In this post, I've written something that would have been very helpful to my former self from a few years ago. Given that, it may or may not be helpful to anyone else.

When studying for agent foundations research, I kept finding that I wanted a good general formalism of "stuff happening over time". Applications include;

• Optimization happens over time.
• Agents make observations over time.
• Learning happens over time (although I consider learning theory to be mostly out of scope for my agenda).
• Agents have models of the environment; if the environment has type "stuff happening over time", then the models should maybe also have type "stuff happening over time". (But maybe not!)
• AI is implemented on computers, and computations are a subclass of "stuff happening over time". How does this interact with the above?

For quite a while, I felt pretty overwhelmed and disoriented about all the options. But over time I have slowly come to understand the shape of several sub-fields of mathematics that have their own rich theory of "stuff happening over time", complete with deep theorems and decades of literature. All of these seem potentially useful to me, and so I dovetail between them.[1]

[...]

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Outline:

(01:28 ) Some types of systems

(01:59 ) Stochastic process

(02:39 ) Measure-preserving dynamics (especially ergodic theory)

(03:42 ) Topological dynamics (especially symbolic dynamics)

(05:05 ) Computability

(06:02 ) Interactions between the types

(08:18 ) Levels above mine

The original text contained 2 footnotes which were omitted from this narration.

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First published:

November 14th, 2025

Source:

https://www.lesswrong.com/posts/Q6mxeHMJCzQX3KXz2/types-of-systems-that-could-be-useful-for-agent-foundations

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Narrated by TYPE III AUDIO.