When Inky the octopus escaped from an aquarium in New Zealand, he left a trail of suction-cup prints. (NATIONAL AQUARIUM OF NEW ZEALAND VIA ASSOCIATED PRESS)

To turn off a light, you could use the switch. Or you could squirt a jet of water at a bulb until you short-circuit the power supply. That latter technique is what octopuses have done in at least two aquariums, and it’s a sign that they’re smarter — and much more rascally — than most of us realize.

Peter Godfrey-Smith offers a tour of “The Mind of an Octopus” in the January issue of Scientific American Mind. It’s an essay adapted from his book “Other Minds: The Octopus, the Sea and the Deep Origins of Consciousness.”

He explains that the nervous system of the octopus evolved entirely differently from the human variety. While an octopus has concentrated neurons in a brain that provides some oversight, most of its neurons are in its arms. These limbs can touch, smell and taste independently. An arm that has been surgically removed can still reach and grasp.

“They are probably the closest we will come to meeting an intelligent alien,” Godfrey-Smith writes.

But sharing a planet doesn’t make them any less baffling. Godfrey-Smith offers the example of the fact that octopuses seem to recognize individual humans. At a lab in New Zealand, for instance, one octopus singled out a staff member for special treatment, dousing her with water whenever she passed behind the tank. Studies have confirmed that octopuses can tell people apart, even those who are wearing identical uniforms.

As Godfrey-Smith points out, “This ability makes sense if an animal is social or monogamous, but octopuses are not monogamous, have haphazard sex lives and do not seem to be very social.”

In several other ways, octopuses can seem quite human. He highlights research showing that some will “play” with objects, even after determining that they’re not food. They exhibit short- and long-term memory. Also, Godfrey-Smith writes, “they seem to have something like sleep.”

And when they’re in captivity, they try to escape. They’re clever about it, Godfrey-Smith explains, noting that they’re “unerringly able to pick the one moment you are not watching them.” If that fails, they have other ideas — like that lightbulb squirting trick. It got so expensive at one lab that the octopus responsible got released back to the wild.