In his book The Black Swan, former derivatives trader Nassim Nicholas Taleb describes "black swans" as events that have three characteristics: rarity, extreme impact, and retrospective predictability. In other words, they're powerful events which are completely unexpected and change the landscape in a deep and profound way.

Black swan events change the everyday world around us -- which makes them unbeatable investments.

Welcome to the fourth quadrant
Events such as the terrorist attacks of Sept. 11 and the rise of the Internet are classic black swans. Ever since their unexpected and unprecedented appearances, these events have changed the way we travel, be it locking cockpit doors or booking tickets on (NASDAQ:PCLN) instead of visiting a travel agent. They've also changed the way we communicate and spawned giant new industries, public and private, devoted to enhancing security in the sky and in cyberspace.

In short, they shook things up.

These black swans occur in a space Taleb calls "the fourth quadrant," where normal statistical models do not apply. Could railroad operators have planned for the rise of the automobile as a popular form of transportation? Could a candle maker's business plan have accounted for the unexpected invention and popularity of the light bulb? Could Blockbuster have predicted the rise of Netflix (NASDAQ:NFLX)?

Of course not. So how can we anticipate world-changing companies?

Black swans in the marketplace
Most of the best investing opportunities of the past few decades began as black swans -- companies or products that radically changed the way we did things. But by definition, black swans are only predictable in hindsight. So how can you identify black swans as they're emerging?

For a company to become the industry leader (think technological innovator Apple (NASDAQ:AAPL) or iconic brand Coca-Cola (NYSE:KO)), it can fight its way to the front of the pack -- or it can write an entirely new set of rules.

Fool co-founder David Gardner calls them Rule Breakers -- and he identified six characteristics of an emerging Rule Breaker:

  • Top dog and first-mover status in an important, emerging industry.
  • A sustainable, competitive advantage.
  • Strong past price appreciation.
  • Good management and smart backing.
  • Strong consumer appeal.
  • Grossly overvalued, according to at least one significant constituent of the financial media.

Want an example? Take robotics, where Intuitive Surgical (NASDAQ:ISRG) has dominated the field of robotic surgery with its da Vinci systems. Meanwhile, iRobot's (NASDAQ:IRBT) aptly named Warriors are helping the U.S. military change warfare by replacing human soldiers with mechanical ones.

Or look at LED lighting, which is expected to make incandescent light bulbs obsolete in their turn -- and companies like Cree (NASDAQ:CREE) are riding that wave. LED lights are more efficient than even compact florescent bulbs, and they have a longer life span. The U.S. government likes them so much they are putting them in the Pentagon.

Long before they become household names, Rule Breakers shake up their own industries -- and focusing a keen eye on small, innovative companies will help you notice black-swan events as they're happening.

He who makes the rules ...
But not every small start-up will become the next industry giant. Not every challenge is well-thought-through; not every innovation will grab the customer. That's why finding the next Rule Breakers requires constantly thinking ahead about the products and services that will shape the next decade and beyond.

That's what we do at Motley Fool Rule Breakers -- and advisor David Gardner has made a career of finding Rule Breakers well before most analysts and their conventional wisdom. If you'd like to see which companies he's interested in now, take a free, 30-day trial of Rule Breakers. You'll see all of his current and past recommendations, as well as his best bets for new money now. Just click here to get started -- there's no obligation to subscribe.

Fool contributor Matt Hoffman owns no shares of any of the companies mentioned. iRobot and Intuitive Surgical are Motley Fool Rule Breakers recommendations. Coca-Cola is an Inside Value choice. Apple and Netflix are Stock Advisor picks. The Motley Fool has a disclosure policy.