Adam McLean wrote:In 1616 a very curious book was published in Venice, the Labarinto by Andreas Ghisi.
The title page reads :
"The Labyrinth, newly published by the distinguished Andrea Ghisi, nobleman of Venice, in which are seen 1260 figures, all ready for service, each conforming and corresponding, speaking one to another, and infallibly, on the third turn, the imagined figure will be known, with its secret presented."
It contains a series of 50 little emblems with titles, based on the Tarocchi of Mantegna. There are a few other editions from around this time.
It has always intrigued me. Has anyone been able to solve the secret it poses, which is something to do with the arrangement of these figures into arrays ?
Actually, the arrangement is meaningless. So are the images.
Sorry -- sad but true. It's a trivial parlor trick, a 3-step guessing game. It's more of a trick than a game, because the outcome is assured. The fact that the images are incidental is demonstrated by there being two versions of the game having different images. In 2007 I wrote up some materials on the English language version of the game and its images. (It might even be on Google Books by now! Odd -- they have it but won't show it.) Let's see... ah, upload attachment. Never tried this before... should be interesting. No joy... oh well. I can send you a PDF file with the text and images, but I really don't have time to try and format the images for a post. I'll just include the text.
The same general method is used in a well-known 3-step card trick. There are a number of places on the Web where it is discussed. Back on LTarot, when I first presented this stuff, I suggested this link as a good example. Working through it explains the process of Labyrinth pretty clearly. Then maybe my description below will make more sense.
Twenty-One Card Trick
Another article on the 21-card progressive elimination trick that I posted at that time is much longer and vastly more mathematically sophisticated. It might be helpful if you actually wanted to create a book like Ghisi's.
Expansion/Analysis of a Card Trick
Comprised of Transformations in 2-Dimensional Matrices
The Labyrinth trick began with one person selecting a subject from the 60 shown on the initial page, without telling anyone which item was chosen. The item he selected would then be determined by the person who knew the trick.
The method for determining which figure was selected took three steps. In the first step, the person identified which of four groups, the four groups of 15, his subject was in. This instantly eliminated 3/4 of the possibilities. (If there had been only 4 subjects, this would have been the end the selection process.) Each of the four groups leads to one of four secondary pages, where the person again identified which of the four groups on that page his subject was in. This is where the arrangement becomes important -- because of the arrangement of the pictures on the secondary pages, this eliminated 3/4 of the remaining possibilities. The arrangements were meaningless but crucial, sub-dividing the initial groups so the selection process conveyed far more information than it seems. (If there had been only 16 subjects, this second selection would have ended the elimination process and identified the subject.) This same process takes place a third time. (If there are only 64 subjects -- and there were in fact only 60 -- this ends the selection process.) The selected array on this third turn is the answer array, and there are 60 (of the 84 total) arrays dedicated to this function. Reading the answer panel is easy. The initial letter of the top-left figure is the (n)th letter of the alphabet. (For example, D is the 4th letter.) The selected subject is located in the (n)th position of the array.
It may make more sense after reading the whole instructions. I can't figure out how to attach or upload a PDF file, so I'll include the text.
Variations on that progressive elimination method are also provided for determining numbers and for guessing common names. Exactly what the method was in the 1616 edition is unclear, given that the Italian Studies article says that it varied somewhat from the 1610 English version, which is the only one I've seen. However, the basic method of progressive elimination is quite clear.
Here is the text.
[P.S. Here's a URL that (for the moment, at least) accesses ProQuest (I think) for their PDF version of the book. I don't think it's supposed to work unless you are at the Universidad Pablo de Olavide, Sevilla. It's only 24 pages, but you probably didn't want to actually print it out and use it anyway. The first few pages, the ones I used to have online, are the significant ones.
Wits Laberynth, or The Exercise of Idlenesse
THE EXERCISE OF
CONTAINING AN ARTIFICIALL TEXTVRE
OF TWO THOVSAND TWO HVNDRED AND SIXTIE
Figures, so placed and disposed, as by the helpe of a brief Direction for that
purpose, you may tell which of them any man thinketh.
AS ALSO BY THE SAME OBSERVATION, TO
discouer any name, or number, that shall bee imagined.
BESIDES AN AMPLE AND LARGE SVBIECT FOR THOSE THAT
affect such ingenious recreations, by the sharpnesse of their owne conceits,
to drawe out many other delightfull varieties.
FIRST COMPOSED IN ITALIAN BY ANDREA GHISI, AND NOW
Englished and augmented.
