Picture the biggest thing you have ever seen: a skyscraper, a city, a planet. And then imagine that thing extending forever, without ever stopping. This object would be infinite: endless in space and size, impossible to measure or see as a whole. 

Most things we encounter in the world are finite, meaning they have a beginning and an end, a top and a bottom. They have a size that can be measured. If you continually chop something finite in half, eventually you will reach a unit too small to be divided. An infinite thing, on the other hand, can be chopped forever.

This mind-bending concept is the subject of A Trip to Infinity, a new documentary. It has been met with acclaim. Critic John Serba calls it "the greatest, most significant movie ever made, and also the most inconsequentialUnimportant.".

The meaning of infinity is difficult to pin down. "Is infinity a number, an idea, a place?" asks physicist Delilah Gates. "Probably all of the above."

For centuries, the infinite was thought to exist beyond the physical world. In ChristianityA major world religion based on the teachings of Jesus Christ. , only God is infinite. PhilosophersPeople who ask big questions about the meaning of life and how we should live. saw the infinite as something too big for the human mind to grasp.

Parallel to this, maths has treated infinite as if it were a number. The ancient Greek Zeno of EleaThe founder of the Stoic school of philosophy. tried to show that infinity was physically impossible. He used the example of an arrow. If the world could be infinitely divided, an arrow would have to travel an infinite number of steps. It would never reach its target.¹

In 1655, mathematician John Wallis invented a symbol for infinity, which looks like the number 8 turned on its side.² By the early 18th Century, the idea of infinity was well-known enough that Jonathan SwiftAn Anglo-Irish satirist who wrote Gulliver's Travels. could make fun of it: "Nat'ralists observe, a Flea / Hath smaller Fleas that on him prey, / And these have smaller yet to bite 'em, / And so proceed ad infinitum".

Today, thinkers take the idea of infinity very seriously. Space exploration has revealed a universe that might stretch on forever. And the discovery of subatomic particlesThe minuscule pieces of matter that make up atoms. Scientists have discovered 36 so far. has shown that the world could be divided into smaller units than once imagined.

Yet opinions are divided on whether infinity actually exists. For astrophysicistScientists who try to understand the contents of the universe. Sara Webb, the universe is always growing, and therefore can have no end. 

Others note that we do not know whether this expansion will continue. And, as historian Kevin Orrman-Rossiter points out, we can never know: "a voyage of proof would need to be infinite in order to prove... that space is infinite." A traveller into infinity would never report back.

This idea that we can never truly understand infinity is also contested. The physicist David Deutsch believes that nothing interesting is unknowable to us.

Some, however, set strict limits on human ability. As philosopher Jennifer Nagel puts it: "We've only got a certain life span. We're going to die, and we think pretty slowly... We can't just abstract away from all of those limitations and say everything is going to be knowable."

Yes: Modern science has made huge advances. But there are many fundamental things - the origin of consciousness, the true size of the universe, the reason we exist - that remain far out of reach.

No: Time and time again, humans have learnt things that once seemed out of reach. We have gone into space and seen the atoms that make up the world. Who is to say we cannot keep discovering infinitely?

Or... Humans have limits. But we are a species of makers. We may not be able to explore an infinite world with our own skills. But perhaps, one day, we could create technology that does it for us.

Inconsequential - Unimportant.

Christianity - A major world religion based on the teachings of Jesus Christ.

Philosophers - People who ask big questions about the meaning of life and how we should live.

Zeno of Elea - The founder of the Stoic school of philosophy.

Jonathan Swift - An Anglo-Irish satirist who wrote Gulliver's Travels.

Subatomic particles - The minuscule pieces of matter that make up atoms. Scientists have discovered 36 so far.

Astrophysicist - Scientists who try to understand the contents of the universe.