This is very interesting. I am having trouble understanding the experience of imagining the 4x4 block of 16 blocks well enough to note that there are four interior blocks w/o red paint on them without picturing them.
I could imagine that this could be done with just logic (reasoning about how many blocks there must be in different categories, which is maybe how I would do it if the problem were more complex, or took place in four dimensions for example), but you said you had a diagram...
So it sounds like you did have mental imagery, it was just 2-d instead of 3-d.
But apparently that wasn't very vivid, because you still had to do the haptic imagery thing. How vivid is the experience of this motor mental imagery for you? I'm wondering if I'm missing out on that in the way that you're missing out on more vivid visual mental imagery.
Previously: Generalizing From One Example
Summary: I do not have visual mental imagery. I want it. How do I get it? What exercises, if any, will help?
In further detail... Here's Francis Galton's Statistics of Mental Imagery paper. I'm not quite at the 3% level of completely unable to form mental images, but I'm close. In particular there are three times I have vivid, sharp mental imagery, and the existence of such times tells me I have the brain hardware to visualize. It's enough to let me know that I want it all the time. Unfortunately I don't know how to get it. And searching online has proven difficult and frustrating... for example this article is first of all about a different meaning of "visualize", it's talking about some kind of self-help motivational thingy, and second of all it starts by saying "How to Visualize: I want you to relax and close your eyes. Picture a hot, sunny day at the beach."
Full Stop. Halt, Catch Fire and Burn.
That's already too far. For those of us who don't visualize, practice definitely does not consist of pulling up mental images, playing with them in new ways, and expanding our imagination. I'm very good at imagination in some ways, but I lack that first ability to pull up a mental image. That's what I want to learn how to have!
Here is a description of what I can do, what I have tried, what I have learned, etc.
I see vivid visual mental imagery in 3 situations: