Flicking through a fairly recent copy of the New Yorker in the dentist’s waiting room just now, I read a review of Jean Hollander’s translation of (and Robert Hollander’s extensive notes on) Dante’s Paradiso, the third part of the Divine Comedy. To be honest, I never had much patience with the Paradiso, all the fun in Dante was in the Inferno, a point of view this Slate article basically seems to agree with: so I never got to read about the pilgrim’s meeting with God right at the end…

Which is a shame, because there’s something interesting there which deserves a closer look. While it’s not strictly speaking cryptographic, it is linked in with the whole sacred geometry thing which people insist on projecting onto late medieval / early modern paintings and architecture, and which is essentially a form of hidden messaging (“Neoplatonic steganography“, if you will).

In the final canticle (Canticle 33) of Paradiso, Dante struggles to find words to describe the experience of meeting God: and in the end settles on an intense light (but one which the eye is attracted to rather than repelled away from), inside of which can be seen “three orbs of triple hue” (though I think the Hollanders translate these as “circles”). Dante finishes by comparing his attempts at describing the experience as no less futile than attempts to square the circle: where Man (extending the geometric metaphor just that little bit further than other poets would) is the square and God is the circle.

Anyone with even a passing familiarity with Leonardo should be aware of his representation of “squaring the circle” in his ‘Vitruvian man’. But there are a number of other early modern artworks which supposedly use a square to represent Man or Earth and a circle to represent God or Heaven. Jerusalem was supposedly round because it was a representation of Heaven, which (as any fule kno) was perfectly circular (Ptolemaic epicycles notwithstanding): which forms a (forgive me) circular argument within whose causal chains it is hard to disentangle the Platonic from the Ideal from the proto-religious.

Having said all that, Charles Hope’s argument as to the non-existence of most claimed examples of Neoplatonist allegories in Renaissance art would seem to cut a big Wile E. Coyote hole beneath most supposed examples of Renaissance sacred geometry. Even a big modern book in this general vein such as Richard Stemp’s “The Secret Language of the Renaissance” contains hardly any persuasive examples of sacred geometry: Stemp’s discussion of Massaccio’s Trinity (pp.210-213) seems a little forced in the way he ‘finds’ a circle in the background to enclose the square he has constructed around Christ.

But there is at least one artwork of the period with an inherently geometrical construction, and where Man is represented as a square and God as a great big dove at the centre of a circle, with Christ in the overlap between the two (though I can’t for the life of me think of the name of it). I had thought of this as a possible counterexample to Charles Hope’s skepticism about Neoplatonism, in that it does seem to bear the hallmarks of what is generally known as sacred geometry. However, a careful visual reading of it (when I can remember what it is!) may instead simply show it to be no more than an allegory literally derived from the last canticle of Dante’s Paradiso: in which case it may well be that we can basically consign Renaissance sacred geometry to the historical scrapheap.

Something to think about, anyway. 🙂

Another day, another Voynich novel to read: but “Enoch’s Portal” by A.W.Hill is certainly one with a heady sense of ambition. The flame the author wants us readers to touch is nothing short of an occult ‘Theory Of Everything‘: a kind of quantum alchemy, linking Cathar euthanasia with Renaissance magic all the way through to Nazi Germany, the Temple of the Sun (though this is the name of a 1969 Tintin film, the Order of the Solar Temple is what is really meant) and the twin modern magics of finance and Hollywood. And the threads binding this bulging mass of ideas together are the Voynich Manuscript, an impossibly virginal woman called Sofia, an impossibly filmic hero called Stephan Raszer, and… former Czech president Vaclav Havel. Ohhhh yes.

The Voynich aspect of the book is straightforward enough: the author buys in to Leo Levitov’s whole Cathar Endura ritual reading of the manuscript, along with all the John Dee fairy dust that people like to sprinkle on the VMs to make an otherwise unpalatable mystery taste that little bit sweeter. Yet the author has a character called Dr Noel Branch describe the VMs as “A theurgic riddle in the guise of soft-core pornography” and insisting that the “the key might lie in those silly illustrations” which are usually dismissed as nonsense: which would seen to indicate that Hill has at least properly engaged with the VMs on some level. 🙂

But for me, Hill gets enough of the history wrong in important places to break the narrative spell: for example, John Dee was never Emperor Rudolf’s alchemist (though Edward Kelley was, and Sinapius / de Tepenecz arguably came close enough too [though one might perhaps call him the “Imperial Distiller”]). Which is a bit of a shame, as this isn’t really a key support for the story.

