As I mentioned here and indeed here a few days ago, my usually-Early-Renaissance-focused thoughts have of late been turning slowly to the Zodiac Killer Ciphers, in particular to the unsolved 340-character cipher known as “Z340”. Unusually as cipher mysteries go, we also have an earlier cipher called “Z408” (no prizes for guessing its length) by the same person, one that was quickly cracked (using the crib “KILL”). Z408 turned out to be a homophonic simple substitution cipher (but with spelling mistakes, copying mistakes, and a few subtly odd features); and there are plenty of good reasons to think that Z340 will share many of these same basic aspects (but made somewhat harder to crack).

Even though it was originally a crib which helped to crack it, Z408 has other weaknesses, most notably the way it sequentially cycles through homophones (“multiple ciphertext shapes for the same plaintext character”). For example, plaintext ‘t’ maps to the four ciphertext homophones HI5L, and appears in the text as the sequence HI5LHI5ILHI5LHI5LHI5LHI5LI5LHL5IIHI. If you count each successful letter-to-letter transition matching the modulo-4 sequence [HI5L] as a 0.25 success event (=26) and each non-match (=8) as a 0.75 failure event, I believe you get a raw probability of less than 1 in a billion (i.e. of at least 26 successes from 34 events). Please check my maths, though – I used this online binomial calculator with N = 35-1, k = 26, p = 0.25, q = 0.75. For more on these homophone sequences, Zodiac ciphermeister Dave Oranchak kindly pointed me at a full list of Z408 homophone sequences.

Incidentally, the top few match counts are:-
e -> ZpW+6NE – N = 54-1, k = 38
t -> HI5L – N = 35-1, k = 26
s -> F@K7 – N = 20-1, k = 15
o -> X!Td – N = 27-1, k = 13
n -> O^D( – N = 23-1, k = 20
i -> 9PUk – N = 44-1, k = 35
a -> GSl8 – N = 26-1, k = 10

It would be great to tell you how statistically significant these sequences are, but I know enough stats to know that it’s not quite as easy as it looks (for a start, we’re preselecting the best order of letters to use) – any passing statisticians, please feel free to leave a comment. I’m also quite surprised that nobody has apparently tried to use this weakness as a direct way to find the Z340 cipher’s homophones (in fact, John Graham-Cumming also blogged about this in June this year), but – as I’ll show shortly – I suspect trying just that on its own wouldn’t be enough.

Taking a brief step sideways, I’m always intrigued by mistakes in ciphers, because these often point to how the cipher was constructed. One interesting feature (but which I’m still trying to understand to my own satisfaction) is the solid triangle cipher shape in Z408, and how it appears to encipher different letters at different times. The view often put forward elsewhere is that this varied due to copying errors, perhaps arising because the Zodiac Killer’s pen was too thick, causing him to misread his draft version. As for me, I’m not so sure, because the solid triangle decrypts to a curious sequence:-
* “A” in “bec-A-use”
* “S” in “mo-S-t dangerous”
* “A” in “an-A-mal”
* “S” in “mo-S-t thrilling”
* “A” in “with -A- girl”
* “S” in “if it i-S-”
* “E” in “my slav-E-s”
* “A” in “my -A-fterlife”

Of these, only the “A” in “an-A-mal” is possibly a copying error (“I” is enciphered by an empty triangle shape) as compared to just a spelling mistake (the Zodiac Killer has plenty of those). But even that seems a little unlikely when the whole ASASAS[E]A pattern that emerges – so very similar to the homophonic sequences discussed above – is pointed out. I haven’t yet figured out what this implies, but it’s pretty interesting, right?

Moving on to the uncracked Z340 cipher, I have to say that what strikes me most is the difference between its top half (lines 1-10) and its bottom half (lines 11-20). It turns out that back in 2009, FBI codebreaker Dan Olson pointed out to Tom at zodiackiller.com that lines 1-3 and 11-13 contained very few repeats: other people have wondered whether this points to some kind of block-level transposition going on. Me, I suspect there’s a far stronger inference to be made: that even though they share nearly all the same character shapes, I’m pretty sure that the top and bottom halves of Z340 use completely different cipher letter assignments, and hence may well need to be cracked independently. Further, I suspect that the Zodiac may well have intended to send them out separately (Z408 was sent as three independent sections), but (for some reason) ended up sending them both as a single cipher.

[Incidentally, I also don’t believe that the last few letters of the bottom half of Z340 are genuinely part of the ciphertext to be cracked: they seem to spell “ZODAIK”, which is just a touch too coincidental for me. 🙂 ]

Right now, I think that a constructive first big step would be to search for statistically significant homophone sequences in the top and bottom halves of Z340, because we can be reasonably sure that the most frequent letters will probably have four or more homophones, just as with the Z408 cipher: trying this out may well yield some surprisingly revealing results. Any takers at the FBI? 😉

54 thoughts on “Thoughts on the Zodiac Killer Z408 and Z340 ciphers..

  1. The paper “An Algorithmic Solution of Sequential Homophonic Ciphers” by John C King describes an efficient attack that exploits sequential homophones to reduce homophonic substitution ciphers to simple substitution ciphers. King applied the technique to the 340 with little to no success. I think the main weakness of his approach is that it does not take into account the various imperfections of the homophone sequences used by the Zodiac killer.

    I wonder if you can estimate the statistical significance of discovered homophone sequences by counting the total number of ways that such sequences could occur with the same “bag” of symbols. For instance, how many different ways can you re-arrange the symbols in the 340 (preserving their frequency) such that a given homophone sequence appears? Intuitively, a longer sequence of repetitions implies greater significance, so perhaps an exact combinatorial calculation is not necessary.

  2. David: as I wrote, the main thing is that I think the two halves of Z340 are quite different, and so trying to shoehorn them both into a single unitary test (as almost everyone has done in the past, I believe) would likely lead nowhere. Furthermore, I don’t for a minute think that given just the right algorithm an answer would pop out – as you point out, there are too many confoundingly noisy elements at play there too, and from what we’ve seen the Zodiac killer doesn’t tend to follow any rule slavishly. Rather, I think that by following the process carefully you might well see a small handful of distinctive homophone clusters pop out – not enough to solve Z340 directly, but enough to give us confidence that we’re starting to reach some kind of statistically significant signal through all that noise. Fingers crossed! 🙂

  3. Hi Nick,
    Are these sequences statistically significant?

    http://i262.photobucket.com/albums/ii112/tony59b/tickssetsfirst.gif

  4. Tony: calculating the statistical significance of the appearance of individual sequences (or, as in your case, similar-looking patterns) is an exercise fraught with great difficulty. There’s a big difference between what I call “raw probability” and “statistical significance”, which largely comes down to experiment design: in my experience, most stats you’ll find in the wild are bad stats because the underlying data suffer from multiple sampling biases. Similarly, statistical confidence is affected by sample size and sampling methodology, making relatively short cryptograms problematic.

