I recently discovered the Youtube channel It’s okay to be smart, hosted by Joe Hanson, which presents bite-sized chunks of general science at about my level of general science. He finishes each video saying “Stay curious”. I assume that means wondering and eager to learn or know, and not causing interest and speculation by being unusual. I assume the first meaning came first. Because of the two meanings, it is (just) possible to say “Very curious people are often very curious”.
Never Pure and Rarely Simple
Random thoughts about language, life, the universe and everything
Never Pure and Rarely Simple 
“Curious” is one of a class of words with two meanings, only subtlely related to one another, where one is an attribute of a person and the other is something a person either is or does. These are ripe fodder for puns. Two instances that appear frequently in such humorous (and not complimentary) exchanges are “revolting” and “trying.”
On a related note, some Koreans I know frequently confuse “bored” with “boring,” so they will describe themselves as being “boring” while watching a dull TV program or speaker. Actually, they refer to having been bored at the time, but mix up present and past tense as well; thus “I am boring.”
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I have written about fast, with ‘stuck fast’ and ‘running fast’: https://neverpureandrarelysimple.wordpress.com/2019/01/09/not-so-fast/
It’s interesting to ponder which order the meanings came in, what the first person to use the new meaning was thinking at the time, and whether the first person to hear the new meaning understood it. I suspect that “I am curious about that” > “That is curious” > “She/He is curious”.
My experience is that more people (from many countries) say “I am boring” rather than “This is bored”, but my diary from my first stay in Korea has the following story (which was notable enough to record):
“One new student joined the level 3 class yesterday, and said that my colleague who had placed her said “level 3 or 4”. She`s clearly towards the top of level 3, but I`m not sure that she`s quite level 4 yet. This evening, she made a big show of impatience as other students hesitated over their answers, and was flicking through the book. As she left at the end, she said “This book is bored!” (a common error by Koreans). I said “Oh, I hope it gets interested soon”, which of course sailed right over her head.”
It is possible for people to be boring – I often use the example of a blind date or an English teacher (“Hel-lo. I’m your Eng-lish teach-er and I’m bor-ing”.)
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Since you had written about the multiple meanings of “fast”, that gave you another opportunity for a Lewis Carroll reference (as in the title of this thread), where the White Knight, IIRC, tells of having been stuck “as fast as lightning.”
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