Category: Writing

Once you have the grammar parts figured out, most of the rest of the conlanging process is making words. We began to see that in Part 14, when we discussed deriving new words from existing roots. This time around, we’re going back to the roots (pun intended) and looking at a very specific set of words: the color terms.

Color terms are, well, terms for colors. They’re the names you see on crayons or paint swatches. As anyone who has been to a hardware store knows, there are thousands of these, but we’ll focus on the absolute basics. Most colors are named after things that are that color, like “violet” or “salmon”. A few, however, are truly basic: “red”, “yellow”, “black”, and so on. These are the ones that most interest us here.

More importantly, which color terms are considered “basic” turns out to be a way in which languages differ. That makes this subject an excellent illustration of how a language can divide up the “semantic space”. Not every language is the same in this respect, and realizing that is a good step towards creating a more naturalistic conlang, rather than a simple cipher of your native tongue.

The color hierarchy

Every language has at least two basic colors. That seems to be a linguistic and cultural universal. But according to a study by Berlin and Kay (1969), what comes next follows a fairly regular trajectory. To be sure, there are outliers, but the past few decades have only reinforced the notion of a developmental hierarchy of color terms, making it a useful model for conlangs.

The first distinction in color is near-universal: light and dark. This can also be black and white or warm and cool; the specifics won’t matter too much. Mostly, yellow and red fall in with white in this scheme, while blue and green are dark. Other colors, like purple, brown, or orange, fall in somewhere along this spectrum. Exactly where is different for each language. It’s easy to see pink as “light” and purple as “dark”, but what about a soft lavender or a deep ruby?

At some point, probably fairly early in a culture’s history, a new color term comes about, splitting “light” into white and red. This seems obvious, as blood is red, and it’s a very important part of humanity. Yellow also tends to get lumped in with red in this scheme, meaning that most oranges do, too.

The next two colors to “break off” are green and yellow, in either order. Green can come first or yellow can, but they both need to be present before the next stage can begin. Once a language has these five color terms—black, white, red, green, yellow—then it’s on to the sixth and final major color: blue.

These six are the main group, then, and there’s a very good reason why. Human vision, as anybody who took biology knows, has two key parts: rods and cones. The rods are monochromatic, distinguishing only light and dark; in other words, just like a two-color-term language. The cones, however, are how we see color. They come in three flavors, roughly corresponding to red, green, and blue.

So that’s probably a good explanation for the first six basic color terms. Red has the longest wavelength, so it’s the easiest to see, hence why stop signs and a car’s brake lights are red. It stands to reason that it would be singled out first. The eye’s green cones tend to be the most sensitive, but green and yellow are pretty close together, spectrally speaking, so they’re the next two, but their similarity leads to the flip-flop in which comes first. And then that leaves blue.

What about the others, though? Well, there it gets murky. Brown is usually the seventh basic color, distinguished from red and yellow. After that, there’s no real set order among the next four: orange, pink, purple, and gray. But those eleven, possibly accompanied by one or more lighter or darker shades (cyan, magenta, azure, etc.), make up the core color terminology of the majority of languages.

The rest of the box

All the other colors’ names will be derived in some way, and that can include some from the above list, if a language doesn’t have a full complement of basic terms. One way of doing this is with adjectives that specify a particular shade of a color. English has lots of these: dark, light, pale, deep, etc. The new color names produced with them aren’t single words, but phrases like “dark blue” or “pale pink”; other languages might have ways of compounding them, though.

Compounds give us another way of making new color words. By combining two basic colors, we can get new ones. That’s how we have “red-orange” or “blue-green”, to name but two. They’re in-between colors, and they tend to be composed of two colors adjacent on the spectrum. It’s hard to imagine a “yellow-blue” that isn’t green, for instance.

Another possibility is the abstract color word. These aren’t basic terms; instead, they tend to come about as finer distinctions of shade. They may have started off with some other meaning, but they now refer almost exclusively to a specific range of colors. Maroon and cyan are a couple of English examples.

By far, though, the best way of making names for colors is through description. Something that has a certain color becomes a descriptor for that particular color—“navy blue”, for instance—then, eventually, the color’s name. That’s how it worked for salmon, coral, violet, lavender, and hundreds of others. It may have even been the case for orange, as the fruit’s name seems be older than the color term. And if the original reason for one of these names is lost, then it may come to be considered an abstract term; indigo is one color that has gone through this process.

Using all these, a language can easily fill up even the biggest box of crayons. But the more color terms you have, the less of the color space each one covers. There will be overlap, of course, and the general terms will always cover more area than the more specific ones. And every language makes its own distinctions. The border between, say, red and yellow isn’t set in stone.

