What if across your lifetime, you could only choose one book to read?
You can only read so many books in a lifetime. I mean, part of me thinks we’d be better off picking one book and never reading another book, and just getting through that one book very well.
The Cultural Tutor. 48:46
Which book would you choose?
For readers, it would be challenging to only read one. Dipping in and out of books is proven method for determining what to read. But the idea of rereading for a deeper understanding is invaluable.
See philosopher/entrepreneur Johnathan Bi‘s careful reading approach:
One of my smartest friends only reads 3-5 books per year but rewrites every page in his own words as he goes through it. Then, he summarizes the entire book once he's done. He reads only the best books, but very carefully. This is the kind of reading we should be encouraging.
having gone about as high up Hemingway Mountain as I could go, having realized that even at my best I could only ever hope to be an acolyte up there, resolving never again to commit the sin of being imitative, I stumbled back down into the valley and came upon a little shit-hill labeled “Saunders Mountain.”
“Hmm,” I thought. “It’s so little. And it’s a shit-hill.”
Then again, that was my name on it.
This is the big moment for any artist (this moment of combined triumph and disappointment), when we have to decide whether to accept a work of art that we have to admit we weren’t in control of as we made it and of which we’re not entirely sure we approve. It is less, less than we wanted it to be, and yet it’s more, too –it’s small and a bit pathetic, judged against the work of the great masters, but there it is, all ours.
What we have to do at that point, I think, is go over, sheepishly but boldly, and stand on our shit-hill, and hope it will grow.
And–to belabor this already questionable metaphor–what will make that shit-hill grow is our commitment to it, the extent to which we say, “Well, yes, it is a shit-hill, but it’s my shit-hill, so let me assume that if I continue to work in this mode that is mine, this hill will eventually stop being made of shit, and will grow, and from it, I will eventually be able to see (and encompass in my work) the whole world.”
I was that stereotypical third grader who scoffed at his times tables and said, “When will we ever use this when we grow up?”
My theory on why many kids have a poor attitude towards mathematics is that we’re subconsciously taught to avoid problems. Whereas Mathematics is all about embracing problems.
Math wants you to make friends with problems. Spend time with problems, not run from them.
Problems are there to be solved!
True enough, the Altitude-on-Hypotenuse Theorum has yet to be an agenda item on any of my zoom calls. But the skill of problem solving still punches the clock everyday.
And the strategies for solving a math problem, can also be applied to any real world problem.
Grant Sanderson’s 7 tips for solving hard problems are below.
My real-world application take is in italics.
Hopefully at the end, you’ll hate math less.
Use the defining features of the setup
What are the rules of the game your playing? What are the inherent limitations?
Give things (meaningful) names
Naming things helps your mind organize ideas and outline solutions.
Leverage Symmetry
Identify what is similar. Are there any patterns? Have we seen this before in a previous problem?
Try describing one object two different ways
This reminds me of a practice the economist Tyler Cowen has. To improve his understanding of an argument, he’ll write out the point of view of the argument he opposes. Try the opposite of whatever strategy your using.
Draw a picture
Drawing, like writing is a form of thinking. As maker Adam Savage has stated: “Drawing is your brain transferring your idea, your knowledge, your intentions, from the electrical storm cloud at its center, through the synapses and nerve endings, through the pencil in your hand, through your fingers, until it is captured in the permanence of the page, in physical space. It is, I have come to appreciate, a fundamental act of creation.” Doodle. Stickfigure. Sketch. Create a visual form of the problem.
Ask a simpler version of the problem
What’s the smallest part of the problem we can solve first?