There’s a popular and simple magic trick involving multiplying balls: The magician holds a ball, usually red, between her thumb and index finger. They flick their wrist and suddenly, a second ball appears between their index and middle fingers. They keep on flicking and balls keep on appearing.

The secret is simple: the first “ball” is really an empty hemispherical shell, with the second ball nesting inside it. When the magician flicks their wrist, they roll the second ball out of its shell. With a few flourishes, they can then load the third and fourth balls into the shell, before rolling them out in turn. Audience members automatically assume that the empty shell is a full sphere, because it’s indistinguishable from one when viewed from the front.

But there’s more to the trick than that, says Vebjørn Ekroll, a psychologist at the University of Leuven in Belgium. We deeply, strongly, resolutely perceive the shell as a sphere because our brains create a full representation of the ball. The hypothetical back half that we cannot see feels as real as the front half that we actually can.

That’s why it’s so hard to figure out what’s happening if you don’t already know the explanation. In one 2014 study, when German psychologists repeatedly showed the trick to volunteers, fewer than a third worked out how the multiplying balls multiply. Only four other tricks, out of 34 in total, proved to be more inscrutable.

The illusion, as the best illusions are, is “cognitively impenetrable,” says Ekroll. “Even when you know what’s going on, you still experience it.” Watch that video again; you know that the first ball isn’t a ball, but it sure feels like a ball. And that feeling, Ekroll found, is so strong that it can change our perceptions of our own bodies.

He and his colleagues were playing around with the magic balls when he wondered: What happens when I put my finger in the shell? If he looked at it from above, it would still look like a sphere—but surely, with his own flesh poking into the empty space, he would perceive the shell as a shell? Surely now, the illusion would break.

“It turned out that it doesn’t,” he says. Instead, it felt like his finger had shrunk—the perception of the sphere was so absolute that it overrode Ekroll’s experience of his own body. His mental representation of his own finger had effectively made way for the representation of the illusory ball.

He confirmed this in a forthcoming study by asking 22 volunteers to balance the shell on their middle fingers and, with a knitting needle in their other hands, point to where they felt the tip of their finger was. Not where they knew it to be, but where they felt it was. Sure enough, the recruits consistently pointed to a space below their actual fingertip. And if the shell was wider (implying a bigger sphere), the recruits pointed to an even lower position.

They weren’t just making errors because their fingertips were hidden; if Ekroll swapped the hemispherical shell for a flat disk, the volunteers accurately pointed to their fingertips. Likewise, they were accurate if the shell was transparent, rather than opaque.

“Spectators do not merely entertain the intellectual belief that the semi-spherical shell is a complete ball,” Ekroll wrote. “Rather, their visual system creates an immediate and compelling experience of a complete ball, which effectively closes the door to the actual solution before any intellectual problem solving process even starts.” That’s why it’s so hard to work out how the trick works.

“It’s a good example of how helpful magic tricks can be to answer scientific questions,” says Amory Danek from the University of Chicago in Illinois. “I’ve tried the shrunken-finger illusion myself and it does work.”

“I’m surprised at how simple and yet effective it is,” says Susana Martinez-Conde at State University of New York, who has co-written a book about the neuroscience of magic. “I organize the Illusion of the Year contest, and oftentimes, these illusions rely on knowledge or sophisticated computer graphics. I love it when there’s a new illusion that anybody could have discovered at home. We tend to overlook these things.”

“I think that this particular illusion reveals something interesting about how much or how little sometimes we know about our own bodies,” she adds. “You’d think that after all these years of using our fingers every day, we wouldn’t be susceptible to this kind of manipulation. And yet we are. It dramatically affects our very sense of what our body is.”

There are other tricks like this, including a famous one involving a rubber hand. You ask someone to hide their real hand under a table, you place a rubber hand in front of them, and you stroke both hands in synchrony. Presto—they’ll think that the rubber hand is theirs. Again, the illusion is compelling and cognitively impenetrable—which neuroscientists often confirm by stabbing the rubber hand or smashing it with a hammer, and watching their subjects twitch and sweat.

Inspired by the rubber-hand illusion, Henrik Ehrsson at the Karolinska Institute created several other body-warping tricks, some of which I’ve experienced and written about. One afternoon a few years back, he convinced me that I was having an out-of-body experience, that I had shrunk down to doll size, and that I had a third arm.

Ehrsson’s work, the rubber-hand illusion, and the shrunken-finger illusion all show that our sense of self is surprisingly malleable. We constantly use information from our senses to construct our perception of our bodies, and our feeling of ownership over them. Mess with that information—whether it’s by stroking a rubber hand or balancing a hemispherical shell on a finger—and you can shift that feeling in a powerful way.

But not with everyone. Ehrsson once told me that around one in five people is immune to his illusions, and he suspected that dancers and other people with expert bodily awareness might be harder to dupe. The same goes for the rubber-hand illusion: I once watched a disastrous science-communication event where a professor totally failed to instill the illusion in a volunteer on stage. Likewise, Ekroll says that not everyone experiences the shrunken finger. As a next step, he wants to find out why.

And he wants to study other magic tricks. “People have suggested several times that academic psychologists could learn a lot by studying what magicians do and how magic works,” he says. “But this has only recently transformed into a serious line of research.”