Even weirder

A few conlangers like making languages for speakers that aren’t ordinary humans. Since we’re moving into more culture-specific parts of language, this is a good opportunity to look at what needs to be done for that sort of conlang.

If the prevailing theory is accurate, basic color terms come about in the order they do because of human vision, as we saw above. A race that doesn’t follow normal human rules, however, will have a different color hierarchy. Some people, for example, have a fourth set of cone cells, purportedly letting them see otherwise “impossible” colors. Tetrachromats, as they’re called, effectively have a fourth primary color at their disposal.

An entire race (in the literary sense) of tetrachromats would have a language that reflects this. Where their fourth color fits into the hierarchy would depend on the specifics of how that fourth cone cell works, but it would certainly be in that first group alongside red, green, yellow, and blue.

Similarly, red-green colorblindness could be the norm for a race. In that case, red and green wouldn’t differentiate, obviously, but the rest of the diminished color space would also be changed. In fact, it’s easy to imagine such a race never getting past the light/dark stage.

And no discussion of color vision would be complete without including the neighboring portions of the spectrum. The human lens blocks ultraviolet, but some people report being able to see it. Vision reaching into the infrared is a little more plausible for our species. Aliens, though, could have their equivalent to cones reach their peak sensitivity at different points of the spectrum, allowing them to see into the deeper or higher ranges. Their color terms would likely reflect this, and an alien race could have a whole collection of words for color combinations that we simply cannot see.

Next up

Next time, we’ll look at our two conlangs and their color words. Then, it’ll be off to another part of the semantic realm, but I don’t yet know exactly which one. Stay tuned.

Ardari takes a different approach for its word derivation. Instead of compounding, like Isian does, Ardari likes stacking derivational affixes. That doesn’t mean it totally lacks compounds, just that they take a bit of a back seat to affixes. Therefore, we should start with the latter.

Ardari’s three main parts of speech—noun, verb, and adjective—are mostly separate. Sure, you can use adjectives directly as nouns, and we’ve got ky to create infinitives, but there are usually insurmountable boundaries surrounding these three. The most regular and productive derivation affixes, then, are the ones that let us pass through those boundaries.

Making nouns

To make new nouns from other types of words, we’ve got a few choices:

• -önda creates abstract nouns from verbs (luchönda “feeling”)
• -kön makes agent nouns, like English “-er” (kwarkön “hunter”)
• -nyn creates patient nouns from verbs, a bit like a better “-ee” (chudnyn “one who is guarded”)
• -ymat takes an adjective and makes an abstract noun from it (agrisymat “richness”)

All of these are perfectly regular and widely used in the language. The nouns they create are, by default, neuter. -kön and -nyn, however, can be gendered: kwarköna denotes a male hunter, kwarköni a huntress.

Two other important nominal suffixes are -sö and -ölad. The first switches an abstract or mass noun to a concrete or count noun, while the second does the opposite. Thus, we have ichurisö “a time of peace”, oblasö “a drop of water”, sèdölad “childhood”, or kujdölad “kingship”. (Note that a final vowel disappears when -ölad is added.)

Ardari also has both a diminutive -imi and an augmentative -oza. These work on nouns about like you’d expect: rhasimi “puppy”, oskoza “ocean”. However, there is a bit of a sticking point. Diminutive nouns are always feminine, and augmentatives always masculine, no matter the original noun’s gender. This can cause oddities, especially with kinship terms: emönimi “little brother” is grammatically feminine!

The other main nominal derivation is po- (p- before vowels). This forms antonyms or opposites, like English “un-” or “non-“. Examples include poban “non-human” and polagri “gibberish”.

Most other derived nouns are, in fact, adjectives used as nouns, as we’ll see below.

Making adjectives

First of all, adjectives can be made by one of three class-changing suffixes:

• -ösat makes an adjective from an abstract noun (idyazösat “warlike”)
• -rät makes an adjective from a concrete noun (emirät “motherly”)
• -ròs creates a “possibility” adjective from a verb (dervaròs “livable”)

Diminutives and augmentatives work as for nouns, but they take the forms -it and -ab, and they don’t alter gender, as Ardari adjectives must agree with head nouns in gender. Some examples: pòdit “oldish”, nejab “very wrong”.

We’ve already seen the general adjective negator ur- in the Babel Text. It works very similarly to English un-, except that it can be used anywhere. (The blended form u- from the Babel Text’s ulokyn is a special, nonproductive stem change.)

