Many people have as a hobby inventing languages. Yes, inventing languages! So much so that there are many artificial languages, the so-called conlangs (constructed languages), from those created to be international languages like Esperanto and Eurish, through languages used in works of fiction, such as the Star Trek’s Klingon, Avatar’s Na’vi, War of Thrones’s Dothraki and Valyrian and the languages created by J. R. R. Tolkien in novels such as Lord of the Rings, to come up with some crazy people who create languages for fun — or lack of to do.

Inventing languages is a challenging hobby, for it requires linguistic knowledge (in general, language designers are multilingual) and a lot of logical reasoning. After all, natural languages have evolved over centuries, spoken by populations that tested them in practice. Therefore, a natural language is a system that certainly works, or else would have gone — or evolved to another system. In contrast, an artificial language offers no guarantee that it works in all situations. However much its author thinks in detail, always something will escape, that communication situation that they could not predict and which only the actual speakers can handle.

But, if creating a language from scratch is a challenge, the game is even more exciting if the creation takes place according to some parameter. After all, one thing is to invent a language in which you have complete freedom to choose the phonemes, words, syntactic structures; quite another, is, say, to create a new Romance language, a hypothetical language that, however, is based on certain assumptions: descend from Vulgar Latin, be spoken, for example, between France and Italy, etc. This requires us to simulate the entire evolution that this language would have had; how each word derived from Latin to it, which phonetic laws governed the transformation of words, what degree of similarity that language would have with French or Italian, and so on.

Given these goals, the game becomes even more exciting because, if before I was playing according to the rules that I myself invented, now I must obey pre-established rules – not by me, but by reality. So now the creation of the language is like a chess game, where you have to calculate every move, and every move performed by a piece interferes with the others in a sometimes unpredictable way. The creation of this language becomes a beautiful exercise in logic, a challenge for people that gather two passions: languages and mathematics.

Now imagine an even greater challenge: to create not a language in an existing family, but a new family of languages within a large linguistic branch. For example, envision a new group of Indo-European languages. This exercise certainly requires an even greater degree of skill and talent, because this time it comes to designing multiple languages with kinship with each other, but each with its individuality. And as they are all descendants of a parent language which, in turn, descended from Indo-European, you must first create that parent tongue (and consequently the phonetic laws that lead from Indo-European to it) and only then derive the laws that, from it, will generate each daughter language. Moreover, this parent language, as it is of Indo-European origin, should be related to Latin, Greek, Germanic, Slavic, Sanskrit… In short, the creator of this family must have great knowledge of Indo-European languages and historical evolutionary linguistics.

But let’s propose the ultimate challenge: suppose I want to create a family of Indo-European languages based on two others that present a curious and inexplicable series of analogies language by language. That is, imagine two linguistic families that are as the mirror of one another, each language having a corresponding one in the other family that appears to have developed following rules similar to the first. Now you need to create each language of this new family modelled by the two mirror languages of the existing families. Something like, for each language a of family A and b of family B, I created a c language in the hypothetical family C. Consequently, I would have to respect a kind of rule of three: if from a and b I get c by a certain logical law, then of a’ and b’ I get c’, from a” and b” I get c”, and so on. Recalling that the creation of each language has to obey accurate phonetic laws (albeit hypothetical) from the parent language. And that parent language, or proto-language, must also maintain symmetrical relations with respect to the proto-languages of A and B.

But assuming that not only the languages of families A and B show analogies one by one, but also the peoples who speak them have had parallel historical developments, so that the history of one is roughly a Xerox copy of the history of another, then the game assumes its maximum degree of difficulty: recreating, in the hypothetical family, countries with language, history, geography, culture, etc., everything always following the logic rule c is to b as b is to a. (In fact, what should really be sought is the golden ratio: b is for a as well as c is for the whole. In other words, the hypothetical form c must meet the characteristics of both a and b.)

Performing this playful exercise not only helps develop the extreme logical thinking ability — it is a great hobby for nerds — as also allows you to test the extent to which analogies between families A and B are real: the challenge of finding a form c that reproduces the same existing mathematical pattern between a and b leads us to discover relations that we did not realise before. If we are suspicious that this pattern is casual, we can do a test: try to find it in a family D, actually existing. Something like aligning a, b and d to see if the pattern repeats. If you can find many patterns of symmetry between the members of families A and B, but between A and D, A and E, A and F, etc., such patterns are very rare, or even nonexistent, so our suspicion that between A and B there is more than mere coincidence turns into certainty. Every time we find a ratio a : b and set off in search of a hypothetical form c, we run the wonderful risk of finding a new relation a’ : b’ that will lead us to c’, and so the cycle begins again. If this can be called science, then the search for supersymmetries between nations and their languages is an activity that combines science, art and sport. After all, we have the discovery, the invention of countries and languages, and the game with its rules and challenges.

