Rich and Strange Aeons

I don't think I can really do any of the things you mention. When I play tic-tac-toe in my head I'm not really "seeing" the board in any way.

I think the best description I've read of this phenom is from this dude's page on aphantasia:

There was a series of psychology experiments where they'd show the subject two side-by-side pictures, usually line drawings of a bunch of blocks together, and ask whether the two objects so depicted were the same. Sometimes they were; sometimes they were mirror images.

People reported that they way they solved these problems was to 'rotate the first object in my head until it was in the same orientation as the other one, and then see if they were the same'.

Can you solve those problems? How would you describe the process? I don't suppose you do it from the local connectivity properties or anything like that.

The best I can describe it is that I have a more abstract (than purely visual) knowledge of how the object is constructed. For example, you know abstractly what a cube is like without having to actually see it in your head (I hope).

Take a object made of four cubes; three of them in an L lying on its side and one of them stacked on top of one of the leg cubes (sorta the canonical one-is-a-mirror-image-of-the-other object). I don't see it in my head. I do know that if I saw an isometric picture of it, there would be one cube in the lower left cormer, another cube to the NE of that, another cube to the SE of that, and another cube on top of the last one. I could draw that picture trivially. But I don't actually see that picture in my head.

If I'm given a picture of that object and a picture of object B, and am trying to figure out if they're the same or mirror images, I'll kind of 'feel' the first object with my hands (in a virtual way, the same way you might 'see' things with your eyes closed) and feel the second object with my hands and see if they feel the same way. Or I'll use some more theoretical trick like saying, "If I were walking along object A so that I had to take a right turn at the L, I would walk into a sticking-up cube after I took that turn. Would that be true if I were walking on object B?" Maybe that's what you mean by local connectivity properties.

I'm sure a blind-from-birth person, feeling object A and object B in a fixed orientation, would be able to tell if one could be rotated to be the second, without using any visual skills. Or heck, they can find their way around their houses without having a visual representation. I don't know if they do it the same way I do, but at least it proves it can be done.