Printed by Thomas Purfoot, and are to be sold at Britaine Burse
by Iohn Budge. An. Dom. 1610
The Authors Epistle to the Prince of
Mantoa Don Francesco Gonzaga.
In all humane actions, the passage from one extreme to another was euer difficult and dangerous, and therefore for recouery of wearynesse procured by labour and exercise either of mind or body, which of necessity men must doe, was sport inuented, which is no other thing but the Exercise of Idlenesse. For that it being by his owne nature pleasurable, it might ease by little and little the teadiousnesse and burthen of saciety and lassitude, and so gently drawe a man to rest and quiet. Now because labours be of diuers natures, and diuers (also) be the natures of the persons that vndergoe and endure them, to the end that euery one might find recreation proportionable to his disposition, there is graunted unto sport and pastime, the liberty of variety. Variety, wherein nature so much gloryeth, and mans mind, and euery sence of his so much delighteth: which, not satisfied with all that the world can afforde thereof, do runne with restlesse feete, or rather wearylesse winges, but can neuer runne ouer the huge field and the large confines of thinges therein contained. With this variety I being enamoured, by dressing and digging the small Garden-plotte of my weake wit, haue drawne thereout the fruit of this my Laberinth, to which your Highnesse I humbly dedicate.
Your Highnesse most deuoted Seruant,
A direction for the vnderstanding of the
order of this Booke.
You are first to obserue, that the whole Book comprehendeth One and twentie leaves, which are seuerally marked at the top of the margins with the Letters of A, B, C, according to the order of the Italian Alphabet. Euerie opening of the Booke presents you with Threescore Figures or Pictures, aptly distinguished into foure quarters, two upon each side, and fifteen figures in euery quarter. Now if you would know which of those figures a man thinketh, thus you shall performe it.  Let the partie imagine any figure he pleaseth amongst those of the two first Pages of the book, and hauing thought it priuately to himselfe, let him tell you onely in which of the foure quarters it standeth. Then looke with what letter the name of the first figure of that quarter beginneth, and turne to the leave in the alphabeticall order which is noted with that letter: as if the figure he thought were in the first quarter, the first figure is Melancholy which beginneth with M, and you must turne to the leafe which is marked with the letter M on the top of the margent.  This done, bidde him seeke out his figure in the fower quarters of that leafe, and tell you in which of them he findes it there; which knowen, you must againe as before, take the first letter of the first figures name of that quarter, and likewise turne to the leafe that is noted with that letter.  Then the third time aske him in which quarter of that leafe his thought figure standeth, which being tolde, marke what letter is the first of the first figures name of that quarter, and also in what place in the Alphabet that letter standeth, as whatever it be the first, second, third, or fourth in number: and so begin to account the figures of that quarter, calling the first fugure A, the second B, &c. till you come to your letter which is the first of the quarter last mentioned, and when you come to that letter, the Figure it falles vpon in reckoning so the letters by the figures, is the figure that was first imagined.
But by example the matter shall be more easilie conceiued.  Suppose one thinkes a figure in the first quarter, by name the Gnat, looke then for the first letter of that quarter which is M, then turne to the leafe marked with M, and  bid him search out his figure he thought, and he will find it in the fourth place of the third quarter. He hauing told you it is in that quarter, looke with what letter the name of the first figure of that quarter beginneth, and you shall see it is O, then turne to the leafe O, and  bid him tell you in what quarter he finds it there, and he will tell you it is in the fourth quarter of that leafe. Obserue then what letter beginneth the first figures name of that quarter, and you shall find it to be D; and likewise in numbering the letters according to the order of the Alphabet, that D standeth in the fourth place, as A, B, C, D. Then beginne at the 1. figure of that quarter, and say vpon it A, vpon the 2. figure next following B, vpon the 3. C, and vpon the 4. D, and so you shall find where the letter D lighteth, that is the figure of the Gnat, which the partie first thought; And so consequently of all the rest.
Now for the numbers annexed to the pictures of the 4. first quarters of the Book, if you would known which of them any man thinketh; let him first marke and obserue to himself the picture where his number standeth, then bid him seeke out that picture in the leafe M, where he shall find it matched with some other different number, which number let him take and carrie in memorie to the leafe S, where he shall likewise find that nuymber placed with some other picture. That picture let him seeke out in the leafe Z, and onely tell you what number he fins thereto adioyned, from which take 6. and the remainder shall be the number that was first imagined.
Admit the number imagined were 40, which standeth under the picture of Honour; seeke out that picture in the leafe M, and you shall see it marked with 52, which number (turning to the leafe S) you shall find placed under the figure of Fortitude, and that figure sought out in the leave Z gives you 46, from which take 6, and so rests 40, your number desired.
