Well, F = ma.

Three or four very short stories on the difficulty of learning to use simple things. Depends whether you count the last section as a story.

* * *

When I was taking freshman physics and we were stuck on a problem, the professor would say “Well, F = ma.”

True, but absolutely useless. Yes, we know that F = ma. (Force equals mass times acceleration.) Nobody thought “Oh, that’s it. I was thinking F = ma2. That explains everything.” Newton’s laws are simple (in a sense) but subtle to apply. The difficult part isn’t the abstract principles but their application to concrete problems.

* * *

The heart of Bayesian statistics is not much more complicated than F = ma. Its the statement that

posterior ∝ likelihood × prior.

It takes a few years to learn how to apply that equation well. And when people try to help, their advice sounds about as useless as “Well, F = ma.”

* * *

Learning to use Unix was hard. When I asked for help getting started, a lab assistant said “Go read the man pages.” That’s about as hostile as saying “Want to learn English? Read a dictionary.” Fortunately I knew other people who were helpful. One of them told me about the book.

But still, it took a while to get the gestalt of Unix. I knew how to use a handful of utilities, and kept thinking everything would be fine once I knew maybe 10x as many utilities. Then one day I was talking with a friend who seemed fluent working with Unix. I asked him how he did a few things and realized he used the same tools I did, but used them better. It was almost as if he’d said “I just use F = ma” except when he said it things clicked.

* * *

The motivation for this post, the thing that brought these stories to mind, was listening to a podcast. The show had some good advice, things that I know I need to do, but nothing I hadn’t heard many times before. The hard part is working out what the particulars mean for me personally.

It often takes someone else to help us see what’s right in front of us. I’m grateful for the people who have helped me work out the particulars of things I was convinced of but couldn’t see how to apply. Sometimes I have the pleasure of being able to do that for someone else.

5 thoughts on “Well, F = ma.

  1. A thought that just occurred to me after reading this post is that what one needs to be shown or told is almost always what is right in front of their eyes but unseen. This way knowledge is always built upon a fully understood and trusted foundation. Bigger leaps must almost by necessity be taken by faith or filled in later, leaving gaps in the chain of understanding and reasoning.

    (this thought may need further development but I felt it interesting enough to share)

  2. The point is not the equation F = ma, that is just a technicality. The point is how to reason the right free body diagram, and there no one can grind the grind for you. But the examples sure help. How much time would you have spent with the problem given no advice at all, if no one ever in any text book have told you that F = ma; that the total F is the real problem you need to solve?

    Similarly, I’m not yet able to use posterior ∝ likelihood × prior efficiently, as I’m still grinding my way through what would be the likelihood and prior given a real life problem. But I know I’m on the right path, which is priceless.

  3. Stephan said, “Bigger leaps must almost by necessity be taken by faith or filled in later, leaving gaps in the chain of understanding and reasoning.”

    Very perceptive. As an autodidact of alarming mediocrity, it is so hard to give up on that thing, that stumbling block that keeps you from moving on. Later, having given up and moved on, it seems the troubling concept somehow seeps into my brain unawares. Very strange stuff, this learning.

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