The day of reckoning has arrived.

[FatAndFaithless]

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Intuition is faith in your own thoughts. If your intuition tells you the moon is 500 miles from earth, and someone else's intuition is that it is 1000 miles from earth, one or both of you is wrong. How can we go about figuring out what the correct answer is? 

As you note, faith won't do it so... Here is how you check your own thoughts.

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You don't get it Crunchy.
There is nothing wrong with the scientific method that you just show.
Intuition however is a total different thing.
Take Einstein and his theory of relativity.
He try and try to work out how to get it until one day it pop up in his mind.
Where you think it pop up from?
It pop up from his subconscious mind.
Nobody told him.
I already explained at nauseam about this topic and about the conscious mind and the subconscious mind
or what you are aware so far and what is hidden in the subconscious mind.

Intuitional science is all about to allow what is hidden in the subconscious mind to emerge in the conscious mind.  

Bolded mine.  You have a more fundamentally flawed understanding of science than I previously thought.  If you think Einstein's theories didn't involve enormous amounts of testing, refining, and tweaking based on findings...then I really don't know what to tell you.  Nothing about Einstein's work was a sudden, instant revelation or singular spontaneous eruption of ideas.  It required a lot of work..following methods like the one Crunchy depicted.