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This is only true for our conception of Arithmetic as it is based on Hindu-Arabic numerals.
Alternate constructs using different methods of representation based on Roman numerals are also possible, it just didn't occur. (My English vs French example from before is here applicable). Rooney is making the conceptual mistake of thinking our methods exclude that other methods could have been devised.
Roman culture was quite receptive to new ideas, adopting Greek science, Hispanic swords, Gaulish iron smelting, Carthaginian agricultural techniques etc. to name a few. A reticence to adopt the systems of the enemy is not a Roman characteristic and cannot be blamed on them. The Byzantines had a bit more of that Greek pride and hubris which had brought them down before Rome, which probably adulterated their civilisation somewhat.
I agree, but its not as if Arab science was UBER-advanced either and anyway it was based on Greco-Roman science as well.
I don't think Christianity is to blame either, but I disagree that Roman Numerals in and of itself has any responsibility. Likewise, residual Roman culture is also blameless as this also adulterated Islamic Civilisation which had a flowering of Science and helped usher in the Renaissance at a later date.
The primary reason was the Barbarian conquests and fall of Rome in my opinion, which brought primitive cultures and largely uneducated elites into power, who neglected the Roman public works and learning in general. While I agree a conglomeration of distinct cultural, social, political and environmental factors caused the slow down in progress, I think the human factors thereof rest more amongst the Barbarian tribes than the Roman populace.
Well....I think you're right that the Barbarian invasions did quite a number on Europe, but then you have to be able to explain why it was that Europe didn't begin giving up use of Roman numerals and the abacus until after the Renaissance. Let's face it, there wasn't much in the way of grand scientific advancement (of major proportions) from the time of Constantine (or a bit earlier) even till 1500.
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