Most of the other adjective derivations are essentially postpositional phrases with the order reversed. Here are some of the most common:

• nèch-, after (nèchidyaz “postwar”)
• jögh-, before (jötulyan “pre-day”)
• olon-, middle, centrally (olongoz “midnight”)
• är-, above or over (ärdaböl “overland”, from dabla)
• khow-, below or under (khowdyev “underground”)

Many of these are quickly turned into abstract nouns. For instance, olongoz is perfectly usable as a noun meaning “midnight”. Like any other adjective-turned-noun, it would be neuter: olongoze äl “at midnight”.

Making verbs

There are only two main class-changing suffixes to make verbs. We can add -ara to create a verb roughly meaning “to make X”, as khèvara “to dry”. The suffix -èlo works on nouns, and its meaning is often more nuanced. For example, pämèlo “to plant”, from pämi “plant”.

Repetition, like English “re-“, is a suffix in Ardari. For verb stems ending in a consonant, it’s -eg: prèlleg- “to relearn”. Vowel-stems instead use -vo, as in bejëvo- “to rethink”.

Ardari also has a number of prefixes that can be added for subtle connotations. The following table shows some of these, along with their English equivalents.

Prefix	Meaning	English	Example
ej-	for, in favor of	pro-	ejsim “to speak for”
èk-	against	anti-	èksim “to speak against”
jès-	with	co-	jèzgrät “to co-create”
nich-	wrongly, badly	mis-	nichablon “to mishear”
ob-	after	post-/re-	opsim “to reply”
sèt-	before	pre-	sètokön “to precut”
wa-	into	in-	wamykhes “to inquire”
zha-	out of	ex-	zhalo “to expire”

Making compounds

Compounds aren’t as common in Ardari as they are in Isian, but they’re still around. Any noun can be combined with any other noun or adjective, with the head component coming last, as in the rest of the language.

Adjective-noun combinations are the most regular, like chelban “youth, young person”. Noun-agent is another productive combination: byzrivirdökön “bookseller”. Noun-noun compounds tend to be idiosyncratic: lagribyzri “dictionary”, from lagri “word” and byzri “book”.

Reduplicated adjectives are sometimes used for colloquial superlatives: khajkhaj “topmost”, slisli “most beautiful”.

A few words derived from nouns or verbs sit somewhere between compounds and derivational morphemes. An example is -allonda, from allèlönda “naming”. This one works a bit like English “-onomy”: palallonda “astronomy”. Another is -prèllönda, more like “-ology”: ondaprèllönda “audiology”. Finally, -benda and -bekön, from bejë-, work like “-ism” and “-ist”: potsorbekön “atheist” (po- + tsor + -bekön).

Make some words

As before, these aren’t all of the available derivations for Ardari. They’re enough to get started though, and they’re enough to accomplish our stated goal: creating lots of words!

Both of our conlangs have a wide variety of ways to construct new words without having to resort to full-on coinages. We’ll start with Isian, as always, since it tends to be the simpler of the two.

Isian compounds

Isian is a bit more like German or Swedish than English, in that it prefers compounds of whole words rather than tacking on bound affixes. That’s not to say the language doesn’t have a sizable collection of those, but they’re more situational. Compounding is the preferred way of making new terms.

Isian compounds are mostly head-final, and the most common by far are combinations of two or more nouns:

• hu “dog” + talar “house” → hutalar “doghouse”
• acros “war” + sam “man” → acrosam “soldier” (“war-man”)
• tor “land” + domo “lord” → tordomo “landlord”

Note that acrosam shows a loss of one s. This is a common occurrence in Isian compounds. Anytime two of the same letter would meet, they merge into one. (In writing, they might remain separate.) Two sounds that “can’t” go together are instead linked by -r- or -e-, whichever fits better.

Adjectives can combine with nouns, too. The noun always goes last. Only the stress patterns and the occasional added or deleted sound tell you that you’re dealing with a compound rather than a noun phrase:

• sush “blue” + firin “bird” → sufirin “bluebird”
• bid “white” + ficha “river” → bificha “rapids” (“white river”)

In the latter example, which shows elision, the noun phrase “a white river” would be ta bid ficha, with bid receiving its own stress. The compound “some rapids” is instead ta bificha, with only one stress.

Most verbs can’t combine directly with anything else; they have to be changed to adjectives first. A few “dynamic” verbs, however, can be derived from wasa “to go” plus another verb. An example might be wasotasi “to grab”, from otasi “to hold”.

Changing class

Isian does have ways of deriving, say, a noun from an adjective. The language has a total of eight of these class-changing morphemes that are fairly regular and productive. All of them are suffixes, and the table below shows their meaning, an example, and their closest English equivalent.

