On the importance of studying primary sources

Y. B. Karasik,
Thoughts Guiding Systems Corp.,
Ottawa, Canada.

The original works of prominent scientists often look archaic and are difficult to read. Try to study calculus by reading the treatises of Newton, for instance, and you will see it. The purpose of texts is to give a streamlined, modern, and relatively easy way to learn a subject. Nevertheless, studying the original works of great masters might be useful in several respects:

  1. It may reveal interesting methods of problem solving;
  2. It may reveal directions of research, which were later abandoned and forgotten;
  3. It may reveal a differing prospective on the subject than texts present;
  4. It may reveal gaps in calculations and presentation on the whole, filling which could be a beneficial exercise.

This issue of the journal is devoted to analyzing the paper "On the electrodynamics of moving bodies" by A. Einstein. Amongst other it reveals an interesting mathematical trick.

Einstein was looking for a certain function τ(x,t) and derived the following equation for it:

∂τ(0,0)    +    b  ∂τ(0,0)    =    0   (1)
∂x ∂t

Unfortunately, it was not a type of equations which could be found in mathematical texts. It was not a differential equation as the partial derivatives were taken at the point (0,0). So how to solve it ? The texts did not study such equations and did not provide any recipies to solve them.

But Einstein applied his out of the box thinking skills and found an elegant way to cope with the problem. He noticed that solution to the differential equation

∂τ(x,t)    +    b  ∂τ(x,t)    =    0   (2)
∂x ∂t

would also satisfy the relationship (1). So, he solved the differential equation (2) and found the sought for function.

Those who love viewing everything through the glasses of TRIZ could recognize the transition to another dimension here. Indeed, in order to solve the equation of unknown type given for one point (0,0) only, it was extended to the entire plane (x,t) and thereby converted into an equation of the known type, specifically, differential equation. So, it can be viewed as a manifestation of the transition from point to plane.

Although it is debatable whether this TRIZ analogy is useful or not the usefulness of studying primary sources is beyond the doubt.