
The Chairman is quoted as saying to his people "If you have not been to the Great Wall, then you are not Chinese". And has been loosely transferred to "If you have not been to the Great Wall, then you have not been to China". Not wanting to take a chance, we did the Wall on our first day.
After being to a small section, I think there is some truth to these statements. The Great Wall is a tangible piece of many truly Chinese elements. It is huge. It was built almost by sheer will. There is tremendous history in it. It is an engineering marvel in some places and yet was built by very simple brute force in places. There are a lot of people there. For something that "everyone" does it can be quite difficult to see the real thing. Oh, and our first experience with Chinese bartering and all that entails - nothing in this country is sold at list price.
There are only a few options when it comes to seeing the wall - Jump on the big tour bus leaving from you hotel - Get a taxi for the day - Find someone that knows someone that knows how to get to a non-tourist or non-restored portion of the Wall.

Seeing as we don't really like tour buses and we didn't really have the time or desire to try finding someone that would take us to the Wall without taking us for a ride, we got a taxi for the day. Though when they say day they really mean an hour or so. It was surprisingly hard to convince the hotel and the driver that we actually wanted to spend some time there and do some actual hiking.
For 550RMB we got a driver to take us to the Mutianyu section of the wall. This section is touristy, but the main tour buses don't go here. It is a couple hours in the car, about half through semi-windy backroads. Once in the parking lot and through the flea market you can either take the cable car, ski lift, or your legs up to the Wall itself.
The walk took us about 40 minutes. Pretty much straight up. This section of the wall is in a steep area. Once on the Wall you can go right or left. The left having more length and going to the highest point of this section, we went left.

I really liked hiking the Wall. I have heard of people trying to make a continous through hike of the Wall, which I think would be an amazing project. The Wall goes through some tremendous peaks and ridges, and would be a little detective story crossed with navigational challenge. I can put that on the "Win the lottery" project list.
We did not have the best weather for hiking the Wall. The temperature was high, the humidity couldn't be any higher without rain, and the sun was out in full effect. So the sun would beat on us from above and whatever we didn't catch would heat the dark stone and then blast us from below. And with the humidity no sweat could evaporate. Plus the humidy made for hazy views, which while still impressive don't make for the best pictures.

Two of the first things that really hit me while walking the Wall. Wow, imagine the time, resources, and skill it took to build this immense structure in this remote and challenging terrain. Then I would look over on the other side to the heaveliy wooden near sheer cliff. Wow, they actually needed to build a wall through here so that people would not attack through this area? I would think this would be something like Rome building a wall through the Alps because they thought Hannibal was going to take a troop of elephants through them. Yeah maybe it happened, but how many times? And you build a gigantic wall for that one time?
But it was a great hike (even if made more challenging than it really was because of the heat). Beautiful mountains. More friendly people. More people that wanted to take a picture with us. Our first introduction to actual high Chinese prices. These are the tourist prices that we are used to, 2-5 times what you would pay elsewhere. Even our driver told us not to buy anything.

We made it to the end of the restored section (left picture) after the steep climb (previous picture).
Another fun thing here was there is a slide that goes back down to the parking lot. Once you get it going it is really a great ride. We had more time than energy when we got back to the hotel so we mostly stayed in. Got a nice bowl of noodles for dinner and prepared for the next day.