    The case I describe in the post is a little unusual because the repeating n-character cycle allows you to predict what the next character will be (i.e. to model the sequence), which (I think) gives the kind of pretty-much-independent pass-fail conditions you need for binomial calculations. For example, reading characters at random or in the wrong grid direction shouldn’t give you any noticeable modelled sequence at all. Having said that, you still have to select the best order of letters, which I suspect reduces the effective overall probability by 2^n or perhaps 2^(n-1): but I’m more of a practical statistician than a theoretical one, so this is quite esoteric stuff for me. 🙂

  5. Tony: having said all that, can you tell me what the (presumably homophonic?) sets are in the image you linked to and where it’s from?

  6. Nick,
    The image gives the possible homophones whether they cycle sequentially or not i.e. after using his 4 substitutes HI5L he repeats using the same 4 substitutes but in any order.
    In the image lower case letters represent the backward capitals – asterix crosshairs – diamond triangle with dot – the other 2 represent the double J with a dot.
    I agree the ZODAIK on the bottom line is too much of a coincidence especially as it is preceded by NPKS (backward P) – as most of his plaintext letters include the phrase ‘Zodiak speaking’ – This suggests to me that it was written like the image on the cerial packet, having completed his message there are lots of blank spaces to fill and he noticed he could make it similar.
    It’s also interesting to compare the 480 with Poe’s cipher – both use the homophones sequentially and both deteriorate in their accuracy towards the end.
    Tony

  7. “Of course, plenty of people have already tried to crack the two halves independently and failed. . . .”

    You so certain of that Einstein? Says who?

  8. Without actually being Einstein-like, I’m certain of what I said because I’ve been talking with people online (Dave Oranchak, glurk and others on the zodiackillerfacts.com forum) who have done just that and told me so. The main impetus for trying to split Z340 into two came from Dan Olson at the FBI, who in 2009 pointed out that the repeat value pattern had lulls at lines 1-3 (which you’d broadly expect from a homophone substitution cipher) as well as at lines 11-13. If this is indicative of what’s going on inside the cipher, the reasoning goes, then it must be either a rearrangement (i.e. the correct line sequence is 1, 11, 2, 12, 3, 13, or something similar) or two separate ciphers (as I suspect to be the case). However, running each half through zkdecrypto doesn’t produce anything worthwhile, so there’s more going on there than just a simple split.

    By the way, thanks for bringing your pointed cynicism to bear on my lowly blog, it’s a skill that many Zodiac authors would do well to assimilate into their research repertoire. 🙂

  9. This is by far my all time favorite start to a 340
    cipher solution conversation. Thank you for your
    efforts and work. Do you feel at some point it would be beneficial to include in the conversation ideas about coding in acceptable tolerances representing in the least,
    variables in gramatic structures, message content
    acceptability, (patterned) anagraming …,ie, Morse code is sent with less content and focuses on minimal subject transmission. Less nouns..incomplete words. abbrs. and the such?

    If in a narrsasistic rant Z enciphered in a morse code
    style, statistics are altered radically. The consanant
    vowel relationships get skewed off published
    statistics (cvccvc…for 6 letter words) subsequently our effort would be hindered (including the sequences you mention,Dave) using existing decipherment algorithms,
    as may be exampled in the first 10 lines at my site.
    My algoritm looks for those changes and I often wonder if my mile high observation isn’t actually from somewhere further out in space with regards to improving our aim at a solution.

    To ‘Z’,
    Have you been to http://www.340cipher.com? The non solutions
    site. These are not the solution. They are highly
    accurate solves, representing cracking technique
    possibilities.There are two very good examples of two different keys with readable results. After I spoke with Dan Olsen about the article mentioned above years ago, I immediately re-wrote my algorithms to search for
    single and double keys. Of course its possible, every
    thing is until ‘science’ says it isn’t…and science
    often changes its mind about widely accepted knowledge, even math.

    Regards,
    Harold

  10. John King on January 28, 2013 at 11:20 pm said:

    I was thinking along the same lines (more or less) and have been working with a friend on it, but I don’t know any hardcore cipher geeks. I also noted the cyclical substitution in the original 3 part, and also how it is suddenly altered when he gets into the 18 character noise at the end of it. Why even *place* random padding at the end of a substitution code? I think it’s there for a purpose.
    And moving on to the Z340, it’s clear to me that if he’s sticking to his normal habit (cyclical rotation of substitution characters), it’s obviously been transposed as well as substituted. the “(+)ZO^AIK” at the tail end tells me that he’s fairly screaming it. The ^ says “it’s a substitution” and the “AI” says it’s a transposition.
    It’s obvious that he’s not using the original alphabet. There are new characters introduced and some old characters retired. Most importantly, the frequencies don’t match. Especially with the + character, which previously represented E in rotation, but now appears twice as often as any other symbol.
    So here’s my thinking: If this message means anything at all, then we have to go on the assumption that he wanted it to be solved. Accordingly, the answer is simple enough for an intelligent and clever person to figure it out.
    My guess (what I’m working at now) is that this is not only a substitution, but also a keyword transposition. The 18 character garbage at the end of the 420 is (or at least contains) the keyword to the 340 and the almost-plain text “zodiacXX” at the end of the 340 is the pad. After that (if my theory is correct) it should be as easily solvable as the 420 was.
    If any of you can offer me assistance or advice on this, I’d be very grateful!
    -John

  11. John,

    There is good evidence that the cipher author simply copied several groups of symbols from earlier in the 408-character cryptogram:

    http://zodiackillerciphers.com/wiki/index.php?title=Solved_408-character_cipher#Last_18_symbols_of_the_408_cipher

    I’m satisified with the explanation that Zodiac simply wanted equally-sized parts to mail to each newspaper, and his message wasn’t exactly the right length; so, he ended up copying random junk into the last portion of the third section to pad it out. But nobody really knows for sure — there could still be some undiscovered purpose to those extra symbols.

