Perhaps if your hair is particularly dry, this won't pose you problems, but if I go too long without cleaning my hair with anything other than water, it becomes visibly oily. Humans secrete waterproof substances through glands particularly concentrated in the scalp, so a buildup should not readily be cleaned through water alone.
This is temporary. My hairy was quite oily for about two weeks but now it's about as oily as it was when I was shampooing every day.
This is the public group instrumental rationality diary for May 1-15.
Thanks to cata for starting the Group Rationality Diary posts, and to commenters for participating!
Next diary: May 16-31
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