The first stage of learning something new is mostly trial and error. Of course you have to understand some prerequisites before you are capable of learning something new. Simplification is useful at this stage even though it might get in the way. Idealization is a method which you can use to initially create some rough metrics (or something that can be used in ways similar to metrics.) Exaggeration and simplification have some similarities to idealization and so they are useful in this process. The next stage requires that you look at your results and begin to analyze them. Although idealization and simplification are important tools, if they are used inappropriately they can create some interference in the process. The process of analysis is used to find core concepts (or core abstractions) which might to be useful in discovering what went wrong or developing new ideas. Adaptation is a necessary component of new learning. This is the stage when stubborn adherence to some initial idealization or simplification may really interfere in the process of new learning. While you need to continue using simplifications and idealizations, if your simplifications are stuck in the primitive mode they were in during the initial stage of research they will probably interfere in finding an effective adaptation. The next step is to examine some sub-goals which might be useful to discover what seem like necessary pre-requisites for the ultimate goal. Again, you may find that the abstractions and core features of a problem or a hypothetical solution that you thought you understood may be inaccurate. So you may need to refine your ideas about the core features of the problem just as you have to rethink the solutions that you thought might work. I have found that at a later stage of work you may find that you may make advances on sub-goals that go way past what you did at an earlier stage. This recognition may also serve as a kind of metric. Even though you may not have made any substantial progress toward the project goal, the fact that you have made an unexpected advancement in a sub-goal may indicate that it is something worth looking into. Over a period of time, the work which has been done to idealize and simplify, test and experiment, analyze and adapt, and refine the idealizations and abstractions about both the problem and possible solutions should help you to be understand the nature of the problem and the nature of what a solution may look like. I believe that incremental advances are necessary for revolutionary advances in science because they are the basis for revolutionary advancements. But you have to have some experience focusing your imagination on actual experiments to appreciate the significance of the adaptation of simplification, ideals, and abstraction. Jim Bromer
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