Talk:Dionysius Exiguus

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Here is Dionysius Exiguus book, the Liber de Paschate : http://hermes.ulaval.ca/%7Esitrau/calgreg/denys.html

Here a link to a concise reproduction (of course with preservation of correctness) of Dionusius Exiguus' Easter table would be no luxuary, in my opinion. I put one to http://www.janzuidhoek.net/diony2.htm. Jan Z 07:24, 24 September 2006 (UTC)

[edit] Year of the First Christmas

I have an issue with the paragraph below:

Because Dionysius did not place the Incarnation in an explicit year, competent scholars have deduced both AD 1 and 1 BC. Most have selected 1 BC (historians do not use a year zero). Because the anniversary of the Incarnation was 25 March, which was near Easter, a year that was 525 years "since the Incarnation" implied that 525 whole years were completed near that Easter. Consequently one year since the Incarnation would have meant 25 March 1, meaning that Dionysius placed the Incarnation on 25 March 1 BC. Because the birth of Jesus was nine calendar months later, Dionysius implied, but never stated, that Jesus was born 25 December 1 BC. Only one scholar, Georges Declerq (Declerq, 2002), thinks that Dionysius placed the Incarnation and Nativity in AD 1, basing his conclusion on the structure of Dionysius's Easter tables.

The ancients did not count from zero, but from one. (That's why they did not use a year zero; they had no need for one.) For example, they reckoned 31 December as secondo die ante Kalendas Januarias, i.e., "the second day before the January Kalends", although we would place it only one day before January. I have not seen Dionysius quoted in Latin, but I would guess that 525 years "since the Incarnation" would mean the Incarnation was 524 year previous, i.e., in 1 AD.

I guess my problem is that the above paragraph smells anachronistic. I'll try to look up the original in Latin. Rwflammang 14:52, 25 July 2006 (UTC)

From the link above:

Si nosse vis quotus sit annus ab incarnatione Domini nostri Jesu Christi, computa quindecies XXXIV, fiunt DX; iis semper adde XII regulares, fiunt DXXII; adde etiam indictionem anni cujus volueris, ut puta, tertiam, consulatu Probi junioris, fiunt simul anni DXXV. Isti sunt anni ab incarnatione Domini.

If you want to know what number be the year from the incarnation of our Lord Jesus Christ, compute 15 times 34 = 310; to them always add 12 regulares = 322; add also the indiction of the year of which you want, say, the third indiction from the consulate of Probus the Younger, which equal altogether 325 years. These are the years from the incarnation of the Lord.

Rwflammang 15:08, 25 July 2006 (UTC)

I wrote almost all of the article (except for some minor additions by other editors)—only the first two paragraphs are not my own (although I did modify them slightly). The article already gives a site with his tables in both Latin and English at Cyclus Decemnovennalis Dionysii - Nineteen year cycle of Dionysius. I equate your "anachronistic" comment to your statement that "the ancients did not count from zero". I have already stated in the article that Dionysius did know about zero, which can be found via the Latin nulla in the epact column, as well as via nihil in arguments 2, 5, 6, and 8. Because both uses deal with numbers and/or arithmetic, zero is a more appropriate translation than nothing.

The epact column in particular shows that Dionysius did count from zero when he wanted to. In principle, all epacts from zero through 29 existed because they indicated the age of the moon. Although the surviving Ethiopian computus (which is a copy of the Alexandrian computus) also numbers epacts from zero, it has been stated that the Alexandrians gave the age of the moon between 1 and 30 instead. If the latter is true, then Dionysius' innovation of numbering epacts from zero is even more indicative of his ability to number years from zero (although I never said that he actually did so). Granted, that would have been an unusual method of counting years, because all previous eras started with year one. The latter includes the Diocletian years used by the Alexandrians that Dionysius replaced with his anno Domini years. There is no question that the Alexandrians knew about and used zero—see Greek numerals#Hellenistic zero (which I also wrote). This shows that the paragraph is not anachronistic regarding zero.

You have misremembered the Roman inclusive method of counting the days of each month. The day before the calends of January was pridie (literally, the day before). Nevertheless, the day before that, 30 December, was the third day before the calends of January. This only indicates a curious oddity about the ancient Romans (before Christ). I personally think they we well aware of zero, because they could not have constructed their massive civil engineering projects without calculations that must have involved zero as a remainder of division, in the same manner that Dionysius indictated that zero was a possible remainder of division.

