A couple of times in the last few weeks, my wife and I have been settling down to a DVD with the children tucked into bed, when our five-year-old daughter has come down in some distress. Thinking about her late great grandfathers (whom she has never met although she does know one surviving great grandmother), she had become very upset at the prospect of eternal death. I suspect all children have to face this at some point and as Christians, there are good and honest answers we can give to reassure her.
Discussing this after our daughter was peacefully asleep, my wife and I began to wonder what atheist parents do in these circumstances. As chance would have it, I got an email this week from someone who thought I was too hard on Richard Dawkins in my review of The God Delusion. In the review, I mentioned a friend who had had similar existential crises as a child and took them to her atheist father. He just admitted that we are ultimately all worm food. As you can imagine, this did little to assuage my friend’s fears and I doubt it would have made my daughter any happier either.
My correspondent said my friend’s father was a moron (although he is actually a university professor) and that, “Dawkins says life is about enjoying every moment and living life in a happy and fulfilling way. Isn't that good enough? Why does there need to be more?” Clearly this answer wouldn’t satisfy my daughter. If someone is afraid of death, it is rather pointless telling them just to enjoy life.
So, it seems to me that atheist parents can either tell their children, in the kindest way possible, that their fears are wholly justified and they just have to tough it out. Or they can lie. Neither prospect can be very appealing.
This is hardly an argument against atheism or even a criticism of it. Rather the reverse. We tend to think of modern atheism as philosophically and morally rather vapid, but sometimes it can be tough.
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Sunday, March 13, 2011
Saturday, March 12, 2011
Linkagery
Keith Burgess-Jackson, an atheist, has recently linked to three interesting essays. The first is "Engaging Today’s Militant Atheist Arguments" by Ian Hutchinson; the second is "Believe It or Not" by David Bentley Hart; and the third is "David Brooks’s Theory of Human Nature" by Thomas Nagel. Burgess-Jackson's comments on the latter are here. Have at it.
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Discuss this post at the Quodlibeta Forum
Monday, March 07, 2011
The Genesis of Science available now from Amazon.com
The Genesis of Science: How the Christian Middle Ages Launched the Scientific Revolution is already available from Amazon a couple of weeks ahead of the official publication date.
This is the US edition of God's Philosophers, edited for American readers and with a few corrections.
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This is the US edition of God's Philosophers, edited for American readers and with a few corrections.
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Wednesday, February 23, 2011
Calling all Pinker fans
I'm one and as I've been explicit about it, this is now mutual knowledge.
The Royal Society of the Arts have a fun Pinker video. Ten minutes, well spent.
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The Royal Society of the Arts have a fun Pinker video. Ten minutes, well spent.
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Friday, February 18, 2011
Is ancient philosophy ancient history?
Responding to an argument that ancient Greek philosophy is not long for this world, philosopher John Pepple has a slightly more upbeat take on the issue. Interesting and well worth the read.
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Discuss this post at the Quodlibeta Forum
Wednesday, February 16, 2011
Martin Gaskell v University of Kentucky
I have an article today on Comment is Free at the Guardian on the strange case of Martin Gaskell, a devout Christian, who was rejected for an astronomy post at the University of Kentucky. The reasons for his rejection appear to have been based on his religion and he won $125,000 in an out-of-court settlement as a result.
Many of new atheist persuasion seem to feel rather let down by the University settling the case. The comments on my piece give an indication of the diversity of opinion on this matter.
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Many of new atheist persuasion seem to feel rather let down by the University settling the case. The comments on my piece give an indication of the diversity of opinion on this matter.
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Sunday, February 13, 2011
News on the Serapeum
OK, it's not exactly hot off the press, but an article in the Journal of Roman Studies 94 (2004) 73 - 121, Reconstructing the Serapeum in Alexandria from Archaeological Evidence by Judith McKenzie et al, is certainly of interest to Alexandrian Library watchers.