Suffix	Function	English	Example
-do	State adjective from verb	-ly	ligado “lovely”
-(t)e	Verb from noun	-fy	safe “to snow”
-el	Adjective from noun	-y, -al	lakhel “royal”
-m	Agent noun from verb	-er	ostanim “hunter”
-mer	Adjective from verb	-able	cheremer “visible”
-nas	Abstract noun from verb	-ance	gonas “speech”
-(r)os	Noun from adjective	-ness	yaliros “happiness”
-(a)ti	Verb from adjective	en-	haykati “to anger”

For the most part, these can’t be combined. Instead, compounds are formed. As an example, “visibility” can be translated as cheremered “visible one”, compounding cheremer with the generic pronoun ed.

-do is very commonly used to make compounds of verbs (in the form of gerund-like adjectives) and nouns. An example might be sipedototac “woodcutting”, from which we could also derive sipedototakem “woodcutter”.

More derivation

The other productive derivational affixes don’t change a word’s part of speech, but slightly alter some other aspect. While the class-changers are all suffixes, this small set contains suffixes, prefixes, and even a couple of circumfixes. (We already met one of those in the Babel Text, as you’ll recall.)

• -chi and -go are diminutive and augmentative suffixes for nouns. Most nouns can take these, although the meanings are often idiosyncratic. For example, jedechi, from jed “boy”, means “little boy”, and secago “greatsword” derives from seca “sword”.

• -cat, as we saw in the Babel Text, turns a noun into a “mass” noun, one that represents a material or some other uncountable. One instance there was gadocat “brick”, meaning the material of brick, not an individual block.

• a-an was also in the Babel Text. It’s a circumfix: the a- part is a prefix, the -an a suffix. Thus, we can make ayalian “unhappy” from yali “happy”.

• Two other productive circumfixes are i-se and o-ca, the diminutive and augmentative for adjectives, respectively. With these, we can make triplets like hul “cold”, ihulse “cool”, and ohulca “frigid”.

• The prefix et- works almost exactly like English re-, except that you can put it on just about any verb: roco “to write”, eteroco or etroco “to rewrite”.

• ha-, another verbal prefix, makes “inverse” forms of verbs. For example, hachere might mean “to not see” or “to miss”. It’s different from the modal adverb an.

• mo- is similar in meaning, but it’s a “reverse”: mochere “to unsee”.

That’s not all

Isian has a few other derivation affixes, but they’re mostly “legacy”. They aren’t productive, and some of them are quite irregular. We’ll meet them as we go on, though. For now, it’s time to switch to Ardari.

By this point in the series, we’ve made quite a few words, but a “real” language has far more. English, for instance, is variously quoted as having anywhere from 100,000 to over a million different words. How do they do it? Up to now, we’ve been creating words in our conlangs in a pretty direct manner. Here’s a concept, so there’s a word, and then it’s on to the next. But that only takes you a very short way into a vocabulary. What we need is a faster method.

Our words so far (with a few exceptions) have been roots. These are the basic stock of a language’s lexicon, but not its entirety. Most languages can take those roots and construct from them a multitude of new, related words. This process is called derivation, and it might be seen as one of the most powerful weapons in the conlanger’s arsenal.

How to build a word

Derivation is different from inflection. Where inflection is the way we make roots into grammatically correct words, derivation is more concerned with making roots into bigger roots. These can then be inflected like any other, but that’s for after they’re derived.

The processes of derivation and inflection, however, work in similar ways. We’ve got quite a few choices for ways to build words. Here are some of the most common, with English examples where possible.

• Prefixes: morphemes added to the beginning of a root; “un-” or “anti-“.
• Suffixes: morphemes added to the end of a root; “-ize” and “-ly”.
• Compounding: putting two or more roots together to make a new one; “football” or “cellphone”.
• Reduplication: repeating part or all of a root; “no-no”, “chit-chat”.
• Stress: changing the stress of a root; noun “permit” and verb “permit“.

Stem changes (where some part of the root itself changes) are another possibility, but these are more common as inflections in English, as in singular “mouse” versus plural “mice”. Tone can be used in derivation in languages that have it, though this seems to be a little rarer.

Also, although I only listed prefixes and suffixes above, there are a few other types of affixes that sometimes pop up in derivation. Infixes are inserted inside the root; English doesn’t do this, except in the case of expletives. Circumfixes combine prefixes and suffixes, like German’s inflectional ge-t. The only English circumfix I can think of is en-en, used to make a few verbs like “enlighten” and the humorous “embiggen”. Finally, many languages’ compounds contain a linking element. German has the ubiquitous -s-, and English has words like “speedometer”.

Derivations of any kind can be classified based on how productive they are. A productive derivation is one which can be used on many words with predictable results. Unproductive derivations might be limited to a few idiosyncratic uses. These categories aren’t fixed, though. Over time, some productive affixes can fall out of fashion, while unproductive ones become more useful due to analogy. (“Trans-” is undergoing the latter transformation—ha!—as we speak, and some are pushing for wider use of the near-forgotten “cis-“.)

