All these “useless” discoveries were summarized in four mathematical equations. As James Clerk Maxwell was “uselessly” studying these equations between 1850s and 1865, he noted a *mathematical* inconsistency in them. Continuing his “useless” calculations, he found a way of removing the inconsistency by changing the last of the four equations. He then found a solution for the equations — another “useless” exercise in mathematics according to Dewey. This solution predicted the existence of electromagnetic (EM) waves and showed that they all traveled at the speed of light! Twenty two years later, in 1887, Heinrich Hertz, produced the first artificial EM wave in his laboratory in an “exercise for its own sake.” We now call this wave microwave!

Pragmatism severely hampers scientific discovery because any discovery is a discovery of an unknown and an unknown cannot have any practical application.

Even Dewey’s account of the development of science is wrong. On page 201 of *Democracy and Education* he writes: “Physics developed slowly out of the use of tools and machines; the important branch of physics known as mechanics testifies in its name to its original associations.” I showed above that this statement is completely false as applied to electromagnetism: physicists did not use “tools and machines” to discover the laws of electricity and magnetism. As for mechanics, it is naively sophomoric of Dewey to associate it with machines, despite its name! Mechanics is the study of motion, and is based on three laws, the first of which — in its most basic form — was discovered by Galileo. It is well known that Galileo discovered this law, not by looking at machines, but by carefully analyzing motion on inclined planes in his home laboratory as an “exercise for its own sake,” and to Dewey’s surprise, it involved a very abstract ideas:

The first law of motion was discovered not by the popular version of “scientific method,” but by the interjection of no less

abstractan idea than the notion of infinity in the process of observation and conclusion drawn from it!

Dewey published *Democracy and Education* in 1916 and again in 1944. By the second date, both relativity and quantum mechanics, the two pillars of modern physics, were well established. They were, at the time, admittedly highly theoretical. However, many experimental “exercises for their own sake” pointed to the unbelievable accuracy of both theories. The unification of special relativity and quantum theory in 1928 even predicted the intellectually intriguing notion of antimatter, which was discovered in 1932 — in the form of positron, the antimatter of the electron — in laboratory in yet another “exercise for its own sake”. Perhaps because they were theories (even though he attaches importance to the teaching of science) in *Democracy and Education*,

Dewey completely ignores relativity and quantum theories while he devotes an entire chapter on geography and history!

Today, with nuclear power plants, MRI, transistors, microchips, lasers, computers, smart phones, internet, GPS, positron tomography, and a host of other inventions with invaluable “practical applications,” we can see how wrong Dewey was and how much future inventions are in danger if we insist on “practical applications” of scientific and mathematical investigations!

Not very usually I study content articles in this way.

Incredibly useful and interesting! I feel I am about to discuss it.