John Dee and the Magic Tables in the Book of Soyga

Jim Reeds

'Oh, my great and long desyre hath byn to
be hable to read those tables of Soyga'.
     John Dee 1

1. John Dee and the Book of Soyga

Until recently the Book of Soyga was known only by repute, through mention in the diaries of John Dee (1527{1608). Dee's association with the Book of Soyga is conveniently summarized by Christopher Whitby: 2
On 18 April 1583 Dee was unable to nd his Book of Soyga: it has been mislaid. On 29 April 1583 Dee remembered a detail about the missing book: '...E[dward] K[elley] and I wer talking of my boke Soyga, or Aldaraia and I at length sayd that, (as far as I did remember) Zadzaczadlin, was Adam by the Alphabet therof...' On 19 November 1595 Dee
recovered his Book of Soyga. Many years later Elias Ashmole (1617{1692) reported that 'the Duke of Lauderdale hath a folio MS. which was Dr. Dee's with the words on the rst page: Aldaraia sive Soyga vocor'.
In addition to these unremarkable appearances of the Book of Soyga in Dee's nachla |unremarkable, for who does not sometimes mislay and later recover a valued book? | there is the singular exchange held between Dee and the angel Uriel on the occasion of their first conversation, at Mortlake on Saturday, 10 March 1581/1582, the very first scrying session mediated by Dee's most famous scryer, Edward Kelley (1555{1595?), also known as Kelly and Talbot. 3 In the following,      is Dee, VR is Uriel:
      - ys my boke, of Soyga, of any excellency?

I gratefully acknowledge: the Bodleian Library, University of Oxford, for permission to publish the illustration of Bodley 908, fol. 180r; the Department of Manuscripts, British Library, for permission to publish the illustrations of Sloane 8, fols. 102vand 103r, and Sloane 3189, fols. 56vand 58v; and Robert O. Lenkiewicz, for permission to publish the illustration of the 'Tabula combinationum Ziruph'. I am most grateful to Drs S. Clucas, K. de Leon-Jones, J. V. Field, D. E. Harkness, J. C. Lagarias, and K. M. Reeds for their generous help, advice, and encouragement. I am also grateful to Clay Holden, Dr David Kahn, Gerrit Oomen, Joseph H. Peterson, Dr Muriel Seltman, and Dr Allan Wilks. All mistakes are of course my own.

