Phonology of numbers: Symmetry violations

Thu May 16 23:35:09 UTC 2002

The discussion set off by Adam's questions has raised some interesting
points about numerals and (classes of) signs with exceptional
phonological properties. Adam's two original points were:

1. "Symmetry violations":
Certain two-handed number systems can incorporate movements which,
combined with different handshapes on each hand, appear to violate
Battison's Symmetry condition.
2. "Exceptional handshapes":
Numeral systems seem to show other kinds of exceptional properties, for
example handshapes not found elsewhere in the language.

SInce I have a fair bit to say, I'll talk about the Symmetry violations
in this message and deal with exceptional handshapes and related
questions in a second message.

Carol Padden suggested that symmetry violations should in fact be seen
as two simultaneous signs, rather than as a single one handed sign. This
is an interesting possibility that would need to be evaluated against
another one, namely that they may be morphologically complex, but
nonetheless *single* signs. It may well be that the symmetry condition
admits to no exceptions when it comes to monomorphemic signs, but
applies less strictly to morphologically more complex signs.

A couple of examples to illustrate:

First off is a case that to my mind seems to fit best with the "two
simultaneous signs" analysis. (The fact it involves numbers is
coincidental: I think the number signs here are in fact acting as
classifiers.) A deaf L1 signer of LSQ is discussing integration of deaf
children into hearing classes with her two conversational partners (also
L1 LSQ signers). She disagrees with integration where the deaf children
are outnumbered by the hearing children so they aren't on an equal
footing in terms of communication but agrees with integrating *equal*
numbers of deaf and hearing children. She takes the sign INTEGRATE (two
pronated 5 hands converging from the two sides and then moving forward
together) and holds up the two hands, looks at each and says in French
"plusieurs" ('several' or 'many'), then again repeats the sign and says
she agrees with this. Then she signs DEAF with her dominant (right) hand
and signs ONE, TWO (right hand) and the FIVE/MANY classifier (left hand)
simultaneously, bringing TWO and FIVE/MANY together in the same way as
in INTEGRATE, and saying she disagrees with this.

If this is taken to be a single sign, it clearly violates symmetry.
However, I think there are reasons to consider it not only
morphologically complex but syntactically complex, in other words two
simultaneous signs. The signer has analysed INTEGRATE into its component
morphemes (two handshapes referring to the verb's arguments and the
movement referring to the action) and creatively replaced one of them
with a different numeral classifier. However, what she produces isn't a
sign/construction that means "two (deaf) children integrate" but "*two
or three*/*only a few* (deaf) children integrate". It seems to me that
the TWO is part of the NP ONE, TWO and is being inserted into the
sign-reanalysed-as-simultaneous-construction simply because only a
single morpheme/sign can appear on each hand at once.

A second example. In Mali Sign Language as used in Bamako (the capital),
there are two signs for Tunisia: call them TUNISIA(1h) and TUNISIA(2h).
The etymology of this sign is that some years ago, the Malian national
football/soccer team beat Tunisian team in a championship game with a
score of 2 to 0. The score can be shown, in a typical contrast-type
simultaneous construction, with TWO on one hand and ZERO on the other.
This was then applied, via metonymy, to Tunisia: TUNISIA(2h) is signed
with a V handshape on the dominant hand and a baby O on the non-dominant
hand, with a repeated alternating left-right movement. Another violation
of "Symmetry", but unlike the INTEGRATE example I just gave, I think
this is most definitely a (morphologically complex) single sign. Its
meaning is completely non-compositional -- it means 'Tunisia' and not
'two-nil' -- and this is *typically* a characteristic of lexically
stored items and not of syntactic constructions other than formulaic
expressions. Its character as a morphologically complex sign is rendered
by an approximate English equivalent, 'Two-nillia' for 'Tunisia'. It
*definitely* is no longer a syntactic construction, though. Even though
the language allows this sign to (superficially at least) violate
"Symmetry", there is an alternative, TUNISIA(1h), which is a sequential
compound TWO+ZERO (/V/, /Vo/) similar to TWENTY or THIRTY in various
sign languages. Although the language allows the *Symmetry* violation,
it provides for an alternative that conforms to the rule.

