Case study #1: Back in the 1960s, during the height of the Apollo era, an organizer of a space conference asked a college professor named Gerard K. O'Neill to give a presentation on industrial uses of space. In response, O'Neill said it was a silly idea -- that there just weren't any practical industrial uses of space. The conference organizer, undaunted, then asked O'Neill if he could give a presentation on why there weren't any industrial uses for space! This, O'Neill agreed to. And in the course of researching his presentation, O'Neill came to realize that he was wrong; so wrong, in fact, that he ended up writing a book about space colonization (The High Frontier -- ISBN 0-553-11016), and, in 1974, testifying before the US Senate Committee on Aeronautical and Space Sciences about how to establish a sizeable permanent population in space, and becoming so prominent a booster of the notion that permanently habitable orbital structures are commonly referred to as "O'Neill colonies".

Case study #2: While writing Hitchhiker's Guide to the Galaxy, Douglas Adams had a bit of a problem: He needed to send his characters about the Universe in a usefully small amount of time, which of course meant FTL (faster than light) travel. The problem was, the only methods he could think of for achieving FTL were all laughably unlikely. The list of rejected prospects grew longer and longer, and eventually Adams decided that since FTL was so flagrantly improbable, he might as well bite the bullet and exploit exactly that quality. Thus did Adams create the Infinite Improbability Drive which powered the starship Heart of Gold.

Case study #3: When I started work on my first TBP story, I knew that that universe had just a whole lot of "my life turned to shit when I got SCABS" stories, and I didn't want to write yet another one. Thus, I decided that my character's life had already been shit, even before he came down with Martian Flu! And that wasn't the only pre-established pattern I felt it would be more interesting to work against. Most SCABs find that their condition does a number on their economic situation; my boy would actually be better off, in purely financial terms at least, as a result of SCABS. Many SCABs loudly bemoan the sheer injustice of it all; my boy would just sit there and suck it all up in silence, never letting anyone get close enough to see what's behind his "I'm fine, damn it!" façade. In short, I explicitly designed Jubatus to be very much unlike the standard TBP character.

Case study #4: In mathematical proofs, there is a technique called "reductio ad absurdum". You employ this technique when you've got a proposition that you want to prove, but haven't been able to prove it by any other means. How reductio ad absurdum works is simple: You assume your proposition to be false, and then show how that assumption leads to an absurd outcome such as contradiction, or a violation of mathematical rules, or whatever other piece of nonsense.

The common thread here: Instead of just going along with the prevailing trend, someone turned around a full 180° to go exactly the opposite way. Some would call this negative thinking, and to an extent, they're right. But unlike the usual concept of negative thinking, i.e. compulsively nay-saying an idea to death, what I'm talking about here is constructive in nature. You're not going against the grain just to be annoying, but, rather, to reach a goal that you wouldn't otherwise have been able to get at.

This version of negative thinking is basically a specific example of a larger concept, that being: If a problem looks insoluble to you, try examining it from a different angle. You may be surprised to find how often an intractable puzzle becomes much clearer when seen from a different point of view...