"Movement" representation in cortical columns

I have a doubt regarding knowledge representation in cortical columns as proposed by TBT.

Maybe this was already discussed in another topic, or it was explained by articles “A Theory of How Columns in the Neocortex Enable Learning the Structure of the World” or “Locations in the Neocortex: A Theory of Sensorimotor Object Recognition Using Cortical Grid Cells”, and I didn´t get it.

I understand the idea of grid cells representing locations in the reference frame of a specific object, that all knowledge (not only
phisical objects) can be represented by reference frames, and that learning is made possible by movement.

My doubt is related to how valid “movements” for a given object are learned and stored in cortical columns.

For example, in the thread 2D Object Recognition Project, Matt Taylor proposed a sensor
moving in the four directions to learn a 2D region, acquire knowledge and recognize objects in that region.

But if instead of a 2D region, it was a math question to be solved, for example?

A valid “movement” for a geometry question about right triangles is to use Pythagorean theorem to discover the missing side.

Or if you are navigating in the web and want to find a post, a possible move to find it is to google some terms of the post.

These all seem examples of ways of moving to learn structures of the world.

But how movements (and not the knowledge about the object structure itself) would be represented in the brain once they are “learned” as valid possibilities?