The Alan Turing
Want to come over to Manchester for a bit of live crypto stuff, the prize ceremony and an opportunity to meet the organisers?
A mysterious brown-robed figure barges past Mike and Ellie, dropping two pieces of paper. One contains a grid of letters, the other has had holes cut out of it.
This is a Cardan grille (see Wikipedia here). If one aligns the holes with the grid of letters then the visible letters spell out a message. In this case, there are 8 possible combinations (4 possible rotations of the grille, plus another 4 once the grille has been flipped over). If you try them all then you'll see that the message reads:
Seek tomb in old parish church.
Gerolamo Cardano (1501-1576) was an Italian polymath with interests in all major areas of science (or 'natural philosophy' as it was then called), as well as being a professinal gambler. He was one of the first people to do formal manipulations with square roots of negative numbers when solving cubic and quartic equations, thus anticipating the development of complex numbers.
The de Gresle (also Grelley and other variant spellings) were the Lords of the Manor of Manchester. Robert de Gresle is a historical person and is credited with developing Manchester as a commerical centre in the 12th century. (William de Gresle is fictional.) The de Gresle family home was Manchester Castle, a fortified manor house; Cheetham's School of Music now occupies the site.
Eleanor of Aquitaine had an extraordinary life and is a fascinating example of a strong woman in an age where men ruled. You can read about her life here.
Saladin and Richard the Lionheart are well-known historical figures. Saladin was indeed highly cultured and very well educated, particularly in literature and mathematics (and far more so than Lionheart and most other western European nobles of the time). During the 12th century, the mathematics studied in the middle east by Islamic scholars was far ahead of that in western Europe. As Barquith correctly points out in the Epilogue, such scholars (such as Muhammad ibn Musa al-Khwarizmi and Omar Khayyám) developed decimal notation for numbers, constructing proofs by induction, and studying spherical trigonometry. There is no evidence that they did invent (discover?) complex numbers; this is fictional and is there to create a good story!
Mike and Ellie enter the crypt below Manchester Cathedral and discover a fairly recently carved encoded inscription. There is some graffiti 'Ave Caesar!' (Hail Caesar), suggesting that the code is a Caesar cipher. Trying all 26 possibilities yields
Quaerite Logicam Fenestram in Biblioteca Ioannis Rylandswhich is Latin for 'Look for a logical window of John Rylands Library'. The answer required was the Latin text, not a possible translation into English.
Manchester Cathedral does, as the story suggests, have its origins as the Parish Church of Manchester. Construction of the Parish Church was started in 1215 on a site next to the de Gresle family manor house. The de Gresle coat of arms is still associated with the cathedral. The hidden crypt is fictional, but one can see the 'Hanging Bridge' (associated to the Parish Church) in the Manchester Cathedral Visitor Centre.
Mike and Ellie go to the Historic Reading Room in the John Rylands Library. They see a coded message around one of the stained glass windows.
This is a substitution cipher. There are five colours and five symbols, so 25 different colour/symbol pairs in total and each one stands for a different letter. Frequency analysis allows one to make some educated guesses (for example: the yellow alpha is an 'E'). In fact, there is a logic to the order of the symbols, which is alphabetical by colour for each symbol. The symbols are then arranged in the order of the Greek alphabet. Thus 'A' is blue alpha, 'B' is green alpha, 'C' is red alpha, 'D' is white alpha and 'E' is yellow alpha. Then 'F' is blue beta and so on until 'Y'. There is no letter 'Z'.
One slight difficulty is deciding where to start reading the message, which runs clockwise from the lower left corner, starting from the outside first.
The plaintext is
The Gresle family legacy is hidden somewhere in the library. When read aright it tells where wonderous information can be found. The guardians will guide the rightful to the hiding place.
In reality, the John Rylands Library is very similar to how it is described in the story. The stained glass window of Hegel exists (albeit without the code!) as part of a larger stained glass window, featuring artists and philosophers, at one end of the Historic Reading Room. You can see the full window here.
