7413, 19702, and abacuses

I'll grant that ways of writing large numbers in Roman numerals aren't standardized, but the fact that they repeatedly come up in our own history strongly suggests that something like using a viniculum to indicate the number below it indicates a number a thousand times larger would have been adopted on Safehold even before Merlin introduced Arabic numerals.
XIXDCCII (with an overline instead of the underline used here because of BBCode formatting limitations) is far handier than MMMMMMMMMMMMMMMMMMMDCCII. So, Arabic numerals aren't likely to be the game changer in the way portrayed in Off Armageddon Reef.

Similarly, it seems unlikely that something like the Roman abacus which had the beads used for counting in grooves would not have already been introduced, even if not mentioned in the Holy Writ, albeit I can see Merlin introducing one that like the East Asian abacus uses rods to hold the counters in place, which would be an improvement.

Note, introducing Arabic numerals to replace Roman numerals and an improved abacus would be helpful, but I find it difficult to believe that some means of representing large numbers and aiding calculations wouldn't have already been in use on Safehold unless the Inquisition had previously found such things to be anathema, which it clearly hadn't or Paityr Wylsyn would never have approved the use of Arabic numerals or Merlin's abacus.

Also, Cayleb's use of the clumsy MMMMMMMMMMMMMMMMMMMDCCII to represent 19702 could just reflect that he was unaware of methods of representing large numbers.

Moreover, Arabic numerals allow for introducing the decimal point, which is far more flexible than Roman systems for dealing with fractions. So introducing Arabic numerals was important, just not for large numbers as was represented in OAR, but rather the small numbers needed for making precision parts.

Salisria wrote:...

Note, introducing Arabic numerals to replace Roman numerals and an improved abacus would be helpful, but I find it difficult to believe that some means of representing large numbers and aiding calculations wouldn't have already been in use on Safehold unless the Inquisition had previously found such things to be anathema, which it clearly hadn't or Paityr Wylsyn would never have approved the use of Arabic numerals or Merlin's abacus.

Also, Cayleb's use of the clumsy MMMMMMMMMMMMMMMMMMMDCCII to represent 19702 could just reflect that he was unaware of methods of representing large numbers.

Moreover, Arabic numerals allow for introducing the decimal point, which is far more flexible than Roman systems for dealing with fractions. So introducing Arabic numerals was important, just not for large numbers as was represented in OAR, but rather the small numbers needed for making precision parts.

You are correct that the Romans didn't string out 10 or more M's in any extant text I've heard of. They used shortcuts like over lines. [I suspect but do not know that is why some languages--even English in England often still to this day--define large numbers using terms like "ten thousand thousands" etc.] However their algorithms on the abacus were a bit different than the modern decimal algorithms.

But it is also true that not only the representations but also the algorithms themselves get easier once you introduce zero and place notation into the process. I too can't imagine the Church on Safehold didn't use some sort of roman abacus equivalent in their engineering including the original simple piles of pebbles (calculi originally meant "pebbles" in Latin) if nothing else. Well unless there was a calculator included in the holy artifact collection that was secretly used, or something.

Greek geometrical methods surely helped in some ways for some purposes especially in architectural engineering and navigation at sea. Also Greek math defined a "myriad" as 10 thousand which would help a lot with 19702. Greek slaves/professionals were employed as "calculators" as well.

Anyway, David makes little reference to such things that I've noticed in the series and glosses over a number of details that might be interesting to know, but don't really contribute to the story. Surely NO one wants another info dump!

Consider that the whole plan was to gimp progress as much as possible, give people tools for working with math and it can lead to all sorts of "nefarious" discoveries. There's also some textev that says that the general population didn't do "math", at most they used roman numerals for basic adding/subtracting.