Speaking of the story: in it, Stephan Raszer’s job is basically to track down rich women lost in cults, empathize with them, show them his own scarred wrists, have them fall in love with his failed-actor good looks, and convince them to transfer their (implicitly sexual) passion for the cult over to him… so that he can then haul them back to the pampered bland existance in Richville they worked so hard to escape from, thereby earning his handsome fee.

But Raszer is not so much a character as a filmic construct, formed from the unholy merging of a Kundalini/chakra-obsessed later Stevan Seagal (though Raszer never actually fights as such), a later Arnold Schwarzenegger (his “I don’t shoot peepul, I only saif cheeldren” phase), and the asexual 1990s James Bonds, who (along with their audiences) were neither shaken nor stirred by the various Dreary Hi-Tech Plot Devices Of Doom placed in their paths.

Females in “Enoch’s Portal” fare little better: Raszer’s partner comes from the same mop-up-all-the-loose-plot-threads school as did Tom Cruise’s impossibly capable assistant in “The Firm” (Holly Hunter); while the empowered modern women Raszer meets are all so, errrm, “enmoistened” by his good looks that they basically make love to him while his soul leaves his body on a brief spiritual holiday. Ghastly stuff.

All the same, there was a good idea in here: though Raszer lives in a supernatural world of walk-ins, succubi, and the like, the cults he deals with are basically spiritual frauds – which leads to an (actually quite interesting) question of whether Raszer is in fact delusional… but this is never obviously addressed.

Really, the problem I had with the book is that (whether it is actually true or not) it comes across again and again as having been written by someone who has watched too many trashy 1990s action movies and taken too many drugs, all the while not really engaging with the world around them. The thought kept returning when I was reading the book that it could all have been redeemed if only the author had done X or pulled back from Y… *sigh*. All in all, I just wish that Hill had had the courage of his convictions and written a screenplay instead, rather than the book of the film in his head. Oh, well!

I’ve spent a long time (though “far too long” probably covers it better) hunting down obscured fragments of text in the Voynich Manuscript: so my Spidey-sense tingled almost uncontrollably when I saw a claim for hidden text on f1v in the “Marginal Writing” picture gallery on Glen Claston’s Voynich Central.

I’d never heard of this before: just to be sure, I checked Reuben Ogburn’s 2004 page on “Writing in and around plant illustrations” in case it had slipped in there, but no sign. If you run this through Jon Grove’s colour separator filter, you can see that the brown ink used for the drawing and the brown paint used to fill it in are very slightly different: in the image below, the white area is where the filter thinks the overpainting happened.

But is there writing beneath? If you squint at the topmost image here long enough, you can start to make out something that might almost be writing. But if you filter it slightly differently, I think the answer emerges: the “signal” (below) appears to be not writing, but only compression artefacts from the MrSID wavelet encoding. Sorry, guys: false alarm! (Though next time I’m at the Beinecke, I’ll have another quick look, just to be completely sure…)

A quick pop-cultural aside: the song “Eternal Flame” was written by hugely successful American songwriter Billy Steinberg with Tom Kelly and Susanna Hoffs (of The Bangles). The inspiration for the song came from an eternal flame seen by Bangles’ bass-player Michael Steele burning at Gracelands in Elvis Presley’s memory, as well as from one at a Palm Springs synagague Steinberg had seen when very young. Though “Eternal Flame” was produced by Simon Cowell, I won’t hold that against it. 🙂

But historically, claims of actual eternal flames go back a very long way: in my book, I mentioned briefly that many in the Renaissance believed a “perpetual light” burned in the Temple of Vesta in Ancient Rome. Leon Battista Alberti’s 1450 book “Momus” mentions (though admittedly in a fictional context) a “perpetual flame, tending itself even though no material is laid under it and no liquid poured over it“, Giovanni Battista Della Porta documented many attempts at reproducing eternal flames in his Natural Magic in XX Books, while in his libro architettonico Antonio Averlino described a continuously-burning candle he saw in Sant Maria in Bagno. Another related story concerns Abbot Trithemius, who allegedly sold two “unquenchable eternall lights” to Emperor Maximilian I for 6000 crowns.

I thought this was one of those things for which there was unlikely to be any significant literature: I’d collected all the pieces together from scattered footnotes. However, recently I was inspired by Archer Quinn’s, ummm, perpetual ranting to properly read through Kevin Kilty’s well-known page on perpetual motion. All good stuff: and he even mentions eternal flames!

