Mathematics may be considered a universal constant — and surefire way to communicate with extraterrestrials — but there’s no guarantee that the next spacefaring civilization we come in 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 have never evolved appendages? And what if we encounter a race whose understanding of electromagnetic fields is as intrinsic as our own innate capability to catch thrown items from midair? Can we really expect them to understand how radios function in the same way that we do? The problem is that many of our scientific insights and predictions about ETs are heavily influenced by our own cultural biases.

In his latest book, *The 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 the galaxies beyond examining not only the intricacies and contradictions in how we classify life on Earth but how those notions and assumptions may be applied following first contact.

From *The Zoologist’s Guide To The Galaxy* by Arik Kershenbaum. Published by arrangement with Penguin Press, a member of Penguin Random House LLC. Copyright © Arik Kershenbaum, 2021.

We scientists tend to assume that aliens will also be scientists and mathematicians; indeed, more advanced and skillful than we are ourselves. Otherwise, how could they build a spaceship to visit us, or radio telescopes to send messages to us? Popular science fiction would seem to concur, although all too often those alien scientists are performing experiments on hapless humans rather than benevolently sharing their wealth of knowledge with us. But I know philosophers who believe that aliens will be philosophers. Do electricians and plumbers think that alien civilizations will be as reliant on electrical and plumbing skills as we are?

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

Certainly, such ideas have been proposed ever since scientists and philosophers began to give serious consideration to the possibility of alien life. In the 1980s, the astronomer Carl Sagan wrote eloquently about the ways in which alien civilizations could use mathematical principles to establish communication with us, and he himself (together with his wife, Linda Sagan, and Frank Drake, the ‘father’ of the search for extraterrestrial intelligence) designed the famous Pioneer plaque that accompanied two tiny space probes launched in the early 1970s on their mission out of the solar system. As well as a visual representation of two human figures, the plaque gives mathematical representations of the unique rotation periods of fourteen prominent pulsar stars, as well as the directions from the Sun to each of those stars. Any civilization finding the plaque should be able to locate our solar system using this ‘map’. So, perhaps mathematics can help us not only in the search for extraterrestrial intelligence, but also in designing messages to be broadcast into 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 every alien civilization. The laws of mathematics are, after all, truly universal. If we try to communicate using these laws, then we are guaranteed at the very least not to be talking nonsense. A triangle has three sides both here, and on Alpha Centauri. We may choose to signal our intelligence to others by declaring our understanding of fundamental mathematical constants such as π: the ratio between the circumference and diameter of a circle. We ourselves have known of this ratio as far back as our written history penetrates; 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 broadcast abstract mathematical concepts, in the knowledge that whatever our differences in language or body form, whether we live on land or in water or in liquid methane, whether we are the size of humans, fleas or planets, whether we see with sight or sound or electric fields – there is no doubt that these mathematical principles apply to us all. This mathematics, therefore, would be instantly recognized by another species as a sign that intelligent life exists elsewhere in the universe.

But some philosophers have cast doubt on the idea that mathematics is the ultimate universal lingua franca. For one thing, our understanding of mathematics is constrained by our very physicality. We are so used to the three-dimensional world that we rarely think of how alien the 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 to theirs. An ant could walk around its planet as if it were walking across a flat plane – although we could see that it was in fact moving on a three-dimensional ball. And in a world where you can only walk on the surface of a sphere (no burrowing allowed!), π is not, in fact, equal to the familiar 3.14159265 . . . Consider a point on the equator of our imaginary ant planet, and the circle that goes through both North and South Poles. Our ant can walk along the ‘circumference’ of its world, going via North Pole and South Pole back to its starting place. But for the ant, the ‘diameter’ of the world is the path perpendicular to that polar route: along the equator to its most distant point. That line, going along the equator, is precisely half of the circumference of the planet, and so 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 come to us very naturally from generations of throwing spears and catching animals. But a blind mole living underground would find the concept of catching totally unfamiliar, and indeed might not comprehend that such a concept exists, until a mole mathematician capable of Einstein’s abstract insight works out the equations of motion from first principles. Concepts outside of our physical experience are going to be hard for us to discover, and the physical experience of aliens is unlikely to be quite like ours.

As well as being constrained by our physical environment, the evolution of the science of mathematics on Earth has been driven by technological requirements: to build better temples (with walls at right angles to the floor), aqueducts (with arches to support their weight), catapults (and the ballistic trajectories of their boulders), as well as fighter planes and atomic bombs, with legions of scientists and engineers behind them. The trajectory of our mathematical discoveries has been shaped by our desire both to build structures and to knock them down with our propensity for war. A peaceful alien race may have no concept of ballistic technology, and one without religion may never have developed the technology to build imposing temples. Mathematical principles that seem to us fundamental and obvious may hold much less importance for aliens who have arrived at their state of ‘intelligence’ via a very different route.

But what of numeracy itself? Must all intelligent aliens count, for example? Even if they don’t have fingers, or any such equivalent? How did mathematical ability even evolve on Earth, and is it likely to have followed a similar evolutionary pathway on other planets?