Number and Time

1. Numerals

1.1 Introduction

Although much of Labbé's 17th century "Lingua Universalis" was a posteriori, the numerals were distinctly a priori, thus:

	1	2	3	4	5	6	7	8	9
× 1	sa	se	si	so	su	sou	sœ	va	ve
× 10	vi	vo	vu	vou	vœ	xa	xe	xi	xo
× 100	xu	xou	xœ	za	ze	zi	zo	zu	zou

… and last but not least zœ = 1000!

Even in the next century, we find Faiguet's "Langue Novelle" continued the a priori numeral tradition: ba 1; co 2; de 3; ga 4; ji 5; lu 6; ma 7; ni 8; pa 9; vu 10. The tens 20 … 90 are formed by compounds cove … pave; then we return to the a posteriori world with sinta 100, and mila 1000.

19th century Volapük remained largely a priori: bal 1; tel 2; kil;3 fol (← English: four) 4; lul 5; mäl 6; vel 7; jöl 8; zul 9; bals 10, tels 20 etc. Even 100 remains a priori tum; but 1000 is mil, while 1 000 000 (million) is the mixed balion! We find similar a priori systems in other languages related to Volapük. Perhaps the most bizarre was G. Bauer's "Spelin" where the numera;s 1 … 9 are constructed systematically by 3 vowels (i = 1, e = 2, a = 3) and 3 consonants (k = +0, n = +3, p = +6), thus: ik 1, ek 2, ak 3; in 4, en 5, an 6; ip 7, ep 8, ap 9!

But Schipfer's "Communicationssprache" of 1839 had completely a posteriori numerals as, indeed, did several author 19th century auxlangs, such as L. de Rudelle's "Pantos-Dimou-GLossa" (1858), Pirro's "Universal-Sprache" (1868), A. Volk and R. Fuchs's "Weltsprache" (1883) inter alia, as well as, of course, "Esperanto" (1887).

So what did Dr Outis do?

1.2 Zero

The ancient Greeks and Romans did not have the concept of zero and hence did not show it in the numeral systems and had no word for it. So Dr Outis could not go directly to ancient Greek for this. But the western Arabic numeral that we use had been introduced into Europe during the Middle Ages and were well established by the 16th century.

Nevertheless, neither Labbé in his "Lingua Universalis" nor Faiguet in his 18th century "Langue Nouvelle" give a word for zero.

The symbol for zero was called ṣifr in Arabic; the Italian mathematician, Leonardo Fibonacci (c.1170–1250), who is credited with introducing the Arabic numerals and decimal system to Europe, used the term zephyrum, a rendering of the Arabic under the influence of Latin zephyrus "west wind" ← ζέφυρος (zépʰuros). We find that Dr Outis was well aware of this and rendered the symbol and the mathematical concept zero as zeur. But it does not otherwise form any part of number system; he did not, e.g. derive forms for zero(e)th, zero times, zerofold etc.

1.3 Outidic cardinal numbers (1 … 999)

We saw on the Nouns and Adjectives page that pen = 5, which is obviously from πέντε (pénte). But because of limitations Dr Outis had put on the phonetic shape of his root words, a straight a posteriori borrowing from Greek could not be done. What we find are a basic set of bound morphemes for numbers 1 … 9, namely: mo- 1; deu- 2; tri- 3; tra- 4; pe- 5; kse- 6; psa- 7; kso- 8; ne- 9.

Dr Outis formed hundreds, tens and units by suffixing -kat, -kon and -n respectively, thus:

units	mon 1	deun 2	trin 3	tran 4	pen 5	ksen 6	psan 7	kson 8	nen 9
tens	mokon 10	deukon 20	trikon 30	trakon 40	pekon 50	ksekon 60	psakon 70	ksokon 80	nekon 90
hundreds	mokat 100	deukat 200	trikat 300	trakat 400	pekat 500	ksekat 600	psakat 700	ksokat 800	nekat 900

Other numbers up to 999 are formed by placing the higher number before the lower one without any conjunction; Dr Outis wrote them with hyphens, e.g.
11, 12, 13 etc = mokon-mon, mokon-deun, mokon-trin etc.
24 = deukon-tran; 36 = trikon-ksen; 87 = ksokon-psan; 99 = nekon-nen etc.
101 = mokat-mon; 204 = deukat-tran; 350 = trikat-pekon; 738 = psakat-trikon-kson etc.