Kilty, who seems to have derived his information on this subject from Arthur Ord-Hume’s 1977 book “Perpetual Motion: history of an obsession“, mentions that:-

“Fortunio Liceti (1577-1657) made a lifelong study of these lamps, so many of which were supposedly found in old tombs, vaults and temples. Ord-Hume spends several pages examining ways to explain the observation of perpetual lamps. This is giving too much serious attention to a fantasy. It is likely that no one ever observed any such lamp.”

(Though I should of course point out that Averlino claimed to have observed an eternal flame). Fascinating! I was not aware of Fortunio Liceti‘s connection with eternal flames, and so rushed to buy Ord-Hume’s book as quickly as I could. I shall continue this thread when it arrives…

OK, I’ll admit it: people who talk about the Renaissance as a coherent historical phenomenon get on my nerves. There were numerous strands of thought at the time, all vying for the oxygen of attention, all trying to supplant medieval scholasticism: but arguably the two biggest new kids on the block circa 1400 were Renaissance humanism (think of Petrarch, etc) and Renaissance inventorship (think of Brunelleschi). While the former grew out of philology and a theoretical reverence for Classical texts, the latter emerged from the empirical world of clock-making.

Lynn Thorndike was happy enough (in his “Science & Thought in the XVth Century”) to point out that these two major strands were very often at odds with each other: but it should also be noted that the intersection between the two was far from empty. In fact, you might well look at the architects Leon Battista Alberti and Antonio Averlino – both born near Florence near to 1400 – as examples of “Renaissance Men” in the purest sense, in that they exemplified both strands at the same time.

The mystery of the Italian Renaissance (as described by Burckhardt and the generation of gung-ho pro-humanistic historians that followed him) is this: why did it emerge at such a narrow time (circa 1400) and place (Florence)?

For a long time, the dominant view has basically been that this was a random event, just one of those things that happen from time to time. However, some modern writers have begun to speculate whether a particular freak event or a subtle change in diet or eating habits might perhaps been the real “cause” of the Italian Renaissance.

For me, I would be unsurprised if insomnia turned out to be a key: Alberti writes, in his 1441 “On the Tranquillity of the Soul”, of “the agitation of his soul”at night, and how he can relieve this by trying to devise amazing machines for lifting and carrying weights. I wonder if an entire generation of Florentines suffered from a kind of intellectual insomnia, perhaps as a result of effectively becoming hyperthyroid from ingesting a particularly iodine-rich salt being brought into the city?

Or might the Florentines have simply become addicted to the sugar confections that had not long before suddenly filled the city’s apothecaries and markets? Might the Renaissance have simply been a metabolic balancing act as people tried to compensate for a giant communal sugar rush?

But there’s another possibility. If you were looking for a statistical explanation why a particular population produced more geniuses (while the overall bell-curve distribution probably remained intact), there would be two obvious candidates to consider – either (a) the mean IQ got shifted up (i.e. everyone somehow got smarter) , or (b) the variance increased dramatically (i.e. more extreme cases appeared at both ends of the scale).

This set me wondering: as I understand it, one of the problems often put forward with Darwinian evolution is that the natural rate of mutations is too low to support the amount of random change needed. So could it be that stable contexts inhibit mutations (i.e. encourage low adaptation rates), while troubled contexts somehow encourage mutations (i.e. encourage high adaptation rates)?

Interestingly, one medieval obsession presents itself here: that of whether “monsters” (freaks of nature) were signs (de-monstr-ations) of something greater happening in the world. Perhaps “monsters” in the human population were (and possibly still are?) literally a sign that the variance of the population is high.

Thinking about all this, it suddenly then became clear to me why low sperm counts make evolutionary sense: if a body is in significant physical difficulties, it makes no sense for it to try to reproduce offspring that are the same as it, as they would likely experience the same difficulties in the next generation. Instead, perhaps the body deliberately produces crippled, damaged sperm to try to encourage mutations that might be better adapted to the changing physical context. Otherwise, why would the body ever want to deliberately produce poor sperm or eggs? Perhaps the current medical view of “healthy” sperm is somehow clouded by an anti-mutation bias of some sort.

