John Wallis is all but forgotten except among historians and mathematicians, but he was a versatile intellectual force in the seventeenth century: an ecclesiast, academic administrator and man of affairs, scientist (he was a founding member of the Royal Society), mathematical genius, and teacher, the Savilian Professor of Geometry at Oxford University for over fifty years, until his death at eighty-six in 1703. He was intimate with several kinds of invented language, mathematics in particular. In a memoir, he explained that he began pursuing mathematics “not as a formal study, but as a pleasing diversion, at spare hours. . . . For Mathematicks, (at that time, with us) were scarce looked upon as Academical studies, but rather as Mechanical; as the business of Traders, Merchants, Seamen, Carpenters, Surveyors of Lands, or the like; and perhaps some Almanack-makers in London.” Wallis wrote significantly about infinity and infinitesimals, so was a necessary precursor to development of the calculus by Newton and Leibniz.He not only wrote and codified new (that is, invented) mathematical expression, but also introduced the symbol for infinity.

Wallis was expert in classical languages necessary to theological study: Hebrew, Greek, and Latin. He was fluent in French and knew the rudiments of many other vernaculars. He was a comparativist who set the stage for Sir William Jones, the Brothers Grimm, Franz Bopp, Rasmus Rask, and others who, in the eighteenth and early nineteenth centuries, uncovered the systematic relationships among Indo-European languages, much as his mathematics set the stage for Newton and Leibniz. As a cryptographer, he was a prodigy by his own account:

About the beginning of our Civil Wars, in the year 1642, a Chaplain of Sr. William Wallers . . . (one evening as we were sitting down to supper at the Lady Vere’s in London, with whom I then dwelt,) shewed me an interesting Letter written in Cipher. He shewed it to me as a Curiosity(and it was indeed the first thing I had ever seen written in Cipher.) And Asked me between jeast and earnest, whether I could make anything of it. And he was surprised when I said (upon the first view) perhaps I might if it proved no more but a new Alphabet. It was about ten a clock when we rose from Supper. I then withdrew to my chamber to consider of it. And by the number of different Characters therein, (not above 22 or 23:) I judged that it could not be more than a new Alphabet, and in about 2 hours time (before I went to bed) I had deciphered it.

Wallis was a professional polyglot, a writer of mathematical code, a professional cryptologist—he served the English state officially as such for over forty years—and further took an interest in the universal language movement of his time. He was not himself what we would now call a “conlanger ”—that is, one who constructs languages systematically, from the ground up—but he counted some early conlangers among his closest associates, at a time when constructing languages was a hot intellectual activity, and the source of international debate.

Wallis participated in the precursor organization to the Royal Society with John Wilkins, who was a spirited proponent for inventing an international language based on what was called a “real character.” Besides the supposed advantage of everyone understanding one another, universal language had a mythological quality to it, for the Christian West, anyway, because it hearkened back to the language of Adam, the language of one-to-one correspondences used in Eden to name the birds of the air and the fish of the sea, etc., fractured into the languages of the world when human aspiration failed at the Tower of Babel and peoples were dispersed.

Some thought the language of Adam was alive and well but not recognized as such after Babel. Olaus Rudbeck (1630–1702) identified Swedish as the language of Eden (he believed that Sweden was Atlantis, too) in a four-volume work of roughly three thousand pages, which (linguistics aside) may explain why the idea never caught on. His son, also Olaus Rudbeck (1660–1740), wrote comparative work that found supposed cognates among Swedish, Chinese, Hebrew, Sámi, Bantu, Hungarian, and other languages. He outlined the connections between Sámi and Hebrew in a letter to none other than John Wallis. Others thought the language of Adam was lost but might be reconstructed, and that Providence required for the world’s good ending that God’s people would speak again as one, so even if the language of Adam could not be found or repaired, a universal language of modern design would do as well. Wilkins was among these last, and so was Leibniz, another northern European intellectual who knew Wallis and his work from a distance and corresponded with him.