We have noted that Dr Outis was familiar with several European languages and also had some knowledge of Turkish (this, of course, would have been Ottoman Turkish written in a variant of the Arabic adjad; he lived some three centuries before Atatürk changed all that). It is possible, also, that he had some knowledge of Welsh as well, though the evidence is not entirely clear on this point. But he does clearly state that the plural suffix -as is redundant when numbers are used and the noun should have no plural suffix, e.g. tran kun = four dogs; ekat-deukon-pen paid = 125 children.

However, the plural suffix is used in partitive expressions, cf.

• trin-em kun = my three dogs
• trin ke kunas-em = three of my dogs.

1.3.1 Note on etymology

• The prefix mo- is a back formation from μόν- (món-), stem of μόνος (mónos) "alone, single" and in compounds μονο- (mono-) = "one." One might have expected the prefix for two to have been *du- but dun is the subjunctive of dunai ← δύνασθαι (dúnastʰai) "to be able". Dr Outis, therefore, chose to take the e-grade of the stem which is found in δεύτερος (deúteros) second. The prefixes tri- ← τρία (tría), tra- ← τέτταρα (téttara) also bound morpheme τετρα- (tetra-), pe- ← πέντε (pénte) and ne- ← ἐννέα (ennéa) are quite obvious; and kse- ← ἕξ (ʰeks) shows his fondness for metathesis in deriving Outidic morphemes. Both psa- and kso- were presumably adapted from second, and accented, syllable of the Greek ἑπτά (ʰeptá) and ὀκτώ (oktṓ).
• The suffix -n for the units is a back formation both from μόν- (món-) "one" and pen (for both, see above).
• The suffix for multiples of 10 are from Greek -κοντα (-konta) [indeclinable] that one finds on the multiples of ten from τριάκοντα (triákonta) through to ἐνενήκοντα (enenḗkonta).
• One might then have expected Dr Outis to have *-kos for the multiples of 100, since the suffix in Greek for 200 … 900 is -κόσια (-kósia) [n.pl]; but he rejected this, feeling it was too reminiscent of the ending -κοστ- (-kost-) of 20th .. 90th. Also he felt that the Outidic suffix for ×100 should more distinct than the one for ×10. The suffix -kat was suggested both by ἑκατόν (ʰekatón) a hundred, and -κάτια (-katia) [n.pl.] suffix of the western Greek dialects for multiples of 100.

1.4 Outidic cardinal from 1000 and above

The word for a thousand is kil ← χίλια (kʰilia) [n.pl]. But this is not used as a numeric suffix in Outidic; it is always a stand-alone word; e.g. kil drop = a thousand people.

In the ancient language one used a numeral adverb before χίλια for multiples of 1000, e.g. δὶς χίλια (dis kʰilia) = twice a thousand (2000), τρὶς χίλια (tris kʰilia) = three times a thousand (3000), τετράκις χίλια (tetrakis kʰilia) = four times a thousand (4000). Dr Outis did exactly the same in his language; we shall find below that such adverbs are formed in Outidic by suffixing -ais; so, for example: trinais kil drop = three thousand people.

More example of large Outidic numbers:
deunais kil mokon-deun = 2012
trakon-penais kil psakat-trin = 45 703
nekat-penais kil trikat-ksekon = 905 360
nekat-nekon-nenais kil nekat-nekon-nen 999 999.

