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Math and magic: a block-printed wafq amulet from the beinecke library at Yale.

The Beinecke Rare Books Reading Room at Yale University houses an important collection of Arabic papyri and paper documents. Among them are at least two printed texts: P.CtYBR inv. 2016 and P.CtYBR inv. 2367. The latter is a small fragment containing but a few words, and is therefore of little value, while the former is a large fragment of an amulet, and is of considerable interest because it contains two magic squares, that is, squares in which numbers are arranged in such a way as to produce a constant sum in all rows and columns (Ar. wafq, pl. awfaq). Although the use of magic squares in amulets is well attested through theoretical works such as al-Buni's Shams al-maarif al-kubra, and through manuscript specimens, only one other example of a block-printed square is known. (1) What is more, the present piece contains a rare occurrence of a magic square of the order 13 -- perhaps the only such occurrence in all amulets published to date.

P. CTYBR INV. 2016

Provenance: purchased from Alan Edouard Samuel (University of Toronto) in New York, 24 February 1992, who in turn bought the item in Cairo in 1965.

Description: block-printed text on light cream paper; in two fragments: one large fragment (ca. 12x12 cm), representing the lower right-hand corner of a large sheet (approx. 24 x 24 cm or larger), and another small piece of that same sheet.

The verso is blank and smooth; it is devoid of strong creases that would offer clues as to how the sheet was once folded. However, the print of the recto is clearly visible on this side, and in some places -- he recto, a small gap runs though the print from the lower margin upwards, through the small magic square and its containing circle. This appears to stem from a fold in the paper rather than from a cleft in the print matrix.

The print was framed by a band of text enclosed within double borders. Set within this frame, there were a number of separate elements, of which the following remain (counterclockwise from bottom left): a large magic square, a small magic square enclosed by a ring of text, and parts of at least two circles containing text (see the image on p. 618). The large magic square was apparently positioned at the center of the lower margin, while the smaller circular elements were arranged along the right-hand side of the sheet. Assuming that the elements were laid out symmetrically, one can conjecture that at least three more circles are now lost on the left-hand side of the talisman. In addition, there may have been another large magic square at the center of the upper margin of the sheet. Here follows a description of each of the extant elements in turn.

A. Border

The text of the border is in naskhi script, fully pointed and with some vocalization. It is framed on each side by a double line, and its base line is oriented toward the center of the sheet. Beginning on the lower left, the text runs towards the right, then wraps around the corner to continue towards the top. I read


= Qur'an 48:6:

  And that He may chastise the hypocrites, men and women alike,
  and the idolaters men and women alike, and those who think
  evil thoughts of God; against them shall be the evil turn
  of fortune. God is wroth with them, and has cursed them,
  and has prepared for them Gehenna -- an evil homecoming! (2)

Note the omission of three words in this verse. The text continues in the border on the right-hand side:


= Qur'an 2:7-8:

  To God belong the hosts of the heavens and the earth;
  God is All-mighty, All-wise. Surely We have sent thee
  as a witness, good tidings to bear, and warning.

B. Large Magic Square

On the lower left-hand side of the fragment are the remains of a magic square. A block of 6 x 8 cells has been preserved in the bottom right-hand corner of that square, as well as an irregular section of some 23 cells. Altogether, this leaves us with just over one third of the original square of 169 cells, as we shall see below. It is fortunate that this particular corner of the square is still extant, because it includes the number one as well as the beginning of the numerical sequence that follows.

Two peculiarities should be noted: the number four is of the Indio-Iranian type (*), and the number five is represented in the shape of an angular and mirrored capital B, similar to the letter m in Epigraphic South Arabian.

It appears that the square was constructed according to the method for odd-order squares described in detail by Jacques Sesiano, (3) and one can therefore reconstruct the original square in its entirety.