As we know, the persistent story that Christians destroyed the Great Library of Alexandria comes from Edward Gibbon's Decline and Fall of the Roman Empire. He mistakenly assumed that there was a library in the Serapeum when it was destroyed by a Christian mob in 391AD. There was once a library there, but it had disappeared before the mob arrived, so it is not mentioned in any of the various accounts of the destruction.
The earliest mention of the Serapeum library is a comment by Tertullian in 197AD (chapter 18 of his Apology) that the copies of the Septuagint can be found there. It is often assumed that this library had been founded by Ptolemy II in the third century BC but this is not explicitly stated in any source until after 1000AD. So, what light can the archaeology of the Serapeum shed on the question?
The first point to note is that two temples were built on the site. The first was constructed by Ptolemy III and is securely dated to his reign by dedicatory inscriptions. This burnt down in 181AD in what seems to have been an accidental fire. The new Roman foundation was much larger and was complete by 217AD. To me, it looks likely that the library dates from this period and was a new addition to the rebuilt and expanded temple. We know from later literary sources that it was not housed in the inner temple, but in the colonnades that surrounded it.
Under the temple, passages have been found that contain niches. It has been romantically suggested that these niches might once have been used to store scrolls from the library, most recently by Richard Miles in his, otherwise excellent, TV show Ancient Worlds. In fact, these niches appear to be part of a mausoleum, perhaps for mummified animals. In other locations, similar niches have been found to contain animal bones.
Of the destruction of the Serapeum in 391AD, archaeology confirms that it was only the temple within the precinct that was razed. The great colonnade remained standing for another 700 years before it was dismantled by Saladin to prove masonry to defend the city from crusaders. Thus, while the archaeology does not tell us what actually happened to the library, it does nothing to contradict the conclusion that it was not destroyed in 391AD as Edward Gibbon had supposed.
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As we know, the persistent story that Christians destroyed the Great Library of Alexandria comes from Edward Gibbon's Decline and Fall of the Roman Empire. He mistakenly assumed that there was a library in the Serapeum when it was destroyed by a Christian mob in 391AD. There was once a library there, but it had disappeared before the mob arrived, so it is not mentioned in any of the various accounts of the destruction.
The earliest mention of the Serapeum library is a comment by Tertullian in 197AD (chapter 18 of his Apology) that the copies of the Septuagint can be found there. It is often assumed that this library had been founded by Ptolemy II in the third century BC but this is not explicitly stated in any source until after 1000AD. So, what light can the archaeology of the Serapeum shed on the question?
The first point to note is that two temples were built on the site. The first was constructed by Ptolemy III and is securely dated to his reign by dedicatory inscriptions. This burnt down in 181AD in what seems to have been an accidental fire. The new Roman foundation was much larger and was complete by 217AD. To me, it looks likely that the library dates from this period and was a new addition to the rebuilt and expanded temple. We know from later literary sources that it was not housed in the inner temple, but in the colonnades that surrounded it.
Under the temple, passages have been found that contain niches. It has been romantically suggested that these niches might once have been used to store scrolls from the library, most recently by Richard Miles in his, otherwise excellent, TV show Ancient Worlds. In fact, these niches appear to be part of a mausoleum, perhaps for mummified animals. In other locations, similar niches have been found to contain animal bones.
Of the destruction of the Serapeum in 391AD, archaeology confirms that it was only the temple within the precinct that was razed. The great colonnade remained standing for another 700 years before it was dismantled by Saladin to prove masonry to defend the city from crusaders. Thus, while the archaeology does not tell us what actually happened to the library, it does nothing to contradict the conclusion that it was not destroyed in 391AD as Edward Gibbon had supposed.
