I had this thought a few days ago, wrote it down, and today I decided to try to explore it a little more. I made some sprites in Pico-8 and sketched some possible levels. I came to the conclusion the idea is not worth pursuing. I'm sure with enough dedication something neat could come out of it but I have other stuff to work on! so this is why I'm calling this unnamed project Disposable failed game idea.
Here's how it works: you control a log. You can roll it left and right or up and down but you can't turn like that. Your log occupies 2 tiles, and in order to turn you need to stand upright, which can be accomplished by rolling out of a ledge so half the log is on a high level the other half falls to the lower level and thus stands upright. Once upright you can choose which direction you want to fall flat again to start rolling.
This alone turned out to be a bit too shallow. So I started contemplating things like ramps to change your orientation, to slide down etc. This is when it got too complicated for me to keep my interest. But it's a cool idea and I wanted to share it anyway.
I thought about calling this Cool Log, and at the end of each level the log would have shades on it, to show that it is cool and it knows. Or maybe ArcheoLOGist, and you're a log exploring an ancient temple. All I know is the context is very important and detrimental to enjoyment. And you are a log.