Since this method works only with odd-order squares (i.e., squares with n = 2k + l cells on each side), since the number one is always placed beneath the central cell, and since there are six cells to the right of the central column, one can conclude that the square was once thirteen cells in length on either side, and that it contained [13.sup.2] = 169 cells. Indeed, the number 169 appears in its proper place, that is, in the cell just above the central one. The square would originally have appeared as follows (extant cells are in bold italics):
    a    b    c    d    e    f    g    h    i    j    k    1    m

A   79  164   67  152   55  140   43  128   31  116   19  104    7
B    8   80  165   68  153   56  141   44  129   32  117   20   92
C   93    9   81  166   69  154   57  142   45  130   33  105   21
D   22   94   10   82  167   70  155   58  143   46  118   34  106
E  107   23   95   11   83  168   71  156   59  131   47  119   35
F   36  108   24   96   12   84  169   72  144   60  132   48  120
G  121   37  109   25   97   13   85  157   73  145   61  133   49
H   50  122   38  110   26   98    1   86  158   74  146   62  134
I  135   51  123   39  111   14   99    2   87  159   75  147   63
J   64  136   52  124   27  112   15  100    3   88  160   76  148
K  149   65  137   40  125   28  113   16  101    4   89  161   77
L   78  150   53  138   41  126   29  114   17  102    5   90  162
M  163   66  151   54  139   42  127   30  115   18  103    6   91

The initial cell containing the number one is just below the center at position Hg, and all subsequent numbers proceed to the right and diagonally downwards. When the edge of the square is reached, the sequence continues into an imaginary adjacent square, and is then transferred to the corresponding cell in the main square. For example, we see that the sequence leaves the square after 6 at position Ml; it would enter an adjacent square below at position Am, and 7 is therefore entered at that position in the main square. When the sequence meets a cell that is already occupied -- as with 13 at Gf -- the next number is entered two cells below (If, in this example), and the sequence then continues as before. The sequence ends as the last number ([n.sup.2], where n = number of cells on one side, or "order" of the square) is reached and placed in the cell just above the center -- 169 at position Fg. The sum of each row, column, and central diagonal is determined by the order of the square (when filled in with a sequence of positive integers, as in this case), and can be calculated using the formula M = n ([n.sup.2]+l)/2. For a square of the order of 13, this yields 1,105, which is, indeed, the sum of all rows, columns, and diagonals.

This method for constructing odd-order magic squares may seem simple, but it was only discovered around the beginning of the eleventh century c.e. (4) It is certainly easier to apply than some of the methods that were devised for the construction of squares of even order, as we shall see below.

C. Ring with Magic Square

On the right-hand side, in the lower right-hand corner of the larger fragment, one finds a ring inscribed with a line of text, framed by a double border. The ring is surrounded by a quotation from the Qur'an (6:73), set in the corners between the circle and the surrounding elements. Of the originally four words, only three remain (beginning in the upper right-hand corner):


The verse in question reads

  It is He who created the heavens and the earth in truth; and the day
  He says 'Be', and it is; His saying is true, and His is the Kingdom
  the day the Trumpet is blown; He is Knower of the Unseen and the
  visible; He is the All-wise, the All-aware.

The text within the ring is that of the last chapter of the Qur'an (114), and reads counterclockwise, beginning at twelve o'clock. The letters are partly pointed and vocalized. The most peculiar feature is the absence of dots on shin, while all sins are carefully marked with a hacek. Likewise, the dhal of alladhi appears without a dot, whereas dal in sudur bears a hacek.

  Say: 'I take refuge with the Lord of men, the King of men, the god of
  men, from the evil of the slinking whisperer, who whispers in the
  breasts of men, of jinn and men.'

A small magic square is set at an angle within the inner ring. This square, with 4 x 4 cells, is of the peculiar type that has words instead of numbers in the cells of its first line; the remaining numbers in the lower cells are calculated to match the numerical value of the Arabic letters in the top cells.

The words are printed in naskhi characters, with the same features as in the text of the sura surrounding the square; the words and numbers are set at alternating 45 [degrees] angles to the grid lines to create a sort of zigzag pattern across the lines and columns. I read the following:

the numerical equivalent:

     a      b      c     d

A    181    211     83    562
B   (261)    82    212    180
C    209    179   2[6]7    85
D     84  ( 261)    178   210

The words in the cells of the first line (cells Aa-Ad) are taken from Qur'an 2:137:


And if they believe in the like of that you believe in, then they are truly guided; but if they turn away, then they are clearly in schism; God will suffice you for them; He is the All-hearing, the All-knowing.

