One of my biggest pet peeves is when a pessimist says, "I'm not a pessimist. I'm a realist."

Truthfully, most of us think we're "realists." We see the world the way we see it. But how we actually behave is a different matter, and reveals the truth about our outlook. A "realist" who complains about how the country will be worse under President X is really a pessimist. A "realist" who thinks that because she's won three hands in a row means she's more likely to win the next hand is optimistic, but in a very bad way.

Optimism: hopefulness and confidence about the future or the successful outcome of something.

Pessimism: a tendency to see the worst aspect of things or believe that the worst will happen; a lack of hope or confidence in the future.

Generally, pessimism is seen as a bad thing. It prevents us from going after our dreams. Yet, smart investors rely on pessimism to hedge bets and not lose money. And though glass-half-full optimism is typically praised by society and touted by successful entrepreneurs, Bernie Madoff went to prison because of his faith in his ability to beat the financial system without getting caught.

After spending the last few years studying and interviewing unconventional successes and the factors that lead to faster-than-usual progress (and even writing a book about it), I've found that something that's commonly conflated with pessimism actually makes a crucial difference between moderately successful people and incredibly successful people. This trait is a key ingredient in the formula that leads to breakthrough innovation, and goes often unrecognized.

Fact is, Optimism vs. Pessimism—one's measure of faith in the future—is an incomplete yardstick for future success. But when we add second dimension to that yardstick, we reveal a combination that makes optimism much more powerful. That dimension is credulity.

The differences between Optimism and Credulity, Skepticism and Pessimism, are subtle. But they're crucial. On their face, credulity seems to be a marker of good faith, a noble value, and skepticism is thought of as grouchy or stubborn. However, here's how the dictionary defines them:

Credulous: having or showing too great a readiness to believe things.

Skeptical: not easily convinced; having doubts or reservations.

When charted by these two dimensions, it's clear that some measure of success and failure can be found in every category:

A compulsive gambler, is both optimistic and credulous, believing she can and will win. And yet, entrepreneurs are often both optimistic and credulous.

Someone with a persecution complex is both skeptical and pessimistic, believing people have ill intentions and things won't get better. And yet, some hoarders and hermits leave their kin valuable property in their wills.

A conspiracy nut is perhaps worst of all: he is both eager to believe and pessimistic about the future. And yet conspiracy websites make money from advertisements. (Not to mention, some investors make—or avoid losing—lots of money using this attitude.)

Though people can find success with any of these combinations, the most counter-intuitive quadrant is the one where the most breakthrough success can be found: Optimistic, but Skeptical. This is where the innovators reside, where inventors who dare to doubt the status quo ask the questions that need to be asked in order for the world to change. They need a healthy amount of optimism to believe that the world can change for the better, and that drives them to make transformative things happen:

*(Note: I don't intend to downplay the hardship that is clinical depression, re: Quadrant 3. Depression comes with, by definition, an inability to see a better future. You're skeptical of the value of basic things in life including life itself, and that's an incredibly difficult obstacle.)

As you can see, credulous optimists can be quite successful, and do a lot of good. But there's something special about optimists' skeptical counterparts.

While credulous optimists rely on good winds to push their sails (and often find them), skeptical optimists ask questions like, "Do we need sails?"

Once you recognize the trait, it's easy to see why the world's great change-makers fit in this category, and why skeptical optimism is under-appreciated. Steve Jobs was one of the world's greatest optimists, and that's what people remember him for. But he was also incredibly demanding and skeptical. He was constantly unsatisfied, consistently pushing back against what was shown him or what was conventional. He continually said, "That's not good enough."

Jobs was not easily convinced. But he believed in an incredible future. And that combination helped him unlock it.

Harriet Tubman, one of my favorite historical characters, was clearly an optimist when she had many reasons not to be. She was born a slave, lived a hard life, suffered a head injury that caused her seizures; her husband remarried another woman and declined to flee north with her. And yet, after she escaped from her captors, Tubman ventured back into slave territory to rescue people. She clearly had faith in a better future for her and them, and that's what people remember.

But Tubman wasn't credulous. She was extremely careful, carried a pistol with her (and had occasion to pull it out). She was wary of circumstances and people's loyalty and intentions until proven otherwise—and that allowed her to rescue dozens of people from slavery and inspire millions more.

The skeptical optimist believes things can be better, but doubts conventional wisdom. Sure, madmen also fall under this definition. But as I've written before, crazy is one of genius's main ingredients.

For those of us who have faith in a better future, personally or professionally, cultivating a skeptical eye can transform how we operate—for the better. For those that lack confidence, let's harness that doubt into healthy solutions and big ideas.

It doesn't matter if the glass is half full or half empty if you think you can make a better glass.

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If you liked this post, check out my new book, Smartcuts: How Hackers, Innovators, and Icons Accelerate Success!

Shane Snow is Chief Creative Officer of Contently. He writes about media and technology for Wired, Fast Company, Ad Age, and more. Subscribe to more stories at http://eepurl.com/yJaEP