Wallis was not committed to the notion of a universal language for two reasons. First, he was not dissatisfied with vernacular language; as a matter of fact, he wanted to make his own, English, more readily accessible to foreign speakers. So he wrote his Grammatica Linguae Anglicanae (1653), in which he allowed that mother tongues like those spoken by Gauls and Britons may date back to the confusion of Babel. But vernacular languages were nonetheless worth learning and admiring. Wallis, the intellectual and professor, was anxious to share English knowledge with a world willing to learn the English language, but he also believed in a universal and renewed—that is to say, mildly invented—language, in which he wrote constantly and fluently, though he was not in any prominent feature one of its inventors. That is, he wrote his major works in Neo-Latin, the language of science (broadly construed) in seventeenth- and eighteenth-century Europe, indeed, the language of biological classification even today, when we have occasion to name the birds of the air, the fish of the sea, the one-celled organisms of the puddle, effectively the Adams of modern science. He wrote his Arithmetica Inifinitorum and De Sectionibus Conicis and even Grammatica Linguae Anglicanae, a book about English grammar, in Neo-Latin, because by doing so he made his work available to all people of learning in the West.

Wallis lived, to borrow the title of Arika Okrent’s excellent book, “in the land of invented languages.” He discovered mathematics while on vacation. Codes needed unscrambling, so after dinner he worked on them. He learned Latin in school and just kept on using it as a second language. He would meet, as he put it, “with divers worthy Persons, inquisitive into Natural Philosophy, and other parts of Humane Learning; And particularly of what hath been called the New Philosophy or Experimental Philosophy,” but before he knew it, the conversation had turned to universal language schemes; eccentric Swedes wrote to him out of the blue—in Neo-Latin—about the relations among apparently dissimilar languages, relations that would indicate a common, biblical source. All Wallis did was live fully as an intellectual in his time; as such, he couldn’t avoid invented languages.

And neither can we. We all live in the land of invented languages, and they matter as much now, though perhaps differently, as they did in the seventeenth century. You may not have heard of Paul Frommer, but you probably remember Na’vi, the language he invented for James Cameron’s Avatar (2009). You may be blissfully unaware of the Language Creation Society and David J. Peterson, yet not ignorant of Dothraki, the language Peterson developed for HBO’s Game of Thrones, from kernels of it planted in George R. R. Martin’s series of epic fantasy novels, A Song of Fire and Ice (1991–2011). Israelis speak a revitalized language, that is to say, partly invented rather than historical, namely, Modern Hebrew. Hawaiian is also a revitalized or reconstructed language; it is an emblem of Hawaiian heritage, and just one of many such revitalized languages around the world.

Inventing a language is arduous, and no one attempts it without a serious purpose or aspiration. As Suzanne Romaine, one of the world’s leading linguists, argues in From Elvish to Klingon: Exploring Invented Languages, “A similarity of purpose and motivation drives inventors of all new languages, whether in the real or fictional world. The perceived need for them arises from dissatisfaction with the current linguistic state of affairs. Recognition that language can be used for promoting or changing the social, cultural, and political order leads to conscious intervention and manipulation of the form of language, its status, and its uses.” The quality of that dissatisfaction, however, and the language in which it’s reflexively expressed, is particular to the case. We are probably all dissatisfied to some extent with the language we’re given. The question is, What do our responses say about the human condition?

When you hear the term “invented language,” you may think first of the famous imaginary languages of fiction: the mind-numbing Newspeak of George Orwell’s 1984; the Russian-based criminal argot Nadsat in Anthony Burgess’s A Clockwork Orange; Belinda Webb’s feminist repurposing of Burgess’s idea in A Clockwork Apple or the feminist language Láaden in Suzette Haden Elgin’s Native Tongue and its sequels; or Elvish and other languages in J. R. R. Tolkien’s The Lord of the Rings. You may not yet know about Wardwesân, the language of Frédéric Werst’s sensational Ward, published two years ago in France, the first original work of fiction to be written entirely in an invented language, accompanied by a helpful parallel French translation—well, helpful if you happen to read French. Film and television have their invented languages, too: Star Trek in its various incarnations has Klingon.

Many invented languages, however, belong to the real world and have (or have had) real speakers. These are conventionally political, a linguistic means of changing the established order. The most successful, Volapük and Esperanto, were introduced respectively in 1879 and 1887. There aren’t many speakers of Volapük today, but a ‘Circular Letter ’ of the Flenef Bevünetik Volapüka has appeared regularly since 1961, and Volapük has an Internet presence. The tangible effects of Esperanto have also dwindled. By 1910, there were nearly 2,000 books published in Esperanto, 350 periodicals published in forty-eight countries, and nearly 1,500 Esperanto societies worldwide. Today the aspiration behind Esperanto seems moribund. In 1994, the Esperantist Don Harlow placed the number of speakers “at least in the middle hundreds of thousands, very likely in the (low) millions.” All the same, Esparanto’s inventor, Ludwik Zamenhof, remains a compelling figure.

