Incompleteness

“A finite game is played for the purpose of winning, an infinite game for the purpose of continuing play.”

— James P. Carse, Finite and Infinite Games

There is the outer world and then there is the world that exists inside us. The world inside us encodes a map of of the world out there. We use this map to navigate the outer world and update it as we discover new information that fills in previously empty parts of the map, or revises existing portions.

Young children have very sparse map that they fill in with new information they take in. The map is sparse, but not empty in the “blank slate” sense. The lines that they start with on their map are genetic inheritances from millions of years of evolution, or however you prefer to think about it. You can’t bootstrap a system out of nothing. You have to start with something, and that something is what determines how the system processes, stores, and acts on information. Yes, I’m comparing babies to operating systems.

NB: The miracle of life is the fact that the first living organism had to have its basic bootstrap blueprint spontaneously form from the movement and reactions of molecules. The sheer unlikelihood of this may be why many people believe in Creationism.

These first lines on the map represent the child’s most primitive, basic, fundamental, low-level programming. Starting with the same basic programming, children start their lives by taking, storing, and experimenting with information they collect from their environment. What they learn during this time fills in a great deal of their map, so much so that many people never really overcome the conditioning they developed in their youth.

NB: Conditioning in this context means the same thing as learning, or drawing lines on the map.

When a child becomes an adult, his or her map is mostly filled. As time goes on, they continue to fill out the map in greater detail and may find themselves needing to rework large parts of the map when new contradictory information becomes too much to ignore.

A map’s purpose is to guide its user to a destination. In this extended metaphor, each person is given a map without a destination. In the process of filling out the map, they often wonder where they’re trying to go. (What’s it all about? What’s the meaning of life? Existential angst, etc.)

The fact that we given a map without a destination is the first sign of Incompleteness. A map with a destination implies a best route and, as a result, an elimination of possibilities. It is a computer program that is about to run, or a geometric proof about to be written. After the destination is reached, the experience ends.

A map without a destination, on the other hand, implies an infinite number of destinations, each with an infinite number of routes. In this case, the game never ends because there is no final destination, only a series of sub-destinations defined by the user.

A map with a destination is a “finite game”, and a map without a destination is an “infinite game”. Each player in a finite game seeks to win the game and thus to end it; players in an infinite game play in order to continue the game. Read “Finite and Infinite Games” for more background.

Godel’s Incompleteness Theorems state that

  • No consistent system of axioms whose theorems can be listed by an algorithm is capable of proving all truths about the arithmetic of natural numbers. For any such consistent formal system, there will always be statements about natural numbers that are true, but that are unprovable within the system.
  • A consistent system of axioms cannot prove its own consistency.

If we replace “consistent system” with “map”, Godel’s Incompleteness Theorems tells us that every map has two blindspots — the truthfulness of it’s most fundamental lines (the ones given at birth) and the consistency of all new information that’s been added to the map afterwards. In other words, a map cannot simultaneously be a map of the world, and of itself. This fact is another example of Incompleteness, in this case, about the map and not the destination.

If my map cannot tell me anything about itself, couldn’t I make a map of my map, a meta-map? Sure, but you would run into the same problem with your meta-map.

Incompleteness is the defining characteristic of infinite games because Incompleteness is the source of possibilities. Completeness is the defining characteristic of finite games because it extinguishes all possibilities except one, which is the one that is played out.

Suffering is necessary for infinite games/gather info/changing worldview or maps/Quantum randomness/nature describing nature

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John Doe

John Doe

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Processing information, stacking concepts. Writing this down so I don’t keep thinking about the same things over and over again