As for millions, billions etc, these terms could have been known to both Labbé and Dr Outis in the 17th century. The neo-Latin millio (genitive: millionis) is attested from the 13th century, being derived from Italian milione "large thousand."

In the 15th century the French mathematician Jehan Adam coined the words bymillion and trimillion for a 10¹² (million millions) and 10¹⁸ (million bymillions) respectively. Later in the same century another Frenchman, Nicolas Chuquet, shorten the words to billion and trillion and also introduced quadrillion, quyllion, sixlion, septyllion, ottyllion, and nonyllion where trillion = 1000 000³, quadrillion = 1000 000⁴ … nonyllion = 1000 000⁹, i.e. "long scale" values, since it had been the custom to break up long numbers into groups of six digits, not three as we customarily do today.

By the 17th century, it was being felt that a shorter grouping than six digits would be more practical. Dr Outis did think about adopting the Greek μύρια (múria) ten thousand (myriad) and breaking up long numbers into groups of four; but he considered that million was now in "universal usage" and myriads would not fit into a system which used millions. He, therefore, contented himself with mur ← μυρίος (muríos) = numberless, countless, and pondered what to do with million and higher numbers. If he had known that the Chinese, Japanese and others in eastern Asia used the myriad system, he might have acted differently.

It was in 17th century Europe that the custom of breaking up long numerical expressions into groups of three digits began to become common and some French and Italian scientists began using what we know as the "short scale", i.e billion = thousand millions. It would appear that Dr Outis was aware of this development.

However, he thought that calquing billion, trillion etc as *deukil, *trikil etc was not satisfactory as these could be misunderstood as 2000, 3000 etc. Using forms like *kildeu, *kiltri etc he discounted as they produced awkward consonant combinations (cf. *kilkse) and "prefixes should not be suffixes." He hit upon the notion of infixing the 1…9 morphemes in kil, so that, e.g. kimol = a thousand multiplied by itself once, i.e. a miillion; kideul = a thousand multiplied by itself twice, i.e. 1 000 000 000; kitril = a thousand multiplied by itself three times etc.

But he did not actually explain as infixing; rather he re-interpeted kil as being composed of two parts (we would now call them morphemes) in which ki- signified '1000 multiplied by' and Nl signified 'by a 1000 N times'. So according to Dr Outis' way of thinking kil signifies 1000 multiplied by 1000 no number of times, as there was no number specified before -l; whereas, kimol signifies 1000 multiplied once by a thousand (1000 × 1000), and kideul signified 1000 multiplied twice by a thousand (1000 × 1000 × 1000), etc. We may show this in the following table:

n	Multiple of 1000	Short scale	Long scale	Outidic
0	1000 × 10000	thousand	thousand	kil
1	1000 × 10001	million	million	kimol
2	1000 × 10002	billion	thousand million/ milliard	kideul
3	1000 × 10003	trillion	billion	kitril
4	1000 × 10004	quadrillion	thousand billion/ billiard	kitral
5	1000 × 10005	quintillion	trillion	kipel
6	1000 × 10006	sextillion	thousand trillion/ trilliard	kiksel
7	1000 × 10007	septillion	quadrillion	kipsal
8	1000 × 10008	octillion	thousand quadrillion/ quadrilliard	kiksol
9	1000 × 10009	nonillion	quintillion	kinel

It should be emphasized that Dr Outis give no such table as the above. I have deduced it from the few examples he gave. Of course, numeric expression before any of these ki…l words are expressed in exactly the same way as before kil, e.g. deukon-ksenais kimol = twenty six million; trakat-trikon-psanais kideul = 437 billion.

One may ask what comes after kinel. The good Doctor did not even consider it. Indeed, how often do we need to talk about a 'decillion' (or, if using the long scale, a 'thousand quintillion' or 'quintilliard')? Dr Outis in fact mentions no number higher than kitril.