Isolating languages are a special case that deserves a footnote. Since the whole point of such a language is that words are usually simple, you might wonder how they can have derivation. Sometimes, they will allow a more “traditional” derivation process, typically compounding or some sort of affix. An alternative is to create phrases with the desired meaning. These periphrastic compounds might be fixed and regular enough in form to be considered derivations, in which case they’ll follow the same rules.

What it means

So we have a lot of ways to build new words (or phrases, for the isolating fans out there) out of smaller parts. That’s great, but now we need those parts. For compounds, it’s pretty easy, so we’ll start with those.

Compounding is the art of taking two smaller words and creating a larger one from them. (And it is indeed an art; look at German if you don’t believe me.) This new word is somehow related to its parts, but how depends a lot on the language. It can be nothing more than the sum of its parts, as in “input-output”. Or the compound may express a subset of one part, like “cellphone”.

Which words can be compounded also changes from language to language. Putting two nouns together (“railroad”) is very common; which one goes first depends, and it’s not always as simple as head-first or head-final. Combinations of two verbs are rarer in Western languages, though colloquial English has phrasal compounds like “go get” and “come see”. Adjective-noun compounds are everywhere in English: “redbird”, “loudspeaker”, and so on.

Verbs and nouns can fit together, too, as they often do in English and related languages. “Breakfast” and “touchscreen” are good examples. Usually, these words combine a verb and an object into a new noun, but not always. Instrumental compounds can also be formed, where the noun is the cause or means of the action. In English, these are distinguished by being noun-verb compounds: “finger-pointing”, “screen-looking”. They start out as gerunds (hence the -ing), but its trivially easy to turn them into verbs.

Really, any words can be compounded. “Livestreaming” is an adjective-verb compound. “Aboveboard” combines a preposition and a noun. The possibilities are endless, and linguistic prescription can’t stop the creative spirit. You don’t even have to use the whole word these days. “Simulcast”, “blog”, and the hideous “staycation” are all examples of “blended” compounds.

All the rest

Compounds are all made from words or, more technically, free morphemes. Most of the other derivational processes work by attaching bound morphemes to a root. Some of these are highly productive, able to make a new word out of just about anything. Others are more restricted, like the rare examples of English reduplication.

Changing class

Most derivations of this type change some part of a word’s nature, shifting it from one category to another. English, as we know, is full of these, and its collection makes a good, exhaustive list for a conlanger. We’ve got -ness (adjective to noun), -al (noun to adjective), -fy (noun to verb), -ize (adjective to verb), -able (verb to adjective), and -ly (adjective to adverb), just to name a few. Two special ones of note are -er, which changes a verb to an agent noun, and its patient counterpart -ee.

In general, a language with a heavy focus on derivation (especially agglutinative languages) will have lots of these. One for each possible pair isn’t out of the question. Sometimes, you’ll be able to stack them, as in words like “villification” (noun to verb and back to noun) or “internationalization” (noun to adjective to verb to noun!).

Changing meaning

Those derivations that don’t alter a lexical category will instead change the meaning of the root. We’ve got a lot of options here, and English seems happy to use every single one of them. But we’ll look at just a few of them here. Most, it must be said, were borrowed from Latin or Greek, starting a couple hundred years ago; these classical languages placed a much heavier emphasis on agglutination than English at the time.

Negation is common, particularly for verbs and adjectives. In English, for example, we’ve got un-, non-, in-, dis-, de-, and a-, among others. For nouns, it’s usually more of an antonym than a negation: anti-.

Diminutives show up in a lot of languages, where they indicate “smallness” or “closeness” of some sort. Spanish, for instance, has the diminutive suffix -ito (feminine form -ita). English, on the other hand, doesn’t have a good “general” diminutive. We’ve got -ish for adjectives (“largish”) and -y for some nouns (“daddy”), but nothing totally regular. By a kind of linguistic analogy, diminutives often have high, front vowels in them.

Augmentatives are the opposite: they connote greatness in size or stature. Prefixes like over-, mega-, and super- might be considered augmentatives, and they’re starting to become more productive in modern English. By the same logic as above, augmentatives tend to use back, low vowels.

Most of the others are concerned with verbal aspect, noun location, and the like. In a sense, they replace adverbs or prepositions. Re-, for example, stands in for “again”, as pre- does for “before”. And then there are the outliers, mostly borrowed from classical languages. -ology and -onomy are good examples of this.

