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Ohm's Other Law

Ken C. Pohlmann  |  May 7, 2023

The dictionary defines a genius as someone who displays “exceptional intellectual or creative power or other natural ability.” Nowhere in that definition does it say that a genius has to be infallible. That's something you and I share with a genius. Sometimes we are wrong.

Alert readers will recall that we recently discussed Ohm's Law. Georg Ohm proposed a relationship between voltage, current, and resistance that challenged the established science. His heterodoxy earned him widespread scorn and personal humiliation. His peers graded his math with an F. Of course, in fact, his work was A+ and his concise bit of mathematics laid the foundation for our modern world of electronics. It is not hyperbole to say that Ohm's Law is a work of genius. Which brings us to Ohm's other law.

In the course of his scientific career Ohm worked on many problems. Intellectually restless, he tackled issues such as electromagnetic force and molecular physics. He was also fascinated with the question of sound. There is a curious cosmic anomaly there because audio engineers use Ohm's resistance law every day to design audio devices but Ohm could never have imagined today's circuitry that uses his resistance law for audio purposes. Rather, his interest in audio dealt with the question of how we hear music.

In particular, Ohm's other law, sometimes known as Ohm's acoustic law, posits that a musical sound is perceived by the ear as a set of pure harmonic tones. To cut right to the chase, we now know that this is not correct. The ear in fact does not work as his law describes. But we can give him partial credit for his answer.

When he proposed the law in 1843, the perception of sound was a hot scientific question. And in all fairness, it's a question that is still not fully understood. Other scientists such as Hermann von Helmholtz and mathematicians such as Joseph Fourier were piecing together the relationships of pure and complex tones, and beginning to understand that a complex tone could be resolved into a series of harmonically related pure tones, and also could be created from them.

Ohm was not far off base but he erred in one crucial respect. The ear in fact does not perform what would essentially be a Fourier analysis. Another cosmic anomaly: thanks to Ohm's resistance law, we can build Fourier analyzers — circuits that do indeed parse out component harmonics from complex tones. But the ear doesn't work like that.

Postscript: Much of the opposition to Ohm's resistance law stemmed from the fact that his expression of it was fairly cryptic. Simply put, he did not explain his work particularly well. This made it doubly hard for contemporaries to accept a novel idea that already ran contrary to their expectations. The point is that genius is one thing, but genius can be lost unless it is properly communicated. I wonder if Ohm could have proposed a more useful acoustic law, if only he had thought through the problem a bit more. By working harder to better explain his views, it might have caused him to refine his thinking and arrive at a more correct solution.

Post Postscript: In any case, we can conclude that to err is human. Even if you are a genius.

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