This month the blockbuster movie Titanic was re-released in 3D. With special glasses, audience-goers are now able to see the ship crash into the iceberg even more vividly than before. In true Hollywood style, the film depicts a massive iceberg looming over the “unsinkable” ship with the crew scrambling to avoid a head-on collision.

We usually think of threats in this way: something big and dangerous that can sneak up and overwhelm us when we aren’t looking. But the real story of the Titanic paints a different picture. It is a story that, while less dramatic, offers relevant lessons for leaders navigating their organizations through icy waters.

You’ve Been Warned

The Titanic received six warnings of ice on the day of the collision. They were all ignored by the wireless operator, who was preoccupied with transmitting passenger messages and by the crew, who were focused on breaking the speed record. So pay attention. The signs are already there if you listen. Some companies, like Borders, Kodak and Polaroid, ignore the signs. Others, like Domino’s Pizza, catch themselves before it is too late.

Size Doesn’t Matter

The iceberg that the Titanic struck was not very big. It didn’t even come up as high as the bridge of the ship. And the hole in the boat was actually quite small — six cuts measuring a little over three square feet.

Our brains are wired to think of threats as coming from something bigger, but it’s often the little things that become our downfall. Clay Christensen’s work on disruptive innovation shows the power of David against Goliath, the mammal over the dinosaur, the startup over the incumbent.

It’s What You Can’t See

The iceberg that struck the Titanic was almost invisible. Continuous melting had given it a clear, mirror-like surface which reflected the water and dark night sky, like black ice on a wintry road. This type of iceberg is called a “blackberg.” It is possible that the crew could have been looking right at the iceberg from a distance and not seen anything unusual.

Look Below the Surface

Only about ten percent of an iceberg’s mass is above water, with the other ninety percent below (hence the phrase “tip of the iceberg.”) With so much mass below the surface, it’s almost impossible to push an iceberg out of the way. Even a ship the size of the Titanic couldn’t push what looked like a small iceberg out of the way.

Keep Moving

When First Officer Murdoch saw the iceberg, he put the engines in reverse and started turning away from the iceberg. It’s a natural reaction to hit the brakes when you see a threat. But this action may have sealed the Titanic’s fate. Ships turn more quickly when they have forward motion. If the captain had maintained the ship’s speed or even accelerated, he might have avoided hitting the iceberg altogether.

So as you think about your business, think what warning signs you might have overlooked. Consider where the icebergs might be that you can’t see, or where the threats might look deceptively small on the surface. And when you do see a threat, beware of hitting the brakes; the best reaction might be to step on the gas.