Non-English

We’ve heavily focused on English so far, and that’s for good reason: I know English, you know English, and it has a rich tradition of derivation. Other languages work their own ways. The Germanic family likes its compounding. Greek and Latin had tons of affixes you could attach to a word. Many languages of Asia, Africa, and the Pacific have very productive reduplication. Although I used English examples above, that’s no reason to slavishly follow that particular language when constructing your own.

In the next two posts, we’ll see how Isian and Ardari make new words. Each will have its own “style” of derivation, but the results will be the same: near-infinite possibilities.

For the first time in this series, not only will we be able to treat Isian and Ardari in the same post, but we’ll actually look at them at the same time. We can do this thanks to the similarity in the way they treat numerals. Sure, there are differences, and we’ll see those as we go, but the highlights don’t change that much from the “simple” Isian to the “complicated” Ardari.

The numerals

First off, both conlangs use a decimal system, like most languages in common use today. Both are based around the number ten, but in slightly different ways. Ardari is a more “pure” decimal language, although it has a little bit of vigesimal contamination; Isian, on the other hand, likes to work with hundreds for larger numbers. Although that may sound odd, think about how we do it in English: a million is a thousand thousands, a billion a thousand millions, and so on.

Before we get to the meaty grammar bits, here’s a table of numeral words in both conlangs. It shows all numerals up to twenty, all the multiples of ten up to a hundred, and a few selections to illustrate the numbers in between.

Number	Isian	Ardari
1	yan	jan
2	naw	wegh
3	choy	dwas
4	khas	fèll
5	gen	nibys
6	hod	sald
7	sowad	chiz
8	nicul	ghòt
9	pir	ang
10	pol	kyän
11	poloyan	vänja
12	polonaw	braj
13	polochoy	kyävidas
14	polokhas	kyävèll
15	pologen	kyuni
16	polohod	kyävisald
17	polosowad	kyävichiz
18	polonicul	kyävijòt
19	polopir	kyäveng
20	nopolic	darand
21	nopoloyan	darandvi jan
22	nopolonaw	darandvi wegh
30	choypolic	dwaskyän
33	choypolochoy	dwaskyänvi dwas
40	khaspolic	wedarand
50	gempolic	byskyän
60	hobolic	dwasrand
70	subolic	chiskyän
80	nilpolic	fèldarand
90	pirpolic	änkyän
100	cambor	grus

In both languages, the default form of a numeral is as an adjective. For Ardari, this requires adjective inflection for the first four, including changing for the gender of their head nouns. On the Isian side, every number but yan “one” will have a plural head noun, but there is otherwise nothing to worry about.

We can use numerals directly as nouns in Ardari, just like any adjective, but we can’t in Isian, since it doesn’t allow adjectives without head nouns. Instead, we can use the “dummy” noun at: naw at “two things”. (For “one”, we’d use the singular yan a.)

Creating higher numbers in Ardari is, surprisingly, fairly straightforward. As you can see in the table above, numbers like 21 are constructed using the linking conjunction -vi, which appears on everything but the last noun or adjective in the phrase. Thus, darandvi jan is literally “twenty and one”. This pattern extends throughout the system: 123 is grusvi darandvi dwas.

In Isian, things get a little hairier. Up to 109, you take the “tens” numeral, strip off the final -ic, add on a linking -o-, and add the “ones” numeral: nopolic “twenty” plus yan “one” equals nopoloyan “twenty-one”. Past that, you have to make a phrase like polopir cambor at wa nilpolochoy “1,983”, but this takes you all the way to 9,999.

For positively huge numbers, you need more numerals. Isian has two native higher powers: jagor “ten thousand” and ilicor “million”, which can be used just like cambor “hundred”. As an example, the large number 1,048,576 would be represented in Isian by the mouthful ilicor at wa khas jagor at wa nilpologen cambor at wa subolohod. Yes, our way looks more compact, but imagine writing it out.

Ardari instead has separate words for each power of ten up to a million: ulyad “thousand”, minyir “ten thousand”, ovòd “hundred thousand”, and akrèz “million”; these can be “stacked” into a -vi phrase with the others. Our same example in the paragraph above, 1,048,576, then becomes akrèzvi fèll minyirvi ghòt ulyadvi nibys grusvi chiskyänvi sald. (As a shorter alternative, one can simply recite the digits in order, putting yvi before the last: jan zu fèll ghòt nibys chiz yvi sald.)

That last example shows the Ardari word for zero, zu. Isian has one, too: anca. However, it has an added wrinkle in that it doesn’t work the same way as the other numerals. To say “zero” as a noun, instead of using anca at “zero things”, you say anocal, the Isian word for “nothing”.