    Keyword transposition is an interesting possibility. I think to explore this avenue thoroughly, you have to generate test cryptograms that closely resemble the 340, but are constructed via your transposition hypothesis. If you have a way to cryptanalyze and crack the test cryptograms, then failures to crack the 340 the same way will give you confidence that it isn’t constructed using the supposed scheme. A tedious approach, but necessary to confidently exclude some possibilities.

  12. Stacey Stanislaw on September 10, 2013 at 7:43 pm said:

    if the 13 digit cipher read “PATRICIAROGER” the message you get with the Z408 might make some sense.

  13. Stacey Stanislaw on September 10, 2013 at 10:46 pm said:

    I agree in general with Nick and others, there are two systems at work in the Z340 cipher. The system of the Z408 cipher was a clue and training device used by the author for understanding the later Z340 cipher. While the characters used in both overlap, only a subset of the later cipher can be decoded using the Z408 rules. Z340 relies on Z408 being decoded successful and allows some of Z340 to be decoded but not much of it. Some of the reused symbols in Z340 follow a new set of rules, but importantly, this encoding method relies on at least some of the rules from Z408 applying to at least some of Z340.
    By splitting the encoding rules into two different encoding methods yet sharing the same symbology between ciphers, the author makes Z340 much more difficult to solve (if not impossibly difficult at the time) without first solving Z408. To solve Z340, one can use the Z408 solution as a guide to one character subset and assume some other characters in Z340 follow a second rule set.
    As everyone knows but might forget when approaching this problem, a key to understanding this authors cipher method coupled with the timing of the ciphers is to understand that these codes we intentionally meant to be decoded, it’s not like these were secret communication intercepts, these were game pieces between the author, the general public, and decoding experts. Also, everyone knows now, including the author of these codes at the time, that Z408 was (would be) fairly easy to decode. I submit this was intentionally so by the author, Z408 was a stepping stone to decoding Z340 but not a solution for it.
    Could it have seemed obvious to the author of the ciphers that Z408 would be used as an aid to decode Z340 but not directly as a solution? I think so judging by the 13 symbol cipher “my name is” letter (Z13) inquiring about the effort to decode Z340. The author could easily assume that Z13 could never be decoded on its own without first decoding Z340, rather than be a game piece or provide a clue to the decoding methods of Z340, this 13 symbol cipher is an incentive to keep trying to decode Z340. Nothing important has come from applying Z408 rules alone to Z13, because it’s the combination of Z408 and Z340 rules that would be necessary to decode this short cipher. Z13 would also serve as “proof” of identity of Zodiac if Z340 was never cracked, since filling in Z13 would be a solution key for Z340, providing the critical clue for linkage of Z408 and Z340.
    I’m convinced, Z13 doesn’t contain anything directly implicating the author of the ciphers, but rather, the next puzzle piece to this mystery. It’s also, in my opinion, one reason no other ciphers (confirmed attribution to Zodiac) were sent after Z340; the difficulty decoding Z340 suited the authors sense of superiority and as proof to him that he was somehow better than everyone else. In this case, no other ciphers would be needed until Z340 was solved. This perspective of the Zodiac might be further evidenced by the “shutout” he liked to brag about SFPD=0, Zodiac=37.
    Challenge: Is Z340 solvable using known Z408 and Z13 = PATRICIAROGER?

  14. mr 4488N on November 27, 2015 at 3:40 pm said:

    The 340 has been solved about a week ago
    By me ,it is a simple worded one much like the 408 Id say it is a 3rd grade level thing word wise but adult in message
    I am no cipher master ,it was my 1st one ,but I found the code key
    Will be released soon ,looking for the most bang for my work

  15. mr 4488N: that would depend on whether you define “bang” as money, fame, or whatever.

    For what it’s worth, I’d add this: unless the plaintext helps identify the Zodiac Killer in some way, or unless you used a unusually insightful way of getting to that plaintext, or unless this was the culmination of a lot of other Zodiac Killer research, it probably isn’t externally worth a great deal.

  16. boyfriend , Champollion,,. :-) on November 27, 2015 at 8:22 pm said:

    Friends. I have to disappoint you. Zodiac never not find. He had perfect coverage. He worked for the Agenci. He made a mistake just once. He had to take a picture. Nice photo.

  17. Rick A. Roberts on November 28, 2015 at 12:34 am said:

    ZODIAC KILLER APRIL 20, 1970 SAN FRANCISCO CHRONICLE NEWSPAPER. ” MY NAME IS _ “. The cipher reads, ” A, E, N, Circle with Cross Centered in it, Circle with ” B ‘ in it, K, Circle with ” B ” in it, M, Circle with ” B ‘ in it, ” Double Hook Shaped Character “, N, A, M “. The deciphered message reads, ” T E N D on L on H on R N T H “, or ” DENTON LON HONRATH “.

  18. Rick A. Roberts on November 28, 2015 at 1:03 am said:

    408 SYMBOL CIPHER FINAL 18 LETTERS was, ” EBEORIETEMETHHITI “. Deciphered it is, ” ENEOLCESEOESTTECSC ” or ” ENE OL CE SE OUEST TEC SC “. ENA was (ECOLE NATIONALE ADMINISTRATION) established in 1945 as a French Civil Service School. There were 56,000 French Senior officials and 2,600 Foreigners who graduated from the ENA, This allowed civil servants in France to enter politics, science, or legal professions more easily than normal. There was a two part exam (verbal & written). It was also known as the Institut d’etudes Politiques de Paris.

  19. Rick A. Roberts on November 28, 2015 at 1:15 am said:

    Here is another cipher from the Zodiac killer. It has four lines in it. The first line of cipher starts with, ” L ” and ends with ” W “. The second line starts with, ” C ” and ends with ” T “. The third line starts with, ” W ” and ends with, ” B “. The fourth line starts with, ” N ” and ends with, ” A “. The deciphered message of the four lines of cipher read, ” SETS IN EAST FIVE IN SAINT SS (Saint Simeon) YOU ARE IN ONE END IN EAST “.

  20. Rick A. Roberts on November 28, 2015 at 1:28 am said:

    ZODIAC KILLER LOCATION OF BOMB Z32 CIPHER – MAPCODE CIPHER. This cipher has two lines. The first line begins with, ” C ” and ends in ” G “. The second line begins with, ” X ” and ends with ” TRIANGLE SHAPE “. The deciphered message reads, ” IS IN FRONT LEFT CORNER SUNLIGHT SETS ON BOX I DIE “.

