Friday, July 3, 2009

Thomas Jefferson, Cryptology, and Fossil Shark Teeth – Brought to You by the Letter J

It’s not surprising that the U.S. presidency’s greatest polymath Thomas Jefferson was into cryptology. The challenge and mystery of an encrypted message must have had great appeal for this consummate political intriguer who counted a wheel cipher for encrypting messages among his inventions. Cryptology was apparently a frequent subject of his correspondence as well. In December 1801, University of Pennsylvania mathematician Robert Patterson sent Jefferson a letter with a coded message which, until recently, had remained unsolved.

In his letter, Patterson laid out the rules he followed to encrypt the message:

–write the message down in columns arranged from left to right, thereby creating rows or lines of gibberish text
–divide the aligned columns into blocks of text, each block having the same numbers of lines and columns
–rearrange the lines in exactly the same way within each block (e.g., make the fourth line the first in each block)
–add different numbers of additional (decoy) letters at the beginning of each line.

Patterson believed that the code was virtually unbreakable. To read the message, one would have to have the series of number pairs that showed (1) where each line of encrypted text was moved within each block, and (2) the number of letters added at the beginning of the line. For example, if each block had three lines and those lines were rearranged so the third line was now first, the first line was second, and the second line was third, the series of numbers could be something like 35 14 25 – the first number pair, for example, indicating that the third line in each block was moved to the first position and five additional letters were added to the front of the line, and so on. Armed with the series of paired numbers, the message could be recreated.

Lawren Smithline, a mathematician with the Center for Communications Research, has broken the 200 year old encrypted message. He used digraph (letter pairs) frequency analysis and dynamic programming, coupled with some guessing, to decipher the message (he asserts the decoding was “doable” in Jefferson’s day). For more on the story and the text of the message Patterson sent to Jefferson, see the following articles: Two Centuries On, a Cryptologist Cracks a Presidential Code, by Rachel Emma Silverman, Wall Street Journal, July 2, 2009; Coded to the Last: Jefferson’s Conundrum, by Craig Lambert, Harvard Magazine, July-August, 2009.

The Letter J

Both articles make passing references to simpler methods of encrypting messages, mentioning letter frequency and simple codes consisting of letter substitution. The key to deciphering a message encrypted using simple letter substitution is knowing the frequency with which letters are likely to appear in normal usage. For instance, in English, the letter E is the most frequently used letter, so one can begin with the assumption that the most frequent letter in the coded message is a substitute for the letter E. The Cornell University’s math department has posted an English letter frequency table based on a sample of 40,000 words (182,303 individual letters). According to that table, for example, about 12% of the letters will be an E, a little more than 9% will be a T, and just 0.07% will be a Z.

This bring me to the letter J. Over the past couple of weeks I have been bedeviled by an uncooperative key on my computer keyboard. At first, the key for the letter J just balked at responding but, if well struck, would agree to post a J. Then two days ago, all communication ceased. Okay, one could possibly live without J since the Cornell table tells me that, with the exception of Z, J is the least used letter, only 188 of the 182,303 letters in the sampled 40,000 words (or 0.1%) are Js. But, say your name is Jefferson, all bets are off, and there are several reasons, not worth getting into here, that make the letter J a more frequent visitor in my word processing than the Cornell frequency table would have it.

Now, I have no particular technical or mechanical aptitude, though I have added internal memory and the like into various PCs and, indeed, resurrected the notebook computer in question from a Coke spill and subsequent keyboard malfunction. So, I was willing to try to see what ailed the J key on my keyboard. I popped the J key cap off the keyboard, expecting to see a tangle of cat hair in a spot of sticky Coke beneath. Surprised, I saw a small black object nestled under the little wire Xs of the decapitated key. I went in with a kitchen knife (computer repair tool of choice) and gently freed the offending object. I was even more amazed when I realized what had thwarted my J’ing:

At just 4 millimeters in length, this broken (how hard did I hit that J key?) fossilized shark tooth showed surprising strength in bringing down a bit of 21st Century technology. I have several theories about how it got here, including one that involves beached Viking funeral ships (there's a prior post on this).

I have to believe that Jefferson would have been interested in this fossil (and, of course, in the computer, disassembled keyboard and all). The entrance hall at Jefferson’s home Monticello was a de facto museum featuring, among other objects depicting the history and pre-history of this country, a display of mastodon fossils. Some of his fossils are now in the collection of the Academy of Natural Sciences in Philadelphia, including two megalodon shark teeth from the Cooper River in South Carolina sent to him in 1806 by William Reid. In the picture of one of the teeth posted by ANS you can see Mr. Jefferson’s faded signature. Jefferson and paleontology, a natural combination.

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