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Saturday, February 12, 2011
History of Vaccines
A new (to me at least) website is The History of Vaccines (via Glenn Reynolds). They have an article on the history of anti-vaccination movements and I am delighted to say they do not repeat the canard that Pope Leo XII banned vaccines, something Humphrey thoroughly debunked. However, they do make the more plausible claim that "Some objectors, including the local clergy, believed that the [smallpox] vaccine was “unchristian” because it came from an animal", and they reference the following article in support:
Now I'm in the final throes of my PhD and so don't have the time to follow-up on this reference. If anyone else does, I'd be fascinated to hear the evidence that Durbach offers. I should point out that I'm not particularly skeptical that this happened, since one can find "local clergy" who advocate just about any position. It seems odd, however, since 1) the New Testament specifically states that no animal is "unclean"; and 2) the smallpox vaccine came from cowpox, which in turn came from ... wait for it ... cows. Cows are considered "clean" animals in the Old Testament. So it's difficult to see how the smallpox vaccine could be considered "unchristian" or even "unjewish".
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Durbach N. "They might as well brand us: Working class resistance to compulsory vaccination in Victorian England." The Society for the Social History of Medicine. 2000; 13:45-62.
Now I'm in the final throes of my PhD and so don't have the time to follow-up on this reference. If anyone else does, I'd be fascinated to hear the evidence that Durbach offers. I should point out that I'm not particularly skeptical that this happened, since one can find "local clergy" who advocate just about any position. It seems odd, however, since 1) the New Testament specifically states that no animal is "unclean"; and 2) the smallpox vaccine came from cowpox, which in turn came from ... wait for it ... cows. Cows are considered "clean" animals in the Old Testament. So it's difficult to see how the smallpox vaccine could be considered "unchristian" or even "unjewish".
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Friday, February 11, 2011
Ernan McMullin
Readers will be saddened to hear of the death of Professor Ernan McMullin last weekend. I met him only once, at Cambridge last year, where he roundly criticised the continuity thesis (against the scientific revolution) I had put forward at the conference we were both speaking at. His work on Galileo is of the first importance and he was a lovely man even when he disagreed with you.
Michael Ruse has written an appreciation which is well worth a look.
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Michael Ruse has written an appreciation which is well worth a look.
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Thursday, February 10, 2011
Richard Carrier and the Domesday Watermills
Richard Carrier is without doubt a courageous and relentlessly revisionist historian and his ideas are often interesting and provocative. Back in 2002 he argued in Free-thought Today that Adolf Hitler was ‘unmistakably a God fearing Christian’ [1] . Elsewhere he has claimed that the Ancient Greeks were on the brink of a scientific revolution before the 3rd century crisis erupted and that medieval intellectual culture achieved nothing of note in Science until the revival of pagan ‘scientific values’ during the Renaissance. His forthcoming book will argue that Jesus probably never existed based on the application of Bayesian probability theory to history [2].Now Richard has looked at the evidence for widespread watermills in Domesday England and concluded that the claims made by historians are factually dubious.
Scholars of the Domesday book have claimed that all the mills listed within it’s pages (as 'molendinum' or 'molendini' or sometimes just 'mol') are all watermills and that there were something in the region of between 5,624 (Margaret Hodgen’s ‘Domesday Water Mills’ Antiquity 13 1939, p. 261-79) and 6,082 of them (H.C Darby’s ‘Domesday England’, p. 361).
By contrast Richard Carrier writes:
'Though this claim is repeated often, I’ve actually read the Domesday Book, and the scholarship on it: not a single watermill is ever mentioned in it. Scholars who study the book concede this. Only one word is used for “mill” and it is used of all mills of whatever type, including hand and donkey mills. Those “5,624” mills are thus not all watermills. We don’t in fact know what proportion of them actually are. The assumption is often made that when a mill’s tax is paid in eels, this indicates a watermill (as eels could be captured in its race), by which logic the number of watermills is claimed to have been close to 5,000, but since taxes are paid in eels even in towns without any mills at all, that assumption is clearly wrong. Eels just indicate a nearby stream or river. The mere fact of a nearby stream or river does not entail any of the local mills used that stream or river, much less that all of them did.'
