Regarding the probability interpretation of the wave function, we need to distinguish two cases: normalisable and non-normalisable wave functions.

The question here is whether the biochemical processes observable on Earth would be replicated on another planet. Take photosynthesis as an example. This is the means by which plants utilise sunlight in the production of adenosine triphosphate (ATP) and glucose as sources of energy. During this process oxygen is given off and carbon dioxide is absorbed, hence the value of photosynthesis for environments on our planet. The actual process is highly complex and involves electrons going through intricate chemical reactions leading at the end to glucose formation. There is also a kind of reverse process, which involves the release of energy through the oxidation of a chemical derived from carbohydrates, fats and proteins. This is known as the citric acid cycle, an essential metabolic pathway used by aerobic organisms.

As humans we are confronted with devices which are supposed to work and often do not. Just think of all the domestic appliances you have at home. Do all of them work? I am sure that you can remember the time when the toaster gave up the ghost or the torch in the garden shed did not work. We have a notion of device and we have an expectation that it will work. But when we say a device does not work, what do we mean? Generally, we mean that it does not perform the function we expect of it. If you put sliced bread into the toaster and press down the lever at the side and nothing happens you utter a sigh of frustration because the device is not working.

In classical physics, a distinction is made between two different concepts: waves and particles. However, various experiments have shown that this strict distinction must be replaced by a new concept.

In mathematical terms, an operator transforms a given function into a new function. To better understand operators, we summarise the analogies with matrices below.

What might exobeings really be like? To begin answering this question consider the deep history of our own evolution. Would the evolution of exobeings show the same key turning points we find in our own evolution? Would they develop complex multicellular life forms at an early stage and then move on to become vertebrates with a central nervous system controlled by a brain, allowing them to move around freely in their surroundings?1 Indeed, to what extent would what appear to us as preconditions, vertebrae and a skeleton to stabilise an animal’s body, be necessary on an exoplanet?

The degree of variability on an exoplanet could be similar to that found on Earth, with a certain range for cognitive ability (types of intelligence), personality, aspects of physical appearance such as size, eye and hair colour or shape of skeleton (observable in body build, hands, feet, arms, legs, etc.).

A key question that is often posed is, ‘Are we alone in the universe?’ If the answer to this question were simply ‘Yes’ or ‘No’, this book would probably not have been written. But what looks like a simple question is actually a complex and multifaceted set of issues which can hopefully be elucidated by discussing the many aspects involved.

First, by ‘the universe’ we can only mean the small corner of the galaxy which we inhabit, say within about a 100-light-year or, at maximum, 1,000-light-year radius. This is a tiny fraction of our Milky Way galaxy (at least 100,000 light years in diameter) and we cannot even see half of the galaxy which is beyond the central bulge of the disk on the other side. The Milky Way is an infinitesimally small part of the entire universe.

Normally the final section of a book on language matters would simply be labelled ‘Conclusion’, where the author reviews the main arguments in the book, draws the threads together and presents the results and insights in summary form. However, with this book there can be no definitive conclusion as the subject matter is speculative. But what one can do is summarise the possibilities of exolanguage as a series of questions with tentative answers. Admittedly, the following may be regarded by some readers as unduly anthropocentric, too heavily reliant on what we humans are like. However, in keeping with the principle applied throughout this book, the speculative sections begin with what we know from our existence on our Earth and then move in careful steps to consider what might be the case for exobeings on an exoplanet.

Consider that space exploration is not yet even 100 years old nor is digital technology, which is advancing at a breath-taking pace.1 Assuming that such technology will continue unabated and that there are no negative impacts from other quarters,2 we can further assume that the ability of humans to probe the universe with increasingly powerful instruments will continue to increase and allow us to discover ever more about the planets around other stars.

The great advances in astronomy in the past century or so were initially theoretical in that they rested on predictions about what the universe is like and how certain phenomena such as light would behave on scales much larger than those on Earth.

The ability to speak a language rests on physical aspects of our brains. We can identify areas which are especially important for language, and we can examine individuals with language impairments to gain some insights into the manner in which knowledge of language is stored in the brain. This study of language in relation to the brain is called neurolinguistics. It is a special field which is becoming increasingly a focus of interest for linguists. It is true that it is not possible to pinpoint linguistic activity in the brain, to put the transmission of minute electrical currents between nerve cells in correlation with the production of language. Nor can linguistic structures be assigned to the information stored in these cells.