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Summary

Preamble
        Early Shakespeare decoding was total nonsense
        Historically hidden messages are a fact
        What about the dedication to the Shakespeare sonnets?
        Are recent published findings and odds calculations correct?
        An astronomical number of possible words?

Introduction
        Sonnet and funerary monument cryptograms
        Shakespeare sonnet dedication is very short
        Are the hidden texts real?
        Shakespeare in the bible --- not all 'hidden' text is a cryptogram

Shakepeare sonnet dedication cryptogram
       Who is 'Henry Wriothesley'?
       Facsimile of Sonnet dedication
       Rollett's sonnet dedication paper (1999)
         Three texts in dedication
         My reading of x18
         1) Order is correct
         2) Read only down
         Rollett's x18 reading
         Estimate of the odds
         Letter frequency in sonnet dedication text
         Is the long name Rollett found in an 18x8 grid of the dedication real?
         One five letter fragment
         Three two letter fragments
         Four fragments in correct order
         x18 result
         Reduction #1 -- multiple spacings
         Reduction #2 -- other fragment combinations
         Reduction #3 -- other relevant words

Shakespeare funerary monument cryptogram?
         Is the stone engraving original?
         The claim
         Reduced message
         Critical look at Shakespeare funerary monument poem
         Odds of 'Vere'
         Raw look at x34
         Calculating the probability of key words
         Two letter words

Appendix I
         David Roper on Rollett's sonnet dedication
         x19 discussion
         Give me a break!
         Roper on 'Henry'
         Roper's odds calculation
         Errors in Roper's odds calculation
Appendix II
         One way to spell 'Henry Wriothesley'?
Appendix III
        Monument trial runs
Appendix IV
        Ten monument decode trials
Appendix V
        Notes on Latin lines of Shakespeare funerary monument text
         Is Æ one character or two?
Appendix VI
        Four old versions of the monument poem: 1631, 1656, 1721, 1825
        Four poem versions compared line by line
        Importance of 1825 version --'sith' not 'sieh'
Appendix VII
        Shakespeare monument poem images
Appendix VIII
        History of the Shakespeare monument
Appendix IX
         Woolpack man?
         Dugdale's 'woolpack' sketch from another perspective
         Adding a feather
Appendix X
         Stratford monument poem -- first write up
Appendix XI
        Some acrostic messages are real
Appendix XII
        Overview of probability vs word length
Appendix XIII
        Equidistant vs grid decoding
         Words that span two columns
Appendix XIV
        Prof Albert Burgstahler's view
Appendix XV
        Baconian decoding is all nonsense
        Friedmans' Shakespearean cipher book
         'Some Acrostic Signatures', by William Stone Booth, 1923
         Bacon 'Bote-swaine' cipher
Appendix XVI
        Ben Jonson's First Folio poem --- an elaborate Cryptogram?
Appendix XVII
        Shakespearean spelling
Appendix XVIII
        Critical look at sonnet 76

Summary
        The focus of this essay is to assess mathematically the strength of two recent claims that two different Shakespearean documents have been found to be cryptograms. This is not a pro-Oxford or pro-Marlowe screed. I just want to know if any of the recently discovered 'hidden' texts are real. The two candidate cryptograms examined, both dated from the time of Shakespeare, but neither written by Shakespeare, are

            Dedication to the Shakespeare Sonnets  --- 1609
            Shakespeare funerary monument poem in Trinity church --- 1616 to 1623

Dedication to the Shakespeare Sonnets
        Is the Dedication to the Shakespeare Sonnets a cryptogram? The math definitely says yes! A name related to the sonnets pops out whose strongest elements are two five letter strings. Because each contain a rare letter, the odds of each string (alone) is about 1,000 to 1. There is also a confirming hint with the text being rather odd and its layout keying a hidden, relevant phrase.

Shakespeare funerary monument poem in Trinity church
        Is the Shakespeare funerary monument poem in Trinity church a cryptogram?  Maybe (maybe yes, maybe no). The math can only take us so far in this case because the output is a phrase not a name, however the odds of the words in the phrase can be calculated. A phrase relevant to authorship pops out whose strongest elements are two four letter strings. However, the math of four letter strings that are composed of common letters is not compelling. For example, the odds of the string 'Vere' plus 'e' and 'de' appearing by chance (at some spacing) is 10%. 'e' is a very common letter. The other four letter string, 'test', is composed of even more common letters.

        The odds are moderately improved (factor of 33 or so) if two hints can be relied on that decoding should be done using x34 spacing. One hint is that 34 is an integer multiple of 17 and Edward de Vere was the 17th Earl of Oxford. This is clean. The other hint is the number of characters in the only indented line is 34, but this hint is valid only if Æ is counted as one letter. The engraved text on the monument is full of combined letters and all (but Æ) need to be expanded for the cryptogram to work. So this hint hinges on whether Æ (in Latin) is one letter or two. A very technical question. Dr. Spittle, who found this hint, says Æ is a single letter in Latin, but Wikipedia says that Æ in Medieval Latin was an optional ligature (in effect two letters), so there is some measure of doubt about this hint.

        Another problem is whether the engraved monument text is really from Shakespeare's time. It is a fact that in the first two hundred years of its existence the text on the monument was recorded three known times, and in all three of these cases the cryptogram fails. For example, all three observers wrote 'monument', not 'monvment', deleting the 'v' in 'Vere', killing the key word for the Oxfordians. For the funerary monument text to be a hidden message from Shakespeare's time all three observers who recorded the text had to have done so inaccurately! Now this may very well have been the case given the flexibility of Elizabethan spelling, but still it introduces some level of doubt.

         The odds of its words forming a phase that is both relevant and (crudely) grammatical is hard to evaluate mathematically, but still it adds to the strength of the argument that it is a cryptogram. (The claim is made by Roper that the phase is grammatical, but this is achieved by moving things around.) There is also some confirmation in that the funerary monument text has some odd features, like inconsistent spellings and the famous phase, 'read if thou can't'.

Preamble
        As a retired engineer, I know enough mathematics to understand that recent claims that cryptograms have been found and solved in some early short documents closely associated with Shakespeare should not be dismissed out of hand. In this essay I focus on the strongest cases where the decoding is simple, just reading with skips (no letter reversals, no wild jumping around, no X's, S's, diagonals, or arrows, no mathematically weak, undisciplined and discredited deciphering like the Baconians used in years past to discover Bacon's name hidden in Shakespeare's works).

        When the hidden text discovered turns out to be a name, probability calculations based on letter counts are possible. In cases where the hidden text is a phrase probability must be estimated from empirical tests and auxiliary factors. When the odds (correctly calculated) come out to be high, say 10,000 to 1 (or higher), which in at least one case they do, then I am convinced that the hidden text discovered is probably real, that it was deliberately, and at great effort, encrypted into these documents 400 years ago. It is hard data.

Early Shakespeare decoding was total nonsense
        Beginning in the 1880's the followers of Francis Bacon wrote a huge number of books claiming that they had found hidden messages within Shakespeare's works proving that Bacon was the author. The impetus for all this decoding was that Bacon had written about codes, even inventing one himself (Bacon biliteral cipher). In 1957 professional cryptographers William and Elizabeth Friedman in 1957 wrote a classic book, Shakespearean Ciphers Examined, that exposed all the Baconian decoding work of the previous 70 years as nonsense. Author after author had combed through Shakespeare's plays using a variety of elaborate, pliable decoding rules, inconsistently and imaginatively applied, such that almost any 'message' could be read out. There is no evidence that the Bacon's biliteral cipher was ever used to hide messages in books of the time, and while in theory it was usable, in practice it was not, because it was not compatible with the sloppy printing practices of the 16th century. (My long Amazon review of the Friedmans' book here.)

        This early (Baconian) work gave Shakespearean ciphers (and cryptograms) a very bad reputation that has lingered. However, some newer (Oxfordian) work is in a different class, using simple decoding applied to short documents with odds that are calculable. The best of it might even be valid!

Historically hidden messages are a fact
        The early search for hidden messages in Shakespeare, while poorly carried out, was not crazy, because historically hidden messages in works of literature are a fact, they do exist. The Friedman's book gives some examples of real hidden messages. Edgar Allen Poe in an 1846 poem called, 'The Valentine', hid the full name of a woman he was attracted to while both were still married to other people. One letter from each line of his 20 line poem taken in order (following a strict formula called a progressive acrostic) spells out her name: 'Frances Sargent Osgood' (exactly 20 letters). Another mathematically convincing case is a 53 letter (simple) acrostic from a work published anonymously in 1616, the year the First Folio was published. The first letter of each of the 53 sections of the book taken in order spells out (in Latin): 'Franciscus Godwinvvs Landavensis Episcopus hos conscripsit' (exactly 53 letters), which in English is 'Francis Goodwin, Bishop of Llandaff, wrote these lines'. So here we have an historical example from Shakespeare's time of an author who really did hide his name within the text!

        Another example of real hidden text (not from the Friedman book) occurs in the famous book 'Alice's Adventures in Wonderland', where its author (Lewis Carroll) coded in the name of the little girl that inspired the book, often known as the 'real Alice'. String together the first letters of 21 consecutive lines (technically an acrostic) of a poem at the end of the book, and it spells out 'Alice Pleasance Liddell', the full 21 letter name of a little girl Carroll knew and often photographed! Mathematically these cases are all slam dunks, 20 or more letters in a row yielding a relevant name or phrase will simply not arise by chance in this universe. Here is the Alice poem.

21 line poem ending Lewis Carroll's 'Alice's Adventures in Wonderland'.
First letters (an acrostic) of the 21 lines spell the name of the real Alice,
'Alice Pleasance Liddell'

        Here is a summary of why I find the decode of the 'Dedication to Shakespeare's Sonnets' done in 1997 by Dr. John M. Rollett is so interesting:

            1) Text is very short, only 144 letters

            2) The sonnet dedication text and format are both very odd (period after every word, and a strange line format). It has been
                 suspected for years that it might be a cryptogram.

            3) Decode procedure is simple, just write out the text on graph paper, read down (or up/down)

            4) Decode fragments (pieced together) yield a 16 letter full name (Henry Wriothesley)

            5) Name found is relevant to the sonnets (leading candidate for W. H.)

            6) Odds of a specific name arising by chance can be calculated, because it requires a specific sequence of letters, and letter frequency
                  of the dedication is known exactly (by counting).

            7) Five letter first name ('Henry') and five letter fragment of last name ('esley') each contain a 'y', and there is only one 'y' in the 144 letters
                  of the dedication.

            8) The odds of a specific five letter name (or string) with a 'y' is about 1,000 to 1, which makes the odds of two five letter strings
                  (in same name, both with a 'y') about a million to one.

            9) The line format and word-periods taken as key to a word skip decode yield a grammatical phrase possibly relevant to the author
                  of the sonnets. ('These sonnets all by ever (E. Ver)'). A possible 2nd cryptogram in the same 144 letters.

Are recent published findings and odds calculations correct?
        Not always. There are odds calculations out there that are misleading or plain wrong. Some researchers in the field are quite conservative, while others let their imagination run free 'seeing' complex and fanciful patterns and phrases that I find hard to take seriously.  One mathematically correct, but misleading approach, is to calculate the odds only of exactly what has been found rather than for the universe of (similar) possibilities. For some perspective on all of this see the Appendix where I contrast the work of Rollett and Roper on the 144 letter sonnet dedication.

An astronomical number of possible words?
        I know one reason many people do not take cryptograms seriously is because they suspect the hidden names or word arises from an astronomical number of possible words (letter combinations). A well known Shakespeare book author told me this was one reason he avoided all cryptograms. For a long document like the Bible astronomical may not be too far off the mark, but for short documents this is simply not the case. For texts of a few hundred letters the number of combinations is measured in thousands.

        When documents are very short, the chances that a relevant long name or phrase will arise by chance is very small. This is why in this essay I focus on two very short documents with text of only 144 letters (sonnet dedication) and 220 letters (Shakespeare monument poem). Mathematically these are the strongest cases.

Introduction
       In recent years a few researchers have discovered previously unknown text and names that appear to have been coded (at great effort) into short documents lauding Shakespeare, documents that were written while he was alive or soon after his death. The texts revealed by the decoding are curious and interesting and can be interpreted as clues that Shakespeare was not the true author. If these hidden texts are 'real', meaning statistically significant, which some of them appear to be, they should be a part of the authorship debate.

        In a long document like the bible it's easy to discover lots of (supposedly) hidden messages by applying various decoding techniques. But finding text (phrases, names), which is both readable and relevant, in very short documents like the dedication to the sonnets, all of 144 letters, or the Shakespeare monument poem, only 220 letters, is a whole other ballgame. Readable and relevant text that uses a significant fraction (say 10% or so) of the available text is very, very unlikely to have arisen by accident.

Sonnet and funerary monument cryptograms
        A few short documents from Shakespeare's time have in recent years been put forward as being cryptograms, meaning they contain additional, hidden text (phrases, names). These are not documents written by Shakespeare, but documents from 400 years ago lauding him that are intimately associated with his work or life. The two I find the most convincing mathematically as cryptograms are:

            1) 144 letter dedication to the Sonnets (1609)
            2) 220 letter poem on the Shakespeare monument in Trinity Church Stratford on Avon (1616 to 1623)

        The first is signed 'T.T.', and this is generally taken to be the initials of the publisher of the sonnets (Thomas Thorpe). Wikipedia says, "Popular belief, however, is that Shakespeare is the author of the (sonnet) dedication", but no reference is given. The second is unsigned, but a favorite candidate is Ben Jonson who worked on the first folio. But in truth no one knows who wrote either one.

       In a cryptogram the hidden text is only revealed when the cryptogram is solved. The first, sonnet dedication, was solved by Dr. John M. Rollett, who wrote it up in a couple of papers in the late 1990's. The second, funerary monument poem, was solved by David L. Roper, who discusses it in two recent Shakespeare books he has written and on his homepage.

        What has aroused great interested in the few that have looked into these Shakespearean cryptogram is two things. One, these documents are very short and the hidden messages revealed use in the range of 10% of the letters, which it is obvious would be extremely unlikely to occur by chance. Two, the hidden texts revealed are clearly relevant and may offer clues to the solution of several Shakespearean mysteries, like who is Mr. W. H. of the sonnets and even who is the author of the works. They don't necessarily 'prove' anything, but they should be treated as real and and hard data in the authorship debate.

Shakespeare sonnet dedication is very short
        The shortest Shakespearean (related) document that appears to be a cryptogram (with hidden text) is the 1609 dedication to the sonnets. It is written out in two grids below (on graph paper). Two five letter strings (marked in red) stand out: 'Henry' and 'esley'. These are both part of the 16 letter full name 'Henry Wriothesley', a leading candidate for W.H., and all the other letters of his name are there too and in the correct order ('wr', 'io' 'th').

        There is only one 'y' in the sonnet text, the odds of the two five letter strings marked can be calculated by multiplying out the letter frequency of the other four letters in each string. For example, there are 9 r's in the 144 letter text, so the odds that an 'r' will precede the single 'y' is [9/(144 - 1)] = 6.3%. The odds for the five letter string 'henry' come out to be about 1,000 to 1 (see below for details), and for 'esley' about 600 to 1 because it has two vowels. Making the odds of the whole name formed from two five letter strings plus the rest of the name from shorter strings at least a million to one. It's odds like this that have convinced me that this dedication (and maybe some other Shakespearean documents) was composed as a cryptogram, the solution of which reveals hidden text (name or a phrase).

       There is yet another cryptogram (probably) in this 144 letter dedication. Incredibly this short dedication was found by Dr. John M. Rollett to be a double cryptogram. The second cryptogram hides a text phrase that (possibly) points at the author of the sonnets. It is a word skip cryptogram. Here is the facsimile of the dedication in the original 1609 printing (see below for full version with 'T.T.' signature).

         Elizabethan typography is weird, but the typography of this one is really strange. Note, there is a period after every word! Inverted pyramid patterns are often seen in Elizabethan typography (see examples in my other Shakespeare essay, 'Who Wrote Shakespeare?'), but here that structure is oddly uncoordinated with the text. Are these two hints that this weirdly structured word pattern (typography) might be a cryptogram and here is how to solve it? Looks likeit. Reading in a pattern the 6th, 2nd, 4th, etc words (from beginning) with words indicated by the periods (and dashes) out comes: 'THESE SONNETS ALL BY EVER'.

        This is not subtle. It's like the man in the moon, once pointed out it is obvious. So how come it was not until the 1997 that this was first figured out by Dr. John Rollett?  Rollett in his 1999 paper (here) provides a convincing answer. He shows how almost every Shakespearean editor over the years, not understanding that this was cryptogram, slightly altered ('cleaned up') the typography and spelling when they printed the dedication in their Shakespeare editions, obliterating the cryptogram!

Are the hidden texts real?
        When I first heard about this years ago I was intrigued, but only recently have I taken the time to read the papers, do the decoding and calculate probabilities myself, to see if I could convince myself if any of these hidden texts were real. Having been trained at MIT as an EE engineer and having worked for years with noisy systems, I think I have a leg up one most literary types who probably don't know how to do probability calculations nor how to assess the strength of probability claims put forward by others.

        After several months of work, including reading paper of the papers of the discovers and making email contact with some of those working in the field, I am convinced that one, and maybe two, of the two documents above have (at great effort) been crafted as cryptograms, that the hidden texts found there are real, meaning they were deliberately encoded (hidden). And what makes this important is that the hidden texts are clearly relevant to Shakespeare and very interesting, perhaps providing clues to the solution of some long standing Shakespearean mysteries. I personally take no position as to what these hidden texts mean (if anything), nor do I think they 'prove' who wrote Shakespeare. My only objective in this essay is to lay out the argument that the hidden texts found in these two cases are real.

        If any of these cryptogram solutions are real, which at least in one case I think statistical is very, very likely, this is hard evidence both for Shakespeare authorship problem and a mystery associated with the sonnets. Hard evidence with Shakespeare is hard to come by so it deserves to be more widely known.

        As far as I can tell, cryptogram arguments are known (or understood) by only a very small group, mostly Oxfordians. I never see a mainstream reference to cryptograms nor do I find any reference to them in Shakespeare articles on Wikipedia. Some of those working on the problem put this down to mathematical illiteracy of most literary scholars. I suspect some reject cryptograms because their intuition tells them an astonomical number of possible words exist. (Not true when the text is short.) It must also be said that some decoding pushes the boundaries of reasonableness, and published odds calculations need to be taken with a grain of salt, because not only are a lot of them pulled out of the air, but some are just plain wrong (see appendex). I have had a general interest in this topic for a decade, but until recently I had only ever heard of one case (Shakespeare monument poem).

Shakespeare in the bible --- not all 'hidden' text is a cryptogram
       There is (what at first appears to be) a surprising reference to Shakespeare in the King James Bible. I read that the church in Stratford where Shakespeare is buried keeps open a King James bible to Psalm 46.

        In 46th chapter of Psalm's count in 46 words from the beginning and you will find the word 'shake'. Then count back from the end of the same chapter 46 words (with some fudging) and you find the word 'spear'. In 1610, the year the King James is being finalized for the press, Shakespeare is age 46. With all these coincidences this had got to be deliberate, right? Isn't it obvious that this is a cryptogram, a hidden reference to Shakespeare inserted into the King James by the translators (or God!)? Well, when you did into it a little, not really.

        In three earlier english bibles translated before Shakespeare was born (Great Bible of 1539, Geneva bible of 1560, and Bishops' Bible of 1568, the primary reference for the King James) 'shake' and 'spear' are already there in Psalm 46 and very close to their locations in the King James, respectively at 46/48, 48/44, 47/48. With this information the mystery and surprise is gone. From bible to bible texts vary a little all the time (note the letter count in each of the three previous bibles is different), so clearly it could easily have happened by chance. It's impossible to a non-expert to put a number on the odds, but in a letter to the London Times in 1976 by a professor of classics he details how the King James translation guidelines would indeed have shifted 47/48 spacing of the reference text to 46/46.

No mathematical rigor
       Clearly this is a case with no mathematical rigor. While we can't rule out it was deliberate, there is a a very good chance it happened by chance. And even if it was deliberate, it's a tiny little cryptogram requiring only one or two word substitutions. (For links and more details on this case see my general Shakespeare essay.)

        The most convincing case for hidden text in early Shakespeare related documents I think is the 144 letter dedication to the Shakespeare sonnets, which was published with the sonnets in 1609. It is a double (even triple) cryptogram. At one equidistant letter spacing is found 'Henry' and at another spacing is found 'Wriothesley'. This is the first and last name of one of the two leading candidates to be mysterious W.H. of the sonnet dedication and a candidate to be the 'fair youth' of the sonnets. The odds of this particular name ('Henry' +  'Wriothesley') at any (two) equidistant spacings being real, i.e. that is not being a statistical fluke, can be rigorously calculated. In round numbers the result is

                Henry                (five adjacent letters)                                             1,000 to 1

                Wriothesley
                                          (five adjacent letter fragment 'esley')                   1,000 to 1
                                          (three two letter fragments, Wr, io, th)                      10 to 1
                                          (all four last name fragment in order)                       10 to 1
                                                                                                ---------------------------------
                                                                                                   total     100,000,000 to 1

        The odds against 5 letter 'Henry' popping up by accident is 1,000 to 1. The odds against 'Wriothesley' as a five letter fragment (1,000 to 1) plus three shorter fragments all in order (100 to 1) popping by accident is their product 100,000 to 1. Probability rules specify that probabilities, if independent, be combined by multiplication. Hence the odds of his full name ['Henry' 'Wriothesley'] appearing is the odds of the two names multiplied or 100 million  to 1. The odds that all this hidden text (long full name, structured as indicated above) could have arisen by chance is as near zero as you can come in this world.

Who is 'Henry Wriothesley'?
        Henry Wriothesley was a nobleman, the 3rd Earl of Southampton. He inherited the Earldom at age 8 when his father died and he became a ward of Lord Burghley, chief advisor of the queen, and essentially the prime minister.

        Lord Burghley also shows up frequently in the anti-Stratfordian world. One of his jobs was watching out for peerage orphans. Years earlier Edward de Vere, whose father died when he was 12, became a ward of Burghley. When Southampton was twenty, Burghley suggested that he marry Elizabeth Vere, daughter of Edward de Vere, Burgley's step granddaughter. De Vere's son Henry was a close friend of Southhampton. There is a 1624 painting ('Noble Henries') of them together on horseback in command of troops in Holland.

        Thus Southampton (Henry Wriothesley) and the older Edward de Vere are essentially family having had the same step father with De Vere's son a friend of Southampton, whereas there is no known relationship other than possibly patron, between the man from Stratford and Southampton.

        When Wriothesley was age 20 in 1993, Shakespeare's long narrative poem, Venus and Adonis, was published and dedicated to him, and a year later Shakespeare's poem 'The Rape of Lucrece' was also dedicated to him. Some scholars have long thought Southampton might be the the 'fair youth' of the sonnets and/or possibly the 'W. H.' of the sonnet dedication. Maybe Burghley commissioned Shakespeare in 1590, when Southampton was age 17, to write the first seventeen sonnets encouraging him to marry (Southampton Sonnets). Southampton does marry in 1598 at age 25. Three years later (1601) he gets involved with Essex who had screwed up a military attack on Ireland and who came back to challenge the queen (Essex conspiracy). Essex has his head cut off in Tower of London, and Southampton is sentenced to death, but is saved by Burghley and is out of jail and back to court when a new king replaces the queen.

        It's a little stretch, but not too bad I think, to interpret 'ever' as 'e ver', or E. Vere. (I don't do anagrams, and as the Friedman's point out in their book looking for anagrams led the earlier Bacon decoders badly astray, but nevertheless it is true that 'ever' is an anagram 'vere' for what it's worth.) Curiously the 6,2,4 pattern matches the letter count in 'Edward de Vere' too. Another coincidence? Well maybe, but nonetheless suggestive. (There also a way to tie Edward de Vere to 'the forth' too say some, but I have not looked into that.) I don't see really how to really calculate the odds of a phrase like this, but the common sense and apparently relevant message arising when using the skip spacing pattern suggested strongly by the typography implies that this is very likely to have been crafted deliberately. The discover of this, John M. Rollett, said for fun over 20 years he looked at this pattern in the first paragraphs of text he was reading. He figures he did this with 20,000 paragraphs and only one did he get a reasonable looking sentence (or phase), and its meaning was totally unrelated to the document. (Good for him, he ran an experiment, the scientfic method at work.)

        There you have it. Two (or three) cryptograms in one very short 144 letter dedication. The full name with its 16 letters uses 11% of the 144 letters in the sonnet, and the five words of the (shorter) phrase use 17% of its words. The two part cryptogram that reveals the name 'Henry Wriothesley' has odds that calculate out to be 100 million to one. If the the 3rd cryptogram is also considered, the word skip cryptogram that yields a readable and relevant phrase, 'These  sonnets  all  by  e ver', then I would argue that all three cryptograms together push the odds that the dedication was written deliberately as a cryptogram to -- I don't know, but it's really high! I am convinced by statistical arguments like this that some early Shakespeare related documents do contain hidden text (names and phrases) that are real, and they should be taken seriously.

        So I am not misunderstood. I am not saying hidden text proves de Vere wrote Shakespeare. I am not an Oxfordian, just an anti-Stratfordian. I am only saying I know enough mathematics to be convinced that this stuff is real, that the original author(s) of these documents went to great effort to conceal some names and phrases in these documents. The mathematical odds tell us that the text we find by solving (the best of) these cryptograms was very likely to have been deliberately put there, so it should be taken as real and included in the Shakespeare authorship debate. What the hidden names and phrases mean is for others to argue about. For all I know it could be Elizabethan graffiti or a joke!

        Notice the weird layout. Notice the period after every word. Who writes 'real' text like this?  (update -- I later did see one other document like this, a Roman Latin document.) These are (or could be) clues that this is a cryptogram, and they hint at how to decode it. Rollett writes that a well known Shakespearean scholar, John Leslie Hotson, came to the this conclusion in his 1964 book (Mr. W.H.), but he was unable to solve the cryptogram. But Dr. John M. Rollett, after many years thinking about it on and off,  (spectacularly) solved the cryptogram(s), wrote it up and published in 1997.