'This is yet another example of how Christian apologists not only love to boost medieval Christianity with logical fallacies, but also by not checking the facts (even when they are suspicious: a watermill for every fifty families in 1086 AD England ought to have been downright suspicious), and instead just believing anything you read that makes medieval Christians sound clever .' [3] [4]
'See Finn's "guide" to the DB, pp. 60-61, describing their flawed methodology, although Finn simply trusts it, not noticing the fallacy it entails; in his earlier "introduction" to the DB, however, Finn concedes the data is flawed for these kinds of counts on pp. 187-90, but he doesn't realize what this entails; e.g. p. 188, a single hamlet, population 52, had "nine mills" of a total value of a single pound; these are counted as watermills by the Darby criterion, but clearly that is massively absurd, as they could not possibly have been anything of the kind; indeed, they are unlikely to have been anything more than hand mills. Similarly, Finn says Darby counts "winter mills" on the presumption that intermittent mills must be watermills, but that makes little sense: water would be low in winter, not high, so a watermill would only operate on a seasonal waterway in spring or summer, not winter; winter mills thus are more likely ordinary mills put into operation during the winter months because they were near grain storage facilities which would be left dormant during harvest seasons where grain could be ground closer to market, and the storehouses were being filled, not emptied.'
In a similar vein he writes:
Most taxed mills would have been donkey, ox, or man driven, not hand mills (or watermills). In other words, most mills had long been capstan mills (since Roman times at least). This is basic economic history. Saying no one in England had a capstan mill is like saying no one in America owns a truck.
Donkeys weren't taxed so far as I know (and if they were, they would not be taxed separately by job), and if driven by oxen (or horses) they would come from the standing stock of the manor, not singled out. So unless a manor has zero oxen and horses in its entire holdings, you can't reference which animals would have been doing which jobs (much less when) just from tax filings, and even if there were no oxen or horses, there would be donkeys, and of course a capstan mill can be and often was driven by people.
Indeed, the undeniable widespread fact of capstan mills guarantees that they aren't being distinguished in the tax documents. As if the entire continent somehow forgot the existence of the most common bulk milling machine ever invented and had no capstan mills anywhere! That's why the numbers cannot refer to watermills, but to bulk millstones (period), regardless of motive source. So we have no reliable measure of how many watermills there were (and there definitely were not that many--because most of those numbers had to be capstan mills)…. And it is a scandal that these numbers for "mola" (millstones) are constantly being conflated as numbers of "watermills." This really needs to stop.
Why does any of this matter ?. Well if Carrier is right then numerous scholars – including the likes of Lynn White Jr, Reginald Lennard and W H G Armitage have cited an erroneous figure, one which has been used to justify the thesis that watermills were widespread throughout Anglo-Saxon England and that this represented a ‘far reaching cultural and technological change’.
Accordingly I got in contact via email with three of the leading experts on Ancient and Medieval milling; John Langdon, Professor in the Faculty of history and Classics at the University of Alberta and author of ‘Mills in the Medieval Economy 1300-1540’; Dr Adam Lucas of the Science and Technology Studies program at the University of Wollongong and author of ‘Wind Water, Work – ancient and Medieval Milling Technology’; and Richard Holt, Professor of History at the University of Tromso in Norway and author of ‘The Mills of Medieval England’. All of these cite the figure of 6,000 watermills in their writings on the subject and I decided to present them with Richard’s argument to see whether they would stand by their use of the figure and whether there would be any revision of the field.
I think it’s fair to say that their reaction was pretty negative……
To explain why will require adding a lengthy treatment to an already lengthy post but bear with me. On one point I agree with Richard. In 'Industrial Milling in the Ancient and Medieval Worlds' Adam Lucas argued convincingly that the Classical era was more advanced in terms of the use of waterpower than previously thought and that this technology was widespread. It also points to Chinese innovations (watermilling was commonplace in China from the 10th century onwards) and milling in the Islamic world to argue against some of the stronger claims for Medieval exceptionalism that have been made (e.g Bloch – ‘Triumph and advent of the Watermill’). All the important innovations in industrial milling originated in earlier Islamic civilizations, ancient China and the Roman Empire. This would make it all the more surprising if there weren't similar developments in Anglo-Saxon England
Let’s look at the reasons for believing that all the mills mentioned in the Domesday Book are Watermills and not animal mills, windmills or hand mills as has been argued.
