Megas 2

Missing piece

2011-04-15T08:56:00.001-07:00

Truque

2011-02-03T06:24:00.000-08:00

Jogar e trabalhar... santíssima díade !

2010-08-25T08:19:00.001-07:00

Games like World of Warcraft give players the means to save worlds, and incentive to learn the habits of heroes. What if we could harness this gamer power to solve real-world problems? Jane McGonigal says we can, and explains how.

Jane McGonigal asks: Why doesn't the real world work more like an online game? In the best-designed games, our human experience is optimized: We have important work to do, we're surrounded by potential collaborators, and we learn quickly and in a low-risk environment. In her work as a game designer, she creates games that use mobile and digital technologies to turn everyday spaces into playing fields, and everyday people into teammates. Her game-world insights can explain -- and improve -- the way we learn, work, solve problems, and lead our real lives.

McGonigal directs game R&D at the Institute for the Future, a nonprofit forecasting firm where she developed Superstruct, a massively multiplayer game in which players organize society to solve for issues that will confront the world in 2019. She masterminded World Without Oil, which simulated the beginning of a global oil crisis and inspired players to change their daily energy habits. McGonigal also works with global companies to develop games that build on our collective-intelligence infrastructure -- like The Lost Ring, a mystery game for McDonald's that became the world’s biggest alternate reality game, played by more than 5 million people. (Not to mention the delightful Top Secret Dance-Off, which taps that space in our brains where embarrasment and joy mingle.) She's working on book called Reality Is Broken: Why Games Make Us Happy and How They Can Change the World.

"Instead of providing gamers with better and more immersive alternatives to reality, I want all of us to be become responsible for providing the world with a better and more immersive reality."

Jane McGonigal

A Década dos Jogos - a camada lúdica

2010-08-25T08:17:00.000-07:00

"Proud Princeton dropout" Seth Priebatsch runs SCVNGR, a mobile start-up trying to build the game layer on top of the world.

Play, Culture & Religion

2010-08-17T07:53:00.001-07:00

Campeonato diferente

2010-08-02T14:50:00.000-07:00

Do ATITUDES

2010-06-30T06:19:00.000-07:00

Aqui vai a página 15 do ATITUDES, jornal da E. S. com 3º Ciclo do EB de Matias Aires (Ano 13, nº 60, 3º período 2009/2010)

Tarde animada no Taguspark

2010-05-03T01:18:00.000-07:00

Ontem foi dia de festa no Taguspark.
O Público dá a notícia.

A equipa açoreana regressa a casa após brilhante participação no CNJM6, em Santarém. 4/4.

2010-03-20T08:11:00.001-07:00

A equipa açoreana regressa a casa após brilhante participação no CNJM6, em Santarém. 3/4.

2010-03-20T08:09:00.001-07:00

A equipa açoreana regressa a casa após brilhante participação no CNJM6, em Santarém. 2/4

2010-03-20T08:08:00.001-07:00

A equipa açoreana regressa a casa após brilhante participação no CNJM6, em Santarém. 1/4

2010-03-20T08:04:00.001-07:00

Campeonato Regional de Jogos Matemáticos dos Açores

2010-02-04T06:13:00.000-08:00

Em Janeiro de 2010. Parte 1.

O Campeonato Regional foi uma organização do Departamento de Matemática da Universidade dos Açores e da Associação Ludus.

Campeonato Regional de Jogos Matemáticos dos Açores

2010-02-04T06:10:00.001-08:00

Em Janeiro de 2010. Parte 2.

O Campeonato Regional foi uma organização do Departamento de Matemática da Universidade dos Açores e da Associação Ludus.

truk

2010-01-12T13:35:00.001-08:00

About the second trick - when one draws 4 different cards from a single deck, there always will be a pair among them whose numerical value differs by not more than 3.

The extreme case would be 1,5,9,12 , but the distance among 12 and 1 is less than 4. Similarly 2 different suits differ by not more than 3 (with appropriate convention).

So if we choose the smaller card of the pair whose numerical difference is less than 4 and use this card as a marker we need 9 different values to describe the mystery card. Let the marker be always the leftmost opened card.

For all 3 open cards we have 2 different possibilities arranging the remaining open cards in either decreasing or incrasing order. The cases where one or 2 cards are closed give us 6 different configurations. So we have 8 different configurations. Since we have only one deck, this is enough , because the “zero” case where the marker is the same as the hidden card will never happen.

truk

2010-01-12T13:34:00.001-08:00

About the second trick - when one draws 4 different cards from a single deck, there always will be a pair among them whose numerical value differs by not more than 3.

The extreme case would be 1,5,9,12 , but the distance among 12 and 1 is less than 4. Similarly 2 different suits differ by not more than 3 (with appropriate convention).

The Royal Game of the Ombre

2010-01-10T05:38:00.001-08:00

The Royal Game of the Ombre.

Written At the Request of divers Honourable Persons.

London

Printed for Thomas Palmer, at the Crown in Westminster-Hall, 1665.

The Royal Game of the Ombre.

L'Ombre is a Spanish Game at Cards, as much as to say, The Man: so he who
undertakes to play the Game, sayes Jo so l'Ombre, or, I am the Man. And
'tis a common saying with the Spaniards, (alluding to the name) that the
Spanish l'Ombre as far surpasses the French le Beste, as a Man do's a
Beast, There are divers sorts of it, of which, this (which we shall only
treat of, and which chiefly is in vogue) is called the Renegado, for
reasons better supprest then known.

_How many can play at it, and with what Cards they are to play._

There can only three play at it, and they are dealt nine Cards a piece: so
by discarding the Eights, Nines, and Tens out of the Pack, there remains
thirteen Cards in the Stock.

_Of the Trump_

There is no turning up Trump, nor no Trump but what the Player pleases,
the first hand having alwayes the choice to play or pass, after him the
second, &c.

_Of the Stakes_

For Stakes there are two sorts of Marks or Counters, the greater and the
less; for example if you value the great ones at 12. pence, the lesser may
be pence the piece (and so according as you please) of which great Marks
you stake each one one for the Game: and the lesser for passing, for the
hand, if you be eldest, and for taking in, giving for each Card you take
in, one Mark or Counter.

_Of the names of the Cards, and order in ranking them_

_Of the Black Suits_

1. The Spadillio, or Ace of Spades.
2. The Mallilio, or black Deuces of either suit.
3. The Basto, or Ace of Clubs.
4. The King.
5. Queen.
6. Knave.
7. Seven.
8. Six.
9. Five.
10. Four.
11. And Three.

_Of the Red Suits_

1. The Spadillio, or Ace of Spades.
2. The Mallilio, or Sevens of either Suit.
3. The Basto, or Ace of Clubs.
4. The Punto, or Ace of Hearts or Diamonds according as they are Trump.
5. The King.
6. The Queen.
7. The Knave.
8. The Deuce.
9. The Three.
10. The Four.
11. The Five.
12. The Six.

_Observations._

By this you see first that the Spadillio, or Ace of Spades is always the
first Card, and alwayes Trump, be the Trump what suit soever; and the
Basto, or Ace of Clubs alwayes the third. Secondly, the of Black, there
are but eleven Trumps, and of Red twelve. Thirdly, that the Red Ace enters
into the fourth place when it is Trump, and then is called the Punto,
otherwise 'tis only rank'd after the Knave, and is only call'd the
Ace. Fourthly, that (excepting the Deuces of Black, and Sevens of Red,
which are call'd the Mallilio's, and are alwayes the second Cards when
they are Trumps) the least small Cards of the Red are alwayes best, and
the greatest of the Black.

_Of the Matadors._

The Matadors or killing Cards, as the Spadillio, Mallilio, and Basto, are
the three chief Cards, and for these, when they are all in a hand (else
not) the others pay three of the greater Marks or Counters the piece; and
though there be no counting the Matadors without these three, yet these
three for foundation, you may count as many as you have Cards in an
interrupted series of Trumps; for all which the others are to pay you one
Mark or Counter, the piece, even to nine sometimes.

_Of taking in, and the order and manner of it._

1. Who has the first Hand, has choice of playing the Game, of naming the
Trump, and of taking in as many of or as few Cards as he pleases, and
after him the second, &c.
2. Having once demanded whether any one will play _without taking in_, you
oblige your self to take in, though your Game be never so good: wherefore
you are well to consider it before.
3. If you name not the Trump before you look on the Cards which you have
taken in, any other may prevent you, and name what Trump they please.
4. If (as it often happens) you know not of two Suits which to name
Trump; e.g. with the two black Aces you have three Trumps of either
sorts: First, the Black Suit is to be preferr'd before the Red, because
there are fewer Trumps of it. Secondly, you are rather to choose that Suit
of which you have not the King, because besides your three Trumps, you
have a King, which is as good as a fourth.
5. When you have the choice of Going in three Matadors, or the two Black
Aces with three of four other Trumps, if the Stakes be great, you are to
chuse this last, (as most likely to win most Tricks) if it be but a simple
Stake, you are to chuse the first; because the six Counters you are to
receive for the Matadors, more then equavales the four or five, you lose
for the Game.

_Observations._

1. He is to ask _if any will play without taking in._ (when they have the
choice of those who will not.) Secondly, he is never to take in, or play,
unless he have three sure Tricks in his hand at least: To understand
which the better we must know

_The End of the Game_

The End of the Game is (as at Beast) to win most Tricks; whence he who can
win five tricks of the Nine, has a sure Games; or if he win Four, and can
so divide the Tricks, as one may win Two, the other Three: if not, 'tis
either Codillio or Repuesto, and the Player loses and makes good the
Stakes.

_Of the Codillio._

The call it Codillio when the Player is beasted, and another wins more
Tricks then he; when this takes up the Stakes, and tother makes it good:
where note, that although the other two alwayes combine against the
Player to make him lose, yet they all do their best (for the common
good) to hinder any one from winning, onely striving to make it Repuesto.

_Of the Repuesto._

They call it Repuesto when the Player wins no more Tricks then another:
for example, if he win but four, another four, and the third but one, or
each of them win three Tricks the piece; in which case the Player doubles
the Stake, without any ones winning it, and it remains so doubled for the
advantage of the next Player, &c. whence you may collect, that the Player
is as much concern'd in making Repuesto, in case of nesessity, as any of
the rest, by which means the Stakes oftentimes increasing to a
considerable summe, the Player is to be very wary what Games he playes.

_What Games are to be played_

One is never to play unless he have three sure Tricks in his hand at
least, as we have said before; as the three Matadors, or six or seven good
Trumps without them; where note, the Kings of any Suit are alwayes
accounted as good as Trumps (since nothing but Trumps can win them) mean
while all other Cards but them and Trumps, are to be discarded.

_Observations._

He who playes having taken in, the next is to consider the goodness of his
Game; and to take in more or less, according to his Game is probably like
to prove good or bad, alwayed considering, that 'tis as much his advantage
that the third have a good Game to make it Repuesto, as himself. Neither
is any one, for Covetousness of saving a Counter or two, to neglect, the
taking in, that the other may commodiously make up his Game with the Cards
which he leaves; and that no good Cards may lye dormant in the Stock,
except Player playe without taking in when they may refuse to take in, if
they imagine he has all the Game.

_Of playing without taking in._

When one has a sure Game in his hand, he is to play without taking
in; when the others are to give him each of them one of the greater Marks
or Counters, as he is to give them, if he play without taking in, a Game
that is not sure, he'd(?) loses it.

_Of the Voll._

If you win all the Tricks in your hand, or the Voll, they likewise are to
give you one Mark or Counter the piece; but then you are to declare before
the fifth Trick, that you intend to play for the Voll, that so they may
keep their best Cards, which else seeing you win five Tricks (or the
Game) they may carelesly cast away.

_Of the Forfeitures_

If you Renounce, you are to double the Stake, this(?) also if you have
more or fewer Cards then Nine, (to avoid all wrangling or foul play) to
which end you are carefully to count your Cards both in dealing and taking
in, before you look on them; besides according to the Rigour of the Game,
if you speak any thing that may discover your Game, or anothers (excepting
onely Gagno as we shall declare afterwards) or play so, as wittingly to
hinder the making it Repueto or Codillio (and if ignorantly, you are not
fit to play.)

_Of playing Trumps_

In playing Trump; you are to note, that if any playes an ordinary Trump,
and you have onely the three best Cards, or Matadors, singly or can
jointly in your hands, you may refuse to play them, without Renouncing,
because of the priviledge which those Cards have, that none but commanding
Cards can force them out of your hands; as for example, the Spadillio
forces the Mallilio, and the Mallilio the Basto; for all the rest you are
to follow Trump.

_Of what you are to say_

You are to say nothing but onely, _I pass_, or _play_, or Gagno, that is,
'tis mine, simply, when you play your Card, to hinder the third from
taking it; or Gagno de l' Re when you play your Queen to hinder them from
taking it with the King, &c. but this you cannot say till it come unto
your turn.

_General Rules_

'Tis impossible to provide against all accident in the Game, onely these
general Rules may be observ'd in playing: First, the chiefest Art
consisting in knowing the goodness of ones Gane, and how it may be
improved to the best, one is never to win more then one trick, if they
cannot win more then two because of the advantage they give the Player by
it in dividing the tricks. Secondly, you are alwayes to win the trick from
the Player if you can, unless you let it pass for more advantage, wherein
note the second is to let pass to the third; if he have the likelier Game
to beast the Player, or if he be likely to win it.

_Of the Tenaces_

There may be divers advantages in refusing to take the Players trick, but
the cheifest is if you have Tenaces in your hands, that is, two Cards,
which if you have the leading, you are sure to lose one of them. If the
player lead to you, you are sure to win them both; for examples, if you
have Spadillio and Basto in your hand, & he have the Mallilio & another
Trump, if you lead you lose one of the; for either you lead your

Spadillio, and he player his lesser Trump upon it and wins your Basto
the next trick with his Mallilio, and so the contrary; whereas if he
leads, he loses both; for if he lead his Mallilio, you take it with your
Spadillio, and with your Basto win the other Trump; or if he lead with
that, you take it with your Basto; and then your Spadillio wins his
Mallilio, and 'tis called Tenaces, because it so catches you betwixt
them, there is no avoiding it, &c.

_Of the Players playing his game for his best advantage_

Of this (becuase every one playes according to his own fancy) I will only
say, that if you are not sure of winning five Tricks, but have only the
three Matadors, (as for example) and Kings be your Auxilary Cards, if you
have the leading you are to begin with a Matador or two before you play
your Kings, to fetch out those Trump perhaps which might have trumped
them; and if you have three Matadors with two other Trumps your best way
is first to play you Matadors, to see how the Trump lie, and if both
follow, you are sure that if three Trump be Red, there remains onely one
Trump in their hands; if Black, none at all; it importing so much that the
player counts the Trumps, as the miscounting only one, do's often lose the
Game. In fine, if they have but a weak Game, they are to intimate cunning
Beast Players, in dividing Tricks, and consult them in playing of their
Cards. And these few Instructions may suffice, leaving the rest to each
one's particular observation.

Certain other more Questions there are; as whether any may look on the
Tricks to see what Cards are played beside the Ombre, or he who playes the
Game, which ordinarily is resolved on the affirmative; or when any Cards
are left in the Stock, whether any may look on them or no, which the Table
lef once, usually is done. Only observer to lay your Tricks Angle-wisse.

[Transcribers note: Several diagrams here have been omitted], to the end
that one may easily perceive whether they be two, three, or four.]

F I N I S.

This etext was retrieved by ftp from ibiblio.org/pub/docs/books/gutenberg
It is also available from www.ibiblio.org/gutenberg

Produced by Imran Ghory while at the University of Bristol

[Transcribers note: This transcription was made from a copy of the work
held in the British Library as Jessel #1249. Original spelling and
punctuation has been preserved where possible.]

António Silva Araújo sobre Damiano

2009-10-06T02:38:00.000-07:00

Aqui.

BOARD GAME STUDIES COLLOQUIUM XIII

2009-10-03T07:58:00.000-07:00

BOARD GAME STUDIES COLLOQUIUM XIII

PARIS

Wednesday 14th to Saturday 17th April, 2010

The 13th Board Game Studies Colloquium will be held in Paris, from Wednesday 14th to Saturday 17th April, 2010.

The Colloquium will be hosted at the FIAP Jean-Monnet Centre, a large convention and hostel centre situated in the 14th arrondissement of Paris.

The Colloquium will offer a large scope of papers (typically eight to ten per day), dealing with the archaeology, mathematics, history of art, computer science, anthropology, cognitive psychology, history, linguistics, design, economy of board games and their accessories (dice, gameboards, counters, etc.). We will also visit a few public collections.

CALL FOR PAPERS

We invite submissions from scholars, researchers, students and collectors on these topics. We seek papers that offer real research. Talks should not be longer than 25 minutes. They can be in French or in English. Papers read in French will be translated orally (though not simultaneously).

Subjects must be sent before November 30th, 2009 to: Organising Committee c/o Thierry Depaulis 24 rue Francœur - 75018 Paris (France) email: thierry (dot) depaulis (at) free (dot) fr
Abstracts (500-600 words) must be sent before January 31st, 2010, because they all must be translated into the other language.

The Colloquium fee is not yet set but will be around EUR130/150 for the whole programme, including a few meals. Two-Day (and perhaps One-Day) pass will also be available.

Further details and hotel booking will be posted later.

Seega

2009-09-13T08:18:00.001-07:00

Rules of Seega? Look for them here. Or here and here.

Jeux de princes, jeux de vilains

2009-07-17T08:51:00.000-07:00

Aqui.

Gargantua - Rabelais

2009-07-07T15:16:00.000-07:00

François Rabelais (1483-1553) escreveu Gargantua. Aparecem jogos.

In "Pantagruel", chapter XVIII, it is said that Panurge plays two of these games.

Numerais gregos no Rithmomachia

2009-06-26T06:46:00.000-07:00

Aqui.

Bridge is good for you

2009-06-12T14:47:00.000-07:00

Even if you are not young. NYT article, here.

2009-04-28T02:39:00.000-07:00

First printing of rules for the lottery game Chronicon Cameracense et Atrebatense, sive historia utrisque ecclesiae, III libris, ab hinc DC sere annis conscripta. Nunc primum in luce edita, & notis illustrata Per G. Colvenerius.
BALDERIC LE ROUGE.
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Book Description: Douay, Ioan. Bogarde, 1615., 1615. Sm.8vo. Contemp. vellum. With engraved printer's vignette on title, 9 engraved illustrations of seals and dice in text, and 3 large folding plates, 2 in woodcut and 1 engraved, showing three different playing boards for a lottery game. (40), 601, (1 blank, 16) pp. Rare first edition of a medieval chronicle of Cambray and Arras, containing also the first printed description and illustration of a lottery game, invented by Wibold, a French divine from Cambray who died in 965. Inspired by the "Rythmomachia" or "Philosophical Game" of Pythagoras, the game was called by Wibold "Ludus regularis seu clericalis", but it was also known as "Alea regularis contra alea secularis". It was played with a dice with letters instead of numbers and a playing board with the names of 56 virtues arranged in squares around the centre. At the end of the book 3 different playing boards are shown to play the game, two with square boards to be played with dice, and one circular board to be played as a wheel of fortune with a turning pointer in the middle. On verso of the two woodcut plates explanatory text is present, and the game is extensively explained in chapter 88 of the first book, pp. 143 ff., and is further discussed in the notes at the end, on pp. 461 ff. The folding plates, sizes ca. 42 x 37 cm, were meant to be cut and mounted and to be actually played with, including the engraved figures of dice, which should also be cut and used in practise. In the text the list of names of the virtues and the figures on the dice are given as well. The chronicle itself is of interest too, written by the French historian Balderic the Red, bishop of Noyon and Tournay. The work presents numerous accounts of scholarly research and curious historical details, covering the period from Clovis to 1090. The author died in 1097. But the most important is today the first description and illustration of the lottery game in print, which according to the inventor could be used at schools or played for charity. The importance of this chronicle was discovered in 1834 by Le Glay, who published a new text-edition based on three manuscipts, and in the preface he discussed and explained the lottery game found in it. This new Latin edition then was also translated into French in 1836, by Faverot and Petit. But our copy is from the very rare early 17th century 'editio princeps'. Good copy, with ms. note on bottom of title: "Dono Compilatoris".- (Old owner's ms. notes on first blank; sl. browned; sl. traces of use). Brunet I, 621; Graesse I, 260; cf. Introduction to the new edition by Le Glay, Cambray & Paris, 1834; NUC lists one copy only. Bookseller Inventory # 17310

George Berkeley plays games!...