His contemporary Labbé in his "Lingua Universalis" gives zœ (1000) as the highest numeral denoted by a single word. But he did write: "immo & zœzœ, & si opus fuerit, etiam vlterius" (indeed also zœzœ and, if there should be need, even further). Thus we have: zœzœ = million; zœzœzœ = thousand million, billion (short scale); etc. Indeed, in theory Labbé's language allows numbers to be named ad infinitum, which Dr Outis' system does not. But I think Outidic kinel is a little more easily read than zœzœzœzœzœzœzœzœzœzœ!

Dr Outis' development of kil…kinel numbers perhaps reflects the interest in mathematics of this 17th century polymath. Faiguet's "Langue Nouvelle" of the 18th century gives no words for a number greater than a thousand nor gives any indication whether mila (1000) may be repeated in the manner of Labbé's zœ or not. Even in the 19th century many auxlang designers do not seem to go beyond a word for a million. The earliest post-Outidic attempt to deal with "larger numbers" that I am aware of is E. Courtonne's "Néo-Latine" of 1885.

1.5 Adverbs, Ordinals & other derived forms

Above we saw some examples of numeric adverbs ending -ais and saw that the suffix was attached either to a single number or to the last item in a compound, e.g. monais = once; deukon-trinais = 23 times; trakat-ksekonais = 460 times; psakat-psakon-psanais = 777 times; kilais = a thousand times; kimolais = a million times.

The suffix will not be added to any numeric adverb that may precede kil or one of the ki…l numbers, cf. trakon-trinais kil = 430 000 ~ trakon-trinais kilais = 430 000 times.

These rules apply to all the suffixes listed below.

1.5.1 Ordinal numbers

Ordinal numbers are formed by adding the suffix -os (← -οστός -ostós), e.g.
monos = first
psanos = seventh
deukonos = twentieth
ksekon-ksenos = 66th
trakat-nenos = 409th
ksokat-trikon-tranos = 834th
kilos = 1000th
ksokat-trikon-tranak kilos = 834 000th.

1.5.2 N-tuples (single, double, etc.)

These adjectives are formed by adding the suffix -ap, e.g.
monap = single
deunap = double, psanap = sevenfold
deukonap = twentyfold
mokatap = a hundredfold
kilap = a thousandfold.

1.5.3 Collectives

These are nouns denoting a group of so many units are formed by adding the suffix -ad, e.g.
monad = unit, monad
deunad = group of two, a couple, pair, dyad
psanad = group of seven, septet
deukonad = a group of twenty
mokatad = a group of a hundred
kilad = a group of a thousand, a chiliad.

1.5.4 Fractions

Fractions are shown by the suffix -om, e.g.
deunom = half
tranom = a quarter
trin tranom = three quarters
psan mokonom = seven tenths
deukon-trin trikon-deunom = 23/32

2. Time: Day, week, month & year

2.1 Day

mer = day

It seems that mer meant 'day', both in the sense of a 24 hour period and also meaning 'daytime' as opposed to 'night'. The various parts of the 24 hour period are:

tror = dawn deil = afternoon mesunuk mid night

proiz = morning pser = evening

mesumer mid day nuk = night

The Outidic words for the units of time which make up a day are: gor = hour and min = minute. Presumably in the 17th century Dr Outis didn't think that smaller units than a minuted needed bothering about for normal purposes.

Dr Outis gave no formal description of "how to tell the time." The few examples that we come across seem to indicate that:

• Hours were indicated by using ordinary cardinals numbers thus:
  ain trin gor = there are three hours = it is three o'clock.
  Sometimes he adds the partitive expression, ke glog = of the clock, e.g. ain tran gor ke glog = it's four o'clock; also the word gor may be omitted if the context is clear, e.g. ain pen (ke glog) = it's five (o'clock).
• Quarters and half are expressed thus, e.g. ain ksen te tranom (gor) (ke glog) = there are six and a quarter (hours) (of the clock) = it's a quarter past six; ain nen te deunom (gor) (ke glog) = there are nine and a half (hours) (of the clock) = it's half past nine; ain mokon-mon te tran trinom (gor) (ke glog) = there are eleven and three quarter (hours) (of the clock) = it's quarter to twelve.
• Other times are expressed as so many hours and minutes of the clock, e.g. ain trin gor te pen min (ke glog) = there are three hours and five minutes (of the clock) = it's five past three. Just as gor may be omitted if the context is clear, so may min, e.g. ain tren te deukon (ke glog) = it's twenty past four; ain kson te trakon (ke glog) = there are eight and forty (of the clock) = it's twenty to nine.

