The other day, I was wondering where in East London (according to the story the owner told me) the Blitz Ciphers were found: and also wondered if they might have been left behind by some kind of mathematical society.

As an aside, the problem with any speculative mathematical link to Freemasonry is that even though Masonic theoretical historians like to talk about (capital-G) Geometry and how the Great Architect of the Universe (errrrm: God, basically) is somehow ineffably mathematical, their rather grand Platonic-Christian narrative breaks down when you bother to look at the details. The short version is that if there is any genuine maths in Masonry beyond basic Euclid-for-Dummies, it seems to me to be extraordinarily well-hidden.

(As always, if you happen to know of specific examples of mathematical Masonic societies that run counter to this sweeping generalization, please feel free to leave a comment below.)

So I instead went looking for genuine historical mathematical societies in London’s East End: and was delighted to discover the all-too-brief splendour of the Spitalfields Mathematical Society.

The Spitalfields Mathematical Society, Crispin Street

Conspiracy theorists and armchair cold case amateur detectives know this part of London well: the Ten Bells pub just around the corner was frequented by Jack the Ripper’s victims, the last of whom was found in Millers Court (close to Crispin Street). (Pastry chef geezer Jamie Oliver’s great-great-grandfather was for a while the Ten Bells’ landlord, for all you TV trivia fans.)

Incidentally, I found a rather nice website that blends historical photos of Spitalfields (taken by C. A. Mathew around 1912) with modern photographs taken on the same spot, to give an eerily evocative effect (such as the following image of Crispin Street):

But long before even C. A. Mathew, the history of the area revolved around Huguenot weavers, whose houses in Fournier Street are still there:

And it was the Huguenot immigrants who the Spitalfields Mathematical Society was originally aimed at, according to most accounts. De Morgan’s (1872) “A Budget of Paradoxes” describes it thus:

Among the most remarkable proofs of the diffusion of speculation was the Mathematical Society, which flourished from 1717 to 1845. Its habitat was Spitalfields, and I think most of its existence was passed in Crispin Street. It was originally a plain society, belonging to the studious artisan. The members met for discussion once a week ; and I believe I am correct in saying that each man had his pipe, his pot, and his problem. One of their old rules was that, “If any member shall so far forget himself and the respect due to the Society as in the warmth of debate to threaten or offer personal violence to any other member, he shall be liable to immediate expulsion, or to pay such fine as the majority of the members present shall decide.” But their great rule, printed large on the back of the title page of their last book of regulations, was “By the constitution of the Society, it is the duty of every member, if he be asked any mathematical or philosophical question by another member, to instruct him in the plainest and easiest manner he is able.” We shall presently see that, in old time, the rule had a more homely form.

I have been told that De Moivre was a member of this Society. This I cannot verify : circumstances render it unlikely ; even though the French refugees clustered in Spitalfields ; many of them were of the Society, which there is some reason to think was founded by them. But Dollond, Thomas Simpson, Saunderson, Crossley, and others of known name, were certainly members. The Society gradually declined, and in 1845 was reduced to nineteen members. An arrangement was made by which sixteen of these members, who were not already in the Astronomical Society became Fellows without contribution, all the books and other property of the old Society being transferred to the new one. I was one of the committee which made the preliminary inquiries, and the reason of the decline was soon manifest. The only question which could arise was whether the members of the society of working men for this repute still continued were of that class of educated men who could associate with the Fellows of the Astronomical Society on terms agreeable to all parties. We found that the artisan element had been extinct for many years ; there was not a man but might, as to education, manners, and position, have become a Fellow in the usual way. The fact was that life in Spitalfields had become harder : and the weaver could only live from hand to mouth, and not up to the brain. The material of the old Society no longer existed.

London had a fair few broadly similar societies – the Mechanic’s Institution and the London Architectural Society to name but two – but if you were looking for a mathematical society in East London that had long disappeared and some of whose papers might -possibly- have been the Blitz Ciphers, the Spitalfields Mathematical Society would seem to be at the very least an interesting candidate, right?

But the immediate question is…

Was Crispin Street bombed in WWII?

