There are lots of different things in the world, and some of them are similar. Profound, I know, but allow me to explain. I have spent a sizable bit of time learning how to engineer stuff and do math. For those who may not be familiar with this sort of thing, a good portion of engineering and math is understanding rules and applying them to translate a situation into something that makes sense. That is a broad sweeping generalization but we can apply it to a specific example.
We’ll take something simple, like an airplane, and we want to know if it will fly. We first make assumptions about the situation: the air is normal, the plane won’t randomly fall apart, and the rules we use are correct. If we have the specs of the airplane, the problem is essentially complete. Will it fly? Of course, the rules and specs tell us it will.
Ah, if it were only that easy. Unfortunately, it’s difficult for us to look at specs and rules and see something meaningful. Sooooo, we must simply translate the answer into a form that makes sense. More specifically, plug in the airplane specs into flight calculations (based on our rules) and ultimately find that the weight is less than the lift, or something.
Same with math. If we are solving a problem (rather than proving relationships or some other theory type thing) we are simply using rules to translate what we have into a more recognizable form.
The way to get good at math or engineering is to really know the rules and formulas. Know, like understand where everything comes from and why it only works a certain way (tangent: that is why mathematical proofs are important). You’ve got to make the rules your own so you can command them to work for you. A fundamental understanding of the rules allows for adaptation and flexibility when solving problems. The opposite of that is only understanding how to get an answer for a specific problem. This is not good; rarely does one encounter an identical problem. It’s much better to be flexible.
However, at the moment, I am a German language student and I find many similarities with the styles of learning. We are learning grammar, the logical and mathematical aspects of language. We learn new words, verbs, and constructions, different rules that can be applied to different situations. Like in engineering and math courses, we learn the rules, and practice examples. The only way to really remember a grammatical construction is to understand the rules behind it and a good understanding helps the speaker to be flexible in building sentences and phrases.
When I encounter a text or conversation in German, it is similar to an engineering problem. The answer (complete understanding, or English translation) is mostly right in front of me. I have the specifications (the German sentences) and the grammatical rules so all I have to do is literally translate the German into a form that is more recognizable. My goal is naturally to know all of the rules so I am equipped to handle all sorts of German language. As rules get used more frequently (both German and math), they get engraved into the brain and the translation happens quicker, with the rules being applied instantly in the subconscious. That is what I would call language fluency or mathematical competency.
As languages go, German is pretty logical and I’m enjoying working at identifying rules and practicing on my host family. It would seem engineering and languages are not as different as they are made out to be. Well, at least in learning styles.
Fantastisch.
-H
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