# Knight to e4

A player sits for 5 minutes before making a move. As we have discussed before, their thought processes involve plenty of virtual movement. Is an explanation of this activity possible based solely on a fixed [math]\mathbf{W}[/math] and a moving [math]\vec{r}[/math]? For example, if the final move is simply a 'reflex' associated with a pre-existing Vornonoi cell, then why can't the player get to it straight away?

Of course, there is also a pre-existing bishop-to-e4 Voronoi cell (assuming, for the sake of argument, that this is the main alternative move) so the existence of either cell does not pre-determine the move. The sensory information - the layout of the pieces - is always the same during these 5 minutes, but [math]\vec{r}[/math] changes. Imagine the player physically moving the pieces, exploring different options, reaching dead-ends and crossing off these branches of the tree, but leave out the movement.

The idea is that each of these steps could be accomplished by moving from one Voronoi cell to another, including the process of labelling a branch of the tree that is several layers deep with a 'value' (not necessarily a correct one, of course - that is quite a different problem). That is what is required to decide between the knight and bishop moves. So, which of the two moves is chosen depends on an exploratory process. Nothing changes in [math]\mathbf{W}[/math] during this process but it is not possible to arrive at either the knight or the bishop Voronoi cell without travelling along this exploratory path.