2009-02-02T16:18:00.000-08:00

Jogos de quê?

2009-01-25T13:11:00.001-08:00

Francisco Cervantes de Salazar (ver M. C. Díaz y Díaz; Aires A. Nascimento; J. M. Díaz Bustamante; M. I. Rebelo Gonçalves; J. E. Lopez Pereira; A. Espírito Santo, Hislampa. Autores latinos peninsulares da época dos Descobrimentos (1350-1560), Lx: INCM, 1993: pp. 271-272) escreveu três obras sobre jogos, suspeito que são todos jogos de bola mas... (as traduções dos títulos que dou podem ser bastante disparatadas porque não faço ideia da descrição do jogo:
O primeiro tem por título Obeliscorum sive lignearum pyramidularum ludus (jogos dos obeliscos ou pirâmides de madeira)
O segundo: Pilae palmariae ludus (joga da bola de palmeira (coco?)
O 3º Saltus, Ludus sphaerae per anulum ferreum (Dança, jogo de meter uma esfera no anel de ferro)
segundo inventário acima citado só se encontram na British Library (cota: 10480.ee.3)

http://chessderivatives.blogspot.com/

2009-01-14T09:15:00.000-08:00

RYTHMOMACHIA

The mayor chess variant
through the years 500 to 1,800

During the investigation of the Subject Rythmomachia,
the editor has substantially added new material during the year 2004 to
text as below, and specifically the two first paragraphs

BALDERIC LE ROUGE.

Chronicon Cameracense et Atrebatense, sive Historia utrisque Ecclesiae, III Libris, ab hinc DC sere annis conscripta. Nunc primum in luce edita, and notis illustrata Per G. COLVENERIUS.

Douay, Ioan. Bogarde, 1615. Contemporary vellum.

With engraved printer's vignette on title, 9 engraved illustrations of seals and dice in text, and 3 large folding plates, partly in wood cut and partly engraved, of three different tables for a popular lottery game.

Editio princeps of a mediaeval chronicle of Cambray and Arras, containing the earliest known description and representation of a lottery game, which had been invented by Wibold, a French divine from Cambray who died in the year 965.

Inspired by the "Rythmo-machia" or "Philosophical Game" of Pythagoras, the game was referred to by Wibold as "Ludus regularis seu clericalis". However, it was also known as "Alearegularis contra alea secularis".

It was played with a dice with letters instead of numbers, and a board with the names of all 56 virtues arranged in squares around the middle.

At the end of the book three different tables are given to play this game, two with square boards to be played with dice, and one circular board to be played as a wheel of fortune with a turning pointer in the middle.

On verso of two of these tables explanatory text is present, and the game is extensively explained in chapter 88 of the first Book and is further discussed in the notes at the end on pp. 461 ff.

The folding tables, size ca. 42 x 37 cm, were meant to be cut and mounted to be played with, including the engraved figures of dice. In text the list of names of the virtues, and the figures of dice were given too.

The chronicle itself is of interest, written by the French historian Balderic the Red, bishop of Noyon andTournay, as it gives numerous accounts of scholarly reseach and curious details.

The book presents the history from Clovis to 1090, as the author died in 1097. The outstanding feature now is the representation of a mediaeval lottery-game, which according to the inventor could be of use at schools or for charity ( Lottery games initially are invented and used to draft new militairy-personnel and create money).

The importance of this chronicle was rediscovered in 1834 by Le Glay,who published a new edition based on three manuascipts, and in the preface discussed and explained the lottery game present in it.

His Latin edition then was also translated into French in 1836, by Faverot and Petit

Firs edition, with the bookplate of Pierre Briffaut.- (Ms. entry on title) Brunet I, 621 Graesse I, 260 cf. Introduction to the new edition by Le Glay, Cambray & Paris, 1834 NUC.

New data pertaining to -integral change txt

RHYTHMOMACIE

Geschichte & Literatur des Schachspiels, (prof.) Antonius van der Linde (curator & chess literature collector from NL / DE), 1874 original, reprint in German 1981.

RHYTHMOMACIE, Rhythmomachya, Victoria Ritmachie;
Notation Parlante / Figurines
Hippogonal (round) - use Pawns - name: Rotundi
Diagonal - use Couriers - name: Trigoni
Orthogonal - use Rook - name: Tetragoni
(rook = pyramid)

Array notation on 8*16 board

..PPPP..
BBPPPPBB
QQBBBBQR
QQ....QQ

Based on the *old system* of moves of the chess game.
Translator Barozzi states that chess has been developed from
Rythmomachy, since it is older. However the original Greek
transcripts have never been found.

Other variant::

METROMACHIA ; Metromaxia ; Sive Ludus Geometricus.

Board with 53*33 squares, the figurines are geomatrical.

Rythmomachia
===========

Equipment::

The Rhythmomachy board is rectangular.

Generally 8 squares wide by 16 long. Each player begins with his men arrayed on one of the short ends.

In some descriptions, the board is shorter (8 x 14) or even 8 x 9, but the 8 x 16 arrangement seems to be most common.

It is unclear whether the board became checkered or not; there is no intrinsic reason why it should be, and most of the historic images don't depict checkering, but a few do.

We assume that both the size and the occasional checkering resulted from the fact that the game is easy to play on two chessboards, set side-by-side; since chess was quite common in pretty much all cultures that had Rhythmomachy, this was likely a common way to play.

The checkering with chessboard was introduced during the years 1,000 - 1,300, and also was introduced the longer range of some or the pieces (easier to move long distance). The black sheckered fields depict the grainfields and the historic chessboard was the city of Babylon.

Thus, the checkering was probably an accident of that, and the board size standardized on the convenient double-chessboard.

Array::

Each player has 24 men, eight round, eight triangular, and eight square.

Each man has a number on it; the rationale behind the numbers is discussed below.

Rhythmomachy is unusual in that it is an "asymmetrical game" --
although each player has the same number of pieces,
the numbers written on those pieces differ widely.

We usually think of one side as "even", and the other "odd", but the reality is more complex than that.

The two sides have contrasting colors, usually but not always black and white.

We usually play black as odd and white as even out of habit, but that is a semi-arbitrary choice, based on the illustrations in Fulke.

On average, the odd numbers are significantly higher than the even numbers.

The men are usually flat, and double-sided, with the same number in the opposing color on the opposite side.

For my personal sets, we paint the edges of the men with the color of the side they start on, to make them easier to sort for setup.

The Numbers on the Men on each side fall into six "ranks": two ranks of circles, two of triangles, and two of squares. Each rank contains four men on each side. The actual numbers come from straight forward mathematical progressions.

The first rank of rounds can be thought of as the "seeds" for the rest; they are the odd or even numbers less than ten. That is, the evens have 2, 4, 6, and 8; the odds have 3, 5, 7, and 9. Since each rank has four men, each of those flows from a particular seed. (Thus, for the first rank of squares on the even side, one man is based on 2, one on 4, and so on.)

The second rank of rounds are the first rank of rounds squared; thus, on the even side, they are 4, 16, 36, and 64, and on the odd are 9, 25, 49, and 81.

The first rank of triangles are the two rounds added together; thus, on the even side, they are 6 (2 plus 4), 20, 42, and 72, and on the odd are 12, 30, 56, and 90.
The second rank of triangles are the seed plus 1, squared. Thus, on the even side they are 9 (2 plus 1 squared), 25, 49, and 81, and on the odd are 16, 36, 64, and 100.

The first rank of squares are the two triangles added together. Thus, on the even side they are 15 (6 plus 9), 45, 91, and 153, and on the odd are 28, 66, 120, and 190.

The second rank of squares are twice the seed, plus one, squared. Thus, on the even side they are 25 ((2*2)+1, squared), 81, 169, and 289, and on the odd are 49, 121, 225, and 361.

Summarizing all of that into a table, we get::

Evens
Odds
1st Rounds (x)
2
4
6
8
3
5
7
9
2nd Rounds (x2)
4
16
36
64
9
25
49
81
1st Triangles (x + x2)
6
20
42
72
12
30
56
90
2nd Triangles ((x + 1)2)
9
25
49
81
16
36
64
100
1st Squares (x + x2 + (x + 1)2)
15
45
91
153
28
66
120
190
2nd Squares ((2x + 1)2)
25
81
169
289
49
121
225
361

The Kings::

On each side, one square is replaced by a "King" instead. The king is a large number which happens to be a sum of some square numbers, and takes the form of a pyramid of pieces.

On the even side, the King is the 91, and is composed of a pyramid of six pieces: a square 36, a square 25, a triangular 16, a triangular 9, a round 4, and a round 1. On the odd side, the King is the 190, and is composed of a pyramid of five pieces: a square 64, a square 49, a triangular 36, a triangular 25, and a round 16.

The Kings are generally treated specially: in most variants, they have enhanced powers of movement, and capturing the opponent's King is at least part of the objective of the game. Usually, the King can be captured intact or piecemeal, capturing its component pieces out of the pyramid.

Details vary from version to version, however.

Play::

Since each variant is a bit different, I will only speak in broad generalities here. Roughly speaking, movement happens by turns, as in most board games; each player gets to make one move on his turn.

The three shapes move differently; in general, the squares move furthest and the rounds move least.

Movement is never affected by the number on a piece -- the numbers are relevant mainly for capture.

While each version has a couple of degenerate captures (eg, surrounding a piece completely), capture is generally done mathematically.

The details of this vary greatly, but in general you capture opposing pieces by creating mathematical relationships between those pieces and your own. For example, if two of your men are positioned by an enemy man, and they add up to his value, they capture him. Note that capture frequently does not require actually jumping into the enemy's space, as Chess does; you can often capture simply by setting the position up.

In most versions, captured men can then be subverted; when you capture the man, you flip him over (so that your color shows), and re-enter him on your side. This is essential in some cases, since most numbers exist only on one side or the other.

Mathematical Proportions::

There are many different kinds of mathematical relationships that can figure in Rhythmomachy. we assume that the reader is capable of dealing with basic arithmetic: addition, subtraction, multiplication, and division.

These will serve you fine in most of the basics of the game. But for the more advanced versions of the game, and for the higher victories, you need to understand the three major forms of Proportions:

Arithmetic, Geometric, and Harmonic

Don't worry about learning these upfront; they can come later. Also, all of the proportions available in the game are available as tables in Fullke's book, the period source from which we took these reconstructions. It is common to look up the proportions in tables, especially at first.

In general, all of these proportions are ways of defining a relationship between three numbers. In all of these examples, we will talk about three numbers A, B, and C, where A is the smallest number and C the largest. we will give examples for each, as well.

Arithmetic Proportion::

Three numbers are in arithmetic proportion when the difference between A and B is the same as the difference between B and C. For example, the numbers 2, 4, and 6 form an arithmetic proportion, because (4 - 2) = (6 - 4). Similarly, 5, 25, and 45 form an arithmetic proportion, because (25 - 5) = (45 - 25).

In other words, the numbers are rising in a simple progression, adding the same number each time. 5 plus 20 is 25; 25 plus 20 is 45; so 5, 25, and 45 form an arithmetic proportion. Another way to think of it is that there is a number X, such that (A + X) = B, and (B + X) = C.
There are 49 arithmetic proportions available among the numbers in Rhythmomachy, according to Fulke.

Geometric Proportion::

This is similar to arithmetic proportion, except that instead of adding the same number to go from A to B and B to C, you multiply instead. That is, the ratio between A and B is the same as the ratio between B and C. Similar to the last concept above, there is a number X, such that (A x X) = B, and (B x X) = C.

So for example, 3, 12, and 72 are in geometric proportion, because (3 x 6) = 12, and (12 x 6) = 72. 2, 4, and 8 are in geometric proportion, because (2 x 2) = 4, and (4 x 2) = 8. A more sophisticated example would be 4, 6, and 9, which are in geometric proportion because (4 x 1.5) = 6, and (6 x 1.5) = 9. (Yes, this is a period example; they understood fractions perfectly fine.)

There are 27 geometric proportions available in Rhythmomachy, according to Fulke.

Harmonic Proportion ::

Harmonic, (or Musical in many period sources) proportion refers to the way that musical harmonies relate to each other. Mathematically, it is the relationship (C / A) = ((C - B) / (B - A)) -- the ratio between the largest and smallest numbers equals the ratio of the differences between both of those numbers and the middle one.

So for example, 3, 4, and 6 are in harmonic proportion, because (6 / 3) = 2, and ((6 - 4) / (4 - 3)) = 2 as well. Or 25, 45, and 225, because (225 / 25) = 9, and ((225 - 45) / (45 - 25)) = 9 also.

There are 17 harmonic proportions available in Rhythmomachy, according to Fulke.

Example proportions: 2 3 4 6

Arithmatical 2 3 4
Musical 2 3 6
Geometrical 3/2 = 6/4 (old system, before zerro)

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Rithmomachia, the Philosophers' Game::
A Medieval Battle of the Numerical Harmonies

Therefore a Arithmomachia is the "battle of the numbers", or better still the "battle of the numerical harmonies", referring therefore to the substance of the game that is, like we will see, that one to create of the numerical proportions between numbered pawns.

Game privileged from medieval the intellectual class, is known also with the expression of ludus philosophorum ("the game of the intellectuals").

Objective of the game it is to construct with the own pawns one or more proportions (or "harmonies") numerical, therefore to realize a "triumph".

When the triumph happens through a capture (v. over), is worth the classic rule for which the capturing pawns they must be found to the debita distance of movement from that adversary.

Different is the situation if the pawns belong already all to the player.

In the first place, the triumph must be realized in the half opposing chessboard; moreover, not be a matter itself of a capture, the distance of movement of the pawns does not have value.

Then, because a harmony of three pieces is valid, they must find themselves online (horizontal, vertical or diagonal) in adjacent cases or to form three you concern us of a side square three cases.

For the harmonies of four pieces, they must obligatorily form the four concern us of a side square three cases.

1. Introduction

'A knowledge of the battle of numbers is a source of enjoyment and of profit.' John of Salisbury stated this praise in his Policraticus (I,5) in 1180, when reporting about the use and abuse of games.

When the medieval scholar talked about this competition of numbers, he meant Rithmomachia, which he got to know as a useful and pleasant teaching aid for arithmetical lessons. This game had spread from monastery schools in southern Germany to England. (Evans 1976)

What kind of game is it that John of Salisbury highly praises? What made him and other people talk about Rithmomachia so long ago, after it had been almost forgotten after a prime of about 700 years?

Roger Bacon also recommended Rithmomachia to his students in his 'communio mathematica' (I, 3,4) in the 13th century. He listed seven points on how his students should learn their arithmetics according to Boethius, and at the end he advised that they use the game Rithmomachia as a teaching aid.

As Thomas More was convinced of the good character of the game, he let the fictious inhabitants of 'Utopia' (1516. II,5) play it for recreation in the evening hours.

As well Robert Burton regarded the use of Rithmomachia as an efficient cure for melancholy, because it is a good exercise for the human spirit. (The Anatomy of Melancholy. 1651. II,4)

The name of the game is of Greek origin.

The first part 'Rithmo-' is derived from a combination of arithmos and rhythmos. Arithmos means number and rhythmos had, besides rhythm, also the meaning number and proportion of numbers in the Middle Ages, because not only is the game about the numbers on the pieces, but also about the relation between numbers.

The second part of the name '-machia' comes from machos, which means battle. Therefore Rithmomachia can be described as a 'battle of numbers'. In England the game was also known as the 'Philosophers' Game'.

Rithmomachia is a strategy game for two players. A black and a white party of numbers face each other, similar to chess.

There was a time when Rithmomachia was in competition with chess and was even more respected than chess, for example in some medieval treatises Rithmomachia was favoured. (Folkerts 1989) The reason was, that Rithmomachia was the only game in the curriculum of the mediaval schools and universities - an honour which chess had never received, because it was played as a tactical war game in the nobility for pure entertainment, but it did not suit the canon of the seven liberal arts. In Rithmomachia the aim is not to fight against each other with armies of numbers, rather to take part in a contest, where the players must bring some of their pieces into a harmonious order.

Contrasts between black and white, even and odd, equality and inequality develop and are in the end resolved into harmony. Especially the latter two pairs appear in the philosophy of numbers of Boethius, which dictates a selection of numbers on the pieces. (Borst 1990).

The Boethius number theory is based on the Pythagorean philosophy of numbers, which deals with classification, sequences, and figured presentation of numbers (figurative numbers), and the harmonical proportion between the numbers.

All of these features of Boethius' number theory recur in the game of Rithmomachia. Pythagoras' number symbolism, as a part of Boethius' philosophy of numbers, was of particular interest during the period of origin of Rithmomachia. The complete world order was searched for within and represented by this number symbolism. (Coughtrie 1984).

Rithmomachia was an entertaining way to memorize the number theory of Boethius. Basically, it was a pleasure to play Rithmomachia, the only game accepted by the Christian scientific community of the Middle Ages, because, unlike chess and dicing games, it was of great use.

2. The History of Rithmomachia

In many old records Boethius or Pythagoras were presumed as the inventors of Rithmomachia, however, they only created the mathematical basis of this game.

It is certain, that the oldest written evidence of Rithmomachia was found in Wurzburg around 1030. At a competition between the cathedral schools of Worms and W?rzburg, both well-known for their leading position at arithmetics, a disputational text was written with arithmetical sequences of numbers based on 'De institutione arithmetica' of Boethius.

On the basis of these writings a monk by the name Asilo created a game - Rithmomachia - which illustrated the number theory of Boethius for the students of monastery schools.
The first outline was adapted by other scholars.

Hermannus Contractus, respected monk in Reichenau, checked the rules of the game written by Asilo, enlarged them and added music theoretical remarks. At a school in Li?ge, they worked out a way of realising the game practically not only to enhance the game itself, but also to improve the training of the students in arithmetics. (Borst 1987).

In the 11th and 12th century Rithmomachia spread through monastery schools in southern Germany and France. There the rules were collected, ordered and summarised. The rules became more extensive, and sufficient enough to be played without a teacher.

Rithmomachia was an excellent teaching aid. Gradually it was also played by intellectuals just for pleasure. In the 13th century Rithmomachia spread through France and swept over into England. The mathematician Bradwardine and some of his colleagues wrote a text about Rithmomachia, and even in the pseudo-ovidian poem 'De vetula', Rithmomachia was highly praised.

Rithmomachia reached the greatest expansion at the time of book printing. The books written about Rithmomachia had various intentions. Faber (1496) and Boissi?re (1554/56), both professors of mathematics, wrote their treatises for their students at the university of Paris.

***********

The Philosopher's Game

This file is a transcription of a 1563 translation by William Fulke (or Fulwood -- the sources disagree) of Boissiere's 1554/56 description of Rythmomachy. It is entry 15542a in the Short Title Catalog of Pollard and Redgrave, and on Reel 806 of the corresponding microfilm collection.

Annotation will occur occasionally throughout; they will appear in square brackets and italics, [like this]. Spelling will be erratic; I'm transcribing quickly, so I will often be modernizing the spelling, but will leave original spelling whenever I consider there to be doubt about the meaning. I also will sometimes modernize the punctuation and paragraph breaks in the interests of readability. This is not intended to serve as a definitive critical edition, merely a working copy, good enough to understand the game.