Because of the way in which the word in the first cell (Ad) is placed, it is not entirely clear if it should be read as yakfikahum (= 185) or fa-yakfikahum (= 265), but it can certainly not be interpreted as fa-sa-yakfikahum. Since the related cells Ba, Cc, and Db all bear numbers in the 200s, I conclude that the value of cell Ad must be 265, and that the word reads fa-yakfikahum, omitting the sin of the Qur'anic verse. There is a small lacuna in cell Cc, affecting the middle digit of the number therein, but this can be reconstructed as a 6, because the related cells all have values in the 260s.

Although the values for all cells can thus be assigned, it turns out that the square -- as it appears in the amulet -- is not "magic" at all, for the sums of lines A to D are 740, 735, 740, and 733, respectively. At the same time, one can observe that the square contains three sequences of numbers that remain intact, namely, 181, 180, 179, 178; 212, 211, 210, 209; and 82, 83, 84, 85. One may conclude that the problem lies in the last sequence (cells Ad, Ba, Cc, and Db).

Indeed, it would seem at first glance that the method of construction for this type of magic square was not properly understood by the author of this amulet; for even though errors in magic squares are not uncommon, (5) we here find the same number (261) repeated twice. In any case, these values are doubtful, and will have to be revised. In order to do so, it is necessary to consider the various methods for constructing magic squares of the fourth order, discussed at length first by Ahrens, (6) and later by Sesiano. (7)

By far the most common pattern for constructing a fourth-order square for a given sequence of four numbers w, x, y, and z is the following:
    a    b    c    d

A    w    X    y    z
B  y-1  z+1  w-l  x+1
C  z+2  y+2  x-2  w-2
D  x-1  w-3  z+3  y+1

After entering the numbers (or letters with numerical value) in row A of the square, the remaining cells are filled by adding or subtracting from those original numbers in such a way that those subtractions and additions cancel one another out in each row, column, and diagonal. In each sequence, the moves from one row to the next can be described in terms of chess moves (e.g., the move from x [Ab] to x+1 [Bd] is a knight's move), and this method is therefore often called the "knight's move" method. (8) The overwhelming majority of fourth-order squares in al-Buni's Shams follow this pattern, as Ahrens noted, (9) and the same may be true of fourth-order squares found in primary sources.

One such source is the talismanic shirt pictured and described by Francis Maddison and Emilie Savage-Smith in their catalogue of magical artefacts in the Khalili collection, (10) which contains no fewer than eight magic squares of a similar type to the one presented here. As the authors noted correctly, seven of these contain the same error: they show reversed values for cells Cb and Cc.

Returning now to the magic square in our block print, one notes that the values in rows B-D are not arranged in a pattern of knight's moves. (11) Instead, the sequence beginning with al-'alim (= 181) in cell Aa jumps to cell Bd at the other side of the square, then to Cb and Dc. By the same token, the sequence beginning with fa-yakfikahum (= 265) in Ad must jump first to Ba, then Cc, then Db. Since the former sequence is descending (181, 180, 179, 178), the latter must be ascending to compensate, and I therefore reconstruct the original values of cells Ba and Db as 266 and 268, respectively. This yields a magic square with a sum of 740 in each row, column, and diagonal.

One is left to wonder why these cells contain incorrect values. As stated earlier, a possible explanation is that the template from which this square was copied was itself corrupt. Alternatively, one might suggest that parts of the final numerals in cells Ba and Db failed to print, namely, the hook of the Arabic numeral 6 in cell Ba and the right-hand stroke of the number 7 in Db. However, in cell Ba there hardly seems to be enough space between the 6 and the final number to accommodate a left hook, and a mistake on the part of the artist who carved the print matrix therefore appears to be the more plausible explanation.

On a related note, I find that the magic square in Michaelides (charta) E33, as edited by Karl Schaefer, (12) also contains an error: the values for cells Aa and Ba are reversed. This is due either to a printing error in the edition or to the fact that the numerals presented in that print have very peculiar, non-standard forms: 4 is represented as a sort of trident, identical to the Epigraphic South Arabian h, while number 3 is a simple angle, similar to gimel in Hebrew manuscripts. Neither form is attested in the secondary literature at my disposal, but the values of both symbols are established by the position of the cells in the square where the sum of each line must equal 15.

