So enter the comparative psychologists.

Nicola Clayton didn’t start studying octopus. As a professor at Cambridge, she built her career on the remarkable behavior of the bush jay, a tiny blue-black bird that saves food for later. In 1998, she and her colleagues showed that the birds can remember how long it was since they hid food. They can plan for the future and hide food in places where they have reason to believe they will be hungry later.

Their behavior is more sophisticated than simply learning that food appears when you push a button or see a pattern, which many animals can do. Apart from monkeys and other corvids such as crows, only a few animals studied so far possess the full portfolio of the mental abilities demonstrated by these birds.

But octopuses and other cephalopods can be a fascinating test case. When octopus and squid hunt, they don’t take the same route for two days in a row, marine biologists have observed. Christelle Jozet-Alves, a comparative psychologist, wondered if this meant that they had a memory like that of corvids and were able to relive what had happened to them in the past. In 2013 she published together with Dr. Clayton and a coworker ran a tempting octopus study that suggests they did. Dr. Clayton, Dr. Schnell and her colleagues started asking: Do squids have any sense of the future and the recent past? Can you make decisions about what you think will happen in the future?

Octopuses have long amazed observers with their apparent cunning – in a YouTube clip with more than 2 million views, an octopus scoops up coconut shells and carries them away, perhaps to use them later as a tool. Squids also have large brains and sophisticated behavior. But squids are easier to breed in the laboratory than squids and easier to work than squids, who are often aloof and refuse to bother with an experimenter, said Dr. Fast.

There is of course the Houdini factor too.

“You get little escape artists with octopuses. You come in in the morning and no matter how tightly you close an aquarium, you will find them crawling out, ”she said.