[M]athematicians and physicists think alike; they are led, and sometimes misled, by the same patterns of . - George Pólya

Life is full of surprises: our approximate condition for the fall of a body through a resisting medium is precisely analogous to the exact condition for the flow of an electric current through a resisting wire [of an induction coil<nowiki>]</nowiki>. ...
<math>m\frac {dv}{dt} = mg - Kv</math>
This is the form most convenient for making an analogy with the "fall", i.e., flow, of an electric current.
...in order from left to right, mass <math>m</math>, rate of change of velocity <math>\frac {dv}{dt}</math>, gravitational force <math>mg</math>, and velocity <math>v</math>. What are the electrical counterparts? ...To press the switch, to allow current to start flowing is the analogue of opening the fingers, to allow the body to start falling. The fall of the body is caused by the force <math>mg</math> due to gravity; the flow of the current is caused by the electromotive force or tension <math>E</math> due to the battery. The falling body has to overcome the frictional resistance of the air; the flowing current has to overcome the electrical resistance of the wire. Air resistance is proportional to the body's velocity <math>v</math>; electrical resistance is proportional to the current <math>i</math>. And consequently rate of change of velocity <math>\frac {dv}{dt}</math> corresponds to rate of change of current <math>\frac {di}{dt}</math>. ...The electromagnetic induction <math>L</math> opposes the change of current... And doesn't the inertia or mass <math>m</math>..? Isn't <math>L</math>, so to speak, an electromagnetic inertia?
<math>L\frac {di}{dt} = E - Ki</math>

To write and speak correctly is certainly necessary; but it is not sufficient. A derivation correctly presented in the book or on the blackboard may be inaccessible and uninstructive, if the purpose of the successive steps is incomprehensible, if the reader or listener cannot understand how it was humanly possible to find such an argument....

We need heuristic reasoning when we construct a strict proof as we need scaffolding when we erect a building.