Re: [tied] Dice

And yet dicemakers have almost invariably used the "less intuitive" add-up-to-seven design ever since the cubic dice was invented. We find it on nearly all surviving dice from Egypt, Greece, Italy and other places. There are dice from Etruria with pips in lieu of words, and the pips add up to seven on opposite faces. How to arrange the numbers on a dice is something that any apprentice in the dicemaking business would have been told by members of the dicemakers' guild, alea players and diviners who were his customers, etc. If there is a preferred design, you can be sure that all interested parties will know about it.

Why was that design preferred by the ancients? Well, why is it still preferred nowadays? Any schoolchild knows (or should know) that the arrangement doesn't affect the odds, so why do our dice manufacturers follow a pointless ancient custom? Deference to tradition is a sufficiently strong factor. However, prior to Blaise Pascal's gambling experiments in the 17th century nobody knew how to define or measure probability. I suppose dice enthusiasts vaguely believed in a "fair" or "balanced" arrangement iw which none of the three orthogonal directions was favoured. Perhaps the fact that 6+1 = 5+2 = 4+3 = 7 had some mystic importance (dice were magical or even sacred objects, like magic squares with their slightly more complex constant sums).

Piotr

----- Original Message -----
From: Glen Gordon

To: cybalist@egroups.com

Sent: Tuesday, January 23, 2001 2:53 AM

Subject: [tied] Tetrapolis and Half-assed Etruscan dice-makers

Now, I've been thinking more about those pair of dice that supposedly prove that four=/s'a/ and six=/huth/. If I were a half-assed dice-maker, a certain layman without mathematical knowledge, it wouldn't seem altogether self-evident to me that I must place the numbers opposite to each other in order to add up seven. I'm no mathematician, so perhaps Piotr can help me, but I can see no manner in which "numerical symmetry" on a die terribly affects the odds. Rather, I, the layman dice-maker, would be more interested in attaining geometrical symmetry. A more intuitive method of placing numbers on a dice might be to start with one side, writing "one", giving the dice a quarter-turn, and writing "two", then another quarter-turn, "three", another quarter-turn, etc. until I had marked all sides of the dice. If the person had done "zigzagging" quarter-turns (turn right, then up, then right like a winding snake...), the pattern from this would end up being one where each face with number N is adjacent to the faces with N-1 and N+1 by single quarter-turns. In other words, the dice do not illuminate on whether the mathematical method or the more intuitive "zigzagging quarter-turn" method was used, however the latter would allow the sides to not be equal to seven in total and would allow four to be /huth/ (agreeing with the Tetrapolis arguement and IE *kWetwores) and six to be /s'a/ (agreeing with an early Semitoid borrowing arguement). While it might have been common for the sides of these die to equal seven elsewhere, it would appear to me that this trivial mathematical symmetry would first have to be explained to all Etruscan dice-makers. Surely, there were some dice-makers who knew nothing of these number games. Perhaps I've missed something? Well, I'm sleepy. Must sleep and get up early 2morrow. Konban wa, yo'll. - gLeN