We have a tendency to get lost in our own thoughts, and end up staring off into nothing and nowhere. One of the problems with this is if another person happens to be in front of us while we are staring off into N & N. They sometimes think we are staring rudely at them, and can get angry, especially as it can take us a minute or two to come back to Earth when they confront us about staring at them. Or we won't be staring towards anyone, but someone will see us staring and want to know what we are looking at. Again, it takes us a while to return to Earth to answer their question as to what we are staring at. We don't often have a good answer, so this causes difficulties. Still other times we may be staring off into N & N while walking, which can lead us into blundering into things or people, who may get annoyed about being blundered into.
So, the Aspie stare is not really a good thing for us. If you come up with a cure for it, please post it here at WP, as I and many others here would like to have it. 
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If a man does not keep pace with his companions, perhaps it is because he hears a different drummer.
Let him step to the music which he hears, however measured, or far away.--Henry David Thoreau