Having once idly flicked through a copy of “The London County Council Bomb Damage Maps 1939-1945” hardback when it came out in 2015, I half-remembered that the London bomb maps were all at the London Metropolitan Archive, and had once upon a time been in an exhibition there. There’s also tons more stuff in the National Archives in Kew (in whose downstairs bookshop I saw the book, incidentally).

But this being the Internet, there are also online bomb damage maps to try out. And it turns out that even though nearby streets were hit (such as Frying Pan Alley)…

…it would seem that Crispin Street escaped WWII unscathed.

So it would finally seem that we may well be out of luck with any possible connection between the Blitz Ciphers and the Spitalfields Mathematical Society. But all the same, I’m glad I looked. 🙂

And finally…

The Astronomer’s Drinking Song

Augustus De Morgan’s “A Budget of Paradoxes” includes the lyrics of a song sung at a Mathematical Society dinner in 1798, in honour of its solicitor, Mr. Fletcher. He had defended it against charges brought against them by “Informers”, but refused all offers of payment. Splendidly, De Morgan included the lyrics, which I reproduce below.

Of course, classic comedy song connoisseurs will instantly spot the connection with Monty Python’s “Rhubarb Tart Song“, which also mentions René Descartes (The principles of modern philosophy / Were postulated by Descartes. / Discarding everything he wasn’t certain of / He said ‘I think therefore I am a rhubarb tart.’)


WHOE’ER would search the starry sky / Its secrets to divine, sir,
Should take his glass I mean, should try / A glass or two of wine, sir !
True virtue lies in golden mean, / And man must wet his clay, sir ;
Join these two maxims, and ’tis seen / He should drink his bottle a day, sir !

Old Archimedes, reverend sage ! / By trump of fame renowned, sir,
Deep problems solved in every page, / And the sphere’s curved surface found, sir:
Himself he would have far outshone, / And borne a wider sway, sir,
Had he our modern secret known, / And drank his bottle a day, sir !

When Ptolemy, now long ago, / Believed the earth stood still, sir,
He never would have blundered so, / Had he but drunk his fill, sir :
He’d then have felt it circulate, / And would have learnt to say, sir,
The true way to investigate / Is to drink your bottle a day, sir !

Copernicus, that learned wight, / The glory of his nation,
With draughts of wine refreshed his sight, / And saw the earth’s rotation ;
Each planet then its orb described, / The moon got under way, sir ;
These truths from nature he imbibed / For he drank his bottle a day, sir !

The noble Tycho placed the stars, / Each in its due location ;
He lost his nose by spite of Mars, / But that was no privation :
Had he but lost his mouth, I grant / He would have felt dismay, sir,
Bless you ! he knew what he should want / To drink his bottle a day, sir !

Cold water makes no lucky hits ; / On mysteries the head runs :
Small drink let Kepler time his wits / On the regular polyhedrons :
He took to wine, and it changed the chime, / His genius swept away, sir,
Through area varying as the time / At the rate of a bottle a day, sir !

Poor Galileo, forced to rat / Before the Inquisition,
E pur si muove was the pat / He gave them in addition :
He meant, whate’er you think you prove, / The earth must go its way, sirs ;
Spite of your teeth I’ll make it move, / For I’ll drink my bottle a day, sirs !

Great Newton, who was never beat / Whatever fools may think, sir ;
Though sometimes he forgot to eat, / He never forgot to drink, sir :
Descartes took nought but lemonade, / To conquer him was play, sir ;
The first advance that Newton made / Was to drink his bottle a day, sir !

D’Alembert, Euler, and Clairaut, / Though they increased our store, sir,
Much further had been seen to go / Had they tippled a little more, sir !
Lagrange gets mellow with Laplace, / And both are wont to say, sir,
The philosophe who’s not an ass / Will drink his bottle a day, sir !

Astronomers ! what can avail / Those who calumniate us ;
Experiment can never fail / With such an apparatus :
Let him who’d have his merits known / Remember what I say, sir ;
Fair science shines on him alone / Who drinks his bottle a day, sir !

How light we reck of those who mock / By this we’ll make to appear, sir,
We’ll dine by the sidereal clock / For one more bottle a year, sir :
But choose which pendulum you will, / You’ll never make your way, sir,
Unless you drink and drink your fill, / At least a bottle a day, sir !

