Complex numbers and imaginary detectives

I recently discovered that a good friend of mine, a highly educated and erudite man, does not know what complex numbers are. Yes, he learned about them in school once upon a time. Yet, he says, he has long since forgotten what they are.

Those people reading this who know that understanding complex numbers is a fundamental prerequisite to describing the universe around us — gravity, electronics, magnetism, springs, sound, light, weather, car engines, why a swing set works, and many other things as well — will probably realize what this means.

There may in fact be a yawning chasm in our society. It is not merely likely that the majority of highly intelligent, educated and literate people do not understand how the physical world around us works. It is likely that they cannot understand these things, because so much of the world around us is very difficult to describe without complex numbers.

Then again, one could argue that there is no reason to understand so much of the world around us. I am reminded of the scene in A Study in Scarlet when Watson recalls of his friend Sherlock Holmes:

I found incidentally that he was ignorant of the Copernican Theory and of the composition of the Solar System. That any civilized human being in this nineteenth century should not be aware that the earth travelled round the sun appeared to be to me such an extraordinary fact that I could hardly realize it.

“You appear to be astonished,” he said, smiling at my expression of surprise. “Now that I do know it I shall do my best to forget it.”

“But the Solar System!” I protested.

“What the deuce is it to me?” he interrupted impatiently; “you say that we go round the sun. If we went round the moon it would not make a pennyworth of difference to me or to my work.”

Of course, in order to really understand why the earth goes around the sun it is useful to know complex numbers. Then again, Sherlock Holmes was not a real detective, but an imaginary one, so I suppose we should cut him some slack.

3 thoughts on “Complex numbers and imaginary detectives”

  1. Curiously, I feel the same way about the natural world too.

    I don’t think it’s possible to really understand the world if one doesn’t understand animals and plants – how & why they behave the way they do and the effects of the myriad interactions between them (and us).

    I agree with you, but also see another yawning chasm – as more and more people become thoroughly urban, where virtually every aspect of their lives falls under some form of human control, their understanding of the natural world and their place in it fades out of consciousness.

  2. Ah yes. In the words of Rufus E. Miles Jr.: “Where you stand depends upon where you sit.” 🙂

  3. This post makes me want to relearn stuff about complex numbers. I’ve forgotten most of what I’ve learned over the years about them (since I rarely hear about them, no less use them in my daily life and work), but the promise of being able to understand their connection to gravity, electronics, magnetism, springs, sound, light, weather, car engines, why a swing set works, etc. makes them ever so intriguing!

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