Saturday, December 15, 2007

Leibniz and the beginnings of AI

I had to take a little break from posting for a couple of reasons: the application process for graduate school and my laptop dying the true and final death (as opposed to a blue screen, which is more akin to a fainting spell). (Those also are the reasons for the postponement of the email game, if you were wondering.) But the application was marked complete as of yesterday.

Also, I've been outlining a book. The book would be nonfiction, nominally about toys and games, but wandering off into the same kinds of topics this blog normally covers, i.e. anything that strikes my fancy. More specifically AI and philosophy.

Here is the list of chapters I've come up with:

pop-up books
war games/RPGs

So I was researching pop-up books, and thought you might like to read some of my notes for the chapter.

The first paper engineering was in a book by Ramon Llull. It was designed to be a machine for thinking, an artificial intelligence. Borges points out that "in mere lucid reality... [it is not] capable of thinking a single thought, however rudimentary or fallacious... For us, that fact is of secondary importance. The perpetual motion machines depicted in sketches that confer their mystery upon the pages of the most effusive encyclopedias don't work either, nor do the metaphysical and theological theories that customarily declare who we are and what manner of thing the world is. Their public and well known futility does not diminish their interest."
It consisted of a stack of three concentric disks, of successively smaller size, which could be spun freely. Around the edges of each disk were sixteen terms, which combined made various phrases. By rotating the disks, it was possible to make all possible phrases combining those terms.

Four hundred years later, in the late 1600s, the mechanism fascinated Leibniz, who recognized that while Llulls's choice of terms was capricious and his execution of the idea simplistic, the idea of a machine for performing reasoning by mechanical combinatoric means was not, in itself, unreasonable. Beginning at age 12, he started work on this project which was always the closest to his heart, though it went uncompleted at his death.

The project consisted of a few parts, any one of which would be ambitious:
1. An ontology which contains all concepts expressible by language. An ontology can be thought of as a kind of dictionary, in which all ideas are defined by simpler ideas, until we reach the simplest concepts, the alphabet of thought. (Such an ontology is at the heart of the CYC artificial intelligence project and the Semantic Web.)
2. A simplification and making precise of grammar. Adverbs would be reduced to adjectives, which in turn would become nouns. Verbs would also be reduced to their -ing or noun form. Gender, declension, and so forth would be eliminated.
3. Every simple concept would be represented by an ideogram, a picture that would be immediately intuitive.
This Characteristica universalis would be the perfect language.
"Thus the name of each thing (or, rather, of each idea) would express its definition, and as all the properties of a thing follow logically from its definition, the name of a thing will be the key to all its properties. This does not prevent the same thing from having several other names, insofar as it possesses different properties. However, there will be one that is the key to all the others: the one that expresses the complete reduction of the idea into simple elements. All this is explained by the combinatory, which always serves as a basis for the characteristic: the formula of a concept that is in any way complex can be reduced to "factors" in a variety of ways, but there is only one reduction to "prime factors," that is, to simple elements, and it is the latter that serve as the foundation and explanation of the others.

"Such a nomenclature, in which the name of each thing (or idea) would be an adequate and transparent symbol for it and, as it were, its description or logical portrait, would clearly constitute a sort of natural language, such as Plato dreamed of in the Cratylus. It would be the Adamic language, as it was called by mystics, that is, the nomenclature that, according to Hebraic legend, the first man established in the terrestrial paradise and which men spoke until the confusion of languages at the Tower of Babel (The Logic of Leibniz by Louis Couturat, Chapter 3)."

"Leibniz thought that this supposedly primitive language was certainly unknown to us (Phil., VII, 205). Hermann von der Hardt asked him if the Adamic language was not Hebrew (Dutens, VI.2, 225). Leibniz replied, "Saying that the Hebrew language is primordial is the same as saying that the trunks of trees are primordial"; and he added that the only question is to know whether Hebrew is closer than the others to their common root, otherwise unknown, and that this would be the work of comparative philology (Leibniz to Tenzel, Dutens, VI.2, 232) (The Logic of Leibniz by Louis Couturat, footnote 107)."

"In Sections V and VI of his Discourse on Metaphysics, Leibniz asserts that God simultaneously maximizes the variety, diversity and richness of the world, and minimizes the conceptual complexity of the set of ideas that determine the world. And he points out that for any finite set of points there is always a mathematical equation that goes through them, in other words, a law that determines their positions. But if the points are chosen at random, that equation will be extremely complex ("Epistemology as Information Theory: From Leibniz to Ω," by Gregory Chaitin)."

4. There would be logical operations to act on these symbols, an algebra for logic. This idea was carried forward and eventually became the "For all" "There exists" "The union of" logical operators we use today for mathematics, philosophy, and AI.

5. There would be a mechanical system to perform these logical operations.

The overall system is a familiar one. English, a natural language, is translated into a precise language with simplified grammar and limited vocabulary. This in turn is transformed into binary notation (which Leibniz also invented for this purpose) and fed into a device which performs logical operations on it. The result is that processes which were previously performed by human thought (arithmetic, proofs, if/then statements) are performed automatically. He suggested that "all disputes could one day be settled with the words 'Gentlemen, let us compute!'"


Mom said...

Great stuff so far. I'll buy the book!
The idea of a thing being defined by its name is still very strong in Hebrew; perhaps that is evidence of the antiquity of at least its way of thinking, if not of the language itself. Commentary on the alphabet on the website tries to express the pictograph origins of the letters and their inner meanings: three-letter words thus become complex sentences. This may be more the manner of 'reading' that Nibley is doing with Egyptian on the JS Papyrus.

D said...

I have read that proto-Babylonian root words are all one syllable, so that each multi-letter proto-Babylonian word is a compound word. I'm not sure whether the idea is widely accepted among scholars, though.

D said...

Here is the link "The proto Sumerian Language Invention Process"