D. Middle Circle with Text

The current arrangement of the two fragments of this print suggests that there were once two circles with text just above the ring containing the small square.

The first of these circles appears on the upper part of the larger fragment, and only the lower third of the circle survives. It has a double line as a border, which appears to continue on the second fragment. Close inspection reveals that this is not so, however, for the text of this circle is arranged horizontally, whereas the remaining traces of writing on the smaller fragment are clearly aligned around the border. It is clear that the latter once formed part of a ring similar to the one described above, and possibly contained yet another magic square. We will consider the smaller fragment in more detail below.

As in the remainder of this talisman, the text of the circle on the large fragment is in naskhi script. Of some seven lines, only four lines remain in their entirety or in part.

1. and he is the All-knowing [...]

2. God, enter into a contract with him who [carries] this in [...]

3. [and from any] forceful [hand], and any moving foot

4. but the best, by God!


Notes: line 1, al-sami': the lower part of the 'ayn remains; line 2, i'qid: I would like to read this as u'idhu "I invoke God's protection [upon someone]," a common formula in such amulets, which would fit nicely with the text in line three, but the third letter appears to have two faint dots above it, not below. Since the statement is addressed explicitly to God, I take this to be an imperative of form I, not a 1 sg. ind.; line 2, hamala: the first two letters are unclear, and there may be faint traces of an alif in the middle of the word; line 3, wa-min kull ...: the upper part of the kaf and lam are visible in kull, as are the short vowels, including the tanwin kasra of the missing noun before batisha. The space between the waw (or rather its accompanying vowel) and kull is rather large, and calls for the preposition min; line 3, batisha: usually an epithet of the hand, particularly the hand of God. This does not fit the context, however, since the purpose of the text is to invoke God's protection against the items specified -- hence the vague "forceful" in the translation.

E. Circle with Text on Separate Fragment

I have already pointed out that the present arrangement of the two fragments appears to be incorrect. In fact, one can observe that the arrangement of elements on the small fragment is similar to the top part of the large piece: a double border on the right, a circle with double border, containing lines of horizontally arranged text, and traces of another circle, containing text in a circular arrangement. What is more, the "mysterious letters" kaf ha' ya' 'ayn sad (Q 19:1) are set in the corner next to the remains of the lower circle, which would suggest that these traces belong to a ring with text and magic square similar to the one described above. Altogether, one is led to conclude that the fragment was part of the upper left-hand corner of the sheet.


1. [...]

2. [...] with it him who is afraid, and fetch him [...]

3. [...]

4. and adorns (?) [...]

5. and the contract, [God is most kind, all-knowing?]

6. God willing.

Notes: line 1, fragment of a word printed in bolder, larger letters; only the dots of the ya' and the final nun are legible; line 2: vocalized as shown. The last word may be yajlibuhu "he will fetch it," but that would mean that the dots of the ya' were omitted, which is uncharacteristic for this text; lines 3-6: these lines are smudged, and my reading is tentative.

Although only a few isolated words and parts of phrases remain of these two short texts, it is clear they once contained the main part of the amulet, namely, the invocation of God's protection over the bearer. The latter is described here as "him who carries this amulet ...," and formulas of this type are quite characteristic for amulets. Indeed, they can be seen as a kind of "directions for use."

Interestingly, God's protection is not invoked by the more common formula u'idhu man ..., but is construed as a "contract" between God and the bearer of the amulet. The amulet itself embodies this contract, and the owner enters into it simply by wearing it. If my reading of i'qid is correct, then these texts are conceptually quite different from the simple u'idhu-amulets, which invoke God's protection without offering a guarantee -- not because of limitations on the power of God, but because of limits on the delivery method. Indeed, some amulets have exceptionally long invocations, presumably to enhance the amulet's potency, and to ensure that the actual request be heard on high. (13) However, the use of i'qidl'aqd implies something rather different, namely, that the grant of protection is a fait accompli.