Zamenhof ’s linguistic invention was not encouraged at home. His father burned his linguistic manuscripts. Undeterred, Zamenhof reconstructed his universal language from memory. Umberto Eco, in The Search for the Perfect Language (1995), describes Zamenhof ’s situation movingly: “Born of a Jewish family in Białystok, an area of Polish Lithuania then part of the Tsarist empire, Zamenhof passed his childhood in a crucible of races and languages continually shaken by nationalistic ferment and lasting waves of anti-Semitism. The experience of oppression, followed by the persecution of intellectuals, especially Jewish, at the hands of the Tsarist government, ensured that Zamenhof ’s particular fascination with international languages would become mixed with a desire for peace between peoples.” It is hard to argue with Zamenhof ’s motive, dissatisfaction, and hard to argue against language as the agent of community and fellow feeling.

Some did, however. W. L. Alden wrote caustically in the New York Times on August 15, 1903, when Esperanto was the next big thing, “Of all crazes, the scheme of inventing a new universal language is the most preposterous. It recalls those amiable persons who from time to time find the divisions of Christianity intolerable, and so start a new sect and add another to the many divisions which they deplore. There are already too many languages in the world, and it would be far better if everyone spoke the same language. How this undesirable state of things is to be cured by adding a new language to those already in existence is not clear.” Ido, Rosentalographia, Spelin, Dil, Adjuvanto, Eulalia, Ariana, Geoglot—all of these International Auxiliary Languages or IALs were conceived with the best intentions; all had enthusiastic adherents, at least for a while. Mostly, however, they prove the adage that you can lead a horse to water, and he may even drink, but that won’t make him Mr. Ed.

Not all invented languages of the real world serve utopian universalism. Some revitalized and reconstructed versions of natural languages, like Modern Hebrew, Hawaiian, Maori, Cornish, and Néo-Breton, instead honor heritage and are, in a sense, deliberately and comfortably parochial, thus politically at the opposite pole from Esperanto, but intensely political, nonetheless. In part, languages like Modern Hebrew and Hawaiian are reconstructed to meet the lexical challenges posed by material and social conditions of the twenty-first century. But they are also ideologically motivated, asserting a right and an importance of national or ethnic expression and, by extension, expression of national or ethnic identity. Thus, they mark one group off from another, constructing political distinctions and relationships hitherto unknown, drawing together small communities, not fostering the Brotherhood of Man.

Revitalized languages, like Cornish, can cause political strife within the heritage group. As Romaine summarizes in From Elvish to Klingon, “In 2004, the installation of a welcome mat in Cornish at the Camborne county offices in southwest Cornwall sparked a heated dispute over how to spell ‘welcome.’ Although the county government tried to defuse the tension by installing signs using all the different spellings (e.g., dynnargh on the welcome mat outside the county offices, but dynargh on another sign inside the building), this approach did not bring the community to consensus.” Paradoxically, then, inventing language in order to define, enact, and empower a community, can fracture said community in the course of its creation. Language ideology is unavoidable, even within the land of invented languages, but the dangers have not deterred the inventors, because the inventors have as much or more to gain as they have to lose.

The bookish person, however, most often encounters invented languages in fiction, especially fantasy, and the value of literary invented languages is perhaps less obvious than that of their worldly counterparts. In Francis Godwin’s The Man in the Moone (1638), the first work of science fiction in English, Moon language “hath no affinitie with any other,” because speakers “utter their mindes by tunes without wordes.” In the twentieth century, Orwell used a smattering of Newspeak in his dystopian novel 1984, but thought the language central to the book’s point, so explained it fully in an appendix. Or, one might argue, the appendix is part of the fiction, a type of bureaucratic annotation typical of Oceania’s new world order. In Burgess’s A Clockwork Orange, the juvenile delinquent antihero and his comrades speak an argot that separates them from the community they terrorize while also distracting readers (perhaps also the delinquents) from the inhumanity of the crimes they commit. Then, there are the most famous and fully articulated invented languages in English literature, the languages of Middle-earth in Tolkien’s The Lord of the Rings.

