Quote - "I for instance, almost never read the manual."

I took a quick look at some Vue images in your gallery and I did spot a couple of details where reading the manual would have helped... ;-)

Quote - "Instead with a new program I ask myself the question, "Is this and that possible?". Then I turn heaven and earth upside down trying to find that out, including searching the internet. Sometimes I succeed or I don't. But the thing is even if I don't solve what I set out to do, in the process I have learned a ton of other useful information."

I don't understand why you refuse to just press F1 and do a quick search in a PDF manual and instead you opt to spend a lot of time more to (hopefully) get that information.
If you want to learn "a ton of useful information", as you say, you can always do it, whenever you want. That may have nothing to do with finding an answer to a specific question. Your method seems extremely inneficient to me, but to each his own.
I also search the net, of course... if I couldn't find the answer by myself with an experiment or searching the manual.

Quote - "The problem with manuals is that only about 1/10 of what you need to know is in the manual."

I don't know about that percentage but I could say the same about any tutorial. If you want to know all you need to know, you have to watch all the tutorials out there... and it still probably won't be enough.
Anyway, I never advocated reading the manual as a replacement to watching tutorials. What I wrote was: "IMO, those tutorials you mention are an excellent addition after one reads the manual."

In other words, the manual lays the foundations which are necessary to take full advantage of the tutorials.

Quote - "What use is the function editor if you not are allowed to see the actual formulas and know exactly what they do to the material? "

Huh?! I don't need to see a formula to see what moving a slider does to my material. But anyway what does that have to do with tutorials? Did you see in a tutorial how to see the formula behind the function?
Anyway, like Artpearl said, there's information about those things in the FE and in the manual and lots of it is standard mathematical knowledge.