Given that block-printed amulets were not necessarily produced to be read, one could argue that my interpretation of subtle semantic differences is somewhat idle. Yet again, the texts of the amulets were obviously drafted by persons who could read, and I do wonder if the use of 'aqd in the Yale amulet reflects an evolution in thinking about the relationship between spirits, medium (here, the magic object), and supplicant. (14) This leads us to consider the issue of dating.


There is no direct evidence in the Yale block print that would allow us to date the piece with certainty. However, it does contain some clues that may offer at least a rough dating. The first clue consists of the hacek-shaped diacritical marks to distinguish unpointed letters from pointed ones, i.e., dalldhal and sin/shin. Such marks were not at all uncommon. Taking random corpora for comparison -- such as Arberry's Handlist of the Chester Beatty Library and Lewis and Gibson's Forty-One Facsimiles (15) -- one can observe that hook- or hacek-shaped markers were used in manuscripts possibly as early as the ninth century C.E., and as late as the sixteenth. In the earliest examples (ninth to eleventh centuries), these hooks appear somewhat rounded, but in manuscripts of the twelfth to sixteenth centuries they are quite angular, rather like the letter v. (16)

The next clue is given by the shape of the numerals. When comparing these to the table compiled by Georges Ifrah, (17) one notes that the symbols used in the block print correspond roughly to those found in Arabic manuscripts of the eleventh to seventeenth centuries C.E. The reversed B symbol used for the numeral 5 is particularly noteworthy -- in fact, this is an archaic form, and close to the Nagari prototype from which it was adapted. According to Ifrah's table, this symbol continued in use until the seventeenth century, during which it gradually developed into the simplified, drop-shaped symbol that is still in use today. Ifrah's findings are supported by the evidence of other manuscripts, too. To cite a random example, one finds that a copy of al-Buni's Shams al-ma'arif held at Princeton (Garrett no. 258Y) contains magic squares in which the numerals have shapes that are remarkably similar to the ones in our print (e.g., fol. 128). In this manuscript, dated 873/1468, the two loops of the symbol for five are decidedly angular.

To sum up, it appears likely that the Yale block print dates to the period between the twelfth and sixteenth centuries. This corresponds roughly to the dating of other Arabic block prints, which Schaefer has dated (tentatively) to the Fatimid to Mamluk periods. (18) Because of its complex composition, as well as its fine workmanship, I am tempted to attribute the present specimen to the latter half of that period, probably around the fifteenth century.

"modern" magic

Even though the dating is rather vague, one has to consider that amulets of the kind described here make use of a technology - printing -- that was quite modern for its day. In fact, most of these artifacts are thought to predate the invention of printing with movable type by Gutenberg. Unlike the works of early European printers, however, the Arabic block prints did not reproduce literary texts, or so it would seem.

In fact, most, but not all,19 Arabic block prints known up until now are amulets, and do not contain text that was designed to be read. They are, in some sense, examples of a mass-produced commodity that may have fulfilled the needs of the "common man." As such, one might have expected the prints to be primitive, or plain in execution, but, as we can see, the exact opposite is true: the amulets are highly artistic in layout and execution, though not necessary faithful in their representation of sacred text -- and the reason may be that these products were aimed at a group of consumers that was at least partly illiterate, and therefore less interested in the words of the text than in its appearance.

The block-printed Arabic amulet described above illustrates these points rather well: it is obvious at first glance that the print is skillfully composed and well executed even in minute details such as the diacritics; the large magic square is eye-catching and reproduced accurately, while the quotations from the Qur'an are not. The emphasis is certainly on appearance, but altogether this is a highly sophisticated product, unlike some of its handwritten counterparts.

The magic squares in this print may have served to reinforce the impression of sophistication created by the print. One has to remember that the methods for creating large magic squares -- such as the one shown on this print -- were partly very complex, and not widely known; one could even argue that the careful arrangement of numbers in squares holds a certain fascination even today. As its very name suggests, the magic squares must have conveyed an air of magic by and of themselves.

