Armin Buch
Numerals
Typology of Number Systems
Bases
Exceptions
Comparative lexical semantics
Numerals, colors, and more
Armin W. Buch1
2012/11/07
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Relying heavily on material by Gerhard Jäger and David Erschler
Colors
Concepts
Lexical semantic maps
Linguistic relativity
Regularities in Numeral Systems
Armin Buch
Numerals
Typology of Number Systems
Bases
Exceptions
Colors
English
ten
twenty
thirty
forty
fifty
sixty
seventy
French
dix
vingt
trente
quarante
cinquante
soixante
soixante dix
Georgian
at-i
oc-i
oc-da-at-i
or-m-oc-i
or-m-oc-da-at-i
sam-[m-]oc-i
sam-[m-]oc-da-at-i
Concepts
Lexical semantic maps
Linguistic relativity
Some irregularities
Armin Buch
Numerals
Typology of Number Systems
Bases
Exceptions
Colors
Concepts
Lexical semantic maps
Linguistic relativity
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French vingt (20) is not obviously connected with dix (10)
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elf/eleven is not obviously connected with 10 either
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Hebrew: esr-im (20) ten-PL
Counting base
Armin Buch
Numerals
Typology of Number Systems
Bases
Exceptions
Colors
Concepts
Lexical semantic maps
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numeral expressions are constructed with multiplication
and addition
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general pattern: x1 + x2 b + x3 b2 + . . .
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with a base b
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four (4) hundred (102 ) fif-ty (5 ∗ 10) six (6)
Linguistic relativity
What is the base in Georgian?
Armin Buch
Numerals
Typology of Number Systems
Bases
Exceptions
Colors
Georgian
at-i
oc-i
oc-da-at-i
or-m-oc-i
or-m-oc-da-at-i
sam-[m-]oc-i
sam-[m-]oc-da-at-i
Concepts
10
20
30
40
50
60
70
Lexical semantic maps
Linguistic relativity
Common bases
Armin Buch
Numerals
Typology of Number Systems
Bases
Exceptions
Colors
Concepts
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Decimal system: base 10 (x100 + y10 + z)
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Vigesimal system: base 20 (x20 + z)
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Hybrid decimal/vigesimal systems: (x100 + y20 + z)
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Practical reason: consistently vigesimal expressions are
very long
Lexical semantic maps
Linguistic relativity
Vigesimal systems
Armin Buch
Numerals
Typology of Number Systems
Bases
Exceptions
Colors
Concepts
Lexical semantic maps
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In Eurasia, vigesimal systems are very common in the
Caucasus (North East Caucasian, North West Caucasian,
South Caucasian, Indo-European: Ossetic)
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Ainu (isolate, nearly extinct, Japan) also used to have a
vigesimal system.
Linguistic relativity
Vigesimal example
Armin Buch
Numerals
Typology of Number Systems
Bases
Exceptions
Colors
Concepts
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Iron Ossetic
Lexical semantic maps
Linguistic relativity
(1)
farašt fonzy-šš5zy 5št-d5š 5m5 dywi-šš5z miny
nine five-twenty eight-ten and two-twenty 1000
syppar fonzy-šš5zy nud5š 5m5 5rti-šš5zy
four five-twenty 19
and three-twenty
‘958,479’
Hybrid decimal/vigesimal systems
Armin Buch
Numerals
Typology of Number Systems
Bases
Exceptions
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Basque
Colors
Concepts
(2)
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(3)
berr-eun
eta berr-ogei-ta-hama-sei
two-hundred and two-twenty-and-ten-six
‘256’
Danish (bankers use base 10!)
seks- og- halv- tred- s(inds- tyve)
6
and half third (times 20)
‘56’ (lit. ‘six and half of the third score’)
Lexical semantic maps
Linguistic relativity
Rare bases
Armin Buch
Numerals
Typology of Number Systems
Bases
Exceptions
Colors
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Base 3: Ambulas (Papua New Guinea)
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Base 4: North America, South America, New Guinea,
Africa
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Probably related to hand-counting by considering the
spaces between the fingers.
