Intuition...

Intuition...  I ran across this blog post in my reading this morning.  It caught my attention mainly because it has a Feynman story in it; one that I was familiar with, but hadn't thought about in a while.  In it, Feynman talks about the importance of developing an “intuition” about physics problems, in addition to understanding the mathematics describing them.  Sometimes that intuition will get you to an answer long before you can prove it with the math.

I think that same observation applies across many kinds of science, and even some math itself.  I've noted the same phenomenon with arithmetic many times.  In particular, developing the skill to do arithmetic mentally or on slide rules (which actually involves quite a bit of mental arithmetic) helps you develop an intuition for the general value of a solution to an arithmetic problem.  Almost any problem in more advanced mathematics (say, a differentiation problem) involves, in the end, simple arithmetic, then having such an intuitive grasp on arithmetic helps you avoid errors in the more complex math.  I've used a variation of this to argue for the value of slide rules over calculators or spreadsheets.  As I read this blog post, it occurred to me that what I was really arguing for was developing an intuition for arithmetic, as Feynman argues for physics.

Several other fields I'm familiar with demonstrate the same value of an intuition.  Analog electronics, for example – having an intuitive understanding of how the basic components (resistors, capacitors, inductors, diodes, transistors) work is an incredibly powerful base to build an understanding of electronics on.  As Feynman might have said, you could analyze any circuit with mathematical tools, but it's far easier if you have a good intuition for how the parts work.  I think the same thing could be said for programming, or mechanical engineering, or concrete mix design...