Earlier this year in an email to staff, Elon Musk referred several times to third-party contractors at Tesla as ‘barnacles’, ending his email to the company: “Time to scrub off the barnacles.”

Musk was clearly using the metaphor of Tesla as a ship to describe how everyone on board was pulling together in the same direction, on a voyage of discovery. But some employees saw it as an attack.

“When the big alpha dog of the factory uses that word to describe people, it allows other people in the factory to start thinking about people like that and acting that way,” a Tesla employee who had originally been engaged through a contracted staffing agency, told The Guardian. “When Elon calls lower-paid workers barnacles, then you have managers saying, ‘Get out of here barnacle’… I’ve heard that word more in the last week than in the rest of my life.”

What’s in a word? Even though Musk was speaking metaphorically, he’s already proved himself a visionary leader whose voice is powerful. The symbols he employs create an impact that goes right down to the factory floor. And not always necessarily in the way he intends.

In The Shed Method, Sara Milne Rowe tells the story of a CEO who put up a picture of a big red button in her office. It represented the emergency stop that would halt the factory line when something went wrong. Symbolically, it expressed the principle that when a failure is discovered, or a flaw detected, leaders and their teams needed to pause to find out what had happened and make changes to remedy it.

Symbols play a vital part in leadership. If this sounds unlikely to you, then pause for a moment and consider the role of the leader themselves. What does a leader actually do?

At a simple level, leaders act through other people. I would go further and argue that leading is specifically about driving innovation that promotes change, which is to say finding and developing new processes, behaviours and products to continually drive an edge for the organisation. In that case, leadership is about getting your team to be successful at running tests. It’s about making it possible, acceptable and even desirable to fail and return with insights.

Leaders don’t primarily derive the important insights themselves. They have to encourage others to do that. They harness the power of a diverse team that brings with it a range of perspectives, experience and expertise, and bring them all together under the banner of a unifying purpose.

While acknowledging that Apple does not have as much diversity throughout its company as it wants, CEO Tim Cook told Fast Company earlier this year: “We’re all very different. You could walk down this aisle and talk to ten people, and they’d be totally different, but we all have the same common purpose. That’s the thing that joins us all together.”

Purpose is the pursuit of something which isn’t there yet. Until it is discovered, no one even knows what ‘it’ looks like. It’s an idea, which until it is realised exists entirely as a symbol. Powerful symbols can join together vast organisations and create the space for different perspectives to play in.

The New York Stock Exchange is a new client of ours and can furnish a perfect example. The ringing of the bell is one of the most recognisable symbols in the world. When it sounds in the morning it signals that the world is coming in to commence trading. At the end of trading, the bell issues a call that all traders are required to respect.

The bell is a symbol of opportunity, fairness and good order. Many find it powerfully inspiring. For others it’s a symbol of capitalism, which is more divisive. This is a prime example of where symbols can invoke strongly contrasting images for different people.

Although the NYSE bell is strongly associated with tradition, symbols can also be a powerful tool of innovation. When our partners IDEO wanted to change their staff’s negative feelings about visiting the IT help desk with a problem, they transformed it into a daytime café which becomes a whisky bar at night. It’s a way of reframing problems as opportunities to interact across the company.

The symbolic language of a company is often deeply personal. It’s also incredibly important. When Potential Squared went through a de-merger in 2007, we’d just had our highest ever turnover. But I no longer believed that we were practising what we preached. There was a disconnect between the language of purpose we shared and what we separately meant by it, that ultimately led to the realisation that my partner and I had come to want different things.

When your house is not stable you have to look at the foundations. Addressing this created extra work in the short term, but we’ve got a firmer base now and have ultimately come out stronger than ever.

In the office we now often talk about ‘squirrel moments’, referring to the Pixar film Up. These are the distractions that can cause us to lose focus, they’re the tempting tangents or what Michael Bungay Stanier calls the ‘bright shiny objects’. Being able to call a squirrel moment with each other helps bring us back to the purpose behind what we’re doing, testing and learning from.

All leaders resort to symbolism to define the purpose that brings their people together and drives them out alone to test and fail. As Tesla found, an ill-chosen metaphor can have unintended and destructive consequences. But symbols are the essence of storytelling, which is the leader’s power to push others out to go out and be more wrong. The picture you paint as a leader can build the ship and set the course that people want to join you on.