Infinity, ∞, can be thought of as a meta-cognitive symbol that meta-cognitively stops what would otherwise be an infinite process. In other words, Infinity, ∞, is the symbolic representation of a process that does not end. One derivation of the continuity of space is based on subdividing an existing space between two points, an infinite process of epsilon going to zero, in the limit, continuity exists. Continuity is similarly a meta-cognitive recognition of a process that will never complete. Xeno divided distance by 2 in an infinite geometric series that approached but never actually reached its target.
One way to be rational about Infinity is to use a finite model to represent the process and another finite model that is capable of recognizing that the first process will not stop running. This is similar to the halting problem but it is different because while in theory it is impossible to generally predict whether a process will stop, in practice it is relatively easy to predict if many simple types of processes are going to stop or not.
The recognition of Infinity, the symbolic representation of the fact that a process will not end, is a function useful in meta-cognition. I’m thinking of meta-cognition as a meta-level cognitive process observing and managing the ambiguity in an object-level cognitive process. For the meta-level process to be able to predict whether the object-level process will complete is analogous to the ability to determine whether not or not a sub-process will accomplish a goal. One of the main jobs of a meta-cognitive process is to create, manage, and shut down cognitive processes. Each cognitive process is attempting to accomplish its own given goal.
Another useful meta-cognitive ability is to predict what a process will do if it is run, before it is actually run. The meta-cognitive process runs abstract simulations of the lower-level cognitive processes that it manages, so that the meta-cognitive process can predict what the lower-level cognitive process will do before they are created and run.
Consider the why game. Why is the sky blue? Because blue light scatters more than other light in the atmosphere. Why does blue light scatter more? Because blue light has a shorter wavelength. Why does blue light have a shorter wavelength? Ultimately, the game must end. One might joke, “Because God said so.” Something must be done to end what has been meta-cognitively recognized as a process that will not end, and perhaps more importantly, there is a feeling that the process must be stopped somehow, and thus the game of it. The why game gives an analogy of Infinity to “Because God said so.”