[Title Page]
THE MOST NOBLE
ancient, and learned playe, called the Phi-
losophers game, invented for the honest re-
creation of students, and other [sober?] persons, in
passing the tediousness of time, to the release of
their labours, and the exercise of
their wittes.
Set forth with such playne precepts, rules and ta-
bles, that all men with ease may understande
it, and most men with pleasure practice it.
by Rafe Lever and augmen-
ted by W. F.
[Picture, probably stock, of two men playing at a game on a square 10x10 board.]

Printed at London by James Rowbothum, and are
to be sold at his shop under Bowchurch
in chepe syde.
[Page]

The Lord Robert Duddedlye.

[Picture of Lord Robert, with the motto "Vulnere virescit virtus" alongside.]

The Physiognomie here figured, appeares by Paynters Arte:
But valyant are the vertues that, possesse the inward parte.
Whych in no wise may paynted be, yet playnely so appeare,
& shine abrod in every place with beames most bright & clear.

[Page]

[The Epistle Dedicatory]
TO THE RYGHT HO-
norable, the Lord Robert Dudley, Mai
ster of the Queenes Maiesties horse,
Knight of the most honorable order
of the Garter, and one of the Queenes
maiesties privie Counsell, JAMES
ROUBOTHUM heartelye wisheth long life, with
encrease of godly ho-
nour and eternall
felicitie.
Sith that your honour is full bent,
(right honorable lord)
To wisdom & to godlines
with true faithful accord.

Sith that in deed you do delyte,
in learning and in skyll:
The show wherof doth well expresse
a perfect godly wyll.

Sith that also you have in hand,
affayres of force and waight:
And study do both day and night,
to set all thinges full straight.

[Page]

I thought therfore your honour should
not lacke some godly game:
Whereby you might at vacant times
your self to pastyme frame.

Whereby I say you might release,
such travailes from your mynde:
And in the meane while honest mirth
and prudent pastyme fynde.

Remembring then this auncient play,
where wisdome doth abound:
Called the Philosophers game,
me thinkth I have one found.

Which may your honour recreate,
to read and exercise:
And which to you I here submit,
in rude and homly wise.

Pithagoras did first invent,
this play as it is thought:
And therby after studies great,
his receation sought.

[Page]

Yea therby he would well refreshe,
his studious wery braine:
And still in knowledge further wade
and plye it to his gaine.

Accompting that a wicked play,
wherin a man leudely:
Mispendes his tyme & wit also,
and no good getts thereby.

But grevously offendes the Lord,
and so in steed of rest:
With trouble and vexation great,
on every side is prest.

Most games and playes abused are,
and fewe do now remaine:
In good and godly order as,
they ought to be certaine.

For why? all games should recreat,
the hevy mynde of man:
And eke the body overlayde:
with cares and troubles than.

[Page]

But now in stead of pleasant mirth,
great passions do arise:
In stead of recreation now,
revengings we practise.

In stead of love and amitie,
long discords do appeare:
In stead of trueth and quietnes,
great othes and lyes we heare.

In stead frendship, falshode now,
mixed with cruell hate:
We finde to be in playes & games,
which dayly cause debate.

Pithagoras therfor I saye,
to make redresse herein:
Invented first this godly game,
therby to flye from sinne.

Since which time it continued hath,
in Frenche & Latin eke:
Still exercisde with learned men,
their comforts so to seeke.

[Page]

Wherby without a further prose,
all men may be right sure:
That this game unto gravitie,
and wisdome doth allure.

Els would not that Philosopher,
Pithagoras so wyse:
Have laboured with diligence,
this pastime to devyse.

Els would not so well learned men,
have amplified the same:
From tyme to tyme with travell great,
to bring it into fame.

But let us nerer now proceed,
and come we to theffect:
And then shall we assuredly,
this pastime not neglect.

For it with pleasure doth asswage,
the heavy troubled hart:
And with lyke comforts drives away,
all kynde of sourging smart.

[Page]

The mynde it maketh circumspect,
and heedfull for to bee;
The tyme that theron is bestowd,
is not in vaine trulye.

The body it doth styrre and move,
to lightsomnes and ioye:
The sences and the powers all,
it no wyse doth annoye.

It practiseth Arithmeticke,
and use of number showth:
As he that is conning therein,
assuredly well knowth.

In Geometie it truly wades,
and therein hath to do:
A learned play it is doutlesse,
none can say nay thereto.

Proportion also musicall,
it ioynes with thother twayne:
So that therin three noble artes,
are exercisde certayne.

[Page]

What game therfore lyke unto this,
may gotten be or had?
There is not one that I do know,
the rest are all to bad.

It causeth no contention this,
nor no debate at all,
By this no hatred wrath nor guyle,
in any wise doth fall.

It stirreth not such troubles that,
our frend becomes our foe:
It moveth not to mischiefe this,
as many others do.

Let us avoyde the worst therfore,
and cleve we to the best.
So shall we shunne all wickednes,
and purchase quiet rest.

So shall we serve the living Lorde,
and walke after his will:
So shall we do the thing is good,
and flye that which is yll.

[Page]

So shall we live right christianlyke,
and do our duties well:
So shall we please both god & prince,
none shall us need compell.

And then the Lord of his mercie,
will prosper us alwayes:
And graunt us here to have on earth,
full many godly dayes.

Yea then the Lord of his goodnes,
and grace celestiall:
Will guyde and governe our affaires,
and blesse our doings all.

Which Lord graunt to your honour here,
good dayes & long to have:
with much encrease of helth & welth
and from all hurt you save.

Your honours most humble,
James Roubothum.

[Page]

To the Reader.
I Dout not but some man of severe judgement so soone as he hath one read the title of this boke wyl immediately sai, that I had more need to exhort men to worke, then to teach them to play, which censure if it procede not of such a froward morositie that can be content with nothing but that he doth himself, I do not only well admit, but also willingly submit my self therto. And if I could be persuaded that men at mine exhortation wold be more diligent to labour, I would not only write a treatise twise as long as this, but also thynke my whole time wel bestowed, if I

[Page]

did nothing els, but invent, speake, and write that which might exhort, move, & persuade them to the furtherance of the same. But if after honest labour and travell recreation be requisit, (and that nede no further probation because we favour the cause wel inough) I had rather teach men so to play, as both honestye may be reserved, their wittes exercised, they them selves refreshed, and some profit also attayned, then for lacke of exercise to see them either passe the tyme in idlenes, or els to have pleasure in thyngs fruitles and uncomely. And if great Emperours and mighty Monarches of the world have not bene ashamed by writing bookes to teaches the art of Dyce

[Page]

playing, of all good men abhorred, and by all good lawes condemned: have I not some colour of defence, to teache the game, which so wyse men have invented, so learned men frequented, and no good man hath ever condemned.

The invention is ascribed to Pythagoras, it beareth the name of Philosophers, prudent men do practise it & godly men do praise it. But because many herein (as in a play) have challenged much authoritie, they have filled this game with much diversitie. In which as I could perceive the most differens of playing to consist in thre kindes, so have I playnly and briefly set them forth in Englishe not as though there might not more diversities be espied, but

[Page]

that I thought these to them whom I have written to be sufficient. yet for that I woulde be lothe, from playe & game, to fall to earnest contention, if any man in this doing or any part thereof shall think I have done amisse, and will do better himself, so far am I from envying his good proceding, that I wil be right glad, and geve him heartye thankes therefore.

All things belonging to this game
for reason you may bye:
At the bookeshop under Bochurch
in Chepesyde redilye.

[Page]

The bookes verdicte.
Wanting I have bene long truly,
In english language many a day:
Lo yet at last now here am I,
Your labours great for to delay,
And pleasant pastime you to showe,
Mynding your wits to move I trowe.

For though to mirth I do provoke,
Unto Wisdome yet move I more:
Laying on them a pleasant yoke,
Wisdom I meane, which is the dore,
Of all good things and commendable:
Dout this I thinke no man is able:

CATO
Interpone tuis interdum gaudia curis:
Yt possis animo quemuis sufferre laborem.

[Page]

The diffinition
That moste auncient and learned playe, called the Philosophers game, beinge in Greeke termed [...], is as much to saye in Englishe, as the battell of numbers. Numbers be either even or odde, wherefore the even parte is against the odde, either parte havinge a kyng, whych being taken of the adversaryes part, and a triumphe celebrated within his campe, the game is ended.

Of diverse kyndes of playinge.
Amonge the dyverse kyndes of playing thys game, we shall sette forth three sortes, of which the reader maye chose whether of them he lyketh beste. And of all those three, we shall

[Page]

gyve suche shorte and easye rules, that no man (althoughe he were altogether ignoraunt in Arithmetike) shall fynde the game so hard, but that he may learne to playe it.

Of the partes of thys Game.
He that wyll learne thys game, any of the three waies, muste first be enstructed of these sixe partes.

The table as the fielde
.2. the menne and the numbers of them as the hoste
.3. the placynge of them, as the encampynge
.4. the order of playe and removynge the men, as the marchynge and fyghtynge
.5. the manner and lawes of conqueryng and taking
.6. and last of al the triumphe after the victorye.
Of these partes in the fyrst kynd of playng.
[Page]

The table muste be a playne borde conteynynge .128. squares that is .8. in breadth and .16. in length sette forthe in two dyverse collours. Or for a plainer understandynge, the table is a doble chesse bord, as it were two chessebordes joyned together, the length of twoo, the breadth of one, whereof thys is an example.

[Page]

[Complex picture, showing a 16x8 checkerboard, with various letter and symbols on various parts. This can't be fully represented in text, so I won't try to show the whole thing now. The middle section -- rows 6 through 12 -- have letters on them, and look somewhat like this:]

K L M
X F Z
B S C
R H Y A T I N
E V D W
G
Q P O

[Later sections will refer back to this table frequently, to describe movement.]

[Page]

Of the men.
The men be in number .48. Wherof .24. be of one side & must be knowen by one colour, and .24. on the other syde, whyche also must be marked with a contrarye colour, as White and Blacke, Blew and Redde, or what colours els you lyke best. But in the colering there .3. thinges must be observed, the bottome or lower part of every man (excepte the two kinges) muste by marked wyth his adversaries colour, that when he is taken, he maye chaunge his coate and serve him unto whome he is prisoner.

The seconde thinge considered in the men, is their fashion: for of euther syde .8. are rounds, other .8. are triangles & .7. (the king making .8.) are squares. There fashion is such [small inset showing roundes, triangles, squares].

The kynges because they consist of all three sortes, as it is knowen by the learned speculation of the numbers, beare

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the fashion of all thre kindes, his foundations are two squares, on which are sette, two triangles & upon them rounds. But this difference is betwene the kinges, the king of the even numbers, hath a pointed toppe, the king of the odde numbers is not pointed, the cause dependeth upon the consideration of these numbers by which they arise into piramidall fashion. The third thing considered in the men, is the number that must be written or graven upon them which to learne plainely for practise marke these short rules.

There be of eche kynde of men, two rankes or orders.

The first ranke or order of roundes be the digites even or odde namely of the even .2.4.6.8. of the odde .3.5.7.9.

The second order of rounds are found by multiplyinge these digites by themselves as .2. times .2. is .4.3. times .3. is .9. Of the even they be .4.16.36.64. of the odde they be .9.25.49.81.

The first order of the triangles are found by addinge two of the roundes together

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one of the firste order and another of the seconde order, as .2. and .4. make sixe .3. and .9. make twelve, on the even syde they are these .6.20.42.72. on the odde syde .12.30.56.90.

The second order of triangles be made by addynge one to every one of the first order of roundes, and then multiplying that number in hym selfe: as .2. is one of the firste order of roundes, thereto adde one, that is .3. then .3. tymes .3. is .9. a triangle of the seconde order, on the even syde. Likewise to thre a round on the odde side, adde .1. so it is .4. then .4. tymes .4. is .16. On the even parte, they be .9.25.49.81. on the odde parte .16.36.64.100.

The first order of squares (in whyche are contayned the kynges) be made by addynge two triangles together, one of the fyrste order, and another of the secondes, as .6. and .9. make .15. likewyse .12. and .16. make .28. Amonge the even they be .15.45. and .91. the kynge .153. amonge the odde they be .28.66.120. and .190. the kynge.

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The last order of squares be found, by dobling of every one of the firste order of roundes, and after adding one, last of all be multiplying that number in itself, as twise .2. is .4. and .1. added is .5. so .5. times .5. is .25. likewyse twyse .3. is .6.1. added is .7. then .7. tymes .7. is .49. These be on the even syde .25.81.169.289. And of the odde syde .49.121.225.361.

These numbers must be sette uppon the men both on the upper side, & also on the nether side. Except one of the kynges, which must with the whole number of their pyramid, be marked, onely on the bottome. Because the sydes muste have other numbers, namely the highest point of the even kyng, must have .1. the rounde next under him marke with .4. the uppermost triangle with .9. the nethermost with .16. The uppermost square muste have .25. The nethermost square shall have .36. The king of the odde upon his head, whiche is a rounde, not pointed hath .16. upon his first triangle .25. on the second triangle .36. uppon the fyrste square .49. upon the lowest square .64.

[The numbers in the next paragraph are in circles and triangles, to illustrate.]

Finally it shalbe good for the avoydance of confusion, to drawe a line under every number. Ells may you take one for another, as 6 the even round & 9 the odde rounde, may be taken one for another with oute this lyne or some suche marke, lykewise 6 and 9 Tryangles bothe of one syde. And this sufficient for the men, the fashion, colours and numbers.

The reason of these numbers and the knowledge of their proportione.
For them that seke the speculation of these numbers, rather then the practise for playing, and have some sight in the sciens of Arithmetike, some thyng must be sayde of proportion. For this purpose there be three kyndes of proportion. Multiplex, superparticuler, and superpartiens.

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Of multiplex.
MULTIPLEX proportion, is when a great number conteyneth a lesse number manye tymes, and leaveth nothing, as .8. conteyneth .2. fower tymes and nothing remaineth .16. conteyneth .4. &, this proportion semeth best to agree with roundes because the one number conteyneth the other and nothynge remaineeth as the fyrste order of roundes be.

[The following table shows the white (even) and black (odd) rounds.]

2 4 6 8
3 5 7 9

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The second order be these.
[This table shows the first and second orders of rounds for both sides.]

double. quadruple. sextuple. occuple.
2 4 6 8
4 16 36 64 proportion.

triple. quintuple. septupl. nonuple
3 5 7 9
9 25 49 81

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Of superparticuler proportion.
Superparticuler proportion is when a greater number contayneth a lesser with one part of it, which may measure the whole, as .12. contayneth .9. and .3. whiche is a thyrde parte of nine .6. contayneth .4. and .2. that is one halfe to .4. Thys proportion beinge the cheife, next unto multiplex, is beste figured by a trianguler forme, whyche hathe fewest lynes and angles next unto a circle. For the manner of thys proportion consider thys figure.

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[This table shows each base number above two rows of triangles, and appears to be badly fouled up. I believe the rows of base numbers are wrong -- the first set should be the evens (2, 4, 6, 8), and the second the odds (3, 5, 7, 9). That would make each Latin header match the number below it, the first row of triangles would be the superparticulates for that base number, and the second row would be the second order of triangles for that base number, which is (x+1)2.]

sesquialter. sesquiquart sesqui.sext sesqu.oct.
3 5 7 9
6 20 42 72
9 25 49 91

sesquiter. sesquiquint. sesquisept. sesquinona.
4 6 8 10
12 30 56 90
16 36 64 100

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Superpartiens proportion.
The superpartiens proportion is when the greater number conteyneth the lesser and mo partes of it then one as .15. conteyneth .9. and .6. whiche is two thirdes of .9. lyke wyse .28. conteyneth .16. and .12. that is 3/4 of .16. This proportion conteineth divers parts beside the whole number therfore is wel figured in the square, which also conteyneth more corners and sides. For the maner of their proportion consyder thys table.

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The first order of squares.
[The following table contains the two rows of triangles, with the corresponding square beneath.]

6 20 42 72 supparticulares added
9 25 49 91
15 45 91 153 being the squares.

12 30 56 90
16 36 64 100
28 66 120 190

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The second order followeth.
third fyft seventh ninth
5. 9. 13. 17. These two rows are just plain numbers.
10. 36. 78. 136.
15 43 91 153 These two rows are the two white orders of squares.
25 81 169 289
superbipartiens tertias supquadrupartiens quintas supsextupartiens septimas supoctupartiens nonas

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fourth sixth eight tenth
7. 11. 15. 19. These two rows are just plain numbers.
21. 55. 105. 171.
28 66 120 190 These two rows are the two black orders of squares.
49 121 225 361
supertripartiens quartas supquinpartiens sextas supseptupartiens octavas supnonpartiens decimas

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Of the kings.
[Image of the two kings. Each is a pyramid of numbered pieces, with two squares, two triangles, and a round; one has a little triangular "cap" on top. The images make it look like higher-numbered pieces are actually larger -- I wonder if this is true...]

The kinges conteine in them suche numbers, as beyng all added together, make the whole piramidall number, the lowest square of the even is .36. which riseth of the multiplying of .6. in it selfe. The next square that must be lesse, is .25. arisinge by the multiplyinge of fyve in it self and so followeth .16. of .4. then .9. of .3. laste .4. of .2. and single .1. all these added together make up .91. After the same maner consisteth the king of adde. The lowest square is .64. arisinge of .8. multiplied in himselfe. The next .49. of

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.7. times .7. then .36. of .6., .25. of .5. and .16. of .4. these numbers make the whole pyramidall number .190. which because it riseth not to the poynct of one, oughte not to be sharpe poyncted, as hathe beene sayde before.

Of the placing, encamping or setting in araie.
To retorne againe to the plaine and easye playing of this game, next to the armie & their armour, follow ether the order of their battel or encamping. Which because it is more playne and easely seen which the eye, then learned by the eare, I referre thee unto the table where the battell is appoynted in suche order as thys kynde of playe requireth.

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[The table below shows the layout of the board. To illustrate this through text, I put squares into square braces, triangles into angle brackets, and rounds into parentheses. Kings are signified with an asterisk. Note that the top half, the evens, should be upside-down.]

[25] [81] [169] [289]
[15] [45] <25> <20> <42> <49> [91]* [153]
<9> <6> (4) (16) (36) (64) <72> <81>
(2) (4) (6) (8)

(9) (7) (5) (3)
<100> <90> (81) (49) (25) (9) <12> <16> [Error in original: 2 instead of 12]
[190]* [120] <64> <56> <36> <30> [66] [28]
[361] [225] [121] [49]

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Of the marchinge or removing of the men.
The battell beyng duely placed, it followeth next, to know the maner of marching & removing, for every kynd of men, hath their proper kynde of motion, and fyrste we muste speake of the roundes.

The motyon of the roundes.
The roundes muste move into the space that is next unto them cornerwyse, as in the table, from the space .A. to any of these .B.C.D. or .E.

[Yes, this is clearly saying that rounds only move diagonally.]

Of the triangles.
The triangles passe three spaces counting that in which they stande for one, and that into whych they do remove for another, that is leaping over

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one space. As from the space .A. he maye remove into any of these space .F.G.H. or .I. this is the motion of the triangle in marchying or takyng. But in flying he maye remove the knyghtes draught of the chesse, as from .A. into .X. or .W. &c.

Of the Squares.
The Squares remove into the fourth place from them, that is leaping over two, right forwarde or sydelong, as from the place of .A. to any of these spaces .L.N.P.R. flyinge they maye remove after the knyghts draught, but that they must passe foure spaces, as from .P. to .Y. or .T. &c. And this for the marchinge and removyng of the men, where note, that with theyr flying draughte they can take no man, but if needed by helpe to besiege a man.

