by Fred Steinhauser, OMICRON electronics GmbH, Austria
Mathematics is a stand-in for a subject that not everyone understands. But instead of admitting their personal limits of competence, many prefer to undermine the competence of the experts.
When clearing out old stuff, I came across an article from a youth supplement in a daily newspaper from the 1970s that I had cut out and kept. It was an article about a 14-year-old boy who had found a construction for a 7-sided polygon using a compass and a straightedge. Such problems had already been investigated by ancient greek mathematicians. Around 1800, Carl Friedrich Gauss worked out the theory for constructible polygons, and the 7-gon is not among them. Only a few years earlier, at the age of 19, Gauss had found the construction of the 17-gon.
What the boy had constructed was the value of (on a circle with radius 1), whereas the true value for the length of a side of a 7-gon is sin (/7). As one can easily convince himself with a calculator, the values are close, the relative difference is only 0.2 %, and someone fondling around on a piece of paper with a pencil and the said tools might not notice the difference. But this was not a construction of the 7-gon in the mathematical sense.
However, the author of the article emphasized on the ignorance of the mathematical establishment that rejected the boy’s supposedly groundbreaking discovery. Not reflecting his own incompetence in this matter, he tried to undermine the competence of the experts. Can you recognize a pattern?
What we usually learn in school and even in university studies that rely on math, is not math itself, but just how to calculate. It makes perfectly sense that, e.g. electrical engineers learn to crack Maxwell’s equations, but that may not include the whole story of how the methods came about. Only in the study of mathematics itself is it shown how to start with a few well-chosen axioms and then rigorously derive and prove what follows from them. Without these fundamentals, it is all too easy to dismiss mathematics as incomprehensible and illogical when encountering difficulties.
On the other hand, math professors all over the world are haunted by people who claim to have found a proof for Riemann’s hypothesis. Just as patent offices are flooded with inventions of the perpetual motion. Leading mathematicians in this matter confess that they do not yet have a clue how to get a handle on this famous problem. Nevertheless, in a fit of overconfidence, wannabe mathematicians dare to claim that they have mastered it. In most cases, their arguments lack any basis for a sound mathematical justification. The lack of recognition for these “proofs” is often attributed to the ignorance and jealousy of the established mathematicians, instead of recognizing one’s own limitations. The argument shifts from objective considerations to personal feelings and attacks.
As a prominent component of STEM, math is only one visible example of how scientific thinking is under attack. Some of those who do not understand it try to undermine the credibility of science, for whatever reason. But science and scientific thinking and decision making, in all disciplines, not only STEM, is what has awarded us with the current state of civilization.
In electrical engineering, we are deeply embedded in STEM and we understand the importance of scientific thinking. But we also must foster and support this attitude in the general society. Otherwise, there is a risk of regressing to the Middle Ages
Biography:
Fred Steinhauser studied Electrical Engineering at the Vienna University of Technology, where he obtained his diploma in 1986 and received a Dr. of Technical Sciences in 1991. He joined OMICRON and worked on several aspects of testing power system protection. Since 2000 he worked as a product manager with a focus on power utility communication. Since 2014 he is active within the Power Utility Communication business of OMICRON, focusing on Digital Substations and serving as an IEC 61850 expert. Fred is a member of WG10 in the TC57 of the IEC and contributes to IEC 61850. He is one of the main authors of the UCA Implementation Guideline for Sampled Values (9-2LE). Within TC95, he contributes to IEC 61850 related topics. As a member of CIGRÉ he is active within the scope of SC D2 and SC B5. He also contributed to the synchrophasor standard IEEE C37.118.
