It has a lot tondonwith whether you tried to learn writing, found good teachers or other resources. Learning to write won't make your thinking different, but you will be able to express things.
It has a lot tondonwith whether you tried to learn writing, found good teachers or other resources. Learning to write won't make your thinking different, but you will be able to express things.
I'm not saying that you should be the next Robert Penn Warren or James Joyce if you're writing about an endofunctor or something, but I genuinely do think that learning how to write fairly well has actually made me understand mathematics and computer science better, in addition to becoming better at explaining it. My thoughts can be all over the place, and even if I know every single "fact" about a subject, I feel like writing about it (and in particular trying to write well about it) helps me fully realize how these facts actually relate to each other, and building a bigger mental picture that I might not otherwise have.
To be clear, I don't think writing is the only way of doing this. I think, for example, getting good at data visualization or learning formal mathematics can also have similar effects in regards to most forms of engineering. I just think that getting good at writing about a subject is a one of many really useful tools for developing an understanding of a subject.
Forcing yourself to interact with concepts in different ways improves understanding, definitely.
This doesn’t say that being able to teach or write well about a topic correlates with understanding. Understanding is an effect of writing not the other way around.
I am sure he didn't originate the sentiment but
“Writing is thinking. To write well is to think clearly. That's why it's so hard." -- David McCullough
(Interview with NEH chairman Bruce Cole, Humanities, July/Aug. 2002, Vol. 23/No. 4)”
This is precisely what I strongly disagree with.
You don't have to write to think and trying to is often detrimental. You can use writing to think, in situations where it helps or if you want to.
But it is not necessary and don't necessary improves your thinking.
And writing for you to understand is different then writing for others.
I think the better way overall though is just to try different methods of thinking and do what works for you. I also think more than one method is almost always better than just using one.
Writing is bad because it needs to fit in a human head and ultimately needs to be spoken by a human mouth. Maths is bad because it is still stuck as being written on blackboards or pen and paper if you're unlucky.
The few times I have build up these dsls formally have let me understand a topic both more deeply and remember it more easily. The downside is that time invested in inventing it in the first place. E.g.
(for-all x (implies
(member x integers)
(exist-unique y
(and (member y integers)
(equal? 0 (+ x y))))))
Is the way to say that all integers have additive inverses. It's ridiculously long but logically sound and quite easy to prove mechanically given that every operator in that sentence also have definitions in that vain.