The Magnet 23: The Impossible Boxes

Why do three boxes feel lighter than one?


The impossible boxes

In The Magnet 22 I linked to a Mental Floss article showcasing six “aural illusions,” or sounds that trick the ear in the same way optical illusions trick the eye. I recently came across a somatosensory illusion. It involves three small boxes. The boxes are opaque and identical in size and shape. Two of the boxes weigh 30g. But the third box hides a slug of zinc so it weighs 250g.

Researchers at Johns Hopkins University invited 30 people to participate in an experiment with the boxes. They asked 15 subjects to lift the three stacked boxes together and set them down, then lift the 250g box by itself. They asked the other 15 subjects to lift the heavy box first, followed by the stack of boxes. The subjects in both tests reported the same thing: the 250g box felt heavier than the stack of three boxes (which had a total weight of 310g).

From the paper:

Indeed, the experience was so striking that subjects often spontaneously and astoundedly commented on its impossibility to the experimenter, and even requested to lift the objects again after the experiment was over. (This is perhaps why a variant of this phenomenon is known to magicians, who apply an “at the bar” version involving a stack of matchboxes.) Anecdotally, those subjects reported that the illusion persisted even during these repeated lifts, including when subjects placed all three boxes on their palm and then suddenly removed the two lighter boxes—distilling the phenomenon into a single impossible “moment” wherein removing weight caused the sensation of adding weight.

The authors of the paper provided a link to the 3D printer files for the boxes.

Here are other somatosensory illusions, if you’re interested:

  • The rubber hand illusion, “in which a person reacts to a fake hand as if it were her own.”

  • Aristotle’s illusion: “Cross your fingers, then touch a small spherical object such as a dried pea, and it feels like you are touching two peas.” (If you don’t have a dried pea, the tip of your nose will do.)

  • Jelly or velvet: “Get some coarse chicken-cage mesh, preferably mounted in a wooden frame. Then hold the mesh between the palms of your hands. Nothing peculiar so far. Now start rubbing your palms against each other with the wire between them. Remarkably, your palms will feel like jelly or velvet. “

Thanks for reading! The Magnet is written by Mark Frauenfelder and edited by Carla Sinclair.