In general, all engineering is the same. Here and there, however, there are idiosyncrasies that don’t make much sense to the uninitiated. Foremost in electrical engineering is the ubiquitous complex j.
Similar to “teetotaler”, “imaginary” was used as an insult by Rene Descartes, staunchly opposed to the concept of roots for negative numbers. “Imaginary” caught on and became the de-facto terminology used and the resulting base unit, the square-root of negative one, became simply i. Fortunately for us, imaginary numbers are not, well, imaginary, despite confusing nomenclature. Descartes was wrong, imaginary numbers do occur in the natural world and have become foundational in understanding physical phenomenon both seen and unseen.
Now, millions of schoolkids are confused when faced with imaginary numbers, as the name indicates they belong to a subset of education that will never apply to their real lives. This is truly a shame, and in an effort to resolve this, many references to imaginary numbers have been modified to “complex numbers”. Somewhere, Descartes is laughing at his successful smear, because “complex” is actually an entirely different term referring to a number that is a composite, made up of both “real” (numbers without i as a factor), and “imaginary” numbers. Pick your poison, terminology will always be wrong, I’ll stick with “complex” from here on out for anything involving an i.
Electrical engineering is considered the weirdest version of engineering. Most people assume the concepts are more abstract, which is partially true. As it turns out, most specialties within the field all have math that is going to involve complex numbers. Had Descartes lived today, he never would have made his foolish mistake, because as it turns out electrons and light particle-waves all get some help from our friend i. The irony is that the complex numbers involved in these equations really aren’t abstract, all engineering really is the same, but we’ve learned a lie that continues to confuse us all the way up in higher education.
But the j, why is it a j? If you guessed another silly convention, you’re correct! Electrical engineers love the flow of electricity: current. They love it so much they often find ham-fisted ways to fit it into acronyms related to whatever sexy start-up they’ve concocted that week. One of the greats, Andre-Marie Ampere, was the first to discover that electricity flowed in a current, and managed to call dibs on it. The first element of his dibs isn’t so bad, the unit for current is Amperes or simply Amps. The second is his folly, the variable for current in diagrams and equations is now standardized as the lowercase “i”. He was French, so maybe the word for current starts with “i” in French? No, it does not. “i” refers to “current intensity”. A cruel joke. If it’s not obvious, there are many different intensities in electrical engineering.
To be fair, there’s not enough letters in the Latin alphabet to represent all of our scientific variables (or Latin and Greek combined). Still, the use of “i” for current is one of the first lessons taught to all good little electrical engineers, so the symbol was off the table when we realized that we’re going to be seeing a lot of complex numbers.
Engineers are a practical folk, so what do you do when you need i but it’s taken already? Just flip the tail and make it a little longer: j. It drives mathematicians mad.
Really, everything is made up anyway! To be specific, the ways in which we can relate to reality are made up. That’s the point of this blog. On a bi-weekly basis, I’ll explore an aspect of electrical engineering I find intriguing and I’ll explain it in a way that the uninitiated can enjoy that aspect alongside me. Some of these will be other idiosyncrasies, and others will just be cool ways the world works. I often find myself thinking about these concepts in generalized terms which add helpful context to my entire life. Maybe you will too, who knows?