Gulliver and the Markov Chain

Long long ago, before Claude Shannon modeled the distribution of English Words as a Markov process, before Larry and Sergey modeled the Random Surfer as a Markov Chain on the Graph of the Internet, before SciGen made Markov Chains the legend of Slashdot, before even Monte-Carlo and Metropolis-Hastings, there was Jonathan Swift.

Martin Gardner’s “Logic Machines and Diagrams” is a highly recommended book. Especially for those who are interested in the early history of computing from a symbolic logic processing perspective as opposed to the history of the numeric processing computer. The book opens with the curious character of Ramon Llull. If you ever studied AI from Russell & Norvig’s legendary AIMA and remember the cover image – Among Lewis Caroll, Turing, Frege, Babbage and Aristotle you can find this messy drawing in the left hand corner that belongs to Mr. Llull.

Ramon Llull was a curious character. He believed in logic and he believed in religion. (Much like Aumann or Kripke for contemporary examples). He believed that he could encode the principles of Christianity into a consistent formal system and use it as a tool to derive propositions, detect contradictions and convince the Crusading Muslims about the nature of God and Truth. He got killed for talking batshit and pissing people off before he got around to doing any of this but there was something interesting he did manage to concieve – The Lullian Circle – Seen in the cover of the aforementioned AIMA.

The Lullian Circle is a series of concentric disks with markings along the circumference. The markings represent words or phrases. By rotating and aligning them you generate a combinatorial number of sentences. For each of them, an Index is referenced as the answer which either asserts the truth value of the statement or offers a proposition for the question. Most of Lull’s works did not have Socratic appeal and was pseudo-scientific in nature. But the Lullian circle apparently inspired Leibniz in his syllogistic pursuits.

This is where Jonathan Swift comes in. In Book 3, Lemuel Gulliver visits the Grand Academy of Lagado, where he sees “The Engine” – A 20 x 20 grid of cubes inscribed with words on their sides. Each of the 20 rows and 20 columns are rotated by levers. The Professor calls upon his students to rotate the lever and randomly stops them. Whenever they encounter a sequence of 3 or 4 words that could be reasonably fit into a real sentence, they transcribe it and produce “great works of art and science without genius or study” as the parody goes.

According to Gardner, this is Swift pulling a fast one at the expense of Llull. Not only that, but we also have one of the earliest recorded instances of a Markov Chain in action. Instead of stochastically extracting words from a distribution, the students of Lagado generate random words and see if they fit a distribution. And they beat SciGen to it by a few hundred years.

Happy St. Patrick’s Day to everyone in Dublin [1]

[1] – As coincidences happen, Swift is interred in St. Patrick’s Cathedral here.

Filed under: Books, Computer Science, Dublin, Mathematics