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1. Literally, to fly an airplane without the ability to see, relying on the plane's instruments instead. The huge plume of ash sent into the air by the volcano forced the pilots to fly blind for nearly an hour.
2. By extension, to do something based on guesswork, intuition, or without any help or instructions. As this is our first attempt at building a smartphone app, we'll be flying blind as we figure out how to get things working correctly. I've never filed my own taxes before, so I'm sort of flying blind.
Feel one's way, proceed by guesswork, as in There are no directions for assembling this furniture, so I'm flying blind. This hyperbolic expression dates from World War II, when it was used by pilots who could not see the horizon and therefore had to rely on instruments. It was transferred to broader use soon afterward.