        Until spring of 2011 I had heard only of one possible Shakespearean document with a hidden message, the funerary monument poem, the work of David Roper. But from a draft overview paper by Albert Burgstahler ('Verifying Shakespeare's de Vere Authorship' by Albert Albert Burgstahler, PhD, professor emeritus of chemistry Univ of Kansas, prepared for an upcoming joint Shakespeare Fellowship and Shakespeare Oxford Society meeting in Washington DC, Oct 13-16, 2011) I learned about the sonnet dedication (double) cryptogram, the work of Dr. John M. Rollett in the late 90's.

        Dr. Burgstahler is an Oxfordian and his upcoming paper focuses on hidden texts that point to de Vere as the author. Curiously, Rollett, who had been an Oxfordian, is no longer. In the online 'Declaration of Reasonable Doubt' (& here) petition he states he currently has no favored candidate for Shakespeare. I also have no favored candidate, but my interest is not in the content of the hidden texts, but on their mathematical strength. My aim in this little essay is to lay out the case, based on Rollett's and Roper's work, that one (or two) Shakespeare related documents really are cryptograms, and that these cryptograms have been solved revealing relevant and interesting text.

Rollett's sonnet dedication paper (1999)
        John M. Rollett's original paper on the sonnet dedication was published in 1997 in Elizabethan Review. I have not been able to find it online, but Dr. Burgstahler kindly sent me a scan of it, so I have read it. Later I found online a slightly later paper by Rollett covering the same ground published in the journal The Oxfordian, Vol II, 1999 (link below).  This later paper was prepared for several talks he gave in 1998.  Rollett's decoding of the sonnet dedication is a fantastic piece of work and his (16 page) paper below is beautifully written, a classic. It deserves to be better known and I have some ideas for making it better known.

         http://www.shakespeare-oxford.com/wp-content/oxfordian/to-99-rollet-dedication.pdf

Three texts in dedication
        Rollett discovered three separate hidden text (names and phrase) in the 144 word sonnet dedication:

            1) 6-2-4 word code
                         THESE SONNETS ALL BY E VER

            2) At x15 equidistant spacing the name 'Henry' is spelled out

            3) At x18 equidistant spacing the name 'Wriothesley' is spelled out. Rollett sees the name spelled in three fragments, however they are not in the correct order and to pull out 'ioth' he must read up, whereas the others are read down. While I agree it's impressive, it's messiness makes it (on the surface) a little suspect, but mathematically it does stand up. As shown by my mark up near the beginning of this essay, I show another way, not mentioned by Rollett, that 'Wriothesley' can be read out at x18.

                         Wr    esley   ioth     (Rollett)
                         Wr   io   th   esley    (Fulton)

My reading of x18
        Prior to finding Rollett's paper I had written out the dedication at x18, because I had read in Burgstahler's draft paper that it contained the name 'Wriothesley'. What I saw (and prefer) is 'Wriothesley' spelled out in four fragments. This may not look quite so impressive as Rollett's three fragments, because the moderately difficult to form four letter fragment 'ioth' has been replaced by two easy to form two letter fragment 'io' 'th', but much of the statistical rigor is recovered because the (four) fragments are in order. When the odds are calculated out, it is exceeding unlikely to have occurred by chance (less than a million to 1), and I think it is cleaner than Rollett's three fragment version for two reasons:

1) Order is correct
       The four fragments come out in the right order to spell 'Wriothesley'. In contrast Rollett is forced to reverse the order of his 2nd and 3rd fragments to make it spell 'Wriothesley'.

2) Read only down
        The four fragments are all read down. In contrast Rollett is forced to read both up and down ('wr' and 'esley' are read down, and 'ioth' is read up). The Shakespeare monument poem decode is done only reading down. The only (slight) bending of the downward read 'rule', is that the 'io' fragment spans two columns ('i' is on the bottom row and 'o' is at the top of the next row). I see this as perfectly allowable. (For more on this see Appendix 'Equidistant vs grid decoding')

My x18 decode of the sonnet dedication
showing 'Wriothesley' spelled out in four fragments
'Wr'  'io'  'th'  'esley'

Rollett's x18 reading
        I also see Rollett's four letter up fragment 'ioth', and I outlined it above in ink (11th column). Rollett in his paper uses this up and misplaced four letter 'ioth' fragment to provided the middle letters of the name, but I prefer to use the two letter fragments 'io' and 'th' (marked in yellow), both of which are correctly placed and are read downward (like 'wr' and 'esley').

        I don't use Rollett's 'ioth' fragment in my odds calculation, but I agree it is striking (even if 'misplaced' and read the 'wrong way') because it is long (four letters) and relevant. I consider it a compounding factor.

        So is reading up and down a stretch or just wrong? That's not for me to say, maybe the encoder intended a longish fragment to be read 'up'. Who knows? My point is that you don't need the upward 'ioth', because two downward fragments 'io' and 'th' are there located just where they should be, in order between 'Wr' and ''esley'! I find this impressive. The loss of some statistical strength from breaking up a four letter fragment 'ioth' is partially recovered by four fragments coming out in order.

x18 equidistant decoding
        The same type of equidistant decoding used with the Shakespeare monument poem can be applied to the Sonnet dedication. Here the equidistant spacing I want to examine is x18 (reading every 18th letter). An easy way to do equidistant decodes is to use graph paper. For a x18 decode we just write out the 144 letters of the dedication (sans punctuation and expanding any compound letters) in rows of 18, then any words or names that exist in the original text at x18 spacing can easily be read off the graph vertically. No computer needed, it takes just a few minutes by hand.

Estimate of the odds
       The result of a simple x18 (equidistant) decode yields the long name 'Wriothesley'. Clearly 'Wriothesley' is relevant (to the Sonnets) as Henry Wriothesley is one of the leading candidates to be the 'W.H' mentioned in the dedication, the 'begetter' of the of the sonnets. This 11 character name appears in four isolated fragments, one of which is five characters long, and all arranged in the correct order, as shown below:

        There is only one way to spell this name (see Appendix), so that means we can calculate the odds of 'wriothesley' appearing by chance in the four fragment form seen above.  There is only one 'y' in the dedication (see table below), so we can work forward from the rear 'y' multiplying out the odds as each letter is included. And the letter frequencies are easily found just by counting how often each letter occurs in the dedication.

Letter frequency in sonnet dedication text
       First step in calculating the odds is to count the frequency of occurrence of the name letters in the dedication text. 'w' occurs four times in the 144 characters that make up the dedication text, so the odds 'w' will appear in a specific location on the graph is the ratio of the numbers of 'w's to the number of unoccupied letter blocks on the graph. For example, [4/144, or 4/143, or 4/142, etc], which is approximately 1/36 or (36 to 1).
 

Is the long name Rollett found in an 18x8 grid of the dedication real?
        Rollett found an 11 character name 'wriothesley', one of the two leading candidates to be 'W. H' of the dedication text, turns up at x18 spacing. This name uses 7.6% [= 11/144] of the available characters and is built from an unlikely five letter fragment with shorter fragments all in order. But what is the probability that any long relevant name (or phrase) will appear at any equidistant spacing. Below I estimate the odds of the long name found at x18 spacing at about 10 million to one, and any long name at any spacing maybe 1,000 times more likely, giving us odds of 10,000 to 1.

One five letter fragment
        Even before we work out the details we can make a quick estimate of what we are likely to find. It's easy to guess that the odds of the specific five letter fragment 'esley' are going to be pretty low, after all I worked ten cases in the monument poem of 220 characters and not a single five letter word showed up. Below is the calculation with the result the odds are about one in 15,000. The odds of the five letter fragment 'esley' is figured as follows.

        It's easiest to start at the end because, there is only one 'y' in the text. So we locate the one 'y' on the graph. This letter has a probability of unity. To spell 'wriothesley' the letter preceding our single 'y' on the graph must be an 'e'. We can see from the table above that 22 of the 144 dedication letters are 'e'. With 'y' removed there are 143 letters remaining, so the odds the letter preceding 'y' is an 'e' is (22/143), about 15%. So multiplying out for the four characters that must precede 'y' in order, we get the odds for the five character fragment 'esley'

                'esley'      (21/140)  x (10/141)  x  (6/142)  x  (22/143) x 1 = 1/14,460

Three two letter fragments
        A back of the envelope calculation shows that the two letter combinations 'wr', 'io' and 'th' are quite likely to occur, especially 'io' and 'th', because all four of these letters are common. Here's how to estimate the probability of 'wr': Find an 'r' and ask what is the probability that the preceding character is 'w'. That's easy, there are only four 'w's in the dedication text, so the probability of a 'w is [144/4) = 36 to 1. But this is not the answer. There are 9 'r's so to a first approximation this reduces the 'w' odds of 36 by 9, giving us odds of 'wr' as [36/9] = 4 to 1. This is an 'OR' probability calculation and below is the exact calculation.

        Above shows our back of the envelope calculation of 4 to 1 odds for 'wr' was pretty good, as the exact answer is 4.4 to 1. The back of the envelope method gets less accurate for 'io' and 'th' predicting their odds as close to one. The exact calculations are (in same manner as above)

We multiple the above three for the odds three two letter fragments 'wr', 'io', and 'th' appear (here in any order)

Four fragments in correct order
        Finally we need to figure the odds that the four fragments come out in order. To simplify the calculation I am going to assume there is only one of each fragment, not quite right, but close so we won't be far off in out final estimate. With our simplifying assumption the order calculation is very simple.

        The odds of any specific fragment of four (here 'wr') being first is 4 to 1. Odds of a specific fragment of remaining three (here 'io') being next is 3 to 1, the odds of the two remaining fragments being in order is 2 to 1. Multiplying out the odds that the four name fragments line up correctly to spell ['wr io th esley'] we get

When I checked, I found two 'th' on the x18 graph, so there is a minor correction to above. It is a little too high, 2 really is 1.5, so 24 becomes 18. In the big scheme of things it makes no difference.

x18 result
        The final result is the odds of the five letter fragment 'esley' [15,000 to 1] times the odds of the three two letter fragments 'wr', 'io', and 'th' [12.7 to 1] times the odds the four fragments are in the right order [24 to 1]. Since all these conditions must be met we multiply the three odds to find the odds of 'wriothesley' appearing at x18 spacing.

                                                           14,000 x 12.7 x 18 = 3 million to 1 (approx)

But this is not the final answer.

Reduction #1 -- multiple spacings
        The above estimate of 3 million to 1 (approx) is for 'wriothesley' appears at one spacing (x18). But if there is nothing strongly special about x18 spacing, then we need to reduce this by an estimate of the number of reasonable graphs that could be drawn. With a 144 characters and min of 5 char per row or column we get x5 to x29, or roughly 24 possible graphs. So reducing 3 million by 24, we get an estimate of the odds of 125,000 to 1 for 'wriothesley' appearing on any possible graph (i.e. at any equidistant spacing).

Reduction #2 -- other fragment combinations
        (pending)

Reduction #3 -- other relevant words
        But why limit ourselves only to ['wr' 'io' 'th' 'esley']? There are other relevant names that might have shown up.  What is obviously striking about what was found is that it includes a long five letter fragment with very low odds (14,000 to 1) just for this fragment. Obviously the probability depends strongly on the length of the longest fragment of a name or phrase.

'Vere'
       For a short name like 'vere', the probability, that it might occur by chance intuitively is pretty high. In fact it is. There are five 'v's in the dedication, so starting at the beginning 'v' and (roughly) correcting for the five 'v's

        To accommodate 32 possible spacing we divide by 32, giving us [135/32 = 4.2] or about 4 to 1. In other words the probability of a 'vere' popping out if we look at 32 different spacings we can estimate to about 4 to 1, in other words it has barely any statistical significance.

Summary
        Because 'Wriothesley' can be spelled only one way (well sort of, see Appendix), it is possible to do a hard calculation of the odds this name will appear as it does on the x18 chart in the four fragments ['wr' 'io' 'th'  'esley'] ordered correctly. The result of this calculation is about 3 million to 1.  Knocking down our 3 million to 1 odds for 'wriothesley' at x18 to accommodate a wide range of spacing gives us [3 mil/24] = 125,000. And reducing 125,000 by an order of magnitude or so to allow for the possibility of other long relevant names or phrases (with a five character fragment) gives us 10,000 to 1. Since this is partly calculated and partly estimated, I would call it an engineering estimate.

        In other words for ''wriothesley' at x18 spacing, where we have hard numbers (based on counting), we get 3 mil to 1 odds. We extrapolate to a wider search range of any equidistant spacing by dividing by 24 (approx). We further extrapolate to include a range of relevant long names or phrases, but requiring them to include a five character fragment, by dividing again by roughly 10. These two extrapolations reduce the 3 million to 1 odds by a factor of 300 giving us a final estimate of a chance occurrence of 10,000 to 1.

        I am happy with 10,000 to 1. I would call this definitely statistically significant.

        Note, one reason the odds of 'Henry Wriothesley' come out so high is that the five letter string of the first name ('henry') and in the last name ('esley') each include the letter 'y', and there is only a single 'y' in the text of the dedication. For perspective, see the calculation of the word 'write' below, which is a word with two vowels and four of its least common consonant ('w').

'Henry' at x15 spacing
        At x15 equidistant spacing in the dedication Rollett found the five letter name 'Henry', and guess what, this is Wriothesley's first name! Meaningful five letter combinations are quite rare. Rollett found only a handful at the wide range of spacings he looked at. I found no five letter words in ten spacings of the monument text (below) I looked at. Below from letter counts in the dedication I show the probability of this five letter name appearing at this particular spacing (x15) is about 23,000 to 1. Diving this by 24 other possible spacings gives us the probability of 'Henry' appearing at any spacing to be (in round numbers) 1,000 to 1. Rollett in his 1999 Oxfordian paper has the same number (1000 to 1) for 'Henry' at all spacings.

For perspective --- Calculating the odds of another five letter word ('write')
        For perspective here is the calculation of the odds of a different five letter word, 'write'. The expectation is that 'write' will be more likely then 'henry' for two reasons. One, it has two vowels (vs one for henry) and vowels are two or three times more common. Two, its least likely consonant, 'w', occurs four times in the text, whereas there is only 'y' in the text. The procedure is find a 'w' (unity) then multiply by the odds for the following four letters 'r i t e', finally to account for the four 'w's we multiply by four since we can do this four times. (This calculation is not exactly rigerous, but close enough)

               Odds of  'w r i t e' (in a specific grid)    = 4 x [ (1) x (9/143) x (14/142) x (17/141) x (22/140)] = 4/8,500 = 1/2,100

        In round numbers the odds of 'write' not popping up in 24 grids of the dedication is about [100 to 1], or about ten times higher than the [1,000 to 1] odds of 'henry'. My memory is that Rollett in his Oxfordian paper makes an offhand comment that the odds of pretty much any five letter word is about the same as 'henry' or [1,000 to 1]. This little example here shows that's probably wrong. Compared to other five letter words (or names) 'Henry' is quite unlikely since it has a consonant ('y') that occurs only occurs in the text, and it has only one vowel ('e').
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This link (below) is a paper by William Ray discussing Rollett's work and his views on Oxford.

         http://www.wjray.net/shakespeare_papers/Rollett_In_Reverse.pdf
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        Shakespeare is buried in the Holy Trinity church in his home town, Stratford-upon-Avon. High up on the wall of the church is a monument to him that consists of large bust with a plaque below containing eight lines of text: two lines of Latin and a six line, 220 letter English poem. There is mention of a Shakespeare monument in the introduction to the first folio,  "thy Stratford moniment" usually taken to mean this monument in Trinity church, which places its time of construction sometime between 1616 (Shakespeare's death) and 1623 (first folio).

Is the stone engraving original?
       The working assumption of those doing the decoding of the funerary monument poem is that the poem we see today is exactly the same in wording and spelling as when it was installed. To what extent the monument has been reworked in its nearly 400 years is not fully known. With equidistant decoding even a minor change in spelling of one word can easily damage or destroy a (supposed) hidden message, so the value of the funerary decoding hinges on the poem text being unchanged. Hence the history of the important and I spent a lot of time (too much time!) researching it.

        I eventually tracked down four early versions of the poem: 1631, 1656, 1721, 1825 (see Appendix for details). The first recorded version of the poem (1631) is from a notebook written only a few years after the monument went up. The last from a 26 page booklet describing Trinity church published in 1825. The wordings and spellings of the four poems are all slightlydifferent from each other and from the current monument! It's easy to show that of these four versions only the 1825 version supported the claimed hidden message. (I also have an Appendix with pictures of the bust from different times.)

        So is this the deathnell of the funerary monument decoding? I don't think so. The fact that these four versions are all slightly different from each other, while at the same time being quite close to the current monument text, argues that more likely than not the spelling and wording differences originated with the observers, that the text we see today on the monument is the same as the original. A confirming fact is that the text recorded in 1631 is very close to the text on the current monument.

Nevertheless, risk remains
        There is an inherent problem with hidden messages that depend critically on details of spelling and abbreviations. As the cryptographers Friedman pointed out in the case of the Bacon cipher, the instructions to the printer or engraver for text containing such a hidden message must be don't change anything, copy my manuscript exactly. At least with a printed document, even if later editors fiddle with the text (as they often do!), copies of the first edition remain, so the message is not lost. But what about an engraved stone tablet?

        What if in four hundred years the engraved stone tablet of the Shakespeare monument got worn or damaged (cracked, water damage, who knows). This is the monument to Shakespeare, what the church is famous for, of course they are going to repair it.

        Now here is the problem. The instructions to the original engraver to not change anything are of course long lost. A new engraver's view would likely be that if he needs to add or remove a contraction to make a line fit that is his business. After all the original engraving is full of combined letters (eq of typographic ligatures) and abbreviated words too (Ys and Yt). Surely it's the words and layout that are important. Or suppose he changes (modernizes) the spelling of a word or two, what's the difference? That was clearly the view of those who recorded the poem i 1631, 1656 and 1721. Suppose by mistake he engraves 'monument' (maybe his usual spelling) instead of 'monvment', what is he supposed to do start over? If he doesn't, 'Vere' is gone from the message!

        He has decoded it with x34 equidistant spacing. This is easily done by writing out the poem on graph paper (34 letters to a line) and looking for words vertically. The additional claim is made that there are two hints that x34 spacing is the decoding key. One, there is only one line on the plaque that is indented, and it has 34 characters. (Well, it does if the compound character 'ae' is treated as one character not two! I address this issue in an Appendix.)  Two, Edward de Vere being the 17th Earl of Oxford points to 17 or (possibly) 34 as a possible key, and this is confirmed, so think the Oxfordians, when 'Vere' pops out with x34 decoding.

        Here a graphic image of the text on the engraved stone below the funerary monument bust. (See an Appendix for a lot of pictures of the monument that confirm this.)

Reduced message
        A straightforward x34 decoding, which I prefer to Roper's all too flexible decoding, gives what I call a reduced 'message' (below).

        This (raw) hidden 'message' in the 220 letter monument poem at x34 spacing is a quasi-grammatical 'sentence' that is clearly relevant to the Shakespeare authorship debate. It is obtained by reading vertically downward with no rearrangement of the words. Here's a scan of my x34 decode with the (above) message words marked in yellow.

        Roper gets a much longer and even more grammatical sentence (below), but I don't like how he plays fast and loose with equidistant decoding rules to get it.

        For example, to get 'Shakespeare' into the message Roper changes to reading horizontal, then he sort of glues it in with 'as' and 'he', but I see this as a cheat because not only is it ad hoc, but a horizontal word is always there. To get Ben Jonson's 'signature' ('B. I.'), which the Oxfordians (apparently) see as critical, he resorts to reversing the 'I. B.' found on the right side. I am not saying he is wrong, just that I think simpler is better, and the reduced message is still impressive.

'Vere' and 'test' with clusters
        The case for trial 34 strengthens, says Roper, when a 2nd four letter word, 'test' can be woven in with 'vere'. It strengthens more when two and three letter words adjacent to these two four letter words can be woven in

Roper calls these adjacent word groups clusters, and they do look unlikely.

       The case for trial 34 is again strengthen when it is found that between these two clusters relevant shorter (fill) words can be woven in ['he', 'vow', 'is'], and we can add in the common 'i' too that precedes 'vow', giving what can be read as a simple, fairly grammatical message below: (Note, use of 'vow' here is a little suspect, since Shakespeare himself in his introduction to an early poem of his spells this word 'vowe')

        There is another way to group the above words, which I did not see at first. Three of the four fill words  ['he', 'i', 'vow'] are in fact adjacent to the first cluster and can be grouped with it. ( 'h' of 'he' is to the right of the last 't' in 'test' and to the right ot 't' is 'w' in 'i, vow'.) With this grouping the first cluster is not as compact, but still since all the words are in successive columns and partly adjacent to each other, it is a cluster, if a somewhat extended and dangly one.  With some of the fill words regrouped and attached to the first cluster it's the same message, but it gives at least the appearance of it being less likely a chance occurrence

                                                            {'him', 'so', 'test', 'he', 'i', 'vow'}   ['is']     {'E', 'Vere', 'de'}

Critical look at Shakespeare funerary monument poem
        At first blush this all seems pretty convincing, but let's take a critical look. Does it really contain a cryptogram? Is above really the solution? Let's do some math.

Is the 'v' in 'monvment' really a 'u'?
        There is a weakness underlying the Stratford monument poem cryptogram. Is the 'v' in 'monvment' really a 'u'? I think the answer is yes. There is a printing/engraving convention that in headers and titles written in capitals a 'V's is used in place of a 'U'. (This swap can be seen in engravings on the concises of many buildings even today.)  Shakespeare always spelled in his text the word monument as 'monument', never 'monvment'. The capital 'U' to 'V' swich can be seen in his work in some titles and headers, for example, the title page of his first published poem is 'VENVE AND ADONIS'.

        Only after studying spelling conventions of Shakespeare with respect to u,v, did I realize that the 'V's found in the monument poem are really 'U's. Shakespeare's spelling across all of his works, poems, sonnets and First Folio plays, is remarkable consistent. As I describe below in detail, 'v' is found only at the beginning of words and 'u' only inside words, but there is an exception. The exception seen in headers and titles that are printed in capitals is that what an inside 'u' is printed as 'V'. For example, a search of Shakespeare works finds many instances of 'monument' and none of 'monvment'. But if 'monument' were to be printer (here engraved) as a title or heading and in capitals, the printing convention is to switch the inside 'u' to 'V'. And this is what it appears has been done in the monument poem.

        The 'v' in 'Vere' comes from the 'v' in 'MONVMENT', but the spelling patterns of Shakespeare, confirmed by searches of his works in original spelling, show clearly that when used in text the spelling is always 'monument'. In other words the only reason there is a 'V' in the critical spot on the engraving to form 'Vere' is that it is a printing/engraving convention with capitals to show a 'V' instead of 'U'. It's really a word 'u' that by a printing/engraving convention with capitals comes out as a 'U'.

Early versions of the poem
       First problem, not mentioned by Roper online (I don't know if his books address this issue as I am not willing to spend $50 to buy each of them), is that the three early published version of the funerary poem (1631, 1656, 1721) are just different enough from the current plaque that it kills the hidden message. In the message the 'v' in 'Vere' comes from the 'v' in 'monvment', but in all three early versions you find the spelling is 'monument'. Bye, bye 'Vere'!

        Is this fatal? Well, probably not. After researching this in depth (see Appendixes) , I think it is more likely than not that the observers were sloppy in reading or recording the poem and that the text we see today is the original. However, it must be noted that the early versions of the poem with alternate spellings (and wordings) do introduce some measure of doubt about the claimed crytogram hidden message really comes from 400 years ago.

Math
        And what can the math tell us?  For starters one number that pops out (see below) that puts some perspective on Roper's finding is that the odds of  ['E. Vere de' or 'E. de Vere'] arising by chance on some grid is 10%.

Odds of 'Vere'
       The key word in the message, certainly to Oxfordians, and one of the two 4 letter words in the message is 'vere'. After doing a letter count of the poem [11 or 5% of letters are 'v',  25 or 11.3% are 'e', and 9 or 4.09% are 'r']), the odds of 'vere' arising by chance are easily calculated. (I do the calculation below.) The result for it arising (by chance) on x34 grid is 0.57% or 1 part in 174. OK, that seems moderately strong, but if we ask what is the probability that 'vere' will appear on any grid, say on any of 35 possible grids, then it is 35 times more likely, or 1 part in 5, or 20%.

        Wow, 20%. From this perspective finding 'vere' with equidistant decoding (at some spacing) does not look all that surprising. And while there are hints x34 might be special, it must be remembered that these arguments are only hints and were made after the (so-called) message was found at x34.

Pushing the calculation
        This calculation can be pushed further. So what are the odds of  'E. de Vere' or 'E. Vere de' (as it is in the raw message) appearing by chance on some (not necessarily x34) grid? Ans: wow 10%. There are 'e's scattered all over every grid, so the odds of finding a preceeding 'e' is virtually unity. The odds of 'de' appearing on a particular grid are .50, so the odds of 'e', 'de' and 'vere' appearing on the same grid are .10 or (1 part in 10)

        We can go still further and ask what is the probability that all the shorter words of the (reduced) message appear on the same grid with 'Vere'. Below is the calculation for 'vere' with all the words of the reduced message except 'test', 'vow', 'him'. Ans: 5% (approximately).

                         'e'          'de'        'vere'          'he'           'so'          'is'          'i'
                         1    x     .50    x    .20    x    .886    x    .71    x    .71    x    1      =     .0447  or (1 part in 22)

        The odds for 'Vere' plus 6 of the words of the reduced message comes out to be 4.47% or 1 part in 22.  No mathematical rigor here. What mathematical strength the funerary message has is carried by the minor words: 'test', 'vow', and 'him', not all that reassuring.

        The odds of two letter words, like 'so', 'he', or 'is', arising by chance on every grid is very high (odds greater than 75%), so I didn't mark them. [Roper's claim that a two letter fragment 'wr' had odd of a 1,000 to 1 in an equidistant decoding of the sonnet dedication is total nonsense.]

Final odds
       Since the (proposed) funerary poem cryptogram is a phase, no simple calculation of the final odds are possible. Below I take as stab at estimating it, getting a wide range 16 to 1,600. (The odds would be 35 times higher if restricted to x34.) This is moderate to very little mathematical rigor.

