The World Chess Federation in Las Vegas, NV is involved in a dispute over trademark infringement. The web site for the World Chess Federation has a profile of its founder Stan Vaughan which includes this claim:

Grand Master Stan’s expertise as a cryptanalyst led him being noted for having solved two of the most important previously unsolved ciphers in the world: The Shugborough Hall Monument cipher for which he had received an award from the Reform Club, and the Zodiac Serial Killer 340 character cipher. Stan was also a National Trivial Pursuit Champion of 1986.

I cannot find any references that mention his solution. Does anyone know anything about it? I am attempting to contact Mr. Vaughan to see if he will give more information about his solution.

Much has already been written about the dubious content of the recently published book The Most Dangerous Animal of All: Searching for My Father . . . and Finding the Zodiac Killer by Gary L. Stewart and Susan Mustafa. It joins a crowded pantheon of weakly supported books, and yet went on to make a profitable appearance on the New York Times bestseller list for non-fiction eBooks.

Michael Butterfield does a good job of pointing out the major problems with the evidence presented in Stewart’s book. There is also a lengthy thread on Mike Morford’s forum, and many posts on Tom Voigt’s forum. You can look at Stewart’s evidence and judge for yourself.

But here I will focus on the the book’s claims about the ciphers. The authors write that Stewart’s sleazy father, Earl Van Best Jr., was the Zodiac Killer, and his name appears in three of the killer’s cryptograms. The authors suggest that this is proof that their suspect is indeed the Zodiac killer.

Let’s look at how they found his name in the Zodiac’s 340-symbol cryptogram:

Using the kanji style of writing he had learned as a child in Japan, [Earl Van Best Jr.] began on the right side of the page, arranging letters and symbols in vertical columns. Instead of a coded message, he included his full name, written backwards.
…
[One of New York’s Christian literary agents B. G. Dilworth] pulled up some images of the ciphers on his computer and at random began studying the 340 cipher, looking for my father’s name. He began by looking for the name Best.
…
Working his way from right to left backwards across the cipher, he found the name, Earl Van Best Junior. Van had put one letter of his name in each column.

Here’s what Dilworth’s discovery looks like:

Each column has one symbol marked. Here’s what they look like when you write them out from left to right:

But let’s write them from right to left instead, as Dilworth found them:

So, we’re getting closer, but it still does not look quite right. To overcome this, Dilworth allows some symbols to resemble other letters. For example, he treats the half-filled circle as the letter E. Here are the symbols with Dilworth’s interpretations:

Dilworth indulges in a bit of freedom with his approach. The problem, though, is that it causes at least hundreds of thousands of other names to appear in the ciphers. How can you know for sure that Earl Van Best Junior, a name among thousands, is the correct one? You can’t, unless you assume that you’ve already correctly identified your suspect.

Here’s a small sampling of the abundant names you can find using the same approach.

Timothy B. Greenwood

Clifton D. Pritchett

Carl B. Powell Junior

Earl Vasquez Junior

In fact, using Dilworth’s method, you can find many other similar Earls, such as: Earl Van Cook Junior, Earl Van Bell Junior, Earl Van Diaz Junior, Earl Van Cole Junior, Earl Van West Junior, Earl Leo Best Junior, Earl Bob Best Junior, Earl W Powell Junior, Earl B Little Junior, Earl T Howell Junior, Earl Clayton Junior, Earl Clifton Junior, Earl Wendell Junior, Earl B Patton Junior, Earl C Abbott Junior, Earl L O’Neill Junior , Earl a Osborn Junior, Earl O Hayden Junior, Earl C Albert Junior, Earl V Madden Junior, Earl Tolbert Junior, Earl F Bowden Junior, Earl Colbert Junior, Earl Boswell Junior , Earl Conklin Junior, and on and on and on. They are all appearing due to coincidence. Earl Van Best Junior is appearing due to the same kind of coincidence.