1) Geographical Spread

As the map on the right from Margaret Hodgson's article shows, the distribution of mills mentioned in the Domesday Book clearly follow water resources – not only that but they cluster on the tributaries of the three main waterways and in particular the smaller, shorter streams fringing the coastline of England. There are a few exceptional cases where the mills exist in places that are now un-watered but this has been identified as being due to the drying up of formally water filled valleys due to changes in rainfall [5]
The mills do not correspond to the more or less urban conglomerations of 11th century population as one might expect if they were animal mills for reasons I will explain shortly. Instead they are located in smaller rural communities and the headwaters of smaller watercourses. This becomes much clearer if you look at the regional surveys which were conducted by the historian H. C Darby and his team.
To take one example the map on the left shows the Domesday Mills in the county of Somerset – (this is from The Domesday Georgaphy of South West England). The mills are quite clearly associated with the rivers, and they are especially frequent along those rivers which flow through extensive areas of arable land, the Tone and tributaries, the Chew, the Frome, the Brue, the Parrett, the Isle etc etc.. Exactly what you would expect if they were watermills. The other regional surveys reach the same conclusions (for example the East Riding of Yorkshire in 'The Domesday Geography of Northern England)2) Californication – What are the Winter Mills ?
When referring to the winter mills that appear to operate intermittently, Carrier writes ‘water [in England] would be low in winter, not high, so a watermill would only operate on a seasonal waterway in spring or summer, not winter’.
Unfortunately here, Carrier is projecting the Californian climate onto England. As anyone who hails from the UK knows the winters are usually cool, wet and windy and miserable with plentiful precipitation – so much so that flooding is quite frequent. This is certainly the case today and would have been the case in the 11th century.
By contrast, in California, heavy snows accumulate in the Sierra Nevada which create an annual reserve of water – this is then released in the spring and summer adding meltwater to the rain fed streamflow. To be fair – according to Richard Holt, Carrier is far from the first American to think Anglo-Saxon England had an identical climate to the United States. Another historian – Kealey argued that the streams in England would have been frozen in winter and therefore some of the alleged watermills were really windmills (he was from New England – the arctic wilderness I currently live in) It seems likely therefore that HC Darby was right and that the intermittent mills are in fact watermills that can only work when winter arrives and there is enough water in streams.3) H.C Darby’s Eel Tax
Carrier writes of HC Darby’s method -' The assumption is often made that when a mill’s tax is paid in eels, this indicates a watermill (as eels could be captured in its race), by which logic the number of watermills is claimed to have been close to 5,000, but since taxes are paid in eels even in towns without any mills at all, that assumption is clearly wrong. Eels just indicate a nearby stream or river.
As John Langdon has pointed out, here Richard Carrier misrepresents Darby’s method. ‘In truth Darby only noted that many of the ‘mills’ (molendina or molina) had their valuations sometimes expressed in numbers of eels (e.g., Domesday England, p. 270)'. Actually – as we saw in the ‘geographical spread’ section H C Darby spent much of his career with his team authoring multiple volumes of regional Domesday surveys. These specifically note where mills do not pay renders of eels – some render honey, salt, malt rye and grain.
Is a partial rent of eels evidence for a watermill? Not conclusive but I think an objective observer would have to agree it’s pretty good evidence – especially when viewed as part of a cumulative case. Another guide for example is that the value of many of the mills given in the Domesday Book are high, showing them as obviously powerful.