Of the kynge marching.
The kings because thei beare the forme of al the thre kynds, may remove any

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of all theyr draughts when they list, into the nexte with the rounde, into the thyrde with the triangle, and into the fourth with the square, and finally in all poyntes lyke the Queene at the Chesse, saving that he can not passe above foure spaces at the most.

Of the maner of taking.
The men may be taken sixe wayes, namely by Equalitie, Oblivion, Addition, Subtraction, Multiplication and Division, and also if you wyll, and so agree by

/ Arithmeticall.
Proportion <> <42> <20> <6{r}>
<81> <56> <30> <12>

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The seconde order of triangles, have all excepts one (whiche is the number of .100.) their cossicall signes, as .9. bothe of the roote and of the quadrate, .25.36. and .49. have the signe of the quadrate .64. of the quadrate and the cube, and also the quadrat of the cube .16. and .81. of the quadrate, and the foure squared quadrate.

<81{24}> <49{2}> <25{2}> <9{r2}>
<100> <64{236}> <36{2}> <16{24}>

In the first order of squares, onely .15. is marked with the roote, all the rest doe want theyr cossicall sygnes in thys game.

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[A rather odd little illustration here, showing the two kings in some detail, with each constituent pieces marked both with its number and the square root of that number, and the complete number of the king on the top. Also, a couple of odd little images of a round and a square with a peculiar symbol on top; this symbol may be peculiar to king components. Note also that, in the table of squares below, the 91 and 190 have a picture of the king on them.]

[153] [91] [45] [15{r}]
[190] [120] [66] [28]

The seconde order of squares hath .3. numbers marked with cossicall signes, that is .25. and .225. wyth the signe of the quadrate .81. is marked with the sygne of the quadrate and the fouresquared quadrate.

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[289] [169] [81{24}] [25{2}]
[361] [225{2}] [121] [49]

And thys have you all the men that be marked with cossicall sygnes.

The setting in aray.
The teachers of this kynde of playing, doe not so well allowe, the former kynde of placing or any other, as the naturall placing of every man under him of whome he aryseth. So thei conteyne .6. ranks in length, extending to the furthermoste edge of the Table after this sorte.

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[Note that, in this table, the odds are colored black, while the evens are left white.]

[361] [225] [121] [49]
King [120] [66] [28]
<100> <64> <36> <16>
<90> <56> <30> <12>
(81) (49) (25) (9)
(9) (7) (5) (3)

(2) (4) (6) (8)
(4) (16) (36) (64)
<6> <20> <42> <72>
<9> <25> <49> <81>
[15] [45] King [153]
[25] [81] [169] [289]

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The marching or moving.
The men maye remove every way, into voyde places, forwarde, backewarde, towarde both sydes, direct or cornerwyse. So that the rounde men remove into the next space, the triangles into the third place, and the squares into the fourth place, accompting that place in which they stande for one.

Also every man savyng the two kynges to besiege his enemie, or to flye from the siege himself, may remove the knights draught in chesse, but neither take anye man (except it be by siege) nor erect a triumphe by suche motions. The kynges move even as squares, but that they have not the flyinge draughte.

It is compted lawefull amonge suche as wyll to agree, that the Triangles and Squares, maye remove into voyde places, thoughe the spaces betwene be occupyed of other men.

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The maner of taking.
The men may be taken seven ways by Oblivion, by Equalitie, by Addition, by Subtraction, by Multiplication, by Division, and by Cossicall Sygnes.

Of takynge by Oblivion.
All men maye be taken by Oblivion when by foure men they be letted of theyr ordinarie draughte, as hath bene taught before.

Of takynge by Equalitie.
By Equalitie maye these men take or be taken, as hathe bene sayde before, .9.16.25.36.49.64.81., as yf after you have played your .9. stande in

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your mans draught, you may take him by not removing into his place, unlesse you espye him standing in your draught before you playe, then muste you take him up and remove into his place.

Of takynge by Addition.
The takyng by Addition is all one with the first kynde of play, in all respectes, saving that some require the men that shoulde take by Addition to stande in the next spaces to him that is taken, either directly, or cornerwyse, but the former waye is better.

Of taking by Subtraction.
That whiche was sayde in the first kinde of subtraction and that whiche was last sayde of Addition may be bothe referred together. For this subtraction

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differeth not from the former, but for the opinion of them, that would have the two takers stande onelye in the nexte spaces to him that is taken.

Of takyng by Multiplication.
Takyng by multiplication doth differ. For in this kynde of playng, it is thus. When your man standeth so, that beyng lesser than your adversaries man, you may multiplie your man by the voyde spaces betwene them, and the product is all one with the adversarye, you maye take hym upm not removynge into his place, except you espye hym so, before you remove your man.

Of takynge by Division.
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Lykewise by Division, yf your man beyng greater then the adversarye, stande so, that beyng devyded by the voyde spaces, the quotient is all one with the adversarye, you maye take hym up, not removyng into hys place, unlesse you see hym so standynge before you drawe.

Of taking by Cossicall signes.
By Cossicall sygnes anye man that hath these signes, {2}.{3}.{4}.{6}. meeting with his roote in his ordinary draught that hath this signe {r} taketh him up, or elles is taken of him, without removing into his place, except he maye take him before he remove.

Of the kynges, and their taking.
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The king of the even must be foursquare, havyng sixe steppes, every one lesser then other, on one syde he muste have on him these rootes .1.2.3.4.5.6. on the other syde the quadrates arising of these rots, that is .1.4.9.16.25.36.

The king of the odde men, muste have but fyve steppes, that is .4.5.6.7.8. lackyng the rootes that he can not ende in .1. The quadrates of hys rootes by these .16.25.36.49.64. These muste be so set on, that the least must be hyghest and the greatest lowest.

The kinges be taken by Oblivion, or yf theyr Pyramidall number, be taken by anye of the aforesayde meanes. Also yf by suche meanes you can take all his quadrates one after another.

The privilege of the king.
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If anye of the kynges quadrates be taken, he maye redeme it by anye of his men having the same number, and muste remove into his place, whiche redemed hym. But yf he have none of the same number, he maye redeme hym for anye man of hys, that his adversarye wyll chuse, and lykewyse remove into his place by whome he is redemed.

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A table to take the men by Multiplication and Division.
Even against odd
spaces
6 2 12
8 2 16
15 2 30
45 2 90
4 3 12
4 4 16
9 4 36
16 4 64
6 5 30
20 5 100
2 6 12
15 6 90
20 6 120
4 7 28
8 7 56
2 8 16
8 8 64
4 9 36
9 9 81
25 9 225
9 10 90
21.

odd against even
spaces
3 2 6
36 2 72
3 3 9
5 3 15
12 3 36
5 4 20
9 4 36
16 4 64
3 5 15
5 5 25
9 5 45
12 6 72
7 7 49
5 9 45
9 9 81
3 12 36
3 14 42
17.

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For Division.
even against odd
spaces
6 2 3
72 2 36
15 3 5
36 3 12
9 3 3
20 4 5
36 4 9
64 4 16
15 5 3
25 5 5
45 5 9
42 6 7
72 6 12
49 7 7
72 7 9
45 9 5
81 9 9
36 12 3
91 13 7
42 14 3
20.

odd against even
spaces
12 2 6
16 2 8
30 2 15
90 2 45
12 3 4
16 4 4
36 4 9
64 4 16
100 4 25
22 5 45 [sic -- 22 should be 225]
30 5 6
100 5 20
12 6 2
36 6 6
90 6 15
120 6 20
28 7 4
56 7 8
16 8 2
64 8 8
120 8 15
3 9 4 [sic -- 3 should be 36]
81 9 9
225 9 25
90 10 9
66 11 6
28 14 2
27.

To take by cossicall signes

2 16{4}
2 64{6}
3 81{4}
3 9{2}
4 16{2}
4 64{3}
5 25{2}
6 36{2}
7 49{2}
8 64{2}
9 81{2}
15 225{2}

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Of the triumph.
The triumph is after the Kynge be cleane taken away, to be create in the adversaries campe, as well of your owne men as of your adversaries men that be taken, or of both in proportion as hath bene shewed before, and proclaimed that those men ons placed, may not be taken, as it was declared sufficiently, and no difference betwene the triumphes, savyng that some wyll not alowe a triumphe but of foure numbers, and two proportions at the lest. All three for the greater victorie, makynge but two kyndes of triumphes.

Here foloweth the thyrd kynde of playing at the Philosophers game.
There must also in this thyrd kynde be considered the table, the men, their markyng, the order of theyr battell, the motions, their taking, and last of all theyr triumphing.

The table is the same that hath bene twyse already discribed. Yet some wyll not have it so longe, but at the lest is must conteyne .10. squares in length and alwayes .8. in breadth. The longest is best.

Of the men.
The men be .48. as it hath bene told of two contrary collor, the head and bottom all of one collor, because men ons taken be no more occupyed in thys kynde of playing.

The inscription and fashion.
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The fasion is as hath bene last declared both of the men, and of the kynges, the inscription of numbers the same, but without cossical signes.

Of the order of the battell.
The order of battell is after the firste maner, but not so farre from the bordes end, namely the .4. squares standynge in the plattes nearest to the bordes end the rest accordingly joined to them, as in the first kynde of playing.

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[Note that, in this diagram, the odds are colored black. Also, it actually shows the odds and evens on reverse ends from this textual representation; I'm not redoing the whole thing right now...]

[25] [81] [169] [289]
[15] [45] <25> <20> <42> <49> [91]* [153]
<9> <6> (4) (16) (36) (64) <72> <81>
(2) (4) (6) (8)

(9) (7) (5) (3)
<100> <90> (81) (49) (25) (9) <12> <16>
[190]* [120] <64> <56> <36> <30> [66] [28]
[361] [225] [121] [49]

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Of their motions.
The men move frowarde and backward, to the right hand, and to the left hande, but not cornerwise, except the gamesters so agree, the rounds into the next space, the triangles into the thyrde, and the squares into the fourth, the kyngs move as squares. And these be their ordinary draughts in marching.

Of their taking.
They are taken by encountering, bu eruption, by laying wayght, and by Oblivion.

Of takyng by encountering.
To take by encountering is to take by Equalitie, as hath bene twyse before declared.

Of taking by eruption.
To take by eruption is when a lesse number beyng multiplied by the spaces that are betwene him & hys adversary, the product is asmuch as his adversary, he may take his enemie awaye whether he stand directly from him or cornerwise.

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For men that may be taken by eruption looke in the table of takyng by multiplication in the second kynd of playing.

Of takyng by deceypt or lying weyght.
To take by deceypt or lying weight, is to take by addition, not as before when the adversary standeth within the draught of two men which being added make the juste number of the adversary, but when the .2. numbers that are to be added, stande in the next spaces to the adversarie. For to take by deceipt, looke in the table that was set forth for takyng by addition in the first kynde of playinge.

Of taking by Oblivion.
By Oblivion all men may be taken, when foure men besiege the adversarye, standynge in the foure nexte

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spaces about him directly, or cornerwise, the man so besieged can not escape, because he can not remove cornerwyse, therefore maye be taken up, so soone as the last of the foure is set in his place.

In all three kyndes of playing no Oblivion can be of any man with some of his fellowes, but all foure muste be hys adversaries.

In this thyrde kynde, these men can be none otherwyse taken but by Oblivion. Namely amonge the even .2.4.4.135. among the odde .3.5.7.190.

In all maner of taking this is to be noted, that we muste not place the man which taketh in place of him that is taken, but when he maye be taken before we drawe, then shall we remove our man into his place.

The privilege of the king.
The king standeth for so many men as he hath steppes, that is the even for .6. the odde for .5. if anye of these

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(except the lowest and greatest) be taken the king may redeme hym, by any man of his that is of the same number. If he have none of the same number, he maye redeme him be any of his men that hys adversary wyll chuse. But if his lowest square be taken, no ransom will delyver him. Also if the whole kyng at ons that is the whole number of Pyramis be taken, he can not be redemed.

Of the triumphe.
To take awaye the tediousnes of long play from them that be yonge beginners, wryters of this game have invented divers kyndes of shorte victories, wherefore they devide victory into proper and common. Of the proper victory need nothing here be spoken, for all things thereto belonging are sufficientlu set forth in the first kind of playing.

Of the common victory.
The common victorie (they say) is after fyve maners, for men contende either for bodies, goods, quarrelles, honour, or els for both quarels & honor.

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Victory of bodies.
Victory of bodies is only to take a certain number of men, as if the gamesters agree, that he which first taketh .4. or .5. or .6. or .10. men &c, shall wyn the game.

Victorye of goods.
Victorie of goods, is to take a certain number without respect of the men. As if it be covenanted, that he which first taketh men amounting to the number of .100. or .200. shall have the victorie.

Victory of quarell.
Victorie of quarell is when neither the men, nor the number, but the characters of the number be considered. As if it be determined that he which first taketh .100. in .8. characters not regarding in how many men they standes, shall winne. As .2.4.5.8.24.64. so you have .100. in .8. characters it skilleth not, although there be more then .100. as in this example there is more then .100. by .4.

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Victorie of honour.
Victorie of honour, is whe a determined number is made in a determined number of men, as if it be determined that he whiche first cometh to .100. in .8. men, shall winne the game. As in these .2.4.6.8.4.16.45.15. And though there were somewhat more then .100. so it be in .8. men, it skilleth not.

Of victorie of honour and quarell.
The victorie of honour and quarell, is when one obteyneth the decreed number, in the decreed number of men and the decreed number of characters: as let .100. be the decreed number .8. the determined number of men, and .9. the determined number of characters. He that obteyneth .2.4.6.8.4.6.9.64. obteineth the victorie of honour and quarell. It shalbe no hinderance though .8.

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men and .9. characters conteyne somwhat more then .100. so that there be not .100. upon one man, as in the victorie before.

Victorie of standers.
They have invented another victorie, that is of standerdes, by counterfeyting two armies, one of the Christians, another of the Turkes. The whyte men, that is the even hoste, conteyneth .1312. footemen (not compting the rootes of squares expressed in the kynges) let the first and last be captaines and let them devide the whole armye into .10. standerds so every standerd shall have .130. men, besyde the two captaines and the ten standard bearers. The black men, that is the odde armie (except the kings rootes) be .1752. The two captaynes and ten standerd bearers taken out, there remayneth .1740. souldyers, to every standerd .174. He that wynneth more standers have the victorye. If the even hoste

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wyne .348. men he hath obtayned two standerds if he wynne .522. he hath gotten thre standerds and forth of the rest.

If the odde armye wynne .260. they wyn two standerds .390. three standerds and so of the rest.

Table of the victorye of standerds.
One standerd of the even, conteyneth 130.
Two standerds. 260.
Three standerds. 390.
Foure standerds. 520.
Fyve standerds. 650.
Sixe standerds. 780.
Seven standerds. 910.
Eyght standerds. 1040.
Nyne standerds. 1170.
Tenne standerds. 1300.
One standerd of the odde, conteyneth 174.
Two standers. 348.
Three standerds. 522.
Foure standerds. 696.
Fyve standerds. 870.
Sixe standerds. 1044.
Seven standerds. 1218.
Eyght standerds. 1392.
Nyne standerds. 1566.
Tenne standerds. 1740.
You maye use anye of these syxe kyndes of common victorie, in every one of the three kyndes of playing.

FINIS
Prynted at London by Rouland Hall,
for James Rowbothum, and are to
be solde at his shoppe in
chepeside under Bowe
churche.
1563.

***********

( above transcription of a 1563 translation by William Fulke (or Fulwood -- the sources disagree) of Boissiere's 1554/56 description of Rythmomachy. It is entry 15542a in the Short Title Catalog of Pollard and Redgrave, and on Reel 806 of the corresponding microfilm collection.)

Faber and a later Italian adapter, whose text is called 'Florentine dialogue' (1539) adopted even the form of the Greek didactic dialogue and the Pythagorean tradition again according to their times. Shirwood (1474) and Fulke/Lever (1563) wrote their book about Rithmomachia for their sovereigns or patrons.

The hand-written manuscript by Abraham Ries (1562) was written with the same intention. Abraham Ries was the second son and heir of the mathematical talents of the most well-known German Rechenmeister (arithmetic teacher) Adam Ries. Selenus (1616), whose real name is duke August II of Brunswick-L?neburg, published his Rithmomachia as an appendix to his book about chess.

All these texts were characterised by the fact that Rithmomachia was merely played by intellectuals for pure pleasure and mental recreation. (Illmer 1987) Rithmomachia was known at this time mainly in Italy, England, France, and eastern Germany.

At the end of the 17th century Rithmomachia lost its great popularity. The mathematician and philosopher Leibniz knew only the name, not the rules of the game. The main subject of mathematics changed during that time.

The introduction of the zero, the integration and differentiation of integrals, the calculation with fractions and smallest units did not fit into the number theory of Boethius. Mathematics moved towards the calculation of chance with probability calculus.(Folkerts 1989).

Chess became the great game of that time, and protected the traditions of Rithmomachia mainly in Germany despite its unpopularity of the time. Because Selenus, as a great enthusiast of chess printed his version of Rithmomachia in the appendix of his book of chess, later writers of chess books included Rithmomachia as 'arithmetical chess' in German speaking area. (Allgaier 1796, Waidder 1837, also Koch 1803) In a similar way Zimmermann (1821) adapted Rithmomachia to checkers (in German, Dame) as 'Zahl-Damenspiel' (numerical checkers).

Until now Rithmomachia is described particularly in game books. (Archiv 1819, Jahn 1917, Strutt 1801) Two German teachers were also inspired by Selenus to announce Rithmomachia again. Adler, a passionate mathematician and chess player, discovered the didactical profit of Rithmomachia and published a text with the rules in his school programme in 1852, but he received no greater attention. (Jahn 1917). 65 years later Jahn, parish priest and rector of the Z?llchower Anstalten near Stettin, took up the game in effort to contribute to a greater popularity, but he suffered the same meager results. (1917, 1929?).

For more than 100 years the academic research of the origin of Rithmomachia and the mediaeval history of it developed independently to the traditions of the game. In 1986 this academic research obtained with 'Das mittelalterliche Zahlenkampfspiel' by Borst a basic work, in which the oldest source texts are edited.

The mediaeval traditions of Rithmomachia are certain. Illmer (1987) however suspects, that Rithmomachia is older. There are conspicuous parallels between the raising and the moves of the pieces and the raising and the mobility of Roman armies. Already in approximately 1070 in Li?ge this Roman model provided the players with an easier way of playing. (Borst 1986) There are, however, no testimonies of texts, but generally the sources of texts about ancient board games are very short, like, for example, in different works by Plato.

An exact description or even a rule of the game is difficult to reconstruct. Also no archaeological evidence has been hitherto found. There have been no pieces found neither ancient nor medieval.

3. The Rules of Rithmomachia::

The rules have changed over the centuries.

During the 1000-year history of the game the rules have changed often. The extent increased from few hand-written pages to more than 100 printed pages, in which detailed the mathematical and harmonic backgrounds are described. But the rules have the following things in common: the number of pieces with the numbers printed on them, the two pyramids and a rectangular board.

In addition the goal of the game is common::

Two players try to build through fixed moves an arrangement of three or four pieces on the opponent's side of the board. The numbers of the pieces must be in a specific proportion to each other and with the arrangement of one of these groups the player gains victory. In the process the opponent's pieces can be captured according to certain rules. Depending on whether one seeks a perfect game or an easier version of it, the size of the board and other details of the rules may vary.

The rules presented here correspond mostly to the way Rithmomachia was played during the 17th century, before it retreated in a shadowy existence. (1).

These rules are suitable for playing today.

A. Preparations

Rithmomachia is played on a board of 16 by 8 squares. The white and black pieces have numbers written on them according to the number theory of Boethius.