  21. Rick A. Roberts on November 28, 2015 at 1:44 am said:

    ZODIAC CIPHER – Three lines of cipher. First line starts with ” + ” and ends in ” 9″. Second line starts with “> ” and ends in ” O “. The third line starts with ” TRIANGLE SHAPE ” and ends in ” + “. The cipher deciphers to, ” ENEONE EIEKEN IANNCS(IS)E “., or ” ANYONE KEYS IN IN A CASE “.

  22. Rick A. Roberts on November 28, 2015 at 1:52 am said:

    TWO LINE CIPHER ZODIAC KILLER. First line starts with, ” B” and ends in “.”. Second line starts with, ” BACKWARDS “C” ” and ends in ” “O” with line horizontally through center of it “. The deciphered message is, ” YOU ARE ONLY LENS I EVEN HAVE “.

  23. Rick A. Roberts on November 28, 2015 at 2:01 am said:

    ZODIAC CIPHER – It has two lines of cipher. The first line begins with, ” CIRCLE FILLED IN ” and ends in ” CIRCLE WITH CROSS CENTERED IN IT “. The second line begins with, ” END SIGN ” and ends in ” > “. It deciphers to, ” THE DAY I DIE ON END DEPENDS ALL EYES REST SEE KRNE “.

  24. Rick A. Roberts on November 28, 2015 at 2:14 am said:

    LOCATION OF BOMB – ZODIAC KILLER CIPHER. One line of cipher. It begins with, ” TRIANGLE SHAPE ” and ends with ” + “. It deciphers to, ” IANNCS(IS)E ” or ” IS IN A CASE “.
    LOCATION – One line of cipher. It starts with, ” H ” and ends in ” < ". It deciphers to, " TEWENNNNHNTN " or " TWO & FOUR IN HUNTINGTON ". Zodiac Killer could have been talking about his second and fourth victims in Huntington, Beach, California ?
    SINGLE LINE CIPHER – Starts with, " TRIANGLE SHAPE and ends in " I ". It deciphers to, " ISKREOT " or " RISKETO", " RISKY TO ".

  25. Rick A. Roberts on November 28, 2015 at 5:24 am said:

    ZODIAC KILLER CIPHER – One line cipher. It begins with, ” S ” and ends with ” CIRCLE WITH TOP HALF FILLED IN “. This deciphers to, ” AEEANAAEBNENEEGMI “, or ” BEGINNING A BIG GAME “.
    SECOND One Line Cipher. It begins with, ” OUTLINE OF SQUARE “, and ends with, ” A LARGE CIRCLE WITH A CROSS THROUGH THE CENTER OF IT, with four surrounding Smaller Circles with a Cross Through each one ( Each of these is evenly spaced around the largest one with one in each quadrant ). This deciphers to, ” YINHNDDDDD “, or ” HY FIVE IN SND “, or ” HIGH FIVE IN SAN DIEGO “.

  26. Davb here
    that site http://www.zodiacciphersresolved.com
    now he gives the 408 remainder cipher solution free
    I don’t see what it says ,
    but you masters to PHD’s should have it seconds

  27. Davb: I saw this a while back and thought it was probably nonsense, broadly of the type that tends to infest YouTube – and the person’s 408 remainder cipher decryption doesn’t now fill me with any confidence that the other attempted decryptions will be any better.

    Specifically, the problem with homophonic ciphers is that they give decryptors the ability to overfit a part of an (imagined) message to a corner of the ciphertext (in that case, the backwards “zodiak” at the top right), which often then leaves the rest of the message as a kind of weird language-like babble (as here). But this isn’t a real solution, or even a real way of solving homophonic ciphers: it’s just a way of not solving it, while thinking that you have. Happens all the time, sadly. 🙁

  28. but your wrong ,it is not homo but a polyphonoic code key .
    most solvings are not even words , let alone a sentence , this is .
    most make no sense as to the zodiac killer, this does.
    most have far.far fetched logic accompanying them to make any sense as to zodiac ( see your posts.)
    again this is not me saying, I think this symbol is a D.. or let me try it as a L .it is from a code key that I know it is __
    This is your blog and you can surely think and say what you want …..I just hate to see you waste your time
    No one wants the ciphers /zodiac solved …they want to solve it .

  29. Davb: do you mean “polyalphabetic”? “Homophonic” has a specific meaning in code-breaking: you say a cipher is homophonic if it uses multiple different (cipher) shapes for individual (plaintext) letters, which is exactly what the Zodiac Killer did in his Z408 cryptogram. Given the similar look and similar statistics his Z340 cryptogram presents, there would seem to be good reason for thinking that it, too, employs some kind of homophonic cipher.

  30. Okay ,polyaphabetic I have seen homophonic shown as one for one swap

    For what it’s worth, I’d add this: unless the plaintext helps identify the Zodiac Killer in some way, or unless you used a unusually insightful way of getting to that plaintext, or unless this was the culmination of a lot of other Zodiac Killer research, it probably isn’t externally worth a great deal.

    I can answer yes it does to those 3 questions above

  31. Davb: it doesn’t matter how many supportively good things you do if the core cryptology is broken.

    And when someone claims to have cracked a whole load of too-short cryptograms all at once, there are two basic scenarios: (a) this person is a self-taught cryptological genius, of the kind that comes along once in a generation, or (b) this person is (at best) delusional. Whether you like it or not, (a) is an exceptionally big claim, and requires more evidence than ‘PayPal me some money and I’ll show you’.

  32. (a) a cryto genius ,
    (b) has delusions , he’s ccrazzy
    or (c) a more realistic chance
    just what he said on the web page ,he did not say he solved all the ciphers by ESP or a vision ,etc.
    he says he found a code keys that gives meaningfull words in the ciphers

    you would least admit, that if the ciphers do translate into sentences like the 408 cipher … he Zodiac or an partner used a code key of sorts .
    very possibly a easy to remember one ….like his name
    why his name ? so he would get credit for it at some point in time .
    requires more evidence
    2+2 = hmm??? ..4 ,pretty sure
    alot of people can add that up ,
    you are 1/4 of the planet away from the zodiac scenes or maybe the zodiac himself
    some people are 1/4 miles away

  33. Mr. Pelling:

    I just posted this on David Oranchak’s 2015 symposium You Tube video. Since I mention you in the comment, I thought you might be interested:

    Okay, Dave, you can relax. As it turns out, Gareth Penn was wrong about The Confession Letter containing 1623 characters. I created a 20-column table grid in Microsoft Word and entered The Confession Letter into it by reading the original (instead of copy-and-pasting someone’s diplomatic version) letter by letter, and The Confession Letter contains exactly 1630 letters, not 1623.

