Timeline for Thinking and Explaining
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 21, 2019 at 21:52 | comment | added | Student | @SamDerbyshire Thank you; I really like your answer. I also found Thurston's counting method astonishing.. | |
| Sep 15, 2010 at 22:48 | comment | added | Bill Thurston | @drvitek. Thanks for the reference. When I was a teenager, I realized that the standard way people count with fingers is inefficient, so I developed skill at counting in binary. It works without much conscious attention up to 1024. With that method, I can count while carrying on a conversation, or thinking of something else. In the days of typewriters when I had to manually center the title, I was unable to do it reliably in my head using word counting, but finger counting makes it trivial. ALSO: I think most people count small numbers subconsciously by rhythm, as when climbing stairs. | |
| Sep 15, 2010 at 22:25 | comment | added | Sam Derbyshire | That's the exact passage I'm referring to; I provided a link to the text. | |
| Sep 15, 2010 at 22:01 | comment | added | dvitek | Sam: There's another Feynman passage you may be interested in, where he talks about trying to count at a steady pace and talk at the same time and finds he's unable to do it. However, a friend of his does so easily. There's another task (I forget the exact details, and I don't want to go grab the book and look for it!) that Feynman can do, and his friend can't, however. The two of them try and figure out what the exact barriers are, when they realize that Feynman is counting verbally in his head while his friend is watching numbers go by on a tape! | |
| Sep 14, 2010 at 20:07 | comment | added | Sam Derbyshire | I find that you expressed this perfectly above: "What's important is not the process by which you arrived at an idea, but a story that gives the idea context and meaning. It's a story you make: a setting of meaning and reason for the idea, rather than the history of how you stumbled on the idea." | |
| Sep 14, 2010 at 20:05 | comment | added | Sam Derbyshire | @Bill: Indeed, there is a lot of value in finding methods to present ideas in a fashion that really enables the formation of good mental models. Indeed, I often have the impression of understanding what is presented before me, but feeling I am missing the "big picture", of having a convenient state of mind within which to understand the whole theory. But I think it might be more about finding this fertile environment than trying to convey our own mental models (even though the latter certainly contributes to bettering the environment). Great question. Wish I had good examples to contribute! | |
| Sep 14, 2010 at 19:27 | comment | added | Bill Thurston | @Sam: I agree, we often have very different and personal mental models. Random models are confusing. I often have several different models at once. I often work on them in my head, trying to get them to fit better to the context. I find that they can change, and improve, dramatically through this process, and when they are happy enough, they're worth communicating. But, for me: reliable precision comes only after finding a good overall mental model. I think many students are often blocked by false or inadequate mental models --- they're hard to excavate and hard to convey, but important. | |
| Sep 14, 2010 at 16:05 | history | answered | Sam Derbyshire | CC BY-SA 2.5 |