For the record, Michael Deckers translated the first argument as:

If you want to find out which year it is since the incarnation of our Lord Jesus Christ, compute fifteen times 34, yielding 510; to these always add the correction 12, yielding 522; also add the indiction of the year you want, say, in the consulship of Probus Junior, the third, yielding 525 years altogether. These are the years since the incarnation of the Lord.

— Joe Kress 21:00, 25 July 2006 (UTC)

[edit] wikipedic medieval zero

See Talk:Number —The preceding unsigned comment was added by Jan Z (talk • contribs) 22:34, 8 January 2007 (UTC).

I'am sorry. Jan Z 21:31, 9 January 2007 (UTC)

Dear Joe Kress. I would appreciate it if you could continue your contribution to the discussion concerning both the Wiki items Number and [Dionysius Exiguus]. Jan Z 21:31, 9 January 2007 (UTC)

In this Wiki item [Dionysius Exiguus] I demur at the suggestion that DE should know the number zero, “knowing the number zero” meaning of course “using the number zero in ones calculations” (DE and BV did not use the number zero in their calculations). For the sake of the wikipedic neutral point of view it is the editor of the paragraph in question (Joe Kress?) who must argue for what reason Wikipedia should abandon the common assumption that nobody in early medieval Europe knew the number zero. In that paragraph we find only one argument in favor of his opinion, but in my opinion it is a very weak one (“Zero can probably be found in earlier Latin mathematical treatises”). To begin with, I would invite him 1 to take cognizance of my arguments explained in Wiki item [Talk:Number] (which arguments, I think, demonstrate the impropriety of his subjective interpretation of Dionysius’ ‘nulla’ and ‘nihil’), and 2 to formulate his arguments or to reconsider his particular point of view. It were much better to let ‘nulla’ untranslated or to put a hyphen instead of it than any subjective interpretation of it as a zero. I look forward to receiving his reply. Jan Z 07:56, 14 January 2007 (UTC)

Owing to my sources, either implicitly (D.E.Smith: History of Mathematics, B.L.vanderWaerden: Science Awakening, D.J.Struik: a concise History of Mathematics) or explicitly (G.Declercq: Anno Domini), DE and BV did not use the number zero. The only sources for what they did do are DE' own "Argumenta Paschalia" and BV' own "De Temporum Ratione". It is not difficult for us to convince ourselves (by objectively analyzing their texts) that they were no exception to the generally accepted rule that in early medieval Europe nobody used the number zero. It is our modernized brain which tries to hoax us into believing to see the number zero where by early medieval scholars only ‘nothing’ was meant. Jan Z 07:22, 17 January 2007 (UTC)

I will continue my discussion at Talk:Number. It takes some time to access the relevant sources, and I have other things to do. — Joe Kress 23:20, 17 January 2007 (UTC)

I would invite Joe Kress (after his last contribution of 17-1-2007) to take cognizance of the new contributions of JPD and of me to the discussion concerning Wiki item [Number] and the ones to the discussion concerning Wiki item [Dionysius Exiguus] and to react to them. But I would ask him and JPD and other ones to react to the discussion concerning Wiki item [Dionysius Exiguus], specially to my proposals to improve Wiki item [Dionysius Exiguus], at this Talk:Dionysius_Exiguus (the only right place for this discussion after all), at which I would continue this discussion. Jan Z 19:07, 19 February 2007 (UTC)

I would repeat my request to Joe Kress to react. To make it easier for him to do that, I would propose to depart from the following points of Talk:Number:

Joe Kress, to defend your claim that Dionysius Exiguus and Beda Venerabilis should have been acquainted with the number zero (which claim needs a “cited author” indeed) you refer to Faith Wallis (she is, as we are, a child of our time after all). But it is not the number zero itself of which she speaks, but only any ‘zero’. Moreover, where FW indicates (loosely speaking) that DE and BV used ‘zero’, this interpretation is only based on her own in fact too free translations. BV’s “nullae sunt epactae” (literally “there are no epacts”) and “nulla epacta” (literally “no epact”) need a more objective translation than hers. And so does BV’s “de octaua decima in nullam facere saltum”. For our modern (updated) brain it is difficult to read here something else than “to jump from 18 to 0”. But even modern people use phrases such as “jump into nothingness”. The interpretation of “no epacts” as ‘zero’, is FW’s, not Bede’s. And the interpretation of Bede’s “nullae” as the number zero is yours, not hers. Since she (being conscious of the relativity of the meaning of the term ‘zero’) gives no further argument, FW can not make a decisive contribution to our discussion. Neither the isolated abbreviation N for BV’s “Nullae” is decisive (by the way: in the same table of epacts we find epact 30 instead of epact “nullae” again). Shortly, analyzing them (see my contribution to Talk:Number), always DE’s “nulla” and BV’s “nullae” will be proved to be nothing else than ‘nothing’ (either as such or as a placeholder for zero). At most they can considered to be precursors of the number zero.

Although DE’s “nulla” numband BV’s ‘nullae’ are very zerolike things indeed, neither DE nor BV was familiar with the number zero, for 1 in early medieval Western Europe the number zero was unknown (common assumption), 2 DE’s “nulla” and BV’s ‘nullae’ mean only ‘no epacts’, 3 DE and BV did not use “nulla” or “nullae” in their abstract calculations (see my contribution to Talk:Number), and 4 even in the case that JK’s interesting suggestion that the ps.-Cyrillan Easter table (which was used by DE to construct his one) contained as an epact Ptolemy's omicron o instead of epact 30 is correct, DE’s “nulla”, according to JK’s own interpretation being a “translated” o as well as according to my interpretation that not only DE did not “translate” this symbol but also simply did not accept it because he had not the slightest need for any symbol and contented himself with his familiar “nulla” (meaning literally “none”) instead, cannot be more than a precursor of the number zero. Anyhow, we cannot escape the conclusion that BV’s “nullae” as much as DE’s “nulla” were far from the (purely mathematical) number zero itself. So it is quite premature to “render false” the current opinion that in medieval Western Europe one had to wait as late as the second millennium before one got dispose of the number zero. In early medieval Europe the times were not yet ripe for the coming into being of the number zero. Not only the birth of the number zero was a maturing process, but also its dissemination across Asia (beginning around the year 600) as well as the one across Europe (beginning only in the twelfth century) took centuries.

Maybe DE’s “nulla” and BV’s “nullae” are precursors of the number zero, but there is no “cited author” claiming they are the (purely mathematical) number zero itself. Faith Wallis, being conscious of the relativity of the meaning of the term ‘zero’ into which she BV’s “nullae” translated, never claimed seriously something like an early medieval number zero (to my knowledge), only Joe Kress did (to my knowledge), but he is no cited author, I think. So, for the sake of the wikipedic neutral point of view, first of all we have to tone down the term “number zero” in the paragraph in question in this Wiki item. To begin with, I would propose, leaving intact as much as possible in that paragraph, 1 to replace in that paragraph “Latin medieval writer to use the number zero” with “medieval Latin writer to use (a precursor of the number) zero”, 2 to delete the superfluous third sentence of that paragraph, and 3 to replace the last sentence of that paragraph with something like “Both zeros continued to be used by (among others) Beda Venerabilis, by whose extension of Dionysius’ Easter table to a great Easter cycle all future Julian calendar dates of Easter Sunday were fixed unambiguously after all. However, in medieval Europe one had to wait as late as the second millennium before one got dispose of the number zero itself, which had come into being around the year 600 in India.”. Jan Z 18:31, 3 March 2007 (UTC)

Additional remark: Ptolemy’s omicron o as well as Ptolemy’s own “zero” was a digit zero (namely in the Babylonian sexagesimal positional system) as well as a placeholder for (the number) zero (namely related to Greek numerals such as λα = 31), but not the (purely mathematical) number zero itself. We may speak of the number zero as soon as calculations with positive integers are carried out in combination with its symbol. But DE’s “nulla” and Bede’s “nullae”, being related to Roman numerals such as xxxi = 31 indeed, are only placeholders for zero. Jan Z 20:12, 4 March 2007 (UTC)

I’m still waiting for Joe Kress’ reaction to my proposal of 3-3-2007. Jan Z 14:31, 18 March 2007 (UTC)

Additional remark: on second thoughts it seems to me to be preferable to speak of ‘precursor of the number zero’ rather than of ‘placeholder for zero’. Jan Z 18:34, 31 March 2007 (UTC)