Huck said:
According what I've read the astronom Peurbach "invented" the use of Arabic numbers. Likely this doesn't mean, that he really was the first who used them, but possibly he was a greater distributor for their use. This might have happened 1455 - 1460, perhaps earlier. He was a professor in Ferrara 1448 - 1450, so he might have used the system already in his teachings, which are called successful and impressive.
As 1448 - 1450 is early for Tarot and the way from Peurbach in Ferrara to the actual producers of Tarot cards, also in Ferrara, is rather short .... it stays, that the Tarot producers could have used "0" very early.
Actually I've also read from Ifrah, that they appeared much earlier in Europa, as signs on imported Arabian abaci, but it is a difference between small distribution and a broad distribution of an idea ... Actually I remember a years number inscription from 10 years before in Austrian (emperor) context. Then Peurbach was still a little young to have that big influence, but the emperor loved astronomy and astrology, too. So perhaps it was not Peurbach, but the astronomical school of Vienna, which used it.
Perhaps it was new use in Italy. At least it's true, that Peurbach and later Regiomontanus were able to impress Italians.
I've to correct me, it's said, that:
"Peurbach has been called the father of observational and mathematical astronomy in the West. He began to work up Ptolemy's Almagest, replacing chords by sines, and calculating tables of sines for every minute of arc for a radius of 600,000 units. This was the first transition from the duodecimal to the decimal system."
So the use of 12 for time measuring systems became replaceable by the decadic system. Generally it's said somewhere:
"By the mid 13th century algorithmic arithmetic was established in Italy well in advance of anywhere else in Europe, the immediate reason for this being the commercial pre-eminence of the northern Italian cities. Dissemination was slow: although by the 15th century one could learn algorithmic addition and subtraction in Germany, instruction in the arts of multiplication and division could still only be found in Italy. By the beginning of the 16th century, just before the scientific revolution, the Germans were still 200 years behind!"
"The algorithmic revolution made zero into a number by expanding the meaning of number, a process driven by expanding its use."
Well, I'm a little puzzled and I've Ifrah not at hand. But this sentence gives the riddle, that Peurbach and Regiomontanus from North of the Alps could improve some complex astronomical viewing points with responding Italian enthusiasm about it, although, as attested, being 200 years behind and possibly not able to teach multiplication and division in their own countries.
But I guess, the question around a "0" in use on playing cards touches the question, what "common behaviour" did ... as far I observed it, Roman numbering system was
still in use in mid 15th century.
Roman numbering system does run well with abacus use. And Abaci can easily be used for multiplication and division. So what is this guy talking about?
Anyway, the writer above seems to have the impression, that using the "0" as cipher was already given in commercial circles in mid 13th century.
Is that, what Ifrah also talked, kwaw?