The second and proceeding rows of numbers are derived from the first. The white pieces are called the even and the black are called the odd, but there are odd numbers in the even party and vice versa.

On the round pieces the multiples (multiplices) are placed. The base row is built from multiples of 1. In the second row the base numbers are multiplied with themselves.

The numbers on the triangles are the superparticulares. They contain the preceding number and one fraction of it ([n + 1] / n). T

he numbers on the squares are built with the preceding number and a multiple fraction of it ([n + 2] / [n + 1]). They are the superpartientes.

There are many mathematical relations between the numbers. Boethius gave several procedures for derivation of the numbers. One of these mathematical relations is that the first row of triangles can be built by adding the numbers of the two preceding circles. In the same way the first row of the squares is obtained from the two rows of triangles.

At the position of the white 91 a pyramid is located. The square numbers 36 and 25 on square, 16 and 9 on triangular, and 4 and 1 on round pieces add up to the total sum of 91 of the white pyramid. Corresponding to this the black 190 is replaced by a pyramid with the total sum 190, consisting of the square numbers 64 and 49 on squares, 36 and 25 on triangles, and 16 on a circle.

The pieces are set up according to the array.

The tables of harmonies, in which all combinations of pieces for harmonies are recorded, are very helpful in playing. (2)

B. The Aim of the Game ::

Through tactical moves, the players should attempt to arrange a harmony out of three or four pieces in a specific proportion in the opponent's field. The players should however pay attention to the opponent and prevent him from blocking his harmony. The first player who arranges a harmony is the winner.

C. The Moves of the Pieces ::

The players move alternately into an empty space. No piece is allowed to be jumped over. Black starts, because white has better possibilities for capturing and arranging harmonies. This inequality is a special attraction of Rithmomachia, because through this a balanced playing is possible between unequal players.

The circles move into the second field, forwards, backwards or sideways, but not diagonally. The triangles move into the third field, only diagonally. The squares move into the fourth field, in all directions (including diagonally). When moving, both the starting and finishing field are counted.

The 5 or 6 piece pyramids move according to their individual components.

D. The Capture of Pieces ::

Pieces can capture others that stand in the way of their movement, but they remain at their place and do not take the field of the opponent's captured piece.

By meeting: If a piece is so placed, that in its next regular move it could take the place of an opponent's piece with the same number, the opponent's piece is taken away.

By ambush: If two or more pieces of ones party are in a position in which in their next move they could move into the field of an opponent's piece, and the sum or difference equals the number of the opponent's piece, the opponent's piece is taken away.

By assault: If in its ordinary direction a piece could meet an opponent piece, and its number equals by multiplication or by division the number of fields between the two pieces, the opponent's piece is taken away from the board. The fields of the capture and the captured piece are counted.

By siege: If an opponent's piece is encircled by pieces of the other party in such a way that it could neither move nor be set free by one piece of its party, the besieged opponent's piece is taken away from the board.

The individual components of the pyramids can both capture and be captured. If single components are missing, the pyramids can be captured by their total sum, but they cannot capture other pieces with their total sum in this case.

Partial sums are inadmissible.

E. The Victory::

The game is finished, when one player has built up a harmony of three or four pieces in the opponent's field. Therefore the pieces must be arranged in an ascending row, in a right angle, or four pieces also in a square, and must be equidistant. The captured opponent's pieces may also be used in creating a harmony, however, they may not be the last piece of a harmony. There are three ways of creating harmonies with three pieces:

In an arithmetical harmony the difference between the two smaller numbers equals the difference between the two bigger ones, e. g. 2, 4, 6 => b - a = c - b.

A geometrical harmony exists, when the ratio between the two smaller numbers equals the ratio between the two bigger ones, e. g. 5, 10, 20 => (a / b) = (b / c).

By the musical harmony the ratio of the smallest and the biggest number equals the ration between the difference of the two smaller numbers and of the two bigger ones, e. g. 6, 8, 12 => (a / c) = [ (b - a) / (c - b) ].

To enable a rapid game, the harmonies need not be calculated; rather, they can be looked up in the tables of harmonies.

Three different grades of victories can be gained from different harmonies:

1.) A small victory is reached by an arithmetical, geometrical or musical harmony of three pieces.

2.) A big victory is gained by building two (but not more than two) different harmonies with 4 pieces.

3.) A great victory is reached by 4 pieces containing all three harmonies.

The players agree on which victory or victories they are aiming for. It is possible to play with even simpler goals.

If the players desire a simpler game, a victory could be possible when a predetermined number of opponent's pieces are captured, or a certain sum or number of digits of the captured pieces is reached or exceeded.

The most essential features of Rithmomachia have been represented. Because of the briefness some smaller details are missing; but players can certainly work with this outline and work out smaller details as necessary. A few variations of Rithmomachia have been presented, which players can try.

Unfortunately, to play Rithmomachia today, one must build a game for oneself, if one is not interested in using one of the two computer games from Italy or from the USA. In the 16th century it was easier, because the game could be bought in Paris and London, as Boissi?re and Fulke/Lever wrote in their books on Rithmomachia. Presumably Jahn (1929?) offered a set of the game for sale.

In the past treatises about Rithmomachia were published more often, and it also appeared in game books. So there is still hope, that Rithmomachia will be known better again.

This desire was expressed in the pseudo-ovidian poem 'De vetula' in the 13th century: 'Oh, if only more people had enjoyed the battle of numbers! If it was only known, it would on its own accord be highly respected.' Hopefully this wish, that Rithmomachia be played again, will come true.

***********

Rithmomachia: The Game for Medieval Geeks (Culture)

In 965 Wibold, bishop of Cambrai, suggested to the local monks that they give up playing dice games and instead play "the battle between virtues and vices". In all likelihood this was the game rithmomachia, otherwise known as the ludus philosophorum. Today we are familiar with a number of ancient board games but unfortunately rithmomachia, as well as some related games Ouranomachia and Metromachia have all but disappeared

Rithomachia was played by the intellectuals of Europe, often Church employees and most likely male. Although it is obscure today, rithomachia played an important part in the lives of this elite group. The rules were complex and convoluted and required considerable computational skill. Its players also claimed that its benefits extended well beyond numerical training - it supposedly improved the moral character of players and even gave deep insights into religious truth.
There are many different versions of the rules of play but there are many common features. There are two players who take turns moving pieces on a board, much like chess or checkers. The board is something like a chess board, though rectangular and not square, with 48 pieces, each inscribed with a number. The size of board varies with rule set but eventually it was standardized on 8 by 16.

But now the complication starts. Rithomachia was inspired by a type of mathematics made popular by Boethius. This work was dominated by various types of numerical progression: in particular arithmetic progressions (where the nth number is a+b*n for constant a and b), geometric progressions (a*b^n) and harmonic progressions (1/(a+b/n)). There were also other more complex types of progression such as multiplex progression or the progression of superparticulars. At the start of the game the initial layout of the numbered pieces, in three ranks for each side, was such that the numbers formed various types of progression. One side had odd numbers in the first rank, the other side even. So even before the game had started quite a bit of mathematical knowledge was required. And don't forget that in earlier times arabic numerals were unknown so any calculations were carried out using Roman numerals. (By the way, these proportions played an important part in medieval music theory. Consider the harmonic progression in particular.)

Pieces from the first rank could move one square, those from the second rank two and those from the third three. As a mnemonic the pieces in these ranks were sometimes circles, triangles and squares respectively (a slightly illogical mnemonic!). Like in chess, pieces could be captured, however there were many ways to capture. One way was to move a piece with a number onto another with the same number. Two pieces could take another if it was the case that if they were simultaneously to make legal moves that would land them both on the captured piece and the sum of the numbers on the two pieces sums to that of the captured one. Another way to capture was to occupy all the spaces that another piece could move to making it unable to move - this was called besieging it. Here is another example of a capture rule taken from Lever and Fulke's "The Most Noble and Auncient, and Learned Playe" published in 1563:

Of taking by cossical signs
By cossical signs: any man that hath these signs, 3, &, 33, 3&, meeting with his root in his ordinary draught that hath this sign z taketh him up, or else is taken of his, without removing into his place; except he may not take him before he remove.

Obviously there has been a little semantic drift over the centuries. There were also some much more complex capture rules requiring the pieces to be arranged in a progression.

Now we've warmed up we can get onto the conditions to achieve victory in the game. Typically a player had to line up a series of pieces in certain arrangements, often as a Boethian progression of a certain length. Whoever did this would win. There were many different choices of victory conditions based on such progressions and players would negotiate before to game to decide which were in play for a particular game. An example simple victory condition follows:

Victory of goods

Victory of goods is to take a certain number without respect of the men. As if it be covenanted that he which first taketh men amounting to the number of 100 or 200 shall have the victory.
There was even a victory condition based on simulating the armies of the Christians and Turks at war.
As you can see, this was no game for weenies and yet it was played all over Europe from Medieval times, through the Renaissance into Elizabethan times. Many rithomachia manuals still exist today and doubtless many more were originally published. It seems to me there is only one explanation: Rithomachia is a geek game and the players were predecessors of today's game playing geeks! They spent their time shut up in dark rooms hunched over books and games believing themselves to be superior to the masses because they were experts in difficult and arcane, but largely useless knowledge.

Today Boethian mathematics is almost unheard of. This is the key to the decline of rithmomachia. Boethian mathematics was highly technical but today it's abstruseness seems completely arbitrary and useless. As it was replaced by more modern approaches to mathematics the rules to rithmomachia came to seem more and more arbitrary until interest in the game completely waned. However it is worth noting that this game did have a lifetime of 500 years and was played by such illustrious luminaries as John Dee and praised by Roger Bacon.

***********

Appendix III:Table of harmonies
1. Harmonies for a small victory

Geometrical harmony:

2 4 8
2 12 72
3 6 12
4 6 9
4 8 16
4 12 36
4 16 64
4 20 100
4 30 225
5 15 45
9 12 16
9 15 25
9 30 100
9 45 225
16 20 25
16 28 49
16 36 81
20 30 45
25 30 36
25 45 81
36 42 49
36 66 121
36 90 225
49 56 64
49 91 169
64 72 81
64 120 225
81 90 100
81 153 289
100 190 361

Arithmetical harmony:

2 3 4
2 4 6
2 5 8
2 7 12
2 9 16
2 15 28
2 16 30
3 4 5
3 5 7
3 6 9
3 9 15
3 42 81
4 5 6
4 6 8
4 8 12
4 12 20
4 16 28
4 20 36
4 30 56
5 6 7
5 7 9
5 15 25
5 25 45
6 7 8
6 9 12
6 36 66
7 8 9
7 16 25
7 28 49
7 49 91
7 64 121
8 12 16
8 25 42
8 36 64
8 49 90
8 64 120
9 12 15
9 45 81
9 81 153
12 16 20
12 20 28
12 42 72
12 56 100
12 66 120
15 20 25
15 30 45
15 120 225
16 36 56
20 25 30
20 28 36
20 42 64
28 42 56
28 64 100
30 36 42
42 49 56
42 66 90
42 81 120
49 169 289
56 64 72
72 81 90
81 153 225
91 190 289

Musical harmony:

2 3 6
3 4 6
3 5 15
4 6 12
4 7 28
5 8 20
5 9 45
6 8 12
7 12 42
8 15 120
9 15 45
9 16 72
12 15 20
15 20 30
25 45 225
30 36 45
30 45 90
72 90 120

2. Harmonies for a big victory
Arithmetical and musical harmony:

3 4 5 6
3 4 5 15
3 5 7 15
4 5 6 12
4 6 12 20
4 12 15 20
5 7 9 45
6 7 8 12
9 12 15 45
9 15 30 45
9 15 45 81
12 15 20 28
15 20 25 30
15 30 36 45
30 36 42 45
72 81 90 120

Geometrical and musical Harmony:

2 3 6 12
3 4 6 12
3 5 15 45
3 6 8 12
4 6 12 36
5 9 15 45
5 9 45 225
9 12 16 72
9 15 25 45
9 15 45 225
9 25 45 225
20 30 36 45
20 30 45 90
25 30 36 45
25 45 81 225

Arithmetical and geometrical harmony:

2 3 4 8
2 4 5 8
2 4 6 8
2 4 6 9
2 4 8 12
2 7 12 72
2 9 12 16
2 12 42 72
3 6 9 12
3 9 15 25
4 5 6 9
4 6 8 9
4 6 8 16
4 8 12 16
4 8 12 36
4 8 16 28
4 12 20 36
4 12 20 100
4 16 28 49
4 16 28 64
4 20 36 100
4 30 56 225
5 9 15 25
5 15 25 45
5 15 30 45
5 25 45 81
6 9 12 16
6 36 66 121
7 16 20 25
7 16 28 49
7 49 91 169
8 9 12 16
8 64 120 225
9 12 15 16
9 12 15 25
9 12 16 20
9 15 20 25
9 25 45 81
9 45 81 225
9 81 153 289
12 16 20 25
15 16 20 25
15 64 120 225
16 20 25 30
16 36 56 81
20 25 30 36
20 25 30 45
25 30 36 42
30 36 42 49
36 42 49 56
42 49 56 64
49 56 64 72
49 91 169 289
56 64 72 81
64 72 81 90
72 81 90 100
81 153 225 289

3. Harmonies for a great victory
Arithmetical, geometrical and musical harmony:

2 3 4 6
2 3 6 9
2 4 6 12
2 5 8 20
2 7 12 42
2 9 16 72
3 4 6 8
3 4 6 9
3 5 9 15
3 5 15 25
3 9 15 45
4 6 8 12
4 6 9 12
4 7 16 28
4 7 28 49
5 9 25 45
5 9 45 81
5 25 45 225
6 8 9 12
6 8 12 16
7 12 42 72
8 15 64 120
8 15 120 225
9 12 15 20
12 15 16 20
12 15 20 25
15 20 30 45
15 30 45 90

(1) This description of the rules is based for the most part on Illmer (1987), who used the rules of Selenus (1616) as basis. There are some differences in Stigter's version (199?). His rules include many details with a good structure and the mathematical basis, they could not be represented here because of the necessary briefness. It contains a more extensive derivation of the numbers. More extended descriptions of the rules of the Rithmomachia can be found in Coughtrie (1984) and Richards (1946). In my master's thesis (1996) I have also listed many different variations for playing.

(2) More extensive tables of harmonies can be found in Richards (1946), Illmer (1987) and Mebben (1996).

***********

More Rythmomachia and techniques

Arithmomachia laughed them to 1030, Wurzburg.

In a competition between the schools of the cathedral of Worms and Wurzburg - both many rinomate in the field of the Arithmetic - a text of containing dispute was written up numerical sequences based on the "De arithmetica institutione" of Boezio; on the base of this text, monaco of name an Asylum it created a game - Arithmomachia, exactly - useful to the students of the two monasteri in order to learn the numerical theory of Boezio.

The first drawing up was adapted from other scholars. Hermannus Contractus, respected monaco to Reichenau, rimaneggiò the rules of Asylum and added to some notes on the musical theory (a second version wants instead that the author originates them is just Hermannus Contractus).

There is also who thinks that the attribution is gives is given to the bishop of Cambrai, Wibold, than in the 965 it invited the monaci local to stop to play to dice and to play instead "the battle between the virtues and the defects". There are however various hypotheses that rivendicano an origin still more ancient, sights some correspondences between the disposition and the movement of pieces and the disposition and the movement of the armys Roman. Between the XI and XII the Arithmomachia century diffuses po' to the time in all a Germany and France.

The rules came ulteriorly extended. Between the XII and XIII the century the game reached also in England. Giovanni di Salisbury writes in its "Policraticus" (1180) that "the acquaintance of the battle of the numbers is one source of divertimento and profit".

Also Roger Bacon comment the Arithmomachia, in its "mathematica Communio". To along Arithmomachia it remained in competition with chess and there was a period in which even more it was respected of same chess.

The reason of that is in the fact that Arithmomachia was the only game previewed in the programs of the medieval schools and university - I privilege that chess will not never receive, in how much game of military inspiration that did not respect the canoni of the seven liberal limbs.

Arithmomachia found the maximum spread in XVI the century, in particular as consequence of the invention of the press. Rules were written from Shirwood (1474), Faber (1496), Boissiere (1554/56), Ries (1562), Fulke/Lever (1563), Selenus (1616).

The greater centers of rinascimentale spread were England, France, Italy and the Germany orients them. To the end of XVII the Arithmomachia century lost popolarità and fell in the oblivion. Signals on the numerical theory of Boezio Anicius Manlius Severinus Boethius nacque around to the 480 to (or near) Rome and died to Pavia in the 524.

The witnesses matemati us of Boezio, for how much of insufficient quality, were between the best that could be found in the high Middle Ages and were use you for centuries in a rather rear Europe in the field of the mathematics. The Arithmetica di Boezio was based on the job of Nicomaco and for the medieval scholars it was the maximum base of study for the numerical theory of Pitagora. Boezio was one of the greater sources of supplying for the crosss-roads.

The mathematics of Boezio is dominated from the concept of "numerical progression"; there are arithmetical progressions (a+b*n), geometric progressions (a*(b^n)), harmonic progressions (1/(a+(b/n))) and other anchor... The rules of the game As we have been able to see, an only set of rules for Arithmomachia does not exist. During the history to plurisecolare of the game they they are often changed and in consisting way; their complexity, as an example, is last from the little pages written by hand of the first version until beyond one hundred printed publication pages in the later versions.

Probably, in the first phase of spread of the game, every school adopted of the own rules, that is those deductions more adapted for an understanding of the arithmetical bases of the game.

Moreover obvious E' that the greater documentary sources regard the rinascimentali versions of the game, while on the first medieval versions it is not equally remained material; the only medieval version available is that one of Asylum (XI sec.). Archaeological evidences do not exist at the moment: no pawn never has been found again, neither medieval neither rinascimentale. The present set of rules, therefore, does not mean to represent a specific version of the game: the objective that is placed me has been that one to create a reasonable set of rules for uses in Italian area in the second half of XIII the century, extrapolating i characters generates them and the rules base of the game, with particular reference to the version of Asylum, and taking part with personal corrections where it is seemed to me not were clarity in the consulted sources here. With the same spirit who - creed - has animated in the time the various authors, in all the doubt situations I have decided to resort to the criterion of the maximum giocabilità, also without to neglect the more fascinating and educational aspect than this game, that is the manipulation of the numbers.

The table from game The table from game is composed from 112 cases: 8 cases of width and 14 of depth. The pawns The pawns are in number of 23 more 1 king for every player; the king is formed from 5 or 6 disposed pawns in guisa pyramidal (will see one more ahead detailed description more).

The pawns, except that constituent king, are painted on the two faces with contrasting colors (R-bianco.e.nero, red and blue...) and on ciascuna of they they bring back a numerical value; the use of the two colors derives from the fact that the pawns captured to the enemy come introduced in game from the own part.

It makes exception the king, than he does not change alignment and, if captured, he comes simply removed: its pawns are of a single color, but they bring back anch' they a numerical value.

The pawns have also one various geometric shape: 8 are round, 8 triangular and 7 square ones.

The two king has to the base two square pawns, sormontate from two triangular ones and, finally, one or two round pawns. We see hour which numbers must be brought back on ciascuna pawn.

The pawns are uniforms in six ranks from 4 elements everyone.

The first rank of circles is constituted from the numbers base: 2,4,6,8 for a player (than from hour in then, for this reason, will come defined like equal side) and 3,5,7,9 for the other player (that we will call uneven side).

According to rank of circles base is constituted from the square of the numbers: 4,16,36,64 for pars and 9.25.49.81 for the odd number.

The first rank of triangles is constituted from the sum of the two previous ranks: 6,20,42,72 for the pars; 12,30,56,90 for the odd number.