If you would known by a meere coniecture what name any one thinketh (whether of himselfe, his friend, or his Mistris) so it be no strange or new diuised name but the vsuall proper name of a man or woman: thus by helpe of the former rules you shall performe it:
Let the party which hath conceiued such a name in his mind, choose some figure (amongst those of the first quarters of the booke) which beginneth with the same letter that his supposed name doth: and hauing thought such a figure, you shall vnderstand which it was by the direction of the first Rle. So haue you certain knowledge of the fist letter of his imagined name. Which resuruing to your self (without telling him as yet what picture he thought) bid him reckon with himselfe how manny letter there are in the name he thought, and choose a picture that hath the same number annexed to it, which number you are sufficiently instructed by the second Rule how to find out, and hauing found, you then known both the first letter of the name he conceiued, and likewise how many letters it containeth: vpon which ground it is easie to tiue so neer a gesse to the truth, as shall not once fayle in many tryalls. And so by this meanes you may discouer, both what name, what number, and what picture is thought all at one time. But note that when you are to find out any name beginning with A, or WQ, though generally you vse the letters of the Italian names of the pictures, and not the English, yet there you must take the first letters of the English word; Adamant, and Wraith, because there is none of the pictures names in Italian begin with those letter. By example this Rule wil be cleared of all difficult:
Suppose one thought his Mistresses name, and her name were Elizabeth, the first quarter of the first leafe of this Book presents him with a picture, whose Italian name beginneth with the same letter, namely Essercito, the Armie. And following the order of the first Rule, the first letter of the 1. figures name of that quarter being M, you are thereby directed to the leafe M, where he finds the picture of the Armie in the fourth quarter, whose 1. figure is the Quaile, swhich sends you to the leafe Q, and there his figure standing in the 2. quarter, and the second quarters 1. figure beginning with B, you conclude therevpon that the figure he thought was that of the Armie, and consequently that his imagined name beginneth with E, answerable to the first letter of the Italian word Essercito. This kept in memory, you proceed to inquire what number of letters the name containeth, which being 9. and that number conceued in his thought he findes is vnder the picture of Fate. Then by order of the second Rule, seeking out that figure in the leafe M, it is there marked with 21. and from ????????? to the leafe S, the same number shall be found with the picture of the Fencer, who in the leafe Z hath only 15. from which abate 6. there remains 9. heiust [just the?] number that was thought, equall to the letters of the name imagined. Thus knowing that the name beginneth with E, and comprehendeth nyne letters, for that there is no other ordinary name consisting of the like number and beginning with the same letter, calling to mind what hast past in all this proceeding, you resolue at once that the figure he thought was the Armie, the number 9. and the name Elizabeth.
To tell a man how much money he hath in his purse, both Poundes, Shillings, and Pence, beeing within the compasse of three Pounds, this Book shall likewise effect it, in this manner. First, for as many shillings as he hath in his Purse or conceaueth in his mind, let him finde out a number answerable there vnto in the first leafe of the Booke, and likewise obserue what picture that number is placed withall: which Picture, bid him tell in what quarter it standeth, and then proceed (according to the first rule) till you come to the knowledge thereof: which keepe to your selfe, and at the instant bidde him adde the number of his Pence to the number of his shillings, and giue you the summe of both, whilste in the meane time turning carelessely backe to the leafe A, you shall there discouer the nuymber of his shillings, standing with the Picture he thought: which number seperate from the whole summe he giues you, and so haue you in seuerall numbers the iust summe of shillings and pence which he first imagined.
Admit the summe which the partie hath or thinketh were 2.Pounds, 6.Shillings, and 8.Pence. The number of sshillings is then 46. which number beeing placed with the figure of the Griffin, in the third quarter of the first leafe, giues him occasion to think that picture: and having tolde you where his figure standeth, you proceede on according to the direction of the first Rule, till you knowe the picture he thought was that of the Griffin. Then bidding him put the number of shillings and pence together, and in the mean while returning to the leafe A, you see there 46. the number of shillings which he thought, vnder the Picture of the Griffin: and separating that from 54. (the totall which he giues you of shillinges and pence together) then haue you the accomplishment of this Rule in two numbers, namely 46 and 8. expressing 2. Poundes, 6. Shillinges and 8. Pence.
Note, that in the leafe Z, the two pictures of Kairo, & Essercito are misplaced, the one standing in the others roome, and the number which is with the one, should be with the other. Also in the same leafe the number 14. at the Picture of the Fencer, should be 15. And in the leafe M, the number 22. at the Picture of Fate, should be 21.