The symmetry between the two families of peoples is so great that we could invent a third family of countries whose history, geographical disposition and languages had the same symmetries in relation to the Latin and Germanic families that they keep between each other. Of course, this playful exercise of creation would have no practical purpose other than to prove the existence of a fabulous specularity between the Latin and the Germanic countries.

We could create for each pair of mirror countries (France and Great Britain, Italy and Germany, etc.) a third country that would be the mirror these other two. Each of these hypothetical countries would have a history analogous to that of the real countries – with coincident or mathematically analogous dates, similar historical facts, etc. These fictitious countries would be geographically arranged in a similar way to the Latin and Germanic countries (evidently, the real geography of Europe does not allow a new series of countries to be introduced north of the Teutons or to the south of the Latins, nor in an intermediate position between both families). Moreover, the countries thus created would have languages that were perfect similes of the Romance and Germanic languages, keeping in relation to these total analogy, in phonetics, phonology, morphology, syntax, and lexicon.

By the principle of proportionality, we would have a correspondence of the following type:

I must confess something: after so long finding symmetries between the peoples of the West, I ended up inventing my own family of peoples, that would be the third proportional of the Latin and Germanic peoples. I have never revealed this to anyone and, for shyness or shame, I do not intend to do it (maybe after I die it may come to light). But the fact is that this family has a name, each country has its history, its language (or languages), its geography (it was hard to fit them on the map, even more respecting as much as possible the territory of countries that actually exist and, above all, obeying the laws of supersymmetry), its culture… I started it as a joke, as young as a teenager, and I’ve been doing it ever since. I have accumulated numerous notebooks with notes and as much computer files. In this material there is everything: maps, drawings, sketches, biographies, chronological lists of monarchs, meticulous descriptions of languages, including phonetics, phonology, morphology, vocabulary, syntax…

From mere playful exercise, this hobby has gradually become a way to test scientific hypotheses. At every new discovery of a symmetry between Western countries, here I go and try to create a similar fact in my imaginary world. Sometimes it takes a long time and requires great powers of concentration and reflection. Sometimes it takes me days, weeks to find the solution. Not always do I find. (Many issues are pending and only much later are resolved — or not.) In any case, the discovery of this solution is as rewarding as for a poet to find a rhyme that fits in that verse, as rewarding as for a mathematician to prove a theorem. And in this case, the solution has something of poetry and mathematics at the same time. After all, it should fall into patterns that, at the end of the day, are mathematical. On the other hand, this solution also requires a strong dose of creativity: creation of a word or a grammatical rule, setting a date for a historical fact, idealisation of the characters of this historical fact (name, biography). And if, at first, by ignorance of a hidden relation, I create something arbitrarily, I may have to review this creation time later, since a new pattern of symmetry has revealed and should be applied to previously created fictitious facts. That is why the similarities between the Romanic and Germanic peoples are so intricate that sometimes there is no third available form because the two possible ones are exactly the ones adopted by each family. So, I can only repeat one of both. For example, if in a particular aspect the Romance family presents a configuration AB and the Germanic BA, any other combination (AA, BB, AC, etc.) would escape mirroring, therefore my invented family will be AB or BA. However, the criterion of choice also follows a pattern: if in this given aspect it is AB, in another it should be BA, to maintain balance. Additionally, certain features, once established, should be kept forever. If the Romance languages tend to shift the stress to the end of the word, and Germanic, to the onset, then either the languages I invented follow the Romance or the Germanic pattern — you cannot mix both.

But as supersymmetry does not reach only countries and peoples, I also found analogies between persons — historical figures, rock bands, pop world celebrities, statesmen — and in many cases I allowed myself to let the imagination come into play and create a third following the transitive rule according to which a is to b as b is to c. It sounds kind of crazy? Maybe. Therefore, I do not show it to anyone, even under torture. But this exercise of fictional creation parallel to my research work has been very rewarding, and a great mental hygiene for someone who is not satisfied with banal hobbies, like watching talk shows on TV (except occasionally for relax, for everyone needs a break!).