Retinal saccades are group actions, the inner eye also does saccades, and other random conjectures.

I have a conjecture and I think a blog is the right format to express it.

The conjecture goes as follow: retinal saccades can actually be understood as group action taken on the visual scene, and there is some evidence that other group actions are possible, but in the minds eye, using the same saccadic-like process, but internally. Also, movements of the hand can be interpreted as taking group actions in real life.

So where to start? With Tootel of course. He was the first to show that because the retina has some sort on increase in density, a grid shaped as a target can largely be seen as a normally shaped grid in visual cortex. Why does this matter. Well it turns out that this transformation is close to the log-polar transform, which maps a rotation to a translation, and a scaling to a translation. How do you convince yourself of this? just imagine an image centered on the target grid, and rotating around that center. What would that correspond to on the V1 flattened grid? To a translation! That's it. Same for a scaling.

Why does this observation matter? Well to understand why it matters we