    The interesting thing is that when I copy-and-pasted someone’s diplomatic version and then removed the spaces and punctuation marks, and checked it with MS Word’s WORD COUNT feature, it first showed 1624 letters, and then 1625 when I added a letter to correct that version (whose version it was isn’t important, I clicked on an online link to get it). I did the table grid to see how accurate the WORD COUNT feature was, and it was off by 5 letters (1630 instead of 1625).

    1624 would have made sense, since the symbol sequence for the letter E in the Z408 cipher text is ZPW+ONE (according to Gareth) and ZPW+6NE (according to NIck Pelling). The second and third symbols, PW, would be 1623 by alphabet numbers, so 1623 + ONE gives you 1624. The fifth of the seven symbol sequence is the letter O or the number zero with a dot in the center, so I suspect Gareth’s interpretation (the letter O) is closer than Nick Pelling’s (the number 6).

    However, they’re both wrong.

    As I think I mentioned in one of my 1990 books, the letter E symbol sequence in Z408 ISN’T ZPW+ONE.

    It’s actually Z9W+ONE.

    That second symbol in the sequence is a ‘9’, not a ‘P’. Nick Pelling gets ‘P’ because he’s reading it as “backward-P.”

    However, I think within the context of Z408, ‘Z9W’ makes more sense.

    Why does ‘Z9W’ make more sense than ‘ZPW’?

    Because, if you look at the Harden solution, which as I’ve said now for almost 30 years isn’t a solution at all, but only the first step in the direction of the solution, the plain text contains 23 of the 26 letters of the alphabet.

    The three missing letters are J, Q, and Z.

    What do those three letters have in common?

    Each of those letters is a single Caesar shift (i. e., +ONE) from a natural square in the alphabet.

    The letter I is the 9th letter (3 x 3), the letter P is the 16th letter (4 x 4), and the letter Y is the 25th letter (5 x 5).

    The five letters that represent natural squares in the alphabet are A, D, I, P, and Y.

    Those letters are an anagram (I know how much you love anagrams!) for the expression “pi-Day,” just as the pi sequence itself (3 1 4 15 9 26), C A D O I Z as alphabet letters, is an anagram for ZODIAC.

    By the way, is there a reason your favorite message board, ZodiacKillerSite.com, won’t attribute that insight to me? It’s from my 1990 book. Every time someone points it out on that board, they don’t cite me as the source for it. It’s almost as if I’m persona non grata over there!

    So ‘Z9W’ becomes the following equations, with the central number 9 standing for the letter I.

    “I (am) Z (Zodiac), and also 23 (W = 23rd letter), because the Zodiac Project begins when I’m 23 (Michael O’Hare was 23 years old on October 30, 1966).”

    Also:

    “I (am) Z (Z = 26th letter), 26 letters of the alphabet, of which I use 23 (W = 23rd letter) in this cipher’s plain text (all except J, Q, and Z).”

    Gareth Penn pointed out Michael O’Hare’s name in the binary-to-Morse form of pi (M.ERAHO), and also that O’Hare’s birth date (1-22-43) contains the same numerical sequence as the supplement of the truncated form of the radian angle (122° 43’, and 57° 17’). Those are coincidences, obviously. But when you’ve been a suspect in a notorious serial murder case for decades, and choose NOT to defend yourself against the charges, and the author of the Zodiac ciphers seems obsessed with the same sort of pi-manipulation that Gareth has demonstrated applies to you . . .

    Z9W+ONE = take the 3 missing letters (26-23), do a single Caesar shift, and you arrive at the pi-DAY sequence. And the author of the cipher has to know that that sequence will be noticed by the codebreakers, because it’s a multiple substitution cipher, and those are the symbols for the most common letter, ‘E’.

  34. Here’s another recent post you may find of interest:

    As a bonus to Drew for reading my book, I’m posting a section from Chapter 18 which was originally edited out of ZODIAC KILLER SOLVED back in June 2015 because I was trying to avoid making points that were too “cryptographic,” particularly cryptography that might be seen as too manipulative of the source text.

    In retrospect, I find this point, which goes back at least to 2008 in my computer notes, very striking, and will probably upload at least to the Kindle version of my book when I get a chance.

    SIGNATURE PHRASE

    The biggest mistake cryptographers make, when they try to analyze the Zodiac ciphers, is that they assume a serial killer who was sending them ciphers would necessarily come up with some convoluted key involving bigrams and trigrams and transposition schemes (sounds like “Lions and tigers and bears, oh my!” from the Wizard of Oz!).
    I don’t think a serial killer who was writing letters to the newspapers, trying to make the police and public look stupid, would do anything that complicated.

    I think he’d come up with something very simple, the way that magicians performing card tricks do, where they fool you with sleight of hand, which is a form of misdirection.
    The simpler the trick, the stupider the mark will look when it’s revealed, right?

    Let’s also assume that the Zodiacs were trying to reveal their secret identities in almost everything they did.
    It then follows that whatever “The Zodiac” said the most would contain the most significant information.

    When a writer or fictional character says the same thing over and over, we come to refer to it as his signature phrase.
    For example, Sherlock Holmes was known to say, “Elementary, my dear Watson!”

    Except in this case, the signature phrase would actually contain the Zodiac signature, telling us who the trigger man was in real life.

    So what was the Zodiac signature phrase?

    If you ask Zodiac hobbyists, they’ll be happy to tell you:

    This is the Zodiac speaking.

    After all, the killer says “This is the Zodiac speaking” eleven times:

    1. The “This Is The Zodiac Speaking” Letter (August 4, 1969)
    2. The School Bus Threat Letter (October 13,1969)
    3. The Oakland PD Phone Call (October 22, 1969)
    4. The Pen Card (November 8, 1969)
    5. The Bus Bomb Diagram Letter (November 9, 1969)
    6. The Dear Melvin Letter (December 20, 1969)
    7. The 13-Character Cipher Letter (April 20, 1970)
    8. The Mt. Diablo Letter (June 26, 1970)
    9. The Kidnapping Confirmation Letter (July 24, 1970)
    10. The Mikado Letter (July 26, 1970)
    11. The LA Times Letter (March 15, 1971)

    That’s a lot.

