Slide Rule Accuracy and F=ma

Earlier this week, we were talking about drawing a Large diagram as one of the lasting and important things I learned in Prof. Collins’ Structure & Materials course.

Here are some of the others:

‘Slide Rule Accuracy’

This is the idea that in the real world[1], you’re never going to use more than three digits of accuracy (or four if your number starts with a ‘1’)[2]. Beyond that, things will get lost in the noise, or other inaccuracies, whether it’s budget contingencies, manufacturing defects, or whatever. (It would be interesting to see whether this has changed for manufactured parts with increased automation.)

The ‘3 laws of engineering'[3]:

1) F=ma

Simple, yet profound. When you’re dealing with non-relativistic systems (pretty much all of them), you push on something, it will move or react proportionally. This is not limited to physical systems.

2) You can’t push on a rope.

Also simple, has a number of applications for mechanical systems, but is probably the most ‘Engineer-y’ useful statement for dealing with other people.

3) In order to solve an engineering problem, you must first know the solution.

This one doesn’t really make sense on first blush, but I’ve experienced it. I mentioned earlier that the brain is often a structure that problems flow through, and in a sense this is a statement of that. You’re going to try to fit a new problem you’re looking at into the structure(s) of all the problems that you’ve seen before, and you have a huge advantage if you’ve seen similar problems before, or seen other problems you can apply by analogy.

We also had a ‘notebook’ that we put all of our class notes in, including cut and pasting from technical sheets, and this ‘notebook’ was our open book for the exam. It was a great exercise in focusing note-taking and coalescing your thoughts onto a medium-small piece of paper.

“When someone is paying you $100 for an hour of work, it’s worth paying a few extra cents for a good sheet of paper to give it to them on.”

The course had special ‘engineering notepaper’ that they wanted us to hand problem sets in on. There wasn’t any penalty for not doing so, but the lesson was that a little bit of professional presentation went a long way.

[1]This is when you’re dealing with things of reasonable size. I’m guessing when you’re looking at gravity waves or Higgs bosons, you might be using somewhat more accuracy. But at the same time, you’re probably not really looking at more than the last few digits…

[2]This is one of those subtle things which is actually quite important and powerful. On a slide rule, the portion which starts with a ‘1’ is fully 30% of the length (log10(2) ~=0.301), so unless you use the fourth digit here, you’re losing a substantial portion of your accuracy. There is a better explanation of this here:

[3]For a slightly different set of three Engineering laws, look here:

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