A core tenet of writing is clarity of thought.
I’m always excited by the rare applicant who clearly has thought through a research area, and has some ideas and real thoughts about problems he/she wants to tackle. It’s fine if the ideas are not likely to succeed, or if the thoughts are not realistic for current research. What matters is that the student showed their logical reasoning skills, and their passion for research at the same time.Professor, University of Chicago*
William Zinsser, a renowned non-fiction writer and one of my inspirations, has said that writing is thinking on paper with clarity.*
As long as you can think clearly, you should be able to write clearly.
This ability to think with clarity is more rare than you would imagine, and requires a good amount of introspection. Before you begin writing, remember to first think through your ideas clearly. Take walks. Outline key points. Only when the ideas are clear should you transfer them onto paper.