    But he says something else more often. He says “Please Rush To Editor” at least 14 times on letter envelopes. Let’s count:

    1. Cryptogram 1 (Vallejo Times-Herald) 7/31/69—twice
    2. Cryptogram 2 (SF Examiner) 7/31/69—twice
    3. Cryptogram 3 (SF Chronicle) 7/31/69—twice
    4. School Bus Threat 10/13/69—twice
    5. Pen Card 11/8/69—twice
    6. Bus Bomb Diagram 11/9/69—twice
    7. LA Times 3/15/71—once
    8. The Exorcist 1/29/74—once

    That’s 14 times the phrase “Please Rush To Editor” is used, total.

    He may also have used the phrase on the “This Is The Zodiac Speaking” letter envelope of August 4, 1969, but no photos of that envelope have been published to date.

    In any case, it’s fair to say that “Please Rush To Editor” is really the Zodiac signature phrase, the phrase “The Zodiac” uses most, and NOT “This is the Zodiac speaking.”

    Since we know that the Zodiacs pack their every utterance with information, we can be sure that “Please Rush To Editor” is perhaps the most significant Zodiac statement of all.

    It’s also important to remember that, at least in the first six letters sent as “The Zodiac,” and possibly in the first seven (since we don’t have the August 4, 1969 letter envelope to look at), “The Zodiac” said “Please Rush To Editor” not once, but twice, once on each envelope’s front, and once on each envelope’s back. In other words, the Zodiac signature phrase was really

    Please Rush To Editor
    Please Rush To Editor

    If you wanted to impart the most significant identifying information about yourself that you possibly could, what would it be?

    I’ve mentioned that “The Zodiac” harps on his DOB (January 22, 1943), but there are still lots of people that that would include.

    What about DNA? Even if you had “The Zodiac”’s latent DNA and someone to compare it to, that still wouldn’t narrow it down to one person, because the suspect could have an identical twin, who would have the same DNA.

    So if the DOB doesn’t do it, and DNA doesn’t do it, there’s only one piece of information left that identifies a specific person—his SSN.

    I worked for the federal government for 37 years, and that’s what the United States Postal Service uses to differentiate among its employees: their social security numbers.

    I’m saying in this book that Michael O’Hare was the trigger man of The Zodiac Project, and we know that his social security number is

    117-32-2128

    And, as we’ve just established, the Zodiac’s actual signature phrase is

    Please Rush To Editor
    Please Rush To Editor

    So if the most significant identifying information would be in the Zodiac signature phrase, and if the most specific identifier would be his SSN, and O’Hare is the Zodiac trigger man, then this equation should be true:

    Please Rush To Editor
    Please Rush To Editor = 117-32-2128

    The trigger man for The Zodiac Project uses the binary phrase PLEASE RUSH TO EDITOR/PLEASE RUSH TO EDITOR because it (almost) specifically identifies him as his SSN. To be slightly more precise, the transposition is as follows:

    Please Rush To Editor
    Please Rush To Editor = 11732 212 (8)

    Let’s begin by using the simplest form of letter-to-number code, which is alphabet numbers (A = 1, B = 2, and so forth) to effect the conversion. PLEASE is 58 by alphabet numbers.

    P L E A S E
    16 + 12 + 5 + 1 + 19 + 5 = 58

    And RUSH is 66 by alphabet numbers.

    R U S H
    18 + 21 + 19 + 8 = 66

    PLEASE RUSH therefore gives us the number sequence 58-66.

    58 66 TO EDITOR
    58 66 TO EDITOR = 11732 212 (8)

    But we are going to read 58-66 as one number, 5866.

    5866 TO EDITOR
    5866 TO EDITOR = 11732 212 (8)

    Now, since the phrase is written twice, let’s multiply 5866 by two.

    5866 TO EDITOR
    +5866 TO EDITOR = 11732 212 (8)
    11732 TO EDITOR = 11732 212 (8)

    Are you with me so far?

    When the alphabet number totals for PLEASE (58) and RUSH (66) are read as a single horizontal number, 5866, and then multiplied by two (because the phrase is stated twice on each of the first six mailings in the Bay Area, with the 8-4-69 envelope an unknown), the result is the first five digits of Michael O’Hare’s SSN.

    So let’s continue, this time reading those last eight letters, TO EDITOR, as a single alphabet total:

    T O E D I T O R
    20 + 15 + 5 + 4 + 9 + 20 + 15 + 18 = 106

    5866 TO EDITOR
    +5866 TO EDITOR = 11732 212 (8)
    11732 TO EDITOR = 11732 212 (8)

    5866 106
    +5866 +106 = 11732 212 (8)
    11732 212 = 11732 212 (8)

    11732 212 = 11732 212 (8)

    Granted, PLEASE RUSH TO EDITOR, read this way, only gives you 8 digits of Michael O’Hare’s SSN. In that sense, the final number, 8, may be implied by the first eight.

    11732 212 = 11732 212 (8)

    In any case, 8 digits of a SSN narrows it down to ten people.

    When we add it to other things we know about Michael O’Hare (that he strongly resembled the Zodiac WANTED poster in 1969, that he lived and worked in San Francisco during the murders, that his fingerprints aren’t on file anywhere, that he is the author of several bizarre artifacts that seem to connect him to the case, and that he refuses to defend himself against the charge of being the 20th century’s most notorious serial killer), I suspect that he would be the strongest Zodiac suspect among those ten people.

    And, with all due respect to the cryptographers out there, I don’t think this reading is the result of a selection bias on my part.

    Please Rush To Editor
    Please Rush To Editor = 117-32-2128

    11732 212 (8) = 117-32-2128

    Now, is there SOME selection bias here? Yes, of course.

    I could for example interpret PLEASE (58) and RUSH (66) as separate quantities, double them, and then do the same with TO (35) and EDITOR (71).

    PLEASE (58) RUSH (66) TO (35) EDITOR (71)
    PLEASE (58) RUSH (66) TO (35) EDITOR (71)
    116 132 70 142

    And granted, that wouldn’t fit the O’Hare SSN. That would get us a sequence of 116-132-70-142, or a SSN of 116-13-2701, with -42 left over).

    However, as Bently/Wrench pointed out about my pi/ZODIAC correlation on Morf’s private board back in 2010—

    3.1415926 = 3 1 4 15 9 26 = C A D O I Z = ZODIAC

    —there are only a handful of letters that you can put to the numerical pi sequence, and CADOIZ makes sense within this context (since the writer also mentioned a pi derivative, radians, which are circleS divided by 2pi).

    I would say the same thing about the PLEASE RUSH TO EDITOR phrase; if you’re going for a STRAIGHTFORWARD letter-to-number conversion, there are only a few ways to do it. And one of them gets us to the O’Hare SSN.