4) Lack of evidence for Animal Mills
As Richard Holt pointed out in his response to my email, ‘we have no reference to animal mills before the 12th century (and just one possible example of archaeological evidence at Cheddar)’. By contrast we have lots of evidence to watermills from the 8th century onwards. According to H C Darby (Domesday England p270) ‘the earliest reference to a water-mill in England comes from a document referring to Chart in Kent and dating from 762. References to watermills becomes relatively numerous after about 800 or so’.
Holt also pointed to later evidence saying that:
‘Manorial records are starting up in the 1120s, actually (Peterborough, Burton), and then it's a cascade after 1200. All the evidence then is for watermills (plus the new windmills after c.1185). Where one does comparisons with Domesday (I did it for Peterborough, Glastonbury, Ramsey, Ely, etc.) there is a clear correlation with DB - i.e., the watermills of 1125 /1189 /1221 etc. (proved to be watermills by contemporary accounts that detail repairs to water systems, etc) are in the same numbers on the same manors etc. as in 1086. One can trace an estate's mills through from 1086 to the 14th /15th century in lots of cases. Oh, and the manorial accounts, even the earliest, detail repairs to existing water systems and mills, not to new ones. So one can push the estate documentation back even further. But they DON'T detail work on animal mills, or mention rents from them'.
Related to this point, later evidence relating to milling in England comes from the hundred rolls of the late 1270s and (as noted above) from detailed estate surveys. Using this evidence Richard Holt in ‘The Mills of Medieval England’ and - focusing on the West Midlands - John Langdon in his article ‘Watermills and Windmills in the West Midlands’, used this data to calculate the number of watermills around 1300 as around 15,000. If the Domesday figure from 200 years earlier is wrong then this estimate looks decidedly odd.
Why would animal mills not be as prevalent as watermills in our sources? Holt suggests that perhaps one reason is the watermills – especially of the horizontal variety are:‘relatively easy to build and operate. All European cultures build them in preference to animal mills which need an expensive animal - one finds animal mills in the context of castles, large noble households, urban bakers and brewers, etc. - all exceptions, all situations where people want effective milling right on the spot, and are willing to pay the cost of that.'
This is similar to what John Langdon states in ‘Mills in the Medieval Economy’ p125. According to him animal mills were useful for Lords in urban situations particularly when water power was not accessible. As Langdon argues on page 24 they are underrepresented in – for example manorial records – as they were more often attached to peasant holdings or subsumed in particular industries such as brewing. They were capable of filling a gap in milling in towns and cities where sources of energy were very stretched. This being the case, if they were the mills shown in the Domesday book we would expect them to be located in urban areas.......which, as we saw earlier, they aren’t.
5) What about hand mills and windmills?
Other culprits for the mills mentioned in the Domesday Book include hand-mills and watermills. The population of England at the time of the Domesday book is approximated at roughly 1,400,000 people in Hodgson’s article (She cites H de B Gibbins – Industry in England (1920). A handmill looks like this (see the pic on the right)Assuming the figure given by Hodgson hasn’t been revised by later research 6,000 handmills in a population of 1.4 million is quite clearly laughably low.
Furthermore according to John Langdon in ‘Mills in the Medieval Economy’ (p24) handmills were not usually included at all in most records ‘since they were not considered to be sufficiently important to act as commercial enterprises, as watermills, windmills and (occasionally) horse-mills were’. However, despite being overshadowed Langdon speculates that they may have accounted for as much as 20% of grain milled in 1300.
Nevertheless recall that Richard Carrier argued that the nine mills found in a single hamlet were 'unlikely to have been anything more than hand mills'. It seems strange that the Domesday surveyors would have bothered to document nine hand mills of negligible tax value - not impossible but decidedly unlikely. However an Anglo-Saxon pound was worth 20 shillings meaning the 9 mills had an average value of 2.22 shillings. About right for a small watermill but pretty high for a hand mill given that 2.2 shillings would have been equal to 26.4 pennies (a penny could buy you a quarter of a sheep’s carcass in 1130 (see Robin Fleming, Britain After Rome (2010), Allen Lane, p310 - H/T Mr Tolkein)
Windmills specifically driven by wind first appear in Europe in documents dating from the 1180s. According to Darby (Domesday England p270) ‘the first mention of a windmill does not appear until 1191 in a document relating to the Abbey of Bury St Edmunds’. So it is safe to say the mills in Domesday are not Windmills either.
Final Count
While John Langdon categorically rejected Carrier’s insights, he did agree that the area could do with some rethinking. For example ‘multiple mills on a manor may have been referring to sets of millstones on a manor rather than to separate water mill sites - that is, a single mill site on a river might have operated two or more sets of millstones’. This means that the final count is something of a conjecture. Nethertheless Langdon thinks that Darby’s estimate of 6,082 watermills is the more authoritative yet especially when you consider that many mills to the far north were not reported in the Domesday survey.
Overall the experts I consulted concluded that – whilst the evidence isn’t conclusive – you can safely say beyond reasonable doubt that the Domesday mills are in fact watermills. If Carrier wants to argue against decades of scholarship and dozens of historians and archaeologists then he needs to bring more to the table.
For my part there is something humorous about the Anglo-Saxon England Carrier has concocted – one in which toothless, god fearing peasants run expensive and underpowered capstan mills for their milling while standing mere yards away from abundant fast flowing rivers. Must have been quite the ‘doh’ moment when they finally figured it out.
[1] Though Goebbels oddly seems to have mistaken it, - writing in his diary ‘the Fuhrer is deeply religious but entirely anti-Christian. He regards Christianity as a symptom of decay. Rightly so. It is a branch of the Jewish race.' December 28, 1939
[2] His skepticism arises from the fact that 'P(H/B) = as low as .51 or as high as 0.70 P(~H/B) = as high as 0.49 or as low as 0.30 P(E/H&B) = as low as 0.20 (model A) or as high as 0.80 (model B) P(E/~H&B) = as low as either 0.15 or 0.19 (on model A) or as high as either 0.70 or 0.79 (on model B) [Note that for those unfamiliar with Bayes, P(H/B) and P(~H/B) must always sum to 1, but P(E/H&B) and P(E/~H&B) do not have to sum to 1] P(H/E&B) = P(H/B) x P(E/H&B) / [P(H/B) x P(E/H&B)] + [P(~H/B) x P(E/~H&B)] Therefore, best case scenario for ~H: P(H/E&B) = 0.51 x 0.20 / (0.51 x 0.20) + (0.49 x 0.19) = 0.102 / 0.102 + 0.0931 = 0.102 / 0.1951 = 0.523 (rounding up) That would constitute mythicism being slightly more likely than historicism'.
[3] On this point – Archeologists could find a combined blast furnace / astrolabe with dual steam turbines and heat seeking crossbows which had originated in Medieval England and it still wouldn't have any bearing on the truth or falsity of Christianity as far as I can see.
[4] 6,000 mills divided among an estimated 1,400,000 comes out at 1 mill per every 233 persons. This isn't particularly unlikely given that many would have been pretty simple, consisting of a wheel laying horizontally in the water. This would have turned on a shaft fixed to a stone in the bed of a river. The upper end of the shaft would then have passed through the lower end of two quern like grinding stones and the mill wheel, the shaft and the upper stone turned together. The whole structure would have been extremely small and adapted for use on a minor stream or rivulet.
[5] According to Hodgson this study is - G M Myer – Early Water Mills in relation to changes in rainfall in east Kent – Quaterley Journal of the Royal Meterological Association (1927 LIII 407-19)
References
Margaret Hodgen’s ‘Domesday Water Mills’ Antiquity 13 1939
John Langdon - ‘Mills in the Medieval Economy 1300-1540’
John Langdon - ‘Watermills and Windmills in the West Midlands’
Adam Lucas - Industrial Milling in the Ancient and Medieval Worlds: A Survey of the Evidence for an Industrial Revolution in Medieval Europe
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