I would suggest that the combination of the decidedly "modern" technology of printing with relatively advanced, yet readily accessible mathematical knowledge was born of a deliberate attempt to increase the potency of the magical product, and to make it more attractive to the consumer. Amulets could be difficult to sell, if one can believe the anecdotal evidence of adab works. Whether this attempt was successful we cannot tell. It is certain, however, that we owe to the amulet-makers of Mamluk Egypt some of the most interesting examples of early printing in the world.


(1.) Cambridge University Library Michaelides (charta) E33; image and description in Karl R. Schaefer, Enigmatic Charms: Medieval Arabic Block Printed Amulets in American and European Libraries and Museums (Leiden: Brill, 2006), 76-79, pl. 8.

(2.) The translations of Qur'anic verses are taken from A. J. Arberry, The Koran Interpreted (Oxford: Oxford Univ. Press, 1986).

(3.) Jacques Sesiano, Les carre's magiques dans les pays islamiques (Lausanne: Presses Polytechniques et Universitaires Romandes, 2004), 23-26; idem, "Wafq," in Encyclopaedia of Islam, 2nd ed. (Leiden: [E. J.] Brill, 1954-2004), 11: 27.

(4.) J. Sesiano, "Magic Squares for Daily Life," in Studies in the History of the Exact Sciences in Honour of David Pingree, ed. Ch. Burnett et al. (Leiden: Brill, 2004), 729.

(5.) The first to note the common occurrence of errors in magic squares from Arab sources was Wilhelm Ahrens, in "Die 'magischen Quadrate' al-Buni's," Der Islam 12 (1922): 157-77. Exasperated by the innumerable errors in the Cairo 1317/1899 edition of the Shams al-ma'arif, he exclaims: "So groB ist die Zahl der fehlerhaften Quadrate, daB man fast daran irre werden konnte, ob hier uberhaupt 'magische Quadrate' [...] beabsichtigt waren" (pp. 157-58). He attributes these errors -- rightly, I believe -- to the dynamics of the transmission process.

(6.) Ibid., 163-68.

(7.) Sesiano, Carres magiques, 194-97.

(8.) J. Sesiano, "Construction of Magic Squares Using the Knight's Move in Islamic Mathematics," Archive for History of Exact Sciences 58 (2003): 1-20. For a treatment of fourth-order squares, see Sesiano, Carres magiques, 195 ("deuxieme methode").

(9.) Ahrens, "Magische Quadrate," 166.

(10.) F Maddison and E. Savage-Smith, Science, Tools and Magic (The Nasser D. Khalili Collection of Islamic Art, vol. 12; London: Nour Foundation and Oxford Univ. Press, 1997), 119-21.

(11.) Although this pattern seems unrelated to that of the common "knight's move" square, the two are structurally related; as Ahrens showed, the distribution of the number sequences in the knight's move square is simply turned by 90 degrees (Ahrens, "Magische Quadrate," 166-67 and figs. 12-14).

(12.) Schaefer, Enigmatic Charms, 76-79 and p1. 8.

(13.) Misc. mss. Atiyah Gift No. 9 (Lilly Library, Indiana University, Bloomington) = Schaefer, Enigmatic Charms, 170-77; also Mark Muehlhaeusler, "Eight Arabic Block Prints from the Collection of Aziz S. Atiyah," Arabica 55 (2008): 528-82. ' y

(14.) Hans A. Winkler (Siegel andund Charaktere in der muhammedanischen Zauberei [Berlin: Walter de Gruyter, 1930]) describes at length what he called the "contractual relationship" between the "Muhammadan sorcerer" and his demon (pp. 110-14). For the purposes of this essay, it is important to note that he considered magic squares as a type of "seal" that concludes and ratifies this relationship. Winkler argued that magic squares in particular came to embody a contract with the supernatural, and were therefore seen as endowed with magic power. However, i'qid is not used in al-Buni's Shams, as far as I can ascertain.

(15.) A. J. Arberry, The Chester Beatty Library: A Handlist of the Arabic Manuscripts (Dublin: Emery Walker; Hodges, Figgis and Co., 1955-1966); A. Smith Lewis and M. Dunlop Gibson, Forty-One Facsimiles of Dated Christian Arabic Manuscripts: With Text and English Translation (Studia Sinaitica, vol. 12; Cambridge: Cambridge Univ. Press, 1907).

