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I think that in this article Steve discounts the effect of actually doing the math for yourself. It's comparatively easy to read about something and think that

by nagrom 15y ago

I think that in this article Steve discounts the effect of actually doing the math for yourself. It's comparatively easy to read about something and think that you've understood it. It's another thing entirely to be able to do that math on paper and get the 'correct' answer without needing help.

anonymoushn 15y ago
There's actually a place slightly beyond "able to do it on paper" at which you grok the maths so well that you can apply it in non-obvious situations without any conscious effort. I'm not sure how to get there in general, but I've noticed that I'm more likely to be able to do this for subjects that I learned in proof-heavy classes.
- dsrguru 15y ago
  I've always envied people who could do that. A friend of mine told his mathematics professor a riddle (http://en.wikipedia.org/wiki/Random_permutation_statistics#One_hundred_prisoners http://en.wikipedia.org/wiki/Random_permutation_statistics#O...) that had taken my friend hours to logic out. The professor began talking it out and, within about 15 seconds, had produced the simple group theoretic solution that Wikipedia gives.
- dagw 15y ago
  I have a Masters in math and the applying things in non-obvious situations is one of the things that I really gained from it. Several times I've been in situations where someone is struggling with a problem, and where I can quickly spot a simple mathematical approach to solve it. Many times the mathematics itself is quite simple advanced high school or early college stuff, stuff the person struggling with problem has also studied. The difference is that to them linear algebra (for example) is something abstract you use to solve linear algebra problems, while to someone with a more deep and solid understanding of math, linear algebra is a simple and general tool that can be applied in all manners of situations.
- Deestan 15y ago
  One of the school math topics that I have made us of a lot is function transformation and translation. Being able to see things like "what I really need here is this part of a sine curve, stretched along the X axis, compressed along the Y axis, and moved up into the positive", and then write a simple one-liner to do slideshow animation, has proven useful again and again. To be honest, I didn't really understand the point of it during class, and actually failed that part of the exam. A few years later when I needed it, it just popped out of my brain attic and made sense.
- khafra 15y ago
  > I understand what an equation means if I have a way of figuring out the characteristics of its solution without actually solving it. -- Paul Dirac
- ImprovedSilence 15y ago
  "In mathematics you don't understand things. You just get used to them" - John von Neumann

by nagrom 15y ago

anonymoushn 15y ago

There's actually a place slightly beyond "able to do it on paper" at which you grok the maths so well that you can apply it in non-obvious situations without any conscious effort. I'm not sure how to get there in general, but I've noticed that I'm more likely to be able to do this for subjects that I learned in proof-heavy classes.

dsrguru 15y ago
I've always envied people who could do that. A friend of mine told his mathematics professor a riddle (http://en.wikipedia.org/wiki/Random_permutation_statistics#One_hundred_prisoners http://en.wikipedia.org/wiki/Random_permutation_statistics#O...) that had taken my friend hours to logic out. The professor began talking it out and, within about 15 seconds, had produced the simple group theoretic solution that Wikipedia gives.
dagw 15y ago
I have a Masters in math and the applying things in non-obvious situations is one of the things that I really gained from it. Several times I've been in situations where someone is struggling with a problem, and where I can quickly spot a simple mathematical approach to solve it. Many times the mathematics itself is quite simple advanced high school or early college stuff, stuff the person struggling with problem has also studied. The difference is that to them linear algebra (for example) is something abstract you use to solve linear algebra problems, while to someone with a more deep and solid understanding of math, linear algebra is a simple and general tool that can be applied in all manners of situations.
Deestan 15y ago
One of the school math topics that I have made us of a lot is function transformation and translation. Being able to see things like "what I really need here is this part of a sine curve, stretched along the X axis, compressed along the Y axis, and moved up into the positive", and then write a simple one-liner to do slideshow animation, has proven useful again and again. To be honest, I didn't really understand the point of it during class, and actually failed that part of the exam. A few years later when I needed it, it just popped out of my brain attic and made sense.
khafra 15y ago
> I understand what an equation means if I have a way of figuring out the characteristics of its solution without actually solving it. -- Paul Dirac
ImprovedSilence 15y ago
"In mathematics you don't understand things. You just get used to them" - John von Neumann