Enriqueta Rylands should be better known than she is. You can read about her remarkable life on Wikipedia here. She founded the John Rylands Library to commemorate her husband, the Manchester industrialist John Rylands. She had a formidable personality and had countless arguments with the architect, Basil Champneys. She took a direct interest in the placing of the statues in the Historic Reading Room and insisted, as in the story, that scientists must face scientists, artists must face artists, etc.
The mysterious brown-robed figure drops a piece of paper from the balcony of the reading room. The piece of paper has 'Wife', 'Cook' and 'Physician', together with some numbers, written on it.
This is a book code. In a book code, letters (or words) of the plaintest are indicated by their position in a pre-determined key text. Cracking a book code thus requires knowing (or guessing) which key text is used.
The Canterbury Tales by Geoffrey Chaucer is one of the earliest, and one of the most famous, literary work in Middle English. The Canterbury Tales takes the form of a series of short stories ('The Cook's Tale', 'The Miller's Tale', 'The Knight's Tale', etc) told by a group of pilgrims to each other as they travel from London to Canterbury. Thus the words 'Cook', 'Physician' and 'Wife' suggest The Canterbury Tales is the key text.
One problem with a book code is that it will normally only work with a specific version (edition, translation, etc) of the key text. The Canterbury Tales has been translated from Middle English to Modern English many times and in many different ways. However, there are only a few different versions in the original Middle English, and the differences are mostly minor (at least in the way that the text is used in this code). Several of the original versions can be found online (here for example), The number n.m in the code refers to the initial letter of the mth word of line n in the corresponding tale (ignoring the prologue). This suggests using an original text, rather than a translation, as a key text.
The message reads
Find the fifth folio.
The reference in the story to Turing's court case refers to his well-known conviction for gross indeceny at a time when homosexual acts were illegal; the case is well-documented on Wikipedia. His convinction did lead to his security clearance being revoked for certain projects.
The passing reference to chess in the story is not accidental. At about this time, Turing and his student David Champernowne (on whom the backstory of the character of Barquith is partially based) wrote a theoretical computer programme to play chess. No computer at the time was powerful enough to run it, so Turing and Champernowne would play against each other with Turing pretending to be the computer and running the algorithm for generating the next move by hand.
Mike distracts the twins as Ellie, pretending to be the mysterious robed figure, throws a ball of paper at them. On the piece of paper is a code.
This is a polyalphabetic cipher where a given letter in the plaintext can be represented by several different letters or symbols in the ciphertext. A good polyalphabetic cipher will defeat frequency analysis, but in this case frequency analysis can still be used to identify several common letters and it is then a process of trial and error to reconstruct the plaintext. The two symbols used for each letter are shown in the list below, but not all symbols were used in the code.
The plaintext is
You are on the wrong path. The others are ahead of you but I feel that yours is the more rightful claim. You must return to the historical reading room and seek out a copy of Sir Gwain and the Green Knight I have hidden detailed instructions on the location of the mediaeval manuscript within the pages of the oldest copy.Sir Gawain and the Green Knight is a Middle English romance of unknown authorship written at a similar time to The Canterbury Tales. Note that Ellie writes Gwain instead of Gawain maybe because she was in a hurry; maybe to make the code a little harder to crack; or maybe because she is a fan of the BBC series Merlin in which the Gawain character is known as Gwaine.
Michael Ventris is a historical person. He is most famous for deciphering Linear B, an ancient script used by the Minoan civilisation that existed on and around what is now called Crete. Despite their very similar backgrounds, there is no evidence to suggest that Turing and Ventris ever met.
Ignoring what appear to be diacriticals (accents), there are three 'words' in the text consisting of one letter. There are only two words in English comprising one letter ('I' and 'a'). This suggests that the diacriticals play a key role in modifying how the symbols behave.
