What was Ramon Llull's Ars Magna, and why is it linked to computing?

Ramon Llull wanted a tool that could settle arguments. His answer was the Ars, or "Art": a system in which a handful of basic ideas, each marked by a letter, could be combined in every possible way by turning concentric paper circles. Each combination became a statement or a question to examine. The most complete version, the Ars generalis ultima ("the ultimate general art"), is also known as the Ars Magna, the "Great Art."

Llull built no machine and had no notion of a computer. Yet historians of computing keep returning to him, because he tried to turn part of reasoning into a procedure that anyone could follow step by step.

Who Llull was

Ramon Llull was born on the island of Majorca around 1232 and died around 1316. He wrote more than 200 works in Catalan, Arabic and Latin, and he is counted among the first writers to use Catalan for serious philosophy.

According to an account of his life written by a friend in 1311, Llull was a married man with two children, busy writing a love song, when repeated visions of Christ on the cross changed his direction. He set himself three goals: to convert non-Christians, to write books against what he saw as their errors, and to found schools that would teach missionaries the languages they needed, especially Arabic.

During a retreat on Mount Randa in Majorca in 1274, he conceived the method that would occupy him for the rest of his life. He revised it many times. The final phase includes the Ars generalis ultima, dated about 1305 to 1308 and finished in Pisa, and a shorter version, the Ars brevis of 1308.

What the Art was for

Llull's purpose was religious debate. He wanted to persuade Muslims and Jews by reason rather than by authority, so he built his Art on ideas the three faiths shared: that God is good, great, eternal, powerful, wise and so on. If everyone accepted the starting points, he reasoned, then a fair method for combining them should lead everyone to the same conclusions.

He also had a broader ambition. Llull believed every field of knowledge rests on a limited number of basic principles, and that studying all their combinations would reveal what can be known about it. From a few principles, an unlimited number of arguments could be found.

How it worked

The later Art uses an alphabet of nine letters, B through K. Each letter stands for six different terms at once. Here are three of them:

Letter	Question	Divine quality	Subject	Relation	Vice	Virtue
B	whether?	goodness	God	difference	avarice	justice
C	what?	greatness	angels	concordance	gluttony	prudence
D	of what?	duration	heaven	contrariety	lust	fortitude

The Art also uses figures: circles, triangles and tables that show how letters can pair up. The most famous is the Fourth Figure, three concentric circles, each marked with the nine letters, that can be turned against one another.

Here is how a user would work with it:

Turn the circles until three letters line up, for example B, C, D.
Read the combination using one of the meanings for each letter. "BC" can mean "goodness is great," or, switching meanings, "difference is great."
Treat each reading as a statement or question to examine, such as "Is goodness great?" or "Of what does greatness consist?"
Turn one circle a notch and repeat. Llull describes walking through the combinations in order, BCB, then CCB, and so on, so that none is skipped.

The circles do the bookkeeping. They make sure every combination appears exactly once, so the person using them can focus on judging each one.

Try it: Cut three paper circles of different sizes, write the letters B, C and D around each, and pin them together. Turn them and list every three-letter combination you get. How many are there? Now imagine doing it with nine letters and six meanings each.

Who picked up the idea

Llull's Art drew followers and critics for centuries. In the 16th century the philosopher Giordano Bruno developed it in his own direction. In the 17th century the German philosopher Gottfried Leibniz wrote his dissertation about Llull's Art and called the general idea ars combinatoria, the art of combination.

Was Llull's Art an ancestor of AI?

It is fair to call it a distant ancestor, as long as we are careful. Some computer scientists treat Llull as a founding figure for information science, and the case rests on three ideas his Art contains. First, symbols can stand for concepts, so letters can be manipulated in place of ideas. Second, a fixed procedure can generate every combination of those symbols systematically. Third, a physical device, even one made of paper, can carry out part of that procedure.

All three ideas are central to computing. Early AI programs in the 1950s and 1960s, which proved theorems and solved puzzles by searching through combinations of symbols, worked in a spirit Llull would have recognized.

What the Art cannot do is decide which combinations are true or useful. That judgment stays with the human user and with Llull's religious framework. Much of today's AI works differently: systems such as the game-playing program AlphaGo learn patterns from vast amounts of data instead of combining a short list of agreed principles. Even so, the question Llull asked, whether a careful procedure can do some of our thinking for us, is still the question the whole field is built on.