The book says:

To assure himself this was not a coincidence, B. G. used the same method to try to find his own name. It wasn’t there

He must not have looked hard enough, because it is there:

B.G. Dilworth

“Dilworth” even appears in the 408!

Gary Stewart himself appears

Gary Stewart’s full name appears in the decoded 408

Even his co-author Susan Mustafa appears in the 408

Dilworth also says:

He then looked … for more common names like Jane Brown and Mary Smith. He couldn’t find any first and last names in the same sequence

Once again, he didn’t look hard enough. Jane Brown can be found if you apply the method from top to bottom, and other common names are easily found:

Jane Brown

Betty Scott

Dorothy Collins

You can try it for yourself with this search gadget. You can also look at the 170,000 names I’ve found so far here (male names) and here (female names).

The book also says:

Even though the cipher had been decoded, they couldn’t take the next step of deciphering the killer’s name, because they didn’t know what name to look for.

Unfortunately, what this really means is: If you start with a name ahead of time, you can force it to appear within the cryptograms. This is how so many unreliable solutions are conjured from thin air. We see it repeatedly, and the pattern is usually this: The solver tries to generate a specific name, and eventually figures out a technique to make it appear. But the technique usually generates many other names. Since the solver has a strong desire to promote their suspect, all the other names are conveniently ignored.

You still need to prove that your solution isn’t just appearing by chance, like a face in the clouds.

Now let’s look at the authors’ claims about the 408 cipher:

I found a version on the Internet where the decoded message had been typed above the Zodiac’s cipher. I approached the three sections of the cipher as if they were a seek-a-word puzzle, looking at a particular letter and then looking vertically, diagonally, and across for my father’s name.

I saw it right away, plain as day: EV Best Jr.

Here’s the 408 with the decoded message printed above the cipher:

And here’s where he found E.V. Best Jr:

Notice how the name is permitted to flow in multiple directions, and can skip a symbol. As expected, that name is appearing purely by chance. Many other names can be found by chance as well:

Stewart

A.T. West Jr.

H.T. King Sr.

N.L. Peck Sr.

William

Milton

Wanda

Will Blair

Will Bean

Theo Nash

Lee Allen (Arthur Leigh Allen?)

Ted O’Dell

Ned Williams

Rob Forrest

Theodore (Kaczynski?)

Dan Eilliot

(Richard) Gaikowski

(Fred) Manalli

F(red) Manalli

Groucho

Gilligan

Again, there’s no way to accept “E.V.Best Jr” as a correct interpretation unless you already accept Stewart and Mustafa’s story.

Lastly, Stewart attempts to connect their story with Zodiac’s 13-letter cryptogram:

My father then included a new cipher with thirteen characters, including letters and symbols — the exact number of letters in Earl Van Best Jr.

The only connection there is that the length of “Earl Van Best Jr” is the same length as the 13-letter cryptogram. This is an extremely weak connection, since there are millions of names that are thirteen letters long. And the authors don’t bother to explain what any of the symbols mean!

I don’t doubt that Stewart’s father was a bad man and committed many terrible acts. But Stewart and Mustafa have tried to convince us that simple coincidences in the ciphers are proof Van Best was the Zodiac Killer. Stewart has made many rounds in the media to promote his book. His efforts were very successful – his “non-fiction” book sold many copies. But both the media and his publisher remain agnostic over the truth of his claims, sadly reinforcing the profit cycle of folklore and misinformation.

(Part 1 | Part 2 | Part 3 | Part 4 | Part 5)

A generous Zodiac researcher loaned me a copy of Gareth Penn’s hard-to-find book Times 17: The Amazing Story of the Zodiac Murders in California and Massachusetts, 1966-1981. Gareth Penn is one of the most prominent and prolific people among the many who have inserted themselves into the folklore surrounding the Zodiac case.

