hen I was a university student, I had a unique mathematics professor. A formal man, he only came alive when solving differential equations on a blackboard. One day, he taught me a fundamental truth about knowledge by drawing a small circle in chalk.

“Imagine,” he said, “that everything you know is contained within a circle, and everything outside of the circle is unknown. The more you learn, the bigger the circle grows.”

Admittedly, as life lessons go, this one did not look promising.

Then he said, “When the circle grows its circumference does too – like a balloon, it stretches to touch more of the unknown. Learning doesn’t just increase what you know; it shows you more of what you don’t know, and just how much there is to discover.”

Now, if I have any claim to an ethos, it’s that. All elegantly contained in one chalk line drawn by a math professor.

This chalk line, I think, holds universally true. Especially at Christie, where I try and operate right at the edge of our knowledge circle, pushing at the limits of what the world thinks is possible.

If you have ever marveled at an Olympic Games Opening Ceremony, you were watching our AV innovations shine. When you last saw a Hollywood movie at the cinema, chances are you saw it on one of our projectors. And when Expo 2020 opens in Dubai, it will be our kit that lights up the Al Wasl dome. All of this is very corporately pleasing, but hardly the point.

None of that jaw-dropping, eye-pleasing, storytelling spectacle would have been possible if we hadn’t given someone – or, more often, many people – the confidence to step beyond their circle of knowledge and make it so.

Take laser. Everyone had long known that pure laser illumination could revolutionize projection. It made images brighter and pure colors leap from the screen. But nobody thought it practical. Lasers, they said, ran too hot. They were big, they were bulky, they were headed nowhere. Then we gave a small engineering team the freedom to step out of the circle and into the unknown.

Their efforts, with our support as they tried to make the impossible possible, brought the world projectors of unprecedented power and beams of the purest red, green, and blue light.

What surprises me most about those minds is just how generous they are with their knowledge, working on the principle that if someone’s thirsty, you give them water. You don’t ask why.

From artists like film director Ang Lee, I’ve learned that when you share knowledge, you don’t give it away, you multiply its power. Put in hard business terms, artists are world-class at leveraging their greatest asset. They don’t see the point in hoarding ideas the way a miser hoards gold because their work doesn’t benefit anyone until it’s out in the open and reaching an audience. They see that expanding someone else’s circle of knowledge by sharing their own widens everyone’s foundation.

While business, as it ought, prizes property and protects heavily the investment of knowledge, that doesn’t mean there is nothing to learn from the collaborative way artists operate. Most people working in commerce, whatever their job, really want to tell you about what they do. Give them time, listen with respect, and your own knowledge circle will expand exponentially.

Throughout the years, we’ve made some pretty cutting-edge equipment. But it wasn’t until we asked about eye bolts – a $6 fixing that allows riggers to chain and fly machines fast and easy – that our knowledge circle really expanded.

It turns out that making their long days and nights a few hours shorter was as simple as building a screw thread and adding eye bolts. Our circle was rightly focused on building better and brighter, theirs just as importantly on getting the show up. We just had to step outside our circle and into theirs to see a way to serve both.

All those years ago, my professor may have thought he was lecturing in mathematics, but he taught me something far more fundamental. Be generous with your knowledge, accept it willingly from others and, once you have it, share it freely. There’s more than enough for everyone.

As Isaac Newton famously said: “What we know is a drop, what we don’t know is an ocean.”

Let’s share and let’s learn.

Let’s step outside the circle.