  35. Ray: you have your reasons for your conclusions, and it’s possible that the Zodiac shared your numerological world view. But… viewed from the outside, this does seem a little unlikely, sorry. 🙁

  36. “Ray: you have your reasons for your conclusions, and it’s possible that the Zodiac shared your numerological world view. But… viewed from the outside, this does seem a little unlikely, sorry.”

    Nick: Thanks for the response, exasperating as it was. If you would like to learn about the Zodiac case, email me or post (in your Comments section) an email address and I will gift you Kindle copies of both my books, ZODIAC KILLER SOLVED and ZODIAC KILLER FOR DUMMIES. If you would prefer paperback copies of my books (which I think are very handsome), send me a mailing address and I will have both books shipped to you via Amazon. Reading the books may help dispel the perplexing notion cryptographers like yourself seem to have that the Zodiac ciphers fell from the sky.

    It’s interesting that one doesn’t see this phenomenon with other cipher mysteries. If one goes to http://www.voynich.nu/, for example, a significant fraction of the website content is taken up with the CONTEXT of the Voynich MS.

    It’s also disappointing when supposedly educated people don’t understand what the term NUMEROLOGY means. Here’s Wikipedia:

    “Numerology is any belief in the divine, mystical relationship between a number and one or more coinciding events. It is also the study of the numerical value of the letters in words, names and ideas. It is often associated with the paranormal, alongside astrology and similar divinatory arts.

    The term numerologist can be used for those who place faith in numerical patterns and draw pseudo-scientific inferences from them, even if those people do not practice traditional numerology. For example, in his 1997 book Numerology: Or What Pythagoras Wrought, mathematician Underwood Dudley uses the term to discuss practitioners of the Elliott wave principle of stock market analysis.”

    I clearly don’t practice traditional numerology (e. g., ‘666’ means the Devil), and neither am I suggesting a numerical pattern here. We know the Zodiac letters contain cryptography of some sort (i. e., Z408, Z340, Z13, and Z32); so how much of a stretch is it to assume that their author(s) were using a cryptographic approach outside the four ciphers?

  37. Ray: thank you for your kind offer, I’ll email you through my Kindle details later.

    I’ll clarify my previous reply: while I think it is entirely possible that the Zodiac Killer had a numerological world view, there are countless different numerological world views to choose from (at least as many as there are numerologists), and so I don’t see how you can be certain that the specific numerological angle you have inferred is the same one as the Zodiac Killer’s. That is, I think what you put forward is unlikely to be correct not because it is numerology, but because there are so many different possible numerological variants to choose from, all different. Hope that’s clear!

  38. milongal on August 3, 2017 at 9:21 pm said:

    Interestingly Sherlock’s signature phrase doesn’t actually come from a Conan Doyle book – it only appeared in movies (and I’m not really sure he said it ‘over and over’ even then).

  39. In other words, I’m assuming a world view that the Zodiac might not share, and since there are so many possible world views, the sheer numbers (not the numerology on its own terms) argue against my being right?

    Okay, but again, that’s a viewpoint which stems from the “The Zodiac Ciphers Fell From The Sky” assumption. And that assumption, which all cryptographers interested in the case seem to adopt, is wrong on the face of it.

    Nick, why do you make that assumption, when you don’t make it, for example, about the Voynich Manuscript? And there is certainly scads more accompanying evidence associated with the Zodiac ciphers than there is with the Voynich Manuscript, whose dating we aren’t even sure about.

    The first twelve chapters of ZODIAC KILLER SOLVED examine the evidence in the case and don’t touch on any cryptography. The gist of those twelve chapters is that the Zodiac murders were orchestrated, with the first three victims (Bates, Faraday, and Jensen) actually being abducted and then placed on the landscape.

    There is, in my view, no alternative to the “staged murders” interpretation of the evidence, and that backs up Gareth Penn’s Radian Theory: Faraday, Jensen, Ferrin, Stine, and for that matter Robert Salem and Donna Lass, were all placed at points along the Mt. Diablo Radian. Granted, the position of the bodies does not conform perfectly to the radian angle, but the letter of July 26, 1970 still mentions ‘radians’ twice. That, along with the circling of the apex of Mt. Diablo on the map accompanying the June 26, 1970 letter, suggests fairly strongly that Gareth’s interpretation is correct.

    But let’s go backwards a moment and look at your own interpretation of the appearance of Z340. The Zodiac Killer worked long and hard on Z408, and then, hardly a week had gone by when the solution appeared in the newspapers. And the solvers were amateurs! Stung, a killer whom most cryptographers like Dave Oranchak assume was a drooling idiot suddenly constructed the most fiendish cipher in history. And he was able to do that despite the cipher’s being mailed on November 8, 1969, long before personal computers were common, and despite the multiplicity of professional cryptographers and computer science people like Glurk who have a framed copy of Z340 on their living room walls.

    This scenario may make perfect sense in the crypto-world, but, to quote NIck Pelling, viewed from the outside, this does seem a little unlikely, sorry.

    How likely is it that a drooling Zodiac Killer along the lines you envision either successfully constructed a message that can’t be deciphered, or that he deliberately mailed a random message that doesn’t reveal itself as random? I don’t think either alternative is likely.

    But.

    If we look at the actual evidence, we come away realizing that the crimes were deliberately staged to look like relatively random and spontaneous mundane murders (a coed murder, lover’s lane murders, and a cabbie murder), so that the only thing connecting them would be the letters and peripheral events like the phone calls.

    If that’s the case, and assuming there’s validity to the Radian Theory, that gives us a completely different picture of the cipher construction.

    Because, if you’re trying to demonstrate that the police and public are a bunch of idiots that you can manipulate at will, constructing a complex cipher wouldn’t be the way to do it, even if you were the greatest cryptographer in the world.

    The way to do it would be to construct something very simple, in plain sight, so that people were fooled by misdirection. That would be more fun, right? And it’s worked like a charm for almost 50 years!

    And my solution to Z340 is consistent with that approach. The Zodiac fired 10 shots (Lake Herman Road), 9 shots (Blue Rock Springs Park), and 1 shot (Presidio Heights), for a total of 20 shots fired. He even mentions the number of shots fired at LHR in the Z408 cover letters.

    He stabbed Bryan Hartnell 7 times, and Cecelia Shepard 10 times, for a total of 17 stabs.

    So there were 20 shots and 17 stab wounds. In The Exorcist Letter, he says

    Me – 37

    SFPD – 0

    which is completely accurate. He’d struck exactly 37 times.