According to rank of triangles it is obtained adding 1 to every number base and elevating to the square the turning out value: one obtains 9.25.49.81 for pars and 16,36,64,100 for the odd number.

The first rank of squares is given from the sum of the two ranks of triangles: 15,45,91(re),153 for the pars and 28,66,120,190(re) for the odd number.

According to rank of squares it is obtained adding 1 to the double quantity of every number base and elevating to the square the turning out value: one obtains 25,81,169,289 for pars and 49.121.225.361 for the odd number.

The values of the two king are given from the sum of the faces on ciascuna of the constituent pawns the same ones.

The equal king is constituted from 6 pawns, that they bring back the following numerical values: 1 on the smaller circle; 4 on according to circle; 9 and 16 on the two triangles; squared 25 and 36 on the two.

Analogous, the uneven king is constituted from 5 the following pawns with values: 16 on the only circle, 25 and 36 on the two triangles, squared 49 and 64 on the two.

Preparation To the beginning of the game the pawns come disposed in "order of battle". The beginning of the game is up to the uneven player, which it has minors possibility to capture pieces and to realize harmonies. Thanks to this disparity, it is possible to make to meet players of various level. Scope of the game Through tactical movements, every player must per.primo.cosa eliminate the enemy king. Subsequently, he must realize a "triumph" (v. beyond).

The realization of a "excellent triumph" door to the definitive conclusion of the game. With the smaller triumphs ("mediocre triumph" and "great triumph") the game continues, but the players can come to an agreement themselves for giving they a partial value of Victoria.

The movement of pieces The players alternatively move one pawn to the time in one empty case, according to characteristic rules of ciascuna geometric shape. Also the cases crossed from the pawns in their movement must be empty: it is not possible "to jump" other pawns.

The pawns can be moved in whichever direction (horizontal, vertical and diagonal). The circles move exclusively of one case. The triangles move exclusively and exactly of two cases. The squares move exclusively and exactly of three cases. The king moves like the piece that is found to its base.

To the beginning of the game, therefore, muoverà of three cases, like a square; but if, in the course of the game, it had to lose both squares, muoverà only more than two cases (like the triangles) and, if it had to lose also both triangles, muoverà only more than one case (like a circle).

The king cannot voluntarily be separated in its constituent units.

The capture of pieces Five various ways exist in order to capture pieces of the adversary: encounter, I besiege, ambush, onslaught and proportion.

In all the cases the king can capture is with its number total (given from the sum of the numbers that constitute it in that moment) are with a single piece; partial sums are not admitted.

In any case, the distance for the capture is equivalent to that one of movement, even if the capturing piece is of a geometric shape that normally you would preview a various distance (to es. a still complete king moves and capture to three cases of distance, even if the single used element is a triangle or a circle).

Analogous it can be captured in the its totality or a piece to the time, except that in I besiege where can be captured single in its interezza. Every time that a piece is captured, it comes rigirato so as to to change alignment. They make exception constituent pieces the king, than they cannot change alignment and they come therefore simply it eliminates to you from the table from game.

In order to capture an opposing piece, it does not have to be entered physically in the case from occupied it: it is necessary only that there is this possibility, that is the piece to capture must be found to a distance that corresponds to the movement of the capturing pawn.

In practical, if a pawn before or after just the movement is found to the own distance of movement from an opposing pawn, and exists the conditions for the capture, the opposing pawn is captured. In the case in which the capture it happens before the movement, that replaces the same movement and the turn of the player is ended. The capture are not obligatory

***********

Number Games ; Rythmomachia / Rithmimachia

Aritmomachia::

The game is of ancient derivation and involves
pieces moving on a board.

Together with Courier Chess (Germany and
depicted by e.g. Lucas van Leyden), Aritmomachia
(rithmomachia / rithmimachia, latest: rythmomachy),
is considered to be one of the two (dormant) successors of
the ancient game of chess (peaked in popularity at appr.
1,000 ac - 1,800 ac, and was referred to as The Pythagoras Game).

Rythmomachy:

Ritmos = Number
Mache = Battle

Latin: Pugna (certamen) numerorum

Board:

The board8*16 (two chessboards; face long side,
right hand is home board). The board as shown above is considered
a practice board seized 8*9.Pieces: Total 24 pieces;
Round, Triange, Square. White is Even (feminine) en
black is Odd (masculine).

Arithmetic / Geometrical / Harmonic progression

The competition board 8 * 16

An Italian Manuscript Dec 1539 concerning "Pythagoras'Game"
or the "Rithmimacia", with an intriguing insert loosely attached
to the body of the text with the appropriate numbers and
positions. From the Giannalisa Feltrinelli Library as sold at
Christie's in December 1997 (lot 220) with a letter that explained
that the second half of the MS was found in the studio of the
Aristotelian polymath Jacques Lefevre d'Etaples and sent to
Cosimo Rucellaiin Florence.

The practice board 8 * 9

from Jordanus and Faber Arithmetica decem librisdemonstrata;
Paris 1496a page from Claude de Boissiere's Rythmomachia,
Paris1556. According to Smith/Plimpton, the book is
profusely illustrated and "was connected with the medieval
number classifications and ratios..."

Origin:

Pythagoras of Samos, Nicomachus of Gerasa, Anicius Manlius
Severinus Boetius. Six levels of numbers.

Integral and proportional (equal - unequal 5 different ways).

Constillation:

Roman militairy; Vegetius (writter: Flavius Vegettos
Renatus), Belisar's battle formation.

CAVALARY CAVALARY

PHALANX

INFANTRY & CAVALERY

***********

Books::

RHYTHMOMACHIA (1987) by Illmer, Detlef , Gadeke, Nora, & Henge, Elisabeth Pfeiffer, Helene & Spickler-Beck, Monika. ISBN 3880343195.

Furthermore, these book titles should be available at your library:

1.) OXFORD HISTORY OF BOARD GAMES by James Parlett
2.) BOARD AND TABLE GAMES FROM MANY CIVILIZATIONS
by Robert Charles Bell
3.) DISCOVERING OLD BOARD GAMES by R.C. Bell (Shire Publications LTD)
4.) BOARD GAMES AROUND THE WORLD by Robbie Bell and Michael Cornelius
(Cambridge University Press).
5) Murray History of Boardgames xx
6) Oxford History of Boardgames xx

All these books contain solid information regarding the rules of Rithmomachia.

Historical books::

Selenus, Gustav (d. i. August II. Herzog von Braunschweig-Lüneburg) Das Schach- oder König-Spiel.

(translation UK)

Selenus, Gustav (D i August II. Duke of Braunschweig Lueneburg) chess or king play. Into four distinctive books, with special diligence, creating and properly binded.

This is too end, angefueget, a very old play, genandt, Rythmo Machia. Leipzig, Kober 1617. Fol. (26), 495, (3) sides with 6 stung TitleBroderies, 1 doublesince. Table, 2 Kupfertafeeln, 83 (28 full-page) text-copper and 1 printer mark at the conclusion.

Pgt. of the time with handschriftl. Back title - - Van of the lime tree 1955 265 - Schmid, Schachlit. 118 - Title edition of the first edition 1616, large D J appeared with Henning. - the most important and determining chess text book of its time, a revision from Lopez of Tarsia.

With a listing of the used literature. The attaching work is a pythagoreisches number play, from the Italian of the franc.

Barozzi translates and works on. - the broad Titelbordueren with representation of game of chess scenes.

Chessmen and play positions show the copper.

Further References

Borst, A. 1986. Das mittelalterliche Zahlenkampfspiel. Supplemente zu den Sitzungsberichten der Heidelberger Akademie der Wissenschaften, Philosophisch-historische Klasse, vol. 5.
Heidelberg: Carl Winter Universitsverlag
Borst, A. 1990. Rithmimachie und Musiktheorie. In Geschichte der Musiktheorie. Vol. 3, Rezeption des antiken Fachs im Mittelalter. edited by Frieder Zaminer, 253-288. Darmstadt: Wissenschaftliche Buchgesellschaft
Coughtrie, M. E. 1984. Rhythmomachia: A Propaedeutic Game of the Middle Ages. Ph.D. diss., University of Cape Town (in typewriting)
Evans, G. R. 1976. "The Rithmomachia: A Mediaeval Mathematical Teaching Aid?" Janus 63:257-273
Folkerts, M. 1989. Rithmimachie. In Ma?, Zahl und Gewicht: Mathematik als Schl?ssel zu Weltverst?ndnis und Weltbeherrschung. edited by M. Folkerts and others, 331-344, Ausstellungkataloge der Herzog August Bibliothek, no. 60. Weinheim: VCH, Acta humanoria Illmer, D. and others. 1987.
Rhythomomachia: Ein uraltes Zahlenspiel neu entdeckt von --. Munich: Hugendubel
Mebben, P. 1996. Rithmomachie - Ein aus dem Mittelalter ?berliefertes Zahlenspiel: Neu entdeckt f?r die Schule. Master's thesis, P?dagogische Hochschule Freiburg (available by the author upon request) Richards, J. F. C. 1946. "Boissi?re's Pythagorean Game". Scripta Mathematica
Stigter, J. 199?. The History and Rules of Rithmomachia, the Philosophers' Game: An Introduction. London: (will be published soon)
Appendix I Some old, famous and well-known printed books about Rithmomachia
John Shirwood. 1480. Ad reverendissimum religiosissimumque in Christo patrem ac amplissimum dominum Marcum cardinalem Sancti Marci vougariter nuncupatum Johannis Shirvuod quod latine interpretatur Limpida Silva sedis Apostolicae protonotarii Anglici, praefatio in Epitomen de ludo arithmomachiae feliciter incipit. Rome: Ulrich Han.
Jacobus Faber Stapulensis (Jacques Lef?vre d'Etaples). 1496. Rithmimachie ludus qui pugna numerorum appellare. In Jordanus Nemorarius. Arithmetica decem libris demonstrata. edited by Jacobus Faber Stapulensis. Paris: David Lauxius of Edinburgh.
Claude de Boissi?re. 1554. Le tr?s excellent et ancien Jeu Pythagoriqhe, dit Rhythmomachie. Paris: Amet Breire. Or the latin translation: Claudius Buxerius. 1556. Nobilissimus et antiquissimus ludus Pythagoreus (qui Rythmomachia nominatur). Paris: Guilielmum Canellat. (Translated into English by Richards 1946)
Rafe Lever and William Fulke. 1563. The Most Noble Ancient, and Learned Playe, Called the Philosophers Game. London: Iames Rowbothum.
Francesco Barozzi. 1572. Il nobilissimo et antiquissimo Givocco Pythagorea nominato Rythmomachia cioe Battaglia de Consonantie de Numeri. Venice: Gratioso Perchacino.
Gustavus Selenus (Duke August II of Brunswick-L?neburg).1616. Rythmomachia. Ein vortrefflich und uhraltes Spiel desz Pythagorae. In Das Schach= oder K/nig=Spiel. 443-495. Leipzig: Henning Gro? jun. Reprint 1978. Z?rich: Olms
Appendix II
Texts of modern era with a description or rules of Rithmomachia until 1940 - The special German tradition
Johannes Allgaier. 1796. Das pythagor?ische oder arithmetische Schachspiel. In Neue theoretisch-praktische Anweisung zum Schachspiel. Vol. 2, p. 73-97. Wien: Franz Joseph R/tzel.
Johann Friedrich Wilhelm Koch. 1803. Die Rythmomachie. In Die Schachspielkunst nach den Regeln und Musterspielen der gr/?ten Meister. Part 2, p.V-VI, 127-154. Magdeburg: Georg Christian Keil.
Archiv der Spiele. 1819. Das Zahlenspiel (Rythmomachie). In --. vol. 1, sect. 2, 11., p. 94-106. Berlin: Ludwig Wilhelm Wittich.
Ferd. Zimmermann. 1821. Zahl-Damenspiel. In Volst?ndiger Codex der Damenbrett-Spielkunst. p. 365-404. K/ln, Rommerskirchen.
S. Waidder. 1837. Das arithmetische Schachspiel. In Das Schachspiel in seinem ganzen Umfange. Vol. 2, sect. 2,C., p. 118-142. Wien: Mich. Lechner.
Karl-Friedrich Adler. 1852. Beschreibung eines uralten, angeblich von Pythagoras erfundenen, mathematischen Spieles. Schulprogramm des K/niglichen und St?dtischen Gymnasiums in Sorau. Sorau.
Fritz Jahn. 1917. Rythmomachia. In Alte deutsche Spiele. p.1-4, 15. Berlin.
[Fritz] Jahn. 1929(?). Zahlenschach f?r Mathematiker. In Verzeichnis Weihnachtskrippen und Spiele der Z?llchower Anstalten 1929/30. Z?llchow.
Joseph Strutt. 1801. The Sports and Pastimes of the People of England. p. 313-316. London.

***********

THE RULES OF
BOOLEAN RITHMOMACHIA
(A New Twist On An Old Game)

Boolean Rithmomachia
by L. Lynn Smith

The following game is in homage to the Medieval game of numbers. It was thought
that the ideas of this game should be updated and could even be utilized in the
teaching of computer math.

PLAYING FIELD

In order to bring this game into the 21st Century, it was thought that it should
be played upon a 3D field. To make this play as simple as possible, a 4x4x4 field
was selected.

PIECES

The playing pieces consist of two of each of the following. Such pieces, except for the Pyramids, are two sided and have different colors of either side, black or white, but the same value(1 - 14) represented by the binary code. The Pyramids are whole pieces of solid color, two black and two white, one of each particular value(0 and 15) represented by the binary code.

Value Shape
----------------
0000 Pyramid
0001 Circle
0010 Circle
0011 Triangle
0100 Circle
0101 Triangle
0110 Triangle
0111 Square
1000 Circle
1001 Triangle
1010 Triangle
1011 Square
1100 Triangle
1101 Square
1110 Square
1111 Pyramid

SET-UP

The pieces of each player are arranged in two seperate planes, seperated by two planes. Players can occupy opposite sides of the playing field, either horizontally or vertically, in the following manner:

[S][C][C][S]
[T][T][P][T]
[T][P][T][T]
[S][C][C][S]

C=Circle P=Pyramid S=Square T=Triangle

Players have the option of which values may be placed in their respective cells. This form of set-up could be considered one phase of the game as each player may take turns placing a piece upon the field. Or they may agree to a standard form of set-up.

MOVEMENT

Circles move one orthogonal or one diagonal, Triangles move one diagonal or one triagonal, Squares move one orthogonal or one triagonal, Pyramids move one orthogonal or one diagonal or one triagonal. The Pyramid may by landing on any piece then move that piece(regardless of owner) by any normally legal Pyramid step to an adjacent empty cell, such a piece does not change ownership solely by this action but may if it then becomes part of a capture equation. All other pieces must move to empty cells.

[The triagonal movement is a move from one cell to the next cell which is adjacent by
only one of its eight corners. Whereas, the orthogonal move is a change along one axis and the diagonal move is an equal change along two axes, the triagonal move is an equal change along all three axes of the 3D field.]

CAPTURES

The capture of opponent pieces involves flipping the piece to its opposite color. Pyramids are removed from the playing field when captured. The game is over when one player no longer has possession of either Pyramid.

Captures are preformed by legally moving a particular piece then flipping all appropriate enemy pieces.

EQUATIONS

Captures are preformed by applying Boolean equation to and through adjacent pieces.

Capture by the NOT equation. When the appropriate enemy piece is located in a cell which, if empty, would be a legal move for the capturing piece and it is its NOT equivalent, that enemy piece is then captured.

NOT equivalents:

0000 - 1111
0001 - 1110
0010 - 1101
0011 - 1100
0100 - 1011
0101 - 1010
0110 - 1001
0111 - 1000
1000 - 0111
1001 - 0110
1010 - 0101
1011 - 0100
1100 - 0011
1101 - 0010
1110 - 0001
1111 - 0000

This is the simplest take as the attacking piece needs no assistance in capturing its
opponent. Examples: Circle(0001) is able to capture Square(1110) if it becomes
orthogonally or diagonally adjacent. Triangle(0110) is able to capture Triangle(1001) if it is diagonally or triagonally adjacent.

The remaining captures involve the use of two pieces by which to take the target. It is necessary that the second piece used in this form of capture be also owned by the player.

These captures take two forms, Compiling and Filtering.

Compiling, each of the two pieces used to determine the capture must be adjacent to the target piece by their individual legal move.

Filtering, the played piece must be legally adjacent to one which is legally adjacent to the target.

Several takes can be made during a player's turn, if the pieces and positions allow.

There are five forms of operations which can be preformed in order to make such captures; AND, OR, XOR, NAND and NOR.

The following table can be used as a quick reference during the game:

-----------------------------------------------
X Y AND OR XOR NAND NOR
-----------------------------------------------
0 0 0 0 0 1 1
0 1 0 1 1 1 0
1 0 0 1 1 1 0
1 1 1 1 0 0 0
-----------------------------------------------

In such equations, the played piece will be referred to as X, the Compiler or Filter piece will be Y and the target piece will be the answer. If the answer is True then the piece is captured, if False the piece is left as is.

If X = Circle(0100) and the Compiler or Filter = Triangle(1100) then the target must equal the Circle(0100) to be captured using the AND Equation.

Using the OR Equation, the previously stated values could capture Triangle(1100).

Using the XOR Equation, they could capture Circle(1000).

Using the NAND Equation, they could capture Square(1011).

Using the NOR Equation, they could capture Triangle(0011).

The Pyramid is also used to preform such captures. If its moves involves the displacement of a piece, it still may preform the appropriate captures moves. The displaced piece can become either a Compiler, Filter or even a Target.

All captures are mandatory, it is the obligation of either player to assist the other in determining any possible captures which may have resulted from a particular move. Neither player is obliged to suggest any particular move to an opponent.

WINNING THE GAME

When an opponent's last Pyramid is captured, or there are no legal moves or potential captures, victory is determined thus:

Pyramid Victory:

The player who has the most number of Pyramids remaining on the playing field.

Piece Victory:

The player who has the largest number of pieces, including Pyramids, on the playing field.

Value Victory:

The player whose value of pieces, including the Pyramids, on the playing field is the highest total.

The Simple Victory consists of one of the above victories.
The Compound Victory consists of two of the above victories.
The Perfect Victory consists of all three victories.

It is possible that not all of the victories will be available. Example: Both players may have the same value of pieces on the field but not the same number, so neither would be awarded the Value Victory.

Addendum 01.03.2002

It is not necessary to use all formulae in every game. The players may choose to play a NOT-NAND game, a game using the NOT and NAND equations. Or they may play an OR-XOR-NOR game. The desired formulae to be used should be clearly stated before the start of each game.

Addendum 07.11.2002

Allowing the Pyramid to "push" another piece can be optional. Denial of the "push" can increase the opportunity for the game ending with a player having Pyramids but no legal moves. There is no direct penalty for a game ending in such a manner.

--------------
Addendum 02.16.2003

Here is an interesting way to select the equations to be used during the game: Each player secretly writes down two choices, then simultaneously reveals them. This allows for the possibility of either a two-function, three-function or four-function game.

** END **

Aulon(?)

2009-01-14T09:09:00.000-08:00

aruska Di Giannattale, I giochi musicali nel Medioevo e nel Rinascimento

Associato al solo divertimento, nell’antichità e nei primi secoli del Cristianesimo il gioco era spesso considerato inutile e affatto formativo. Solo tra l’XI e il XII secolo avvenne una sorta di rivoluzione nel mondo della cultura che consentì la nascita di una scientia ludorum, che lo affermò definitivamente anche come piacevole e utile strumento di esercizio intellettuale.

