One method to create or identify effective mental exercises would be to use the fMRI machine. We could view the brain activity under different "loads". "loads" could be mathematics problems, logic problems, physics problems, reading, arguing, etc. Then we could look for patterns in the areas of the brain used in those "loads".
Then we design a set of mental exercises, we may categorize them according to the different areas of the brain we think it may target, OR the different areas of thinking it may target. In fact the fMRI machine may be able to help us identify which areas of the brain may be involved when thinking about a certain category of problems, then we can use these results to design exercises to target those areas of the brain used in thinking about certain problems. This is similar to a thinking map, where a category of thoughts may be associated to a pattern of brain activity.
Some of the problems may be that different people use different brain patterns to process the same thought, also different people may have a slightly different conception of a thought so it uses a different part of the brain. I suppose this may require further thought, but there may be sufficient similarity in brain activity for similar thoughts to elucidate the brain patterns.
This will help us to develop mental exercises that "elucidate" similar or the same type of brain patterns that are used in solving problems.
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John Gonzalez