I think that no. Writing is separate skill. It has nothing to do how you internal thinking os nor whether it is sloppy.
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.
Granted, I'm speaking with no neuroscience or psychological background, but anecdotally I think I completely disagree.
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.
You are saying something different. Writing about something or teaching somebody something can be excellent ways of improving your own understanding of a topic.
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.
If you can't encode it with your neocortex, your neocortex doesn't understand it well enough. You might understand it, but your high level reasoning center does not. Give it a writing hand and pull it out of the tarpit.
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)”
I do agree that writing is not _necessary_ to improve your thinking. However, I think that writing about a topic will often if not always improve your understanding of that topic as well as your ability to communicate it.
I think that's because when writing about something you have to be slower, more deliberate and more structured than thinking about something in your head which helps you identify gaps in your understanding which you can easily miss when the idea is in your head.
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.
I find that writing and mathematics are just a poor way of trying to structure a context free domain specific language for the problem.
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.
There are people who are visual thinkers, and people who are more language based. For language based thinkers, writing always helps. For visual thinkers, maybe not always, although I think that combining visual and language thinking is very powerful.
I think I read the quote somewhat differently: if you think clearly, you will write well. Not that writing is necessary for thinking clearly, but thinking clearly is necessary for writing well.
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.