Con la nascita delle scuole monastiche e capitolari la formazione religiosa dell’alto clero era stata ampliata con l’introduzione dell’aritmetica delle proporzioni: le due «scienze sorelle», l’aritmetica e la musica, iniziarono a rivestire un ruolo primario nell’ambito del quadrivium. Il nuovo modo di concepire l’apprendimento investì anche il campo dei giochi, per cui il ludus iniziò ad essere connesso alla disciplina, alla serietà e alla scienza. Oltre ad utilizzare l’abaco, il monocordo, la sfera di armilla e l’astrolabio, infatti, gli studenti delle scuole vescovili dell’Impero di Ottone il Grande si esercitavano con la rithmomachia (‘battaglia delle consonanze dei numeri’) o ‘ludus philosophorum’, un gioco da tavolo il cui fine era ricercare, come veri e propri musici di boeziana memoria, i rapporti che regolavano le consonanze musicali; ciò si realizzava mediante pedine numerate che, poste su un tavoliere, venivano mosse secondo complicati e continui calcoli matematici. Il gioco si diffuse rapidamente anche in Francia, Inghilterra e Italia. Con la ripresa delle opere classiche del Rinascimento ebbe la massima diffusione, dimostrata dalla copiosa produzione di trattati sulla rithmomachia.

Nel corso del XVI secolo furono prodotti diversi manuali sui giochi intellettuali. Nel 1551 il letterato bolognese Innocenzo Ringhieri diede alle stampe i Cento giuochi liberali, et d’ingegno, in cui descrive cento differenti giochi, ciascuno dedicato ad una particolare arte o scienza. Singolari sono i ludi connessi alla musica, definita ora scienza dei numeri, ora come una essenza magica dal meraviglioso potere di dilettare anche «gli orecchi di coloro che non l’intendono».

La fusione dell’aspetto ludico con quello relativo all’armonia aritmetica e musicale è patente nella rithmomachia, una specie di gioco di scacchi creato del secolo XI che preparava allo studio della teoria musicale: nato «pour donner vie au De institutione arithmetica de Boèce», consisteva nello scontro di numeri pari e dispari scritti su pedine bianche e nere di forma differente che si muovono su un tavoliere di scacchi raddoppiato (8×16 caselle). Ogni giocatore disponeva di 24 pedine e l’obbiettivo del gioco è di mettere uno accanto all’altro nel campo avversario le pedine i cui numeri formano la progressione 6, 8, 9, 12, che la teoria musicale pigagorica considerava armonicamente perfetta, sia dal punto di vista musicale, che geometrico, che aritmetico. La ritmomachia è dunque un sistema per apprendere i rapporti armonici fra i numeri, giocando. Come nell’universo si oppongono due principi così in questo gioco si oppongono i numeri pari e dispari: le armonie superiori vengono riflesse sul tavoliere degli scacchi.(Paolo Canottieri)

Está a chegar!

2008-06-25T05:15:00.000-07:00

On Irving

2008-06-20T09:46:00.001-07:00

Wednesday, Jun. 18, 2008
Big Game Hunter
By William Green/London

Irving Finkel's unruly beard is a living relic from another era, a
gleefully eccentric declaration that he cares little for the conventions
of modernity. Indeed, few people live in the past with such delight as
the 57-year-old Englishman, who has worked for the past three decades in
London's British Museum, where he is the assistant keeper in the
Department of the Middle East. At university, Finkel learned to read
cuneiform, the oldest known type of writing, in which wedge-shaped
symbols were pressed into clay with a reed. His Ph.D. thesis was on
ancient Mesopotamian exorcistic magic - the art of getting rid of
demons. If you want to know how men were cured of impotence in Babylon
thousands of years ago, Finkel can tell you the spell.

But no subject, however esoteric, has consumed him more than the history
of board games. At 11, Finkel became so captivated by a book about it
that he wrote to the author and went to stay with him. "He showed me his
huge game collection," says Finkel, "and it transformed my life." Finkel
was especially fascinated by what he learned of the Royal Game of Ur,
which was popular in Mesopotamia 4,600 years ago. As a boy, he made a
wooden replica of the game, but the rules had long been forgotten.
Today, he is the world's foremost expert on the game, and has solved the
mystery of how it was played.

Age-Old Obsession In our era of endless distractions, it's easy to
forget how important board games were to our ancestors. "There were no
entertainments for such a huge period of human existence," says Finkel.
"In that environment, games had a fantastically strong hold.
They reigned supreme." For centuries, even millenniums, the Royal Game
of Ur served as the PlayStation of its day.

Ur was a great Sumerian city in what is now southern Iraq. In the 1920s,
an Englishman named Sir Leonard Woolley excavated its royal tombs and
dug out five playing boards. The British Museum displays the finest of
them - a board that dates from 2,600 B.C. and that is beautifully
crafted in shell, red limestone and lapis lazuli, a prized stone
imported at great cost from Afghanistan. This "was a state-of-the-art
piece of luxury," says Finkel, and it was buried with a princess to
entertain her in the afterworld.

Finkel insists that he knew from the age of 7 that he wanted to work at
the British Museum. In 1979, he was hired there as an expert on
cuneiform inscriptions, "fulfilling in one moment my life's ambition."
One of the joys of the job was that he gained access to the museum's
undisplayed stash of obscure treasures, including 130,000 cuneiform
tablets mostly acquired in the 19th century. Finkel says he has looked
at each of them twice. In the early 1980s, he found one with a unique
pattern on the back that resembled the squares of a game board.

Written in 177 B.C., the tablet was the work of a Babylonian scribe
copying from an earlier document. As Finkel translated the bewildering
blend of Babylonian and Sumerian words, he began to realize it was a
treatise on the Royal Game of Ur. The author speculated on the
astronomical significance of the 12 squares at the center of the
20-square board and explained how certain squares portended good
fortune: one square would bring "fine beer"; another would make a player
"powerful like a lion."

To Finkel's delight, the tablet also revealed a slew of long-lost
details about how the game was played - for example, how the two
opposing players used dice made from sheep and ox knucklebones, and what
numbers they had to roll before their pieces could be launched onto the
board and begin racing around it. According to the tablet, each player
had five pieces (though in Ur, they each had seven) and the winner was
the person who moved all of them off the board first.

Armed with this new insight, Finkel persuaded the museum to create and
sell a replica of the game. Not long afterward, chess legend Garry
Kasparov, along with his wife and bodyguard, visited the museum for a
private tour, and Finkel gave him a copy of the game. Kasparov's agent
later phoned to say the Russian master had spent an entire weekend in
Moscow playing it with the French chess champion. The Frenchman "had won
by something like 36 games to 29," recalls Finkel, "and was the new
world champion of the Royal Game of Ur."

Spread by traders, soldiers, missionaries and other pioneers of
globalization, Ur caught on as far afield as Iran, Syria, Egypt,
Lebanon, Sri Lanka, Cyprus and Crete. While religion has often been
"transmitted by violence," says Finkel, games transcend borders because
we share a craving for entertainment and competition. The Royal Game of
Ur jumped classes, too. In the British Museum, there is a 2,700-year-old
graffito version scratched onto a limestone gateway to a palace in
Khorsabad, once the capital of Assyria. Carved with a sharp object like
a dagger, this makeshift board would have been used by soldiers to
distract themselves from the tedium of guard duty.

But all games are vulnerable to the forces of creative destruction, and
this one was killed primarily by the arrival of backgammon - a more
sophisticated race game in which better players routinely win because
the balance between luck and skill has improved. And so it was that the
Royal Game of Ur died out nearly 2,000 years ago.

Or so Finkel thought until, to his astonishment, he stumbled upon a
remarkable photograph. Tucked away in an obscure journal published by a
museum in Israel, it showed a scratched-up wooden board game that had
belonged to a Jewish family in the Indian city of Cochin. Finkel
collects Indian games, but he had never seen anything like this in
India: the board had 20 squares - just like the Royal Game of Ur. He
knew that Cochin had, until recent decades, a vibrant community of
Jewish traders who came from Babylon more than 1,000 years ago. Was it
possible that the game had stayed alive in this insular community, while
elsewhere it had become extinct?

Staying Alive Most of Cochin's Jews had long since emigrated to Israel.
Finkel has a sister who lives in Jerusalem, so he dispatched her to a
kibbutz in the north where many of the Cochin Jews had settled. Finkel's
sister went door to door with a drawing he'd done of the board until she
found a retired schoolteacher in her 70s named Ruby Daniel, who
remembered playing the game as a child in Cochin.
Finkel flew to Israel, interviewed Daniel and played the game with her.
She told him it was a popular pastime for women and girls when she was
growing up, and that she had played it with her aunts on wooden boards,
using cowrie shells for dice. By then, each player had
12 pieces, and the placement of the 20 squares had shifted slightly.
But it was clearly the descendant of the game played in their ancestral
homeland of Babylon 4,600 years ago.

This pattern of what Finkel calls "spread and evolution and decline and
rescue and unstoppability" is at the heart of what fascinates him about
board games. Intermittently, governments have tried to curb
them: China outlawed mahjong during the Cultural Revolution, and the
Taliban threatened chess players with execution. But games defy control,
mutating and leaping boundaries with an inexorable life of their own.
Pachisi, says Finkel, was played in India for centuries, jumped to
Britain by 1875 and was repackaged there as ludo, which was exported
back to India around the 1960s: "Nowadays, Indian children play ludo
completely oblivious to the fact that it is a monstrous decomposition of
their own fantastic board game."

Monopoly has proved equally mutable. Invented by a Quaker woman a
century ago, it was intended "as propaganda against the wicked practice
of speculation in property," says Finkel, but it turned into a
blockbuster that "can rouse the most placid aunts to a state of virulent
materialism." Finkel is a huge fan, noting that the idea of renting out
a square was the last "momentous" innovation in board games. After a
lifetime of studying the greatest games, Monopoly is the one he plays
most with his five children. But true to the tradition of eternal flux,
the family has made some adjustments. "We have a rule in our house,"
says Finkel. "We all pick on one person and drive them into a fury,
which works very nicely. If they kick over the board and say, 'I'll
never play again,' that's perfection."

Learn more about the game of UR at

Play an online version of the game at

Buy the game at

Romans Used 20-Sided Dice

2008-06-20T05:16:00.001-07:00

Romans Used 20-Sided Dice Two Millennia Before D&D

By Dave Hinerman June 15, 2008 | 6:00:00 AMCategories: Games

Many of us geeks take great pride in the ability to recite the history of role-playing games based on the 20-sided die, but what about the history of the die itself? Apparently it predates the original Dungeons and Dragons by almost two millenia.

Christie's, auctioneer to the rich and famous, sold a glass d20 from Roman times. It was included in a collection of other antiquities that sold in 2003. The markings on the die don't appear to be either Arabic or Roman numerals, but it's probably a safe bet that it was used in a game of chance. As the auction catalog notes that several polyhedral dice are known from the Roman era, but remarks, " Modern scholarship has not yet established the game for which these dice were used."

I wonder - how do you say "critical hit" in Latin? (Ed. note: "maxima plaga")

The seller acquired this die from his father, who picked it up in the 1920s in Egypt. Sounds like the beginning of an Indiana Jones movie, doesn't it?

(Thanks to Marty for the pointer. Photo from Christie's web site.)

Retirado de http://blog.wired.com/geekdad/2008/06/what-version-of.html

A Dream

2008-04-20T09:51:00.001-07:00

The Dream : A Rebus
by Kim Palmer

In 1988, Pagoda Books (in the UK) and Salem House (in the US) published a little puzzle book called "THE DREAM: A rebus, fully illustrated", by Kim Palmer. Except for a short preface, the book consisted of a series of pictures, forming an elaborate rebus. The inside jacket of the book announced that a prize (an attractive lapel pin) would be awarded to every person who deciphered the puzzle and submitted a correct solution along with a corner of the jacket as proof of purchase.

I bought a copy of the book, and worked on it for months, penciling in my guesses, and struggling to figure out some of the more obscure pictures. I pestered my friends to help me, and in some cases, they were able to figure out parts of the puzzle that I could not decipher. At some point, in desperation, I even posted a message on the Internet, asking for help, but got no answers. After working out about 60% or 70% of the text, we got no further and the remainder of the text remained wrapped in obscurity. Several years later, I opened the book again, decided I was never going to be able to finish it, and passed it on to a friend.

In January, 2005, I received a charming letter from Chiara Lagani, a dramaturgist in Italy, who adapts, rewrites, and creates productions for a theater company. She was planning an event that involved rebuses (in Italian!) but had stumbled across "The Dream", and thought that she might like to include some of that work in her presentation. She had managed to decipher several of the first pages on her own, and then had gotten stuck.

Somehow, an Internet search she made turned up the posting I had made back in 1988 (I have not been able to locate this message myself!). So when she wrote to me, she had some hope that I'd had enough time to work out the solution! I had to confess that I had given up, and given away the book, and forgotten everything. But I ordered another copy of the book from Amazon, (for $2.00!) and began working my way back; in a month, it seemed like I'd recovered everything I had the first time; for a few more months, I was able to make excruciatingly slow progress. I begged for help from friends, and from time to time one more word or phrase would pop out, but there followed months of no further insight.

The solution was only completed due to the help of friends, and a few total strangers who somehow had also been bitten with the bug, and had been working independently toward the same goal.

Thanks to my friend Deb Nigra, who suffered with me through the first attempt at a translation, back in the Stone Age of 1988!

Hats off to my friend Jeff Borggaard, for several productive sessions which gained us "F-STOP" and "TOOL", "LONG" and "GAMAY".

Thanks to my friend and former office mate Greg Hood, who came up with "WEAVER DEW TEE"! (Please let me know when Stu has vacated my chair so that I can come back!)

Thanks to Internet correspondent Chris Rubeo, who corrected "MAY IBIZA ARAB ALICE" to "MAY IBIZA MOOR ALICE", and corrected "INTERN ASH SHEAR OWL" to "INTERN ASH SHORN OWL".

A very humble thanks to Lois McCormack, who independently worked out most of the puzzle, (although, she said, that at one point the process had become so painful that she hid the book in her attic) and cleared up words, phrases, and entire sentences on pages 14, 22, 23, 27, 29, 30, 31, 32 and 43, after I had gotten into the most dreadful mental deadlock.

After a little thought and consultation, Lois sent even more information that cleared up pages 26 and 27, and 33, and pretty much ended the job.

Thanks to Teresa Di Staso who wrote in February 2007, confessing that she had also been working on the puzzle, off and on since 1988. She supplied some alternate readings of lines that made more sense. In particular, I was unfamiliar with "globe artichoke", and the best I had come up with was "hearts" (from artichoke hearts) where "globe" was surely intended. Where I had "DISH EWES" she suggested the more sensible "PROBE LAMBS". Where I had the clumsy "PLACE CARDINAL SIGNS" she had "SET TIT WRITE", and my "SHEET TACK KIT TRIP" was bettered by "SHEET TWO KIT TOUR". The Humpty Dumpty figure I interpreted as "EGG" but she suggested "RHYME", which I'm not completely sure about, yet it makes the more pleasing "APE RHYME X SAMPLE" instead of "APE EGG X SAMPLE". And finally, she asks, what is going on with the mysterious "pyrex plate"? I too remain mystified by that phrase, and yet nothing else comes to mind.

Thanks, of course, to Chiara Lagani, for causing all this trouble!

These new breakthroughs have answered the final clues; while some of the answers may seem a bit fanciful or stretched, and there are a few clues for which alternate readings exist, the entire narrative is in place and makes sense.

Cover

A GRATE TAIL FOUR HOUR THYME

A Great Tale For Our Time.

Page 6

DOUGHNUT LETTER CONE NUN DRUM BEET U.

Do not let a conundrum beat you.

Page 7

THIRD EEL LIGHT FULL TAIL OVEN ALLEY

The delightful tale of an alli-(gator)

Page 8

GATE OAR HOOF HOUND ASS SOUP HERB WEIGHT TUBE

(alli)-gator who found a superb way to b-(ring)

Page 9

RING PEAS SAND CENTS TWO HOUR GLOBE (a kind of artichoke) (TRAFFIC STOP)

(b)-ring peace and sense to our heart.

Page 10

LAST MARCH CHIDE DAD REAM WITCH

Last March I had a dream which

Page 11

EYE CAN KNOT PERM MITT MICE ELF TWIG GNAW (UPRAISED HAND)

I cannot permit myself to ignore.

Page 12

INN A PHAROAH FUND DISC COVERED PLACE CLOSE TWO

In a faroff undiscovered place close to

Page 13

HORSE TRAIL EAR MEN KNEE CRETE JAWS DICE/DIX (French "10")

Australia many creatures de-(cided)

Page 14

SIDE HEAD TWO DISCUS HUMOR KNIT

(de)-cided to discuss humanit-(ty)

Page 15

TEA HAND REEL LATE HEAD PROBE LAMBS (FINISH FLAG)

(humani)-ty and related problems.

Page 16

SEAL IRON TOLL DOVER CAT ASS TROPHY HAT CHURN

Sea lion told of a catastrophe at Chern-(obyl)

Page 17

KNOB BILL DASH APE EGG/RHYME X SAMPLE OVEN

(Chern)-obyl - a big/prime example of a(n)

Page 18

KNEAD FOUR GRATER SAFE TEE (BUS STOP SIGN)

need for greater safety.

Page 19

ANT ELOPE SPOKE COUGH POP YULE

Antelope spoke of popul-(ation)

Page 20

ASIAN CRY SEA SAND CHILLED WREN GO

(popul)-ation crisis and children go-(ing)

Page 21

WING HUN GRIEF FOUR DAZE SAND DAYS (CAMERA F-STOP)

(go)-ing hungry for days and days.

Page 22

I SEE LEA TELL PIECE SAW LOVE HIP

I see little peace or love hip-(popotami)

Page 23

POPE POT TAME EYE COMB PLANED (POLICEMAN SIGNALING STOP)

(hip-)popotami complained.

Page 24

WEAVER DEW T(-square) TWO SET TIT

We've a duty to set it

Page 25

WRITE SEDAN ALLEY GATE ORE (FLAGMAN SIGNALLING STOP)

right, said an alligator.

Page 26

LETTUCE SCENTER MESS AGE HONOR PIE REX PLAY

Let us send a message on a pyrex pla-(te)

Page 27

TANNED LET TEAT SAIL TWO C HONOR WAVE (MUSICAL STOP)

(pla)-te and let it sail to sea on a wave.

Page 28

WHEEL WEIGHT HAND FINE DOUBT HOOK

We'll wait and find out who

Page 29

COMBS STACK CROSS SITAR CITIES FLOAT TING (STOP WATCH)

comes across it as it is floating.

Page 30

KNOT LONG AFT TERRACE MAUL KID K

Not long after, a small kid c-(ame)

Page 31

MAE CROSS SIT BUYER BEECH (MORSE CODE S-T-O-P)

(c)-ame across it by a beach.

Page 32

SHEET TWO KIT TOUR PEAR RENTS HOOP ROME

She took it to her parents who prom-(ise)

Page 33

MISS DATE RIGHT TWO INTERN ASH SHORN OWL FIG HERS (STOP BUTTON)

(pro-)mised they'd write to international figures.

Page 34

BEE FOUR TOOL LONG GAMAY JURY VENT

Before too long, a major event

Page 35

TOFFEE NOAH MOUSE IMP PORT TENTS SOCK HERD (TYPEWRITER PERIOD KEY)

of enormous importance occurred.

Page 36

WORLD RULERS UNIVERSE AWL LEAP PROP

World rulers universally prop-(ose)

Page 37

POSED TWO MEAT TIN ORDER TWO

(pro-)posed to meet in order to

Page 38

IMP ROOF HOUR PLAN NET

improve our planet

Page 39

FOUR COMB MING GENERATIONS (ARM SIGNALS SPELLING S-T-O-P)

for coming generations.