VR - Liber ille, erat Ada[m]e in Paradiso reuelatus, per Angelos Dei bonos. [That book was revealed to Adam in Paradise by God's good angels.]
      Will you give me any instructions, how Imay read those Tables of Soyga?
VR - I can|But solus Michael illius libri est interpretator. [Only Michael is the interpreter of that book.]
      I was told, that after I could read that boke, I shold liue but two yeres and a half.
VR - Thow shallt liue an Hundred and od yeres.
     What may I, or must I do, to haue the sight, and presence, of Michael, that blessed Angel?
VR - Presentias n[ost]ras postulate et invocate, sinceritate et humilitate. Et Anchor, Anachor, et Anilos, non sunt in hunc lapidem invocandi. [Request and invoke our presence with sincerity and humility. Anchor, Anachor and Anilos are not to be called into this stone.]
      Oh, my great and long desyre hath byn to be hable to read those tables of Soyga.
VR - Haec maxime respiciunt Michaelem. Michael est Angelus, qui illuminat gressus tuos. Et haec revelantur in virtute et veritate non vi. [These things are mostly to do with Michael. Michael is the angel who illuminates your steps. And these things are revealed in virtue and truth and not by force.]
      Is there any speciall tyme, or howre to be observed, to deale for the enioying of Michael?
VR - Omnis hora, est hora nobis. [Every hour is ours.] ... 4
To summarize: Uriel conrms Dee's high estimation of the Book of Soyga's value. Dee wants angelic help in understanding his Book of Soyga, but only the angel Michael is cleared to talk about this topic. If, as some scholars believe, Kelley was a charlatan, then here we nd him (in the voice of Uriel) being characteristically evasive. As a newcomer to Dee's household he does not want to commit himself to any more specic statements about the Book of Soyga, about which he knows very little beyond the fact that it fascinates Dee. 5
There things rested for roughly four centuries. Dee prized his Book of Soyga, but since the book was lost, modern scholars could only guess about its contents and possible inuence on Dee's magic system, especially for the version in his Book of Enoch. 6
But then in 1994 Deborah Harkness | like the hero of Poe's 'The Purloined Letter', located not one but two copies in the obvious places, in this case in two of England's greatest libraries. They had been catalogued under the title Aldaraia instead of Soyga. 7
At last we can examine the Book of Soyga, and in particular its tables, and see for ourselves what it was that Dee prized so highly.
The Book of Soyga is an anonymous late-mediaeval or early modern Latin magical work extant in two sixteenth century manuscript copies: one in the Bodleian Library, which I refer to as Bodley 908, and the other in the British Library, which I refer to as Sloane 8. 8 Since there is as yet no edition or translation of either of the two manuscripts for me to refer to, nor even a synopsis of their contents, I oer the following brief description. 9
The Sloane 8 copy (but not the Bodley 908 one) bears the title Aldaraia sive Soyga vocor at the head of the text and on the leaf preceding the text, both in the same hand as the text, tting Ashmole's description. Sloane 8's preceding leaf also bears the description Tractatus Astrologico Magicus, written in a dierent hand. Both copies contain the equation of 'Adam' with 'Zadzaczadlin', so there can be no doubt that Harkness's Book of Soyga is closely related to Dee's Book
of Soyga; on Ashmole's Aldaraia sive Soyga vocor evidence, and based on the arguments I present at the end of section 5, it is easy to guess that Sloane 8 was in fact Dee's copy of the Book of Soyga. 10
The 197 leaves of Bodley 908 contain three named works, Liber Aldaraia, Liber Radiorum, and Liber decimus septimus (of 95, 65, and 2 leaves, respectively) as well as a number of shorter unnamed works totalling about 10 leaves. The nal 18 leaves contain the tables that are the subject of this paper. Sloane 8 has 147 leaves, and seems largely identical with Bodley 908, except that the tables occupy 36 leaves and the Liber Radiorum is present only in a 2 leaf truncated 'executive summary' version.
A cursory inspection of the Book of Soyga shows it is concerned with astrology and demonology, with long lists of conjunctions, lunar mansions, names and genealogies of angels, and invocations, not much dierent from those found, say, in pseudo-Agrippa. 11 A single example, of a list of spirits of the air, is illustrative of the whole:
Adracty, Adaci, Adai, Teroccot, Terocot, Tercot, Herm, Hermzm,
Hermzisco, Cotzi, Cotzizi, Cotzizizin, Zinzicon, Ginzecohon, Ginchecon, Saradon, Sardon, Sardeon, Belzebuc, Belzscup, Belcupe, Saraduc, Sarcud, Carc, Sathanas, Satnas, Sacsan, Contion, Conoi, Conoison, Satnei, Sapnn, Sappi, Danarcas, Dancas, Dancasnar. 12

Some of the spells or incantations have a vaguely Christian or alchemical air to them, as 'Petra Ouis Angelus Agnus Lapis Sponsus' and 'Diuinitas Christus Venturus Iustorum Humanitatis Vnitas', 13 but the overall impression is that it is no more an alchemical treatise than it is a devotional work.
Several features of the Book of Soyga seem worth particular mention, as being untypical of a standard late mediaeval or Renaissance magical work, or of the run-of-the-mill necromancy handbook. 14 In contrast to most mediaeval or Renaissance works, the text has extremely few references to known authors or personalities. There are no recognizable auctores. Other than the occasional mention of a few Old Testament names, and two references to Libro Geber, and a puzzling marginal gloss 'Steganographia' in the same hand as the text, which is presumably a reference to the work of Johannes Trithemius (1462{1516), there are no references to recognizable personalities. 15
Instead, it makes numerous references to what are presumably mediaeval magical treatises, works such as liber E, liber Os, liber dignus, liber Sipal, liber Munob, and the like.
Throughout the book much importance is placed on writing words backwards. This can be seen in some of the titles mentioned above: Sipal backwards is Lapis, and Munob reversed is Bonum. Phrases such as 'Retap Retson' occur throughout. This principle is reected in the form of the tables, as discussed below. The name of the work, Soyga,
is itself explained to be 'Agyos, literis transvectis'. 16
Throughout the book there is a preoccupation with letters and combinations of letters, assignments of numerical values to letters, assigning letters to planets and to elements, listing combinations of letters associated with houses of the moon, recombining letters and syllables in incantations to form new magic words, listing new names for the 23 letters of the Latin alphabet, sometimes taken in reversed Z through A order, listing new symbols for the 23 letters, and so on.
And, towards the end of the book there is the set of thirty-six large square tables, described in section 2 of this paper, lled with a seemingly random jumble of letters. (One of these is illustrated in my Plates I and II.) These tables do not appear to be like any illustrated in, say, Shumaker's survey of mediaeval and early modern magic works. 17
The Book of Soyga's preoccupation with letters, alphabet arithmetic, Hebrew-like backwards writing, and so on, is of course characteristic of the new Cabalistic magic which became popular in the sixteenth century, exemplied by the great compilation of Agrippa of Nettesheim (1486{1535), and borrowing authority both from the Renaissance humanist interest in the Kabbalah expressed by such gures as Pico and Reuchlin and from the supposed Biblical antiquity of the Kabbalah. 18 Although large square tables are not themselves a characteristic feature of the traditional Kabbalah, they had by Agrippa's time become an integral part of the Christian magical Cabala. 19
Such a work must have appealed to Dee since it encompassed so many of the ingredients associated with early modern magical and Christian Cabalist texts; we know the tables in the Book of Soyga excited John Dee's interest, as seen in the dialogue with Uriel. They certainly also excited mine as a professional cryptologist. Were they, I wondered, lled with a random (and hence pointless) selection of letters, or were they a cryptogram (with a hidden 'plain text' meaning, which might at least in principle be recoverable by cryptanalysis), or was there some other structure or pattern to them? I approached the tables as I would any cryptographic problem, rst transcribing the data and entering it into the computer, and then trying out what I knew of the bag of code-breakers' tricks. The results, which I describe in sections 3 through 6, were unexpectedly gratifying.
This paper, then, indirectly addresses the question of the Book of Soyga's possible inuence on Dee by examining and comparing the form (or method of construction) of the tables in the Book of Soyga and those found in other early modern magic tables (including Dee's and Agrippa's), rather than their function (i.e., purpose or method of use).

