Ender’s Game is about a misunderstanding.

I know, I know. The story is about a terrible war and child soldiers and morality and all that. But at the core of the movie, which opens this weekend, and the book it’s based on is the failure to understand an alien species. Not to be too spoilery, but it is this basic confusion that fuels the conflict between humans and the alien civilization known as the Formics. And this inability to comprehend another intelligent species might be closer to the truth than is generally thought.

In most popular works of science fiction, communicating with extraterrestrials is one of the easiest things ever. There is some perfect translator technology, an excellent grasp of alien languages, or some hilarious coincidence that allows humans to talk to other intelligent species in the universe. This makes sense. It would be a pretty boring plot line if aliens came down to Earth, went “Blorg krazap” and then we spent 500 years trying to decipher that.

But a lot of the earliest scientific thinking on communicating with aliens, much of it from researchers working with the Search for Extraterrestrial Intelligence (SETI), has also thought it would be relatively trivial. They beam us some prime numbers, we respond, and bam, you’ve got a direct link.

“For a long time in the SETI community, there was an assumption that science and math are naturally universal and we’d use them as some sort of cosmic Rosetta Stone,” said psychologist Douglas Vakoch, who works on interstellar message composition at SETI. “But over the last 10 or 15 years, there’s been an increasing awareness of how challenging it will be to communicate.”

It’s typically been folks in the hard sciences – physicists, mathematicians, and chemists – who think that we would use something like basic math as the decryption key for an alien language. But over the decades other researchers, particularly anthropologists, linguists, and cognitive scientists, have weighed in, pointing out the ways that communication with minds unlike our own would actually be very difficult if not completely impossible.

After all, we’re talking about alien intelligence here. Think about how complicated our brains are. Figuring out how the mind of another species works is probably going to present problems on par with many other things we barely understand: dark matter, the origin of life, or why the stock market behaves the way it does.

Let’s start with some history. In November 1961, a group of 11 scientists and engineers got together in Green Bank, West Virginia to talk about creatures from another world. This conference, one of the foundations for what would eventually become SETI, yielded a lot of landmark results. It was the first place where astronomer Frank Drake presented his Drake equation, which estimates the number of intelligent extraterrestrials we might detect in our galaxy. And two of the attendees, physicists Giuseppe Cocconi and Philip Morrison, had written a paper on interstellar communication in Nature a couple years earlier concluding that an ideal signal would contain “a sequence of small prime numbers of pulses, or simple arithmetical sums.”

On some level, this makes a lot of sense. There’s only one universe and we would presumably make the same observations of reality as another intelligent species. On the other hand, the universe is also vast and there are essentially an infinite number of different types of observations you could make about it.

In a 1998 paper, Vakoch writes about a Russian astronomer, B. I. Panovkin, who said ”it was not valid to assume that humans and extraterrestrials could communicate with one another just because they have in common certain real physical objects… [Panovkin] believed that most civilizations would have sufficiently different histories of contact with the same ‘real objects,’ therefore, only a small percentage of extraterrestrials would be similar enough to humans to allow communication.”

A lot of this comes down to what you are using to view reality with; that is, your senses. Many depictions of aliens presume that they would be similar to us: eyes, ears, two arms, two legs, etc. But that’s not necessarily going to be true. If you restarted evolution on Earth, there’s no guarantee that anything like us would appear again.

A very interesting 1974 paper by the philosopher Thomas Nagel asks us to imagine what it is like to be a bat. OK, simple enough. You can fly around, use echolocations to catch prey, and sleep upside-down. But that’s just what you know about bats. You can imagine what it would be like for you to be a bat, but you still don’t know what it’s really like to be a bat.

“To be another form of animal life is impossible,” said anthropologist John Traphagan of the University of Texas at Austin, speaking at SETI in 2009. “What goes on in their heads is very different than what goes on in ours.”

To take something basic, a shiny object to a bat is something that reflects sound very well, not light. A bat’s model of the world involves planning ahead for where their flying prey is in three dimensions, not chasing down an animal on legs in two dimensions. Even if you learned everything you could about how bats behave and observe reality, you’d still be missing that key thing: what it is like to actually view reality from their perspective.

So what does this have to do with math? Well, it’s entirely possible that the mathematics humans developed happens to be particularly attuned to the types of things we observe in the world. As Vakoch points out, we have created many different types of mathematics over our history, such as Euclidian geometry or non-Euclidian geometry, that start from different basic assumptions.

