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I suspect that consciousness as currently understood has several different elements/components, each of which might be binary, or might not, I dunno. I picked gradient-based as that is the closest available option.
I also answered based on what I think would happen if we had infinite time to explore and research and discovered every discoverable thing eventually. There's a decent chance we extinctify ourselves fairly soon while leaving many answerable scientific questions unanswered, but I notice your options don't allow for that, so I assume risk of extinction is out of scope.
@equinoxhq Good point. Another 'No' option covering - it may be possible but too difficult or unlikely would have been good to have. The possibility of us extincting ourselves first is not zero.
Personally I think if it is solvable it will be solved - possibly by some more advanced future AI. It would be really strange if it's so challenging that only AI manages to figure it out and then struggles to explain it to us. Even stranger if AI is able to create a metric that demonstrates a test for consciousness that proves AI itself isn't consciousness (although I lean towards the last option myself.)