Our number is up

That’s all there is to it for counting numerals in our conlangs. They’re fairly simple, mostly because I stuck to a decimal number system. If you want to use something more “exotic”, like base-12, well, have fun with that. I’ve tried, and it’s a lot harder than it looks. Still, the “dozenal” people don’t seem to mind. Also, there’s a lot of grammar stuff I could have added, and we haven’t covered ordinal numbers, but those can come later. We can count in our languages now, and that’s good enough for the time being.

After learning how to speak, counting is one of the first things children tend to figure out, for obvious reasons. And language is set up to facilitate learning how to count, simply because it’s such an important part of our existence as human beings. The familiar “one, two, three” of English has its counterparts around the world, though each language has its own way of using them.

These numerals will be our focus today. (Note that we can’t really call them numbers in a linguistic context, because we’re already using the term “number” for the singular/plural distinction.) Specifically, we’ll look at how different languages count with their numerals; in math terms, these will be the cardinal numbers. In a later post, we can add in the ordinal numbers (like “first” and “third”), fractions, quantities, measurements, and all that other good stuff. For now, let’s talk about counting.

Oh, and since numerals lie at a kind of intersection of linguistics and mathematics, it’ll help if you’re familiar with a few concepts from math. While we won’t be going into things like positional number systems—I’ll save that for a post about writing systems, far into the future—the concept of powers will be important. More information shouldn’t be that hard to find on the Internet, so I’ll leave that in your capable hands.

Count the ways

How a language counts is highly dependent on its culture. Remember that counting and numeral words predate by far the invention of writing. Now think about how you can count if you can’t write. One of the best ways is by using parts of your body. After all, it’s always with you, unlike a collection of stones or some other preliterate method. Thus, bodily terms often pop up in the context of numerals.

In fact, that’s one of the simplest methods of creating numerals: just start numbering parts of your body. A few languages from Pacific islands still use this today, and it’s entirely possible that it’s how all ancestor languages did it. Words for the fingers of one hand usually cover 1-4, with the thumb standing for 5. After that, it depends on the language. Six could be represented by the word for the palm or wrist, and larger numbers by points further up the arm. In this way, you can continue down the opposite arm, to its hand, and then on to the rest of the body.

Once you need to work with larger numbers, however, you’ll want a better way of creating them. The “pointing” method is inefficient—you need to remember each point on the body in order—and there are only so many body parts. This is fine for a hunter-gatherer society, and many of those have a very small selection of numerals (anywhere from one to five), using a word for “many” for anything higher. But we “advanced” peoples do need to refer to greater quantities. The solution, then, is to use a smaller set of numerals and construct larger ones from that. That’s how we do it in English: “twenty-five” is nothing more than “twenty” plus “five”.

For our language, the key number is 10. Every number up to this one has its own numeral, while larger ones are mostly derived. The only exceptions are words like “hundred” and “thousand” which, incidentally enough, represent higher powers of 10. Thus, we can say that English uses base-10 counting—or decimal, if you prefer fancier words.

At the base

Every language with a system of numeral words is going to have a numerical base for that system. Which number is used as the base really has a lot to do with the history of the language and how its people traditionally counted. Not every number is appropriate as a base; Douglas Adams once said that nobody makes jokes in base-13, and I can state with confidence that nobody counts in it, either. Why? Because 13 is awkward. It’s a prime number with essentially no connection to any part of the body. Since counting probably originated with body parts, there’s no reason for a culture to ever develop base-13 counting. Other numbers, though, are quite suitable.

• Decimal (base-10) counting is, far and away, the most common in the world. Look at your hands, and you’ll see why. (Unless, of course, you don’t have ten fingers.) Counting in decimal is just the finger counting most of us grew up with, and decimal systems tend to have new words for higher powers of 10. In English, we’ve got “hundred” and “thousand”, and these are pretty common in other decimal languages. For “ten thousand”, we don’t have a specific native word, but Japanese (man) and Ancient Greek (myrioi) do; the latter is where we get the word “myriad”.

• Vigesimal (base-20) is not quite as widespread as decimal, but it has plenty of supporters. A few European languages use something like base-20 up to a certain point—one hundred, in fact—where they switch to full decimal. But a “true” vigesimal system, using powers of 20 instead of 10 (and thus having separate words for 400, 8,000, etc.), can be found in Nahautl (Aztec) and Maya, as well as Dzongkha, in Bhutan. Like decimal, vigesimal most likely derives from counting, but here it would be the fingers and the toes.

• Quinary (base-5) turns up here and there, particularly in the Pacific and Australia. Again, it comes from counting, but this time with only one hand. It’s far more common for 5 to be a “sub-base” in a greater decimal system; in other words, 10 can be “two fives”, but 20 is more likely to be “two tens”. The alternative, where the core terms are for 5, 25, 125, and so on, doesn’t seem to occur, but there’s no reason why it can’t.