As promised, here are my work-in-progress transcriptions for the newly-released pages #7 and #8 of the Blitz Ciphers. I’ve had to add a few new symbols to the transcription alphabet, so there are now about sixty or so: doubtless some will prove to be duplicates, but I’d rather slightly expand the alphabet when transcribing than make a wrong assumption that can’t easily be undone.

And what do they tell us? Well, I’ve already tried a series of statistical tests on them, though without anything jumping out so far. Even though they have a trailing-off instance count distribution with E at the top of the heap and D not far behind it, the rest seems fairly arbitrary.

Unlike Dave Oranchak, I haven’t spent years thinking about how to crack unbroken homophonic ciphers, so I don’t really know if this is expected behaviour. Some of the symbols could well be nulls, but I don’t (yet) have a good tool for predicting homophonic nulls: but maybe that’s just too old-fashioned a thing to hope for.

Here are some analysis links to Dave Oranchak’s Webtoy: page #7 analysis and page #8 analysis. Note that these only worked for me in Firefox (not IE), but other browsers may also work.

Overall: as of right now, I’d say the Blitz Ciphers looks a bit loose and patternless: in particular, the contact tables don’t quite ‘feel’ right.

Yet unlike Rich SantaColoma commenting on Klaus Schmeh’s page from a few days ago, I’m not yet ready to call this as an outright fake. Rather, what I’m saying is that the Blitz Ciphers seem to combine the instance frequency counts of monoalphabetic ciphers with the disorder of polyalphabetic ciphers and the inscrutability of homophonic ciphers. Two out of the three I could probably still feel comfortable with simultaneously (and work with), but having all three in play at the same time leaves me a bit… suspicious.

Basically, the jury’s out on this one, and they’re asking for pizza.

Page #7 (rotated 180 degrees from the image as released):



Page #8



Note that my expanded transcription alphabet looks like this (click for larger image):-


I’ve just been contacted by the owner of the Blitz Ciphers, with five more scans of Blitz Cipher pages we hadn’t previously seen.

These continue the original set’s apparent theme of mystifying geometrical shapes combined with unhelpful-looking annotations in a 50-odd symbol cipher alphabet: feel free to bang your head against the walls of these strange diagrams, Voynich researcher style, if you like.

Me, I’m much more interested in the prosaic-looking text-only pages #7 and #8, particularly page #7 (ignoring the tiny annotation in a second hand). My Plan A is therefore to transcribe these two pages carefully (even though there’s a fair bit of what looks like water damage, most seems legible with only light amount of image enhancement) and then throw various cryptological / statistical tests at them to see what emerges.

#7: 15491625601_57c6aec33d_o

My hunch? Just as I noted before, this still looks to me like a homophonic cipher with possibly a few nulls, in broadly the same vein as the Copiale Cipher. As such, I’m guessing the plaintext will be a well-known European language, particularly English or German.

But what my nose isn’t sniffing here is anything that would sit in a mainstream Masonic tradition: these, such as the (now comprehensively cracked) Action Line Cryptogram, would probably be dominated by text describing candidates knocking at doors to be initiated via faux-historical rituals than a set of curiously arcane geometric diagrams.

…unless you know better? 🙂

I’ve just added a new permanent page on the mysterious Blitz Ciphers to Cipher Mysteries. Basically, I discovered a few days ago that I had much higher resolution versions of the three scans so far released than I remembered having (i.e. 4MP rather than 1MP), which gave me a good-sized shove to put a proper page up for them. Also, a big hat tip to Edward B for asking if I had anything so useful as decent-sized scans. 😉

But that has also prompted me to revisit the issue of why the Blitz Ciphers aren’t apparently trivially crackable with normal crypto tools (e.g. zkdecrypto etc). And that prompted me to think again about how to go about detecting / predicting nulls.

As always, I had a look for null detection algorithms on the Internet, just in case there was some kind of magical analytical framework out there that I had somehow missed (there’s nothing in Cryptool etc). The closest mention I found was a 2005 message from Brian Tawney on the Voynich mailing list that basically described his independent version of my own homebrewed null character detector: which basically comes down to comparing the distribution of letters preceding / following nulls and seeing how closely that distribution approximates the context-less distribution of letters in the message.

