Division again

Previous mathy item was a topic that should have been familiar to me but wasn’t. I had to think about it for the first time, and I’m not satisfied with my thinking. This topic is thoroughly familiar but still benefited from a rehash.

A peculiar online argument about Marx’s math is raging. The usual sides are saying the usual things for the usual reasons.

Overall it doesn’t matter what Marx said about anything. The Soviet system and the New Deal were NOT Marxian. They tried to fix capitalism’s sins, and used SOME of Marx’s thoughts to point out SOME of the sins. Both systems were returning to the advantages of feudalism, not inventing a new way of doing business.

The online ragers are quibbling about a footnote where Marx shows that he misunderstands the purpose of the calculus notation dy/dx. In typical German style he takes it literally and “proves” that it doesn’t work because it reduces to 0/0.

I learned calculus in college and later taught it as part of electronics.

DY/DX is not a division! Like imaginary or complex numbers, dy/dx is just a handy notation tool for blackboard math in math class. (It’s NOT handy for real math on real computers!) You’re not supposed to punch it into a calculator or set it on a sliderule and divide the result.

In real life there’s no such thing as infinity or an infinitesimal.

My freshman calc teacher William Kirby, though annoyingly theoretical, was crystal clear on this point, and the textbooks were also clear. (Come to think of it, Kirby was an avowed Marxist, which was NOT fashionable in 1967.)

You’re always dealing with a ratio of a finite change in output vs a finite change in input or time. You will OFTEN have a zero DY, no change in output. The car is at a stop sign, or the voice is silent between sentences. You won’t need to handle a zero DX (zero change in input or time) because you don’t need to handle an unchanging input or a stopped clock. So the denominator DX will never be zero in real math.

At a larger scale, all of math is just a notation tool. MATH IS NOT THE BASIS OF THE UNIVERSE. MATH IS A LANGUAGE. Real life, economics or electronics or neurology, DOESN’T KNOW MATH and DOESN’T USE EQUATIONS. When we write equations to describe a speech wave, or use boolean logic to analyze a legal document, we are NEVER truly describing what happens. Words, math and logic can help us to deal with real life, help us to predict what’s likely to happen the next time we see this pattern. That’s all.