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Base 6: New Guinea, probably some African languages
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Base 8: extremely rare
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Base 12: extremely rare
Concepts
Lexical semantic maps
Linguistic relativity
Base 3: Ambulas
Armin Buch
Numerals
Ambulas
nawurak
vétik
kupuk
kupukiva
kupuk’etik
taabak
taabak kaayek
taabak kaayek vétik
taabak kaayek kupik
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Typology of Number Systems
Bases
1
2
3
4
5
6
7
8
9
The etymology of the forms reveal that the system is much
like a commonplace 5-10-20 or 5-20 system except that
the hand is seen as having six features!
Exceptions
Colors
Concepts
Lexical semantic maps
Linguistic relativity
Several bases
Armin Buch
Numerals
Typology of Number Systems
Bases
Exceptions
Colors
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Some languages combine several bases;
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Many "exotic" systems have only relatively low numerals;
Some numerals are formed irregularly:
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Russian sorok 40 is monomorphemic (cf dva-tţatj 20,
tri-tţatj 30, dva 2, tri 3, Ùetyre 4)
Turkish: each of the tens in the range 20–50 is
monomorphemic (yirmi 20, otuz 30, kırk 40, elli 50; cf.
iki 2, üç 3, dört 4, beş 5)
Concepts
Lexical semantic maps
Linguistic relativity
Systems lacking a base
Armin Buch
Numerals
Typology of Number Systems
Bases
Exceptions
Colors
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Extended body-part system, typically found in Highland
New Guinea
Kobon: body parts (left side) are used in order to count
from 1 to 12: little finger, ring finger, middle finger, index
finger, thumb, wrist, middle of forearm, inside of elbow,
middle of upper arm, shoulder, collarbone, hole above
breastbone. The count can then continue down the
right-hand side of the body
Concepts
Lexical semantic maps
Linguistic relativity
Body part counting: Fasu
Armin Buch
Numerals
Typology of Number Systems
Bases
Exceptions
Colors
Concepts
Lexical semantic maps
Linguistic relativity
(Source)
No numbers
Armin Buch
Numerals
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Some languages are reported to altogether lack numbers
above one
Such languages are mostly located in Amazonia and
Papua New Guinea
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Nadëb (Brazil): According to Weir (1984:103f.), the
words for 2 and 3 are inexact.
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And there is always Pirahã
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Gedaged (Oceanic/Austronesian, Papua New Guinea):
Sehr viele Papuas kennen die Zahlwörter ihres
eigenen Dialektes nicht. In Mitebog fragte ich fünf
oder sechs Eingeborene, aber die Angaben waren
widersprechend und jedenfalls unrichtig, nur olam
(eins) konnte ich als sicher notiren [sic!].
(Miklucho-Maclay, cited in: Hammarstroem 2010)
Typology of Number Systems
Bases
Exceptions
Colors
Concepts
Lexical semantic maps
Linguistic relativity
Distribution of numeral systems
Armin Buch
Numerals
Typology of Number Systems
Bases
Exceptions
Colors
Concepts
Lexical semantic maps
Linguistic relativity
(Source: WALS)
Color terms
Armin Buch
Numerals
Typology of Number Systems
Bases
Exceptions
Colors
Concepts
Lexical semantic maps
Linguistic relativity
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see slides by G. Jäger
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also see WALS features 132, 133, 134, 135
Typology of concepts
Armin Buch
Numerals
Typology of Number Systems
Bases
Exceptions
I
Translation of words is not one-to-one
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A typical dictionary entry will list several translations
These words in turn have several translations
Thus between languages, the meaning of words overlap
partially
And within one language, each word may cover a range of
meanings (colexification/polysemy)
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Other words are very specific and cannot be translated (by
a single word!)