My prediction here is that that there will turn out to be reproductive mechanisms by which (a) healthy eggs repel damaged sperm and (b) damaged eggs discourage healthy sperm: leaving the two pivotal cases of (healthy eggs + healthy sperm) => low mutation rate (low variance, well-adapted to environment), and (damaged eggs + damaged sperm) => high mutation rate (high variance, poorly-adapted to environment).

But there’s a timing issue. Whereas sperm production is essentially a “just-in-time” process, women’s eggs are produced all in one go, and so form a lagging indicator to environmental adaptation (i.e. egg health in reproduction gives an indication of environmental fit 15-25 years earlier). So, could it be that, when looking for the source of the Renaissance circa 1400, we should instead look for a traumatic event in Florence circa 1380 that significantly affected women’s reproductive health, causing a change in the population’s IQ variance?

I really don’t know (this is a blog, not an article in Nature): but it is tempting to speculate whether it was simply coincidence that the Florentine Renaissance began two generations after the plague had ravaged Florence in 1348 (Boccaccio famously wrote about it). Might children born after the plague have stirred the Florentine gene-pool up in just the right way to set the Renaissance in motion a generation later?

It all started off with a plausibly-phrased story making an incredible claim via a dodgy animated GIF…

A March 2008 article by Ryan Ball in Animation Magazine claimed that the oldest piece of animation had been discovered: a 5,200-year-old rotating bowl from Tehran, a bit like an inside-out zoetrope depicting a jumping goat. When I saw this, I immediately wanted to blog about it: but there was something wrong about the 9-frame animated GIF at the bottom that held me back…

Reading a little more (as you do), I found a 2006 post on Neil Cohn’s Visual Linguist website (apparently the jumping goat bowl had originally been news in 2005) that deconstructed the GIF: the sequence of frames had been doctored to make it look more like an animation (a term Cohn felt wasn’t really justifiable) than it really was, because there were only actually 5 “frames” in the sequence on the bowl.

The last comment on Cohn’s page points to Alexis Chazard’s more appropriate 5-frame animation of the goat, taken directly (as far as was possible) from actual pictures of the bowl. There’s also a nice set of photographs from Iran that put the bowl more into context here.

All in all, I think it’s a huge shame that someone went to the trouble of mocking up a dodgy 9-frame GIF, apparently to try to oversell the animation aspect of the bowl. If that person had simply assembled the 5 frames exactly as they appeared (particularly if they had found specific evidence of an axis of rotation and had specifically taken 5 pictures at 72 degree rotation intervals, la la la), it would have been a perfectly acceptable demonstration. Basically,in a 5000-year-old artefact, nobody’s expecting Shrek to jump out at us, och no, Donkey. 😉

Incidentally, the first documented zoetrope came from the Chinese inventor Ting Huan in about 180AD: not many people know that, unless you’re a bit of a Wikipede (or should I say “Wikipedant“?) (or “Wikipedophile“?)

I know, I did blog about this only three days ago: but science moves ever onwards, OK?

A nice email arrived from Robert Matthews, the author of an excellent page on the d’Agapeyeff Cipher: he mentioned that he had received an email in February 2006 from John Willemse in Holland, who had suggested a novel kind of transposition cipher based around a spiral:-

I’m in no way a cipher expert, but I am a very curious person and I was wondering if the positioning of the 14×14 digram table could have anything to do with a spiral. The reason I suspect this, is that a spiraling positioning of numbers have the property that each upperleft corner of such a spiral (when starting with zero in the center) is a perfect square number. I’ll try to illustrate my point:

16 15 14 13 12
17 .4 .3 .2 11 ..
18 .5 .0 .1 10 ..
19 .6 .7 .8 .9 26
20 21 22 23 24 25

Starting from zero, and counting up, anti-clockwise, you will encounter a perfect square of each even number in the topleft corner. 196 is also such a number.

The ’04’ digram almost in the center could be a break point. If you ‘break’ after the zero and shift the 4 to the right, creating a new set of digrams, you end up with a set of digrams before the zero and a set after the zero. The set after the zero should probably be reversed, either the whole set or the individual digrams, to create a similar set as the first one (the digrams starting with higher digits and ending with lower digits).

You might then be able to construct a spiral like positioning, with the zero in the center or the zero obmitted. The first set might then be ‘twisted’ around it clockwise, and the second set anti-clockwise, possibly interweaving each other.

These are just some wild ideas, and I’m in no way capable of constructing and verifying such a table myself, but maybe it’s something to investigate?