Invented languages force us to think in cultural terms different from our own. Eric Rabkin, in The Fantastic in Literature, argues that fantasy challenges “the very nature of ground rules, how we know things, on what bases we make assumptions.” According to the Sapir-Whorf hypothesis, differences among natural languages reflect and perhaps impose different conceptions of the world. As the linguist Edward Sapir, who put the Sapir in Sapir-Whorf, explained, “The ‘real world’ is to a large extent unconsciously built up on the language habits of the group. No two languages are ever sufficiently similar to be considered as representing the same social reality. The worlds in which different societies live are distinct worlds, not merely the same world with different labels attached.”

We take everyday language for granted. We rarely stop to consider the structure of the natural language or languages we use regularly—we understand the stream of sounds that comes out of us as we talk or into us as we hear, the yards of text we scroll through daily on the screen, almost as unconsciously as we breathe. In fiction, an invented language is objectified: We must account for it, like anthropologists encountering any other artifact of an unknown culture, in order to understand and enjoy the fiction. So, when we encounter an invented language in literature, we focus, not only on the language in its fictional context, but on the very nature of language: We confront and admire its world-shaping power. Natural languages are similarly powerful, of course; but when the language in question is familiar, the world shaping is less obvious.

Most invented languages in literature are quoted in texts otherwise written in natural languages. Readers have their limits. As Tolkien wrote to his American publishers, “I should have preferred to write in ‘Elvish.’ But, of course, such a work as The Lord of the Rings has been edited and only as much ‘language’ has been left in as I thought would be stomached by readers. (I now find that many would have liked more.)”

The more recent Ward is an anthology of folklore (prayers, poems, stories) left to posterity by the Wards, a fictional people who lived in a fictional kingdom called Aghâr, written in their elaborately invented language, Wardwesân. Wardwesân is the real thing, a plausible fictional language: Its nouns exhibit a complex array of plural forms (probably representing a history of plurals like that of English—consider cats, mice, moose, children). It has a complete system of numbers, as well as a verb system (without be). The book includes a thorough grammar of Wardwesân and a glossary of some 3,500 words. Werst commented on his motive for writing Ward wholly in Wardwesân in The Times of London: “It makes it more real and multiplies the strangeness. . . . This way you get the illusion that this is another civilisation.” Surely, this applies to many an invented language in many a fiction.

But Werst’s is extreme language invention—no natural language exposition, except, that is, for the parallel French translation. English speakers, then, have the opportunity (and the challenge) of grasping the Wardish worldview mediated by the French worldview, a sort of Sapir-Whorfian overload. It is a fascinating experiment in language and literature, pressing to see just how far the invention of either can go, and how an invented language can promote the literary paradox that more strange makes things more real.

Shifting the ground rules, upsetting our epistemological balance, these are certainly motives underlying use of invented languages in literature, but there are several more, and they are by no means mutually exclusive. In cases like Elvish or Wardwesân, the inventors achieve something monumental—they climb a linguistic Everest and fully deserve the stature thereby earned. Certainly, one can engage political argument via invented languages, like that implicit in Orwell’s Newspeak, a warning against the dystopian politics of which Newspeak would be an inevitable effect. Aesthetically, as Tolkien explains of his own experience in the lecture, “A Secret Vice,” where the supposed vice is inventing languages, the motives can be personal and mostly to do with pleasure, pleasure in the making, and pleasure in the resulting linguistic artifact, a pleasure which, obviously, many readers of Tolkien’s works share.

Evidently, there is a lot at stake in inventing languages. Apparently, too, there’s a lot at stake in the very idea of invented languages. Erin McKean has proposed that “the greatest motivation [for inventing a language] must be the desire to create a new community—and to belong to it.” The conlanging community is serious and well organized, and it considers the land of invented languages its domain. Some people, conlangers might argue, are citizens of the land of invented languages, and others wander across the cultural border into it, not illegally, but aliens nonetheless, and perhaps unwelcome.

“Oirish,” for example, need not apply. I recently edited a volume of essays on invented languages, and a frequent target of criticism was a chapter by the scholar Stephen Watt on what he called “Oirish Inventions,” meaning certain examples of literary language of James Joyce and other Irish writers. Several reviewers believed it shouldn’t have been in the book, though the book seeks out interrelations among various kinds of invented language, which it considers as an aspect of linguistic behavior generally. As editor, I never intended to draw a bright line between what counts as an invented language and what doesn’t. Watt characterized Joyce’s language as unusual even in literature. Joyce invented language to express Irishness and modernism because, from Joyce’s cultural position, English was inadequate to the task—he registered his “dissatisfaction with the current state of linguistic affairs.”