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Words are not concepts, concepts are not words
Colors
Concepts
Lexical semantic maps
Linguistic relativity
Polysemy
Armin Buch
Numerals
Typology of Number Systems
Bases
Exceptions
Colors
Concepts
Lexical semantic maps
Linguistic relativity
I
Polysemies are somewhat arbitrary, but certain concepts
share a single word more often than others (river/stream,
acid/sour)
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This can be studied cross-linguistically
Examples of colexification associated with
Armin Buch
BREATHE
Numerals
Typology of Number Systems
Bases
Exceptions
Colors
BREATHE
take a rest
be on vacation
cease to do
(wind) blow
(s.o.) blow
whisper
utter, speak
E NGLISH
breathe
+
[+]
RUSSIAN
du[x]
+
[+]
[+]
+
+
+
+
[+]
[+]
M WOTLAP
mōkheg
+
+
+
N ÊLÊMWA
horêân
+
+
A RAKI
soRo
Concepts
F RENCH
souffler
Lexical semantic maps
Linguistic relativity
+
+
+
[+]
(Francois 2010)
+
+
+
+
+
+
+
Armin Buch
Numerals
Typology of Number Systems
Bases
Exceptions
Colors
Concepts
Lexical semantic maps
Linguistic relativity
Figure: Graphical representation of above table (Francois 2010)
Lexical semantic maps
Armin Buch
Numerals
Typology of Number Systems
Bases
Exceptions
Colors
Concepts
Lexical semantic maps
A semantic map is a geometrical representation of
functions in ‘conceptual/semantic space’ that are
linked by connecting lines and thus constitute a
network.
(Haspelmath, 2003:213)
Linguistic relativity
Armin Buch
Numerals
Typology of Number Systems
Bases
Exceptions
Colors
Concepts
Lexical semantic maps
Linguistic relativity
Figure: Semantic map for breathe (Francois 2010, cited in Annis
2012)
Armin Buch
Numerals
Typology of Number Systems
Bases
Exceptions
Colors
Concepts
Lexical semantic maps
Linguistic relativity
Figure: Common polysemies in some African languages, plus French
and English Perrin (2007)
Linguistic synaesthesia
Armin Buch
Numerals
Typology of Number Systems
Bases
Exceptions
Colors
Concepts
Lexical semantic maps
Linguistic relativity
(Annis, 2012)
The Great Eskimo Vocabulary Hoax
Armin Buch
Numerals
Typology of Number Systems
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The more important a concept, the further it will be
subdivided
Original example: It is plausible to think that the Inuit
have several words for snow (Boas; Whorf, 1940)
By now, the quoted number has reached 100-200
Discounting morphology, there are 4 different roots in one
language:
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aput: snow on the ground
qana: falling snow
piqsirpoq: drifting snow
qimuqsuq: a snowdrift
cf. English: blizzard, flurry, pack, slush, drift, sleet, and
powder
Bases
Exceptions
Colors
Concepts
Lexical semantic maps
Linguistic relativity
German words for snow
Armin Buch
Numerals
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Neuschnee (maximal drei Tage alt) und Altschnee
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Pulverschnee (locker, unter null Grad gefallen)
Typology of Number Systems
Bases
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Harsch (überfrorener Pulverschnee)
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Bruchharsch (eine besonders massive Schicht aus
Eisschnee)
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Pappschnee oder Feuchtschnee, Sulzschnee (nass und
schwer)
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Schneematsch oder Faulschnee (gemischte Konsistenz
ohne Zusammenhalt)
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Griesel (wiederholt gefrorener, körniger Schnee)
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Firn (mindestens ein Jahr alt, wiederholt gefroren)
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Dazu kommen weitere Unterschiede zwischen den
schweizerdeutschen und bairischen (inklusive den
österreichischen) Dialekten.
Exceptions
Colors
Concepts
Lexical semantic maps
Linguistic relativity
Better examples
Armin Buch
Numerals
Typology of Number Systems
Bases
Exceptions
Colors
Concepts
I
Arbitrarily fine distinctions in terminology do exist, where
it’s useful
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46 words for camels in Somali
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Extensive reindeer terminology in Sami
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It’s just the case that the Inuit don’t talk about snow all
that much
Lexical semantic maps
Linguistic relativity
Conclusion
Armin Buch
Numerals
Typology of Number Systems
Bases
Exceptions
Colors
Concepts
Lexical semantic maps
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Similar to color categorization, any given word ranges
over a (coherent2 ) set of meanings
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Different though, concept space is not as clearly defined as
color space; it is shaped by the use of language itself
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Maybe even convex, in some mathematical description of semantic space.
Linguistic relativity