Page 40

B LEAF FIT TORE KNOT TIN

Believe it or not, in n(o)

Page 41

O THYME THERMOS TAM MAIZE SING REVOLUTION

(n)o time, the most amazing revolution-(s)

Page 42

SIN WORLD CLIMB EIGHT A ROSE

(revolution)-s in world climate arose

Page 43

A LASS BUTTER DREAM (ORGAN STOP)

alas but a dream.

Page 44

MAY IBIZA MOOR ALICE

Maybe the moral is:

Page 45

SIEVE YOU AIM TWO IMP PRESS POLLY

if you aim to impress poli-(ticians)

Page 46

TITIANS U LAUGHTER RIGHT TOOTH

(poli)-ticians, you'll have to write to th-(em)

Page 47

HEM EWES SINGER RAY BUS (FINISH LINE)

(t)-hem using a rebus.

Back Cover

THISTLE A MUSE YEW FOUR SHORE

This'll amuse you for sure.

Jogos Intemporais

2008-04-02T12:18:00.001-07:00

Um Jogo de Alquerque no quotidiano da Praça de Almeida e os Jogos do Moinho em Castelo Mendo

Castelo Mendo, Jogo do Moinho (58X40cm), época medieval. Jogo inscrito numa pedra encontrada na Devesa, exterior da cerca.

“Há jogos inerentes aos estádios evolutivos, aos ciclos sociais, aos sexos, às actividades e sectores tradicionais, jogos intemporais que se perpetuam local e regionalmente, que por razões culturais se prolongam no colectivo atravessado os limites geográficos da criação”.
As actividades lúdicas sempre foram praticadas pelo ser humano, motivo pelo qual vemos inúmeros vestígios disseminados pelo espaço humanizado. É certo que na actualidade há uma especificidade tecnológica que nos faz esquecer que, no passado recente, as actividades lúdicas desenvolvidas representavam a modernidade conceitual do lazer. É nesse contexto que a cultura ancestral de intercâmbio lúdico entre dois seres humanos se desenvolve, desde a mais tenra idade até ser adulto.
Há jogos inerenteS aos estádios evolutivos, aos ciclos sociais, aos sexos, às actividades e sectores tradicionais, jogos intemporais que se perpetuam local e regionalmente, que por razões culturais se prolongam no colectivo atravessado os limites geográficos da criação, ou outros que crescem e desenvolvem, mas também perecem de forma efémera, dos quais o rasto se diluiu na poeira da Humanidade. Por vezes há actividades lúdicas que surgem num determinado local, por mero acaso, fruto de um sem número de factores, sem sabermos os motivos das suas funções ou razão de ser.
No início começam por ser estranhas ao meio, passando a inovadoras de tal forma que rapidamente se enraízam no seio local, abraçadas como se tradicionais fossem e sem memória da sua existência ancestral. Perduram por vontade própria da sociedade que as pratica, por prazer ou negócio, lícito ou ilícito, mais por encanto, mais por um passatempo que os ajude a desbravar o seu ócio temporal.
É precisamente sob esse aspecto que vamos analisar a existência de dois tabuleiros do jogo do alquerque no quotidiano da Praça militarizada de Almeida e de dois jogos do moinho existente num monólito e num afloramento em Castelo Mendo.
Foi por volta de 1994 que encontrei os jogos do alquerque na Sala da Guarda, lateral esquerdo das Portas interiores de Santo António, no reduto fortificado da Praça de Almeida. Estão incisos no chão e no banco conversadeira do designado Quarto do Sargento da Guarda. O jogo em causa está integrado no grupo dos jogos de interior e foi, sem dúvida alguma, praticado por quem tinha acesso ao local; isto é, os militares que se encontravam na Praça ou, e quanto a nós, pelos presos políticos que aí se encontravam no período designado de Guerras Civis liberais (1832-1834). Durante esses fatídicos anos alguns dos equipamentos militares, da Praça de Almeida, foram utilizados como prisões políticas prendendo-se um conjunto de presos que divergiam ideologicamente do regime vigente, de cariz absolutista.
Nos outros espaços destinados a prisões e a quartéis não encontramos mais nenhum testemunho destinado ao lúdico, sendo, até ao presente, os dois tabuleiros do jogo do alquerque os únicos exemplares.
Os jogos apresentam-se integrados na tipologia do jogo do alquerque dos doze, e tem as seguintes características:
Descrição – jogo completo, o tabuleiro é composto por um rectângulo de onde saem duas asas, ou aletas, onde o jogador colava as suas pedras para iniciar o jogo. Cronologicamente situamos os tabuleiros no séc. XIX. Matéria – inscrição em granito.
Exemplares deste jogo localizam-se, na Fonte das Bicas e na Igreja de Nossa Sr.ª do Soveral, em Borba, na Domus Municipalis, em Bragança, no Paço de D. Dinis, em Estremoz, para além de outras localidades, quer em Portugal quer em Espanha.
Também em Castelo Mendo encontramos dois tabuleiros lúdicos incisos num afloramento granítico e num monólito, e que representam o Jogo do Moinho.
O mais antigo é o que se localiza no afloramento, na antiga cerca medieval de D. Sancho, bem perto da igreja de Stª Maria do Castelo. Já apresenta sinais de muito desgaste, pois está em local de passagem, sendo apenas visível os quadrados laterais direito. A informação foi-nos fornecida por Rosa Martinho Ramos, em Setembro de 2006, quando fotografávamos o outro tabuleiro existente na povoação.
O jogo apresenta, na sua origem, três quadrados inscritos que apresentam, em cada um dos lados, um traço perpendicular e não ultrapassa os limites, interior e exterior, dos rectângulos.
Apontamos a sua cronologia para um período medieval, encontrando-se inciso num afloramento granítico. Há diversos exemplos em território peninsular, considerando este tabuleiro bastante simples e sem qualquer particularidade.
O outro tabuleiro do jogo do moinho foi encontrado fora da cerca medieval, no lugar chamado da Devesa e foi transferido, por mim e por Américo Morgado, para a porta do Museu Local em 1999, quando desenvolvi o referido projecto museológico como salvaguarda da memória local, no âmbito da medida de salvaguarda e protecção, pois já estava descontextualizado do seu local de origem. O tabuleiro está completo.
Encontramos um tabuleiro do jogo do moinho com as mesmas características do de Castelo Mendo na Vidigueira, com uma concavidade no centro do tabuleiro, apesar dos materiais serem completamente diferentes, pois o da Beira é inscrito em granito e o do Alentejo é em argila, podendo este ser um tabuleiro de transporte, tal como se deduz pelas reduzidas dimensões do mesmo (12X8.5cm).
No contexto regional encontramos um jogo do moinho em Longroiva, proveniente do interior do castelo, e referenciado no imprescindível catálogo Pedras que Jogam.

Board Games Evening

2007-09-30T12:24:00.001-07:00

Game theory at its best

2007-07-31T08:51:00.000-07:00

Games and cancer! Here.

BALDERIC LE ROUGE.

2007-06-10T03:42:00.001-07:00

BALDERIC LE ROUGE.
Chronicon Cameracense et Atrebatense, sive Historia utrisque Ecclesiae, III Libris, ab hinc DC sere annis conscripta. Nunc primum in luce edita, & notis illustrata Per G. COLVENERIUS.
Douay, Ioan. Bogarde, 1615. Sm.8vo. Contemp. vellum. With engraved printer's vignette on title, 9 engraved illustrations of seals and dice in text, and 3 large folding plates, partly in woodcut and partly engraved, of three different tables for a popular lottery game. (40), 601, (1 blank, 16) pp. Editio princeps of a mediaeval chronicle of Cambray and Arras, containing the earliest known description and representation of a lottery game, which had been invented by Wibold, a French divine from Cambray who died in 965. Inspired by the "Rythmomachia" or "Philosophical Game" of Pythagoras, the game was called by Wibold "Ludus regularis seu clericalis", but it was also known as "Alea regularis contra alea secularis". It was played with a dice with letters instead of numbers, and a board with the names of 56 virtues arranged in squares all around the middle. At the end of the book 3 different tables are given to play this game, two with square boards to be played with dice, and one circular board to be played as a wheel of fortune with a turning pointer in the middle. On verso of two of these tables explanatory text is present, and the game is extensively explained in chapter 88 of the first Book, pp. 143 ff., and is further discussed in the notes at the end, on pp. 461 ff. The folding tables, size ca. 42 x 37 cm, were meant to be cut and mounted to be played with, including the engraved figures of dice. In text the list of names of the virtues, and the figures of dice were given too. The chronicle itself is of interest, written by the French historian Balderic the Red, bishop of Noyon and Tournay, as it gives numerous accounts of scholarly reseach and curious details. The book presents the history from Clovis to 1090, as the author died in 1097. But the outstanding feature now is the representation of a mediaeval lottery game, which according to the inventor could be of use at schools or for charity. The importance of this chronicle was rediscovered in 1834 by Le Glay, who published a new edition based on three manuascipts, and in the preface discussed and explained the lottery game present in it. His Latin edition then was also translated into French in 1836, by Faverot and Petit Good copy of the rare first edition, with the bookplate of Pierre Briffaut.- (Ms. entry on title) Brunet I, 621 Graesse I, 260 cf. Introduction to the new edition by Le Glay, Cambray & Paris, 1834 NUC lists 1 copy only

A ROOK HOUSE FOR BOBBY

2007-05-01T15:40:00.001-07:00

A ROOK HOUSE FOR BOBBY

2007-05-01T11:44:00.001-07:00

They've made mountains out of mole hills
Let them climb
They can chase me to the ends
Of the Earth
And if they find me
Let them indict me
I just don't care any more
They've pushed me too far, too far
They've pushed me too far, too far
All this talk of war
But it's only a game
All I ever wanted to do is play chess with you
But if they find me
They will indict me
I just can't fight anymore
They've pushed me too far, too far
They've pushed me too far, too far
We'll build this rook house here for Bobby
We'll build this rook house here for Bobby
We'll build this rook house here...

---

The Ballad of Bobby Fischer, recorded in 1972 by Joe Glazer & The Fianchettoed Bishops.
No Bishops, fianchettoed or otherwise, can be heard on that disc, nor any real singing - it's some sort of a Country & Western style spoken poem, backed by aimless acoustic guitar riffs. It tells, in 7 minutes, the story of Fischer's life.

He was born in nineteen forty-three
Right away I knew he'd make chess history,
Cause he opened his mouth on the day he was born,
And instead of crying, he said, "Move that pawn
to King four"
When Bobby was three, he went to nursery school
and the things he had to do made him feel like a fool
he had to listen to fairy tales and dance in a ring
but Bobby preferred to do his own thing
like studying the Najdorf Variation of the Sicilian Defence
the kids learned about Red Riding Hood
and all the things that little kids should
about Hansl and Gretl and the wicked old witch
but Bobby, he was studying Nimzovich
(...)
sitting in the classroom he barely could think
cause chess was his food, chess was his drink
(...)
That Bobby Fischer was a chessplaying fool
sharp as a needle, stubborn as a mule
he studied all day and played all night
but he didn't play a match unless things were just right
And I mean right
I mean double right
I mean two hundred percent right
That's right

And so on.

Despite his attempts to innovate
Larsen was bent right out of shape

2007-04-19T04:21:00.001-07:00

La storia e di conseguenza l'esposizione, inizia in Gran Bretagna. Qui i giovani benestanti inglesi negli anni Settanta dell'Ottocento, senza muoversi dalle loro case cittadine londinesi o dai palazzi immersi nel verde delle campagne, viaggiavano. Questo nuovo "Grand Tour", immobile, vissuto sul tavolo di legno massiccio, lo si faceva lanciando i dadi e leggendo le descrizioni di un libretto dalla copertina verdina. Erano le avventure proposte da Alberth Smith nel suo The new Game of the Ascent of Mont Blanc. Da questo gioco da tavolo inizia il percorso della mostra attraverso il mondo (reale o immaginario). L'organizzazione di questa esposizione, che presenta le raccolte appartenenti al Museo, porta alla rivalorizzazione delle "scatole di giochi", vecchie e nuove, fino ad ora guardate con sufficienza, non apprezzate, forse perché non eravamo capaci di capire fino in fondo il loro valore. L'itinerario interminabile di caselle, pedine, dadi e traguardi raggiunti, fa scoprire anche gli angoli più inconsueti del mondo; ad esempio il Klondike, a cui il Museo ha recentemente dedicato una rassegna, percorso in modo parallelo, avanzando casella dopo casella verso l'oro. Sono anche stati trovati molti modi di scalare l'Everest senza usare la piccozza e le corde reali, in proposte del mercato britannico-americano. Molte di più sono le occasioni per scendere con gli sci i pendii innevati di molte tavole da gioco, lasciando la scia dalle Alpi alle montagne Nord-americane. Inoltre, molti avvenimenti, e questa è una delle "scoperte" della mostra, rivivono trasposti nei giochi da tavolo, dalla prima salita dell'Annapurna alle vittorie della campionessa di sci Nancy Greene, dalla processione rituale al Monte Fuji ai viaggi di Nansen in Artide, dal sorvolo dell'Antartide di Byrd a Stanley in Africa! Ma il mondo dei giochi è fatto anche di tanti altri "viaggi" più rilassanti: in carrozza, in auto, in treno. Le mete: il Tirolo e la Baviera, l'Harz, la Svizzera con gli immancabili riferimenti alle cime e ai luoghi simbolo, con una descrizione geografica tale da far rivivere le emozioni e le sensazioni della scoperta di luoghi nuovi, come avviene viaggiando. Oltre al Monte Bianco, non mancano poi le possibilità di salire con poca fatica, e nello stesso modo dell'Everest, la Jungfrau e il Cervino e tante montagne di fantasia. Agli avvenimenti si affiancano anche personaggi nati dall'immaginazione, da Topolino al Sergente Preston; ovviamnente c'è anche Heidi, la pastorella svizzera! La mostra - pur vincolata alla grande collezione del Museo Nazionale della Montagna, di cui è presentazione - costituisce il primo lavoro completo su di un settore dimenticato, un po' snobbato. Forse poco serio, ma molto educativo e, sicuramente, molto divertente. La raccolta del Museo torinese - parte dallo sterminato patrimonio conservato al Monte dei Cappuccini, un patrimonio diversificato e (spesso) anticonvenzionale - è nata per caso; si è arricchita con una prima ricerca; si è completata nella prospettiva dell'esposizione nell'ultimo decennio. Oggi si contano circa 150 pezzi, dalla fine degli anni Sessanta dell'800 alle recenti Olimpiadi Invernali di Torino 2006; una raccolta tanto ampia da rappresentare un punto di riferimento per chi volesse studiare il fenomeno. La straordinaria rassegna si avvale, in modo positivo, di due tipi di "professionalità"; quella di "conoscitori di montagne", rappresentata da Aldo Audisio, direttore del Museomontagna, con tutto lo staff del museo torinese, a cui si è affiancata quella di Ulrich Schädler, "conoscitore di giochi", direttore del Museo Svizzero del Gioco a La Tour-de-Peilz in Svizzera. Alla mostra si affianca ancora un programma didattico, curato dal Museo con la Città di Torino, pensato per aprire anche al mondo della scuola tutte queste "avventure a passo di dadi".

MATEMÁTICA em JOGO no CCB

2007-03-21T12:53:00.001-07:00

Xadrez

2007-03-10T18:06:00.000-08:00

(De: http://www.mocoloco.com/art/)

Simplicity rule(s)

2007-03-05T15:37:00.000-08:00

here.

Pacioli's De ludo scacchorum!

2007-01-09T08:51:00.000-08:00

It is with great pleasure that the Fondazione Palazzo Coronini Cronberg of Gorizia announces an important discovery made in its library collections and related to the Renaissance history and culture.

The bibliophile and book historian Duilio Contin has in fact discovered among the manuscripts and antique books gathered by Count Guglielmo Coronini a document dating from the end of the 15th C and considered lost for centuries: it is the manuscript of the famous mathematician Luca Pacioli (1445c.-1517c.) called “Game of Chess”, often mentioned in bibliographical documents but never found.

This manuscript called by the author “De ludo scacchorum ...” and known as “Schifanoia” was dedicated to the marquise of Mantova, Isabella d’Este.

During his research commissioned by the Centro Studi of Aboca Museum of Sansepolcro concerning bibliographical studies on Pietro della Francesca and Luca Pacioli (both born in the Tuscan town), Duilio Contin had applied to the prestigious Fondazione Coronini Cronberg of Gorizia to examine the rich library containing more than 22,000 volumes.

Only by chance Serenella Ferrari Benedetti, cultural co-ordinator of the Fondazione, drew Contin’s attention to the anonymous manuscript on the game of chess, in which several scholars had been interested, ignoring it was Luca Pacioli’s most researched book.

Chessboxing, official presentation (WCBO)

2006-12-10T05:33:00.001-08:00

Chinese chess in Zhangye

2006-12-07T03:38:00.001-08:00

Game Theory, One More for Saint Michael 1987

2006-12-07T03:16:00.001-08:00

LMAO board game strategy

2006-12-06T05:58:00.001-08:00

Présentation du Go

2006-12-06T04:39:00.003-08:00

GO Time Frames, game of GO/WeiQi/Baduk in images

2006-12-06T04:39:00.001-08:00

Game of GO small introduction - (japanese)

2006-12-06T04:38:00.003-08:00

Japanese game of GO (Baduk, WeiQi)

2006-12-06T04:38:00.001-08:00

Megas 2

Missing piece

Truque

Jogar e trabalhar... santíssima díade !

A Década dos Jogos - a camada lúdica

Play, Culture & Religion

Campeonato diferente

Do ATITUDES

Tarde animada no Taguspark

A equipa açoreana regressa a casa após brilhante participação no CNJM6, em Santarém. 4/4.

A equipa açoreana regressa a casa após brilhante participação no CNJM6, em Santarém. 3/4.

A equipa açoreana regressa a casa após brilhante participação no CNJM6, em Santarém. 2/4

A equipa açoreana regressa a casa após brilhante participação no CNJM6, em Santarém. 1/4

Campeonato Regional de Jogos Matemáticos dos Açores

Campeonato Regional de Jogos Matemáticos dos Açores

truk

truk

The Royal Game of the Ombre

António Silva Araújo sobre Damiano

BOARD GAME STUDIES COLLOQUIUM XIII

Seega

Jeux de princes, jeux de vilains

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Numerais gregos no Rithmomachia

Bridge is good for you

George Berkeley plays games!...

Jogos de quê?

http://chessderivatives.blogspot.com/

Aulon(?)

Está a chegar!

On Irving

Romans Used 20-Sided Dice

Romans Used 20-Sided Dice Two Millennia Before D&D

A Dream

The Dream : A Rebusby Kim Palmer

Jogos Intemporais

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Game theory at its best

BALDERIC LE ROUGE.

A ROOK HOUSE FOR BOBBY

A ROOK HOUSE FOR BOBBY

MATEMÁTICA em JOGO no CCB

Xadrez

Simplicity rule(s)

Pacioli's De ludo scacchorum!

It is with great pleasure that the Fondazione Palazzo Coronini Cronberg of Gorizia announces an important discovery made in its library collections and related to the Renaissance history and culture.

This manuscript called by the author “De ludo scacchorum ...” and known as “Schifanoia” was dedicated to the marquise of Mantova, Isabella d’Este.

Only by chance Serenella Ferrari Benedetti, cultural co-ordinator of the Fondazione, drew Contin’s attention to the anonymous manuscript on the game of chess, in which several scholars had been interested, ignoring it was Luca Pacioli’s most researched book.

Chessboxing, official presentation (WCBO)

Chinese chess in Zhangye

Game Theory, One More for Saint Michael 1987

LMAO board game strategy

Présentation du Go

GO Time Frames, game of GO/WeiQi/Baduk in images

Game of GO small introduction - (japanese)

Japanese game of GO (Baduk, WeiQi)

The Dream : A Rebus
by Kim Palmer