Motivation:
So here I was in possession of an interesting, but suddenly incomplete, matrix. After the deletions and insertions from the previous step, the bottom row only has 6 characters. Since I seek the “original matrix”, there seemed nothing better to do but count the characters and form a complete matrix…
Pre-Step Observations:
There are 703 characters in the current array, and that number has only two prime factors: 19 and 37, each of multiplicity one. So, if I want to form a filled rectangle, it must be 19 by 37 (or its transpose).
Step Process:
Form the remaining text into an array that is 19 rows tall by 37 columns wide. If you do so, then you will have a matrix such as the one labeled “The Abscissa” below.
Post-Step Observations:
At this point, I was very glad that I had selected unique colors for the different sections K1-K3, because it was easy to observe how the text of K2 (see the green text of “The Abscissa”) landed perfectly along the center row of the array, which I have labeled as the X-axis. (Coordinates seem to be playing a role in K2, so it seemed natural to imagine an X and Y axis superimposed on this nicely shaped array.)
Thus came my second “Aha!” moment. As observed earlier, K2 is aligned perfectly with the presumptive X axis. But what is the keyword that was used to encode K2? That’s right… “abscissa”, which is another word for the X-axis. This may be another nice “Easter Egg” courtesy of Mr. Sanborn.
And then, my “Aha!” moment was trumped by an “AHA!” moment. I mentioned earlier that coordinates seem to be playing a role in K2. Well, to be more specific, geo-coordinates are playing a role. Imagine that the X-axis of this array were to be thought of as the Earth’s equator. Then if one were to describe latitudes in 10 degree increments, one would need 9 rows above and 9 rows below the equator in order to cover the full range of possibilities. Including the equator itself, that would result in exactly 19 rows (or “parallels”). Imagine also that the Y-axis of this array were to be thought of as the Prime Meridian, passing through Greenwich, England. Then one would need 18 columns to the left and 18 columns to the right in order to cover the longitudes, for a total of 37 columns (or meridians). So a “flat map” representation of the Earth would include 19 parallels (including the poles) and 37 meridians (including overlap at the international dateline, as maps typically do). But that is exactly the shape of the only complete matrix that can emerge from this step. See the figure labeled “The World” below. (By the way, if you use my “World” to find Langley, it would fall in a cell that is occupied by an “L”. I believe this to be coincidence, but it is cute anyway.)
I don’t even know how to compute a probability for this. Consider these facts:
• these steps have resulted in a number of characters that can only be fashioned into one particular complete array,
• the array has precisely the right shape to represent the Earth,
• the K2 plaintext describes the Earth and its coordinate system,
• K2 is aligned precisely with the equator, and
• K2’s keyword for encryption is “abscissa”
These facts form a set of observations that are very compelling and which provide the necessary transition from the “doorway instructions” (1 and 2) to the “Earth instructions” (3 and 4), lending extra credibility to my “text as instruction” premise. While it is true that the freedom of interpretation involved with “removing debris” or “inserting a candle” could be responsible for the shape of the array, it could not simultaneously explain the perfect alignment of K2 plaintext with the abscissa, at odds of 703 to 1. (And I likewise challenge anyone to provide a more natural and literal interpretation of those two instructions, starting from the previous step. It should be clear that I was not “reaching” in order to obtain a nice result.) This fact cannot be overstated: by a simple application of the literal instructions (1 and 2) my array has transformed from the shape of a “doorway” to the shape of the “world” precisely at the moment that it needed to in order to support instructions (3 and 4) and, just as a bonus, we get the correspondence to the keyword “abscissa” in the process.
Through the previous sequence of steps, it is apparent that each of the plaintext sections (K1-K4) were highly constrained with regard to the number of characters in each. Mr. Sanborn must have put forth significant effort to present the veiled messages in precisely the right number of characters and with misspellings in prescribed locations. This fits well with some of his remarks in various interviews regarding careful wording of plaintext.
Now we have “Palimpsest”, the instructions of K1, the locations of the misspelled characters, the instructions of K3, “Abscissa”, and the “Earth Coordinates” theme of K2 incorporated into the approach. This is the fifth step along the path of creating the desired “original matrix“.
Note: We have reached the half-way point of my work (roughly). There have been quite a few steps taken already (although they were each simple and motivated). One of the “knocks” against this multi-step approach is that there is a danger of “propagation of error”. If you are interested in reading about that dispute, and my response to it, you can click here.