        Bottom line the nature of the funerary poem only allows for a limited mathematical odds calculation. It does, however, remain interesting with hints that it is moderately unlikely to have arisen by chance, but that's as far as the math can take us. Certainly it doesn't have the mathematical rigor of the sonnet dedication cryptogram, where the solution is a long name, not a phrase.

I do ten trials --- So what's the result?
         Well in the ten trials no five or more letter words were found and relatively few four letter words. In six of ten trials the longest word has three letters. In the other four trials six four letter words were found: hale, tide, stem, shim, test, Vere. Three of these ['shim', 'test', 'Vere'] come from trial 34, while ['hale', 'tide', or 'stem'] each arise in a different trial. The (after the fact) key word is, of course, is the (proper) name 'Vere', father-in-law of one of the dedicatees of the first folio, and in the 20th century considered as a major candidate to have written some (or all) of Shakespeare's plays and poems.

Calculating the probability of key words
        Calculating the odds a name will appear by chance is straight forward, but calculating the odds of a phrase is no so easy. While it may be hard (or impossible?) to calculate the probability of a phrase being relevant and grammatical, at least the odds of its key words can be calculated. The procedure is the same as with the sonnet dedication name. First count the count to find the letter frequencies in the 220 letter funerary monument poem. Here they are with a comparison to general (modern) English usage.
 

        Notice the big disparity between the funerary text and modern english text is the letter 'v'. It occurs x5 times more frequently in the engraved stone funerary poem (5% vs 1%). This is partly because where there would be a 'u' in modern english, like in 'quick, nature and monument', there is a 'v' in the funerary text.

Dugdale/Hollar 1656 version
        When Dugdale records the monument and its poem for his 1656 book many of the 'v' are gone. He writes 'quick, nature and monument' not 'qvick, natvre and monvment'. This is important to the x34 Roper message because the 'V' for 'Vere' comes from 'monvment' and the 'v' for 'vow' comes from 'qvick'.

        With the 1656 Dugdale version of the poem (the original version?) the 'v's for 'Vere' and 'vow' are missing, there is no hidden message!

                                                V             e               r                e
                                   11 x [ (1)     x   .113  x   .0409    x   .113] = .00574  or (1 chance in 174)

                                                t             e               s                t
                                   27 x [ (1)     x   .113  x   .0864    x   .1227] = .0323  or (1 chance in 31)

                                                v             o              w
                                   11 x [ (1)    x   .0636   x  .0364] = .0255  or (1 chance in 39)

                                                h             i              m
                                  7 x [ .0818   x  .0636   x   (1)] = .0364  or (1 chance in 27)

Two letter words
        Two letter words contribute only a little to the odds. Two letter word of common letters, like 'is', 'so' 'he', contribute almost nothing. The odds of 'is' and 'so' (calculated correctly as inverse of it not appearing) are .71, that is, there is almost a 3 out of 4 chance of either of them appearing in any grid, and the odds of 'he' is still higher are .88! Sure enough when I looked at a few of my trial runs I quickly spotted two occurrences of 'is'. The odds of 'de' is 0.50 or 50%.

Two letter word odds calculation
        Odds calculations for two letter fragments tend to come out greater than unity if done approximately, so they must be done more exactly. This means an OR calculation or (easier) the inverse of an AND calculation that the fragment will not appear.

        The calculation for 'he' using the letter count from the table above (18 h, 25 e) is done this way. For each 'h' on a grid the odds that the next letter (read vertically downward) is not an 'e' is [(220-25)/220 = .8864]. There are 18 h's on each grid, so for 'he' to never appear on a specific grid, 'h' must not be followed by 'e' 18 times, which means taking the 18th power of .8864 [(.8864)^18 = .114]. Subtracting this result from one gives the odds that 'he' will appear one (or more) times in a specific grid [1 - .114 = .886] or 88.6%.

        In other words the odds are almost 9 out of 10 the the word 'he' will appear on each and every grid of funerary monument poem, and the odds for 'so' and 'is' are almost as high. Their location may contribute to an odds calculation, but their existence contributes almost nothing.

                                1 part in [174 x 31 x 39 x 27] or 1 part in 5.6 million

        OK, a big number, and it is a hard number directly calculable from the letter count probabilities, but what does it mean? We need to do some dividing. The argument that x34 grid is 'special' is made after the 'message' had been found at x34 and is thus suspect. We can find the probabilities for these four particular words on any grid by dividing our calculated 5.6 million for one grid by (about) 35 for all possible grids, and we get 160,000. This too is a hard number, but we are not done, and now things get a lot more squishy.

Word order
       Having words appear in a specific (grammatical) order can contribute a one or two orders of magnitude (for example: 4 x 3 x 2 = 24 and 5 x 4 x 3 x 2 = 120), but I would argue the grammatical order should be 'test him' whereas what we find is 'him ... test', made more palatable by finding the common 'so' in between, giving 'him so test'. I will grant that the odds of 'so' appearing in the small gap between 'him ... test' is small (visually we can estimate it at 2-3%), but still the result is only quasi-grammatical. How many quasi-grammatical wording are there?

How many different words?
      The problem with calculating the odds of a phrase, as opposed to a name, is trying to guess how many different words (and what order) would be accepted as constituting a message? I don't think there is any way to calculate this. All that can be done is to guess a dividing factor. We just have to guess at a dividing factor.

Bottom line
     My hip shot estimate: 100 to 10,000 possible word combinations. It's just a guess. Applying this divider to 160,000 we get odds for a quasi-grammatical message on any grid of the funerary poem: 16 to 1,600. The core problem is this. There is no five letter word/name anchor in the funerary message (though it could be argued 'evere' stands for E. Vere, and this is good for anther factor of 10), just two four letter words ('vere' and 'test').

        The key word for Oxfordians is undoubtedly 'Vere', but a hard calculation shows the odds of 'vere' appearing on any grid is [174 (for x34)/35 possible grids = 5] or 1 part in 5. In other words there is 20% chance of 'Vere' showing up at some grid of the funerary poem with a 1 part in 16 to 1,600 odds that enough other (mostly small) words will surround it to make a quasi-grammatical phase that can be read as a message. Moderately unlikely, but lacking real mathematical rigor.

I recreate the 'rule of 34' analysis of the funerary monument text
        For this 'rule of 34' decrypting to work the exact text with its original archaic spellings must be used, this is crucial. A lot of references (supposedly) give the original spelling, followed by modern spelling, but I see they differ. I wanted to start with a clear photograph of the funerary monument plaque that sits under the bust of Shakespeare high up on the church wall. It took some searching to find what I needed (the Wikipedia photo is unreadable), but I located a clearly readable photo of the plaque on a Marlowe site run by Peter Farey (below).

        Unfortunately the plaque may have been fixed up, or replaced, when the monument was restored after it was vandalized in the 1970's. It does look awfully clean for a 400 years old plaque! In comparison with old photos Farey sees at least one change in punctuation and the 'C' in 'Canst' (2nd line) now looks like a 'G'. This is disturbing, but the photo is the best reference I had, so it is what I used.

        With more searching (see appendix) I now agree with Farey about the changes to the 'c' in 'canst'. I located what appears to be an old photo of the monument, a BW photo that shows two finger tips missing, and in this photo 'canst' clearly starts with a 'c'.

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Comparing my chart to David L Roper's (6/2/2011)
        I generated my 34 char chart above entirely independently from Roper's version. I make no claim to originality as I know I had read his analysis years earlier and had a vague memory of it, though I did not find currently active links to his stuff until after I finished.

        Below is the link to Roper's 2009 'Cryptology' essay, which contains his analysis of the Shakespeare funerary poem. My chart and his chart are for all practical purposes identical. Facts are facts. In the write out of the poem in a 34 char/line format they are exactly the same. This confirms no fudging and no errors, we both have the poem text from (modern) pictures of the plaque beneath the Shakespeare bust written out as 34 char/line with with spaces and punctuation dropped. We both highlight the key De Vere related 'text' that appears in vertical columns, but in auxiliary text I highlight a couple of words he did not, and vice versa. He has a fairly lengthy commentary on the results.

Roper's cryptographic message arguments
        He quotes a cryptographer who gives guidelines for interpreting if text found by cryptographic analysis is a real message and not random: Message should be grammatical, informative, and unique. These seem to me a good standard, and Roper says the message meets all three criteria. Well, I pretty much agree, though as to grammatical this is a judgment call, as it is roughly in the right order, but not strictly so.

        His other key point is that the mathematics of a quasi-grammatical, informative message like this coming out randomly are impossibly small. The paper of his I just read does not give the details of his math, but my intuition as an engineer familiar with math is that his argument is probably sound.

Important find
        In other words if this is Roper's discovery, which he says (or implies) it is, then he has found something very important in the Shakespeare authorship debate. And he doesn't oversell it, saying only that this message is 'Ben Johnson's "avowal" that Edward de Vere was Shakespeare'. And I agree with him that this finding may not be appreciated as its strongest argument is mathematical and most literary types are unfamiliar with math, and therefore unlikely to grasp the (likely) strength of the probability argument.

        There are quite a few 'little things' that fit with the big picture too. The most obvious being that the spacing on the equidistant code is 34 = 2x17, where de Vere with the 17th Earl of Oxford. Roper also points out that what many critics have puzzled over 'sieh' as a strange spelling (or incorrect) old spelling for 'since' is needed to make the Ben Johnson initials work.

        Roper identified 'I,B' in the right corner as standing for Jonson's initials, a signature of the hidden message if you will. But they are reversed initials from how Jonson signed (see below). A 'B,I' does exist in the 34 equidistant rewrite (lower, center) and I marked it red dotted above. (Did Roper not mention the reversal to strengthen his argument? Don't know, but the 'B,I' I found and marked is pretty obvious.)

First Folio poem --- To the Reader
        I searched out a facsimile of the First Folio introduction and located a page with a poem by Ben Jonson to see how he signed. Here it is and as you can see he signs 'B. I.' not 'I. B.'.

        I have noticed some curious correspondences between this poem and the poem on the funerary monument, like wit/writ. Both were (supposedly) around the same time, and some think both by Ben Jonson. But notice the facsimile spelling of the four key words below is different in the two poems. A strong argument I would think they were not written by the same person.

                                             First Folio 'To the Reader'                     Funerary poem
                                            ------------------------------                     ------------------
                                                         writ (vvrit)                                           writt
                                                          wit                                                        witt
                                                         nature                                                   natvre
                                                     Skakespeare                                         Shakspeare

        Of course, I recognize that this argument can be inverted to argue that the alternate spellings in the funerary poem are an indication that it is a cryptogram. However, the extra 't' in 'witt' doesn't made any difference because it is the last word in the funerary poem, except possibly to visually match 'writt'.

Weird spelling of 'Shakspeare' in the poem -- missing 'e'
        Shakespeare's first published works in 1593, the poems Venus and Adonis and Rape of Lucrece, which he is thought to have helped publish, spells his name 'Shakespeare' ('s' written in a stylized swooping way) (see below). The title page of the First Folio (see above) in 1623, edited by Shakespeare's acting colleagues and fellow writer(s) identifies the author of the plays as 'William Shakespeare.'  So major authorized publications of Shakespeare works spanning his working lifetime and recent death spell his name the same: 'Shakespeare'. Why the hell then does the funerary poem on his monument in the Trinity Church spell his name 'Shakspeare'? This is not just an alternate spelling of some word, this is the name of the man being memorialized.

        Robin Williams in her 2006 book 'Sweet Swan of Avon' has addressed the issue of the spelling of Shakespeare's name too. After mentioning the well known fact that all his signatures on legal documents spell his name differently, and none of these spellings is 'Shakspeare', she says in "Yet in all but two printings of every play that beares his name over a 32 year period, the plays were attributed to 'Shakespeare' "(p189). In her notes she identifies the two anomalies as Love's Labor's Lost in 1598 by 'W. 'Shakespere' and King Lear in 1608 by 'William Shak-speare'. I would add that the poems, which Shakespeare supposedly helped publish, also spell his name 'Shakespeare'.

 Spell check
      I did a quick check on William's claim by looking at a bunch of facsimiles title pages (dated prior to first folio) and indeed all that I could find spelled Shakespeare's name in the modern way. The 3rd folio of of 1664 title page has 'Shakespear's', which leaves out the trailing 'e', but this is the possessive form, and of course this is the same portfolio that includes seven new Shakespeare plays, only one of which is now accepted as being by Shakespeare.

  Bottom line
        So bottom line the (so-called) Shakespeare funerary monument in Trinity church in Stratford on Avon appears to celebrate the writing of some clyde named 'Shakspeare', a name which appears in not a single authorized, or unauthorized, contemporary published work of the author we know as 'Shakespeare'.

        The 3rd line has [37 letters characters + 6 spaces], about average for the poem, but its length is shrunk by five merged letter pairs ['th' (3 times), 'me' 'nt']. The 2nd line has [40 letters + 8 spaces] with three merged letter pairs. The 2nd line (loosely speaking) has 7 more characters [3 more letter, 2 more spaces and 2 less merged letters] to fit than the 3rd line, but the typography and spacings of these two lines have been adjusted so that 2nd line comes out only a little longer than the 3rd line, which contains 'Shakspeare'. The typography adjustments can be seen near the ends of the two lines. In the 2nd line 'eath hath plas' containing [12 letters + 2 spaces'] is directly above, and takes up no more length than, 'with whome' containing only [9 letters + 1 space] on the 3rd line. Still even with these adjustments, the 2nd line, is longer than the 3rd line and longer than any other line in the poem.

        The key point, as can clearly be seen below, is that there is easily enough space for 3rd line to have expanded by one character, to have allowed 'Shakspeare' to expand to 'Shakespeare', the spelling used in Shakespeare's poems and the first folio. There is a hole, a blank spot, under the 't' of 'plast'. (And if 'whome' at the end of the line had been spelled 'whom' as in the line above, then the available space An 'e' added to 'Shakspeare' would make the 3rd line just about the same length as the 2nd line. It clearly fits with no adjustments. So where is the 'e'?

        Did the engraver perhaps not know beforehand that the 3rd line would fit and maybe just left out the 'e' as a precaution? Can't he count? The 3rd line contains about 7 less characters than the 2nd line, it's going to be shorter, it is going to fit.

        To be fair I suppose it could be argued that the poem now has a right justification based on couplets. The two lines of the first couplet are slightly longer (by one character) than the four lines of the next two couplets, whose right justification is excellent. And to get the right justification of the last four lines of the poem, the removal of 'e' from Shakespeare in the 3rd line, it could be argued, was required. However, this argument is weakened by the fact that the 1st line looks shorter than the 2nd line, that this couplet is not really right justified. To right justified the first couplet the 1st line would need a fully formed question mark to lengthen it, but pictures only show a rump (or no) question mark at the end of the first line.

Bottom line on missing 'e' in 'Shakspeare'
        There are four possibilities (that I can think of):

                  1) Alternate spelling of Shakespeare's name (I don't believe it, not consistent with his major publications
                                               or virtually any printing of his plays, poems, or legal signatures.
                  2) Local (Stratford) family spelling, or maybe the name on the church records. (maybe)
                  3) Done for aesthetics, to right justify the last four lines (2nd and 3rd couplet pairs). (maybe)
                  4) Done as part of encoding the hidden '34 equidistant space' message (maybe)

        It is certainly true that the presumed message is destroyed if an 'e' is added to 'Shakspeare'. Lost is the strength of the message, both four letter words, 'trust', 'vere', as well as the three letter words 'vow' and 'him' and what Roper reads as Ben Jonson initials, 'I,B'.

        In summary while this is an argument in favor of the hidden message it is not a strong argument. It's true the 3rd line could easily be lengthened to accommodate the extra character by shifting the remaining characters right a little. But to do so without adjusting it typography and spacings of the 3rd line would take away a little from the aesthetic view of the text by messing up the right justification of the 2nd and 3rd couplets. I mean this is a poem intended to go on a plaque on a monument!

        On the other hand if the 2nd line typography could be adjusted so that with seven extra characters it only extends out by one character, couldn't the same type of adjustment easily be done on the 3rd line? Adjust it's typography and spacing to spell Shakespeare's name correctly and still retain the aesthetic right justification. I don't see why not.

        So all in all I take the oddball spelling of Shakespeare's name in the poem ('Shakspeare') as a possible, not so strong, but not too weak (How's that for a hedge!) indication that the poem spellings have been been tweaked to allow it to contain a hidden message. As others have noted, another apparent spelling weirdness in the poem is a repeated word spelled two different ways: 'whom' and whome', but there's a counter argument to saying this is to support the hidden message. 'Whome' is rhymed and visually aligned with 'tombe'.

Old English spelling problem --- Vow vs Vowe
        I was talking about the possible code in the monument text to a friend showing him my page above. He commented that the spelling of the message should be in old english, which hadn't occurred to me, but of course is right. This brings up a problem with the word 'vow' in the message.

        While poking around online looking for original sources I came across the dedication to Shakespeare's first published work the poem Venus and Adonis (1993) for which he is credited with writing the dedication, probably because it is thought he worked with the publisher on publishing the poem, and it is signed my him. What makes it interesting in the context of the message is that the dedication contains the word 'vow' as spelled by Shakespeare, but he spells it 'vowe', not 'vow'! Below is a facsimile of the poem's dedication page. It's clear that the spelling of a large number of the words in the dedication are different from modern spelling. 'vowe' occurs in the 6th line ("and vowe to take aduantage of all idle houres").

        Doing some searching I found a complete facsimile copy of Venus and Adonis at the link below, and it does contain the dedication page above (p79). (A reproduction in facsimile of the first edition, 1593, from the Malone collection in the Bodleian library. Google ebooks)

        http://books.google.com/books?id=9Go3AAAAIAAJ&printsec=frontcover#v=onepage&q&f=false

Spelling footnote
        Spelling of 'aduantage' (above) is interesting. Where we would have a 'v' there is a 'u'. On the other hand in the funerary poem where modern spelling would put a 'u' we nearly always (or always) find a 'v'. (I think I remember seeing this in Ben Franklin's writing too more than 150 years later.) It's but a single example, but it hints that maybe since Shakespeare's time 'u' and 'v' have been reversed in English?

        Yup, in a quick search on a page about Elizabethan spellings I find this, "Couldn't Elizabethans spell properly?" and "Why is there so much confusion with the letters 'u' and 'v' and 'i' and 'j'? (source -- http://www.william-shakespeare.info/william-shakespeare-dictionary-v.htm)

         http://davidroper.eu/Cryptology%2021.10.pdf

        In his paper Roper references two others working on the code. One is Univ of Kansas professor, Albert Bergstahler. The link Roper gives is dead, but I searched out the professor's page on the Univ of Kansas web site. He is a retired emeritus professor of chemistry, and his page does say he has been working on the Shakespeare authorship problem since he retired (1997). The other (Dr. Bruce J. Spittle, New Zealand) has given a reason why the 2nd Latin line might be indented. It is because it has 34 characters says Spittle and Roper a clue that this is the equidistance code spacing.

        However, I counted the char in that line. if you break apart the combined 'AE' into two letters, as the combined 'TH' in the plain text must be broken up, then it contains 35 characters! (update 6/4/11) In an email from Spittle he argues that 'AE' in old english and Latin is really a single character and different from 'TH', which looks to me like a typography thing. This is a technical issue about which I know basically nothing. I have no reason to dispute Spittle's view on this.

Miller's attack
        Here is a link to a recent (2010) 38 page discussion of Roper's cryptographic analysis of the monument poem titled: 'It there a cypher in Shakespeare's Epitaph as claimed by David Roper in his book, Proving Shakespeare (2009)?'.

         http://www.ericmillerworks.com/images/pdf_files/Shak%20Cultural%20Due%20DiligenceAugust.pdf

        Eric Miller (above) here has collected a half dozen or so of early copies of the monument text. They are clearly all the same poem, but in in spelling and word detail they are they all different from each other! Thus they provide no guidance on what the original text detail might have been. But interestingly the last version included in Miller's document (p497 from Life of William Shakespeare by Sir Sidney Lee) is cryptographically identical to the exant monument with one exception that 'sieh' is replaced by 'sith'. Since both have four letters, this only affects one word of the message, the presumed signature of the author 'I,B', which uses the 'i' in sieh.

        Miller's main point of attach on Roper is that in none of the early poems does the word 'sieh' occur. Most have 'sith' (one has 'since'). Roper, perhaps unwisely, emphasized the importance of 'sieh' arguing that it was unusual, a weirdness in the plain text if you will, and thus providing a clue that the text had been 'tweaked' to include a message, here needed to provide the 'i' in 'I, B' (Ben Johnson's initials). But this is one brick in a multi-brick ediface, and with it removed most of the message (So Test him, I vow he is E de Vere....) is still intact.

        Furthermore neither Roper or Miller seems to have noticed what I have noticed. You can still argue that Ben Johnson initials are in the message, because in the center of the text you can find 'B,I', where 'b' ('tombe') is just above 'is' so the 'i' is shared. And 'BI' matches better then 'IB' how Ben Jonson signed his work in the introduction of the First Folio.

        On the absolutely key point of the probability of the message (even if we remove 'I,B') Miller says nothing, begging off saying that he doesn't know enough about cryptography, translation, he doesn't do math.
===========================================================================================================

David Roper on Rollett's sonnet dedication
        I recently came across a short paper on the by David L. Roper (link below image) on the sonnet dedication cryptogram. To be kind I can say in his probability calculations he solved the wrong problem, but my real reaction is Oh My God (as they say in 'Legally Blond' the musical).

        *  Roper claims to have extended Rollett's work by finding a new phrase at x19, but it's formed by moving letters around and flying around the grid picking up single letters. It's not a decode, it's just word play. No one should take this seriously.

        * For some reason Roper rejects one of Rollett's mathematically strongest finds: five letter name 'Henry', clearly relevant as Wriothesley's first name, on x15 grid.

        * Roper's probability calculations are different from Rollett's and totally wrong. Roper includes in his calculations the letter probability for the first letter of a string, but this is incorrect. When calculating if a string can exist anywhere on a grid, the probability of the first letter is unity, because this is where you start. Also Roper doesn't account for the fact that multiple instances of the first letter provide multiple locations where a string might form. And finally he uses the wrong letter statistics, using average English letter statistics instead of letter statistics based on a count of the actual text. These three errors lead Roper to calculate odds that are far too high, and in the case of short strings grossly too high. For example, Roper says the probability of the two letter string 'wr' arising by chance is 1,000 to one, whereas its more like 4 to 1 (or close to 2 to 1 if reading up and down is allowed).

x19 discussion
        Look at the x19 grid below of sonnet dedication. This is the kind of thing in my opinion that turns people off to claims of hidden text in Shakespearean cryptograms. A classic example of 'a bridge too far', of seeing 'way too much'. It's taken from a paper by David Roper on his site (link under image) titled: SHAKE~SPEARES  SONNETS, T(HOMAS)  T(HORPE)'S  ENIGMATIC 'EPIGRAM'. The paper discusses Rollett's decryption work, and then Roper's claimed extension of it.

What?
        Roper reads out from above, by as he admits, "rearranging these words":

                                    TO  VERE,  W.S.,  HIS  EPIGRAM.  W.S.

Give me a break!
        He reads 'ish' (center top, green) as 'his' by moving letters around, but the classic is his reading out the word: 'epigram'! 'Epigram', which he uses in the title of his paper, he gets from: 'pie' (left, green) + 'r' (center, green) + 'amg' (left, green). He admits "questions of authenticity" are raised, but only because it is "split into three parts". But it's much worse than that. Look at what he had done. To get 'epigram' he flips around letters of ''pie' (left) making 'epi', then goes far right for 'g', back to center for 'r', then back far right again for 'am'. This is frankly ridiculous. If you can flip letters around and jump all over the place for single letters, this is not decoding, it's just word play.

       Roper says, "The first major breakthrough into decoding the meaning behind this text (sonnet dedication) was suggested by Dr. John Rollett", implying that his (claim to) finding a phrase containing 'epigram' at x19 is another breakthrough?

Roper on 'Henry'
        Roper mentions briefly Rollett finding 'wriothesley' at x18, but for some reason rejects Rollett's finding of 'henry' at x15. He says, "There are no grounds for concluding that its ('henry') appearance on another grille was the result of a deliberate act on his (Thorp's) part."  But 'henry' is a difficult five letter name to make from the 144 letters of the dedication, because there is only one 'y' in the text and only one vowel in the name (1 in 1,000 odds I calculate). So there are 'grounds', mathematical grounds. I agree with Rollett that having one of the handful of five letter name-words that pop up (considering all possible grids) be Wriothesley's first name, Henry, is striking, and the math confirms it very unlikely to occur by chance.

Roper's odds calculation
        My first thoughts on seeing Roper give the probability of 'wr' occurring by chance in the sonnet dedication as 1,000 to 1 was this: Doesn't this guy have any mathematical intuition? Two letter strings in grids are quite likely to occur by chance. And how come he doesn't mention, or explain, why his calculated odds differ so much from Rollett's?

        Trying to figure what he did, I tracked down Roper's reference, which he gives as a paper by Beker and Piper included in a well known book on coding by Simon Singh. Below is the relevant page from Singh's book giving the Beker and Piper's letter frequency data. Sure enough if you multiply the numbers from this table for 'w' and 'r', you get [0.023 (w) x 0.06 (r) = 0.00138], which rounds to 1000 to 1, so this must be the source of Roper 'wr' odds.

Roper's reference: English letter frequencies in general usage
[.023 (w) x .06 (r) = .00138] or about 1,000 to 1

source --- Beker and Piper table from 'The Code Book,
The Science of Secrecy from Ancient Egypt to Quantum Cryptography'
by Simon Singh, 1999

Errors in Roper's odds calculation
        In doing his 'wr' calculation Roper has made a fundamental error, actually three fundamental errors.

        1) Roper has used letter probabilities for general English usage. Here we have a specific text (sonnet dedication), we can just count the occurrence of its letters. The results for 'w' and 'r' are actually pretty close to the general usage statistics above, 'w' is [(4/144) = 0.028] vs 0.023 (table) and 'r' is [(9/144) = 0.063] vs 0.060 (table).

        The question on the table here is what are the odds than a 'wr' (one or more) will appear by chance in a grid of the sonnet dedication text? What are the odds we will find (at least one) 'w' somewhere in a grid? It is unity. We have counted and know there are four 'w's in the dedication text, so it is 100% certain we fill find four 'w's somewhere on each grid. The calculation we want to make is what are the odds that in the specific locations adjacent to 'w's an 'r' might appear by chance.

