Mauro,
Hi. Thanks for the reply. I wasn't trying to make sense of the notion of "space" but was just using a very small subset of a few points in space as an example to try and make sense of the notion of quantum superpositioning. Separate from this, though, I agree completely, of course, that space is much bigger than just a few points. I disagree, however, that whatever has extension needs many component parts. At the most fundamental level, I think our physical reality must be composed of some type of fundamental existent entity no matter whether that entity is called a qubit, a bit, an it, a mathematical construct, whatever. As the most fundamental of all existent entities, this entity would have no component parts. Yet, in order to physically exist and to serve as the foundation of our physical existence which has extension, this entity must itself have extension. It seems possible to me to have a single unit entity that has extension but has no component parts. Given such an entity, space would then be built out of huge, or possibly infinite, numbers of these fundamental entities with each one defining a position in space. There would, of course, be relationships between all these entities as you point out in your essay. But, to have relationships, one has to first have entities to have the relationships be between. In your game example, I think these would be the players Alice, Bob, etc. in group G.
Thanks!
Roger