For what it’s worth, my implementation of this hack predicts that B / D / E / M / S are the glyphs in the Blitz Ciphers most likely to be nulls: while another null-detector hack I wrote (that calculates the per-glyph difference in 1st order entropy if individual characters are removed from the stream) predicts that E / B / M / C / S / D may well be nulls.

So far so reasonable, you might initially think. But from my perspective, the problem with this is that nulls also behave a lot like vowels, in that they sit comfortably next to many different other letters / glyphs, can occur quite often within a ciphertext, and tend not to contain much information (in the Shannon entropy sense of the word). So I’m very far from convinced that I could tell nulls from vowels, or even from high-frequency nomenclature tokens (such as “the”, “and”, or perhaps “Freemason” 😉 ).

I might be wrong, but arguably the biggest theoretical problem with both of these hacks is that I think we would need to feed them a substantially larger ciphertext (I’m guessing 10x larger?) to get properly significant results in the presence of other cipher mechanisms (e.g. homophonic equivalents). Whereas a decent simple substitution cipher cracker can have a decent go at breaking a monoalphabetic cipher with as little as, say, 30 characters… so it may be clever, but it seems an order of magnitude cruder than proper cryptanalytical kit.

So… where are all the null detection algorithms? It seems to me that the cryptanalytical tools written these days are more focused on the statistical nuances of computer-era cryptography, while old school trickery (such as nulls and homophones) gets relatively little attention outside of the Zodiac Killer Ciphers world. Maybe there just aren’t any out there.

…unless you know better? 🙂

A few weeks ago, some new ciphertexts pinged on my Cipher Mysteries radar: the story goes that they had been found just after WWII in wooden boxes concealed in the wall of an East London cellar that German bombing had exposed. Hence I’ve called them “The Blitz Ciphers”, but they’re probably much older than the 1940s…

They were handed down to the discoverer’s nephew (the present owner), who now finds himself caught between a desire for relative anonymity and a desire to know what they say. So far, he has been good enough to release three tolerably OK photos from a much larger set he took: but will these be enough for us to crack their cipher?

[Of course, despite the story’s plausibility, I have to point out that this might conceivably still be a hoax designed to make cryptographic fools of us: but if so, it’s such a classy job that I really don’t mind. 🙂 ]


Generally, the Blitz Ciphers’ writing appears to have been added in two hands: a larger, paler, more calligraphic presentation hand, and a smaller, darker, tighter annotation hand. While the presentation hand serves to establish the content and layout structure, the annotation hand is restricted to supplementary paragraphs and additional short notes apparently explaining key letters or terms.

Broadly speaking, the text on the first page (the ‘title page’, above) seems to have been laid down in three sequential phases:-
* #1: the circular ‘boss’ / ‘plaque’ and the two large paragraphs – large presentation hand, brown ink, quite faded in places.
* #2: the third large paragraph at the bottom – mid-sized annotation hand, brown ink.
* #3: the annotations to the other paragraphs – small-sized annotation hand, darker ink.
This general construction sequence seems to hold true for the other pages too.

The second page we have contains two curious diagrams: one a drawing of an octagon (though note that there is a square missing from the lines connecting all the vertices of the octagon), and the other an abstract tree-like representation of something unknown.

Our third page contains a large “John Dee”-like 20×20 square table, where each grid square contains individual cipher letters. The table has an array of red dots gridded within it, where each of the 16 internal red dots is surrounded by a letter repeated four times in a 2×2 block. Red dots near the sides all have two dotted square characters on the edge beside them, apart from a single one near the top right, suggesting a possible copying error. There is also a single correction (near the top left of the 20×20 table) made in the presentation hand.

The support material appears to be handmade paper (I don’t have access to them to look for a watermark, sorry!), while the inks for the two hands appear to be quite different. Though I can’t prove it, I suspect that the larger presentation hand was written using a quill pen (suggesting genuine age or some kind of ceremonial presentation aspect) while the smaller annotation hand was written several decades later with a metal nib. They could possibly have been written by the same person using different pens, but differences between the two hands argue against this.

My initial dating hunch was the first layer could well be 16th century and the second layer 17th century: but having said that, the whole thing could just as well be much more recent and instead have been deliberately written in that way to make it appear ‘venerable’ and old-looking. (More on this below.)