        2) The biggest error Roper makes is that only one letter probability is involved not two. A point Rollett in his 1999 paper makes crystal clear. We are asking what are the odds that adjacent to a 'w' we know is there (unity odds) will be an 'r'? Only the probability of 'r' counts in the calculation associated with each 'w', and there there are multiple occurrences of 'w' that lowers the odds further.

        3) Multiple occurrences not accounted for. Another major factor Roper misses is that there are multiple possibilities to form a 'wr' on each grid because there are because there are multiple occurrences of the starting letter 'w'. With four 'w's there are four times more locations where we can have an adjacent 'r'.

        Roper quotes odds of 1,000 to 1 for the two letter string 'wr'. This would be the answer if the problem was the following: Point at a random letter in a random text and ask what is the probability it's a 'w' (2.3% from average English usage tables), then what is probability the following letter is an 'r' (6%). Multiply these to get the probability for the two letter string 'wr' (0.14%), which rounded is odds of 1,000 to 1. But the problem at hand differs from this in three significant ways:

        1) We have not a random text, but a known text. Letter probabilities are arrived at by counting. Four 'w' and nine 'r' in a text of 144 letters yields letter probabilities of 2.8% for 'w' and 6.3% for 'r'. (For these two letters the results are quite close to general usage statistics, but this would not always be the case in a text so short.)

        2) We do not start at a random letter, but at the first 'w'. It must be somewhere on the x18 grid because it is in the text, so the probability of a 'w' is not .023, it is 1. The locations ('r') is now defined as it is adjacent to a 'w', so for 'r' probability we use its count statistics (6.3%).

        3) There are multiple instances of 'w', a fact which Roper ignores. With four 'w's' in the text there are four more locations where an adjacent 'r' might pop up to form an 'wr' string, hence (to the first order) the 6.3% probability rises to about 25% for reading only down (approaching 50% for reading up and down). A far cry from Roper's 1,000 to 1 odds.

Or maybe?
        It's hard to understand how Roper doesn't see that the probability assigned to the first letter of a string on a grid should be unity, especially when Rollett clearly shows this, or that multiple occurrences of the first letter to be accounted for. Is Roper really this bad of a mathematician? Or is possible that Roper understands perfectly well what he is doing and is trying to deceive the reader with inflated odds?
===========================================================================================================

One way to spell 'Henry Wriothesley'?
        Yikes, it seems nothing in Shakespeare is ever simple. Nearly every literary reference spells Southampton's name 'Henry Wriothesley", but looking at some facsimiles of the dedications of the two Shakepeare poems I noticed these alternate spellings: 'Henrie', 'Wriotheslie' and 'Wriothesly'.  However, the first editions of the two Shakespeare poems that precede the 1609 sonnet dedication the spelling of Southampton's name is

                   Venus and Adonis 1593                Henrie Wriothesley
                   Rape of Lucrece 1594                  Henry  Wriothesley

        These poems are the first two published works of Shakespeare. Shakespeare is thought to have been involved in their publishing, and these two dedications are signed by Shakespeare. Yet we find that the spelling of the earl to whom the poems are dedicated is spelled differently ('Henry' and 'Henrie') most likely by Shakespeare himself. The conclusion I draw is that either spelling of his first name is acceptable for the Earl of Southampton. Good news is that the spelling of his last name is the same in both dedications.

        Below are a few early facsimiles and later editions showing how Henry Wriothesley's name was spelled. Notice the Scottish 1627 edition of Venus and Adonis, though nearly identical in spelling to the 1593 first printing, has changed the spelling of 'Henrie' to 'Henry'. Possibly an indication that 'Henry' is, or has become, the preferred spelling of Wriothesley first name, or certainly that 'Henrie' and 'Henry' are both acceptable spellings.

        I read that others have looked at the monument poem at spacings other than x34 and report seeing little of interest, but to form my own judgment about the likelihood of the purported hidden message it was important that I do a bunch of cases myself. I did it manually for ten different spacings (32 to 40, and 17), by writing out the 220 poem letters on graph paper. I then read through (vertically of course) looking for words.

Signal-to-noise
       I am an EE engineer and was trained in the mathematics of noise. Also I did analog circuit design for forty years, so I have some feeling for signal-to-noise ratio. By doing ten cases I hoped to get a feeling for the signal-to-noise, or in other words how much does spacing x34 stand out from the other spacings.

        What I found was in terms of simple word count, meaning the number of 3 and 4 letter words, the signal-to-noise is fairly low. Spacing 34 does stand above the background, but barely with only a couple of more 4 and 3 letter words than other spacings: two (or three) four letter words vs one for several other spacings and ten 3 letter words vs eight for another spacing. In toto spacing 34 has 12 yellow marking vs 7 and 8 yellow marking for two other spacings. It's higher, but not so high that it really jumps out. (More on this below)

Bullseye on barn door problem
        The big problem in assessing the likelihood of a hidden message is fooling yourself.  It is so easy to select or adjust a target to agree with data already in hand. A classic case of this is first firing bullets at a barn door and then painting a target on the door centered where the hits are concentrated. This problem is also rife in large scale medical studies where unlooked for, often surprising, correlations are found. For a long time these correlations (possible cause and effect) have been had been taken seriously, but more and more doctors are coming to understand the probability of such correlations arising in a large study is quite high. My understanding is that a quality large medical studies must specify in advance what is being examined and what correlations are to be looked for, other correlations that may be visible in the data are now disregarded, because the probability is too high that they are statistical flukes, or noise.

        So trying my best to not bias the result, below I treat 34 spacing like all the other spacings. I do not mark out the supposed message on the 34 chart.

So what's the result?
         Well in the ten trials no five or more letter words were found and relatively few four letter words. In six of ten trials the longest word has three letters. In the other four trials six four letter words were found: hale, tide, stem, shim, test, Vere. Three of these ['shim', 'test', 'Vere'] come from trial 34, while ['hale', 'tide', or 'stem'] each arise in a different trial. The (after the fact) key word is, of course, is the (proper) name 'Vere', father-in-law of one of the dedicatees of the first folio, and in the 20th century considered as a major candidate to have written some (or all) of Shakespeare's plays and poems.

'Vere' and 'test' with clusters
        The case for trial 34 strengthens when a 2nd four letter word, 'test' can be woven in. It strengthens more when two and three letter words adjacent to these two four letter words can be woven in

    Roper calls these adjacent word groupsclusters, and they do look unlikely. Below I do a little cluster math.

       The case for trial 34 is again strengthen when it is found that between these two clusters relevant shorter (fill) words can be woven in ['is', 'vow', he'], and we can add in the common 'i' too that precedes 'vow', giving what can be read as a simple, fairly grammatical message below: (Note, use of 'vow' here is a little suspect, since Shakespeare in his introduction to his early poem spells this word 'vowe')

        There is another way to group the above words, which I did not see at first. Three of the four fill words  ['he', 'i', 'vow'] are in fact adjacent to the first cluster and can be grouped with it. ( 'h' of 'he' is to the right of the last 't' in 'test' and to the right ot 't' is 'w' in 'i, vow'.) With this grouping the first cluster is not as compact, but still since all the words are in successive columns and partly adjacent to each other, it is a cluster, if a somewhat extended and dangly one.  With some of the fill words regrouped and attached to the first cluster it's the same message, but it gives at least the appearance of it being less likely a chance occurrence

                                                            {'him', 'so', 'test', 'he', 'i', 'vow'}   ['is']     {'E', 'Vere', 'de'}
or
                                                            HIM SO TEST, HE I VOW IS E VERE DE

Reduced message
        Above is the  (raw) hidden message I find with spacing 34. The other elaborations of Roper I find much less convincing. For example his including horizontal 'Shakspeare' as part of the message,  and then sort of gluing it in with 'as' and 'he'. I reject this as falling into the category of likely to be fooling yourself. The vertical coding rule is being broken, it seems to me, just because it seems to improve the message. Same with some two letter combination 'I, 'B', which are considered to be Ben Jonson's initials written reversed. I reject this too.

        I think of above as a reduced (possible) hidden  message in the poem, in contrast with the much longer, and detailed and more grammatical message that Roper manages to pull out of the funerary poem. This reduced message is as far as I want to go personally in identifying a (possible) message in the poem. No bending the rules to include a horizontal 'Shakspeare', no rearrangement of the words to improve the grammar, no signature, or at least what Roper identifies as a signature ('I, B' for Ben Jonson). Still the 'reduced message' does look like a message, is fairly grammatical, fairly compact, and is clearly relevant to the authorship of Shakespeare's literary cannon.

Marie Merkel
       After I finished, I found a 2009 posting (below) by Marie Merkel in a forum on an Oxford site discussing Roper's book. She like me decided to independently check Roper, to see what pops up with different spacings, and at x34 she reads out exactly the same 'hidden' (reduced) message I find, dropping the final cluster and 'signature', giving it as:

                                      Him so test, he, I vow, is.... (tin) E Vere de (tin, hot)

         http://edwardoxenford.org/forum/index.php?action=printpage;topic=29.0

Actually, if I include all the three and four letter words at x34 (the 'noise'), I get quite a few more small words than Merkel:

                                (pit) (s)Him so test, (t)he I vow, is (tin) E Vere de (tin, hot, set, ham, are)

So what are the odds?
        This reminds me of figuring the odds of life in the galaxy using the Drake equation. While some numbers in the Drake equation can reasonably be estimated, they are swamped by others that are nothing but wild guesses. Same here with the message. We can made a rough estimate the the odds of two four letter words, the odds that shorter words will cluster with them, but these numbers are swamped by the odds of the message will be (reasonably) grammatical and (big one!) relevant either to the text of the poem or the purpose of the monument. I see no way to put a number on the latter, it can only be guessed at.

Odds of two four letter words
        The hidden message is anchored (so to speak) by two four letter words: 'test' and 'vere'. Arguably 'vere' is the key word, and of course it's not really a word, but a proper name. In the 10 spacings I wrote out I found 6 four letter words. So what are the odds that 2 four letter words will appear at one spacing? Actually it's pretty high:

                                    (6/10)^2 = 0.36

Clustering
        Here is an engineer's back of the envelope of clustering. I count 20 short (two and three letter) words at x34 spacing. The odds a short word appearing either in the column before or after each four letter words is very high (83%):

                                        [1 - (14/34)^2] = 0.83

The clustering we see in the message shows this has happened four times

                                        (0.83)^4 = 0.47

Including 'so', 'i' and 'e'

       Above ignored 'so', 'i', e which are in same column as another word. How much do adding them in affect the clustering? Actually they have relatively little impact. There are so many short words (more than 20 if one letter words are included) that the chance of one of them appearing in one of the six columns of the two clusters is about 99.5%, ignoring that less letters are available, so if we allow for this maybe its 96% to 98%. This happens three times so adding in the same column words ('so', 'i', 'e') adds a multiplier of 0.88 to 0.94. Even if we take the lower bound (88%), our clustering probability is reduced only a little

                                    0.47 x 0.88 = 0.41

        Above shows that the odds that six of the 20+ shorter words on x34 will cluster with one of the two four letter words is surprisingly high, approx 0.43.

Message structure --- two four letter words with clustering
        The odds that we would see two four letter words with the shorter words we see adjacent to them forming two clusters? This is the product of the probability above (probability of two four letter words x probability of six shorter words adjoining to form clusters).

                                0.36 x 0.41 = 0.15

        So the odds of the (raw) format or structure of the message we see, meaning two clusters each built around a four letter word, is roughly 15%, or one in six to seven. The chance of the raw message format appearing by chance is actually quite likely, one in six to seven, so in and of itself it means little.

Odds of grammatical and relevant?
        Now we arrive at the key question, What is the probability that such seven short words cluster around two four letter and together with a single short word between them form a 'message', something that is quasi-grammatical and more important that is related to the poem and relevant to the monument?  I have no idea how to calculate this, and furthermore I doubt it is possible to do so.

                                                            HIM SO TEST, HE I VOW IS E VERE DE
                                                {'him', 'so', 'test', 'he', 'i', 'vow'}   ['is']     {'E', 'Vere', 'de'}

        It is like in the Drake equation where some terms, like the 'probability of life arising on an otherwise suitable planet, must simply be guessed at, and guesses range from 1 to infinitesimally small.

Conclusion
       Just a plain reading (without Roper's tweaks and polishing) gives a fairly cogent, grammatical and relevant message. Written strictly in order with only normal english spacing and punctuation

                                                            HIM SO TEST, HE I VOW IS E VERE DE
or
                                                             Him so test, he I vow is E Vere de.

        My (seat of the pants) guess here is that the probability that 24 of the 220 letters of the poem (11% of all its letters) can be shaped into ten words forming a quasi-grammatical long string that reads as a message relevant to the poem and monument is pretty damn low. Odds? Who know, but I would guess, maybe less than 1% or 0.1%. Combining these 'make sense' odds with the word format odds (0.15) calculated above reduces the probability by another order of magnitude to 0.1% to 0.01%, or one part in a thousand to ten thousand.

        It does appear to me, as someone who has worked with numbers all his life as an engineer, that the likelihood of this being random, not deliberately inserted, is highly unlikely.

        Also important is that nothing even remotely similar turned up in the other nine trial spacings I ran.

        Also important is the the plain text of the poem has a weird, but suggestive hook that there might be more to the poem than meets the eye, saying "Read if thov canst'.

        Also important is that there are multiple hints that x34 spacing should be examined. x34 is twice x17 and Vere in the message is the 17th Earl of Oxford. And as Dr. Bruce Spittle has pointed out only one line on the monument is indented and that line has x34 characters. Well sort of, the line has 34 letters if its 'AE' is not expanded. Finally x34 is close to the average number of letters per line (36 2/3) for a poem that on the monument is quite even and rectangular.

        Also suspicious is that the spelling of some words in the plain text appear to have been tweaked for no obvious reason. For example Ben Jonson's poem in the First Folio (see above) contains the words 'writ' and 'wit', but in the monument poem the same two words are spelled 'writt' and 'witt'. The extra 't' in writt is needed to supply the last letter in 'vere', probably its most important word in the message. (The extra 't' is 'witt" may be explained by the fact that it provides a better visual rhyme with 'writt'.)

        Another possible spelling adjustment is the word 'whom', which is spelled differently in its two appearances in the poem, on line 2 spelled 'whom' and on line 3 spelled 'whome'. (A possible non-message reason for the 'whom' spelling difference may be that 'e' was left off 'whome' in line 2 to shorten it, because this line is the longest and most crowded line in the poem.)

        Look at the spelling 'Shakspeare' on line three of the poem. As I show elsewhere, the missing 'e' after 'k' would easily fit on this line. This oddball spelling of Shakepeare is necessary for the message to appear, but it differs from the spelling on nearly all his published works. The nearly contemporaneous first folio and all quartros of the plays and poems (with two exceptions) spell the author 'Shakespeare'. Aside from this being another suspicious spelling tweak in the poem, might it also have been needed for the local town folk who did not identify this town resident as the author of the plays and poems?

When I add it all up, I think the hidden message is for real!

If real, what does it mean?
        First what is meant by real? I see only two possibilities. Any message being now read out, be it my more conservative reduced message or Roper's longer more elaborate message, is either random or it isn't. That is, it is either a product of pure chance or it has been crafted deliberately into the poem. Black or white, no in-between here.

Joke or clue to 'real Shakespeare?
        Suppose we grant that it is real, that the encrypted message has been deliberately inserted into the monument poem in the early 1600's. Does that mean deVere is the author of Shakespeare's works? Absolutely not! All we know is the poem author said this. Maybe he was prankster, maybe it is just a joke. The author of the poem might have doubled over laughing when he thought about what people in the future would think if/when this was found. But, on the other hand, it might not be a joke, it might be a clue that Shakespeare is not the author. Unfortunately, I don't see how we divine the intention of the author.

Is 'V' in Vere really 'v' in the plain text?
        Obviously the key word in the supposedly hidden Vere message is 'Vere, but notice that the first 'v' in 'Vere' comes from the 'v' in 'monvment'. This looks like a weakness, or a possible weakness, to me in the hidden message theory. Elizabethian printing and/or spelling seems to (often) reverse 'v' and 'u'. I had noted this earlier in this essay before I noticed the source of the 'v' in Vere. So is the 'v' in 'monvment' really a 'v' or is the printed 'v' here to be read as a 'u', consistent with the modern spelling?

        The 'v' in 'vow' has the same problem, in spades. Here the 'v' comes from 'qvick'. The letter following 'q' (at least in modern usage) is nearly always a 'u', so is that the case here too? Darn if I know, I'm not a scholar of Elizabethian spelling and typography. But it raises and important question (Is the 'v' in 'monvment' really a 'v'?), which if answered in the negative, could doom the hidden message theory!

        On a scholarly Hamlet site I found a Hamlet concordance, allowing searches for alternate spellings in four versions of Hamlet (three quartros and the first folio). Here is the result of a search for 'mon.ment' that would find 'monument' and 'monvment'.

        The search result (above) gives up some perspective on the interchangability of  'u' and 'v'.  In quatro 6 of Hamlet we find the spelling 'grave' and 'living', but in quatro 2 and first folio of Hamlet we find the spelling in the same line to be  'graue' and 'liuing'. However, in all three versions of Hamlet in which the word 'monument' is found, we find it is spelled with a  'u',  not a 'v' as it is in the funerary poem. A search for 'vow.' finds the spelling 'vow' (like in the hidden message) and 'vowe' (like in Shakespeare's dedication to Venus and Adonis). Notice above that 'hour' sometimes is spelled with a trailing 'e' and sometimes not.

Hidden messages in Shakespeare's time
        First what are the odds that a hidden message might be there? Equidistant coding goes back to antiquity. The book 'Code' discuss battle field coding in antiquity that wrote messages on long strips used wooden encoding and decoding rods of the same diameter. This was a form of equidistant coding.

        Encoding and word play was popular in Shakespeare's time. Bacon, a contemporary of Shakespeare, and was well known for his 'Bacon Cipher' on which there is even a Wikipedia article. Galileo, another contemporary of Shakespeare, is known to have used anagrams (rearrangement of letters) to claim priority for his astronomical discoveries (rings of Saturn and phases of Venus), as did Newton later in the century.
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Ten monument decode trials
        Here are ten trials of the Shakespeare monument poem I did at spacing of x32 to x40 plus x17 with the longer words I found marked. Procedure: The 220 letter monument poem is written out by hand in rectangular form on graph paper, with horizontal widths 32 to 40, and then read vertically (here only downward). This reveals any text hidden at this equidistant spacing.

Summary word count
             Five letter words                    0
             Four letter words                   6
            Three letter words                49

===========================================================================================================

Notes on Latin lines of Shakespeare funerary monument text

Loose translation
        1st:        In judgement Pylian (a wise king), in genius Socrates, in art Virgil (Publius Vergilius Maro, author of the poem Aeneid)
        2nd:       Earth covers, people mourn, Olympus holds

       2nd line has a very curious phase -- Olympus (a greek god) possess him.  ---- This is in a church, a curious way to say heaven!

Whoops --- below is wrong. The first Latin word in the monument photo does look like 'Iydicio', but I now see that the 2nd letter is a 'v'. What I thought was a tail (making it a 'y'), is just the serif on the capital 'T' below it reaching up and (by accident) perfectly aligning with it.

       There is also an oddity in the spelling of the first Latin word. The spelling on the monument is 'Iydicio', but this word does not appear in Latin dictionaries. The church 1825 version (very close to the current monument in most details) spells it 'Iudicio', and this word does appear in Latin dictionaries, meaning judgement. The interchange of 'v' and 'u' is common, but here we see 'y' used for 'u'. Weird.

        'Ætatis 53' in the bottom line means 'age 53' (spelled in Latin dictionaires as 'aetatis').

'Æ' of the 2nd Latin line
       It is claimed by Roper and Spittle that the 2nd Latin line hints that 34 is a decoding key for the cryptogram in the English poem below. I grant the indent is quite odd. This is a engraved stone plaque and for both size and appearance reasons it is desirable for all the lines of text to be about the same length, but the indent of the 2nd Latin line makes its right end project out further than all the other lines by about two characters. Quite odd.

Is Æ one character or two?
        Whether the indent of the 2nd Latin line is a hint, or not, to the decoding key for the monument cryptogram hinges on whether in Latin Æ is one character or two. For the line to have 34 characters and be a hint Æ must be counted as a single character. If it is a ligature (see definition below) or a scribal abbreviation, then it is really two characters that are merged as a typographic or writing convenience. If you look at the pictures of the monument English poem, you will see it full of combined letters, which I would characterize as the engraving equivalent of 'scribal abbreviations', and all these must be expanded into separate letters for the hidden message to appear. So the question on the table is should Æ be expanded too?

        Dr. Bruce Spittle of New Zealand, who first suggested the indent is a hint, says Æ is one character in Latin. Wikipedia says Æ is one character is old English (and a few other old langurages), but in Medieval Latin it was not one character, it was (or could be) a ligature, (two characters cast together for typographic reasons). Neither the modern, nor earlier versions, of the Latin alphabet show Æ as a letter. A Latin dictionary indicates an internal 'e' is sometime rendered 'ae'. So does this support Spittle, is it saying 'ae' is like an 'e', one character, or is it an alternate spelling?

        I have no idea who is right, it's a very complex topic, but it seems to me that Wikipedia's suggestion that in Medieval Latin Æ is an optional ligature does introduces some doubt into the 34 letter count for the 2nd Latin line.
-----------------------
        * Dr. Bruce Spittle of New Zealand, who first suggested the letter count of the indented 2nd Latin line was a hint to the decode key, was asked about Æ and here is his reply (via email):

        "I don't see a particular problem about counting the Latin character, a ligature, Æ as one character to reach a total of 34 Latin characters in the second line in Latin of the inscription. The Shorter Oxford English Dictionary notes that Æ in old English was a simple vowel intermediate between a and e. It was a single character in contrast to a digraph such as ae in which two letters are used to represent a sound. Similarly in Latin Æ was a single character. When Anglicized in it written as a digraph ae. However when counting the Latin characters in the second line it is not necessary to Anglicize the line and the proper count of the Latin characters in the line is, in my opinion, 34 rather than 35."

Wikipedia shows 'ae' in Latin was prior to 5th century AD represented a diphthong.

** Æ comes from Medieval Latin, where it was an optional ligature in some words, for example, "Æneas" (see Wiki, 'Aeneas'). It is still found as a variant in English and French, but the trend has recently been towards printing the A and E separately. Ref: The Chicago Manual of Style, 14th Ed. Chicago: The University of Chicago Press. 1993. pp. 6.61.

        In Old English (Danish, Norwegian, and Icelandic languages) the character Æ is not a typographic ligature. It is a distinct letter—a vowel. In modern English orthography Æ is not considered an independent letter but a spelling variant, for example: "encyclopædia" versus "encyclopaedia" or "encyclopedia".

        scribal abreviation --- Medieval scribes, writing in Latin, increased writing speed by combining characters and by introduction of scribal abbreviation. For example, in blackletter, letters with right-facing bowls (b, o, and p) and those with left-facing bowls (c, e, o, d, g and q) were written with the facing edges of the bowls superimposed. In many script forms characters such as h, m, and n had their vertical strokes superimposed. Manuscripts in the fourteenth century employed hundreds of such abbreviations.

        digraph -- a pair of characters used to write one phoneme (distinct sound).

       diphthong -- literally "two sounds"), also known as a gliding vowel, refers to two adjacent vowel sounds occurring within the same syllable. Diphthong ae is usually collapsed and simply written as e (or e caudata, ?); for example, puellae might be written puelle

http://en.wikipedia.org/wiki/Typographic_ligature

1) What 'Æ' doing in the 2nd line? If this is supposed to be a hint, why complicate it with an ambiguous letter combination?

2) Wikipedia writes phrase containing 'Æ' as "POPULUS MAERET" (note 'Æ' is expanded into two letters) with a translation "the people mourn him"  A check of Latin/English dictionaries for the verb 'mourning' yields 'maeror' or 'meror'. (I am far too rusty in my HS Latin to remember what the ending 'et' means, but I see 'videt means 'he sees'.)

** In 39,000 word Latin dictionary both 'maeror' or 'meror' have the same english definition. With this note: An internal 'e' might be rendered by 'ae'. Does this tend to confirm Spittle statement that Æ is one character (effectively) in Latin?

maeret --- mourn
meret --- soldiers pay/whore pay  (totally different)
maret --- no entry  (spelling in Dugdale. In 1721 Verdue it is mÆret!) ** It does look like Hollar-Dugdale is probably wrong here!
mourn (english) --- maereo, maerere (base words)
cover --- tego, tegere (base words) tegit on monument
http://www.archives.nd.edu/cgi-bin/words.exe?meror

3) A long online history of the Latin alphabet (link below) shows Latin evolved from 21 letters at the beginning, long before the Roman Empire, to 23 in the days of the Roman empire, to in the middle ages 25 as 'i' split into ('i','j') and v' split into ('v', 'u'). At this point its 25 letter alphabet was the same as present English alphabet, except no 'w'. By the end of 15th century (Shakespeare's time) the Latin alphabet letter count was up to 26 with the addition of 'w'.

        http://www.orbilat.com/Languages/Latin/Grammar/Latin-Alphabet.html

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In 1631, a year before his death, John Weever published the massive Ancient Funerall Monuments, which recorded many inscriptions from monuments around England, particularly in Canterbury, Rochester, London, and Norwich. Shakespeare's monument does not appear in the published book, but two of Weever's notebooks, containing his drafts for most of the book as well as many unpublished notes, survive as Society of Antiquaries MSS. 127 and 128. In one of these notebooks, under the heading "Stratford upon Avon," Weever recorded the poems from Shakespeare's monument and his gravestone, as follows:

  Iudcio Pilum, Genio Socratem, Arte Maronem
    Terra tegit, populus maeret, Olympus habet.

  Stay Passenger, why goest thou by so fast
  Read if your canst whome envious death hath plac'd
  Within this monument Shakespeare with whome
  Quick Nature dy'd whose name doth deck his Tombe
  far more then cost, sith all yt hee hath writt
  Leaves living Art but page to serve his witt.

   ob Ano doi 1616 AEtat. 53. 24 die April

http://shakespeareauthorship.com/monrefs.html

Four old versions of the monument poem: 1631, 1656, 1721, 1825
        With some sleuthing I found four (very) old versions of the monument poem: 1631, 1656, 1721, and 1825. I am informed by Prof Burgstahler that the graphic images used by Roper, same as the current plaque, come from an 1880's book. The oldest, says a Shakespeare authorship site,  was found in a notebook of Weever, who published a book on English monuments in 1631, and who died the following year. A few years later is an engraving for Dugdale's 1656 book on monuments of rural England drawn by his engraver Hollar. One reference dates Dugdale's monument original sketches to 1634. Next was drawn by Vertue for the 1721 Pope edition of Shakespeare's works. The last from a publication of 1825.

--------------
1631 version by Weever
        At the Shakepeare authorship site below I found a very early reference (1631) to the monument showing its text. The claim is this comes not from a published book, but from exant notebooks of an author who published on English monuments. I copied the relevant sections.

http://shakespeareauthorship.com/monrefs.html

(from above)
        "In 1631, a year before his death, John Weever published the massive Ancient Funerall Monuments, which recorded many inscriptions from monuments around England, particularly in Canterbury, Rochester, London, and Norwich. Shakespeare's monument does not appear in the published book, but two of Weever's notebooks, containing his drafts for most of the book as well as many unpublished notes, survive as Society of Antiquaries MSS. 127 and 128. In one of these notebooks, under the heading "Stratford upon Avon," Weever recorded the poems from Shakespeare's monument and his gravestone, as follows:

  Iudcio Pilum, Genio Socratem, Arte Maronem
    Terra tegit, populus maeret, Olympus habet.

  Stay Passenger, why goest thou by so fast
  Read if your canst whome envious death hath plac'd
  Within this monument Shakespeare with whome
  Quick Nature dy'd whose name doth deck his Tombe
  far more then cost, sith all yt hee hath writt
  Leaves living Art but page to serve his witt.

   ob Ano doi 1616 AEtat. 53. 24 die April"

Below is a close up of the monument poem from the above Hollar/Dugdale engraving image.

        Hard to read word: 1st line, 'so?', looks like 'soe'
                                         3rd line, superscript on 'W' is probably 'th', but hard to read
                                         5th line, 'si?h', could be 'sieh' or 'sith'

        Punctuation hard to read: 1st line, probably a comma after 'Stay'
                                                    4th line, might be a comma after 'dyed'
                                                    6th line, unclear if there is a comma or period (or nothing) after 'witt'

And not quite as old, this .... Vertue/Pope 1721
        I stumbled across below in the huge Folger Shapespeare online image archive, which popped up accidentially when searching 'Droeshout', the engraver of the Shapespeare image in the First Folio. The Folger description is that its one of three images pasted into a (rare) 1609 edition of Shakespeare sonnets. It is labeled 'Shakespeare memorial? , so it is probably old, but there is no date and no engraver (see below). This is close up of the whole monument image posted above with the other full monument images.

'Ingenio Pylium, Genio Socrates, arte Maronem,
Terra Tegit, Populus Maeret, Olympus Habet.
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Curious changes
       What is really curious with Vertue is all the changes from the standard poem. There are other versions of the poem floating around with small changes, but this has much more than I have seen. This could be very old. Is it possible that this is a sketch for the monument before it was built?  Is it possible that this was the early draft poem later modified to encrypt a hidden message? (see below)

        Even the Latin is changed! Notice the first word here is 'Ingenio', whereas it is 'Ivdicio' (Iudicio) on the present day monument. All the other Latin is the same, there is even a (small) indent in the 2nd Latin line. I went into a Latin dictionary and found that these are two different Latin words, yet both work!

                                    judgment, decision, opinion, trial  : iudicium
                                    innate character, talent, nature  : ingenium

 http://www.thebookmarkshop.com/latin/latindictionary2.htm

The Wikipedia translation of the Latin lines is

        "A Pylian in judgement, a Socrates in genius, a Maro in art," comparing Shakespeare to Nestor the wise King of Pylus, to the Greek philosopher Socrates, and to the Roman poet Virgil (whose last name, or cognomen was Maro), and the second line reads "The earth buries him, the people mourn him, Olympus possesses him," referring to Mount Olympus, the home of the Greek gods.

        In this 1721 sketch we see the Shakespeare figure with the quill, paper and cushion as in the current monument. Note, same crazy position where pen seems to be writing on the cushion not the paper, which is for some reason under the left hand. His collar is also the same, but the hair is different, here bushy. Note the hair on the older BW figure doesn't seem to be the same as the current moument hair.
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1825 Trinty church history
        Doing some Googling I was surprised to stumble onto a version of the monument poem from 1825 contained in a 26 page history of Trinty Church, apparently put out by the church. In 2006 a copy held by the New York Public Library was digitized by the Google book project. When I found the link to this booklet, I was inside and able to page through, and I screen captured the monument text it contained (below). However, I did not capure that link, and when I searched out its title I get lots of hits, but I am unable to search inside. Hence the 1825 text below may be a new (and rare) find in the monument poem history.

A search for the title of this book brings up a lot of hits and one of them must open, I just don't know which one.

Four poem versions compared line by line
        Below line by line is the current monument wording and punctuation compared with four early versions:
1631 (Weever), 1656 (Hollar/Dugdale), 1721 (Vertue), 1825.

Stay Passenger, why goest thov by so fast?                                                 Current monument (upper case => lower case)
Stay Passenger, why goest thou by so fast                                                   Weever 1631
Stay, passenger why goest thou by soe fast,                                                 Hollar/Dugdale 1656
Stay, Passenger, why dos't thou go so fast?                                                  Vertue 1721
Stay Passenger, why goest thov by so fast,                                                   1825 Trinity church history

Read if thov canst, whom enviovs Death hath plast,
Read if your canst whome envious death hath plac'd                                Ref says 'your', but it looks like a misprint
Read, if thou can'st whom envious death hath plac't
Read, if thou cans't, whom envious Death has plac'd
Read, if thou canst, whom envious death hath plast,

With in this monvment Shakspeare: with whome,
Within this monument Shakespeare with whome
W(th) in this monument Shakspeare with whome
Within this Monument; Shakespear, with whom
Within this monvment, Shakspeare, with whome,

Qvick natvre dide: whose name, doth deck Ys Tombe,
Quick Nature dy'd whose name doth deck his Tombe
Quick nature dyed whose name doth deck the tombe
Quick Nature dy'd, whose Name doth deck the Tomb
Qvick Nature dide: whose name doth deck ys. tombe

Far more, then cost: Sieh all, Yt He hath writt,
far more then cost, sith all yt hee hath writt
Far more then cost, sieh all that he hath writ
Far more than Cost, since all that he has Writ
Far more then cost; sith all yt. he hath writt,

Leaves living art, bvt page, to serve his witt.
Leaves living Art but page to serve his witt.
Leaues living art but page to serue his witt,
Leaves living Art, but Page to serve his Wit.
Leaves living art, bvt page to serve his witt.

Version comments
        All five are different! The 1631, 1656 and 1721 differences kill the Roper's (reduced) hidden message, but the missage does work with the 1825 version, even though it has a few spelling differences.

        The Weever 1631 version is very close to the current monument (accepting 'your' as a misprint for 'thov'), but it wipes out the message by an extra letter in the 2nd line ('whome') and no 'v' in 'monument' wiping out the 'v' need for 'Vere. It differes also in the spelling of Shakespeare with Shake having its 'e',which is missing in the current monument.

        The Hollar (1656) text is also pretty close to the modern monument, however the cryptogram is wiped out because most (not all) 'v's are replaced by 'u's. The 1721 Vertue text is surprisingly modern ('since' for 'sieh', 'than' for 'then', 'within' for 'with in', 'plac'd' for 'plast'). The 1631, 1656, and 1721 versios all spell Shakespeare differently!

        The 1825 version from a 26 page history of the Trinty church supports the hidden message. Only one of its words is different from the current momunment ('sith' for 'sieh'), however, some of the 'v' are replaced by 'u's. Nevertheless, the two 'v's need by the message ('monvment' and 'qvick') are there.

Importance of 1825 version -- 'sith' not 'sieh'
        I think the importance of the 1825 version of the funerary monument text is under appreciated. This version of the poem comes from a booklet written by the pastor of the Trinity church. Unlike earlier versions, which would have been written out by someone likely making a single visit to the church (traveling on horseback), this was produce by men who lived with the monument, and who had the time and means to examine the engraving close up. And the monument at that point would have had only 200 years of wear and tear compared with 400 years today.

         The local churchmen's version is very close to the current engraving, except they write 'sith' not 'sieh', which is found on the current monument. To me this is a strong argument that the original word was 'sith'. It can easily be postulated that wear or damage to the 't' made it hard to read and that in a later restoration, perhaps many years later with no one having memory of the original, it got changed to an 'e'. If the 1825 churchmen got it right, it wipes out Roper's theory about the importance of 'sieh'.

Y superscript abbreviation (update 11/6/11)
        The Stratford monument has two Y superscript (Ys and Yt) abbreviations, and I found another one in the First Folio play 'The Tempest' (Ye). In the Second Folio this 'Ye' is replaced by 'the'.

              Ys => this          'whose name, doth deck Ys tombe'                  'whose name doth deck this tomb' (Wiki, modern)
              Yt => that           'sieh all, Yt he hath writt'                                  'sith all that he hath writ' (Wiki, modern)
              Ye => the           'got by Ye diuell himselfe' (1st Folio)            'got by the divell himselfe' (2nd Folio)

        The pattern seem clear: Y seems to stand for 'th' and the superscript is the next letter or a shorthand for a pair of letters. But look at the five versions of the monument poem above. Three time Ys was written out, and never as 'this', instead its transcribed as 'his', 'the', 'the'. We do not see this weirdness in Yt. It was transcribed twice, both times as 'that'. I don't know what to make of this, but it seems very strange.

        Also worthy of comment is a finding of 'Ye' in a First Folio play. I have found only one in looking at three or four pages of facsimiles. Is 'Ye' Shakespeare's usage or a printer's abbreviation?  The editors of the 2nd Folio removed it.
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Shakespeare monument poem images
        The monument text pictured in Roper's document in its punctuation is slightly different from what I first found (from Peter Farey Marlowe site). What I found looks like a picture, but Roper's has more of an art look. Below I detail the (minor) differences between them, which have no impact on the cryptography. In Miller's document, which has a lot of original source material, there is a photo of the whole monument (text and bust). When this photo is expanded the text and punctuation are quite readable, and it is clear that what I have included in my essay is a close up picture of the actual monument poem.

        The slight difference between the Roper and Farey images of the monument text bother me. It seems like one or both of them have been edited or cleaned up. One or both of them have has been cleaned up. To see if I could clarify the starting point for the decoding I went on a hunt for more images of the monument text images. You would think it would not be that hard to find a high resolution photo of the monument text. However, I am aware that it is so high on the wall that only professional photos of it may exist.

        I downloaded all the images of the monument text I could find online that were different, a half dozen or so, and then ordered them. I find there are five versions of punctuation, which I label versions 1, 1a, 2, 2a, 3. Versions 1 are in the form of graphics. Versions 1a is of a copy of the monument. Versions 2 and 2a are photos of the same monument (in Stratford) that can be identified by the pattern of the marble, However, version 2a looks a little different from version 2, so it must have been taken at a different time. Version 3 is an oddball.

        The monument reportedly was damaged by vandals in the 1970's requiring it to be repaired. In an email to me from Prof Albert Bergstahler says the (graphic) version Roper was using, same as version 1 graphic images (with 'Canst'), was taken from an 1880 book.  This would mean that the BW version 2a photo (with 'Canst') was very likely taken before the 1970's  damage repair, and the version 2 photos (with 'Ganst') were taken after of the 1970's repair reflecting the monument as it is today.

        The text is identical in all of the images I found (for example, 'Sieh', 'writt', 'witt'.) with the exception that the 'C' of 'Canst' looks like a 'G' in version 2 photos.

Version 1
        Colon after 'Dide', small titled question mark after 'Fast', right shifted comma between 'Tegit' and 'Popvlvs', 'Canst'

Another Version 1 (with image reversed)

STAY PASSENGER, WHY GOEST THOV BY SO FAST?
READ IF THOV CANST, WHOM ENVIOVS DEATH HATH PLAST,
WITH IN THIS MONVMENT SHAKSPEARE: WITH WHOME,
QVICK NATVRE DIDE: WHOSE NAME, DOTH DECK YS TOMBE,
FAR MORE, THEN COST: SIEH ALL, YT HE HATH WRITT,
LEAVES LIVING ART, BVT PAGE, TO SERVE HIS WITT.

Version 1a
        Note this is a copy, not the monument at Stratford. It might be at the Shakespeare Folger library.
        It's hard to read, but it appears to be a modified Version 1 text. It's like version 1 in that is probably has Colon after 'Dide', small titled question mark after 'Fast', and 'Canst', but unlike version 1 the comma between 'Tegit' and 'Popvlvs' is not right shifted, it is centered.

        Note above shows Shakespeare with both a mustache and a pointed beard. The mustache is hinted at in the cover engraving of the first folio, and the Cobb portrait shows Shakespeare(?) with a beard.

Version 2 (BW photo)
        No colon after 'Dide', comma after 'Fast', centered comma between 'Tegit' and 'Popvlvs', 'Ganst', no period after 'Habet'

Another version 2 (color photo)

Version 2a
        From the marble pattern this is a photo of the same monument as the two photos above. It's at an angle and at lower resolution, but still some differences from above are visible. Most noticeable is 'Canst' not 'Ganst'. 'He hath' looks a little different from above, but it's possible this is due to lower resolution. There is a distinct 45 degree line (or crack) running through the 'm' in 'tombe' here. Part of this line is weakly visible in the photos above.

Version 3a
        This is identified as a "tracing" of the monument in an 1890 book. It appears to be identical with the B&W photo above.

Version 3b
        If above is a tracing, what is this another tracing? Words and spelling are identical to above, but there are spacing differences in some letters. Note here the '5' in (age) '53 is under 'o' in ano, whereas above '5' is in the space after 'ano'. Also 'v' in 'Ivdicio' and 'v' in 'bvt' are more regular here than above. It's like this tracing was cleaned up.

        Punctuation: Colon after 'Dide', large question mark after 'Fast', centered comma between 'Tegit' and 'Popvlvs', 'Canst', period after 'Habet', no colon after 'Shakspeare'

Color photos of the monument bust
       A 2006 hires color photo of the monument bust (below) on Wikipedia shows no damage to the fingers. This is consistent with the the BW photo above having been taken prior to the 1970's before the monument was repaired.

        A higher resolution 2010 photo (below) of the Trinty church back wall (cropped) by Ell Brown posted on Flickr. It's clear from this photo that the monument text we read has been painted with gold paint. The same paint has been used to paint the columns and other parts of the monument. The painting could explain some of the differences is punctuation, for example, any punctuation mark not painted would be very dark and likely not show in a photo.

        Note also the monument right (not identified by the photographer). This gives some perspective on the Shakespeare monument. For one thing the complete photo shows it is larger than the Shakespeare monument and higher up. It has a plaque beneath the bust too, but because its text, which is barely visible in another photo, has not been painted with gold paint it is all but invisible at this distance. There are other monuments in this church still larger than the Shakespeare too, like the Cloypton? monument, included in the Dugdale book.

Monument image with (reduced) message marked
        Here again is the reduced message on x34 graph grid and below an image of the poem text with the message letters marked in red.

Required and not required
        For the message to appear 'monument' (2nd line) must be spelled 'monvment', because its 'v' provides the 'v' in 'Vere'. In the current monument all modern english 'u' are written as 'v', but this is not the case in many early recorded versions of the poem (1631, 1656) where, for example, you find in the 3rd line 'monument', which kills the message, because the 'v' in 'Vere' is gone. The alternate spelling of 'whome' (3rd line) is required because its 'e' is the 'e' in 'test'. The oddball spelling of 'writt' (vs writ) is required to get the second 'e' in 'Vere'.

        Some controversies I read about make no difference to the decoding: 'sieh' (5th line) or 'sith' both work, and 'dide' (4th line) or 'dyed' both work.

Scribal abbreviations
        I also marked on the poem image in yellow the many (13) combined letters, most doubles but even one triple! In decoding these combined letters are expanded into separate letters. No mystery here as it is clear that this is an engraving convenience, probably done to save space. In typograph joined letters are common with two letters on the same piece of movable type called a ligature (Wikipedia has a whole article on 'Typographic ligature'). Of course the monument is engraved not typeset, so they are more like abbreviations. (I got this idea after reading a Wikipedia article on 'Scribal abbreviations', which says Latin documents copied by scribes in the middle ages are full of combined letter abbreviations like this.)

Five Shakespeare family tombs in Trinity
        Five Shakespeare related gaves stretch out in front of the Trinity church altar (below, also by Ell Brown). Left to write: Ann Shakespeare (Shakespeare's wife, 1623), William Shakespeare (1616), Thomas Nash (first husband of Elizabeth Hall, Shakespeare's granddaughter, 1647), Dr. John Hall (husband of Shakespeare's daughter Susanna, 1635), Susanna Hall (Shakespeare's oldest daughter, 1649). Hard to believe the graves/headstones have not been reconfigured. Church records show it was restored twice in the 1800's. It's more than suspicious that since this church building is really old (parts of it were built 800 years ago) that all (or nearly) all the tombs in front of the altar come from one 33 year period (starting with Shakespeare 1616 to the death of his daughter Susannah in 1649).

        The order of the tombs is odd. Will is the big cheese (or so the Stratfordians claim!) and he dies first, but he is neither in the center of the church, the center of the family group, nor at the end, he is 2nd from left. Where is Judith Shakespeare, Shakespeare's youngest daughter (1662), Elizabeth Hall, Shakespeare's granddaughter (1670), and Shakespeare's sister Joan (1646), who lived in Stratford her whole life and died within the time range of the other tombs, or for that matter her husband who died within a week or two of William in 1616? [Wikipedia says Elizabeth is buried in another church. Judith is buried on the Trinity church grounds, but no one knows where, and where Judith's husband (Thomas Quiney) is buried is totally unknown. Nor is there any mention on Wikipedia of where Joan Shakespeare (Hart) is buried. Also Shakespeare had three surviving brothers (Edmund, Gilbert, and Richard) that died between 1607 and 1613. Where are they?] Is this group here because of their support for the church?

        A panoramic view of the church shows that to the right of these five tombs here is room for one (or maybe two) more, but the tops appear to be plain. Also the tomb in the dead center, arguably the most important spot, 4th of these five Shakespeare family tombs, which is John Hall.

Panoramic view of Trinity Church altar (Aug 2013)
        I stumbled on this wonderful image showing the whole the Trinity Church altar taken with an 8 mm fisheye lens. While a fisheye lens distorts it has the virtue of showing nearly everything. From this photo it is clear that five Shakespeare family graves (above) occupy five of six (possibly seven) tomb spaces in front of the altar. On the wall left is the famous Shakespeare bust one of four on the walls (and there are a couple of more in the back corners of the altar). Another thing is clear from this photo that this church was built when architects had figured out how to make a light filled interior.

Erasmus T's images
       Erasmus T's images on Flickr are quite stunning, he has posted 1,800 images there. While he takes realistic photographs, many of his images of historic English building and countryside, like above, are quite unusual in that he has processed them somehow to get a painter-like look, for example:

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History of the Shakespeare monument
        I first found the discussion of the early history of the monument in the link below quite convincing, but with further work less so. (See my added feather to 1634 sketch in Appendix below.) It's author, Richard J. Kennedy, argues that the image of the monument drawn as drawn in 1634 by Dugdale, which is clearly different from the present monument and famously shows the arms resting (or holding) a woolpack, could very well have been a monument to Shakespeare's father, who was a former town mayor (or equivalent) and is thought to have been a wool merchant (some say a glover).

        http://webpages.charter.net/stairway/WOOLPACKMAN.htm

        An engraving from Dugdale's sketch, which supposedly still exists, was included in Dugdale's large book of monuments published 22 years after the sketch (1656), and the book was reissued in 1730, long after Dugdale's death under another editor with the Shakespeare monument image basically unchanged. A reissue in 1730, more than a century after Shakespeare's death, with monument image unchanged is probably important, because during this time with multiple new Shakespeare folios issued his plays were more widely available and his reputation was growing. Kennedy quotes several observers during this period that confirm Dugdale got it right. The only response from the Stratfordians says Kennedy is that Dugdale got it wrong, but he makes a pretty good case that this is unlikely. Sometime after 1730 the monument figure must have been changed because the man is reportedly now holding a pen.

Wait
        But then I found below, showing the whole monument from Dugdale 1656 book side by side with a BW photo of the monument. What to make of this! Every blooming detail in the Dugdale sketch is totally different from todays monument. There's only two possibilities I can think of. One, the monument at some point was totally changed, not just the bust, but all of it. Or maybe, as sort of indicated by the sketch above left, what Dugdale did is just make a quick sketch of the bust, and he wrote notes that described the (classical) elements surrounding the bust. This would be lot quicker, a lot less work. And might be justified because no one really cares about the outside details. Then later the plate engraver, say working from Dugdale's notes and memory fills in the outside. This latter would explain why the major elements are the same (two top cherubs, dia slash on plaque, top roof, rounded cupola, two columns, rectangular poem below. This is my guess as to how Dugdale worked.

        But the two busts don't look anything alike, even the heads. How the hell is this explained? Was Dugdale who traveled around for 20 years sketching monuments, just completely unable to draw? Doesn't seem likely since portrait painters seemed to be a dime a dozen in the days before photos.

No fame?
       But there is a bigger point here. This sketch sloppiness (if that it is what it is) throws a light on Shakespeare fame, or lack of it, in the years after his death. If he was so famous, why was more care not taken with his monument? It seems to have been treated like any other monument in the book. (Is this book available in facsimile?)

Cushion writing surface?
       The writing surface on the current monument is clearly a cushion or sack. The cushion is lying horizontal with large gold colored tassels at the two front corners. This is an extremely odd writing surface, photos of the monument show it to be rounded and as a cushion you would expect it to be soft. Dugdale had it right, then the cushion we see today may have been the cushion/wool sack that the figure originally held, and only the arms and hands have been changed to hold a quill in the right hand and paper in the left.

        But as usual there is one thing that doesn't quite fit. One of the introductory pieces of the first folio (1623) refers to "thy Stratford moniment". Kennedy has no explanation as to why the first folio would refer to it if it represented Shakespeare's father. Did the first folio writer know this, or did Shakespeare deal in wool too?

Above historic monument image
       Inspection of a hires version of the above image (at link above) shows it is identical to the engraving the British Museum identifies as having been done by George Vertue for the 1721 Pope edition of Shakespeare. When compared to modern photographs of the monument, this engraving in its cushion and body are very close to the photographs. The only significant difference is the engraver has improved Shakespeare's face and hair over the sculpture making his apprearance more realistic (and giving Shakespeare curly hair). It is clear from this dated engraving that the monument has not been reworked since (at least) 1721.
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Woolpack man?
        Below is closeup of 'Woolpack' man from 1656 Hollar/Dugdale sketch/engraving of Shakespeare monument in Trinity church (above). (Idea credit: Richard J. Kennedy for his article 'Woolpack Man')

         http://webpages.charter.net/stairway/WOOLPACKMAN.htm)

Dugdale's 'woolpack' sketch from another perspective
        Below left is what purports to be the original sketch Dugdale made in 1634 of the funerary monument bust. Notice how the hands are held differently than in the engraving published in the Dugdale book 22 years later (above). Center is a photo of the current hands of the monument. Both have one hand higher than the other (though they are reversed). The feather in the monument photo is I read a real feather, and it looks real.

        The 'Declaration of Reasonable Doubt' makes the difference between the 1634 sketch and current mounument bust on of its four major points:

        "The Stratford monument effigy clearly depicts a writer; but it does not look the same as the one erected in the early 1600s. A sketch by a reputable antiquarian in 1634 shows a man with a drooping moustache holding a wool or grain sack, but no pen, no paper, no writing surface as in today's monument. Records show that the monument was "repaired." Apparently the effigy was also altered to depict a writer."

        Suppose Dugdale saw the monuument when it had no feather. If we reverse right and left hands, then the hands of the photo and sketch are reasonably close. Also the cushion is not that different either. OK the cushion in Dugdale's sketch sort of looks like it is standing up, but isn't this just another detail. If I visualize a feather (see below right, I drew it in!) in the sketch's left hand (our right), then I could believe it was a (sloppy) sketch of the current monument (sans feather and maybe sans paper).

        I would go one step further in my speculation. The paper in the current monument is rather odd. It is not being written on, it just sticks out. It looks like he is writing on the cushion! I see the monument bust as being complete without the paper, in fact maybe even better. I would speculate that the paper might be a later addition. Without ever having seen the monument, my guess is that the hands and cushion are very likely separate pieces. It does not look like it would have been very difficult for someone in the last four hundred years improving the monument by making a (thin) paper piece and slipping it in.

Adding a feather
         Dugdale's 'woolpack' sketch from another perspective

        Below left is what purports to be Dugdale's original 1634 sketch and right same image with my drawn in feather. I think the feather goes in very nicely. And with the feather added the Dugdale sketch and the monument look pretty close (except for right left reversal). Mystery solved?

Bottom line --- With my speculation Dugdale sketch become consistent with it being a sketch of the current monument (prehaps sans feather and paper). Dugdale's sketch was showing a writer, not a woolman, his hands in writing position on a four cornered (writing) cushion. (However, the cushion in both cases looks to thick (and soft) to write on.)

Crests on top
        I notice that the crests on the Hollar (1656) and Vertue 1721 sketches are pretty close to each other, even though nothing else is similar, and both are very similar to the current monument. I wonder if in the engraving studio they had access to the Shakespeare crest. Crests after all were granted by the crown (upon payment), so there must have been official records of them. My memory is that John Shakespeare (Shakespeare's father) bought a crest (yup), and this is very likely it.

