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Near the end of 1801, his first year as president of the United States, Thomas Jefferson got a letter from Robert Patterson, professor of mathematics at the University of Pennsylvania, containing a page encrypted according to a new method. Patterson described his cryptosystem in detail, and boasted that without the key — which he didn't provide — decryption of his message would "defy the united ingenuity of the whole human race".

After more than 200 years, the code was finally broken by Dr. Lawren Smithline, a mathematician at the Center for Communications Research in Princeton, N.J., using a technique originally developed for biological sequence comparison.

This could be the premise for a new Dan Brown novel, if Patterson's message were sufficiently bizarre and consequential.

Fortunately, his sample encryption turned out to be simply the preamble to the Declaration of Independence. You can read more about the code in an article by Rachel Emma Silverman, "Two Centuries On, a Cryptologist Cracks a Presidential Code", WSJ, 7/2/2009, which also a nice flash animation of the ciphering method. Details of the crytanalysis can be found in Lawren M. Smithline, "A Cipher to Thomas Jefferson", American Scientist, March-April 2009 (subscription required).

One interesting thing in Patterson's letter was his list of desiderata for a system of "secret writing":

1. It should be equally adapted to all languages.
2. It should be easily learned and retained in memory.
3. It should be written and read with facility & dispatch.
4. (Which is the most essential property) it should be absolutely inscrutable to all unacquainted with the particular key or secret for decyphering.

Patterson's system certainly scores well on points 1-3, but as Smithline showed, it fails on point 4.  I'm not sure how it compares in strength to some of the better alternatives available in 1801, for example Vigenère ciphers, either in principle or in the cryptanalytic practice of the time. If Patterson's method were combined with a Vigenère cipher, neither Smithline's method nor the standard methods for solving Vigenère ciphers would work, and perhaps the result would have been effectively unbreakable with the methods available in 1801, I'm not sure. In comparison, Bruce Schneier's low-tech Solitaire algorithm is said to be effectively unbreakable even with modern techniques and machinery, but it's a good deal more troublesome on points 2 and 3.

In any case, Patterson's system seems never to have been used in practice.

The exchange between Patterson and Jefferson reinforces what we already know about Jefferson's intellectual breadth. In 1801, Jefferson was president of the American Philosophical Society as well as of the United States, and Patterson was the A.P.S. vice-president.  For another window on their relationship — and on Jefferson's intellect — see his letter to Patterson of Nov. 10, 1811, on "the subject of a fixed standard of measures, weights and coins".

But reading the biographical sketch of Robert Patterson in Penn's archives reminded me of some other important characteristics of American culture:

Robert Patterson, the son of Robert Patterson and Jane Walkers, was born on May 30, 1743 on a lease-held farm near Hillsborough, County Down, Ireland. His family was respectable, though not affluent. Patterson attended school at an early age and soon became distinguished for his love of learning. He excelled in mathematics, but his family could not afford to pay for a university education. In 1759, when the French invaded Ireland, Patterson enlisted in the militia, and after serving for a year, rose to the rank of sergeant. He devoted himself to his military exercises, and soon became distinguished enough for his skill and good conduct to attract the attention of the officers of a British regiment stationed near Hillsborough, who offered him a commission in the regular army. Patterson refused this commission, choosing instead to return home to work on the family farm.

In October of 1768, determined to try his fortune in America, Patterson embarked for Philadelphia, arriving there almost penniless. After spending a week in Philadelphia, Patterson set out on foot for Bucks County in order to seek employment as a schoolmaster. He was immediately hired at a school in Buckingham.

Although Patterson had a natural talent for teaching, he decided to make more use of his mathematical talents, especially his knowledge of determining longitude through the use of lunar observations, and moved back to Philadelphia to teach navigation. […]

In 1772, with his finances vastly improved, Patterson was persuaded by a friend to invest his money in merchandise and open a country store in New Jersey. However, since he was unsuccessful as a shopkeeper, he was happy to accept a position as Principal of the Wilmington Academy in Delaware in 1774.

At the outbreak of the Revolutionary War, his duties as Principal were suspended due to the fact that many of the students at the Wilmington Academy were called home. After removing his family to a small farm near Roadstown, New Jersey, Patterson enlisted as a military instructor in the Delaware militia, then under the command of Colonel John Haslet. He later served under Colonel David Hall, first in the medical corps and then as a brigade major. He remained in the militia until the British army evacuated Philadelphia and New Jersey in 1778, when his brigade was disbanded.

In 1779, after the College and Academy were reorganized into the University [of Pennsylvania], Patterson successfully applied to Dr. Ewing, the Provost, for employment as Professor of Mathematics. He was Professor of Mathematics from 1779 to 1810, Professor of Natural Philosophy and Mathematics from 1810 to 1813 and Vice-Provost from 1810 to 1813.

I don't think that it happens anymore, in the U.S. or elsewhere, that someone becomes a university professor without ever having attended a college or university as a student.  But America is still a place where immigrants can find opportunities denied to them in their homeland. And it's also a place where people often have second and third chances to find their calling.

One other note in Patterson's bio resonated with me in a personal way:

Patterson resided at nine different locations in Philadelphia, beginning at 148 South Fourth and ending at 285 Chestnut Street. It was said that he only remembered the latter address because the second digit was the cube of the first and the third was the mean of the first two.

I've always had a terrible memory for numbers, and this is exactly the sort of mnemonic that I've always resorted to. For example, after all these years, I still remember the standard Philadelphia telephone area code, 215, by keeping in mind that the second digit is half the first, and the third is the sum of the second and the square of the first.  It seems illogical that this sort of thing should help, but it does!

[By the way, I note that determining longitude by lunars was apparently only described as a practical method in 1767 (at least, that was the date when the Theoria lunae juxta systema Newtonianum was published). So for Patterson to start teaching it in 1769 or so was fast work.

I wonder whether he learned about it from Charles Mason, of Mason-Dixon fame, who seems to have spent parts of 1767-68 in the Philadelphia area.]

July 3, 2009 @ 11:36 am · Filed by Mark Liberman under Language and culture

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