Willemse’s idea is certainly interesting: but let’s look again at the (derived) 14×14 layout. To recap: one of the reasons for suspecting that transposition is involved is that there are two sets of horizontal tripled letters (75 75 75 and 63 63 63), while one of the reasons for suspecting that it’s not a ‘matrix transpose’ diagonal flip is that there are two sets of vertical tripled letters (81 81 81 and 82 82 82). That is, unless the plaintext sadistically contains a phrase like “SEPIA AARDVARK” (a phrase which, I’m delighted to note, Google believes currently appears nowhere else on the Internet).

75 62 82 85 91 62 91 64 81 64 91 74 85 84
64 74 74 82 84 83 81 63 81 81 74 74 82 62
64 75 83 82 84 91 75 74 65 83 75 75 75 93
63 65 65 81 63 81 75 85 75 75 64 62 82 92
85 74 63 82 75 74 83 81 65 81 84 85 64 85
64 85 85 63 82 72 62 83 62 81 81 72 81 64
63 75 82 81 64 83 63 82 85 81 63 63 63 04
74 81 91 91 84 63 85 84 65 64 85 65 62 94
62 62 85 91 85 91 74 91 72 75 64 65 75 71
65 83 62 64 74 81 82 84 62 82 64 91 81 93
65 62 64 84 84 91 83 85 74 91 81 65 72 74
83 83 85 82 83 64 62 72 62 65 62 83 75 92
72 63 82 82 72 72 83 82 85 84 75 82 81 83
72 84 62 82 83 75 81 64 75 74 85 81 62 92


From this, it seems that, yes, you could construct a large number of spiral transpositions without tripled letter sequences. Yet I’m not completely convinced by the idea that the 04 token is a good indicator for the centre of a spiral: from the substitution cipher angle, I’d be quite happy to tag that as a likely ‘X’ or ‘Y’ in the plaintext instead.

However, I would point out that if you examine the various diagonal transpositions of the 14×14 (i.e. reading through the 14×14 one diagonal line at a time), there is (unless I’m somehow mistaken) apparently only a single tripled letter in two of them, and that only over a line-break:-

75 62 82 85 91 62 91 64 81 64 91 74 85 84
64 74 74 82 84 83 81 63 81 81 74 74 82 62
64 75 83 82 84 91 75 74 65 83 75 75 75 93
63 65 65 81 63 81 75 85 75 75 64 62 82 92
85 74 63 82 75 74 83 81 65 81 84 85 64 85
64 85 85 63 82 72 62 83 62 81 81 72 81 64
63 75 82 81 64 83 63 82 85 81 63 63 63 04
74 81 91 91 84 63 85 84 65 64 85 65 62 94
62 62 85 91 85 91 74 91 72 75 64 65 75 71
65 83 62 64 74 81 82 84 62 82 64 91 81 93
65 62 64 84 84 91 83 85 74 91 81 65 72 74
83 83 85 82 83 64 62 72 62 65 62 83 75 92
72 63 82 82 72 72 83 82 85 84 75 82 81 83
72 84 62 82 83 75 81 64 75 74 85 81 62 92


All in all, Willemse’s idea of a spiral transposition does seem intriguing: but perhaps a little more psychologically ornate than d’Agapeyeff would have considered necessary as an exercise for the reader. If I were actively looking for a solution to this cipher (which I’m not), I would instead start with the four basic diagonal transpositions of the 14×14, and see if they led anywhere interesting… you never know! 🙂

While looking at Elonka’s list of unsolved cipher mysteries while composing my post on the d’Agapeyeff cipher, my eye was drawn to the list of solved cipher mysteries she appended to it, and in particular to “The E. A. Poe Cryptographic Challenge“.

Edgar Allan Poe often used codes and ciphers in his stories, most famously in “The Gold-Bug” (which incidentally inspired a very young William Friedman to take up an interest in cryptography). He also asked readers of one popular magazine to send him their ciphers to crack: which he (allegedly) managed to do for the hundred such that arrived.

However, in 1839 Poe published two tricky cryptograms allegedly by “Mr. W. B. Tyler” (probably a Poe pseudonym) which nobody at the time was able to break. These were rediscovered in 1985 by Professor Louis Renza, who then tried to raise their profile: before too long (in 1992), Professor Terence Whalen managed to solve the first one, which turned out to be nothing more complex than a simple monoalphabetic cipher.

