Smile

But I do not interpret this difference between the two tables : one of Boethius and one of Pythagoras as you do.

Pythagoras is shown as relying on an abacus - so probably using either Greek caracters or more probably Roman caracters.
That was the use in the early states of the game.
Boethius is shown as using "modern" Hindu-Arabic caracters.

The players who used Roman caracters were slower and had an important effort of memorization to do : that is the sense of Pythagoras attitude.
Those who used Hindu-Arabic caracters went more quickly...that is the sens of the attitude attributed to Boethius.

Use of Roman and Hindu-Arabic caracters in the game : https://drive.google.com/file/d/0B5Hg6j ... sp=sharing

Use of Greek caracters in the game : https://drive.google.com/file/d/0B5Hg6j ... sp=sharing

The Philosopher's game, p.12
https://books.google.fr/books?id=SNM2tj ... ce&f=false


Greek and Roman caracters were more ancient than the Hundi-Arabic caracters for Medieval Occdental culture.
So normal to attibute the Roman caracters with the abacus to Pythagoras .

Question :
Historically, what were the caracters really used by Boethius?
Hindu-Arabic as on the drawing?
No.
Roman caracters.
see :
image link : https://archive.org/stream/aniciimanlii ... 4/mode/2up

BOUGEAREL Alain wrote: Question :
Historically, what were the caracters really used by Boethius?
Hindu-Arabic as on the drawing?
No.
Roman caracters.

... :-)
Of course. The new number system hadn't arrived in his time. It came much later.

But we're interested, how the people in 15th/16th century celebrated Pythagoras. Boethius was given a modern face, and Pythagoras was seen as old-fashioned. More reduced to his contribution to music.

If you say so...

Pythagoras born 580 av. J.-C.in Samos is older than Boethius born 480 in Roma,

What matters is what is refered to?
I think : the rapidity of calculation with the ancient or modern caracters.
The early use of Roman caracters with abacus in the game was slower
The modern use of Hindu-Arabic caracter is quickier.

So...Pythagoras is shown as slower
And Boethius, quicklier.


NB As for Boethius who used Roman caracters, his Arithmetic and Music comes from Nicomacus de Gerase Arithmetic and Music ...
.

The picture is from 1503, not from Boethius time and not from Pythagoras' time. It tells us something about the state of the world in 1503.

Yes
It tells us that the modern use of Hindu-Arabic caracters in the Philosopher's game is quicklier than the early use of Roman caracters with abacus...that's an evidence

BOUGEAREL Alain wrote:Yes
It tells us that the modern use of Hindu-Arabic caracters in the Philosopher's game is quicklier than the early use of Roman caracters with abacus...that's an evidence

... .-) ... it also tells, that for a few decades printing industry existed, and that some persons weren't fixed on earlier admiration of older world views.

Alain wrote,

Dummett's hypothesis about the early or late dating from the degree of variability is of interest for sure.

I must clarify. That isn't Dummett's hypothesis. It's mine. Dummett's hypothesis is that the variability in the orders is due to local groups of players being isolated from each other, so that different changes can occur spontaneously in different areas, each in isolation from the others. My hypothesis, that the longer the time in isolation, the greater the variation, because of increase in the the chances for variation, is an extension of that, one that I haven't seen anyone else accepting except me. It seems logical to me. But it isn't one that Dummett himself seems to have recognized, because he proposed in 2004 that the virtues were the last cards to enter the tarot, whereas I would say they were among the first (see viewtopic.php?f=11&t=1073#p16421). I am glad to see that he recognized that all 22 might not have entered the sequence at once, but on this point his argument seems to me flawed, as I explained at viewtopic.php?f=11&t=1073#p16460.

mikeh wrote:Alain wrote,

Dummett's hypothesis about the early or late dating from the degree of variability is of interest for sure.

I must clarify. That isn't Dummett's hypothesis. It's mine.

Dummett's hypothesis is that the variability in the orders is due to local groups of players being isolated from each other, so that different changes can occur spontaneously in different areas, each in isolation from the others.

My hypothesis, that the longer the time in isolation, the greater the variation, because of increase in the the chances for variation, is an extension of that, one that I haven't seen anyone else accepting except me. "

...

Thanks for clarifying .

Your hypothesis is original and , for me, a plausible logical relation established upon a rational inference.

It's completely new to me

Thanks. I would welcome more discussion. It's something I proposed 3 years ago, but it wasn't as clear as it could have been (viewtopic.php?f=11&t=975&p=14457&hilit= ... ity#p14457). Actually, there is another part I need to say. That is, there were fairly specific times when the isolation would have broken down to some extent, on some level: when Francesco Sforza and his troops went over to Florence in around 1436 (Sforza was very popular in Florence, according to Dale Kent's book on Cosimo); maybe during the Council of Florence of 1438-1439; and after 1450, Sforza's victory in Milan and the legalization of the game in Florence. Maybe some other times, I don't know. The Council of Florence is something that wouldn't have affected established patterns much, but it might have encouraged the spread of the game to new locations. (In places with courts, even individuals coming in from elsewhere could introduce new elements, if it made for a better game and play was restricted to the elite culture.) The other two events, 1436 and 1450, were more massive, the first just in Florence, although it may have been too early to affect anything, and the other throughout Northern Italy.

So the idea of variability within the groups determining how long a card has been part of the game is one factor among others--but still a big one, I think.

Sure.
A plurality of other factors as those you underline may modify the relation.
But still, as you say, it remains a big factor