Apr 20, 2005

apples are not an explanation

Okay this has been burning me up for a while now. Why is it when you read any kind of article or book (I'm being a little extreme, some rare examples do a good job) about some scientific theory, there is never a good explanation about how the scientists came to their conclusions. There is also rarely a good explanation of how the resulting outcomes from that theory/equation came about. Let me give two examples.

How did Newton come up with the equation for gravitational attraction? This shouldn't be hard to explain. I've never seen it. Even Singh in the book I just reviewed, just shows the equation. Maybe he just guessed it but for crying out loud explain to me how he came up with the guess and showed his guess was correct.

How does E=mc^2 come out of Einstein's general theory of relativity? Never seen it. This is one of the most famous equations and yet I've never seen someone show how it falls out of his equations. Does anyone else find that weird?

It's probably an aversion to showing equations in popular science books but so what. To me the spark of creativity and thinking that leads to these theories is the most precious thing about understanding them. Without that kernel of insight you rarely 'understand' what is being said. A friend of mine went through 3 years of hard core engineering classes with me without understanding what a derivative in calculus was because he never understood how Newton or Leibnitz first calculated a derivative. Understanding that is key to understanding calculus. He just performed the rules as they are supposed to be done. When I finally explained it to him his workload dropped and his grades went up. Crazy.

Anyway. I'm going to figure those two things out here over the next few weeks and report back. If you have any other requests drop them in the comments.


Anonymous said...

Found your page via Iron Yuppie...

Regarding Newton and gravity, I recommend you read the second half of this: http://galileoandeinstein.physics.virginia.edu/lectures/newton.html

And regarding E=mc^2, I recommend you read this:

I think the focus on the equation, rather than the process is just a byproduct of our cultural attraction to ends rather than means. It is more important to have climbed the mountain than to have enjoyed climbing the mountain, so to speak...


C. Fuzzbang said...

Thanks for the pointers. I'll check them out.

I think you are right about lack of focus. However when I used to tutor in calculus and fluid mechanics it seemed like students appreciated a deeper understanding. Perhaps it's because they had no choice as I refused to teach those subjects without teaching the underlying principles. Maybe these things need to be forced on people :)