2. The Magic Tables of the Book of Soyga

The Book of Soyga contains thirty-six tables; each table is a square grid of 36 rows and columns; each grid cell contains a letter of the Latin alphabet.20 These tables turn out to be formed by a completely deterministic calculation method, or algorithm, starting from an arbitrary 'code word' for each table. This construction algorithm is so intricate that it is unlikely that its presence would be detected on casual examination of the tables.
Each of the thirty-six tables is headed with a number and a label. I summarize these in my Table I. For convenience I will refer to them as T1, T2, and so on. T1 through T12 are labelled with the signs of the zodiac, Aries through Pisces; as are T13 through T24. T25 through T31 are labelled with the seven planet names, and T32 through T35 with the four element names. T36 is labelled with the word 'Magistri'.
See my Plates I and II for the Bodley 908 and Sloane 8 versions of T1 'Aries'.
Eight of these tables also appear copied in Dee's notebook, the Book of Enoch, joined in pairs: 'The First Table' in the Book of Enoch is a 72-row table, lling both pages of an opening, the rst 36 rows of which are Soyga's T1 and the last 36 rows of which are Soyga's T13, the two

'Aries' tables, and so on, as indicated in my Table I.21 See my Plate III for the Book of Enoch version of T1 'Aries'.
The tables are written with italic letters, mostly lower case, written into a neatly pencilled regular grid. In Bodley 908 the grid cells measure approximately one quarter of an inch, so a complete table ts on one page. In Sloane 8 the grid cells are approximately one third of an inch in size, and each table occupies the two facing pages of an opening.
In each book there is occasional use of the short s; much more common is the long s. The writing becomes more even after the rst few tables, with greatly diminished use of upper case letters, as if the copyist became accustomed to what must have been an unusually irksome and tedious task of copying completely senseless data which oered no obvious contextual clues for correcting mistakes. In Bodley 908 upper case L is used exclusively, presumably to avoid confusion with long s.
In Sloane 8 lower case l is used exclusively.
The handwriting in Bodley 908 is quite even, and pains seem to have been taken to make the letters clearly distinguishable. The handwriting in Sloane 8 is less clear, so that n and u are often hard to tell apart, as are the pairs c/e and l/i. Sloane 8 shows obvious signs of proofreading, with dots, double dots, and cup strokes marking errors or doubtful readings. Occasionally a cell contains, in addition to its main letter, a tiny f followed by another tiny letter; I surmise f means falso and the following letter is the suggested correction. Some corrections seem to have been made by erasure and overwriting; the handwriting also seems to change part way through.
The left hand margin in each table is special. Each table has a 'code word', e.g., T1 'Aries' has code word NISRAM. The left margin is composed entirely of the code word and the reversed code word, e.g., NISRAM MARSIN NISRAM MARSIN ... repeated until the margin is lled.
The code words are listed in the third column of my Table I. All thirty-six of them are exactly 6 letters long. The treatise in the Book of Soyga which discusses the tables, 'Liber Radiorum', has a series of paragraphs mentioning the code words for twenty-three of the tables, together with number sequences which stand in unknown relation to the words. 22
Note that the code words for T13 - T24 are the reverses of those of the corresponding T1 - T12. Thus, T1 'Aries' has code word NISRAM and T13, also 'Aries', has code word MARSIN.
In Bodley 908, T36 'Magistri' has a blank 13th line - the first line after the first complete MOYSES/SESYOM cycle on the left. The Sloane 8 version the table has the same 35 non-blank lines, but they have 'closed ranks' so it is the last line of 36 which is blank.
In general, the first four or five rows of the tables appear very repetitious.
Often the first row or two consist entirely of endless repetitions of a given two letter 'motif', followed by two or three rows of repetitions of a 4 letter motif, with maybe another row or so consisting of repetitions of a 12 letter pattern. But these repetitions do not start until one has gone some distance into the row; with each successive row, one has
to go further.
This may be seen in T1 'Aries', shown in Plates I and II, where the first three lines soon fall into repetitions of the 4 letter motifs dizb, lytr, and xiba, respectively, and the next two rows into repetitions of the 12 letter motifs qsrnylfdfzly and ohqtauiducis, respectively.
Many of these motifs are found in several of the tables.
A few tables (like T5 'Leo') have a vast triangular area of repeats of yoyo:


