Most of the time I work with spatial/visual intuition, building analogies to the structure of the problem under study as “mechanical systems”, similar to what you do to non-analytically solve stereometrical problems. When the models get sufficiently developed, they usually show the answer directly, or allow to build or recall relevant concepts. It’s very unreliable, but given enough work on getting to know a model and starting to intuitively feel it allows to read off the conclusions.
This is often a difference between getting an intuitive understanding and basic knowledge. One doesn’t often imply another: learning something explicit doesn’t give the intuitive understanding, which leads to missing the conclusions obvious to an expert, and conversely getting the gist of some idea or developing an intuitive solution allows to see many sides of the problem, but has a fair chance of being factually wrong. A solid grip on a concept requires getting both sides of the medal, learning an intuitive model, and enforcing correctness using a more formal and certain foundation.
I don’t know how to do anything constructive with verbalization, I mainly use verbal buffer to store little pieces of data, supporting visual problem-solving.
Most of the time I work with spatial/visual intuition, building analogies to the structure of the problem under study as “mechanical systems”, similar to what you do to non-analytically solve stereometrical problems. When the models get sufficiently developed, they usually show the answer directly, or allow to build or recall relevant concepts. It’s very unreliable, but given enough work on getting to know a model and starting to intuitively feel it allows to read off the conclusions.
This is often a difference between getting an intuitive understanding and basic knowledge. One doesn’t often imply another: learning something explicit doesn’t give the intuitive understanding, which leads to missing the conclusions obvious to an expert, and conversely getting the gist of some idea or developing an intuitive solution allows to see many sides of the problem, but has a fair chance of being factually wrong. A solid grip on a concept requires getting both sides of the medal, learning an intuitive model, and enforcing correctness using a more formal and certain foundation.
I don’t know how to do anything constructive with verbalization, I mainly use verbal buffer to store little pieces of data, supporting visual problem-solving.