Motivation:
Recall my premise that the positions of the misspelled letters are important. Here is the relevant quote:
• “When I asked about the misspellings and asked if they were accidental or deliberate, Sanborn said that they were deliberate, but it was less important *what* they were. He said, and I quote: "it's more the orientation of those letters that's useful there." Later on in the evening he repeated that point, saying it was the "positioning" that was important.”
- Elonka Dunin, post to Kryptos Group
Another premise is that matrix manipulations, and in particular “shifts”, are required. The quote:
• “Getting back to Kryptos, Sanborn commented that he was surprised that no one had tried recovering the original matrix and running it through all possible shifts.”
- Elonka Dunin, post to Kryptos Group
Pre-Step Observations:
So I began to concentrate on the locations of the three black boxes, intentionally focusing not so much on what was in them but rather on their relative positions in the matrix. Eventually, due to the second quote above, I investigated what would become of these locations after performing a matrix “shift”. Consider the operation defined by moving each character one spot to the left. For those that are already in the leftmost column, move them to the column on the right but one row higher than they were before. For the character that is in the upper left corner, move it to the bottom right. Such an operation, if performed repeatedly, would move each character slowly through the entire array until, after 867 instances, they all end up back in their original positions. The hint suggested that we try running the matrix through all possible shifts, so I began to do so. And something interesting happens after the 73rd “shift”...
Step Process:
Perform the matrix shift defined above 73 times, so that the misspelled character “A” moves to the upper left hand corner. The misspelled character “Q” will be found in the lower left hand corner, and the misspelled character “U” ends up precisely on the middle row of the right hand side, completing a natural symmetry that is very interesting. Please see the figure labeled “The Symmetry” below.
Post-Step Observations:
If one were to choose three matrix positions at random, the number of possible arrangements are “867 Choose 3”, or
Actually, I have overstated the number of possible arrangements a bit, because I also ran the matrix through all possible “shifts”. Thus, it is a given that during the shifting process, we would observe a misspelled letter in the upper left position exactly three different times. The question, then, is how many arrangements there are for the other two misspelled characters when this happens. In other words, to compute how many distinct arrangements (modulo shifts) there are for the three misspelled characters, we really need to compute the number of possible arrangements of 2 locations in a set of 866 characters and then divide that result by 3. So we need to divide 3 into “866 choose 2”, which is
The result is about 125,000 possible arrangements that differ from one another even with the freedom of shifts. Thus, any particular arrangement of the three locations, allowing for all possible shifts, has odds of about 125,000 to one against occurring. I understand that these odds cannot be interpreted as indication that my theory has similar odds of being right. My motivation for presenting these odds is to establish that the observation of “the symmetry” is not simply a common by-product of the processes I have used. Common it is not, so it might be significant.
In order to establish significance, we need something more than just steep odds. After all, the odds are steep against winning the PowerBall Lottery, but people still do it. There’s very little reason to question the significance of those events, unless the wife of the PowerBall administrator wins. If that were to happen, somebody would probably investigate to make sure that nothing fishy happened. (Okay, I know that there is probably some policy that even prevents the wife from even playing, but you get the point.) In the next step, I share quotes and other observations which indicate that one would be hard pressed to come up with a different arrangement of the misspellings that was as distinct and relevant as this one. This arrangement is, in fact, the administrator’s wife, and I thought it wise to investigate.
Now we have “Palimpsest”, the instructions of K1, and the locations of the misspelled characters incorporated into the approach. This is the third step along the path of creating the desired “original matrix“.