Various other less pronounced repetitious structures can also be seen in the tables.

3. Analysis of Tables

Because Bodley 908's tables seemed more legible, I transcribed them first. The transcribed text was entered into the computer with many measures taken to prevent or detect copying errors. Once it was entered, repetitions in the text could be sought, patterns counted, and proof sheets printed.
In the course of this work it was noticed that in the vast majority of cases where a pair of adjacent m's appeared, the letter above the second m was usually an n. That is, the pattern                     was almost always actually                     .

                          This led to a tabulation of all triplets of letters occurring in a
conguration, and it was found that in a large majority of cases the letter
occupying the X position was predictable from the letters in the N and W
positions. (The names of these variables are meant to represent the letter at
the spot marked by X, the letter to its North, and the letter to its West.)
This led to discovery of an equation of form X = N + f(W) where f(W) is a  function of W and the addition is taken modulo 23.
Here the letters are assigned numerical values according to their positions in the 23 letter Latin alphabet: a = 1, b = 2, ... , u = 20, x = 21, y = 22, z = 23, so that z + 2 = b, etc. The nal ingredient in this formula, the auxiliary function f, is known to us only by a table of values determined empirically.

Table II. Auxiliary function values.

Expressed another way: a letter is obtained by counting a certain number of letters after the letter immediately above (i.e., north of) it in the table. The number of letters to count is determined by the letter standing to the immediate left (i.e., west). If the letter to the left is an f, for instance, we are to count two letters past the letter above.
So, continuing the example, if the letter above is an l, then the letter in question must be n, which is 2
letters past l:

If the end of the alphabet is reached in this letter counting one starts over at the beginning, treating a as the letter after z, and so on.
For letters in the top row of a Soyga table, for which there is no N letter, the following formula holds: X = W + f(W) where the addition is again performed modulo 23. That is, for letters in the top row one applies the rule for letters in the interior of the table, acting as if the letter appearing to the left also appears above.

4. Directions for Creating the Tables

This, then, is a recipe for recreating the tables, although almost certainly not expressed in the same terms the Soyga author would have used. Starting with a code word, such as NISRAM, and an empty grid of 36 rows and columns:

4.1. Left Column:

Write the code word followed by its reverse into the cells of the left hand column, starting at the top and working downwards, repeating the process until the column is full.

4.2. Top Row:

Fill in the remaining 35 cells of the top line, working from left to right, repeatedly applying the formula X = W + f(W):
In our example, the first application of this formula yields n + f (n), that is, the letter f (n) = 14 places after n in the 23 letter alphabet, which is d. (Thus: n is the 13th letter; 13 + 14 = 27; reduced modulo 23, 27 is 4, which is d.) Write the letter d in the second cell in the top row, just to the right of the n of NISRAM.
The second application yields d + f (d). Since f (d) = 5, this gives us i, the fifth letter after d. Write an i in the third cell of the top row.
The third application yields i + f (i). Since f (i) = 14, this gives us z, the 14th letter after i. Write a z in the fourth cell of the top row.
The fourth application yields z + f (z) = 23 + 2 = 25 = 2 = b; put a b in the fifth cell.
The fifth application yields b + f (b)= 2 + 2 = 4 = d; put a d in the sixth cell. At this point we have fallen into a cycle: the next application yields d + f (d) which we have already seen before is i, and the rest of the first row will continue to repeat dizb dizb...
At this point the top few rows of the partially filled in table will look like this:


4.3. Interior of Table:

Now, starting with the second row and working left to right within rows, fill in the interior cells as follows. With each blank cell encountered, if the work has progressed in normal European page-reading order, the cell just above the blank cell and the cell to the left have both been filled in. Call the letters appearing in those cells N and W, respectively, and
use the formula N + f(W) to determine what to write into the blank cell under consideration.
For example, the first blank cell in row 2 is the second cell. It has a d above it and an i to its left. So the letter d + f (i) = 4 + 14 = 18 = s is written in that blank cell.
The next cell, cell 3, in row 2 has an i above it and an s to its left (the s which we just wrote). So we put i + f (s) = 9 + 8 = 17 = r in cell 3 of row 2. The next cell gets z + f (r) = 23 + 11 = 11 =l, and so on. The top few rows now look like this:


This process, carried out row by row, left to right, will eventually fill the table.
Alternatively, instead of working row by row, left to right in each row, as described here, one could equivalently work column by column, working downwards within each column. The final results would be the same.
Of course I make no claim that the Soyga author intentionally used my X = N + f(W) formula. Whatever means were actually used to construct the tables clearly had this formula's mathematical structure implicitly 'built in', but we can only guess at its implementation. The arithmetic modulo 23, for instance, could have been eected equally
well by paper-and-pencil computations, by consultation of charts, by letter counting on nger tips, or by the use of Lullian wheels.

5. Error Analysis and Genealogy

In fact the tables found in the two extant manuscripts of the Book of Soyga are not identical with those I produced by a computer programmed to carry out the above rules, starting with the same code words as in the manuscripts. This is for two reasons:
1. The law of formation for the tables is suciently intricate that the Soyga author occasionally made mistakes in working out the original tables.

2. The copyists made new mistakes when transcribing so much apparently unpatterned text.

Fortunately for us, these two kinds of errors have radically different consequences. If a cell in the original is miscalculated, the mistake spoils the calculation of the cells to its right and below it, resulting in an avalanche of error with an easily recognizable rectangular shape. A mere copying error, however, will not have a cumulative effect, and will
be classifiable into one of several familiar types: transposition, deletion, eye skip, and replacement.
In short, the constraints placed on the tables by the X = N +f(W) formula allow an aggressive form of textual emendation of the received tables in Bodley 908 and Sloane 8. A similar technique has been used to trace copying of logarithim tables by Charles Babbage (1792 - 1871), but is of course not generally applicable. 23 Only texts with a well-defined mathematical structure are amenable to this method of detecting and correcting errors of generation and transcription.

5.1. Principles of Error Diagnosis: An Artificial Example

This can all be seen in an articial example, concocted so as to display every kind of pathology in the first few lines of the table. Suppose the code word is SARTON. Ideally, the first few lines of the table would be

Call this the ideal original table. Suppose, however, that in working this out a mistake was made: an e was put down instead of a p in the fifth cell of the second line. This mistaken letter will cause mistaken values to be calculated for the sixth cell of the second line and for the fifth cell of the third line, and those mistakes will beget others. The resulting actual original table will be (with the erroneous e capitalized)

Finally, suppose we receive this table, derived from the original but with a variety of copying errors:

Our task is to recover the ideal original and actual original and diagnose the copying errors.

First we inspect the left margin, where we see SARRON UOTR... etc, which is a damaged version of SARTON NOTRAS etc.; the code word is SARTON. (The left margin contains in all six copies | forward and reversed | of the code word, so in practice there is no doubt about what the code word is.)
From this we work out the ideal original table, and examine those positions where the received table diers from it. This diagram displays places where the received table agrees with the ideal original with a dot and places where they disagree with the value seen in the received table:

Here we see an essentially solid rectangular region of disagreement, starting in the fth cell of row 2, with the value e, which is due to an error in the original. The 'pepper and salt' pattern of sporadic disagreements elsewhere is characteristic of copying errors. So we conclude that an e was put down by mistake in row 2, cell 5 in the original.
Now we work out the corresponding putative original, and display the disagreements between it and the received copy:

Since the remaining rectangular regions of disagreement do not reach to the bottom of the table, we conclude that they are not due to errors in the original. (Further examination will show they are due to eye skip.) No further errors seem to have been made in the original, so our putative original table is finished.

Magic Tables in the Book of Soyga - Continued

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