What Does "Thinking Differently" mean?

Copernicus said, "Dare to think differently", and Apple Computers used "Think Different" as an advertising slogan several years ago. What does that really mean? I don't know what originally formed these ideas, but here are some things I apply to different thinking.

1) Problem Definition - I learned from my math classes that a clear understanding and statement of the problem is one of the most important (and sometimes most difficult) parts of discovering the solution. If you don't know what your target is, you likely won't hit it.

2) Pattern Matching - This has always been an interest of mine, and I try to be aware of patterns in music, writing, finance, business, etc. For a hot time, take a look at some geometric sequences! (ok, this may not flip everyone's switch, but we're talking about thinking differently)

3) Commonalities & Differences - Sometimes the world isn't all neat and predictable, so there isn't a perfect formula for understanding the way things work. Still, there may exist commonalities (or at least similarities) that can help us form a metaphor to think about things (for more insight, read "Borrowing Brilliance..." by David Kord Murray). Differences may be just as helpful.

4) Abstraction - I blame my math teachers for this. I have a lot of respect for people who can find a solution to a problem, or analyze a certain piece of data. But I stand in awe of the few people I've met and read about that can take that problem or data to a generic problem, then solve it for all problems or data. Now that's genius.

5) The Elegance of Simplicity - There is tremendous beauty in boiling things down to what really matters, and getting rid of all the stuff that doesn't. This includes the ability to identify "core" issues, define the problem at its essence, solve it without distraction, and explain the solution so that it may be understood by the general population.

6) Perseverance - Thomas Edison said something like, "Genius is one percent inspiration, and ninety-nine percent perspiration." Its hard work to maintain your focus on a problem over time, especially when you try all the things you know. The people who never give up are the ones who think differently.

What do you think?