2.2 Week

blom = week

Dr Outis was aware that for the most part the Romance speaking nations named days after Roman deities and the Germanic speaking nations after Germanic deities, i.e. there was little common currency between the two. But he was aware that the Portuguese had dropped the names of pagan deities and simply numbered the days, except for Sunday (domingo The Lord's day) and Saturday (sabado Sabbath) and he understood the Greeks did much the same.

Dr Outis decided basically to follow the Portuguese model but to extend the numbering to all seven days. To him and, indeed, all his contemporaries in the 17th century there was no question but that Monday was the second day of the week, Tuesday the third etc., as it was not until three centuries later that the International Organization for Standardization would be changing the practice of millennia and prescribed Monday as the first day of the week.

He could, of course, have used forms such as monos mar = first day, deunos mar = second day and so on, but thought that simple compounds wouls be better, thus:
Monumer = Sunday, Deunumer = Monday, Trinumer = Tuesday, Tranumer = Wednesday,
Penumer = Thursday, Ksenumer = Friday, Psanumer = Saturday.

2.3 Month

men = month.

Dr Outis could of course have named the months in a similar way, i.e. Monumem January, Deunumen February … Mokonmonumen November, Mokondeunumem December. But he considered the last two particularly clumsy. Also he noted that the Greek forms of the Latin month names were used at the time of the Roman Empire and that all European peoples (as far as he knew) continued to use names derived from the Latin names. He, therefore, decided to do the same in Outidic, and the months are named thus:

Zan = January	Peb = February	Mar = March
Pril = April	Maiz = May	Zun = June
Zul = July	Gus = August	Pseb = September
Tob = October	Nob = November	Deb = December

Month and day are expressed like the modern British English 1st of May, 4th of July etc. with the word for day 'understood, i.e. the 1st day of May. Dr Outis treated these as partitive constructions, regarding the month names as denoting a set of days, e.g., monos (mer) ke Maiz = 1st (day) of May; tranos ke Zul = 4th of July; deukon-nenos ke Seb = 29th of September; trikon-monos ke Deb = 31st of December.

2.4 Year

net = year.

It has four seasons, and we have already met the word for Winter, namely keim. The other three seasons are:
gair = Spring
ter = Summer
psip = Autumn, Fall.

The years themselves are denoted, as was normal in the 17th century, by an ordinal number, e.g. the 1673th year of the Lord Kur net-ut o kilos ksekat-psakon-trinos. Dr Outis seems to have considered the alternative Kur kilos-ut ksekat-psakon-trinos net to be clumsy and does not use it. However, if Kur (Lord) is omitted, one may have either net o kilos ksekat-psakon-trinos or kilos ksekat-psakon-trinos net.

Appendix: Vocabulary

Reminder:

• For zero and cardinal numbers, see Sections 1.2 through to 1.4
• For ordinal numbers, adverbs and fractions, see Section 1.5
• From days of the week, see Section 2.2
• For months of the year, see Section 2.3

Vocabulary new to this page:

Reminder - Outidic alphabet: A B G D E Z I K L M N O P R S T U

blom = week	mer = day	net = year
gair = Spring [season]	men = month	proiz = morning
glog = clock	mes = middle mesumer = midday, noon mesunuk = midnight	pser = evening
gor = hour		psip = Autumn, Fall
deil = afternoon	min = minute (of time)	ter = Summer
Kur = Lord	nuk = night	tror = dawn