Let's assume that the language is English. The most common one-symbol 'word' in the text is the one that appears at that start of line 6. The most common word in English is 'the', so maybe this symbol represents 'the'. In Old English, Middle English and some other languages, the letter 'thorn' (þ) corresponded to the sound 'th'. This suggests that þ represents 'th' and the symbol above it modifies it to become 'the'. Maybe the diacriticals are behaving as vowels?
The third word on line 11 starts 'th' and then the second symbol has been modified by an 'e', possibly twice. Thus this word is 'th*ee', possibly 'three'. At this point, one might guess that each symbol corresponds to a syllable, with the main part of the symbol acting as the consonant and the diacritical indicating the vowel. Symbols without a diacritical may just represent the consonant. There are 6 diacriticals, which correspond to 6 vowels, a, e, i, o, u, and y (in words where 'y' acts as a vowel). The symbol which resembles an 'o' in the text only appears at the start of a word; this suggests that this is a null consonant, used in cases where the word starts with a vowel.
The second word on line 12 and the second word on line 13 would then be 'theC' and 'thVC' where V and C indicate unknown vowels and consonants. The first word is likely to be 'then' and the second to be 'that'.
Having now identified the symbols representing 'th', 't', 'n' and the diacriticals representing 'e' and 'a', solving the code is now a process of trial and error, noting also that the text is in slightly archaic English. The majority of symbols (minus the diacriticals) correspond to a consonant in the alphabet. The first word on line 3 is 'Coulders' (for some consonant C) and the context of the message suggests that this word is 'shoulders'. Thus 'sh' (like 'th') has its own symbol.
The complete syllabary is shown below. Note that the null symbol is used in the first column to distinguish between diacritical marks that can appear both above and below the consonants.
The text can be deciphered to read
Robert. Forgive me for placing this burthen on thy shoulders. If thou hast learned to read this script then i trust thee wilt have gained the wisdom to make good use of the mysterys of Saladin's court. The mysterys are hidden within the pommel of my sword. Thou must twist the orb three times widdershins and then strike the blade. All that is hidden will be revealed.
Had the text really been written c.1192 then it would in fact have been in Middle English and would be very different to that above. Some archaisms are included (closer to early Modern English) for narrative effect. Burthen is an archaic spelling of burden. 'Mystery' meant 'secret' (and we used an older form of the plural).
In times before clocks were commonplace, 'widdershins' (from the German 'widersinnes', literally 'against direction') meant anticlockwise. To describe the clockwise direction, one would say 'sunwise' or 'deasil'. ('Widdershins' is best known to many people as one of the cardinal directions in Terry Pratchett's 'Discworld' series of novels. However, it is not a word invented by Pratchett!)
The decipherment of the code is similar to (albeit it considerably easier than) the way in which Linear B was deciphered by Ventris (building on earlier work of Kober, Bennett and Chadwick). Linear B is syllabic: each symbol in Linear B represents one syllable. By separately identifying vowels and consonants, Ventris deciphered Linear B and discovered that it was, against what many experts had thought, an early form of Greek.
Ventris did die in a car accident in September 1956.
Following financial difficulties, the John Rylands Library was acquired by the University of Manchester in 1972 and merged with the University's library. That Turing had layed the groundwork for this some 20 years earlier is, of course, pure invention on our part!
The symbols for consonants used in the manuscript (with the exception of þ) are based on those that appear in the Voynich manuscript. The Voynich manuscript is a book, likely dating from the early 15th century, written in an as-yet undeciphered script. You can read about it on Wikipedia here.
The story mentions that the sword is engraved with what appear to be old runes. The runes are standard Anglo-Saxon (more correctly, Anglo-Frisian) runes and a table of them can be found here. The sword is
As discussed in the solutions to Chapter 1, the mathematicians of the Islamic world were far ahead of those in western Europe at the time. However, there is no evidence that they had thought of complex numbers. The first known deliberate use of complex numbers was by Tartaglia and Cardano (see Chapter 1) in 16th century Italy.