• Duodecimal (base-12) doesn’t appear to have an obvious body correlation, but it actually does. Using the thumb of one hand, count the finger bones on that hand. Each finger has three of them, and you’ve got four non-thumb fingers: 3 × 4 = 12. There are a few languages out there that use duodecimal numerals (including Tolkien’s Quenya), but base-12 is more common in arithmetic contexts, where its multiple factors sometimes make it easier to use than decimal. Even in English, though, we have the “dozen” (12) and “gross” (144).

• Other numbers are almost never used as the “primary” base in a language, but a few can be found as “auxiliary” bases. Base-60 (sexagesimal), like our minutes and seconds, is entirely possible, but it will likely be accompanied by decimal or duodecimal sub-bases. Some languages of Papua New Guinea and thereabouts use a quaternary (base-4) system or, far more rarely, a senary or base-6 system. Octal (base-8) can work with finger counting if you use the spaces between your fingers, and a couple of cultures do this. And, of course, it’s easy to imagine an AI using octal, hexadecimal (base-16), or plain binary (base-2).

Word problems

In general, numerals up to the primary base are all going to be different, as in English “one” through “ten”. A few powers of the base will also have their own words, but this will be dependent on how often the speakers of a language need those higher numbers. “Hundred” and “thousand” suffice for many older cultures, but the Mayans could count up to the alau, 20⁶ or 64 million, China has native terms up to 10¹⁴ (a hundred trillion), and the Vedas have lots of terms for absurdly large numerals.

No matter what the “end” of the scale, most of the numbers in between will be somehow derived. Again, the more often numbers are used, the more likely they’ll acquire specific terms, but special forms are common for multiples of the base up to its square (100 in decimal, 400 in vigesimal, and so on), like our “twenty” or “eighty”. Intermediate numbers will tend to be made from these building blocks: multiples and powers of the base. How they’re combined is up to the language, but the English phrasing, for once, is a pretty good guide.

Some languages work with a secondary base, and these may affect the way numeral words work. Twelve and twenty can almost be considered sub-bases for English with words like “dozen” and the peculiar method of constructing numbers in the teens. Twenty is a stronger force in other European languages, though. French is an example here, with 80 being quatre-vingts, literally “four twenties”. In contrast, a full vigesimal system can function just fine with the numeral for twelve derived as “ten and two”, using 10 as a sub-base, although I’m not aware of an example. Any factor can also work as a sub-base, especially in base-20, where 4 and 5 both work, or base-60, where you can use 6 and 10.

Irregularity is everywhere in natural languages, and that includes numerals. There always seem to be a few outliers that don’t fit the pattern. English has “eleven” and “twelve”, of course; it gets them from Germanic, as do many of its cousins. Spanish, among others, has veinte for 20, whereas other multiples of ten are constructed fairly regularly from their “ones” (treinte, etc.). Other examples abound.

Fitting in

How numeral words fit into a language is also a major variable. Sometimes, they’re a separate part of speech. Or they can be adjectives. Or nouns. Or some combination of all three. If they’re adjectives or nouns, then they may or may not participate in the usual grammar. Latin, for instance, requires small numerals (up to four) to be inflected, but everything larger is largely fixed in form. English lets numerals act as adjectives or nouns, as needed, and some dialects allow nouns following adjectival numerals to ignore grammatical number (“two foot of rope”, “eight head of cattle”). It’s really a mess most everywhere.

For a conlang, it’s going to come down to the necessities. Auxlangs, as always, need to be simple, logical, and reasonable, so it’s best not to get too crazy, and this extends to all aspects of numerals. You’re not going to get many followers if you make them start counting by dozens! (Confession time. I did this for a non-auxlang over ten years ago, and I still forget it uses duodecimal sometimes! Imagine how that would be for a language intended to be spoken.)

Fictional languages get a little bit of a pass. Here, it’s okay to go wild, as long as you know what you’re doing. Non-decimal bases are everywhere in conlangs, even in “professional” ones like Tolkien’s. With non-humans, you get that much more rope to hang yourself with. Four-fingered aliens (or cartoon characters) would be more likely to reckon in an octal system than a decimal one. Depending on how their digits are made, you could also make a case for base-6 or base-9, by analogy with Earthly octal and duodecimal finger counting. Advanced races will be more likely to have a sophisticated system of higher powers, like our billion, trillion, etc. And so on.

More than any other part of this series, numerals are a part of a culture. If you’re making a conlang without a culture—as in an auxlang—then think of who the speakers will be, and copy them. Otherwise, you might need to consider some of the aspects of your fictional speakers. How would they count? How would they think of numbers? Then you can start making your own.