Sketched from a verbal description?
        The bust sketch is so puzzling. It differs in virtually every way from the modern version. It's not just that Shakespeare looks totally different. The top of the columns here have lions on top, and their tops do not line up with the top of the arch. The crest shares a diagonal line with the modern version, but all the outside scroll work is different. The two angels are in a different place and holding a shovel and hourglass, neither of which is present in the current monument. It's like Hollar never made the trip (on horseback!) to see the monument, but someone described the monument to him and that was the basis for the sketch. For example, I can see Hollar drawing above if he was told: crest is a shield with diagonal pen, above an armor helmet and sitting on the helmet a bird , curculies drape the shield. An angel holds an hourglass.

        Or alternately, rather than doing a finished sketch on site, he did a rough draft of the bust and just made notes about the outside. This would make sense. Later doing the final sketch for publication in the studio, and not remembering the details of the monument and maybe not considering it very important, he worked from his notes.
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Introduction
       In this appendix I preserve my first write up of the monument poem decoding even though my views of it being a cryptogram have changed: going from, 'it very likely is a cryptogram' to 'maybe it's a cryptogram'. The text below was written soon after reading the papers on the subject, so it reflects mostly the pro views of the advocates. But after putting my skeptical hat, researching the monument, digging into the arguments made by the advocates, and doing my own probability calculations, my views shifted. The core problem with the funerary monument is that math only takes you so far. It gives some, limited support to the claims of it being a cryptogram, but far from convincing, and from there it's clues, coincidences and hidden messages the advocates really want to hear. Hardly the basis for certainty.
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Stratford monument poem -- first write up
         Hidden messages generally have a bad reputation. People have pulled a lot of strange, hidden messages from the Bible for example. It turns out that if you are allowed to 'read' a document in many different ways and importantly the document is long, then the probability of finding a few hidden messages is pretty good. But the exception to this rule seems to be a hidden message in the inscription on the Stratford monument (to Shakespeare), which was erected around the time of the first folio in a church at Stratford-upon-Avon and still exists. The inscription is thought to have been written by Ben Jonson. Here is the hidden message David L. Roper has located in the poem:

        "So test him,  I vow he is E. De Vere as he, Shakespeare name, B.I."  or (cleaned up a little) "So Test Him, I Vow He Is De Vere"  (B. I. is thought to refer to Ben Jonson)

        What makes this very interesting is this (says Roper):

1) Inscription on the monument is very short, only 220 letters, and the message uses over 10% of these letters (23 letters)
2) An equidistant code is used and spacing is 34, which is very suggestive since Edward de Vere was the 17th Earl of Oxford.
3) The message is (fairly) grammatical and clearly says 'he is de vere'.
4) The plain text of the inscription seems  a 'little off' as it would be if it was cover text. Furthermore it includes a challenge which (absent a hidden message) seems to make no sense, saying, "Read if thou canst"
5) A confirming message can (with some contortions) be pulled from the plain text. "QVICK NATVRE DIDE" in plain text  => (with some manipulation) 'Sum Vere' in Latin => 'I Am Vere' in English.

         http://www.dlroper.shakespearians.com/content.htm

        New Roper links
                1994 paper        http://174.122.112.226/~rwest/gm2_dr.htm
                 Ray West page links to Roper and Rollett     http://174.122.112.226/~rwest/gm2_rw.htm

Shakespeare funerary monument (update 5/31/2011)
        The link above (to D. L. Roper) is dead. I remember reading a pamphlet many years ago that detailed the decrypting, and I might still have it, but have not searched it out. (Can't find it.) I always wondered if the output was really as clean as the author presented it, so I decided to see for myself if the code below would appear by taking every 34 character.

For more on the poem variants see the appendix
        I downloaded all the poem and monument images available online that had high enough resolution for the text to be readable. I found four or five variants in the punctuation. All have the identical text (SIEH, Writt, Witt, etc) except for one variant where the first letter in 'Canst' sort of like a 'G'. Comparing all the images, several of which are clearly photos of the Stratford monument, I think the 'Ganst' variant (color image above) shows the monument poem as it currently is. What appears to be an older BW photo shows parts of two fingers missing has 'Cant' in the text. I read there was vandal damage to the monument in the 1970's and a subsequent repair, so my guess is that the BW photo shows the poem areal of the monument before the 1970's repair and 'Ganst' variant (color above) shows it after and currently. Luckily none of this affects the search for a message because the word in question was (and is) clearly 'Canst'.

        Just looking at the photo I tried to read out (counting by 34) the (claimed) beginning of the code: 'So test him'.

Several issues immediately arise
        Do you count spaces? Do you count punctuation? How to decode compound letter combinations, like merged 'TH' in 'thou' (1st line) in 'then' (5th line) and 'Ys' (line 4) and 'Yt' (line 5). Do you use the Latin text? The answers I found after a few minutes (getting out 'So test') is don't count spaces or punctuation, consider merged letters as separate letters, and the small letters in Ys and Yt come second. Don't use the Latin text.

        Thinking about what to do next I realized the way to find where the next part of the message was hiding (if it was there!) was to rewrite the message text (without spaces) as lines of 34 characters. 'So test' and any other message phrases encoded in '34 code' would then be visible vertically, and I remembered seeing figures like this in the original pamphlet. Below is my 34 char/line write up. I have put red around the message fragments that have turned up. [No fudging here, this is all the raw poem text (Latin is excluded) from the photo, and agrees with original text on Wikipedia -- 'Shakespeare funerary monument', just rewritten in lines of 34 characters.]

        Well I find the message text is there (sort of) mostly as the author claimed. From left to right:

        * 'So test' is adjacent to 'him'
        * 'He' 'is' ('i' in is is shared with 'BI')
        * 'E Vere' is adjacent to 'De'
        * 'I vov' and this leads immediately to (written horizontally) 'Shakespeare'
        * Linking into Shakespeare from above are 'as' and 'he'
        * 'BI' (supposedly Ben Johnson, the author's, initials) is lower center  ('i' is shared with 'is')

        So with some arm waving I get, reading vertically left to write {compared to what the original author wrote}

              Him, so test, he is E Vere (De), I vov [Shakespeare] as he (B I)
            {So test him,  I vow he is E. De Vere as he, Shakespeare name, B.I.}

A real message?
        So is this a real message or a mixed up mess of short words we are organizing into a coherent message? Who knows. But I will admit (with zero experience ever doing this before) that there are what appears to be some startling relevant quasi-phrases emerging, and emerging is approximately the right order, and especially impressive in that the code is every 34th letter and Edward De Vere was the 17th Earl of Oxford.

        And when I look over all the vowels, I can find relatively few other words in the vertical columns. Here is the complete list (left to right): 'pit', 'hop', 'cess', 'are', 'tin', 'rove', tee', 'set', 'rot', 'ham'.

Confirmed?
        I have not tried, as did the original author, to figure the odds of this, but looking at the relevant phrases with their approximately right ordering vs the few other words that do show up and the huge number of possible short English words, I would have to say, like in 'Myth Busters', that I confirm that this probably is a real encoded De Vere message!
----------------
Roper's '34 char' analysis of the funerary poem (6/2/11)
        While the link above containing 'dlroper' is dead,  'dlroper' appears to refer to someone named David L Roper, and I found his home page, which is active with material dated as recently as 2011 (first two links below). He also has stuff on another URL (dlropershakespearians.com), 3rd link below.

         http://davidroper.eu/
         http://davidroper.eu/Cryptology%2021.10.pdf
         http://www.dlropershakespearians.com
         http://www.dlropershakespearians.com/Inscription%20as%20a%20cryptogram.pdf

        After some poking around on his site, I found his analysis of possible hidden message in Shakespeare's funerary monument poem by taking every 34th char. It's somewhat hidden, embedded in an essay called 'Cryptology'. This is dated 2009, so it cannot be the same document I read many years ago, but I'm pretty sure it's the same basic analysis. Whether this analysis is original to Roper or not I do not know, but I vaguely remember reading years ago him making a point that his contribution was a mathematical analysis of how improbable it was, so it's possible that this decoding of the monument poem may be from the 19th century when the search for hidden codes was popular. (update --- In other of his articles on a different URL he claims to have come up with the idea of applying an equidistant code to the monument text to look for an encrypted message and to have done the work in one evening. I can belief the latter, a few such charts can be made up by hand is a short time and it takes only a couple of minutes to read them.)

David L Roper
       David L. Roper is a character and no way do I identify with him. His web site says he writes on "literature, philosophy, mathematics". Literature and philosophy turns out to mean he writes on Shakespeare and Nostrodamus. He is a follower of Nostradamus, writing a book about him saying he never made a mistake and his predicted dates are "pinpoint" accurate. In his Shakespeare work Roper claims to have definitely solved all the Shakespeare authorship problems!

Two David L. Ropers
        I at first thought Roper had also written a lot of book on religion, but it turns out that a google search for 'David L. Roper' finds two writers with this name and all the religion book are written by the other one. Apparently to differentiate himself from the religion writer our Roper omits the period from his middle initial: 'David L Roper'.

        He also considers himself a mathematician of a high order (though I suspect of the crackpot school), claiming to among other things to have come up with a solution to Fermat's last theorem using only mathematics available to Fermat! He submitted it to a peer review math journal, but it has not been accepted yet, which he puts down to "cognitive dissonance".

        Nevertheless, even with his quirks and frequent smug assertions that he is 100% right, I find his writings on Shakespeare to be interesting and worth reading. He writes well, and in his arguments he often makes a lot of good points. He appears to be a smart, clever guy (no bio, so I have no idea what his background is). His writing spans a wide and unusual range (mathematics, Shakespeare, ? Nostradamus!). One of his books ('Proving Shakespeare', published 2009) is sold on Amazon ($50!), but has no reviews.

Tacking the problem
        To start I applied x34 spacing decoding strictly reading out the raw message with no changes in word order or letter order. This leads to a shortened and somewhat less grammatical message than its advocates see, but (see below) clearly still very interesting and relevant. Below is the (reduced) raw message, with only a comma added, that I am going to examine. With the strict criteria I have used the Ben Jonson's initials that its advocates point to is gone, because to get it they reverse the (I B) letter order.

        Note a shorter message is clearly more likely (actually much more likely) than a longer message to occur by chance, so if the odds of a shorter message being a statistical fluke are found to be small, then the point is made that someone deliberately encoded deVere's name into the monument poem. I venture no opinion about what this might mean as far as who wrote Shakespeare is concerned. My objective is very limited, to just estimate the probability of the text above arising by chance.

Procedure
        First take a guess (I don't see how it can be calculated) that the text above, clearly relevant and quasi-grammatical, could have arisen by chance. I can hear you yelling foul, I am just guessing the answer! Not really, because the strength of the case for the message being real is that are a lot of supporting (auxiliary) probabilities that also need to be factored in. This is things like the message uses more than 10% of the letters of the poem, there are multiple odd spellings of words in the poem like the spelling of Shakespeare as 'Shakspeare' (omitting the center 'e'), the plain text of the poem contains a suggestive hook ('Read if thov canst'), the equidistant spacing of 34 is twice 17 and deVere was the 17th Earl of Oxford, and more.

        Each of these auxiliary probabilities multiplies the original guess and can substantially reduce the final odds. To show the power of this suppose each of four independent probabilities is quite likely, say with a probability of 0.25 (25%). This reduces the guesstimate odds by a factor of 256 since [(0.25)^4 = 1/256]. If the four auxiliary probabilities are each 10%, then the reduction in odds is by a factor of 10,000, since [(0.1)^4 = 1/10,000].

Strength of the argument
        There are so many auxiliary probabilities to be factored in here that it doesn't matter all that much what is initially guessed. Mathematically this is the strength of the argument that the hidden monument text is real, not a statistical fluke. When many probabilities need to be multiplied together, which is the correct procedure if they are mathematically independent (meaning unrelated to each other), it greatly reduces the odds of the text above appearing by chance. (Roper has a long list of these auxiliary factors.)

        The actual number range will very depending on who does the estimating, but the important point is that if the number comes out tiny, this is all that matters. When I plug in what I consider to be conservative numbers for the individual probabilities, I get final odds (in round numbers) of 'one in million' or less. And this is starting with an initial guess that I think is quite high, 1% to 0.1%, for quasi-grammatical and relevant text, like above, to arise by chance.
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        The mathematics of the 'Alice's Adventures in Wonderland' acrostic hidden name are unassailable. While there may be a lot of lines in the Alice book, the odds that by chance a 21 letter name, the real name of the little girl thought to be the inspiration for Alice and to whom the book is dedicated, would form from the first letters of a poem with 21 lines, i.e. from 21 consecutive lines with no skips or reversals, is effectively zero.
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Overview of probability vs word length
        The odds that a particular name (or letter string) will show up by chance depends on the number of letters it contains and which letters (common or uncommon). Below is a table of letter frequency in general english (compiled by Beker and Piper). Note the wide range between letters with the most common letter 'e' at 12.7% and least common 'q', 'x' and 'z' at 0.1%, a range of x127. Can we use this to come up with a 'rule of thumb' as to how the chance a name will arise by change varies with its length?

Average for all letters
       Well, first thought is just to find the average of all the numbers in the table. It's a starting point, but it will be crude because it does not account for whether letters are common or uncommon. The average comes out to be (see below) .0385 (or 1/26), so as a first order estimate we can say increasing a name length by one letter makes it about 26 times less likely to occur by chance.

                    1st column            542/13 = 41.7                                               - a,e,i,h,j           200/8 = 25.0
                    2nd column           459/13 = 35.3                                               - o,n,r,s,t,q,x,z  100/5 = 20.0
                    all 26 letters       1001/26 = 38.5  => 3.85%     or    (1 part in 26)

Vowels and consonants
       But we can come up with a better 'rule of thumb' by separating vowels and consonants and grouping consonants according to their numbers in the table. Let's calculate the average letter frequency for four groups: 4 vowels, 5 most common consonants (> 6%), 12 moderate frequency consonants (0.8% to 6%), and 5 least common consonants (< 0.8%).

         4 vowels                                                 a (8.2%), e (12.7%), i (7.0%), o (7.5%)                 =>  8.85%
         5 most common consonants                h (6.1%), n (6.7%), r (6.0%), s (6.3%), t (9.1%)    =>  6.84%
       13 moderate frequency consonants                                                                       300/13        =>  2.31%
         4 least most common consonants       j (0.2%), q (0.1%), x (0.1%), z (0.1%)                     => 0.125%

        So what do we do with four categories? For a conservative estimate (on high side) we can assume that for each consonant there is a vowel, so lets pair them up and figure the geometric (multiplicative) mean. The geometric mean is the odds multiplier per (added) letter.

                vowel x high freq consonant                     8.85%, 6.84%    => 7.78%      or    (1 part in 12.8)
                vowel x mod freq consonant                      8.85%, 2.31%    => 4.52%      or    (1 part in 22.1)
                vowel x low freq  consonant                      8.85%, 0.125%  => 1.05%      or    (1 part in 95.2)

        We can simplify things by combining the pairs with high and moderate frequency consonants, since their probabilities are less than a factor of two apart.

               vowel x high & mod freq consonant           7.78%, 4.52%    => 5.93%     or    (1 part in 16.9)
               vowel x low freq  consonant                       8.85%, 0.125%   => 1.05%     or    (1 part in 95.2)

        This simplified things nicely. Pairing vowels with consonants (a conservative assumption), but excluding the four least likely consonants, gives us an average letter frequency of about 6%. This means extending a letter string by one letter reduces the odds it arise by chance by about 17 and for two letters 17^2 = 289.

        If a vowel-consonant pair includes one of the four least common consonants (j,q,x,z), which arise according to Beker and Piper in general english only once in 500 to a 1,000 letters, then it's about 5.6 times less likely for one letter added (5.6 x 17 = 95) and 5.6^2 = 31 times for two letters added (31 x 289 = 8,960).

Five letter string odds estimate
        To figure the odds of a particular five letter string arising by chance anywhere in a selected grid the first step is to locate one letter of the string on the grid. This then specifies the location (or two locations is reading up or down is allowed) of the remaining four letters of the five letter string. The interim calculation is to multiply out the odds for the remaining four letters (two vowel/consonant pairs). From our Rule of Thumb above we find if the string has none of the four rare consonants (which is likely since they are rare!) the odds are

                                                               289 x 289 = 1 part in 83,500

        If the string has one of the four unlikely consonants, then we combine the odds of a typical pair with a rare pair and get a result x31 times larger as follows:

                                                            289 x 289 x 31 = 2,590,000

        I think the easier way to think about this is if a name or word has one rare letter, find this on the grid and use it as the starting letter. Then the interim odds four the four other (more common) letters of the string would be (from above) 1 part in 83,500. To find the odds of the five letter name (or word) arising on any of say 33 grids then the 83,500 needs to be divided by 33 and divided again by the frequency of the rare start letter (probably 1, 2, or 3). In round numbers this gives us final odds for a five letter string on any grid of:

                                    83,500 divided by (1 x 33, 2 x 33, or 3 x 33) = 2,500 to 840

        This justifies the round number estimate used in the text of 1,000 to 1 for a particular 'typical' five letter string arising on any grid, and is the same estimate that John Rollet come up with in his Sonnet dedication paper. Every additional letter (above five) raises the odds of the string by a factor of 17 and by another factor of 5.6 if the letter is a rare consonant.

        These numbers are consistent with trial runs I did looking for long words in a bunch of grids. I found a few four letter words, but not a single five letter word in any of the ten grids I did of the funerary poem (220 letters in grid). If the odds of a particular five letter words is say 40,000 to 1 (80,000 to 1 divided by 2 for with 2 start letters) for in one grid, then it's 4,000 to one for ten grids. So how many five letter words are there? Tough to say exactly. I have seen lists online of like 8,000 words of five letters, but about 90% are so obscure I don't recognize them, so maybe in a 10,000 word vocabulary 1,000 to 2,000 words are five letter words. This would make the odds of finding any word in the ten grids (1,000 to 2,000)/4,000 or 25% to 50%, which is generally consistent with finding none.
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Equidistant vs grid decoding
        The proponents of equidistant decoding (probably following the lead of David Roper) a fond of calling text written out in rectangular or block format and read vertically (like below), a 'Cardano grill' or 'ELS (Equidistant Letter Sequencing) Cardano grill', after Girolamo Cardano, who in 1550 proposed using a grid for writing hidden messages. Sound classy, but this is not really how Wikipedia describes a Cardan grill (see Wikipedia 'Cardan grille'). I prefer to just call it a grid.

        To check text for hidden messages encoded with equidistant spacing you don't absolutely have to use a grid. You could write the text out in a long string and do a lot of counting and marking of letters at specific spacings, but it so much easier to write out the text in a grid whose width is the specific spacing to be examined. Now any equidistant coded 'messages' is easily seen, you just read vertically. The use of graph paper (as in my scan below) makes doing a grid even easier as you just need to write a letter in each box.

        Grids are so natural I have little doubt that those who did the encoding worked with grids, probably sketching out many as they worked to hide a 'message' within the text. (Doing this kind of encoding must be somewhat akin to creating a crossword puzzle.)

Theory vs practice
        The theory may be that the encoding is 'equidistant', but in practice it's really encoding and decoding using 'grids' at specific spacings combined with reading vertical. Why am I making this distinction? For two reasons. How are the cases of reading upward and words that span two columns to be handled? On a grid both practices look fairly natural, or at least not unreasonable. They are, it must be admitted, extensions (minor extensions), and it does seems that they weaken the purity of this type of decoding, at least a little. However, I don't think there is a hard and fast rule here, it's a matter of preference, but I am bothered (a little) in that any preferences, choices, or options introduced into decoding can be a cryptographic red flag.

Reading upward
       Reading upward on a grid is not as easy as reading downward, but it's not all that hard. So should reading vertical upward be allowed? Maybe, it's a matter of preference. Rollet (see 'IOTH' above) and Roper do it, but I don't like it. Reading upward on a grid after all is effectively reading (in an equidistant manner) backwards through the text, something I never see pointed out, whereas reading downward is reading forward.

Words that span two columns
        When reading vertically, what about wrapping a word to the next column?  I do this above with 'IO'. One pro argument is that this looks like the vertical equivalent of what is done in normal writing all the time, where a word is split (with a dash inserted between syllables) and wrapped to the next line.

        Another, and I think stronger, pro argument is that text in grid format has a sort of vertical and horizontal symmetry. When the text is written out horizontally (on a grid), the text is just considered as one long string and is wrapped from line to line. When being read out vertically, cannot it just be viewed the same way, as one long string wrapped vertically from line to line? I think so. Or at least this is my preference over reading upward (and backward). As shown above, in the case of the sonnet dedication, adopting this vertical wrap viewpoint allows to me to find all the fragments of 'Wriothesley' ['wr' 'io' 'th' 'esley'] without having to read upward as Rollet does.

        The con argument of vertical wrapping to the next column is that the purity of 'equidistant' coding is violated. Granted. If you wrap the text around, butting its end to the beginning to form a continuous string, and count characters, you will find that the spacing between the two letters 'io' is 19 not 18. So from an equidistant theory point of view, not clean, but from a practical grid point of view, I think it is clean.
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Prof Albert Burgstahler's view
         "The most detailed and compelling example is undoubtedly that discovered by David L. Roper in the famous Stratford monument inscription dating from the early 1620s."  ... "Using a simple arithmetical procedure to decipher the part in English, Roper found a unique plain-text message concealed in a 34-column ELS grille, whose presence by design is confirmed by additional encryption related to the two lines in Latin above the six lines in English. The decrypted message, signed with the initials B. I. for Ben Jonson (I = J), reads:

                            SO TEST HIM, I VOW HE IS E DE VERE AS HE, SHAKSPEARE: ME B. I.

(1) In Sonnet 76 of Shake-speare’s Sonnets published in 1609, de Vere’s authorship is directly and unequivocally declared in a 14-column equidistant letter sequence (ELS) Cardano grille containing his name “de Vere” in column 9 of the grille, reading upward into “my name” in line 7 of the sonnet (line 16 in the grille).

(2) Similar ELS grilles appear in equally unequivocal testimony by well-educated contemporaries that “Shakespeare” was Edward de Vere in: (a) the Stratford monument inscription apparently written by Ben Jonson, (b) the 1640 poem beginning “Poets are borne not made” by Leonard Digges, and (c) the dedication to Shake-speare’s Sonnets of 1609 by Thomas Thorpe.

        Burgstahler view of Roper's findings in the funerary monument can be found here:

         http://kuscholarworks.ku.edu/dspace/bitstream/1808/5891/3/BurgstahlerCentennial%20ENCRYPTED%20TESTIMONY.pdf
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Baconian decoding is all nonsense
        I had never paid any attention to long standing claims by Bacon supporters that they had found hidden codes proving their man was the author, but how could I write an essay an essay on the mathematical strength of Shakespearean cryptograms without at least taking a quick look at Baconian claims?

Friedmans' Shakespearean cipher book
        In reading about cryptograms I kept seeing references to a classic book from 1957 titled: 'Shakespearean Ciphers Examined: An analysis of cryptographic systems used as evidence that some author other than William Shakespeare wrote the plays commonly attributed to him', by cryptologists William and Elizabeth Friedman. William Friedman was a famous cryptologist, head of the Army Signal divison that broke the Japanese diplomatic code in 1940. The book is out of print, but I found I could buy (used) copy on Amazon for $7, so I bought it and read it. Two Amazon reviews (both 5 star), one of them by me. Here is my Amazon review:

Title: Destroys old Baconian decodes, but what about newer Oxfordian decodes?
September 16, 2011, By Donald E. Fulton

        The search for secret codes or messages hidden in the works of Shakespeare has long had a very bad reputation. Much, perhaps most, of the credit for exposing 70 years of decoding nonsense by Baconians goes to William and Elizabeth Friedman, both professional cryptographers with a long interest in Shakespearean decoding. (William Friedman for years headed the US Army Signals Intelligence Service, which broke the Japanese diplomatic code just prior to WWII.) In this 1957 book they explain in understandable terms what the various authors tried to do and how they all miserably failed.

        In the late 1900's and early 20th century a huge number of books and articles were published by dozens of enthusiastic amateur sleuths who scoured the works of Shakespeare looking for (and finding!) hidden signatures and messages showing that Francis Bacon wrote the works of Shakespeare. The Friedmans show convincingly that the various approaches these Baconians invented to decode Shakespeare were (with one exception) fatally flawed, essentially nonsense, so pliable that with dogged effort and a little creativity virtually any message or signature could be found. Rather than do calculations, as I had expected, the shoot down is usually accomplished with an explanation of the flaws and a counter example; the Friedmans' will use the decoder's method and quickly find something like,'William Friedman wrote these plaies'.

        Baconians originally got the idea to look for hidden signatures or messages that Bacon might have included within Shakespeare because Bacon had actually invented, and described in a book, a code now called the 'Bacon biliteral cipher'. Sounds sexy, but it is actually a simple binary code where two font types ('a' or 'b' flavor) of five consecutive letters (2^5 = 32, enough for an alphabet of 24 letters) in the open text code one letter of the message. The book devotes several chapters to the work of the leading exponent who used the biliteral cipher, a woman they knew personally and once worked for.

        While the Bacon biliteral cipher has the advantage of being cryptologically valid in theory, they show there is no evidence that it was employed, and given the technology of 16th century printing it is unlikely it could have been made to work. No one else could duplicate the decodes of the master decoder, one Elizebeth Wells Gallup, which alone indicates that font differences she claimed to 'see' were largely in her head and chosen (without her being conscious of it they think) to make the message work. Also they argue the many variations in 16th century printing (ink spread, paper imperfections, poorly made type) made it all but impossible to successfully implement a subtle binary font code.

        This book was published more than 50 years ago and now the Oxfordians are doing some Shakespeare decoding. Is the Oxfordian work all nonsense too? Well human nature doesn't change, and much of the Oxfordian decode procedures, while very different from the old Baconian decodes, I find pretty ad hoc and too 'creative' for my taste, but not all. There are one or two Oxford decodes I find (as an engineer) to be pretty interesting, interesting enough so that I duplicated the decoding and have written an essay ('Shakespearean Cryptograms') for my home page. I bought and have read the Friedman book to get some perspective on earlier Shakespearean decode work.