Watt didn’t concoct this critical perspective on Joyce. As Michael Chabon argued recently in the New York Review of Books,

Any reader of the Wake soon learns, thanks to . . .the self-appointed locksmiths and cryptanalytic know-it-alls, that there are a number of viable ways to answer the question of what Finnegans Wake is about. The consensus reply . . . would be that Finnegans Wake attempts to recreate, by means of an invented language that Joyce derived from English, the flow and the flavor of a single night as it passes within the fitful, sleeping consciousness of a Dublin tavernkeeper.

The invented language Watt and Chabon have in mind is everywhere in Finnegans Wake. Here is an example of it, culled at random:

The fall (bababadalgharaghtakamminarronnkonnbronntonneronntuonnthunntrovarrhounawnsk-hawntoohoohoordenenthurnuk!) of a once wallstrait oldparr is retaled early in bed and later in life down through all christian minstrelsy. The great fall of the offwall entailed at such short notice the pftschute of Finnegan, erse solid man, that the humptyhillhead of humself prumptly sends an unquiring one well to the west in quest of his tumptytumtoes: and their upturnpikepointandplace is at the knock out in the park where oranges have been laid to rust upon the green since devlinsfirst loved livvy . . .

Joyce is famous for portmanteau words—think of his language as an invented portmanteau system of discourse.

Chabon’s view has academic counterparts besides Watt’s chapter. Jesse Schotter, in an article titled “Verbicovisuals: James Joyce and the Problem of Babel” from the James Joyce Quarterly in 2010, discusses Joyce’s fascination with IALs, including Esperanto, Volapük, and C. K. Ogden’s Basic English: “Joyce shares the desire for world understanding of Ogden and other creators of IALs, but instead of seeking to impose a new language, he strives to rediscover the supposedly lost genealogical connections between cultures.” Though the genealogical language is supposedly lost, it hasn’t really been lost because, unless one subscribes to the language of Adam myth, it never really existed. Joyce’s inventions imply the genealogical language, which means that he invents both the surface language of his text and, in the imagined depths of language, reefs of historical and cultural relationships, as well.

What motivates resistance to the idea of Joyce as a conlanger and the language of Finnegans Wake as an invented language? It may be Joyce’s place in the canon—it’s syllabus literature, though, to be honest, Finnegans Wake is rarely taught in university courses. Many conlangers believe that conlangers, not academics, get to identify bona fide invented languages. Even Chabon pokes fun at academic pretentions to “know it all.” As one conlanger puts it, “a non-conlanger attempting to analyze conlangs . . . has about as much chance of success as someone who’s only vaguely heard of motion pictures trying to analyze Citizen Kane.”

Any invented language registers dissatisfaction with natural language. It isn’t correctly oriented ideologically, it isn’t expressive enough, it isn’t easy enough for speakers worldwide to learn and use, it isn’t beautiful enough, it doesn’t represent one’s heritage—choose your motive. Further, though, interest in or commitment to invented languages, to the very idea of invented languages, nowadays may express dissatisfaction with institutional modes of cultural authority, not least authority over language and what we might call “the valuing authority.” To some, invented languages are important just because they are counter-canonical except in the land of invented languages.

When one recalls the seamless ease of Wallis’s life in that land, one realizes that, in the seventeenth century, invented languages, like most things, were the province of a privileged few. In our more democratic world, they needn’t, shouldn’t be, because invented languages, in their ubiquity, are important to all of us—they deserve attention and they deserve a context. Knowing our time and place, to some degree knowing ourselves, depends on understanding our relation to invented language as much as to any other significant cultural phenomenon.

Would conlangers accept mathematics as invented language and mathematicians as language inventors? Wallis and his colleagues then and now are writing a language, the only language, really, in which we can express the fundamentals of the physical world, of Creation, if you like. Mathematics may be the language of Adam, or it may be a simulacrum of the language of Adam, or it may be a substitute for the language of Adam. But mathematics is connected to Volapük and Elvish, Klingon and Cornish, Joycean genealogical language and Nadsat. At least once in a while, our business should be to see how they are connected to one another and how they are significant to us, to take the long and broad—the universal, or, as Wallis would see it, the infinite—view of linguistic invention and invented language.