The Depth Of The Gemara

A friend from back in Michigan got me thinking about how people do not understand how much information there is to learn in the Gemara, so I figured it would be educational to post about this.
It is incomprehensible to someone who has not learned Gemara how much information there is. I will try to give you an analogy but anything I come up with will fall far short of the true extent of the amount of information. Me sitting in a class given by the head of the Yeshiva is like a 5-year old sitting in a class taught by Einstein. The only reason I can comprehend anything is because since all the students are comparable to 5-year olds the teacher brings the Gemara down to our level.
In addition the way we think is opposite to how we should think. The first day of class the head of the Yeshiva told us that his goal was to erase the damage that public school did to our brains and return us to our 4-year old inquisitive selves, with the ability to think for ourselves. For instance we are not alowed to guess the answer. In public school the answer to a question is what the teacher wants to hear, here any answer must be backed with reasoning. Even if we give the right answer the Rabbi will question us as if it is wrong. The Rabbi says that he would rather us give the wrong answer with a valid explanation than a correct guess.
We also have to stop thinking like Americans. He gives the example that all Americans think any problem can be solved. Today he said that Americans cannot understand why Israeli's and Palestinian's cannot live in peace, all you have to do to solve the problem is stick them in a room so they can talk it out!!! We have to understand that not all problems are solvable and continue learning even if something does not make sense. It is hard to stop thinking like a public school kid who is trying to please the teacher and start thinking like a person who is trying to work with the teacher in order to find the answer even if it is against what the Rabbi is arguing.
I do not mean to say that I did not learn anything at public school or that there were no classes where I did actually get to think, however for the most part the education a public school in America gives you is how to tell the teacher what he wants to hear. I do not think that is a controversial statement it is a fact of the way we were raised. I remember in 11th grade I got a C on a math test even though I got all the answers right. I was marked wrong because the steps I used to get to the answer were different than what my teacher would have done. I had a way of solving the problem, but it was wrong because my teacher thought her way was better.