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For me, intuition is defined by knowing things - and I mean accurately knowing things - that can't be worked out using IIIrd circuit tools.
If someone logs onto Second Life for the first time and finds their way to the virtual property of a friend by flying around at random, that would be intuition.
It can be explained as coincidence, but it's so statistically improbable, given how big Second Life is, that it's actually very unlikely. Especially when similarly unlikely things happen to them rather a lot. (Not a hypothetical, BTW - I know someone who operates like this.)
What you're calling intuition seems to be more about default assumptions about the world. Most of the time people don't need to know whether it's the earth or the sun that's moving. It's enough to know that when it's daytime the sun is up, and then it gets dark for a while, and there are seasons which make the cycle vary, and that's pretty much it.
The point of science is that it asks lots of 'Yes, but...' questions and eventually you end up in a place which looks nothing like that view of the world. It happens to be more useful and inclusive for certain things, but the fact that it's not rooted in everyday experience is exactly why - it doesn't take things at face value.
So at face value the birthday paradox, or the fact that the odds of a coin showing heads are always a nominal 50%, even after a freak run of 1,000 heads in the past, makes no sense. That's because our face value views of the world didn't evolve to deal with those kinds of problems.
If there's a point to science education it's that the face value view of the world is tentative and usually limited. Chasing after a more comprehensive view is very much a IIIrd circuit thing to do. And - as RAW says - it's easy spin your wheels endlessly in 'Yes, but...' without getting anywhere useful. Especially if you don't have peer review and other kinds of reality checks to stop the process becoming parasitic on your consciousness.
Intuition can sometimes short-circuit that, not by building a more accurate map - which is what the crank-types always try to do, and fail - but by realising that sometimes you don't need either Science[tm] or face value to connect with reality in a useful and fun way.
Similarly with drugs, you can take the experiences at face value. You can analyse them intellectually to build a map. Or you can 'know' what you do and don't need from them, and what's right for you. There is a kind of messianic narrative about drugs which suggests that using them will help you to know. But in practice face-value use seems to be more common than that. and it's the odder non-mainstream drugs, like ibogaine and ayahuasca, that seem to have more potential for persistent intuition. Weed and LSD - not so much, I think.
As for music, it's true that people have to practice. But for some teachers that's an end in itself. It's about teaching values like persistence and hard work for their own sake, and not about making performance skills fit into a bigger picture of Bach's intentions and musical spirit. For me that's a crippling and not a liberating way to teach music.
The basic narrative here is personal liberation. The progressive idea is that if people can function without being crippled, they won't need the kind of oversight that conservatives believe is essential.
Conservatives know what goes on in their own souls more than they understand anyone else. On that basis it's not surprising they want to control the world, lock it up, and declare war on it.
With higher circuits those knee-jerk conservative reactions become frightening first, then pitiful, then rather funny.
But conservatives won't see it like that, because the idea that a world of switched-on people might survive happily without their much coarses responses is something that's completely beyond their imagination.
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