Math can be seen as a universal constant – and a surefire way to communicate with aliens – but there is no guarantee that the next space civilization we come into contact with will understand the universe the same way we do. How are we supposed to explain our base 10 counting system to an alien species that may never have evolved from appendages? What if we met a race whose understanding of electromagnetic fields is as intrinsic as our own innate ability to catch objects thrown in the air? Can we really expect them to understand how radios work the same way we do? The problem is, many of our scientific ideas and predictions about aliens are heavily influenced by our own cultural biases.

In his latest book, *A zoologist’s guide to the galaxy*, Dr Arik Kershenbaum, Professor of Zoology at the University of Cambridge, takes readers on a fascinating xenobiological tour of our planet and galaxies beyond examining not only the intricacies and contradictions in how we classify life on Earth, but how these notions and assumptions can be applied after first contact.

Of *The zoologist’s guide to the galaxy* by Arik Kershenbaum. Published by arrangement with Penguin Press, member of Penguin Random House LLC. Copyright © Arik Kershenbaum, 2021.

We scientists tend to assume that aliens will also be scientists and mathematicians; in fact, more advanced and skillful than we ourselves are. How else could they build a spaceship to visit us, or radio telescopes to send us messages? Popular science fiction seems to agree, although all too often these alien scientists perform experiments on unhappy humans rather than kindly sharing their wealth of knowledge with us. But I know philosophers who believe that aliens will be philosophers. Do electricians and plumbers think alien civilizations will depend as much on electrical and plumbing skills as we do?

Science has a history of biasing its methods and findings by the cultural and social context of scientists themselves. But while aliens may or may not have indoor plumbing or central heating, the laws of science and math are the same for them as they are for us. Surely this is a common point that we and extraterrestrial civilizations can agree on? Human and alien scientists will have made many of the same discoveries, and alien mathematicians will have derived the same mathematical theorems that human mathematicians made on Earth. If so, surely we can use the most fundamental ideas of logic, mathematics, and science to build a common channel of communication between ourselves and alien species, even though we are different in every other way. ?

Certainly, such ideas have been proposed since scientists and philosophers began to seriously consider the possibility of extraterrestrial life. In the 1980s, astronomer Carl Sagan eloquently wrote about how extraterrestrial civilizations could use mathematical principles to establish communication with us, and himself (along with his wife, Linda Sagan, and Frank Drake, the “ father ” of research for extraterrestrial intelligence) designed the famous Pioneer plate that accompanied two tiny space probes launched in the early 1970s as part of their mission out of the solar system. In addition to a visual representation of two human figures, the plate gives mathematical representations of the unique rotational periods of fourteen prominent pulsar stars, as well as the directions of the Sun to each of these stars. Any civilization finding the plate should be able to locate our solar system using this “map”. So maybe math can help us not only in the search for alien intelligence, but also in designing messages to be broadcast in outer space to signal that we too are intelligent.

Since the 1960s, scientists have suggested that mathematics is a universal language, something inevitably shared between us and all extraterrestrial civilizations. The laws of mathematics are, after all, truly universal. If we try to communicate using these laws, then at the very least we are not talking nonsense. A triangle has three sides here and on Alpha Centauri. We may choose to signal our intelligence to others by stating our understanding of fundamental mathematical constants such as π: the ratio of the circumference to the diameter of a circle. We know this relationship ourselves as soon as our written history enters; the ancient Babylonians and Egyptians were familiar with the concept, if not with the precise value of π. There is something appealing about the idea that we can diffuse abstract mathematical concepts, knowing no matter what our differences in language or body form, whether we live on land or in water or in methane. liquid, whether we are the size of humans, chips or planets, whether we see with visual, sound or electric fields – there is no doubt that these mathematical principles apply to all of us. This mathematics would therefore be instantly recognized by another species as a sign that intelligent life exists elsewhere in the universe.

But some philosophers have questioned the idea that mathematics is the ultimate universal lingua franca. On the one hand, our understanding of mathematics is limited by our very physics. We are so used to the three-dimensional world that we rarely think about how foreign mathematics would be in a two-dimensional world. Ant-like creatures living on the surface of a very small sphere would find our mathematics very different from theirs. An ant could walk around its planet as if it were crossing a flat plane – although we could see that it was actually moving on a three-dimensional ball. And in a world where you can only walk on the surface of a sphere (no digging allowed!), Π actually doesn’t equal the familiar 3.14159265. . . Let’s take a point on the equator of our imaginary ant planet and the circle that crosses the North and South Poles. Our ant can walk along the “circumference” of its world, passing through the North Pole and South Pole to its starting point. But for the ant, the “diameter” of the world is the path perpendicular to this polar route: along the equator to its farthest point. This line, running along the equator, is precisely half the circumference of the planet, and therefore in this case π = 2!

As humans, our particular intelligence evolved on the plains of the African savannah, to deal with the problems of the African savannah. We can catch a tennis ball without solving Newton’s equations of motion because throwing and catching it comes very naturally to us from generations of spears and catching animals. But a blind mole living underground would find the concept of capture totally unknown, and in fact might not understand that such a concept exists, until a mole mathematician capable of Einstein’s abstract insight worked out the equations of motion from first principles. Concepts outside of our physical experience are going to be difficult for us to discover, and the physical experience of aliens is unlikely to resemble our own.

In addition to being constrained by our physical environment, the evolution of the science of mathematics on Earth has been driven by technological demands: to build better temples (with walls perpendicular to the ground), aqueducts (with arches for support their weight), catapults (and the ballistic trajectories of their rocks), as well as fighter jets and atomic bombs, with legions of scientists and engineers behind them. The trajectory of our mathematical discoveries has been shaped by our desire to both build structures and tear them down along with our propensity for war. A peaceful alien race may have no concept of ballistic technology, and a race without religion may never have developed the technology to build towering temples. Mathematical principles which seem basic and obvious to us may be of much less importance to extraterrestrials who have reached their state of “intelligence” by a very different route.

But what about numeracy itself? Should all intelligent aliens count, for example? Even if they don’t have fingers or any equivalent? How has mathematical ability even evolved on Earth, and is it likely to have followed a similar evolutionary path on other planets?