        The most interesting Oxford case, I think, is 1997 decode by Dr. John M. Rollett of the dedication to Shakespeare's sonnets. Here is what makes this case so interesting:

            1) Text is very short, only 144 letters
            2) The sonnet dedication text and format are both very odd (period after every word, and a strange line format). It has been
                     suspected for years that it might be a cryptogram.
           3) Decode procedure is simple, just write out the text on graph paper, read down (or up/down)
            4) Decode yields a 16 letter full name (Henry Wriothesley)
            5) Name found is relevant to the sonnets (leading candidate for W. H.)
            6) Odds of a specific name arising by chance can be calculated, because it requires a specific sequence of letters, and letter
                    frequency of the dedication is known exactly (by counting).
            7) Five letter first name ('Henry') and five letter fragment of last name ('esley') each contain a 'y' of which there is only 1
                    in the 144 letters of the dedication.
            8) The odds of a specific five letter name (or string) with a 'y' is about 1,000 to 1, which makes the odds of two five letter
                    strings (in same name, both with a 'y') about a million to one.
            9) The line format and word-periods taken as key to a word skip decode yield a grammatical phrase possibly relevant to the
                    author of the sonnets. ('These sonnets all by ever (E. Ver)')

My writeup on this Oxfordian decode (with references) can be found by Googling "Shakespearean Cryptograms" (with quotes)

        The Friedmans show convincingly all the Baconian decoding, all of it, was total nonsense. With one exception all the various decoding methods used by the Baconians were fatally flawed (anagrams, numerology, root codes, etc), so flexible that almost anything could be read out of the text. Most of these amateur cryptologists had no understanding of probability, they never calculated the odds of their solutions arising by chance, in fact the idea of doing so never even seems to have crossed their minds.

Bacon biliteral cipher
       And what about the one scheme that was cryptologically valid, Bacon's own biliteral cipher?  Friedmans should know about this, because when they were young they both worked for a while under a lady who was its leading exponent. They devote nearly half the book to this valid (in theory) code, showing convincingly there is no evidence that it was ever used. In fact they argue that sloppy printing of the 16th century made it almost impossible to use, and also no one could duplicate the work of the leading biliteral decoder of Shakespeare's works, even Mrs. Friedman who for a time was her assistant. They conclude she was not a fraud, but deluded herself into seeing what was not there. The difficulty of deciding if a letter font was 'a' or 'b' type allowed for a lot of letter choice in the message, allowing someone who was creative to 'read out' what they wanted.

        But why did Bacon's followers put so much effort looking for hidden codes in the works of Shakespeare they thought Bacon had written?  Two reasons. One, Bacon wrote about a code he had invented (Bacon biliteral cipher) describing in detail how by varying a letter's font a hidden message can be inserted into text.  It was a binary code with the font of five consecutive letters in the open text translating to one letter in the message (Bacon gave the decode alphabet). The 2nd reason was the look of the printed text of the First Folio. It is easy to notice a striking and apparently arbitrary use of different letter fonts in the texts, particularly italic fonts, so this is where Baconians started to look. It did not seem all that outlandish to them that the font variations in the First Folio might indicate that a biliteral cipher was being used.

Hidden codes in pop music
        Came across this is a recent New Yorker article: Taylor Swift in her CD liner notes uses capital letters to encode hidden messages about which of her boyfriends her autobiographical songs are about!

       First up in a Google search were articles claiming they see hidden messages in the first (spoken) lines in plays of the First Folio. An old Baconian book ('Some Acrostic Signatures', by William Stone Booth, 1923) includes the table below of the first (spoken) lines of the plays in the First Folio in order. (Well that is what it purports to be, but apparently Booth can't count because there are only 35 lines here, and there are 36 plays in the First Folio, but this doesn't affect his argument.) He calls this an 'acrostic', a word which I had never heard before, but which has an excellent Wikipedia article, saying, it is a "form of writing in which the first letter, syllable or word of each line, paragraph or other recurring feature in the text spells out a word or a message."

        The Baconians say they can read out Bacon's complete name (first and last name) from the first letters of the words of the first lines of each First Folio play in order. Sounds impressive, no? Well not really. Let's look at how they do this. From  the first letters of selected words below they read out the name below. (They read forward from 'B' for the last name, and read in reverse from 'F' in the last word for first name.)

        And with all these these acrobatics they read out not 'Francis Bacon', which is there, but the possessive form of his name in Latin. Why? His latin name, FRANCISCUS BACONUS, is longer than the possessive form, but it is there but only with a  messy overlap of the last syllables of the first and last name. I guess now we can now guess why the odd possessive latin form of the name was chosen by the Baconians, but all this is a quibble.

        Look how many words there are in the figure below, the first letter of each of them available (as an acrostic) to be chosen according to the Baconians. There is something like 300 letters (35 lines with 8 to 9 letter/line average) from which they select out 15 they need to form the name 'FRANCISCI BACONI'. (In the original text the letters they pick are identified by capitalization. To make them clearer I drew a black box around them.)

        Looking at the beginning. After they get 'B' and 'A', they skip 78 words before they find a word beginning with 'C'! There's are similar huge skips in the reverse read between 'F' and 'R' and 'I' and 'S'. (The Baconians called the skipped words 'nulls', apparently to to downplay the huge gaps.) On its face (prima facie) this procedure this looks very dubious, with 300 letters (equivalent of more than ten full alphabets!) won't enough skipping generally get you the letter you are looking for? Yup. Can't you spell out a huge number of names with this many letters to select from? Yup. What are the mathematics of this?

       I was going to do a calculation, but quickly realized a single counter-example would make the point that with their technique you can read out just about any name you want. I decided I would try to find another name, and for fun the first name I tried was my own. I did what they do reading forward and in reverse, and sure enough there is my name (letters marked with red box):

        I quickly found 'Don Fulton' ('Don' reading forward from beginning and 'Fulton' reading in reverse from end), then saw (in just the right place!!) I could add in 'ald' to make 'Donald', and son of gun, there between by first and last name was my middle initial too, 'E'. Yikes, who would have thunk it? I guess this means (according to the Baconians) I must have written Shakespeare!

        My counter-example name was the first name I tried and finding it took all of 5 minutes! I think this makes the point that mathematically this whole Baconian procedure, this Baconian cryptogram (acrostic) is pretty much a joke. It has almost no mathematical rigor. Yet the Baconian author introducing this forward/reverse acrostic cryptogram yielding 'FRANCISCI BACONI', says:

        "We come now to the last part of our work, and, for me, the most intriguing. Here is a cipher that, as far as I am concerned, proves the Baconian argument." (Kenneth R. Patterson)

Bacon 'Bote-swaine' cipher
        The Google search turned up another Bacon cryptogram from a different site (link below) and different author, Penn Leary, that also involves the first spoken line in a play. Here the claim is that the name Bacon is encoded in a single word 'Bote-swaine', which is the first (spoken) word in the first play in the First Folio. 'Bote-swaine' is the first spoken word in the Tempest (see above) and is a character addressing the ship's boatswain. I found this cryptogram at the link below, which is site of Penn Leary (now deceased), author of "The Second Cryptographic Shakespeare" (1990)

         http://www.baconscipher.com/BTSWN.html

Thomas Jefferson coded diplomatic messages using letter substitution
        The decoding the Baconians are using here they trace back to Thomas Jefferson. I researched this and indeed Jefferson when he was Secretary of State under Washington is credited with inventing a 'wheel cipher' machine (see below) that was used to encode and decode diplomatic message sent to France. According to the description on the Monticello web site each disk has the alphabet in random order. To encode the disks are rotated to spell out (a few words of) the message, then any of the other 25 readings can be sent as the scrambled code. The decoder has an identical set of disks. He sets the wheels to match the received code, then by rotating the stack he can find and read the message. These disks provide 25 possible random letter substitution codes.

        As the Baconian Leary describes it, what he is doing is a letter substitution code where letters are replaced by letters of the alphabet just shifted 'x' counts forward or backward. For example, advancing four letters forward would replace 'a' with 'e', 'b' with 'f', 'c' with 'g', etc. (Jefferson's disks would do this if the disks were simplified by having their letters ordered: a, b, c, etc.)

       This sounds interesting and mathematically promising because the starting word is very short (only 10 letters) and has a privileged position (first spoken word in the First Folio). All the letters are advanced by the same count, so you can only transform 'Bote-swaine' into as many letters as there are unique letters in this word, which is 9.

Bacon not possible
        I note right away a problem. The start word, 'Bote-swaine', defines the relative letter spacing and none of its letters are close together ('s' to 'w' is closest), but the first three letters of 'Bacon' are the first three letters of the alphabet, hence it is not possible to get out 'Bacon' from 'Bote-swaine' by making a simple alphabet shift. I was curious as to how this Bacon decode was going to work.

        First problem --- the alphabet. It's pretty clear from looking at a lot of Elizabethan text that to them the modern english pairs 'u,v' and 'i,j' were (in some sense) interchangeable. Many references state that the Elizabethan alphabet had 24 letters. Jonson's book 'De Augmentis' is said to include an alphabet of 24 letters with 'j' and 'u' not included. 'w' is widely seen in Elizabethan texts, but apparently it was a fairly new letter replacing a double 'v' (or double 'u'), in fact sometimes still printed as two 'v' touching. But the alphabet Baconian author Leary uses in the decryption, which he calls Bacon's reduced alphabet, has only 21 letters! What? Not only are 'u' and 'j' missing, but 'w', 'x', and 'z' are missing too. Why?  I don't know. Is there good evidence that this is the way Bacon did his encryption work, or does Leary use it because it gives him the answer he wants?

        I checked the history of the english alphabet in Wikipedia, and it confirmed that in the 16th century there were three differences from the modern 26 letter alphabet, all in the process of closing: interchangeable pairs 'u','v' and 'i','j' were splitting into distinct letters, and 'w' firmed up as a distinct letter rather than as a double 'v' or 'u'.

        What Leary gets from  from 'Bote-swaine', using his 'reduced' alphabet substitution with a shift of +4, is below. Note 'b' to 'f' and 'o' to 's' are straight forward, but to get 'B', first letter of Bacon, from 't' only works because the alphabet is 'reduced', a whole bunch of letters at the end ('u', 'w', 'x', 'z') are inexplicitly missing!

        Does [F S    B I A C E N     R I] look like Francis Bacon to you? It does to Mr. Leary. First ignore 'RI', not part of the name says Leary. 'FS' you see is the abbreviation of Bacon's first name, Francis. Leary tells us that Bacon used this abbreviation. Well OK. And  'B I A C E N', what is this? Well, says Leary this is a phonetic spelling of 'Bacon'. Really? Yup, one of 278 alternate spellings of Bacon that the ever flexible Baconians recognize! Leary also refers to 'B I A C E N' as "another homophone for his last name", but Wikipedia says "homophone is a word that is pronounced the same as another word, but differs in meaning." Whoops.
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Ben Jonson's First Folio poem --- an elaborate Cryptogram?
         Below is an example of a claimed cryptogram solution (by James Ferris) that claims dramatic findings, but when you dig into it you find the the text is read out using flexible decoding and the detection of significant patterns (S and Arrow pattern) in word location. Now it can be argued that who knows what was in the head of the encryptor, the decoder has to go with what he finds. While this approach may make sense to the true believer, it can cause eyes to roll among skeptics. It is asking a lot of people to accept that findings obtained with flexible ad hoc decoding. I don't believe this is the way to convince people that at least some Shakespearean cryptograms are real. It doesn't convince me. The concern with elaborate decoding is that it may be all too easy to 'see' patterns that may not be there. Better I think to stick with simple decoding when making the case to skeptics, which at this point is most people.

        Below I do some calculations and show that it's two four letter strings, which you would expect to be its strongest element, are actually quite likely to arise by chance. There's an 8% probability of finding a grid that has two 'Vere' that also has two 'de'. If the probability calculations include the odds that the locations of the two 'de' should be near the two 'Vere', which in fact they are, then it pushes down the probability of this occurring by chance to about 0.4%.  If it is a cryptogram, it mathematically has only moderate strength even after being 'rigged' (see "two caveats" below).

First Folio Ben Jonson poem
        Is the Ben Jonson poem opposite the engraving in the First Folio a cryptogram? No one claims it is (later I found Ferris' claim), but it's worth a check. The wording of this poem is quite odd.

        Before graphing this up I did a Google search and son-of-a-gun I found there is a 2008 claim that this is cryptogram by Dr. James S. Ferris at the link below. He says he finds stuff at x20 and x22, but on a quick look it's not obvious exactly what. He says he looked at 41 different spacings and that in twelve of them he finds "stunning and meaningful encipherments". This is a little hard to swallow. Of the 12 he says x20 and x22 were the clearest. This is the first I have heard of this claim. A google search of Dr. James Ferris turns up no bio information or other works (except for a short story). He signed the Declaration of doubt, but lists no affiliation.

         http://www.drjsferris.com/Page_Three__.html

        Ferris makes this bold claim about his findings in the First folio engraving poem:

        "Thus, within the equidistant letter sequence shifts of ELS 20 and ELS 22 of the Jonson Commendation of the Droeshout engraving, is perhaps the most elegantly designed ciphertext in the entire body of the study of ciphers and codes, and Shakespeare."

         I am skeptical of such elaborate decoding and reading.

Cooking the books and salting the mine!
        Mr. Ferris, the good Oxfordian I assume he is, has a problem. He would like to find 'Vere' in a grid of Ben Jonson's First Folio poem, but the facsimile of the poem (above) as printed in the First Folio shows it contains no 'v's (none, zero, nada!), so the odds of 'Vere' popping up on any grid is exactly zero. This problem does not arise in the sonnet dedication or the funerary monument, both of which have lots of 'v's.

        Note I am going to assume that the facsimile poem above is definitive. Ferris's work is not the main focus of this essay, so I did not take the time to research this. The above facsimile is a high resolution copy of a First Folio from a reputable institution. (I am aware that there are some (minor) differences between virtually all copies of the First Folio).

                    a) Sneaks it in (no justification)
                    b) Waves his arms and says something like 'u' and 'v' are interchangeable
                    c) Employs a more subtle argument. Something like some particular word is normally spelled with a 'v' and here we find a 'u', so this is hint (or key) by Jonson that as a first step to decode the cryptogram we should swap 'u's for 'v's.

If I was a betting man, I would put odds on b).

Calculating the odds
        Let's calculate the odds of  'Vere' with a 'de' nearby appearing twice on the same grid. The table below shows my count of letters and calculated letter frequencies in the First Folio poem. For the number of grids I will use 82 = (2 x 41). 41 is the number Ferris used, but there is a quasi-hidden doubling, because Ferris included the title of the poem in the grids, but he could just have reasonably excluded it. Another factor of two comes from words being read up or down.
 

Figure the odds of two 'Vere' on a grid
       I will do the calculation in steps. Let's start with the longest string (Vere). The probability of one 'Vere' appearing on a particular grid: (This is not an exact calculation, but it's reasonably accurate. Inside the brackets are the odds that 'ere' will be adjacent to a 'v', and this is scaled by the number of 'v's on a grid and x2 for up/down direction.)

                                                     V             e               r                e
              16 (v) x 2 (up/dn) x  [ (1)     x   .134    x   .067    x   .134] = .038 or (1 chance in 26)

        The probability of two 'Vere' appearing on a particular grid is 1 chance in 26 squared or (1 chance in 676). But there are 82 = (2 x 41) possible grids so the probability of two 'Vere' appearing somewhere, i.e. on any one grid, is 1 chance in (676/82) or (1 chance in 8.25) or 12%. There are so many 'e' and 'v' in the poem that odds are greater >10% one grid can be found that contains two 'Vere'.

Figure in the odds of  two 'de'
        Now we need to figure the odds of two 'de' appearing on the same grid with the two Vere. This is calculated as two 'de' appearing on a particular grid. First we will calculate the odds of one 'de', then square it for two 'de'. Since the 'de' is a short string quite likely to arise by chance, to do this calculation accurately it needs to be done as [1 - (not 'de')]. There are six 'd' in the poem, so there will be six 'd's on every grid. If there is to be no 'de' on a particular grid, then none of the 12 locations adjacent to the 'd's (six above and six below) can be an 'e'.

              Odds of (at least) one 'de' on a particular grid = [1 -  ((283- 38)/283)^12]
                                                                                             = [1 -  (.866)^12]
                                                                                             = [1 - .177] = 0.823  (82.3%)

        The odds of two 'de' on a particular grid is this number squared (0.823^2 = 0.68) or (1 chance in 1.5). These numbers say 'de' forms easily by chance. Most grids would be expected to have at least one 'de', and more than 2/3rd of grids would be expected to have two. The presence of one or two 'de' on a grid carries almost no statistical weight.

Relative locations of 'de' and 'vere'
        Finally we need to figure the probability that a 'de' occurs (somewhat) near a 'Vere'.  I don't see how to calculate this exactly, but for an x22 grid with separated 'Vere' we can make an estimate. Let's consider 'de' is near 'Vere' if it's within 0 +/- 3 columns of it and in the same vertical half (top or bottom). The odds the two 'de' will be in the right columns is thus (7/22)^2 = 0.1 or  (1 chance in 10). The odds that one of two 'de' will be in the upper half and one in the lower half is 0.5 or (1 chance in 2) (since the odds of two up is .25 and two down is .25). Hence the odds that both 'vere' will have a 'de' nearby is (1 chance in 20) or 5%.

 Another viewpoint
          Divide a grid into equal size regions, for x22 about six looks right, two of which contain a 'Vere', then we figure the odds that the one 'de' will arise in each of these two particular regions. The odds for the first 'de' are (1/3), since both target regions are empty, and for second 'de' are (1/6), since only one target region is empty. Thus the odds that one 'de' will arise in each of two particular regions of six are [(1/3) x (1/6) = 1/18] or (1 chance in 18).

Odds caveats
        While odds of 1 part in 250 may seem like moderate strength mathematically, it comes with two big caveats. One, there are no 'v's in the original of the First Folio poem! The cryptogram solution depend totally on a very questionable change of all the 'u's to 'v's.

 'v' in 'picture'
      Look at the last line of the x22 grid above. Note the 'v' in the lower 'Vere' comes from the 'v' in 'pictvre'! What, you didn't know 'picture' was spelled with a 'v'?  If you don't buy this, then Ferris' x22 cryptogram solution is kaput. I did Google searches of the last line of the First Folio poem with 'u's and then 'v's. Here's the results:

        "Not on his Picture, but his Booke"                    12,900 hits
        "Not on his Pictvre, bvt his Booke"                              0 hits

Ferris Footnote
        I read through the essay on Ferris's site where he covers this decode (work in progress he says). The following is relevant to my review above.

        -- I find no justification, or even mention, of the switch of all 'u's of the poem to 'v's in the grid.
                    (I am informed by Ferris that he does explain the 'u', 'v' switch in the text, so maybe I may have missed it.)
        -- He begins with the First Folio poem in facsimile similar to what I have, showing no 'v's.

Grave epitaph
        In the same essay Ferris covers a lot of ground. He has included several ELS grids on the four line Epitaph poem over Shakespeare's grave ('Good friend for Jesus sake forbeare'). He has multiple versions of it at x14 spacing which shows his pliable decoding technique. The engraving has abbreviations with superscript: ye and yt. In some grids he writes them out (like in the funerary monument decodes), and in other cases he drops the superscripts. This adds another factor of two to possible grids.

        Pictures taken in Trinity church show the Epitaph engraving on the grave stone is badly eroded and to the viewer is upside, so the church has made a copy for visitors that sits loose just above the grave (see photo of graves above and below). This white letters on a black background copy is what you normally see in photos. On the copy the first word of the 3rd line (at low resolution) looks to be 'BLESE', but photos of what is probably the engraving on the gravestone and the copy at high resolution (below), appear to show a bridge from the 'S' to the 'E', which makes the spelling 'BLESTE', where 'TE' are merged, the engraving equivalent of a typographic ligature. I checked the 1825 church booklet and (sure enough) it spells it 'Bleste'. Wikipedia also says 'bleste'. However, Ferris, apparently covering all bases, uses both spellings in his grids. This adds another factor of two to the number of possible grids.

===========================================================================================================

Shakespearean spelling
        Until recently I had never concerned myself with Shakespearean spelling, but I found a great resource for viewing and searching Shakespeare's original spelling (in facsimiles) at Univ of Victoria (link below). My focus was on Shakespeare's usage of 'u' and 'v', which is central to the sonnet 76 (potential) cryptogram.

Consistency of Shakespearean spelling
        I found a great resource for the checking of Shapearean spelling in an Internet Shakepeare site run by Univ of Victoria in British Columbia (link below). They have hi-res facsimiles of all of nearly all of Shakespeare's works: poems, sonnets, plays (not only Folio1, but Folios 2, 3 & 4) any page of which can be viewed. They also have a very useful advanced search that can restrict search to facsimiles, particular works, and even allows for search of a single letter. (Search, however, is a little buggy. I have found search is much more sucessful if the search is restricted to the first few letters of a word, say 'ver' instead of  'verse'. I emailed them about this problem.)

         http://internetshakespeare.uvic.ca                                                                      Internet Shakespeare Home
         http://internetshakespeare.uvic.ca/Texts/search.html?e=Son_Q1                  Advanced search page

       I checked 'u' and 'v' words by viewing pages and searching in three works of Shakespeare: Venus and Adonis of 1593, sonnets of 1609, and First Folio of 1623. It is generally thought that Shakepeare participated in the publishing of his first published work, the long poem Venus and Adionis. Venus and Adonis has a dedication to Henry Wriothesley signed, "William Shakespeare".  In 1593 Shakespeare was 29, just beginning his career, and de Vere was 43. The sonnets of 1609 were thought to have been published without help from Shakespeare, and in that year de Vere had been dead for five years. Preperation of the First Folio, containing most of Shakespere's plays, was done long after both Shakespeare and de Vere had died.

         From this history the primary docment to see how Shakespeare spelled words must be Venus and Adonis (including the dedication page). All three of these works, published over a period of thirty years, had different publishers and different editors. Therefore I find it quite remarkable, given the flexibility of Elizabethan spelling, how consistent is the Shakespearean spelling across these three large works.

        However, the consistency if 'u' and 'v' usage is gone when we get to the 2nd Folio published only nine years after the 1st Folio. Now we see 'u','v' spelling much closer to modern usage, both 'u' and 'v' appear inside words and both can start words. 'u', 'v' usage in the 2nd Folio is totally different from earlier Shakespeare works. Did the English language change that much in nine years? Did the new editor change Shakespeare's spelling? Or maybe the 2nd Folio editor understood that 'u','v' usage was not that of Shakespeare, but the spelling preference of the 1st Folio editor and hence felt free to substitute his own spelling preference. I don't think there is any way to really know. Just adds more uncertainty to Shakespearean 'u','v' spelling.

        There is also some 'u','v' spelling variation across various quartos of some of Shakespeare's plays, like Hamlet, published while Shakespeare was alive, but this not ought to be taken too seriously as they were thought to have been semi-pirated publications where even text varies between the quatros, sometimes whole scenes being omitted. Some of the play quartros are referred to by cholars as "bad quartros".

        Shakespeare's u,v spelling convention is clear in the above texts:

                            a) 'u' never begins a word, it is only used inside
                            b) 'v' begins words, it is never used inside
                                       except in titles in capitals where 'v' can replace 'u' inside a word

        Shakespeare begins words with 'v' that in modern English that begin with 'v', like 'vowe' and also words that in modern English would begin with 'u', like 'vupolisht' (unpolished). Inside text words we find no 'v's only 'u's. We find words that in modern English would be spelled with a 'u', like 'your' and 'count', and also words that in modern English would be spelled with a 'v', like 'haue' (have) and 'inuention' (invention). The word 'suruey' (survey) in the next to last line shows both usages of 'u'.

        Exceptions: In a few title pages and dedication headings printed in capital letters what in Shakespearean text is printed as an (inside) 'u' in the title is printed as a 'V'. I have only seen this when the the titles or heading are all in capitals. Examples: title page, 'VENVS AND ADONIS' (1593), dedication page of Rape of Lucrece (1594), "TO THE RIGHT HONOVRABLE".  Honourable is also in the text of the dedication and here is spelled with an inside 'u', 'honourable'. The tradition of printing a 'u' as a 'V' in headings and memorials has a long history. It can be seen in cornice spellings on many building built in USA in late 1900's and early 20th century, below is the engraving over the main entrance to MIT. (I used to think this use of 'V' was because 'U' was hard to engrave, but that can't be right as lots of the engraved letters are full of curves.)

Remarkably spelling consistency across Shakespeare's works
       I find the consistency of Shakespeare's spelling (I only checked 'u' and 'v' words) across his works over 30 years with different publishers and editors quite remarkable. The same u,v pattern noted above is found, without exception as far as I could see in sampling and with searches, in the texts of the poem Venus and Adonis, then the sonnets and later in the First Folio, but not, alas, in the Second Folio of 1632, nine years after the First Folio. Unless there was some printing convention (of which I am unaware) that might explain this, it probably (or maybe) indicates that this really reflects the spellings in the Shakepearean manuscripts from which the publishers were working.

        Here are the results of some seaches of all of Shakespeare's works in original spelling using Univ of Victoria site (below). The first columns is what you find.

                 vp, vpon, vse                                 no search hits for up, upon, use
                 quick, but                                      no search hits for qvick, bvt

        It's worth noting that the words 'quick' and 'but' both occur in the Stratford monument poem, but there are spelled 'qvick' and 'bvt', spellings Shakespeare never used. Of course, the monument poem may very well not be by Shakespeare (Jonson is the favorite), but there is another explanation. The monument poem is engraved in all capitals. So it looks very much like the reason we see 'V's in the engraving is the convention of printing inside 'U's as 'V's in titles, headings and on cornices.

Wikipedia ('u')
        -- During the late Middle Ages (1400's) two forms of 'v' developed, which were both used for its ancestor u and modern v. The pointed form 'v' was written at the beginning of a word, while a rounded form 'u' was used in the middle or end, regardless of sound. So whereas 'valor' and 'excuse' appeared as in modern printing, 'have' and 'upon' were printed 'haue' and 'vpon'. By the mid-16th century (mid 1500's), the 'v' form was used to represent the consonant and 'u' the vowel sound, giving us the modern letter 'u'. Capital 'U' was not accepted as a distinct letter until many years later.

In other words
        'u' begins life as a positional variant of 'v'. The positional usage described in the Wikipedia article ('v' beginning, 'u' inside) matches Shakespeare's usage. First letters are usually consonants and vowels typically are inside, so over time 'v' came to represent the consonant sound and 'u' the vowel sound . Wikipedia says this shift happened fifty years prior to Shakespeare, but this does not look right as Shakespeare always puts 'v' at the beginning and 'u' inside. The slow development of capital 'U' probably explains why 'V' is found inside words of titles that are all capitals.

