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JESUS, BUDDHA, AND GÖDEL: Unraveling the Matrix Mythos
I. The Gödel Sentence and The One
Structurally, the mythology of the Matrix is patterned directly after a central result in 20th-century mathematical logic known as the Incompleteness Theorem, first discovered by the Austrian logician Kurt Gödel in the early 1930’s. For an excellent, mostly non-technical introduction to the Incompleteness Theorem, the interested reader is referred to “Gödel, Escher, Bach: An Eternal Golden Braid” by Douglas Hofstadter. (There are also numerous websites dedicated to the topic, though they vary considerably in both didactic quality and requisite level of mathematical background.)
Gödel was able to demonstrate that any “formal system,” of which mathematics and computers are examples, is inherently incomplete. “Incomplete” has a very specific technical meaning; in broad strokes it means that there are truths that exist within a system that are not provable using the rules of that system. If the system is a set of mathematical axioms, this means that there are mathematical truths which are not provable (or “decidable”) using those axioms. Such an unprovable truth is known as a Gödel Sentence (G) and all formal systems have them (each particular system having its own unique G).
The relationship between Gödel and the Matrix is made evident when Neo confronts the Architect at the end of “Reloaded.” It is explained to him that:
Your life is the sum of the remainder of an unbalanced equation inherent to the programming of the Matrix. You are the eventuality of an anomaly which … is systemic, creating fluctuations in even the most simplistic equations.
Neo is a destabilizing anomaly inherent to every conceivable Matrix: in the language of mathematics, he is the Gödel Sentence itself.
The Prophecy of The One revolves around the fact that the Matrix is a computer and therefore is nothing more than just another formal system. As such, it is inherently incomplete and so there exists for that system the equivalent of a Gödel Sentence, G, which is true but undecidable within its framework. Neo, as The One, is the organic instantiation of G for the formal system of the Matrix. The Incompleteness Theorem tells us that every system has a G just as, in the movie, every version of the Matrix inevitably produces its own incarnation of The One.
According to the Architect’s explanation, whenever G for a particular version of the Matrix is found (i.e. The One is born) its incompatibility with the rules of the system leads inexorably to a “cataclysmic system crash.” In “Reloaded,” this progressive system failure is embodied by Agent Smith. Notice, for example, that his 'new purpose' was a direct and immediate result of Neo assuming his role as The One; he is the destructive consequence of the Gödel Sentence. His continuing 'replication' is simply the exponential spread of the instability (or anomaly) throughout the Matrix, and once it reaches all parts of the system (remember Smith admitting to "wanting everything"?) the Matrix will crash.
Fortunately for the Matrix, there is a way to avoid this disaster scenario. Mathematically speaking, any formal system can be ‘saved’ from a given G by simply incorporating that G into its axiom schema: making it a by-definition part of the system, thereby removing its undecidability. Within the framework of the movie, this is accomplished by having The One “return to the source,” which renews the Matrix and saves it from the instability introduced by his arrival. This is not a permanent fix, however: this new version of the Matrix is susceptible to its own version of the Gödel Sentence, which will ultimately lead to the birth of yet another One and a continuing cycle of death-and-rebirth of the system, ad infinitum. According to the Architect, what happens in the movie takes place during the fifth repetition of that cycle.
That’s the end of the math, but it is only the beginning of the story of “The Matrix,” for while mathematics provides the foundation, the Wachowskis have looked elsewhere for the materials with which to build their mythological edifice.
II. The Hero’s Journey
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