Now try to explain our math to an intelligent creature that is very different from us. Vakoch asks us to imagine a cloudy and dark alien world, one where eyesight is not very useful. Perhaps the environment is naturally very noisy, so hearing is also out of play. Some intelligent species there uses smell as its dominant sense. Now explain the concept of a circle using smell alone. What does pi smell like? (And I’m not talking about cherry or apple here).

“Even time doesn’t operate exactly the same,” said Vakoch. “If you walk into a packed elevator, and there’s a strong perfume smell, did that person just get on or just get off?”

There are plenty of other different sensory modalities that aliens could use. Bees have vision but they can see polarized light, which tells them orientation, so a flower at noon looks different than a flower at 3 p.m. Dolphins, like bats, bounce sound waves off objects to figure out where they are. Electric eels and some other fish use electrical fields to “see” in murky water.

What this comes down to is the idea that mathematics ultimately derives from what we see and experience in the world. As cognitive scientists have pointed out in the last few decades, all language is rooted in metaphor, which allows us to take concrete things and create symbolic ideas. Metaphors are so entrenched in our thinking, it’s often hard to notice that they’re there.

Don’t believe me? Well, I’ve used dozens of metaphors in this piece, some obvious, some not. In the previous paragraph, I wrote language is “rooted” in metaphor. But remember that it's plants that grow roots into in the ground, not abstract concepts into other abstract concepts. As linguist George Lakoff and philosopher Mark Johnson point out in the 1980 book “Metaphors We Live By,” we often use conceptual metaphors to map one notion onto another. So a metaphor like “argument is war” translates to sentences like “You are attacking my position,” or “You haven’t properly defended your point.” (For further examples of how this metaphor plays out, read the comments below.)

And if math is a language – a highly abstract and specialized one at that – then it too is metaphorical. More recently, Lakoff teamed up with cognitive scientist Rafael Nunez to write “Where Mathematics Comes From,” which argues that we take basic ideas like counting and adding one plus one and derive more abstract concepts like the square root of three or infinity.

So perhaps mathematical concepts aren’t the best place to start communicating with alien intelligence. Is there some other means we could use? When Carl Sagan designed the plaques for the Pioneer 10 and 11 probes, which are speeding away from the sun and may one day land in non-human hands, he said they are “written in the only language we share with the recipients: science.”

But humans gathered the scientific knowledge that we have over the course of a particular history. Had we started with different senses or with different ideas, perhaps we could construct our scientific concepts very differently. For example, the youngest child in a species of intelligent electric eels would intuitively grasp everything about electromagnetism that took physicists the better part of the 19th century to understand. What would our science look like if that had been our starting point?

Science fiction has grappled with many of these ideas. The insect-like social structure of the Formics in Ender’s Game is what leads to their war with us. Other writers, like Stanislaw Lem have explored the idea of aliens that might be completely unintelligible, such as the sentient and bizarre ocean in the novel “Solaris.” And scientists have long picked apart the idea of simply using science or math for SETI messages. In 1963, the linguist Russel F. W. Smith wrote that “we can no more assume that extraterrestrial beings, however intelligent, will share mathematics with us than we can assume they will share English with us.”

So that’s it? There’s no way to communicate with ET? Vakoch, whose job it is to think about these things, doesn’t think so.

“I think we need to look head on at the tremendous complexities, then look for as many different possible starting points as we can,” he said.

Some researchers think the best place to learn about communicating with other intelligence is in our own backyard, trying to figure out the best way to talk to dolphins. That could teach us about what might or might not work. And if we are ever able to establish contact with aliens, perhaps we could assume that they can do something as basic as counting or know the chemical weight of different elements. Really, we should just try as many different things as possible.

If the SETI scenario ever happens, and we get a message via radio telescopes, that might at least tell us something about the senders. Presumably, that they know how to build radio telescopes. And possibly, from that, that they know basic math. Or that they are social creatures, because constructing such technology might require a group effort.

But it still won’t be easy. Communicating in this way will be taking place over trillions of miles with decades of time delay. And we still won’t know exactly how to say what we want to say.

“The challenge will always be formatting the information that we send,” said Vakoch. “What seems like an obvious format to us may not be to another civilization.” (Also, asking for clarification in this case will be nearly impossible.)

Vakoch thinks our best bet would be to make sure that the way we transmit also contains information. For instance, if we were trying to tell them that we knew about hydrogen, perhaps we could send it at frequencies of the emission spectrum of hydrogen.

“I think that’s the most fundamental thing we need to communicate at all,” said Vakoch. “To let them know we are talking about numbers, or chemistry, or perhaps sending something they might recognize as being music.”