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But Hatsumi Sensei didn't talk about this in a way us English speakers might normally consider the term fumble, as some kind of clumsy, unskilled, movement. He spoke of it more as a exploration and a searching about the environment to see what you may discover. It was a process of discovery.
So if we fumble about the Japanese language and look at other related terms in our art or just in the Japanese idiom, we may discover something:
You may have heard about the Ashinami Jukka Jo- The ten ways of walking according to the Ninpo book Shoninki, but we also have 探り足 Saguri Ashi and Saguri Aruki which are used for stealth and to feel your way with your feet when your eyes are not enough to set your path.
When you are trying to understand someone else you may use 探り合い saguri ai to probe each other or sound each other out.
Maybe you are uncovering secrets: 探り当てる saguri ate ru - to find out
If you feel like Marcellus from Hamlet that something smells rotten in the state of Denmark: 探り出す saguri dasu to spy out / to smell out
Maybe you lost your house keys and need: 探る saguru to search / to look for / to sound out
Many people use training in the Bujinkan to: michiwosaguru 道を探る to seek a path; to find one's way.
If you have bad manners you could saguribashi 探り箸 using your chopsticks to find a food you like by rummaging in your dish, pot, etc. (a breach of etiquette)
So at the root of understanding 探り回る Sagurimawaru in our training are two contrasting perspectives on your approach as a student in class. Are you fumbling about blindly or are you on a path of discovery? This is a choice you make everytime you step into the dojo, whether you slip in with saguri ashi or trip over the threshold.