The Blitz Cipher Alphabet

The letter forms are clear, distinct, and upright: the presence of triangles, squares and circles and various inversions perhaps points to a cryptographer with a mathematical or geometric education. It’s closer to a demonstration alphabet (designed for show) than a tachygraphic script (designed for repeated large scale use). Here’s the provisional transcription key I’ve been working with:-

Despite some apparent ambiguities in how to parse or transcribe the various cipher shapes used, the fact that the 20×20 table has only a single letter in each cell is a fairly strong indication that each table cell contains a single cipher glyph, suggesting that about 50 distinct characters are in use. The text has a language-like character frequency distribution, with “:” [E] being the most frequently used character (the “tilted Jupiter glyph” [B] and the “joined-up-II glyph” [D] are #2 and #3 respectively). The “Greek phi glyph” [S] often appears at the start of lines and paragraphs.

I’ve shown all this to some cipher historians and codebreakers for their early reactions. Glen Claston notes that “the alphabet is based on the types of symbols used by astrologers, with a few I recognize as alchemical symbols“, though – inevitably contrariwise – I suspect this might well be a coincidence arising from the simple shapes and symmetries employed. Peter Forshaw suggests parallels with some geometric cipher shapes used in Della Porta’s “De furtivis literarum notis“, though Tony Gaffney similarly cautions that such “shapes were very common back then, the numerous ‘ciphers of diplomatic papers’ in the British Library are full of them“.

The Blitz Cipher System

As with the Voynich Manuscript, the peaky frequency distribution probably rules out complex polyalphabetic ciphers (such as Alberti’s code wheel and Vigenere cipher): yet it doesn’t obviously seem to be a simple monoalphabetic substitution in either English or Latin (but please correct me if I’m wrong!)

Unlike the Voynich manuscript, however, I can’t see any obvious verbose cipher patterns significantly above chance: so the main techniques left on the cryptographic smorgasbord would seem to be:
* a homophonic cipher, like the Copiale Cipher (but if so, the encipherer didn’t flatten the stats for “:” [E] very well)
* a nomenclator cipher (i.e. using symbols for common words, like “the”, “Rex”, or “Mason” 🙂 )
* an acrostic / abbreviatory / shorthand cipher.

All the same, there are some intriguing patterns to be found: David Oranchak points out that “‘SBDBlDMDBl’ is an interesting sequence, since it is length 10 but only consists of 5 unique symbols.” I suspect that the presentation hand uses a slightly different enciphering strategy to the annotation hand, which possibly implies that there may be some kind of homophone mapping going on. The fact that there is also an annotation applied to a single letter [c] on the title page may also point to a nomenclator or acrostic cipher.

Personally, I’m intrigued by the circular ‘boss’ at the top of the title page: this has three letters (C, M and E) calligraphically arranged, i.e. the two dots of the colon have been separated above and below the M. To my eyes, this looks suspiciously like a cryptographic conceit – might it be the case that “:” (E) is in fact a kind of letter modifier? For example, it might encipher a repeat-last-letter token (if the text had a lot of Roman numbers), or perhaps a macron-like “overbar” superscript denoting a scribal abbreviation (i.e. contraction or truncation). Something to think about, anyway!

As for the plaintext language: if this was indeed found concealed in an East London cellar, English and Latin would surely be the main suspects, though Tony Gaffney tried Latin and couldn’t find any kind of match.

Blitz Cipher Theories & Hunches

If you’re expecting me to start speculating that these documents were from a 16th century Elizabethan secret society frequented by John Dee and/or William Shakespeare, sadly you’ll be quickly disappointed. Similarly, though I concur heartily with Glen Claston that these genuinely intriguing ciphertexts may well ultimately prove to be high-ranking 18th century Mason or Freemason ciphers, it is just too early to start saying. We simply don’t know as yet enough of the basics.

What I personally have learned from the tragically fruitless, long-term debacle that is Voynich Manuscript research is that speculative theories are almost always a hopeless way of trying to decipher such objects. Hunches are cool and useful, but they need to stay restrained, or everything goes bad. Please, no theories, let’s try to crack these using the proper historical tools at our disposal!