Next, the researchers marked the fish that seemed to be catching on. They injected a bit of brown material (or clear, for a control) under the skin of each fish’s throat. Afterward, some of the fish seemed to study the marks in front of the mirror. Then they scraped their throats against rocks or the sandy bottom of their tanks — a common fish behavior for removing irritants, Jordan said. The fish often followed this maneuver by swimming back up to the mirror. Three out of the four fish that made it this far in the study passed the mirror test, the authors concluded.

The researchers spent more than three years trying to get the paper published. Peer review is a largely cloaked process in which experts in a field respond anonymously to papers that have been submitted to journals. But Gallup signed his reviews of the cleaner wrasse paper, which were “violently anti,” Jordan said.

In Albany, Gallup chuckled at the suggestion that the fish had recognized themselves. To him, the demonstrated behavior was too ambiguous. He wrote in one of his reviews that when a wrasse scraped its throat, maybe it was pantomiming an instruction for what the mirrored fish should do — as in “You’ve got some mustard on your chin,” said Jordan, who called this alternate explanation “incredibly far-fetched.”

Reiss also reviewed the paper several times for different publications, she said. She wasn’t convinced that behaviors like swimming upside down showed that fish were testing how the mirror worked. She and Gallup also found it problematic that the brown mark resembled a parasite — to which wrasses instinctively react — unlike the unnatural marks on other animals. “I think for a claim like this, the evidence has to be much stronger,” Reiss said.

In response to the reviewers’ objections, Jordan and his co-authors added more control experiments to their study. Now that the paper has finally been accepted for publication, Jordan thinks the grueling revision period made the study stronger. “And, you know, I didn’t die in the process,” he joked.

Alexandra Horowitz, a psychologist at Barnard College in New York City who studies dog cognition, called the wrasse study “amazing.” She added, “I think it … challenges our presumptive notions about what fish can or cannot experience.”

Jordan wants the world to know how smart fish can be. But, he said, “I am the last to say that fish are as smart as chimpanzees. Or that the cleaner wrasse is equivalent to an 18-month-old baby. It’s not.” Rather, he thinks the main point of his paper has more to do with science than fish: “The mirror test is probably not testing for self-awareness,” he said. The question then is what it is doing, and whether we can do better.

What Is Self-Awareness?

Sometimes it’s easy to tell that an animal really doesn’t understand mirrors. The writer Mary Laura Philpott has frequently been awakened in the wee hours of the morning by a loud knocking on her door in Nashville, Tennessee. When she opens the door, she finds only a small turtle. She nicknamed the prankster reptile Frank. Eventually she came to suspect that Frank might be challenging or attacking the strange turtle he sees in the reflective part of her door — night after night after night.

But just because one individual animal fails a mirror test doesn’t mean every member of its species would do the same. It’s a more meaningful positive test than a negative one. And even when animals do recognize themselves in mirrors, researchers are divided about what that implies.

“Recognition of one’s own reflection would seem to require a rather advanced form of intellect,” Gallup wrote in 1970. “These data would seem to qualify as the first experimental demonstration of a self-concept in a subhuman form.”

Either a species shows self-awareness or it doesn’t, as Gallup describes it — and most don’t. “And that’s prompted a lot of people to spend a lot of time trying to devise ways to salvage the intellectual integrity of their favorite laboratory animals,” he told me.

But Reiss and other researchers think self-awareness is more likely to exist on a continuum. In a 2005 study, the Emory University primatologist Frans de Waal and his co-authors showed that capuchin monkeys make more eye contact with a mirror than they do with a strange monkey behind Plexiglas. This could be a kind of intermediate result between self-awareness and its lack: A capuchin doesn’t seem to understand the reflection is itself, but it also doesn’t treat the reflection as a stranger.

Scientists also have mixed feelings about the phrase “self-awareness,” for which they don’t agree on a definition. Reiss thinks the mirror test shows “one aspect of self-awareness,” as opposed to the whole cognitive package a human has. The biologists Marc Bekoff of the University of Colorado, Boulder, and Paul Sherman of Cornell University have suggested a spectrum of “self-cognizance” that ranges from brainless reflexes to a humanlike understanding of the self.

Jordan likes the idea of a spectrum, and thinks cleaner wrasse would fall at the lower end of self-cognizance. He points out that moving your tail before it gets stepped on, or scraping a parasite off your scales, isn’t the same as sitting and pondering your place in the universe. Others in the field have supported his contention that the mirror test doesn’t test for self-awareness, he said. “I think the community wants a revision and a reevaluation of how we understand what animals know,” Jordan said.

