'Arrival', AI and Alien Math: Q&A with Stephen Wolfram

"Arrival" movie poster
"Arrival" (November 2016) explores how humanity would discern aliens' purpose on Earth. (Image credit: Arrival Movie via Facebook)

In the new film "Arrival," based on Ted Chiang's novella "Story of Your Life," alien visitors appear all around Earth and humankind scrambles to understand their purpose in visiting.

The movie's creators initially approached the computation company Wolfram Research — creator of the math programming language Mathematica, the online problem-solver Wolfram Alpha and more — to produce some charts for use in the movie. Instead, they wound up with a consultant: company founder and CEO Stephen Wolfram, whose ideas about interstellar travel, alien communication and the progress of science informed the entire movie (even if not much made it onscreen). His son, Christopher, generated visualizations for them to use.

Wolfram explained many of the ideas he came up with, and his experience creating "scientific set dressing," on his blog. As he told Space.com, "Who's to know? Maybe something that I invented for science fiction will turn into some real physics." [8 Modern Astronomy Mysteries Scientists Still Can't Explain]

Space.com talked with Wolfram about the way science fits into movies, how aliens are like artificial intelligences and whether math is invented or discovered — and what that would mean for alien mathematics and alien thought.

Space.com: How were you approached to work on the project?

Stephen Wolfram: Because a lot of scientists use our software systems and we produce a lot of interesting graphics, we have a pretty regular stream of requests from moviemakers of various kinds saying, "Can we show this graphic in our movie." This one was kind of amusing, because it was like — we're about to start shooting this fairly big-budget movie, and we need these screens that should look realistic and can you help us do this? We're starting to shoot in two weeks.

The only way one can do that is to say "show us the script," because otherwise you don't know what on Earth you're trying to dress [the set] for. I don't think the people who approached us for the movie were particularly expecting that I was going to look at them. It's just that in a company like ours, if the request is sufficiently bizarre it eventually winds up at me.

Space.com: What parts of the science were already there before you joined on?

Wolfram: There are three levels that one could take the science at. One is the "what the aliens are really doing" type thing, which is future science we don't know yet, at the other end there's the high-school level physics, and in the middle is the leading edge of what physics might have to say about it if a great big black spaceship showed up in your backyard today. I was trying to channel the last of those things, what the high end of physics today would say about these, and they had ended up quite a lot with what the high school physics version would be, which didn't seem like such a good fit.

They hadn't really thought about it. Movies are made or broken by the personal stories, and the science is mostly just dressing. It's fun for science-types to see the science as right or wrong. There's some movies where the science is close enough to what we have that what you can do in the movie really makes a statement about where science can go today. This movie, the science is far enough away from what we have today that it doesn't point us in any particular direction. I had fun figuring out a few things I hadn't figured out about interstellar space travel, and so on, but this movie is much more about alien communication, which happens to be a topic that I've thought a lot about, than it is about some space travel.

Space.com: What are your thoughts on the challenge of communication?

Wolfram: I think that the basic notion of "what do we mean by intelligence" is — it's very hard to have an abstract definition of intelligence that goes beyond just saying it does sophisticated computation. There's an awful lot of stuff that does sophisticated computation, my favorite example being the weather — which many people would say has a mind of its own, so to speak.

In modern times, there's a lovely parallel between extraterrestrial communication and AI [Artificial Intelligence] communication. They're both cases where we're dealing with an intelligence that doesn't have the same historical lineage that ours does.

You've got a neural net and it's learned to recognize 10,000 kinds of things in the world. Cats and dogs and telephones and chairs and who knows what else. And you look inside the neural nets and it's made all kinds of distinctions about how to describe the world [which] we can think of like descriptive words for aspects of those objects. But they're not words that exist in our historically derived language.

In the "Arrival" movie, the fact that the question of greatest interest is "what is your purpose here" — that has a fascinating resonance with probably what is in many ways what is one of the most important questions for AI, which is, you built an AI, what is it supposed to do, what is its purpose supposed to be. … Among the purposes we don't want is "take over the world and get rid of the humans" type thing. But there's a question of how do you get to the point where you can represent purpose in this kind of way that we humans think about purpose. [SETI: All About the Search for Extraterrestrial Intelligence (Infographic)]

An image analysis of the aliens' writing in "Arrival," as generated by Wolfram Research (Image credit: Wolfram Research)

Space.com: Did you come to any conclusion about the best way to do that?

Wolfram: One thing I thought about for the "Arrival" movie was what do you use to communicate? Do you use math-like stuff or do you use more computation/programming language type stuff? I think the computation/programming language type stuff is actually better than the math-type stuff, but people don't know the words for that so it's not very useful for dialogue in the movie.

