever conversed with a three-year-old knows that you can always ask “why” of anything, and when you give an answer, it just leads to another “why”. One might fairly say that curved space, as described by Einstein, is the mechanism by which gravity, previously described by Newton, works. It may be that we’ll someday discover something even more fundamental, that we could describe as the mechanism by which mass curves space, but we still won’t be done, because there could still be another mechanism underlying that one, and so on.
I’m not fond of statements like this. Anyone who’s ever conversed with a three-year-old knows that you can always ask “why” of anything, and when you give an answer, it just leads to another “why”. One might fairly say that curved space, as described by Einstein, is the mechanism by which gravity, previously described by Newton, works. It may be that we’ll someday discover something even more fundamental, that we could describe as the mechanism by which mass curves space, but we still won’t be done, because there could still be another mechanism underlying that one, and so on.
Let’s just say that phenomena such as dark matter and dark energy have suggested to some that alternative theories of gravitation are possible. The nature of gravity is not really something that is firmly nailed down.
Isn’t it the other way around - dark matter and dark energy are postulated (in part) because they explain anomalous phenomena while retaining the GR framework. Alternate theories of how gravity works (vice “what gravity is”) were created to find a theory of gravity that didn’t need dark matter/energy.
There have been attempts to explain away the evidence that suggests dark matter by means of differing models for gravity, but none of them work particularly well. And really, the lack of existence of dark matter is itself an unnecessary assumption: There’s no reason there shouldn’t exist fundamental particles without charge (in fact, we already know of some of them; there’s just not enough of the known ones).
Dark energy is different. We have less than no idea of what it would be, and in fact, positing different laws for gravity is exactly mathematically equivalent to positing dark energy. The current consensus is that describing it as a sort of energy is in some sense more elegant, though I’m not at all sure that I agree with that.