Forget about solving practical problems for a second. We can just ask the LLM to simulate some arbitrary computation within its context window. But we can in principle require that the output depends on state from arbitrarily many steps in the past. You then need to "carry forward" the required data or otherwise make it available. This is what I mean by moving data. The required associations between data can extend beyond the buffer or available state.
And by extension, the assumption is that animals can carry forward an unlimited amount of information from the past? I.e., humans rely on culture to "carry forward" ideas from the past that are outside their individual contextual window of experience?
I wasn't thinking in those terms, but yeah I like that. Humans are a kind of superorganism and a part of that is due to the power of culture to shape behavior in ways that are responsive to environmental changes deep in history beyond any individuals lifespan.