Reference for Shakespearean spelling
        I found a great resource for the checking of Shapearean spelling in the Internet Shakepeare site run by Univ of Victoria in British Columbia, Canada (link below). They have hi-res facsimiles of all of nearly all of Shakespeare's works: poems, sonnets, plays (not only Folio1 , but folios 2, 3 & 4) any page of which can be viewed. They also have a very useful advanced search that can restrict search to facsimiles, particular works, and even allows for search for a single letter. (Search, however, is a little buggy. I have found search is much more sucessful if the search is restricted to the first few letters of a word, say 'ver' instead of  'verse'. I emailed them about this problem.)

         http://internetshakespeare.uvic.ca                                                                      Internet Shakespeare Home
         http://internetshakespeare.uvic.ca/Texts/search.html?e=Son_Q1                  Advanced search page

Waste of time?
        As a check, I did a little research on the Second Folio. It was published in 1632, only nine years after the First Folio. It is basically a page for page reprint of the First Folio with some spelling changes, having been re-typeset by a different printer. Second Folio claims, like the First Folio, to be 'published according to the true original copies', yet according to Wikipedia there are 1,700 differences, mostly in spelling. One researcher looking at many of the 124 exant copies of the Second Folio found an obvious misspelling on the title page, the word from First Folio 'according' spelled 'accodring'. This is a spelling error on the title page in huge print above the engraving of Shakespeare! Talk about sloppy printing.

        As I detail below, the Second Folio text, and the new intro poem by Milton too, completely trashes the u,v spelling conventions of the First Folio. So in looking at Shakespeare's printed works, are we looking at his spelling or the spelling of the printers and editors? The question is, Did the Second Folio editor fix or modernize (Wikipedia says "modernize", but this is with hindsite) the spelling, or did they go back to Shakespeare's manuscripts and correct the spelling. There are lots of opinions, but really no one knows. The spelling changes made in the Second Folio of 1632 make me wonder if this whole u,v spelling exercise isn't just a waste of time.

Milton poem of Second Folio
        A eulogy poem by Milton that appears first in the 1632 Second Folio shows that it does not follow the spelling convention of not using 'v' inside words. A facsimile shows it has lots of words with a 'v' inside: 'leaves', 'unvalued', 'bereaving', 'conceiving'.

2nd Folio vs 1st Folio
        I put facsimiles of the 2nd Folio and 1st Folio in side by side browser windows and compared a few pages from different plays. It is clear that the 2nd folio is (as claimed) a page copy of the 1st folio. All the pages I looked at have page layouts and line breaks that are almost, but not exactly the same. Line lengths vary a little, so clearly the print has been reset, maybe with a slightly different font by a different printer. There can be little doubt that the printer of the 2nd Folio worked directly from the 1st Folio copying it line by line. And while spelling of the 2nd Folio at first glance looks the same as the 1st Folio, comparing lines carefully soon showed a few (small) differences, usually associated with 'u' and 'v'. The following are all from the 1st column of first page of Romeo and Juliet.

        First Folio                I will bee ciuill with the Maids, and cut off their heads.
        Second Folio           I will be civill with the Maids, and cut off their heads.      'u' to 'v' in 'civill' and 'bee' to 'be'

        First Folio                To moue, it to stir: and to be valiant, is to stand:
        Second Folio            To move, it to stir: and to be valiant, is to stand:              'u' to 'v' in 'move'

        First Folio               That shewes thee a weake slaue,
        Second Folio          That shewes thee weake slave,                                              'u' to 'v' in 'slave' and 'a' omitted

        First Folio               Do you bite your Thumbe at vs sir?
                                          ---------------------------------------
                                          Do you bite your Thumbe at vs, sir?
        Second Folio           Doe you bite your Thumbe at vs sir?
                                          ---------------------------------------
                                          Doe you bite your Thumbe at us sir?                               'v' to 'u' in 'us', but only on 2nd line,
                                                                                                                                       'Do' to Doe', and comma omitted in 2nd line

        The entry above is interesting, because the line ['Do you bite your Thumbe at vs sir?] is in the text twice. In the first folio the text and spelling of the two lines is exactly the same (second time an added comma), but in the Second Folio we find a spelling difference: 'vs' and 'us'.

From first page, 2nd column of Julius Caesar

        First Folio                  Haue you not made an Vniuersall shout,
                                            That Tyber trembled vnderneath her bankes
                                            To heare the replication of your sounds,
                                            Made in her Concaue Shores?
        Second Folio             Have you not made an Vniversall shout,                        'u' to 'v' in 'have' and 'Vniversall'
                                            That Tyber trembled underneath her bankes                 'v' to 'u' in 'underneath'
                                            To heare the replication of your sounds,
                                            Made in her Concave Shotes?                                         'u' to 'v' in concave, and 'shores' to 'shotes'

Second Folio's u,v usage
       In a side by side comparison of just two pages of the First and Second Folios the u,v pattern is clear. The u,v Shakepearean (?) pattern of the First Folio is all changed. The Second Folio published only nine years after the First Folio now uses 'v' inside words where in modern spelling a 'v' consonant appears, like 'have' and 'move', and 'u' is now used to start words, like 'underneath' and 'us', replacing the 'v' first letter of the First Folio. Note, however, that the capital 'V' in 'Vniversall' remains.

        The Second Folio looks to have been poorly proof read. Change of 'shores' to 'shotes' looks like a typo ('concave shores' appears in modern editions), and one instance of 'vs' remained while two lines away it was changed to 'us'. The omission of 'a' in the line [That shewes thee a weake slaue (1st folio)] also looks like a typo.

Second folio references
        Scholarly paper below discusses variants. Shows five different title pages, on one title page 'according' is spelled wrong ('according').

        http://digital.lib.lehigh.edu/eb/supp/2073/index.pdf

        YouTube video of auction house with a copy they were going to auction (estimated sell price 200k to 250k). They describe it as page for page reprint of First Folio.
         http://www.youtube.com/watch?v=bzCSiaYLpgw

        Wikipedia 'Second Folio' says there are 1,700 changes from First Folio.

An aside --- Two facsimiles of First Folio
        While looking at facsimiles of the 1st Folio and 2nd Folio, I was appalled to see how poor some of the facsimiles are. The bleed through from the ink on the reverse side of the page is so bad on some they are barely readable. Here are facsimiles of two different copies of the First Folio from the same site.

First page of 'The Taming of the Shrew' from two copies of First Folio
Bleed through of the facsimile of First Folio at Brandeis (left) is really bad
source -- http://internetshakespeare.uvic.ca/Library/facsimile/bookplay/Bran_F1/Shr/?zoom=5
source -- http://internetshakespeare.uvic.ca/Library/facsimile/book/SLNSW_F1/226/?zoom=5

Is there a cryptogram by Shakespeare?
      I finally decided James Ferris' recent finding of a (potential) skip cryptogram in the sonnets looked too interesting to exclude from this essay. It's been relegated to an appendix not because I think it uninteresting, but because the writing was nearly finished and it falls in a different class. For one thing, it arises from much more text than the other cryptograms I discuss. The sonnets as a group have nearly 70,000 letters, almost x500 more than the sonnet dedication. This shifts the odds, making longer strings more likely to arise by chance. And two, the author of this (potential) cryptogram is not some contemporary of Shakespeare, but is presumed to be the famous poet himself, William Shakespeare (or de Vere).

Critical look at sonnet 76
        Dr. James S. Ferris made a recent (2008) discovery in sonnet 76 that has been widely referenced in the Oxford cryptographic community. On an x14 grid of the sonnet 76 he found immediately below the poem words 'my name' (hor) the six letter string 'devere' (vert) (see below, left). Ferris sees this as a linking of Oxford's name, 'de Vere', to 'my name', which appears in the well known line of sonnet 76, 'That euery word doth almost fel my name'. Ferris asks, 'Why would the Stratford William Shakespeare say: "My Name is Ed de Vere"?'

        Mathematically this does look (at first glance) like it could be pretty strong. One, a six letter string is quite long, so odds of it forming by chance would be low, at least if the source text is short, which here it may not be. Two, the placement of the ''devere' string abutting 'my name' is probably the most striking feature of the grid. It does look quite unlikely, and a product of two rare occurrences will yield high odds. A hidden 'devere' abutting 'my name' in the text does look so surprising that it requires, demands really, a hard, critical look be taken at this apparent cryptogram. And that is what I propose to do in the rest of this appendix.

        I see a bunch of issues here.

1) Motive
        It's generally thought that the sonnets were not written for publication, but of course nobody really knows. If they were written for Shakespeare's intimates, what would be the point of Shakespeare identifying himself by encrypting his name into the sonnets?  Maybe a lark, word play? Shakespeare is famous for word play in his plays, but this doesn't really fit with the serious nature of the sonnets, does it? To me the lack of an obvious motive for this being done deliberately is big problem with this potential cryptogram. In some unquantifiable way it increases the odds that the finding has occurred by chance.

2) Cryptogram is not really clean
        Look at Ferris's figure (left), the alignment of 'my name' and 'devere' looks pretty striking, right?  Must be deliberate, right?  But look again, it's not really that clean. Reading it in the most logical way (hor and then down) it reads ' 'my name' followed by  'ereved'. 'Devere' is reversed (it has to be read vertically upward), and it's not very well centered either. To illustrate this, and a bunch of other possible alignments and string variants, I drew the little sketch above right. I marked what to me is a cleaner version, reversing 'ereved' to get 'devere' and better centering it under the phrase 'my name'.

        Maybe you don't agree. Many Oxford decoders seem to have no problem reading down or up, whatever works to get a message seems to be the practice, but to me the alignment of the hor and vertical words in the x14 grid of sonnet 76 is just not that clean. If horizontal 'my name' is the beginning and below it is the hidden (vertical) name, then I argue that the logical English style reading of the hidden name is downward.

Even cleaner would be finding 'devere' in sonnet 136
        Sonnet 136 also has the words 'my name' in the text, but here we find it linked to 'Will'. The relevant half line is, 'for my name is Will' (capitalization and italic in the original, see facsimile below). This appears to be the author of the sonnets explicitly identifying himself as 'Will'.

        Now if the author, who the Oxfordians think is the Earl of Oxford, had really wanted to leave a powerful hidden message, why didn't he in effect override the 'Will' reference by abutting a hidden 'devere' to 'my name' in sonnet 136?  Would this not be far more impressive, ironic, and cleaner than the finding in sonnet 76? I think so, but alas this is not what was found.

3) Not decoded with Shakespearean spelling
       There is little doubt that in some sense 'u' and 'v', which had not yet split into separate letters of the English alphabet, were (in some sense) interchangeable in Elizabethan writing. The Oxford decoders seem to then immediately jump to the conclusion that a 'u' to 'v' switch-aroo is perfectly justified when decoding. After all they were equivalent in Elizabethan english weren't they?

'u' to 'v' switch-aroo
       The table below shows the 11 different words found in sonnet 76 that include a 'u' or 'v'. Some are used multiple times, they are the basis for the 14 'v' words in Ferris' grid of sonnet 76. Shakespeare's spelling of 'u,v' words was remarkably consistent across his main body of work: Venus & Adonis, sonnets, the First Folio. The first column shows the spelling Shakespearean always used, based on facsimiles. The second column shows how the word is spelled in Ferris' x14 decode grid (above). Clearly what Ferris as done is change all 'u's to 'v's, but in so doing he is not decoding with the words spelled as Shakespeare spelled them!

        This is a very important point. Ferris is not decoding with Shakespearean spelling! 12 of the 14 'v' words in Ferris' x14 grid are spelled differently from the spelling found not just in sonnet 76, but the spelling found in any of Shakespeare's works. And this change made by Ferris is what provides the 'V' in de Vere (string 'ereved'). The decode starting point is a grid with altered spellings, then the claim is made that the name uncovered has been deliberately put there by Shakespeare. What? To me this kind of cryptographic fudging undermine the whole decoding effort of sonnet 76.
 

        Of course, skeptical me suspects the real reason for the 'u' to 'v' switch-aroo is to increase the number of 'v's on a grid making 'Vere', usually the prime target of the Oxfordians, more likely to be found. I ask (I just ask, I do not know the answer), does this 'u', 'v' interchangability apply to proper names too, like de Vere? It has been argued by some Oxfordians that 'de Uere' is equivalent to 'de Vere'. Well if it is, why is the first step in Ferris' decoding, both with the sonnets and First Folio poem, to switch 'u's to 'v's? A Google search for "de Uere" does have some hits, but this is weak support for the idea that it is an equivalent alternate spelling of 'de Vere'.

Zero Google hits
       As I pointed out in an appendix above, doing a 'u' to 'v' switch-aroo, as Ferris does in the last line of the First Folio epitaph poem,

[Not on his Picture, but his Booke]  =>  [Not on his Pictvre, bvt his Booke]

reduces the Google hit count for this phrase from 12,900 to 0.  The likely reason for 0 hits is that Shakespeare never in any of his works spelled 'but' as 'bvt' or 'picture' as 'pictvre'. This can be verified by a search of Shakespearean facsimiles (link below). This tells me that the justification for doing a 'u' to 'v' switch-aroo is pretty weak. It can be argued that hardly anyone but Oxfordian decoders looking for 'Vere' are doing it.

An aside --- Shakespeare's boot licking dedications
       The text of the Venus and Adonis dedication must be a huge embarrassment to those who admire Shakespeare as a writer. If it is not a jest or inside joke, which it might be if the author is de Vere since in the year Venus and Adonis is published (1593) Lord Burghley is trying to arrange a marriage between one of de Vere's daughters and Wriothesley, it shows Shakespeare to be quite a boot licker since Henry Wriothesley surely has no achievements in his life at this point, in 1593 he is just 20 years old, except for his birth. The dedication of the Rape of Lucrece a year later, also to Wriothesley and also signed by Shakespeare, continues the boot licking. (However, I admit that similar bootlicking dedications can be found by Galileo in his books, but at least in his case there was an obvious purpose.)

Why u,v confusion in sonnet 76 cryptogram?
       I ask, if sonnet 76 contains a deliberate cryptogram done by old Will, why the 'u', 'v' confusion? In Ferris' finding the 'v' of 'de vere' comes from 'loue' after it has been modified to 'love'. If this word is the anchor for a deliberate encoding of 'Vere', why do we find it spelled with a 'u' in the 1609 sonnet when a 'v' is called for? I suspect the Oxfordians are now rolling their eyes as they seem to think 'u' and 'v' are fully interchangeable, but to me this is a problem, a serious problem with the decoding of this sonnet. To get out a hidden 'de Vere' it must be decoded not using Shakespearean spelling! This just does not smell right.

        It's a potential confusion that Shakespeare could have easily avoided. All he needed to was work into the text a single word beginning with 'v' at the right spot, like maybe reuse 'verse' from the first line. This is a change of one word in all 154 sonnets to cleanly hide his name! Was Shakespeare so incompetent a poet that he could not arrange for a word beginning with 'v' to appear in the one location of sonnet 76 where he needed it to form 'devere'?  Are the Oxfordians going to argue this was just too tough for old Will, the world's greatest poet? That's a tough sell.

Note to the printer option
       Shakespeare didn't even need to tweak the text. With an instruction to the printer (a scribbled note on the manuscript is all it would take) he could have snuck in a 'v' trivially. If Elizabethan spelling was so flexible and fluid as the experts say, why didn't Shakespeare just switch the 'u' in 'loue' to a 'v'. Who would notice?

Spelling change as cryptogram key
        The argument can be taken further. Suppose someone does notice, then this (odd) shift in spelling, different from his usual consistent spelling, becomes a key (or hint) that a cryptogram might be present!

Why not 'de Uere'?
        I have been heard the Oxfordian claim that 'de Uere' is basically the same as 'de Vere'. Really? Why then, I ask, does Ferris first switch all the 'u's to 'v's before he writes out his grids? Skeptical me, but I suspect the answer is that if he were to publish a grid with a vertical 'ereued' string, it just wouldn't look very impressive.

        The history of u,v in the English alphabet (see Wikipedia 'u' and 'v') gives more reasons to be skeptical of 'de Uere'. In the appendix 'Shakespearean spelling' I list three reasons why is must be 'de Vere' and not 'de Uere'. One, 'u' is used only inside words, two, no capital 'U' exists at this time, and three, first letter of 17th Earl of Oxford's name begins with a consonant, and 'v' is evolving to be the consonant and 'u' the vowel.

5) Cryptographic fudges
        Notice the apostrophe between E and S in Ferris' grid. This supports his reading of this hidden message as 'My Name is de Vere'. Nice english, but where did the apostrophe come from?  Ferris just put it in! And where did most (12 of 14) of 'v's in his x14 grid come from? Ferris switched all the 'u's in the original sonnet to 'v's. Look at his Ferris' published grid (above). It does not have a single 'u', but the facsimile of sonnet 76, and all the sonnets, are full of 'u's. The original spelling of 'loue' has been changed to 'love' to provide the 'v' to anchor 'Vere'.

        This kind of free or creative decoding is seen again and again in Oxfordian decoding. Readings are up, down, or horizontal, whatever works. Letters are switched, word order is changed. The members of the small cryptographic community who search for hidden messages in Shakespeare or related documents seem to have convinced themselves that this kind of creative or free decoding is perfectly OK. It's all about "context", it is argued. And of course you get more and cleaner messages! I remain unconvinced.

        The problem I have with this approach to decoding is that it is too subjective, and too reminiscent of the self-delusion and sloppiness that led the Baconian decoders into the wilderness a century ago. A rereading of the Friedmans' excellent book of fifty years ago I think is useful. The bias I see is that these decoders, mostly supporters of de Vere as Shakespeare, want to find messages. Their decoding is not neutral. When what looks like a message pops up, they see it as perfectly acceptable to 'clean it up' a little. But this tweaking eats away at the mathematical odds calculation, which is essential for estimating the risk that a finding might pop up by chance.

Corollary --- The corollary of this attitude, which I almost never see stated, is that the encryptors, and in the case of the sonnets we are talking about one of the most famous writers of all time, were either just not very competent at encoding, or else couldn't be bothered to do it right. Was it beyond them? Didn't they really care? A rough message does the job? I don't see a credible argument that 'cleaning up' of (supposed) messages is acceptable decoding practice.

6) Sonnets are a lot... of text
        A major, crucial factor in the calculation of odds (that a specific result will occur by chance) is the length of the original text to be searched. A (potential) cryptogram located in the sonnets is not like the other cryptograms discussed in this essay. Why do I say this?  At 448 letters isn't sonnet 76 only modestly longer (x2 to x3) than the length of other cryptogram texts discussed in this essay? Yes, but the length of sonnet 76 is not the point. There are 154 sonnets, of which sonnet 76 is typical. How much text is this? Well sonnet 76 has a little less than half a thousand letters, and there are 154 sonnets, so this is a searchable text length of 70,000 letters (round numbers), and since each sonnet can be written out in about 44 different grids, this is a total of about 6,800 grids!

        In other words what looks like the surprising finding of x14 grid of sonnet 76 doesn't seem quite so surprising when it is realized that it has been selected out of not a few dozen grids, as is the case with the other cryptograms discussed in this essay, but from something like 6,800 grids. Well isn't that a little unfair? After all we have the joining (sort of) of de Vere's name (well, really the string 'ereued') with the text words 'my name'? Well for one thing 'my name' is identified after the fact. How many other phrases could have been woven in (he is, I vow, I am, look here, etc, etc)?  I'm betting a creative decoder can be, well, creative.

        Doesn't 'my name' only occur in sonnet 76? Nope, 'my name' occurs 5 times in 4 different sonnets: 72, 76, 111, and 136 (twice).  ('name' is found 14 times in the sonnets.)

7) Sonnet 136 says, "my name is Will"
        In the sonnet 136 we find a 'my name' reference that appears to contradict the 'my name is de Vere' cryptogram solution of sonnet 76. The text of sonnet 136 looks like a clear message from the author about who he is (and 'is' is actually there, not inferred). The relevant text in sonnet 136 is:

        Note 'Will' is emphasized in the 1609 facsimile: capitalized and initalics ('my name is Will'). The message in the text about who the author is seems pretty clear. So how come de Vere didn't override the text message (so to speak) by encrypting his name in this sonnet and abutting it to this 'my name'? Speculative, but still I think an interesting question, and another indication that maybe de Vere did not deliberately insert his name in sonnet 76, because it was the wrong 'my name' in the wrong sonnet.

8) Auxiliary hints are thin
        The auxiliary hints are thin (to non-existent) in the case of sonnet 76. There's nothing special about x14 grid. Decoders of other texts have pointed to oddball spellings in the text as a hint it might be a cryptogram, but there are no oddball spellings in sonnet 76 that anyone has noticed. Ferris doesn't mention any, I don't see any. Shouldn't the lack of spellings hints count as a negative? There's really nothing special about sonnet 76 either, since 'my name' occurs in several sonnets. I suppose it could be argued that its context "Doth almost tell my name" is a hint, but as I argue (above) the context of 'my name' in sonnet 136, 'my name is Will', I find more compelling.

9) Calculate odds from a universe of possibilities
        It's common in the cryptographic literature to see the calculation of odds for exactly what has been found. This generally gives the highest (most impressive sounding) number number, and from one point of view it seems 'right', because after all this is what was found. But from another viewpoint, this number is meaningless. It doesn't really answer the important question, What are the odds that our finding, which comes from a universe of similar (effectively equivalent) possibilities, could have arisen by chance.

        For example, How important is it, really, that 'devere' touches the 'y', and only the 'y', of  'my name'?  If it touched any letter of 'myname', would not the 'wow factor' (to quote Everybody Loves Raymond) be the same? Sure it would. What if the string read down instead of up, just as impressive? Sure. (Maybe even a little cleaner.) What if the Oxford string abutted 'my name' from above? What if the two strings intersected? Same 'wow' factor? I think so. Therefore all these locations are part of the universe of possibilities and should be included in the odds calculation.

 Like quantum mechanics
      I am reminded of how odds are calculated in quantum mechanics. It matters not in quantum mechanics that say, on the 34th run of the famous double slit experiment, that an electron hits the left detector. Quantum mechanics is inherently statistical. Its odds calculation proceeds by assessing the universe of all possible paths an electron can take (Feynman formulation), and calculating the fraction of this universe of paths that intercepts the left detector.

        This is how I think cryptogram calculations should be done. A finding is like one run of a statistical experiment. The finding arises from a universe of possibilities, by which I mean results, which if found, would have been viewed as similar (equivalent) with the same 'wow' factor. Granted this involves making some distinctions, drawing some boundaries, but it also amounts to framing the problem correctly, so that the calculated odds tell us about the risk that this type of finding is a chance occurrence.

Letter count difference
        I do, however, disagree with one of Ferris' letter counts. He counts 8 'v', but I count 14 in sonnet 76 after his 'u' to 'v' switch-aroo (see Ferrris' x14 grid above). I get very close to his letter counts for 'd', 'e' and 'r' with my counts in the 448 letters of sonnet 76: 'd' (26), 'e' (55), and 'r' (24).) Correcting the 'v' count from 8 to 14 reduces his calculated odds from 8.5 million to 5 million.

        I know 'related findings' is a little subjective, but I see no way around this. As the factors below demonstrate, it's really not that hard to define this universe. Much of it is common sense, just thinking the problem through.

Multiple locations
       Just taking the six letter 'my name' (ignoring Ferris' trailing 's') gives 16 abutting locations for a vertical string (6 below, 6 above, 4 at ends). And it's not just abutting, there is also intersecting. Any of the three 'e's of the Oxford six letter vertical string could share the 'e' of 'my name'. This might be six more locations, but I will be conservative and call it three. All these locations have the same odds, so the odds of a specific string abutting (or intersection) 'my name' at various letters on a particular grid is 5 million divided by 19.

Multiple strings
       How many candidate strings are there? Well there is certainly two: 'ereVed' (found) and 'deVere', equivalent to de Vere read up and down. But with proper high-liting 'de Vere' can be thought of as the four letter string 'Vere' abutted to  the two letter string 'de'. So it's arguable that the following six strings, which mix up the order of 'de' and 'Vere' and reading up/dn, also fit in the de Vere name universe:  'ed Vere', 'de ereV',  'ereV de', 'Vere ed', 'Vere de', 'ed ereV. So we have a name universe of 8 six letter name strings, all containing de + vere is various up/dn combinations. Divide the odds by another factor of 8 for multiple name strings.

Multiple grids
       There is nothing special about the x14 grid. There are something like 44 possible grids for a 448 letter text, so divide by 44 for multiple grids.

Multiple 'my name's
        But why restrict ourselves to sonnet 76?  'My name' occurs five times in the sonnets, so divide by another factor of 5.

                     5 million/(19 locations x 8 strings x 44 grids x 5 'my name') = 5 million/33,000 = 150 to 1 (or 0.67%)

        OK, still some modest mathematical strength remains, but the odds are not an overwhelming millions to one. It's in the ballpark of 150 to 1, about 2/3rd of a percent.

Bottom line
        So is sonnet 76 a cryptogram?  After considering a wide universe of similar findings, a fairly weak mathematically case does remains, but it rests on what I consider to be questionable cryptographic adjustments and fudging. The case is weakened by the lack of motive, there was no obvious reason for Shakespeare to hide his name in a document written for intimates and not intended for publication, and the case is further weakened by the lack of supporting hints (or keys). So while this might conceivably be a cryptogram, the mathematics and surrounding case are so weak that I don't see how we can have any confidence that Shakespeare (or de Vere) really encoded his name deliberately within the sonnets.

Links
Facsimile and searchable original spelling.
http://internetshakespeare.uvic.ca/Texts/search.html?e=Son_Q1   advanced search
http://internetshakespeare.uvic.ca/Library/facsimile/index.html    facsimiles

Searchable concordance of Shakespeare's works
http://www.opensourceshakespeare.org/concordance/
http://www.opensourceshakespeare.org/search/search-advanced.php   advanced search

Essays on sonnets
http://www.williamshakespeare-sonnets.com/sonnet-76

Forum --- Vere is Shakespeare ciphers
http://www.shakespearefellowship.org/ubbthreads/ubbthreads.php?ubb=showflat&Number=51063#Post51063
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