Godel, Hofstadter, Fish

A while back I wrote about how Fez is about the experience of being in an incomplete universe, or running around in the lower dimensions of a universe whose whole we cannot perceive or comprehend. I'd like to expand on this a bit.

There's some interesting symbolism in Fez that I don't really see people talking about. It's the incomplete cube, the shape of that thing in the totem room and the shape of the 3 "heart cubes". As I mentioned before, I see them as a metaphor for incompleteness and for Fez itself. However, in the very last part of the game, the "Temple of Love", the cubes are assembled into a heart shape. I've heard people suggest that it is a gesture of love towards the fans for getting that far, but I prefer to understand it as in-universe. If you pick up an incomplete cube and stamp it on a surface with any of its three incomplete faces, you get the shape of a heart. This shape is the 2D analogue of the incomplete cube. The 3 incomplete cubes in the temple of love are assembled in a formation that reflects this same heart shape, an incomplete square. The 3D shapes are mimicking the 2D shape of their own geometric faces, it is self-referential. The Temple of Love is an demonstration of this simple geometric fact, that the incomplete cube resembles a heart. I think that it's trying to say something through this geometric observation.

Once upon a time, mathematicians attempted to rigorously define reality and logic. However, at every turn, the very nature of logic thwarted their attempts. Naive set theory (the idea that any definable collection is a set) was shown to give rise to paradox, as demonstrated by Russel's paradox (the set of sets which do not contain themselves is both a member of itself and not a member of itself). If such a paradox could result from the system, it must be faulty. In an attempt to save logic from paradox and complete existential implosion, Russel formulated the "theory of types", which attempts to thwart the possibility of self-reference (self-reference being deemed the cause of paradoxes) by defining all things as part of a hierarchy of types which can only refer to objects of a lower type. Armed with this tool, he wrote the Principia Mathematica, an attempt to create an airtight foundation for math and logic and forever defeat the demons of self-reference and paradox. An attempt to "bootstrap" logic itself. Then Godel came along and made the observation that PM was riddled with self reference and that it was fundamentally rooted in the nature of logical systems and impossible to prevent. Thus came Godel's incompleteness theorem, which states the frightening truth that no consistent system can ever prove all truths, or prove its own consistency.

Decades later, Hofstadter wrote GEB, describing this unavoidable phenomena of self-reference as the root of the self, and the means by which systems made of meaningless parts can take on meaning (such as brains giving rise to identities and selves).

I think Fez reflects these things, both in the game itself, and in the way it has impacted its fans. The 32 cube ending is a demonstration of incompleteness, and the melancholy music and visuals give a gloomy feeling about the universe and how there is no level at which it gives way to a complete, cohesive whole. In many parts of the game, the mystery and ineffability of the world is portrayed in a foreboding way. Whether it's the owl statue always watching you in that graveyard, or the skull and Dot's dialogue hinting at deeper history, or the ghosts suggesting that Dot may not be who she appears to be and that your world may not be what you think it is, or the foreboding music in the room with the broken stargate. I think this reflects the human need to understand things, the desire to explain things and the uneasiness of not knowing what is going on.

The incomplete nature of the game (monolith, 4th concentric square) has also had the same effect on its players. There MUST be a solution, there MUST be some legitimate way to obtain these things, we think to ourselves. It's natural human instinct.

But in the Temple of Love, which is also at the end of the soundtrack, the game shifts tone on its presentation of the incomplete. I think the heart represents the meaning which arises from self-referentiality and incompleteness. The incomplete cube is revealed to be a heart, and the music takes on a sweet tone, and ends. This is the final note of the game.