Thus far I have avoided bringing math into my posts about the physical phenomena that underpin modern electronics. Math is one language we can use to discuss physics, and it’s certainly a language that lends elegance and precision. I have an undergraduate degree in math, and partly chose physics because it seemed to me to be the most math-heavy of the sciences, so certainly I see the appeal! However, I think that verbal descriptions are very valuable as well, both for people with a strong math background and for people who’d rather avoid it. The best undergraduate textbooks I used had a combination of verbal and math explanations (for example, the excellent Electromagnetism and Quantum Mechanics textbooks by David Griffiths).
So in general, I think that if you want a really thorough understanding of science, you have to dig into some math. You also have to dig into some physics, and you have to dig into some chemistry, and you have to dig into some biology. You even have to dig into quantum mechanics, which is not as bad as many people think. It’s all interconnected, and the many different languages of science play off each other in interesting and unexpected ways. But if you can only explain something in math, and not using words, then your understanding is incomplete in my view. And for those with an interest in science who don’t need to dig in to all the details, the verbal explanation is usually the best place to start!
On top of which, there are so many ways to explain a concept verbally (or using video or other media, as Erin recently posted). The simplicity of math-based explanations is wonderful, but can feel like a dead end if the math doesn’t click mentally. But if you are open to a diverse range of explanations, it’s possible to try many different approaches until one finally puts all the others into perspective. I have found this to be the best way to get my own head around really bizarre scientific ideas, to approach them from many sides until they finally make sense.
That said, sometimes the mathematical interpretation of an idea leads somewhere new, and thinking about math becomes necessary to understanding the new idea! I plan to keep approaching these topics from the verbal side, and we’ll see how it goes with the subject of the next post!