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Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Boundaries vs Frames, published by Scott Garrabrant on October 31, 2022 on The AI Alignment Forum. This post is partially in response to Critch's boundaries sequence. My best guess is that he would agree with most of it in theory, but disagree with some of it in practice due to tradeoffs with other considerations in defining the concepts. Boundaries and Frames Imagine a world consisting of some atomic objects R={r0,r1,.}. For example, you can think of the ri as physical atoms or cells in the game of life. Each object comes along with a collection of states it can be in ri={s0i,s1i,.}. (I am not committing now on whether or not we are thinking about our model as timeless. Maybe ri should be thought about as a cell in the game of life that passes through time, or maybe it should be thought about as a (cell, time) pair.) There are two sets we naturally want to associate with our world. First, we have R={r0,r1,.}, which I will call the object space. Second, we have S=Πr∈R r, which is the set of all ways to assign state to each object in R. I will call this the state space. Note that partitions of R correspond to factorizations of S. If I want to point at (for example) an agent in R, I might tell you what atoms are inside that agent, and thus express R in the form R=a⊔e, where a is the set of all atoms that are in the agent and e is the set of all atoms that are outside of the agent (and thus in the environment). The agent then has its own state space A=Πr∈a r, while the environment has its own state space, E=∏r∈e r. Now, to point at this agent in S, I can express S in the form S=A×E. Instead of specifying a list of objects in the agent, I specify the state space of the agent. Instead of thinking of the environment as the result of subtracting the agent object out of the world, I think of the environment as the result of quotienting out the agent's state space from the world's state space. Instead of defining a Cartesian Boundary, I am defining a Cartesian Frame. Playing on this naming scheme, in general (when not necessarily talking about agents), I will use the word boundary when talking about partitioning the object space into a disjoint inside and outside, and I will use the word frame when talking about factoring the state space into an independent inside and outside. (This naming might end up only being used within the scope of this post. I'm not sure.) Frames are More General/Basic I usually prefer to think in terms of frames (but not always!). While every boundary can be recast as a frame, the converse is not also true. If we view the state space as primary, then by imagining the world as a collection of objects, we are essentially factoring the state space. The frames that correspond to boundaries are basically those that carve along the joints given by the factorization into basic objects. If the world is given to you pre-factored as a collection of objects, then it makes sense to partition those objects into larger objects and draw boundaries around them. However, I think for interesting problems, this is rarely the case. Further, even if the world is pre-factorized, that factorization could be wrong! Also, the act of drawing a boundary feels similar to me to the act of factoring the state space into atomic objects. Both are carving out interesting features of state space. The initial factorization into atomic objects is identifying microscopic objects, while the boundaries are identifying macroscopic objects. Thus, starting from a pre-factored world feels especially bad when thinking about identifying boundaries, since it is starting with half the problem already done. (Note: I think this argument is weaker than it sounds. The factorization into objects is a different type than the drawing of the boundaries.) Getting Past the Physical Frame The main practical ...