The second (still-unbroken) cipher attracted the attention of Professor Shawn Rosenheim, who not only described it in his book The Cryptographic Imagination: Secret Writing from Edgar Poe to the Internet (Johns Hopkins, 1997), but also put up a $2500 prize to attract solvers’ attention, with the help of Jim Moore of bokler.com who built a website to promote it.

And then, after Rosenheim and Moore had fielded hundreds of fruitless emails and responses, a software engineer from Toronto called Gil Broza finally cracked the second cipher in October 2000: his decryption is detailed here.

For followers of the Voynich Manuscript, this makes for fairly depressing reading: neither of the “W. B. Tyler” ciphers were, even by the standard of Milanese ciphers circa 1465, particularly tricky, yet Broza had to work really quite hard to solve the second one. He worked out his own transcription, wrote his own software… and then still basically had to break into it by hand, a process made even more difficult by the presence of errors in the ciphertext (which were probably introduced in the typesetting). And people wonder why modern supercomputers can’t unravel the secrets of Voynichese – a cipher that is ten times harder than the second Poe Cipher.

The real mystery about Poe is actually the manner of his death: but that’s an intriguing story for another day… 🙂

Here’s a little Voynich Manuscript pop-culture link that got excised from Wikipedia last September. Poor thing: I thought I’d give it a second home here.

In the Esperanto-language comic strip “La Veksilologisto” (The Vexillologist), “Dr. Voynich” is the hero’s arch-enemy. Gifted by aliens with the “Orb of Esperanto” which allows universal translation, Voynich discovers this to be intolerable (animals speak, humans tell the truth), and sets out in search of the “Orb of Babel” which has the opposite effect.

I dug up a second reference to this comic strip here (also in Esperanto), which I tried to translate back into English courtesy of Traduku (an online Esperanto <–> English translator)… which had problems with cookies both in IE and Firefox (*sigh*). But (guessing at the Esperanto, which usually works), it seems as though it is a comic strip drawn by someone called David Bell, and published in the Esperanto magazine “Formoza Folio”.

And then, via this bibliographic page, I found a dead link to a missing file called “ff2.pdf” which (supposedly) contains a copy of the strip (apparently it was published in Taiwan in 2006): but the Wayback Machine didn’t have a copy of it. Oh well: I guess I’ll just have to carry on living without the joy of reading an Esperanto comic strip. But if anyone does manage to find a copy, please let me know! 🙂

Back in 1939, Alexander d’Agapeyeff wrote a tidy little book called “Codes and Ciphers” on cryptography history: though you can now buy it print-on-demand, cheap copies of the original book often come up on the various second-hand book aggregators (such as bookfinder.com), which is where I got my copy of the “Revised and reset” 1949 edition.

What is now generally understood is that d’Agapeyeff wasn’t really a cryptographer per se: he had previously written a similar book on cartography for the same publisher, and so thought to tackle cryptography.

On the very last page of the text (p.144), d’Agapeyeff dropped in a little cipher challenge, saying “Here is a cryptogram upon which the reader is invited to test his skill.

75628 28591 62916 48164 91748 58464 74748 28483 81638 18174
74826 26475 83828 49175 74658 37575 75936 36565 81638 17585
75756 46282 92857 46382 75748 38165 81848 56485 64858 56382
72628 36281 81728 16463 75828 16483 63828 58163 63630 47481
91918 46385 84656 48565 62946 26285 91859 17491 72756 46575
71658 36264 74818 28462 82649 18193 65626 48484 91838 57491
81657 27483 83858 28364 62726 26562 83759 27263 82827 27283
82858 47582 81837 28462 82837 58164 75748 58162 92000

This modest little cryptogram, now known as “the d’Agapeyeff Cipher“, has somehow remained unbroken for 70 years, and is often to be found alongside the Voynich Manuscript on lists of cipher enigmas.

The first thing to note is that adjacent columns are formed alternately from 67890 and 12345 characters respectively: which is a huge hint that what we are looking at is (in part, at least) a grid cipher, where each pair of numbers gives a position in a grid. If so, then we can throw away the “patristrocat” spaces between the blocks of numbers and rearrange them as pairs.

