It is a piece of coarsely woven linen, square, one Flemish ell on a side. She has left a margin all round the edges of about a hand’s breadth. The area in the center, then, is a square perhaps eighteen inches on a side: suitable for an opus pulvinarium or cushion-cover. This area has been almost entirely covered in crewel-work. The style is called gros-point, a technique that is popular among English peasants, overseas colonists, and other rustics who amuse themselves sewing naive designs upon the crude textiles they know how to produce. As it has been superseded, in France, by petit-point, it may be unfamiliar to your majesty, and so I will permit myself the indulgence of a brief description. The fabric or matrix is always of a coarse weave, so that the warp and weft may be seen by the naked eye, forming a regular square grid a la Descartes. Each of the tiny squares in this grid is covered, during the course of the work, by a stitch in the shape of a letter x, forming a square of color that, seen from a distance, becomes one tiny element of the picture being fashioned. Pictures formed in this manner necessarily have a jagged-edged appearance, particularly where an effort has been made to approximate a curve; which explains why such pieces have been all but banished from Versailles and other places where taste and discrimination have vanquished sentimentality. In spite of which your majesty may easily envision the appearance of one of these minute x -shaped stitches when viewed closely: one leg running from northwest to southeast, as it were, and the other southwest to northeast. The two legs cross in the center. One must lie over the other. Which lies on top is a simple matter of the order in which they were laid down. Some embroiderers are creatures of habit, always performing the stitches in the same sequence, so that one of the legs invariably lies atop the other. Others are not so regular. As I examined the Countess’s work through a magnifying lens, I saw that she was one of the latter-which I found noteworthy, as she is in other respects a person of the most regular and disciplined habits. It occurred to me to wonder whether the orientations of the overlying legs might be a hidden vector of information.

The pitch of the canvas’s weave was about twenty threads per inch. A quick calculation showed that the total number of threads along each side would be around 360, forming nearly 130,000 squares.

A single square by itself could only convey a scintilla of information, as it can only possess one of two possible states: either the northwest-southeast leg is on top, or the southwest-northeast. This might seem useless; as how can one write a message in an alphabet of only two letters?

Mirabile dictu,there is a way to do just that, which I had recently heard about because of the loose tongue of a gentleman who has already been mentioned: Fatio de Duilliers. This Fatio fled to England after the Continent became a hostile place for him, and befriended a prominent English Alchemist by the name of Newton. He has become a sort of Ganymede to Newton’s Zeus, and follows him wherever he can; when they are perforce separated, he prates to anyone who will listen about his close relationship to the great man. I know this from Signore Vigani, an Alchemist who is at the same college with Newton and so is often forced to break bread with Fatio. Fatio is prone to irrational jealousy, and he endlessly schemes to damage the reputation of anyone he imagines may be a rival for Newton’s affections. One such is a Dr. Waterhouse, who shared a room with Newton when they were boys, and for all I know buggered him; but the facts do not matter, only Fatio’s imaginings. In the library of the Royal Society, Fatio recently happened upon Dr. Waterhouse sleeping over some papers on which he had been working out a calculation consisting entirely of ones and zeroes-a mathematical curiosity much studied by Leibniz. Dr. Waterhouse woke up before Fatio could get a closer look at what he had been doing; but as the document in question appeared to be a letter from abroad, he inferred that it might be some sort of cryptographic scheme. Not long after, he went to Cambridge with Newton and let this story drop at High Table so that all could know how clever he was, and that Waterhouse was certainly a dolt and probably a spy.

From my records of the cabinet noir I knew that the Countess de la Zeur had sent a letter to the Royal Society at the same time, and that she has had business contacts with the brother of Dr. Waterhouse. And I have already mentioned her suspiciously voluminous and inane correspondence with Leibniz. And so once again applying Occam’s Razor I formulated the hypothesis that the Countess uses a cypher, probably invented by Leibniz, based upon binary arithmetic, which is to say consisting of ones and zeroes: an alphabet of two letters, perfectly suited to representation in cross-stitch embroidery, as I have explained.

I enlisted a clerk from the Embassy, who had keen eyesight, to go over the embroidery stitch by stitch, marking down a numeral 1 for each square in which the northwest-to-southeast leg lay on top, and a 0 otherwise. I then applied myself to the problem of breaking the cypher.

A series of binary digits can represent a number; for example, 01001 is equal to 9. Five binary digits can represent up to 32 different numbers, sufficient to encypher the entire Roman alphabet. My early efforts assumed that the Countess’s cypher was of that sort; but alas, I found no intelligible message, and no patterns tending to give me hope that my fortunes would ever change.

Presently I departed from the Hague, taking the transcript of ones and zeroes with me, and bought passage on a small ship down the coast to Dunquerque. Most of the crew on this vessel were Flemish, but there were a few who looked different from the rest and who spoke to one another in a pithy, guttural tongue unlike any I had ever heard. I asked where they were from-for they were redoubtable seamen all-and they answered with no little pride that they were men of Qwghlm. At this moment I knew that Divine Providence had led me to this boat. I asked them many questions concerning their extraordinary language and their way of writing: a system of runes that is as primitive as an alphabet can possibly be and yet be worthy of the name. It contains no vowels, and sixteen consonants, several of which cannot be pronounced by anyone who was not born on that rock.

As it happens, an alphabet of sixteen letters is perfectly suited to translation into a binary cypher, for only four binary digits-or four stitches of embroidery-are required to represent a single letter. The Qwghlmian language is almost unbelievably pithy-one of these people can say with a few grunts, gags, and stutters what would take a Frenchman several sentences-and little known outside of that God-cursed place. Both of which made it perfectly suited to the purposes of the Countess, who need communicate, in this case, only with herself. In sum, the Qwghlmian language need not be encyphered, for it is already a nearly perfect cypher to begin with.

I tried the experiment of breaking down the transcribed 1s and 0s into groups of four and translating each group into a number between 1 and 16, and shortly began to see patterns of the sort that give a cryptographer great confidence that he is progressing rapidly to a solution. Upon my return to Paris I was able to find in the Bibliotheque du Roi a scholarly work about Qwghlmian runes, and thereby to translate the list of numbers into that alphabet-some 30,000 runes in all. A cursory comparison of the results against the word-list in the back of this tome suggested that I was on the correct path to a full solution; but to translate it was beyond my powers. I consulted with Father Edouard de Gex, who has lately taken an interest in Qwghlm, hoping to convert it to the True Faith and make it a thorn in the side of the heretics. He referred me to Father Mxnghr of the Society of Jesus in Dublin, who is a Qwghlmian born and bred, and known to be absolutely loyal to your majesty as he travels frequently to Qwghlm, at great risk, to baptize the people there. I sent him the transcript and he replied, some weeks later, with a translation of the text into Latin that ran to almost forty thousand words; which is to say that it requires more than one word in Latin to convey what is signified by a single rune in Qwghlmian.