I was given an excellent geometry problem by Dr. Nigel Thomas.
It might be worth attempting to see how you perform on certain types of spatial thinking problems that most people claim to use imagery to solve (although no correlation seems to exist between spatial thinking ability and the vividness that people report their imagery to have). Try to solve the problem below, in your head, without drawing diagrams or making calculations on paper or anything like that. The four narrow sides of a 1 cm by 4 cm by 4 cm block are painted red. The top and bottom are painted blue. The block is then cut into sixteen 1 cm cubes.
- How many cubes have both red and blue faces?
- How many cubes have one red and two blue faces?
- How many cubes have no painted faces? Most people say they use imagery to do this, and count the relevant cubes in their image. Were you able to solve all or any part of the problem at all? Did it seem very difficult? How, in fact, did you solve it (if you did)? Did you have to consciously employ any formal knowledge of geometry or other mathematics (beyond counting)?
When I solved this, I had the interesting experience of Imagining the 4x4 block of 16 blocks, noting that the outside ones (all but 4) had red paint on them, and all of them had blue paint... but I only "put" blue paint on the top. My diagram was flat, oriented like a pancake. None of this was Mental Imagery. Then when I was asked how many cubes had red and blue faces, I felt around the edges of the block. Motor/haptic mental imagery. Then when I was asked how many cubes had 1 red and 2 blue faces, I immediately thought the question was 1 red and 1 blue since I didn't have blue paint on the bottom in my model (I'm not sure if I had a bottom in my model). I thought "when would they have more than 1 red? ah the corners", and then had the distinct vivid motor mental imagery of moving my hand and touching two non-corner side blocks on the left of my model, then two at the far side, then two on the right, then two on the near side, counting "2, 4, 6, 8". This was a different experience than my usual Imagining... but I'm not sure if it was qualitatively different or just more "vivid" motor mental imagery.
Did anyone else have trouble recalling the red vs blue sides? (based on my experience with this (below), it seems as though my mental association was essentially "top and bottom are same" and "narrows are same" but neither really had a color. When I close my eyes, I don't see "red" or "blue")
At first I was imagining a 1cm by 1cm by 4cm block. I then realized that getting the 16 cubes of 1cm each out of this wasn't possible and then went to the accurate idea of a 4 by 4 by 1. I realize I am having a great deal of tro...
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: