The first paper called Jakob Grimm's assertion that Germanic speakers reckoned in twelves "a myth." Yes, Germanic languages often have special words for eleven and twelve that are formed differently from words for thirteen and beyond. Yes, we have special concepts like the Long Hundred (120 of something), the dozen, the score, and the gross. Many of these, the author sniffs, were late creations referring to trade (i.e., how things were packaged). But all available evidence shows that Germanic speakers always counted in tens.
Ah, but counting is one thing; reckoning is another. I don't doubt that ancient Germanic speakers always counted in tens. But though they were smart people, they didn't know any higher math. And they probably hadn't yet gotten used to the idea of talking about numbers as "real" things. If you asked a speaker of Proto-Germanic, "how much is one and one?" he might very well have replied, "one and one what?"
For if you are manipulating things rather than mental concepts, grouping things in twelves is easier for sharing them out than grouping them in ten. If you have ten apples or ten coins or ten cows, you can only divide them evenly between two people or five people. But if you have twelve of something, you can divide them evenly among two people, three people, four people, or six people. Consider a similar problem: dividing something circular, like a pie. Dividing a pie into more or less equal wedges of halves, thirds, fourths, sixths, eighths, or twelfths is easy; you can just eyeball it. Dividing a pie equally into fifths or tenths is a complex geometrical problem.
For very large numbers, the score is the natural way of grouping things. You can count to twenty in your head, but beyond that, you risk losing count, and starting over is not something you want to do. So you count twenty sheep or twenty barrels or twenty bundles and then scratch a mark -- a score, literally -- on a piece of wood. Every fifth score is crossed in our familiar "five-barred gate" tally mark pattern. Five scores is a hundred.
This isn't really math, it's proto-math. It's mostly sorting and sharing and handling large quantities of stuff. So while I agree with the author that the Germanic speakers always counted in tens, I kind of think he missed the point.
The other treatise claims that Middle English -- of which Modern English is the natural continuation -- was descended not from Old English (a West Germanic speech), but Old Norse (a North Germanic speech). Briefly, the argument is that in the Danelaw, Norse and Old English fused into a new language (nobody much disputes this) based upon Norse morphology and syntax, not Old English morphology and syntax. After the Norman Conquest obliterated literary Old English, the Middle English that emerged was that of the Danelaw, which was operatively Norse.
A quick read through was not enough for me to digest the masses of data contained in this monograph. There is a lot of stuff here to back up the authors' assertions. That said, I learned long ago that you have to listen to what is not being said as well as to what is being said. And the way the authors refer to Old English makes me think they are making it a bit of a strawman.
For they always compare the language of the Danelaw to West Saxon OE. And though they cite John of Trevisa's ME essay on the languages (pl.) of Britain, they don't have much to say about Old English prior to the Danish conquest of Eastern and Northern Britain. Yet such scraps of Old Northumbrian or Old Mercian as we have show that the Anglian dialects of Old English were very different from the West Saxon dialect. They already feel more like "English" to us than the stiffer, more diphthongized OE of later WS literature.
The fact is, Old English was never a single dialect, but a cluster of mutually intelligible dialects transplanted from across the North Sea and then undergoing further development in Britain. To show that Middle English (and thus, Modern English) is more North Germanic than West Germanic in origin, I'd like to see more comparisons between Norse and Mercian/Northumbrian, rather than Norse and West Saxon.
In any case, I found it fairly easy to read Old English with minimal introduction, recognizing many words and feeling at home in the grammar from the beginning (my having studied German helped here). But when I have tried to read Old Norse, I have no easy connections therewith. I can puzzle it out with the aid of others, but it seems to come from much farther away.
Likewise, I would like to have seen more discussion of remaining dialectal forms in English. The authors point out that the verbal prefix ge- died out; Middle English verb forms are more like Norse verb forms. But Middle English retained similar prefixes for a long time, as in "y-bounden." And southern American English retains the same thing, as when we say, "He's a-huntin'." For that matter, the authors make a big deal out of the -ing form as somehow more akin to North Germanic than West Germanic, but again, southern American dialect typically "drops the -g"; actually, they never got around to putting it on.
Many morphosyntactical features piled up together make a strong case. But we haven't heard the rebuttal yet, and I'm sure there is one to be made.
The papers I just read are, "How myths persist: Jacob Grimm, the Long Hundred and duodecimal counting," by Ferdinand von Mengden, and "English: the language of the Vikings," by Joseph Embley Emonds and Jan Terje Faarlund. Both are found on Academia.edu.