CADRE Comments

A Rational Look at Christianity; Basing Reason in Truth

Continuing on with the development of the use of zero in Europe, my friend and fellow Cadre member Bede has chimed in after reading Mr. Mann's email on the subject. Bede has a Masters in Historical Research and is working on his PhD in the History of Science, so his opinion is worth more than mine. Check out his blog on the issue here. I include an excerpt:

I would firstly say that I have studied a manuscript written by the Cambridge University maths lecturer in 1508 and it uses zero as a matter of course. So do all 16th century maths textbooks. I've looked at the collected letters of Gerbert (that’s Sylvester II) already and not found anything related to zero. However, he is credited with being one of the first to introduce Arabic numerals into Western Europe. I'll also check Sacrobosco's Algorismus as that was the main medieval textbook on arithmetic. The earliest version I've seen was printed in 1488 and I think that uses zero (I wasn't looking but it covers normal adding up and multiplying that is impossible without zero). I might dig back to look at some of the manuscripts which date from the thirteenth century.

An important question here is whether we are talking about a naked zero or zero used as part of another number (ie. 490 is not zero but we use zero to write it). For most kinds of arithmetic, you don’t need a naked zero and this might be what is rare in medieval sources. Merchants certainly don’t use it unless they are giving their goods away for free. However, the use of zero as part of other numbers is common from at least the early thirteenth century and it doesn’t appear to be controversial. Contrary to what Mann says, all medieval accounting records that I have seen use Roman rather than Arabic numerals. This is what we would expect as merchants continued to use the abacus to add up rather than arithmetic. Hence, they didn’t need a zero.

Bede also notes that we still have little in the way of primary sources on the issue.

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