Gareth Penn (Credit: Mike Martin)

In 1987, Penn self-published Times 17, a collection of his sprawling essays, filled with well-written but delusional speculations connecting Berkeley professor Michael O’Hare to the Zodiac killings. Repeatedly dismissed by authorities, Penn’s claims span almost 400 pages. The book is filled with elaborate mathematical ideas which superficially appear rational, but fall apart quickly when examined. Penn’s most abundant trick is to use math to simultaneously generate and disguise random coincidences. First, he sets up basic systems of mathematical operations that create new information from the Zodiac’s correspondences and other facts surrounding the case. Then he plucks out the interesting bits of new information generated by his tricks, and ignores all the other uninteresting coincidences. This confirmation bias approach is shared by many similarly misguided amateur sleuths and codebreakers. Penn’s complicated mathematical procedures create a barrier for most readers, making his claims tedious to analyze and challenge. For an example, see my previous article about Penn’s letters to the popular Scientific American writer Martin Gardner. There you can see why Penn’s “binary Morse” system quickly falls apart: Morse code has a hell of lot of different interpretations when you let the codes run together.

Times 17 also features Penn’s “radian theory“, in which two of Zodiac’s killings form an angle of approximately one radian with Mount Diablo.

Map code and clues in Zodiac’s correspondences

Penn’s radian observation

It’s arguable whether this is by design by Zodiac. At the least, it’s an interesting observation. But throughout Times 17, Penn takes the idea to ridiculous extremes, connecting his mathematical games to angles formed by key words and elements of Zodiac’s correspondences. Penn spreads the interesting observation thinly across a great deal of poor reasoning.

Example of Penn’s application of pseudo-mathematics and angles to Zodiac’s letters

Penn’s bizarre behavior led some to think he might be the Zodiac Killer himself. And like Zodiac, Penn even has his own copycat. Former postal carrier Raymond Grant also self-published his own book filled with “proof” of Zodiac’s identity. His book is filled with many of the same mathematical coincidence generators employed by Penn. For many years, Grant has been arguing that Penn was part of a larger team which included Michael O’Hare, O’Hare’s mother, and Penn’s father. Grant claims he discovered and disrupted the catastrophic “Terminus Event“, the culmination of the group’s “Zodiac Project”. On web sites and online forums, Grant repeatedly tried to share his theories, which were met with strong criticisms. This led to a pattern of Grant authoring many lengthy responses and rebukes, only to be followed by their removal because of his frustration with other Zodiac researchers.

Grant describes discovering the “Terminus Event”

Penn and Grant seem to be intelligent, capable writers. But any serious analysis of their claims will lead you to question their sanity. Or at least their motivations. The study of the irrational crimes of the Zodiac killer has branched into an entire forest of irrational behavior, fertilizing an expanding mythology, like UFO enthusiasts have done by filling in the blanks on mysterious events in the sky.

You can now read the entirety of Times 17 online, if you want to subject yourself to the experience. The book is split into five parts, and can be viewed at the following links:

Times 17 – Part 1 of 5
Times 17 – Part 2 of 5
Times 17 – Part 3 of 5
Times 17 – Part 4 of 5
Times 17 – Part 5 of 5

You can also download the entire 100 megabyte PDF here: times-17-full.pdf. (UPDATE: Thanks to zodiphile, the book is now available in epub and mobi formats for reading on mobile devices). For more of Penn’s writing, read his Ecphorizer articles, or his followup book The Second Power (read it online here). He is also reportedly working on a third book. And, you can still visit Penn online at his blog, where you will only find the occasional bizarre posting of his cryptic puzzles.

Be sure to read Michael J. Martin’s comprehensive and fascinating article which goes into a deep exploration of the Gareth Penn saga. O’Hare himself has also written an article about his experience with Penn. Michael Butterfield has also written a lot of interesting material about both Gareth Penn and Raymond Grant.

Film reviewer Mike D’Angelo once wrote, “I think the [Zodiac] movie erred in selecting author Robert Graysmith as its source and nominal protagonist. Zodiac buffs know well that the true obsessive is a fellow named Gareth Penn.” Have a look at Times 17 and see if you agree.

Zodiac’s cryptogram symbols made a surprise appearance on The Spaghetti Incident, an album from the hard rock band Guns N’ Roses:

It contains a valid message. Hint: Use the 408’s key.

Click here to see a forum post with more background information on the album and cryptogram.

(Source)

From an upcoming natural language process conference in Seattle comes this paper from UC Berkeley: Decipherment with a Million Random Restarts.

In the paper, Berk-Kirkpatrick and Klein investigate the effectiveness of the “expectation-maximization algorithm” (EM) when it is used to search for solutions to homophonic ciphers. EM explores cipher solutions by using a statistical model of the English language. The paper describes EM getting stuck in local optima, a common problem with these kinds of automatic decipherment algorithms.

To understand the local optima problem, think of a rugged landscape. Your task is to find the largest mountain in the landscape, but you can’t see more than a few yards ahead of you. You walk around, thinking that your best bet is to find the steepest slope and follow it, You get to the top of a hill, thinking you’ve found the tallest mountain, but you’re only standing atop a medium-sized one. How can you find the tallest one?

For the EM algorithm, the answer is to randomly restart the search many times. In the rugged landscape, this translates to randomly and blindly teleporting you somewhere else in the landscape. Eventually, one of the slopes you follow will be the right one.

Zkdecrypto uses a similar approach. At each step, zkdecrypto is making small changes to a solution key, and keeping the changes that make the plain text look a little bit more like English. But it, too, might get stuck on a “small hill”: no matter what changes it makes to the key, the plain text doesn’t improve, and the real one remains beyond its reach until enough restarts are done.

Long story short: If at first you don’t succeed, try, try again.

The paper tries to answer this question: How many restarts are needed to get the right solution? The researchers’ answer is that it depends on the cipher. They looked at the Zodiac’s 408, which turns out to be an easy cipher to solve: Accurate solutions are discovered without more than a hundred random restarts. Then the researchers created their own 340-character cipher, and accurate solutions were found using hundreds of thousands of restarts. They distributed the numerous restarts to the 512 computational cores of a powerful computer graphics card, an approach that is thousands of times faster than running the restarts one at a time in sequence. The increased difficulty in solving the test cipher is attributed to its smaller length, and its larger number of cipher symbols. But even with only a few hundred restarts, more than half of the correct solution to their test cipher is discovered by the program, which is usually enough for a human solver to take over and complete the solution.

The researchers unfortunately repeat the claim that in 2011, Ravi and Knight were the first to crack the 408 using completely automatic methods. Zkdecrypto has been automatically cracking the 408 since 2006.

Finally, Berk-Kirkpatrick and Klein investigated Zodiac’s 340, and mention the possibility that it may not be a homophonic cipher, or even a valid cipher whatsoever. No one even knows its proper reading order. This paper is the first I’ve seen that presents specific evidence to support the argument that the 340 is not a homophonic cipher in a normal reading order. First, the researchers generated 100 more test ciphers that are similar to the 340, and ran their EM algorithm on them with 10,000 random restarts. The result was an average accuracy of 75%, where only two ciphers had less than 51% accuracy. If the real 340 is “normal”, at least part of its message would surely have been revealed by now. When they ran their EM algorithm on the real 340, the best results were still nonsensical. They also found that the search landscape looks much different for the real 340 than it does for their test ciphers, suggesting a strong difference in its construction.

I’m curious about how closely their test ciphers resemble the real 340. Do they contain similar cyclic sequences of homophones? Do they have the weird pivots? What about spelling errors and encipherment errors, which were abundant in the 408? At this point, it seems best to try to guess what Zodiac may have done to make the cipher unsolvable. Then we can generate more test ciphers and automate their solutions. If the real 340 is constructed the same as the test ciphers, then its solution, too, will emerge.

Then again, perhaps we should heed W.C. Fields’ advice:

If at first you don’t succeed, try, try again. Then quit. There’s no point in being a damn fool about it.