This is great. More stream of consciousness while Guy solves math problems please.
I thought it was interesting that it was easier for me to picture the proper shapes than it was for you (I had no trouble getting the lines of my pyramid to join together, and I could easily imagine where the line for the altitude of the tetrahedron went), but you thought of the relations between line segment lengths and came up with the formulas for them much more quickly than I would have.
One thing I want to clarify though, when you said you were imagining the pyramid and dotted line, and then your mental imagine didn't match that correctly -- were you first successfully imagining the pyramid and dotted line, and then trying to also have a mental image, or when you said you were imagining did you just mean that you were starting to form the mental image? And if the former, what did this imagining consist of, other than just awareness of the abstract idea that an altitude should go from a face to its opposing point?
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: