24 February 2024

On Problem Solving XVIII: Practice

"The insights gained and garnered by the mind in its wanderings among basic concepts are benefits that theory can provide. Theory cannot equip the mind with formulas for solving problems, nor can it mark the narrow path on which the sole solution is supposed to lie by planting a hedge of principles on either side. But it can give the mind insight into the great mass of phenomena and of their relationships, then leave it free to rise into the higher realms of action." (Carl von Clausewitz, "On War", 1832)

"One of the most important tasks of the teacher is to help his students. This task is not quite easy; it demands time, practice, devotion, and sound principles." (George Pólya, "How to Solve It", 1945)

"We acquire any practical skill by imitation and practice. […] Trying to solve problems, you have to observe and to imitate what other people do when solving problems and, finally, you learn to do problems by doing them." (George Pólya, "How to Solve It", 1945)

"The trouble with mathematics is that, however diligent you are in going to lectures and in learning the theory, you may still not be able to do the problems." (Maurice Wilkes, "Memoirs of a Computer Pioneer", 1985)

"Design thinking taps into capacities we all have but that are overlooked by more conventional problem-solving practices. It is not only human-centered; it is deeply human in and of itself. Design thinking relies on our ability to be intuitive, to recognize patterns, to construct ideas that have emotional meaning as well as functionality, to express ourselves in media other than words or symbols." (Tim Brown, "Change by Design: How Design Thinking Transforms Organizations and Inspires Innovation", 2009)

"Solving problems is a practical skill like, let us say, swimming. We acquire any practical skill by imitation and practice." (George Pólya)

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