Clarity of ideas
Having learned how to do multiplication and division with a slide rule I never forgot the fundamental properties of logarithms. The tool encoded an idea. This is often how we incorporate fundamental concepts, through using them. This is the argument for working with “primitive” tools; they can ground us in topics so we can use them going forward.
You are grounded!
But there is a “tipping point.” Somewhere along the line, you will hit a point where further use of the “basic tools” has a diminishing return on investment. I never learned how to solve roots with a slide rule and I don’t think I would have benefited from it. How do you determine when you have “tipped”?
How to tip
Unlike a restaurant, there is no set “tip” (15% for basic service in the US). Moreover you can easily miss it if you are not going into the exercise with the correct attitude. To identify the tipping point you need to:
- Actively think about “what am I learning (Y) as I do X?”
- Think about how what you learn could be applied to other situations.
- Recognize when you are are just “getting better at X and not learning about Y.”
Follow those guidelines and you will slide into new areas with ease; after you slide for a while you will get the feel for when you are ready to dive in.