On memorizing equations:
“It is not a good idea to try to memorize that, because that just ensures that you will forget it. But you ought to recognize the cases where life gets interesting.“
Bob Pease, c. 2004
A tale from the cube:
Once upon a time, I was involved with a satellite project. In those days, a high-quality phase-locked loop was constructed of discrete-level parts and needed to be designed at the basic mathematical level. Not an overly difficult task but challenging enough to use as an “Are you ready for advanced solo work” type assignment.
I see such things so much better in hindsight …
There were 3 or 5 of us working on a section of this project – all of us being “groomed” for higher level independence on design projects.
I think the definition’s changed in the eras that have passed since but at that time, a “brass-board” was the final implementation – equivalent in every way to the actual flight board. The last chance to make sure >everything< worked as expected.
I don’t recall how the error propagated to this point, but the PLL failed. It was not my design but one of my tasks was “analyst”. I was one of the group and hence the one selected to perform the “peer review”.
It took a while but the problem was traced down to an error in one of loop equations: the designer had “memorized” what was really not a difficult expression – but forgot to square a term in the denominator.
Had the process not included this brass-board level of verification, the bird would have been launched – and not functioned properly.
I don’t recall what happened to the designer. It was a serious issue and as I recall, there was talk of letting him go. I don’t believe they did, but I’m sure this incident stalled his career with the company.
I stopped “memorizing” equations then. Such memorization is for school, not practice.