[An interesting question] about math and aliens is how much of math is invented by humans as a specific historical accident and how much of it is really just out there and merely discovered by humans. And that's an important question if you're thinking about "Did the aliens make the same math we made?" I think that an awful lot of math is very much in the invented by humans [category].

Space.com: What makes you think that?

Wolfram: The first fact familiar to all kids is that math is kind of hard. It could be the case that once you set up the axioms of math, every question that could be asked would then be easy to answer. That is true for certain kinds of axiomatic systems; it doesn't happen to be true for mathematics. In other words, the fact that there are hard questions in mathematics is the first interesting metafact about mathematics. And as we know from Gödel's [Incompleteness] Theorem, there are in a sense infinitely hard questions in mathematics.

So one of the questions is, how come math is doable but hard, as opposed to being essentially infinitely hard and just full of undecidable questions. I think the answer to that is because human mathematicians have carefully walked along those little pieces of land in this ocean of undecidable, infinitely hard math. Did they walk along the unique such paths? Or did they walk along paths that were just the ones that happened to be historically explored? You could ask the same thing about biological evolution. Are the organisms that exist today the inexorable organisms that have to exist after 2.5 billion years on a planet with this chemistry? Or are they the organisms that are simply the result of a series of historical accidents. The question in both cases of how much historical accident, how much inexorable consequences of the situation.

My guess, for math — I've gradually changed my views, a little bit, about this. I'm softening a little bit in my point of view. I had believed that it was really, deeply historical accident, but I think some aspects, I'm becoming a little bit convinced might be slightly more inexorable than I had imagined.

A still from the 2016 sci-fi film "Arrival.” In the movie, 12 alien spaceships land on Earth in different locations around the globe. (Image credit: Paramount Pictures)

Space.com: So some aspects of mathematics might be common for aliens and humans, but a lot wouldn't overlap?

Wolfram: [Take] binary, base 2 numbers. The I Ching, from ancient China, kind of uses those — and there are places where they'd been kind of invented a long time ago, but really nobody cared until modern times, as computers and the whole wave of technology that makes good use of binary numbers. Would the aliens care about binary numbers? Well, if you'd gone back 500 years in human mathematical history and you'd been talking with [François] Vieta, the inventor of algebra, about binary numbers, he wouldn't have had a clue, probably. And yet, today, binary numbers look to be fundamental, simple, it's-obvious type aspects of mathematics. That's an example of a historical accident. … I think that the challenge in all these cases with alien intelligence of any kind is there's a big computational universe of possible things you can compute about out there, and the particular ones that one has sampled are very dependent on the detailed history of a civilization.

Space.com: Is there any concept you invented for this movie that you're thinking about exploring more?

Wolfram: [One] thing that I did think about for this movie is the following question: Is there an infinite frontier of technology? If we know the fundamental theory of physics, are we done, or is there always more to discover? What you realize is it's very similar to the problem of axioms in mathematics and how math is hard, and ideas like Gödel's Theorem — it's an almost theoretically necessary fact that there is an infinite frontier of technologies to discover. You can always build a more complicated program.

Another question is, is there more interesting stuff to discover? We can write down an infinite number of theorems in some area of mathematics, but we might say we've gotten all the interesting ones. All the other ones are ornate, uninteresting things. That's a really interesting question I don't really know the answer to.

The question of interestingness is very closely related to these questions about purpose and cultural context, because what counts as interesting [depends on] what are you trying to do. A good example of this, coming from the Pythagoreans: They were really into the fact that 1+2+3+4=10, something that we consider now to be just, who cares. But for them, that was a profound fact. And I think that's an example of, is it interesting, or is it just some trivial arithmetical fact? It depends a lot on context.

It's far from obvious that as an alien you are going to be at all into trying to find out as much as possible. That might not be the point. 

This interview has been edited for length.

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Sarah Lewin
Associate Editor

Sarah Lewin started writing for Space.com in June of 2015 as a Staff Writer and became Associate Editor in 2019 . Her work has been featured by Scientific American, IEEE Spectrum, Quanta Magazine, Wired, The Scientist, Science Friday and WGBH's Inside NOVA. Sarah has an MA from NYU's Science, Health and Environmental Reporting Program and an AB in mathematics from Brown University. When not writing, reading or thinking about space, Sarah enjoys musical theatre and mathematical papercraft. She is currently Assistant News Editor at Scientific American. You can follow her on Twitter @SarahExplains.