To make things clear, I'm not trying to argue against your position that logic and reason are valuable tools, but I do disagree with the claim that something which we choose to call 'intuition' doesn't exist in any form. The premise of this thread is misleading insofar as it pits logic and intuition against one another, when really one complements the other. We don't fully understand how the brain works. When we don't have a complete understanding of something, creating definitions and principles can be helpful, but can also create the illusion of certainty where there is none.
If you tell me that intuition doesn't exist in your experience of the world, I'll believe you. It's impossible for me to understand how that would work, but I'll trust you anyway. And likewise, if I tell you that in my experience it does exist, please believe me, even if you can't comprehend it. We all formulate our own interpretation of the world inside our own minds and that's why when you play Go with someone you see a game and a person, instead of vibrations of light and sound.
You're never going to convince me to agree with you by just quoting a selection of what I've said and stating what amounts to the opposite back to me. Think about it. If I did the same back to you, it wouldn't change your opinion either.
We can have an interesting discussion though if you address the important point of whether dogs can do calculus
1. If intuition doesn't exist in any way shape or form, then both people and dogs don't have intuition. How is it that they know where to run to catch balls? Are dogs reasoning logically? Are they doing calculus? Are they some sort of automaton?
2. Are you able to drive a car? Do you have to make hundreds of mathematical calculations while driving and, if so, how can you do them so quickly?
3. I rely on intuition heavily in my own games - something you claim is irrational and doesn't exist. If intuition really is figment of my imagination, I must be some kind of crazed idiot, playing at the level of a retarded gerbil. But, somehow, I manage to play as a 7 dan on Tygem. How is this possible?
For the third point: if, as you said above 'For those who do not care about the reasons, the brain takes care of it nevertheless to process its prior learning "experience".' Which you followed with 'But... experience is not intuition.' Then what should we call the ability to instantaneously apply accumulated experience? Why can't we call that process intuition? We can use your term 'rough reasoning' if you like. How is it not the same thing?
A discussion for another time: I just checked your Joseki 1 and 2 and didn't find a definition of 'heavy' in there. Perhaps you could define it in terms of efficiency, as you suggest, but I think it has more to do with strategic freedom and flexibility on a global scale. The number of stones is much less important than the whole board context. One stone can become heavy if the game develops so that it has no effective way to move and giving it up would entail losing the game.
P.S. Your new book arrived today and I'll start reading it soon. Thanks!