We're all searching for winning stocks. The hard part is finding them.

Some buy stocks that are on a roll, thinking they're hot. Others buy stocks that are out of favor, expecting they'll come back. Many rely on "tips" from friends, pundits, you name it. But how many investors truly have a method of investing (you could also call it a philosophy) that they are confident about? One that promises to deliver above-average returns over the long haul?

All the great investors approached the market with a particular point of view that was the bedrock for how they selected stocks. And while we can learn much from them, there are also plenty of nuggets of insight from the greatest thinkers throughout history to guide us. Today, let's imagine how Copernicus, whose theories forever changed how we view our place in the universe, might approach the stock market.

It's the sun, stupid!
From the second century A.D. onward, all learned people believed, as Ptolemy had said, that the sun -- and everything else in the universe -- revolved around the Earth. The Christian church incorporated this idea into theology, because it fit with the religious view that God created the world to be at the center of everything, and made man in his own image to be the master of the world.

In the 16th century, Nicolaus Copernicus exploded this doctrine by observing that the motions of the planets could simply not be explained by an Earth-centric view. But if you put the sun in the center of the solar system, plotting the movements of heavenly bodies became a piece of cake.

Not winning popularity contests
You can imagine how unpopular this idea was in religious circles. It questioned the authority of the church, and it flatly contradicted the Bible (Psalm 93 says "Thou hast fixed the Earth immovable and firm"). It made no difference that Copernicus was himself a member of the clergy, or that he dedicated his thesis to Pope Paul III. If people were free to question fundamental Christian doctrine, all the authority of the church could come crashing down.

This changed everything
Unfortunately, Copernicus died the year his great work On the Revolutions of the Heavenly Spheres was published. But after Copernicus, our view of the universe, and our place in it, changed forever. His work was the beginning of modern science, leading ultimately to Newton and Einstein. But his greatest influence was in philosophy, not science. We could no longer think of ourselves as the center of the universe, only as inhabitants of one of many planets. This has been a central force in the development of Western society ever since.

What would Copernicus buy?
It seems like a crass question to ask about one of the most revolutionary thinkers of all time, but since you've already invested a few minutes of your precious time in reading this far, hang with me for a few more paragraphs.

I think of Copernicus as the ultimate "Rule Breaker." He was risking his livelihood, and potentially his life, by challenging the established authorities of the day. His investment philosophy would be the same. He would look for innovators who aren't just seeking a better mousetrap, but who are trying to change everything.

In hindsight, it's easy to identify successful rule breakers. Wal-Mart (NYSE:WMT) proved the enormous power of everyday low prices in a one-stop shopping environment. Starbucks (NASDAQ:SBUX) showed the coffee shop wasn't dead, just waiting for someone to make it relevant for the modern world. Amazon (NASDAQ:AMZN) has largely wiped out traditional bookstores with an assortment that can't be matched in a bricks-and-mortar environment, and it is remarkably easy to shop.

The hard part is identifying rule-breaking ideas in advance, and having the courage and conviction to jump in before the rest of the herd. Below is a sampling of the kind of companies I think would be attractive to Copernicus.

Apple (NASDAQ:AAPL) is on its way to turning the cellular communications world upside down. Not only is the iPhone expected to be a world-class example of product design, but the company has also fundamentally challenged how the cellular world operates by insisting carriers adapt to design, rather than the other way around.

Intuitive Surgical (NASDAQ:ISRG) is pioneering minimally invasive surgical robotics. The company's Da Vinci Surgical System enables doctors to perform complex procedures like open-heart surgery through tiny incisions. These capabilities were little more than a dream just 10 years ago.

Garmin (NASDAQ:GRMN) has been a leading force in making GPS technology accessible virtually anywhere. Copernicus would have loved this one. Whether you're in a car, boat, motorcycle, or anything else that moves, you can know your precise location on the planet -- and be told how to easily get to another location. The company even has a GPS device you can attach to your dog, updating Rover's position every five seconds and telling you whether he's running or sitting.

What is your investment philosophy?
My point is not that you should buy these companies today, or even that rule breakers should be a large part of your stock portfolio. They are not for the faint of heart. But companies that follow the path of Copernicus, seeking to change the world, offer the potential to deliver huge rewards.

Most people today don't have the time to identify these companies, or do the diligent research to figure out if they're truly onto the next great idea -- or just the next pet rock. If your days are as hectic as mine, consider jump-starting your research with the Motley Fool Rule Breakers service. Let a team of experts cull through hundreds of stocks for you. Then you can put on your Copernicus hat and decide which ones suit your investment philosophy best. You can even get a free trial.

Feel free to email me with stock ideas Copernicus would think are heavenly. And be on the lookout next week for investment advice from Plato.

For more on the companies shown above, check out:

Wal-Mart is an Inside Value recommendation. Starbucks, Amazon.com, and Garmin are Stock Advisor selections. Intuitive Surgical is a Rule Breakers pick.

Motley Fool contributor Timothy M. Otte surveys the retail scene from Dallas, where he welcomes comments on his articles. He owns shares of Starbucks and Wal-Mart, but none of the other companies mentioned in this article. The Fool's disclosure policy is breaking rules and taking names.