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February 7 - March 30, 2023
Arthur C. Clarke. “Do we use models to help us find the truth? Or do we know the truth first, and then develop the mathematics to explain it?”
“It is by logic that we prove, but by intuition that we discover. . . .
The problem with divorcing what and how in education is that knowing about things is not the same as understanding them.
if you can’t imagine, you can’t invent.
“In creative work, imagination is more important than knowledge.”
Productive thought occurs when internal imagination and external experience coincide.
Mitchell Wilson wrote half a century ago, “I’ll tell you what you need to be a great scientist. You don’t have to be able to understand very complicated things. It’s just the opposite. You have to be able to see what looks like the most complicated thing in the world and, in a flash, find the underlying simplicity. That’s what you need: a talent for simplicity.”
reality is the sum of all possible abstractions
“To perceive a pattern means that we have already formed an idea what’s next.”
“gestalt shift,” in which the same sensory information can take on two or more noncommensurate meanings.
Christian Goldbach suggested, some 250 years ago, that every even number can be described as the sum of two prime numbers. For example, 24 = 13 + 11.
“properly defining your question gets you more than halfway to its solution.”
Thomas Kuhn called a paradigm, a widely applicable pattern used to set up and solve problems within a particular field.
it is not our senses that limit or liberate us, but our ability to illuminate the unknown by means of analogies to the known. Learning itself depends on analogizing.
“The Road Not Taken” in the lines “Two roads diverged in a wood and I—/ I took the one less traveled by.”