One thing on which most scientists in the field do agree is that there’s a link between recognizing yourself in a mirror and being social. The species that perform well on mirror tests all live in groups. In an intriguing 1971 study by Gallup and others, chimpanzees born in captivity and raised in isolation failed the mirror test. The chimps that passed the test had been born in the wild, in social groups. Gallup thought this finding supported the ideas of the philosopher George Herbert Mead of the University of Chicago, who said our sense of self is shaped by our interactions with others. “[T]here could not be an experience of a self simply by itself,” Mead wrote in 1934.

Gallup sees a clear connection between recognizing yourself in a mirror, understanding something about others’ states of mind, and even empathizing. “Once you can become the object of your own attention, and you can begin to think about yourself, you can use your experience to infer comparable experiences in others,” Gallup said. No species evolved looking in mirrors, but some of us can see ourselves reflected in our companions.

The Mirror as a Window

The sociality of Asian elephants helped researchers to design a better mirror test in 2006. Joshua Plotnik, a comparative psychologist now at Hunter College in New York City, worked on the study with de Waal and Reiss. In an earlier test that elephants failed, the animals had been in an enclosure, looking at a small mirror. For the revised test, the researchers used an eight-foot-by-eight-foot mirror, so the elephants could see their whole bodies at once. They also let the elephants approach the mirror so that they could stand on their back legs to look behind it or kneel to peer beneath it.

They also tested elephants in pairs, which “gave them an opportunity to use their partner as a frame of reference,” Plotnik said. When an elephant saw a friend standing in the mirror next to a stranger, she might be able to deduce that the strange elephant was herself.

This time, one of three elephants passed the test. Plotnik said the researchers have promising results from other elephants that haven’t been published yet.

“You have to really try to take the perspective of the animal that you’re working with,” Plotnik said. For example, elephants like being dirty and might not care about marks on their bodies, unlike grooming animals such as chimpanzees. Gorillas groom, but they hate making direct eye contact with others. This might help explain why they haven’t had the same success in the mirror test as chimps or orangutans.

Plotnik thinks future experiments should take an animal’s particular motivations and perceptions into account. For example, the mirror test is visual, but elephants are more interested in what they smell and hear. “Is it fair if you test an animal that’s not a primarily visual animal and they fail?” Plotnik said. “You could make that argument for dogs.”

Dogs are lousy at recognizing themselves in mirrors. But Horowitz recently designed an “olfactory mirror test” for dogs. She found that dogs spent longer sniffing samples of their own urine when it had an extra scent “mark” added to it.

“It’s challenging for us as visual creatures to imagine ourselves into the sensory worlds of nonvisual animals,” Horowitz said. But we have to do it, she thinks, if we want to understand how their minds work.

Reiss, who calls Horowitz a friend, doesn’t think the olfactory mirror study proves dogs can recognize themselves. But she thinks the experiment is an interesting jumping-off point. “How else can we [design] tests to get glimpses into what animals know about themselves?” she said.

As empathetic as Homo sapiens is, we struggle to place ourselves in the viewpoints of other species. Yet this kind of understanding could help us not just to grasp our own place in the world but to protect the world. For example, Plotnik said, a lack of habitat for Asian elephants is driving conflict between the endangered species and humans. “I think a lot of what’s missing from the debate around how to solve this conflict is the elephant’s perspective,” he said. The kind of insight we get from putting pachyderms in front of mirrors might be a helpful window into their minds.

Several mirrors decorate the walls of Gallup’s office, partially hidden behind the towers of papers. It’s just a coincidence, he told me — the mirrors were there when he moved in. He got up from his chair to show me another coincidence born of pareidolia, our mind’s inclination to look for faces. In the black wood grain of his office door, a student had once pointed out the barely discernible face of a gorilla. Gordon traced it for me: an eye, another eye, two nostrils. He directed me to stand in front of the door and move back and forth until I saw it.

Suddenly the light caught the grain in just the right way and the gorilla’s giant face emerged. It stared back at me directly, as a real gorilla never would, like a glimpse straight into the unknowable mind of an animal. “I do see it!” I said. Gallup laughed delightedly. “Isn’t it amazing?” he asked. Then it was gone.