(16.) Arberry, Handlist, 2: pl. 68 (dated 279/829, with reader's note of 425/1060) has somewhat rounded hooks on sin in al-jism (1. 7) and bi-isnad (1. 22); this is not a sukun: compare bunyan in 1. 7, which is clearly marked with a circle; ibid., 1: pl. 50 (autograph of Ibn ('Asakir [d. 571/1176]): angular, hacek-like hooks on sin in anas and rasul (1. 1); ibid, 1: pl. 3 (autograph of Ibn Qayyim al-Jawziyya [d. 769/1367]): hooks on ra' and sin in ruwiya. sallam (1. 1) and al-rakib (1. 2); ibid., 1: pl. 10 (autograph of al-Babi [d. 887/1482]): hook on sin in sallam (1. 1); ibid., 1:pl. 13 (autograph of M. b. A. Ibn Tulun [d. 995/1548]): hooks on sin as in Isma'il (1. 1). Lewis and Gibson, Forty-One Facsimiles, Sinai cod. Arab. 69 (1065 c.e.) has a somewhat rounded hook on the ra' of jazira, and the sin of asiya (ibid., 13, pl. VII, 1. 7); Sinai cod. Arab. 376 (1225 c.e.) has hooks on ra' and sin in qamaran and shamsan, respectively (ibid., 31, pl. XVI, 1. 1); while Sinai cod. Arab. 264 (1574) has very angular hooks on the sin of slqa and al-qiddis (ibid., 69, pl. XXXV, 1. 3).

(17.) Georges Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer (New York: J. Wiley, 2000), pl. 25.3.

(18.) Schaefer (Enigmatic Charms, 7) dates the block prints in his catalogue to the period between 900 and 1430 C.E. His argument is based partly on paleography, and partly on material evidence: the watermark on a print in the Gutenberg Museum has been dated to the fifteenth century c.e., while a print conserved at Strasbourg has been dated to the late thirteenth century by means of C-14 analysis (ibid., 41 ff.).

(19.) There exist a few non-amuletic printed objects, such as a group of Ayyubid hajj certificates from Damascus, which were at least partly block-printed (e.g., Damascus fragments no. 47/24, 53/18, 53/19, at the Turkish and Islamic Arts Museum in Istanbul). Full descriptions can be found in Sule Aksoy and Rachel Milstein, "A Collection of Thirteenth-Century Illustrated Hajj Certificates," in M. Ugur Derman armagant: Altmisbesinci yasi munasebetiyle sunulmus tebligler. Papers Presented on the Occasion of His Sixty-Fifth Birthday (Istanbul: Sabanci Universitesi, 2000), 100-134. For block-printed specimens, see pp. 123-34 and pls. 6-10. Interestingly, the authors show that the hajj certificates were assembled from various blocks (confirming my conclusions in the above-cited "Eight Arabic Block Prints"). For a general description of the Damascus fragments, see Dominique Sourdel and Janine Sourdel-Thomine, Certificats de pelerinage d'epoque ayyoubide: Contribution a l'histoire et a l' ideologie de l'islam au temps des croisades (Paris: Academie des Inscriptions et Belles-Lettres, 2006); see p. 354 (pl. xliv), which contains a block-printed paragraph of text. There are also some prints of the kind shown in Joseph von Hammer-Purgstall, "Sur un passage curieux de l'Ihatet, sur l'art d'imprimer chez les arabes en Espagne," Journal Asiatique (4e s.) 20 (1852): 252-55, but these are quite different types of objects; they are stamps or seals more akin to the common ownership-stamps than they are to the block-printed texts considered here. In the same article Hammer-Purgstall also noted some apparent references to the printing of books and government documents in classical Arabic sources. Unfortunately, no examples of such prints have been found to date. I am grateful to one of the JAOS reviewers of this article for drawing my attention to these sources.

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Author:Muehlhaeusler, Mark
Publication:The Journal of the American Oriental Society
Article Type:Report
Geographic Code:1USA
Date:Oct 1, 2010
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