75 62 82 85 91 62 91 64 81 64 91 74 85 84 64 74 74 82 84 83 81 63 81 81 74
74 82 62 64 75 83 82 84 91 75 74 65 83 75 75 75 93 63 65 65 81 63 81 75 85
75 75 64 62 82 92 85 74 63 82 75 74 83 81 65 81 84 85 64 85 64 85 85 63 82
72 62 83 62 81 81 72 81 64 63 75 82 81 64 83 63 82 85 81 63 63 63 04 74 81
91 91 84 63 85 84 65 64 85 65 62 94 62 62 85 91 85 91 74 91 72 75 64 65 75
71 65 83 62 64 74 81 82 84 62 82 64 91 81 93 65 62 64 84 84 91 83 85 74 91
81 65 72 74 83 83 85 82 83 64 62 72 62 65 62 83 75 92 72 63 82 82 72 72 83
82 85 84 75 82 81 83 72 84 62 82 83 75 81 64 75 74 85 81 62 92 00 0[0]


The first hint that the order of these might have been scrambled (‘transposed’) comes from the two sets of tripled letters: 75 75 75 and 63 63 63. Five centuries ago, even Cicco Simonetta and his Milanese cipher clerks knew that tripled letters are very rare (the only one in Latin is “uvula“, ‘little egg’). The second hint that this is a transposition cipher is the total number of characters (apart from the “00” filler at the end): 14×14. If we discard the filler & rearrange the grid we get:-

75 62 82 85 91 62 91 64 81 64 91 74 85 84
64 74 74 82 84 83 81 63 81 81 74 74 82 62
64 75 83 82 84 91 75 74 65 83 75 75 75 93
63 65 65 81 63 81 75 85 75 75 64 62 82 92
85 74 63 82 75 74 83 81 65 81 84 85 64 85
64 85 85 63 82 72 62 83 62 81 81 72 81 64
63 75 82 81 64 83 63 82 85 81 63 63 63 04
74 81 91 91 84 63 85 84 65 64 85 65 62 94
62 62 85 91 85 91 74 91 72 75 64 65 75 71
65 83 62 64 74 81 82 84 62 82 64 91 81 93
65 62 64 84 84 91 83 85 74 91 81 65 72 74
83 83 85 82 83 64 62 72 62 65 62 83 75 92
72 63 82 82 72 72 83 82 85 84 75 82 81 83
72 84 62 82 83 75 81 64 75 74 85 81 62 92

This is very probably the starting point for the real cryptography (though the presence of tripled characters in the columns implies that it probably isn’t a simple “matrix-like” diagonal transposition. Essentially, it seems that we now have to solve a 14×14 transposition cipher and a 5×5 substitution cipher simultaneously, over a relatively small cryptogram – an immense number of combinations to explore.

However, we know that d’Agapeyeff wasn’t a full-on cryptographer, so we should really explore the psychological angle before going crazy with an 800-year-long brute-force search. For a start, if you lay out the frequencies for the 5×5 letter grid (with 12345 on top, 67890 on the left), a pattern immediately appears:-

** .1 .2 .3 .4 .5
6. _0 17 12 16 11
7. _1 _9 _0 14 17
8. 20 17 15 11 17
9. 12 _3 _2 _1 _0
0. _0 _0 _0 _1 _0

Here, the 61 (top-left) frequency is 0, the 73 frequency is 0, and the final nine frequencies are 3, 2, 1, 0; 0, 0, 0, 1, 0. I think this points to a 5×5 mapping generated by a keyphrase, such as “Alexander d’Agapeyeff is cool” (for example). To make a keyphrase into a 5×5 alphabet, turn all Js into Is (say), remove all duplicate letters (and so it becomes ALEXNDRGPYFISCO), and then pad to the end with any unused characters in the alphabet in sequence (BHKMQTUVWZ)

* 1 2 3 4 5
6 A L E X N
7 D R G P Y
8 F I S C O
9 B H K M Q
0 T U V W Z

For a long-ish (but language-like) keyphrase, rare characters would tend to get moved to the end of the block: which is what we appear to see in the frequency counts above, suggesting that the final few letters are (for example) W X Y Z or W X Z.

Yet 61 and 73 have frequency counts of zero, which points to their being really rare letters (like Q or Z). However, if you read the frequency counts as strings, 61 62 63 = 0 17 12, while 73 74 75 = 0 14 17: which perhaps points to the first letter of the keyphrase (i.e. 61) being a rare consonant, and the second pair being Q U followed by a vowel. Might 73 74 75 76 77 be QUIET or QUITE?

I don’t (of course) know: but I do strongly suspect that it might be possible for a cunning cryptographer to crack d’Agapeyeff’s keyphrase quite independently of his transposition cipher. It can’t be that hard, can it? ;-p

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Update: a follow-up post is here