    Which explains the layout of Z340. It’s 20 rows (BY GUN, vertical, in The Halloween Card), and 17 columns (BY KNIFE, horizontal, on Hartnell’s car door).

    In other words, the message is in the format, NOT in the content.

    What could possibly be simpler?

    But wait, you say: that message doesn’t tell us anything we don’t already know.

    Yes, it does. It tells us that the Zodiac crimes were orchestrated right down to how many shots were fired. It tells us exactly what we’re dealing with, an extremely intelligent adversary (actually, four of them).

    All of this is in my books, so send me your email address so I can gift them to you.

    “Interestingly Sherlock’s signature phrase doesn’t actually come from a Conan Doyle book – it only appeared in movies (and I’m not really sure he said it ‘over and over’ even then).”

    Well, keep in mind that if you asked the average person familiar with the case, and not even the average Zodiac hobbyist, what the Zodiac’s signature phrase was, he’d likely say, “This is the Zodiac speaking.” So in that sense, you’re making my point.

  40. Ray: I’m happy to read your books, but you really should try to understand that your comments here aimed at other researchers probably aren’t going to help anyone warm to your arguments.

  41. milongal on August 4, 2017 at 11:44 am said:

    –quote– (re me saying Sherlock’s ‘Signature phrase’ didn’t come from the original Sherlock)
    Well, keep in mind that if you asked the average person familiar with the case, and not even the average Zodiac hobbyist, what the Zodiac’s signature phrase was, he’d likely say, “This is the Zodiac speaking.” So in that sense, you’re making my point.
    –quote–
    I was merely suggesting that a signature phrase has little to do with how oft it is uttered – which you seem to agree with (but I think it contradicts your orignal point).

    There’s also a very pedantic part of me that wants to point out that you said “This is the Zodiac speaking” was used 11 times and “rush to the editor” was used more frequently – 14 times. You then go on to say that the repetition of it (ie “rush to the editor; rush to the editor”) is the important bit, which means it was only used 7 times (and so less common than the other one).

    But I never set out to disagree or challenge your theory (just reflexively got pedantic about Sherlock).

    However, I do have a bit of a thought/opinion on:
    ‘which stems from the “The Zodiac Ciphers Fell From The Sky” assumption’
    because I think it makes an interesting point (not just about the Zodiac). When tackling any (cryptographic) puzzle, you simultaneously have to look at it in the context of how it occurred and in isolation independent of any circumstance. Sometimes, the circumstance will give context that helps resolve the puzzle, but other times the circumstance merely serves to cloud the facts with sentimental/romantic/somethingelse ideas about how something came to be. So while I can sort of take the point it’s naive to take the ‘fell from the sky’ view point and treat the ciphers as a cryptographic challenge with no context, I think it’s equally naive to assume that the context is key and that the ciphers can only ever be solveable if we first put them in the right context (for what it’s worth, I’m not suggesting either is a flawed approach). One of the problems with these sort of mysteries is that on the one hand the context how something occurred is very important, on the other hand there’s a good chance that the mysterious bit that piques our interest is actually relatively independent of the context – and it’s hard for us to be able to simultaneously consider the implications of a situation both within and outside our assumed context.

  42. Nick, it’s funny you should mention that. Just last evening, in an email, one of my few friends in the Zodiac online community pointed out that I’ve been referred to as a “condescending jackass” by more than one person. I’m always suspicious when multiple witnesses use the same terminology; it smacks of collusion.

    I will take your suggestion to heart and try to tone it down. However, as Steve Jobs once said when facing similar criticism, “We’re just enthusiastic about what we do.”

  43. Ray/Milongal: in many ways, the point of this Cipher Mysteries blog is specifically to kick back against the “fell from the sky” (i.e. taking cryptograms in pure isolation) attitude. For me, a cipher mystery is specifically one where, despite having both mysterious writing and a whole load of contextual clues, we can neither read the writing nor reconstruct the history with any confidence.

  44. john sanders on August 4, 2017 at 3:24 pm said:

    Milongal: Whatever it was that Larry Holmes or Roddy Doyle may or may not have come up with in reference to poor Ray’s quite ingenious Zodiac numeralogically based Zodiac equasion, I’m not going to be the one to ridicule his theory. I’ll always be a plugger for the mugger who sticks to his beliefs no matter. Of course there have been plenty like him who were regarded as cranks and yet proved the naysayers (and their running dogs) to be the bunnies in the end. Just take that wacky US born Irish aviator Corrigan as an example ; he who showed us that the earth is flat afterall, just as those dumb ass Phoenetians had insisted all along. No, i’m prepared to follow my way through our Somerton maze and trust my own judgement for the anwers that are wanting. For those who see things in another light, all I can say is, if you think you’re on a good thing, stick to it and may the force be with you.

  45. Ray: can you please try to post your comments without attacking people? In the end, it’s just a load of opinions, nothing worth getting het up about.

  46. Josef Zlatoděj Prof. on August 4, 2017 at 7:17 pm said:

    Nick. Send me your address. ( emal). And I’ll send you a picture ( foto ) of Zodiak. I’ve been looking for him long enough.
    He too made a mistake and took a picture ( foto ).

  47. Ray: I have a whole load of arbitrary rules about what I allow through as comments, and I’m sad to say that you’re falling foul of a number of them at a time.

    If you can take a deep breath, make comments that aren’t so long they sprawl into Ohio, and try not to top-quote other people’s comments to score points off them in a game nobody but you is playing, I’m sure we’ll get along fine.

  48. Nick: I realize you have a whole load of arbitrary rules about how you operate, but I’m beginning to think they’re not so arbitrary after all.

    [remainder deleted]

  49. Ray: I delete all kinds of comments for all kinds of reasons. I’m particularly happy to delete comments that tell me how to run my blog.

  50. milongal on August 6, 2017 at 7:23 am said:

    @JS: I don’t think I dismissed his ideas, just some pedantry about the idea that the catchphrase is a result of repetition (or something – that was a lot of beer ago).

    @NP: I sort of stand by what I said that with any cryptographic mystery you have to be able to simultaneously see the cipher/puzzle/problem in context and in isolation. I understand your point that there always is a context, however sometimes by pre-assuming what the context might be we blind ourselves to what the solution is. On the other hand, sometimes treating things as a “it fell from the sky” we come up with a solution that then provides a context (which potentially then confirms or disproves the original solution). Although (rereading your comment) I may have missed the point a little – that you’re saying these ‘mysteries’ are intriguing because we have some sort of context, some sort of cipher….but no idea how any of them fit together….

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