Two more similar examples from Italian SL (LIS) and Quebec SL (LSQ). In
LIS, the sign WEEK was originally the two-handed sign SEVEN moving
forward in space. SEVEN in LIS is a sim-compound of TWO (/L/ on dom.
hand) and FIVE on the non-dom. hand. Over time, according to Ellen
Radutzky (in her PhD thesis and an article in the _SLR '87_ proceedings
volume from Signum), the original form of the sign, which is apparently
the only Symmetry exception in the language, is changing to a form with
/L/ on *both* hands. In LSQ, there is a name sign SISTER-BLANCHETTE for
a nun who taught at the girls' school. Since her room number was number
8, her name sign was originally a compound NUN+EIGHT. This EIGHT,
however, was not the common LSQ sign, but rather from a two-handed
number system used in the girls' school, most likely based on the French
Sign Language system. One form of the name sign is thus a /3/ handshape
on the dom. hand and a /5/ on the non-dom. hand, both moving downward
and forward from head level. Again, a Symmetry violation and again, with
a one-handed version (/3/ hand only) that avoids the violation.

What seems to me to be going on in each of these cases is that
un-symmetric signs are allowed if there is a morphological motivation
that is more powerful than the phonological pressure to respect
Symmetry. This seems to be the case quite systematically in two-handed
number systems which compound FIVE on the non-dom. hand with some other
number on the dominant hand, combining them with some movement to derive
numbers beyond 10. This is exactly the case for the BSL numerals that
you talk about, Adam.

If semantic bleaching occurs, though, and internal morphological
structure becomes less semantically obvious in a sign, it seems that
Symmetry takes over and enforces its dominance. (To take just WEEK in
LIS as an example, we find similar equivalents in spoken languages. The
Spanish and French words for 'week' ('semana' and 'semaine'
respectively) are derived from Latin 'septimana', which means 'having to
do with the number seven [septem]'. Over a millennium and a half the
semantic connection with 'seven' has bleached away and at the same time,
the word has undergone phonological change that has resulted in the loss
of any synchronic morphological relationship to the number 'seven' in
either language ('siete' and 'sept').) What's interesting is that Auslan
already seems to enforce Symmetry on morphologically complex signs,
which leads me to ask what the Auslan equivalents look like compared to
the BSL variants? It would be quite interesting to compare the specific
ways Auslan and BSL diverge phonologically: there are some interesting
differences between ASL and LSQ at this level, which I'll touch on in my
next message since they fit better there. (BTW, ASL and LSQ are both
descended from early ASL.)

Cheers,

Chris Miller

On Tuesday, May 14, 2002, at 12:46  pm, Adam Schembri, Deaf Studies
wrote:

BSL has at least four signs that appear not to be constrained by
Battison's (1978) symmetry condition. These are the signs SIXTEEN,
SEVENTEEN, EIGHTEEN and NINETEEN. These signs have a two-handed
variant in which the hands have the same location (neutral space) and
movement (an alternating up and down movement) but different hand
configurations on the dominant and non-dominant hand (the
non-dominant hand has a 5 handshape, while the other hand may have an
I, for example, in one form of the sign SIXTEEN). To my knowledge,
these variants are not found in the related variety, Auslan.

(...)

PS Auslan also has a very small number of signs that appear to break
Battison's (1978) dominance condition, using marked handshapes on the
non-dominant hand.

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Christopher Miller
Department of Linguistics
University of Manitoba
Winnipeg MB
R3T 2N2
Canada

+1 204 474-8343 (office)
+1 204 474-7671 (fax)
+1 204 951-5002 (mobile phone)

millerc at ms.umanitoba.ca
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