Could an unimaginative person learn to perform complex mathematical operations? For instance, could an unimaginative person conceive of a way to do a 100 step proof?
No. But the point I am making is that the capability of the person doing the imagining was honed on smaller things, on simpler things.
Just like memory, the imagination is also special purposed.
The skill is built up through practice. By the time someone is capable of doing a 100-step proof, their imagination capabilities have been honed to do that.
Summarize this for me. I do not see how this would enhance one's imagination to a significant degree.
It is essentially a book of exercises aimed at improving one's imagination. The exercises mainly allow you to access your modalities at will, and enable you to switch between modes of representation.
That is true, as we have earlier established that it is possible to become more imaginative by engaging in tasks that require one to use imagination. Earlier you were arguing that it is possible to improve one's imagination to a significant degree. Explain how this could be done.
I suppose "significant" is a relative term.
Frankly, so is "imagination."
There are many types. One could imagine sights, sounds, and sensations in any combination. What is imagined could be vivid or ephemeral, abstract or rich, colorful or bland, correspond to real world objects or have nothing at all to do with reality.
The particular ability to imagine chess moves for instance does not exist in people who don't know chess. Ask a master how he plays blind-fold chess. He does not imagine the board and pieces in vivid detail--in fact, this has little more use for him than an for an amateur who can actually see the whole board and still blunders. The Master's representation is more partial and abstract. It relates how pieces are attacked and supported, how much room pieces have to maneuver, what his plan is in the game, and what his opponent is planning to do. It is
chess-specific imagination built-up from playing chess.
Similarly, for a mathematical proof. I am by no means a professional, but I am certainly much better at imagining the structure of a mathematical proof than I was before I started my Math degree.
When first learning, perhaps I thought of individual statements, and trid to see particular rules to be applied to transform an expression into another. This is still useful, and I use it from time to time, but later, the process becomes more abstracted, quicker, more ephemeral, almost kniesthetic. I can plan simpler proofs from beginning to end and be fairly confident I can finish the details, I can also speculatively try entire strategies, and approaches to a problem, have them not work, and still learn quite a bit about the original problem. A younger me, would have had to start back from scratch.
All this is Math-Proof-specific imagination, built-up from doing math proofs.
When designing computer programs, an amateur may flow-chart, or think expressly in code. But with experience, an expert can think in high level design patterns or a modeling language, and be confident the actual code can be implemented. This is programming-specific imagination and built up through practice.
Explain how these activities could improve one's imagination to a significant degree. The main obstacle to this thesis that I see is that imagination is not a skill that is clearly observable, like one's logical analysis capabilities. The faculties that are responsible for imagination are amorphous because of this we are not exactly clear on what is necessary to cultivate such skill. We know that the activities you mentioned above do cultivate imagination purely inductively, or our experiences show that people who have engaged in such tasks have enhanced their imagination. The problem remains, however, that we do not know exactly how their imagination was enhanced. For example, certain activities we may find in this book
Amazon.com: Conceptual Blockbusting: A Guide To Better Ideas, Third Edition: James L. Adams: Books... will ignite the imaginations of some, but not others.
What we are talking about here is
representation. How does one
represent what one is thinking about in ones mind? We may not be able to see the representations of other people until expressed, but they are often expressed. What does an artist, painter, or musician express?
The notion of "enhancement" is also a very fuzzy one. Studies of experts in many fields show that the experts themselves maybe the ones with the least vivid of representations--they act on a much more sub-conscious level, and may have the hardest time explaining what it is that they do (or rather explain a much simpler process than what they actually do).
There are many objects of analysis or study when doing an activity. These objects of study will need a representation in ones mind. Once studied, these representations are often stored as memory (as per the discussion above, we will have chess-specific memory, math-proof-specific memory, computer-programming-specific memory). At a later time, these previously imagined representations are pulled forth from memory and enhanced or reused in new imagination activities.
Yet, instructions concerning logical reasoning, if properly presented should ignite the reasoning faculties of all. The only exception we may find to this is on the higher levels of reasoning, those to be found in advanced study of logic and mathematics, but in that case, the problem appears to be not with the instructions concerning how logical analysis is to be conducted, but with the student's lack of imagination.
For example with logical analysis, we have a very clear explanation regarding what one must do to become more proficient at logical analysis. Many mathematics and logic books have thorough instructions regarding this matter, yet this is far from the case for imagination.
Logic and reasoning does not work in a vacuum. They work on particular representations.
In many disciplines, these representations are formalized in some way (whether they are chess pieces, mathematical symbols, elements in a schematic, or phenomenon in the physical world).
When we judge the quality of reasoning, we are also judging the quality of representation.